Guide to methods for assessing the acceptability of flaws ... 7910-2005... · curves 262 Figure T.2 Strain hardening cons truction to obtain incremental strains 263 Figure T.3 Construction

BRITISH STANDARD BS 7910:2005

Guide to methods for assessing the acceptability of flaws in metallic structures

ICS 25.160.40

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BS 7910:2005

This British Standard was published under the authority of the Standards Policy and Strategy Committee on 27 July 2005

© BSI 27 July 2005

The following BSI references relate to the work on this standard:Committee reference WEE/37Draft for comment 04/30111613DC

ISBN 0 580 45965 9

Committees responsible for this British Standard

The preparation of this British Standard was entrusted to Technical Committee WEE/37, Acceptance levels for welds, upon which the following bodies were represented:

Advantica Ltd

Association of Consulting Engineers

British Constructional Steelwork Association Ltd

Engineering Equipment and Materials Users Association

Health and Safety Executive

Imperial College of Science, Technology and Medicine

Institution of Mechanical Engineers

Lloyds Register

Power Generation Contractors Association (part of BEAMA Ltd)

Safety Assessment Federation Ltd

UK Steel

Welding Manufacturers Association (part of BEAMA Ltd)

The Welding Institute (TWI)

Co-opted members

Amendments issued since publication

Amd. No. Date Text affected

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BS 7910:2005

© BSI 27 July 2005 i

ContentsPage

Committees responsible Inside front coverForeword vi

Introduction 11 Scope 22 Normative references 23 Symbols and definitions 34 Types of flaw 135 Modes of failure and material damage mechanisms 146 Information required for assessment 157 Assessment for fracture resistance 238 Assessment for fatigue 499 Assessment of flaws under creep conditions 8410 Assessment for other modes of failure 96

Annex A (normative) Evaluation under combined direct and shear stresses or mode I, II and III loads 102Annex B (informative) Assessment procedures for tubular joints in offshore structures 104Annex C (informative) Fracture assessment procedures for pressure vessels and pipelines 110Annex D (normative) Stress due to misalignment 114Annex E (normative) Flaw recharacterization 121Annex F (informative) A procedure for leak-before-break assessment 122Annex G (normative) The assessment of corrosion in pipes and pressure vessels 145Annex H (normative) Reporting of fracture, fatigue or creep assessments 160Annex I (informative) The significance of weld strength mismatch on the fracture behaviour of welded joints 162Annex J (informative) Use of Charpy V-notch impact tests to estimate fracture toughness 165Annex K (normative) Reliability, partial safety factors, number of tests and reserve factors 169Annex L (normative) Fracture toughness determination for welds 181Annex M (normative) Stress intensity factor solutions 184Annex N (normative) Simplified procedures for determining the acceptability of a known flaw or estimating the acceptable flaw size using Level 1 fracture procedures 232Annex O (informative) Consideration of proof testing and warm prestressing 236Annex P (normative) Calculation of reference stress 239Annex Q (informative) Residual stress distributions in as-welded joints 248Annex R (normative) Determination of plasticity interaction effects with combined primary and secondary loading 253Annex S (normative) Approximate numerical integration methods for fatigue life estimation 259Annex T (informative) Information for making high temperature crack growth assessments 261Annex U (informative) Worked example to demonstrate high temperature failure assessment procedure 275

Bibliography 285

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BS 7910:2005

ii © BSI 27 July 2005

Figure 1 — Linearization of stress distributions 18Figure 2 — Schematic representation of stress distribution across section 21Figure 3 — Procedure for resolving flaws normal to principal stress 22Figure 4 — Flow charts — General methods 24Figure 5 — Flowchart — Level 1 25Figure 6 — Flowchart — Level 2 26Figure 7 — Flowchart — Level 3 27Figure 8 — Flaw dimensions 28Figure 9 — Planar flaw interactions 29Figure 10 — Level 1A FAD 36Figure 11 — Level 2 FADs 40Figure 12 — Level 3A FAD with assessment locus for a known flaw 47Figure 13 — Example of non-unique solutions (schematic) 48Figure 14 — Schematic crack growth relationships 55Figure 15 — Recommended fatigue crack growth laws 56Figure 16 — Quality category S-N curves for use in simplified fatigue assessments 61Figure 17 — Assessment of surface flaws in axially-loaded material for simplified procedure 65Figure 18 — Assessment of surface flaws in flat material (no weld toe or other stress raiser) in bending for simplified procedure 67Figure 19 — Assessment of embedded flaws in axially-loaded joints for simplified procedure 69Figure 20 — Assessment of weld toe flaws in axially-loaded joints for simplified procedure 71Figure 21 — Assessment of weld toe flaws in joints loaded in bending for simplified procedure 77Figure 22 — Determination of the temperature Tc at which 0.2 % creep strain is accumulated at a stress level equal to the proof strength 86Figure 23 — Determination of the time t(T) to achieve an accumulated creep strain of 0.2 % at a stress level equal to the proof strength 87Figure 24 — Schematic behaviour of crack subjected to steady loading at elevated temperature 88Figure 25 — Schematic representation of crack propagation and failure conditions 89Figure 26 — Procedure for creep assessment 91Figure 27 — Schematic diagrams of typical relationships between crack velocity and stress intensity factor during stress corrosion cracking 98Figure 28 — Types of corrosion fatigue crack growth behaviour 100Figure B.1 — Assessment methodology for fatigue crack growth in tubular joints 105Figure C.1 — Algorithm for pressure vessel flaw assessment 111Figure E.1 — Rules for recharacterization of flaws 121Figure F.1 — The leak-before-break diagram 122Figure F.2 — Leak-before-break procedure 125Figure F.3 — Detailed leak-before-break diagram 130Figure F.4 — Example characterization of a complex flaw 131Figure F.5 — Schematic crack profiles at breakthrough 133Figure F.6 — Recommended re-characterization of flaws at breakthrough for predominantly tensile loading 134Figure F.7 — Recommended re-characterization of flaws at breakthrough for predominantly through-wall bend 135Figure F.8 — Unstable crack growth before creep rupture 144Figure F.9 — Rupture before unstable crack growth 144

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BS 7910:2005

© BSI 27 July 2005 iii

Figure G.1 — Flow chart of assessment procedure 148Figure G.2 — Single flaw dimensions 149Figure G.3 — Interacting flaw dimensions 151Figure G.4 — Corrosion depth adjustment for flaws with background corrosion 153Figure G.5 — Projection of circumferentially interacting flaws 153Figure G.6 — Projection of overlapping sites onto a single projection line 154Figure G.7 — Combining interacting flaws 154Figure G.8 — Example of the grouping of adjacent flaws for interaction to find the grouping which gives the lowest estimated failure pressure 155Figure G.9 — Cross section of locally thinned area geometry on spherical shell 157Figure J.1 — Flowchart for selecting an appropriate correlation for estimating fracture toughness from Charpy data 166Figure K.1 — Evaluation of FL for a single primary stress 174Figure K.2 — Three scenarios for the graphical determination of FL in the presence of Ös loads 175Figure K.3 — Typical load factor variation graphs 177Figure K.4 — Load factor variation with flaw size Level 3 analysis 178Figure K.5 — Preferred sensitivity curves 180Figure M.1 — Through-thickness flaw geometry 186Figure M.2 — Surface flaw 186Figure M.3 — Elliptical integral Í as a function of a/2c used for the calculation of K1 for surface and embedded flaws 188Figure M.4 — Stress intensity magnification factor Mm for surface flaws in tension 189Figure M.5 — Stress intensity magnification factor Mb for surface flaws in bending 192Figure M.6 — Long surface flaw geometry 194Figure M.7 — Embedded flaw 194Figure M.8 — Stress intensity magnification factor Mm for embedded flaws in tension (at point nearest material surface) 196Figure M.9 — Stress intensity magnification factor Mb for embedded flaws in bending 198Figure M.10 — Edge flaw geometry 199Figure M.11 — Corner flaw geometry 200Figure M.12 — Corner flaw at hole geometry 201Figure M.13 — Through-thickness flaw in cylinder oriented axially 204Figure M.14 — Through-thickness flaw in cylinder oriented cicumferentially 209Figure M.15 — Through-thickness flaw in spherical shell 214Figure M.16 — Internal surface flaw in cylinder oriented axially 216Figure M.17 — Internal surface flaw in cylinder oriented circumferentially 216Figure M.18 — Long internal surface flaw in cylinder oriented axially 218Figure M.19 — Long internal surface flaw in cylinder oriented circumferentially 218Figure M.20 — External surface flaw in cylinder oriented axially 219Figure M.21 — Long axial external surface flaw in cylinder 221Figure M.22 — Long circumferential external surface flaw in cylinder 221Figure M.23 — Crack and welded joint geometries 223Figure M.24 — Transverse load-carrying cruciform joint 224Figure M.25 — Surface flaw 230Figure M.26 — Circumferential flaw in bolt 231

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BS 7910:2005

iv © BSI 27 July 2005

Figure N.1 — Relationship between actual flaw dimensions and the parameter Œ for surface flaws 234Figure N.2 — Relationship between actual flaw dimensions and the parameter Œ for embedded flaws 235Figure O.1 — Typical warm pre-stress cycles 237Figure Q.1 — Typical residual stress distribution in welded joints 249Figure R.1 — Values of Ô1 for defining Kr 254Figure R.2 — Stress intensity factor for through-thickness cracks with through-wall self-balancing stress distributions 259Figure T.1 — Derivation of strain versus time curves from iso-strain curves 262Figure T.2 — Strain hardening construction to obtain incremental strains 263Figure T.3 — Construction to estimate creep damage in block 264Figure T.4 — Division of operating history into blocks of constant stress and constant temperature 268Figure U.1 — Flaw dimensions 276Figure U.2 — Thermal stress distribution in the region of the flaw 276Figure U.3 — Margin against fracture for high pressure start up 280Figure U.4 — Creep crack growth for period August 1990 to July 2005 282Figure U.5 — Increase in creep damage from start of operation in April 1985 to July 2005 283

Table 1 — Limits for slag inclusions and porosity 48Table 2 — Procedure for assessment of known flaws 50Table 3 — Stress ranges used in fatigue assessments 53Table 4 — Recommended fatigue crack growth laws for steels in air 56Table 5 — Recommended fatigue crack growth laws for steels in a marine environmenta 57Table 6 — Recommended fatigue crack growth threshold, %K0, values for assessing welded joints 58Table 7 — Details of quality category S-N curves 60Table 8 — Minimum values of %Öj for assessing non-planar flaws and shape imperfections 81Table 9 — Limits for non-planar flaws in as-welded steel and aluminium alloy weldments 82Table 10 — Limits for non-planar flaws in steel weldments stress relieved by PWHT 82Table 11 — Acceptance levels for misalignment expressed in terms of stress magnification factor, km 83Table 12 — Acceptance levels for weld toe undercut in material thicknesses from 10 mm to 40 mm 83Table 13 — Temperature below which creep is negligible in 200 000 h 86Table D.1 — Formulae for calculating the bending stress due to misalignment in butt joints 116Table D.2 — Formulae for calculating the bending stress due to misalignment in cruciform joints 119Table F.1 — Guidance on selection of assessment sites around a pipe system 124Table F.2 — Crack opening area methods for simple geometrics and loadings 137Table F.3 — Summary of surface roughness values from Wilkowski et al [124] 139Table K.1 — Target probability of failure (events/year) 170

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BS 7910:2005

© BSI 27 July 2005 v

Table K.2 — Recommended partial factors for different target probabilities of failure 172Table K.3 — Equivalent fracture toughness values to the minimum of three results [152] 173Table M.1a) — Mm* for axial through-thickness flaws in cylinders — Pressure loading 205Table M.1b) — Mb* for axial through-thickness flaws in cylinders — Pressure loading 206Table M.1c) — Mm* for axial through-thickness flaws in cylinders — Bending loading 207Table M.1d) — Mb* for axial through-thickness flaws in cylinders — Bending loading 208Table M.2a) — Mm* for circumferential through-thickness flaws in cylinders — Pressure loading 210Table M.2b) — Mb* for circumferential through-thickness flaws in cylinders — Pressure loading 211Table M.2c) — Mm* for circumferential through-thickness flaws in cylinders — Bending loading 212Table M.2d) — Mb* for circumferential through-thickness flaws in cylinders — Bending loading 213Table M.3 — Mm and Mb for through-thickness flaw in spherical shell 214Table M.4 — Mm and Mb for axial internal surface flaw in cylinder 215Table M.5 — Mm and Mb for circumferential internal surface flaw in cylinder 217Table M.6 — Mm and Mb for long axial surface flaw in cylinder 217Table M.7 — Mm and Mb for long circumferential internal surface flaw in cylindrical shell 219Table M.8 — Mm and Mb for axial external surface flaw in cylinder 220Table M.9 — Values of v and w for axial and bending loading 224Table P.1 — Values of · for bending loading 246Table Q.1 — Parametric ranges for recommended residual stress distributions 248Table R.1 — Tabulation of Ò as a function of Lr and Kp

s/(KIp/Lr) 255

Table R.2 — Tabulation of Î as a function of Lr and Kps/(KI

p/Lr) 256Table T.1 — Constants used to derive creep crack propagation rates in mm/h 265Table T.2 — Typical values of fracture toughness (based on the value of KI at 0.2 mm crack extension) 266Table U.1 — Operating conditions 275Table U.2 — Selected materials data 277Table U.3 — Stress category 277Table U.4 — Data at beginning of each month for deepest point of crack 281Table U.5 — Data at beginning of each month for crack growth along surface 282

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BS 7910:2005

vi © BSI 27 July 2005

Foreword

This British Standard has been prepared by Technical Committee WEE/37. It supersedes BS 7910:1999, which is withdrawn.

As the number of application standards specifying requirements for weld flaw acceptance levels based on fitness for purpose increases, so it is necessary to update and extend the guidance to be used in co-ordinating and rationalizing those requirements. This revision incorporates recent developments in fracture mechanics assessment methods, details of which are given in the appropriate clauses of this guide. While arbitrary acceptance levels will continue to be used for quality control purposes, the complementary use of the methods described in this guide permits the acceptability of known or postulated flaws in particular situations to be evaluated in a rational manner. Applications standards that formerly referred to PD 6493 or BS 7910:1999 should, in future, refer to this guide.

This guide has been revised to cover all failure modes that could be influenced by the presence of flaws. However, it should be noted that, whilst fracture, fatigue and creep are treated thoroughly, the treatment of other failure modes is less detailed.

Improvements in the methods outlined are continuing and users of this document should obtain an appreciation of the status of the various methods before applying them. For the purpose of this document, the treatment of the methods has necessarily been simplified, but appropriate references have been included to assist those willing to obtain further guidance. However, the information will seldom be found in the reference in identical form to that used in this document.

It has been assumed in drafting BS 7910 that the execution of its provisions is entrusted to appropriately qualified and experienced people, having appropriate knowledge of inspection technology, NDT, materials behaviour and fracture mechanics.

This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application.

Compliance with a British Standard does not of itself confer immunity from legal obligations.

Summary of pages

This document comprises a front cover, an inside front cover, pages i to vi, pages 1 to 298, an inside back cover and a back cover.

The BSI copyright notice displayed in this document indicates when the document was last issued.

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BS 7910:2005

© BSI 27 July 2005 1

IntroductionIn circumstances where it is necessary to examine critically the integrity of new or existing constructions by the use of non-destructive testing methods, it is also necessary to establish acceptance levels for the flaws revealed. The derivation of acceptance levels for flaws is based on the concept of fitness for purpose. By this principle, a particular fabrication is considered to be adequate for its purpose, provided the conditions to cause failure are not reached. A distinction has to be made between acceptance based on quality control and acceptance based on fitness for purpose.

Quality control levels are usually both arbitrary and conservative but are of considerable value in the monitoring and maintenance of quality during production. Flaws that are less severe than such quality control levels as given, for example, in current application standards, are acceptable without further consideration. If flaws more severe than the quality control levels are revealed, rejection is not necessarily automatic. Decisions on whether rejection and/or repairs are justified may be based on fitness for purpose, either in the light of previously documented experience with similar material, stress and environmental combinations or on the basis of an “engineering critical assessment” (ECA). It is with the latter that this document is concerned. It is emphasized, however, that a proliferation of flaws, even if shown to be acceptable by an ECA, is regarded as indicating that quality is in need of improvement. The use of an ECA can in no circumstances be viewed as an alternative to good workmanship. The response to flaws not conforming to workmanship criteria needs to be the correction of the fault in the process causing the non-conformance. The philosophy that the methods covered by this standard are complementary to, and not a replacement for, good quality workmanship is inherently assumed in this standard.

A procedure for an ECA is described whereby the significance of flaws under a particular set of circumstances may be determined. All parties need to agree to its use.

It is impossible to provide a single list of flaws that are known not to cause premature failure, since a large number of variables are involved, as enumerated in this document. It is possible, where relevant experience and data already exist, to dispense with the full ECA procedure and to use authenticated previous assessments as a basis for the establishment of acceptability limits. An ECA may also be used as a basis for deferring necessary repairs to a time mutually agreeable to the contracting parties. It needs to be appreciated that the unsatisfactory repair of innocuous flaws could result in the substitution of more harmful and/or less readily detectable flaws.

The implication of flaw assessment on a fitness for purpose basis is the need for thorough examination by non-destructive testing using techniques capable of locating and sizing flaws in critical areas. This document may be used to identify such areas and to assist in optimizing the NDT procedures by identifying those aspects of flaw characterization, size and position which need to be determined. Such non-destructive testing needs to be carried out after any post-weld heat treatment (PWHT) and/or proof test. However, since a major objective of this document is to reduce costs by eliminating unnecessary repair, careful consideration needs to be given to the level of inspection required to implement this document.

The limitations of non-destructive testing methods have to be taken into account. The following are the stages in the assessment of flaws revealed by such tests.

a) If the flaws do not exceed the quality control levels in the appropriate application standard, no further action is required.

b) If acceptance limits have already been established on the basis of an ECA for the appropriate combination of materials, fabrication procedure, welding consumables, stress and environmental factors, flaws need to be assessed on that basis.

c) If no relevant documented experience exists, then an ECA based on the guidance given in this document needs to be carried out.

ECA will help to identify the limiting conditions for failure or the limiting design conditions. It is emphasized that some aspects of ECA are based on new concepts that could be subject to review. The application of these principles will mean that “safe” results will be obtained. The option of using appropriate safety factors has been incorporated or is inherent in each of the relevant clauses. If the accuracy of the input information employed (e.g. stress levels, material properties at the appropriate temperature, flaw size determination) is in question, appropriate additional safety factors need to be agreed. Equally, a flaw will not necessarily be unacceptable when it is found initially to exceed the acceptance levels that are derived from this document. A further assessment can be made following the principles given in this document, but incorporating more precise input data or analysis methods, or by testing structurally relevant components.

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BS 7910:2005

2 © BSI 27 July 2005

This document also gives guidance on the use of safety factors, reliability factors, and probabilistic methods. These factors and methods do not constitute a full risk analysis of the component undergoing assessment, as they do not quantify the consequences of a failure. Where failure of the structure under assessment may pose an unjustifiable or intolerable risk to the surrounding environment or population, then a full risk analysis may be needed, with due recognition of both individual and societal risk [1].

1 ScopeThis guide outlines methods for assessing the acceptability of flaws in all types of structures and components. Although emphasis is placed on welded fabrications in ferritic and austenitic steels and aluminium alloys, the procedures developed can be used for analysing flaws in structures made from other metallic materials and in non-welded components or structures. The methods described can be applied at the design, fabrication and operational phases of a structure’s life.

2 Normative referencesThe following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

BS 5400 (all parts), Steel, concrete and composite bridges.

PD 5500:2003, Specification for unfired fusion welded pressure vessels.

BS 5950-1:1990, Structural use of steelwork in building — Part 1: Code of practice for design in simple and continuous construction: hot rolled sections.

BS 7448 (all parts), Fracture mechanics toughness tests.

BS 7608, Code of practice for fatigue design and assessment of steel structures.

BS 8118 (all parts), Structural use of aluminium.

BS EN 571-1, Non-destructive testing — Penetrant testing — Part 1: General principles.

BS EN 1289, Non-destructive examination of welds — Penetrant testing of welds — Acceptance levels.

BS EN 1290, Non-destructive examination of welds — Magnetic particle examination of welds.

BS EN 1291, Non-destructive examination of welds — Magnetic particle testing of welds — Acceptance levels.

BS EN 1435, Non-destructive examination of welds — Radiographic examination of welded joints.

BS EN 1712, Non-destructive examination of welds — Ultrasonic examination of welded joints — Acceptance levels.

BS EN 1714, Non destructive examination of welded joints — Ultrasonic examination of welded joints.

BS EN 10002-1, Metallic materials — Tensile testing — Part 1: Method of test at ambient temperature.

BS EN 10002-5, Metallic materials — Tensile testing — Part 5: Method of test at elevated temperatures.

BS EN 12517, Non-destructive examination of welds. Radiographic examination of welded joints — Acceptance levels.

BS EN ISO 6520-1, Welding and allied processes — Classification of geometric imperfections in metallic materials — Part 1: Fusion welding.

BS EN ISO 7539 (all parts), Corrosion of metals and alloys.

BS ISO 12108, Metallic materials — Fatigue testing — Fatigue crack growth method.

BS EN ISO 12737, Metallic materials — Determination of plane-strain fracture toughness.

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BS 7910:2005

© BSI 27 July 2005 3

3 Symbols and definitionsFor the purposes of BS 7910 the following symbols and definitions apply.NOTE 1 Where units are given for the variations of the symbol K the following note applies. The two internationally recognized alternative units for stress intensity factor are N/mm3/2 and MPaÆm (which is identical to MN/m3/2). The primary unit adopted in this document (except in Annex J) is N/mm3/2. 1 N/mm3/2 = 0.032 MPaÆm. Equivalent values in MPaÆm are given in parentheses.

Symbol Definition Units

A constant in fatigue crack growth relationship See footnote1

Ac crack area mm2

A1 area of rectangle which demarcates flaw (Annex M) mm2

A2 full load bearing area containing flaw (Annex M) mm2

a half flaw length for through-thickness flaw, flaw height for surface flaw or half height for embedded flaw (see Figure 8)

mm

flaw growth rate with cycles (Clause 8) mm/cycle

rate of crack propagation per cycle in height direction due to fatigue (Clause 9, Annex T)

mm/cycle

rate of crack propagation per cycle in height direction due to creep (Clause 9, Annex T)

mm/cycle

flaw growth rate with time (Clause 10) mm/h

%a increment in a mmeffective flaw parameter for Level 1 fracture assessment (Annex N) mmrate of crack propagation in height direction due to creep (Annex T) mm/h

aeff effective crack size based on elastic analysis (Annex R) mm

aeffÖ effective crack size based on elastic-plastic stress field (Annex R) mm

aeff¼ effective crack size based on elastic-plastic strain field (Annex R) mm

af final flaw size mmai initial flaw size mm

initial value of effective flaw parameter for fatigue analysis mm

maximum value of effective flaw parameter for fatigue analysis mm

tolerable flaw parameter for Level 1 fracture assessment (Annex N) mm

ao initial flaw size (7.4.7.2) mm%ag limit of tearing flaw extension (7.4.7.1) mm%aj intermediate value of tearing flaw extension (7.4.7.2) mm%ao notional extension of flaw defining tearing initiation (7.4.7.2) mmB section thickness in plane of flaw mmB½ effective section thickness (2a + 2p) (Annex M) mm

1 The units and value of A depend on those used to measure da/dN and %K, and on the value of the exponent, m. If A is known in one set of units, Aa, the corresponding value for another set of units, Ab is given by:

where: fa is the conversion factor for da/dN from the first to the second unit system; and fb is the conversion factor for %K from the first to the second unit system.

dadN--------

dadN--------⎠

⎞f⎝

⎛

dadN--------⎠

⎞c⎝

⎛

dadt-------

a

a· c

ai

amax

am

Ab Aa fa

fbm

-------=

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Bmin minimum remaining thickness of a corroded spherical shell (Annex G) mmB0 original, measured, pipe or vessel wall thickness, or wall thickness as

defined in the original design code (Annex G)mm

Bss sub-size Charpy specimen thickness mmb exponent of time in creep strain equations (Annex T)C constant in creep crack propagation equation (Clause 9)C* parameter defining creep crack propagation rate (Clause 9) N/mm..hC1 constant in the stress corrosion crack growth relationship (Clause 10) See footnote2)

CD discharge coefficient (Annex F)c half flaw length for surface or embedded flaws (see Figure 8) mm2cb surface length of crack at breakthrough (Annex F) mm

crack growth rate in length direction due to creep (Annex T) mm/h

%c increment in c mmD diameter mmD½ constant in creep strain equation (Annex T)Dc accumulated creep damage (Annex T)%Dc increment of creep damage (Annex T)DSM mean shell diameter mmd deviation from true circle due to angular misalignment (Annex D) mmdc depth of corroded region (Annex G) mmdi depth of an individual corrosion flaw (Annex G) mmdm depth of interacting corrosion flaw n (Annex G) mmdn depth of interacting corrosion flaw m (Annex G) mmdnm effective depth of combined flaws from n to m (Annex G) mmd1,2,etc depth of 1st, 2nd, etc. corrosion flaws (Annex G) mm

E elastic modulus N/mm2 (MPa)E½ elastic modulus corrected for constraint conditions E½ = E for plane stress.

E½ = E/(1 – É2) for plane strain (7.3.6.1 and T.4.1)N/mm2 (MPa)

ERT elastic modulus at room temperature (say 20 °C) (8.2.3.5)EET elastic modulus at the elevated temperature (8.2.3.5)E1 electrical energy per unit length of weld (Annex Q) J/mme axial misalignment (eccentricity or centre line mismatch) (Annex D) mmFAR reduction factor to allow for loss of load-bearing area due to presence of a

flaw in a tubular joint (Annex B)

Fa, FK, FY reserve factors on flaw size, toughness and yield strength (Annex K)

FL load factor (Annex K)

f frequency of fatigue loading cycle (Clause 9) Hz

2) The units and value of C depend on those used to measure da/dt and %K, and on the value of the exponent, n. If C is known in one set of units, Ca, the corresponding value for another set of units, Cb, is given by:

where: fa is the conversion factor for da/dt from the first to the second unit system; and fb is the conversion factor for %K from the first to the second unit system.

c·c

Cb Ca fa

fbn

------=

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fc total factor of safety in analysis of corrosion flaw = fc1.fc2 (Annex G)fc1 modelling factor in analysis of corrosion flaw (Annex G)fc2 original design factor in analysis of corrosion flaw (Annex G)ff friction factor for flow through crack (Annex F)ffmax effective maximum friction factor for flow through crack (Annex F)fscc factor of safety with respect to stress corrosion cracking (fscc > 1.0)

(Clause 10)fÌ, fw, g correction terms in stress intensity factor for elliptical flaws (Annex M)G constant in tubular joint stress intensity factor solutions (Annex B)H crack-opening area (COA) (Annex F) mm2

Hc creep component of crack-opening area (COA) (Annex F) mm2

He elastic component of crack-opening area (COA) (Annex F) mm2

H½ constant in tubular joint stress intensity factor solutions (Annex B)h weld leg length (Annex D and Annex K) mmJ a line or surface integral that encloses the crack front from one crack

surface to the other, used to charaterize the local stress-strain field around the crack front

N/mm

J0.2BL resistance to crack extension expressed in terms of J at 0.2 mm crack extension offset to the blunting line (Clause 7)

N/mm

Jc value of J at either: N/mma) unstable fracture; orb) onset of arrested brittle crack or pop-inThis term only applies where %a0 < 0.2 mm offset to the blunting line

Je value of J determined using an elastic analysis N/mmJm value of J at first attainment of maximum force plateau N/mmJmat material toughness measured by J-methods (7.1.4.2, 7.1.5.4) N/mm

J s value of J for secondary stresses alone (Annex R) N/mm

Ju value of J at either: N/mma) unstable fracture; orb) onset of arrested brittle crack or pop-in.This term only applies where %a0 > 0.2 mm offset to the blunting line

K stress intensity factor N/mm3/2 See Note 1

KI applied tensile (mode I) stress intensity factor (7.2.5, 7.3.5.1) N/mm3/2

See Note 1%KI cyclic range in KI N/mm3/2

See Note 1KIp stress intensity factor due to pre-load (Annex O) N/mm3/2

See Note 1

KIs stress intensity factor due to secondary stresses

[= (YÖ )sÆ(Ïa)] (Annex R)N/mm3/2

See Note 1

KIp stress intensity factor due to primary stresses

[= (YÖ)pÆ(Ïa)] (Annex R) N/mm3/2 SeeNote 1

KI(p+s) stress intensity factor due to primary and secondary stresses N/mm3/2

See Note 1

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KIpressure contributions to KI of pressure-induced membrane stresses N/mm3/2

See Note 1

KIbending contributions to KI of through-wall bending stresses N/mm3/2

See Note 1KISCC critical stress intensity factor for stress corrosion cracking

(Clause 10) N/mm3/2

See Note 1

K2 stress intensity factor following unload (Annex O) N/mm3/2 See Note 1

KII mode II linear elastic stress intensity factor (Annex A) N/mm3/2

See Note 1

KIIC critical value of KII at onset of brittle fracture in mode II (Annex A) N/mm3/2

See Note 1

KIIp, KII

s values of KII due to primary and secondary stresses, respectively (Annex A)

N/mm3/2

See Note 1KIII mode III linear elastic stress intensity factor (Annex A) N/mm3/2

See Note 1

KIIIp, KIII

s values of KIII due to primary and secondary stresses, respectively (Annex A)

N/mm3/2

See Note 1Keff effective linear elastic stress intensity factor in mixed mode loading

(Annex A)N/mm3/2

See Note 1Kf stress intensity factor at failure (Annex O) N/mm3/2

See Note 1

Kg notional K value after flaw extension %ag (7.4.7.1) N/mm3/2 See Note 1

KIc plane strain fracture toughness (7.1.5.2) N/mm3/2

See Note 1

Kmat material toughness measured by stress intensity factor (7.1.4.2) N/mm3/2 See Note 1

Kps effective stress intensity factor used to define Kr

s (Annex R) N/mm3/2 See Note 1

Kr fracture ratio of applied elastic K value to Kmat N/mm3/2 See Note 1

K(s effective stress intensity factor defined from elastic-plastic

strain field (Annex R)N/mm3/2 See Note 1

KÖs effective stress intensity factor defined from elastic-plastic

stress field (Annex R)N/mm3/2 See Note 1

%K stress intensity factor range (Clause 8) N/mm3/2

See Note 1%Keff effective stress intensity factor range (Clause 8) N/mm3/2

See Note 1

%Ko threshold stress intensity factor range below which fatigue crackgrowth (or corrosion fatigue crack growth) does not occur (Clause 8)

N/mm3/2 See Note 1

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km stress magnification factor due to misalignment (6.4.4, 8.8.1 and Annex D)

kt stress concentration factor (6.4.4)

ktb bending stress concentration factor (6.4.4, 7.3.3, Annex M)ktm membrane stress concentration factor (6.4.4, 7.3.3, Annex M)kt.HS hot spot stress concentration factor in tubular joint (Annex B)kt.IPB, kt.OPB in and out of plane stress concentration factors in tubular joints

(Annex B)L attachment length mmLr ratio of applied load to yield load (7.1.8, Annex M)Lr,max permitted limit of Lr (7.3.1)l distance from axially misaligned joint to load or extremities of region of

angular misalignment (shortest distance = l1) (Annex D)mm

l½ generalized crack length (length of surface, buried or through thickness crack) or equivalent length of through thickness crack after recharacterization [Annex F3)]

mm

lc length of corroded region measured parallel to the axis of a cylindrical vessel or pipe (Annex G)

mm

l½c limiting generalized crack length (Annex F) mml½L length of crack which leaks at the minimum detectable rate (Annex F) mml½L* enhanced length of crack which leaks at the minimum detectable rate

(Annex F)mm

l½r length of crack at rupture (Annex F) mmli length of an individual corrosion flaw forming part of a colony of

interacting flaws (Annex G)mm

lm length of interacting corrosion flaw m (Annex G) mmln length of interacting corrosion flaw n (Annex G) mmlnm effective longitudinal length of a flaw combined from adjacent

flaws n to m in a colony of interacting flaws (Annex G)mm

ltotal total longitudinal length of a colony of interacting flaws and the spacing between them (Annex G)

mm

lw length of weld mmM bulging correction factor (Annex M)Mai, Mao applied in and out of plane moments for tubular joints (Annex B) N.mmMci, Mco fully plastic moments for cracked tubular joints calculated for in and out

of plane loads (Annex B)N.mm

Mm, Mb, Mkm, Mkb

stress intensity magnification factors (7.2.5, Annex M and Annex B)

Mm*, Mb* factors used in calculating Mm and Mb (Annex M)Ms, MT stress magnification factor (Annex M and Annex P)m exponent in flaw growth law (Clause 8)mq exponent in the calculation of FAR (Annex B)N fatigue life (Clause 8) cyclesNc number of corrosion flaws in a colony of interacting flaws (Annex G)

3) In Annex F, l½ has been used for the length of a crack, irrespective of whether it is part wall or through thickness. This is in place of 2c and 2a respectively. This is because Annex F deals with flaws which start as part wall and grow to through thickness.


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%N increment in N (Clause 8) cyclesn exponent of stress in creep strain equation (Annex T)n,m refer to the nth and mth flaw in a series of corrosion flaws 1…Nc

(Annex G)n(scc) exponent in the stress corrosion crack growth relationship (Clause 10)nj number of cycles in stress spectrum at stress range %Öj (Clause 8) cyclesP primary stress (6.4.1) N/mm2 (MPa)Pa applied axial load on tubular joint (Annex B) NPc collapse load for cracked tubular joint (Annex B) NPb primary bending stress (6.4.1) N/mm2 (MPa)Pb,l primary bending stress due to locally applied bending loads (Annex P) N/mm 2 (MPa)Pm primary membrane stress (6.4.1) N/mm2 (MPa)Pm,a primary membrane stress due to global axial loads (Annex P) N/mm 2(MPa)Pm,p primary membrane stress due to pressure loading (Annex P) N/mm2 (MPa)Pm,b primary membrane stress due to global bending moments (Annex P) N/mm2 (MPa)Pf fluid pressure (Annex F) N/mm2 (MPa)Pf failure pressure of a corroded pipe or vessel (Annex G) N/mm2 (MPa)Pf probability of Kmat being less than estimated (Annex J)Pnm failure pressure of combined adjacent corrosion flaws n to m, formed from

a colony of interacting flaws (Annex G)N/mm2 (MPa)

P0 failure pressure of plain unflawed pipe or pressure vessel (Annex G) N/mm2 (MPa)Psw safe working pressure of the corroded pipe or pressure vessel (Annex G) N/mm2 (MPa)P1,2,…,N and Pi failure pressures of individual corrosion flaws forming a colony of

interacting flaws (Annex G)N/mm2 (MPa)

p shortest distance from material surface to embedded flaw mm

p½ internal pressure (Annex P) N/mm2 (MPa)p(F) probability of failure (Annex K)Q secondary stress N/mm2 (MPa)Qb secondary bending stress N/mm2 (MPa)Qm secondary membrane stress N/mm2 (MPa)Qmf mass flow through an equivalent rectangular crack (Annex F) kg/s or g/s4)

Q¶ factor to allow for increased strength observed in tubular joints at ¶ > 0.6 (Annex B)

Qc length correction factor for corrosion flaws (Annex G)Qi length correction factor of an individual flaw forming part of a colony of

interacting corrosion flaws (Annex G)Qnm length correction factor for a flaw combined from adjacent flaws n to m in

a colony of interacting corrosion flaws (Annex G)q exponent in creep crack propagation equation (Annex T)qo fraction of load cycle when crack is open (Annex T)R stress ratio [ratio of minimum (Ömin) to maximum (Ömax) algebraic value of

the absolute stress level (ktmPm + ktbPb + Q)] (Clause 8)

4) The units for Qmf may be kg/s or g/s, but it is essential that they are consistent with those used for Ôf.

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R½ parameter used in creep crack propagation equation (Annex T) mmRa surface roughness of crack (Annex F) 4m

Rp cyclic plastic zone size mmRs

r mean shell radius or radius of round bar or bolt (Annex M and Annex P) mmrh radius of hole mmri internal shell radius mmrm mean shell radius mmro external shell radius mmS stress range or, for variable amplitude loading, the equivalent constant

amplitude stress range (Clause 8)N/mm2 (MPa)

Snom nominal membrane stress for Level 1 analysis (7.2.3) N/mm2 (MPa)Sr ratio of applied load to flow strength load (7.1.8, Annex P)s distance between embedded flaws (7.1.2.2, Figure 9) or longitudinal

spacing between adjacent corrosion flaws (Annex G)mm

si longitudinal spacing between adjacent flaws forming part of a colony of interacting corrosion flaws (Annex G)

mm

sm distance between interacting corrosions flaws m and (m + 1) (Annex G) mmsn distance between interacting corrosions flaws n and (n + 1) (Annex G) mmT temperature (Clause 9) °CTc creep exclusion temperature (Clause 9) °CTK temperature term describing the scatter in Charpy versus fracture

toughness correlation (Annex J)°C

T0 temperature for a median toughness of 100 MPaÆm in 25 mm thick specimens (Annex J)

°C

T1 temperature at pre-load (Annex O) °CT2 temperature at re-load (Annex O) °CT27 J temperature for energies of 27 J measured in a standard 10 mm × 10 mm

Charpy V specimen (Annex J)°C

T40 J temperature for energies of 40 J measured in a standard 10 mm × 10 mm Charpy V specimen (Annex J)

°C

t time (days, weeks, months or years as appropriate)ta time accumulated from initial start-up of plant (Clause 9) htcd time to failure of plant by bulk creep rupture, measured from initial

start-up (Clause 9 and Annex F)h

td required life of plant, measured from initial start-up (Clause 9) htff time to failure by unstable fracture, measured from initial start-up

(Clause 9)h

ti crack incubation time, prior to commencement of creep crack growth (Annex F)

h

tix incubation period corresponding to crack growth x (Clause 9) htR creep rupture life (Annex T) htR(ref) time to creep rupture at reference stress (Annex T) ht(2cb) time to breakthrough of a part wall flaw (Annex F) ht(l½c) time to grow crack to limiting length (Annex F)

reserve strength factorPfPo------=

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t(T) time to achieve specific creep strain at proof stress at temperature T (Clause 9)

h

tr(Ö) time to rupture at the appropriate temperature and at a stress, Ö (Annex F)

h

tw weld throat thickness (Annex M) mm%t time span (Annex B) h%td time to detect a leak (Annex F) hW plate width in plane of flaw (see for example Figure M.1, Figure M.2,

Figure M.6 and Figure M.7)mm

Wc crack opening width (Annex F) mmX factor relating ¸I and KI to account for constraint and work hardening

capability variationXnm failure pressure estimation (Annex G)x parameter used in Figure R.1 (Annex R)Y stress intensity factor correction (7.2.5, Clause 9 and Annex M)Ym, Yb stress intensity correction factors for membrane and bending stress

(Annex B)Ywm, Ywb stress intensity correction factors for the weld location for membrane and

bending stress (Annex P)

(YÖ)p primary stress intensity factor correction function (7.3.5.1, Annex M) N/mm2 (MPa)

(YÖ)s secondary stress intensity factor correction function (7.3.5.1, Annex M) N/mm2 (MPa)y height of peaking due to angular misalignment (Annex D) mmZ circumferential angular spacing between projection lines in the analysis

of corrosion flaws (Annex G)degrees

z measure of position through the thickness (Annex M and Annex Q) mmz0 through thickness depth of tensile residual stress zone (Annex Q) mmzr through thickness depth of repair (Annex Q) mmµ angular change at misaligned joint (Annex D) radiansµ¾ function of a, c, B and W used in calculation of collapse stresses (Annex P)µ(Æ½) bulging factor (Annex F)¶ ratio of brace diameter to chord diameter in a tubular joint (Annex B)¶½ plasticity correction factor, ¶½ = 1 for plane stress, ¶½ = 1 for plane strain¶¾ factor determining state of stress (Clause 9)¶sx factor used in collapse analysis of cylinders (Annex P)¶sy factor used in collapse analysis of cylinders (Annex P)¶r reliability (Annex K)¾ ratio of chord radius to chord wall thickness in a tubular joint (Annex B)¾½ estimate of Kr

s for through-wall self-balancing stress (Annex R)¾Ö, ¾a, ¾K, ¾¸, ¾Y

partial coefficients on stress, flaw size, fracture toughness in terms of K, fracture toughness in terms of CTOD and yield strength, for safety factor treatment (Annex K)

¾c safety factor for use with creep data (Clause 9)¸ crack tip opening displacement (CTOD) mm¸c CTOD at either: mm

a) unstable fracture; orb) onset of arrested brittle crack or pop-in.This term only applies where %a0 < 0.2 mm offset to the blunting line

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¸g CTOD at limit of permitted tearing (7.4.7.2) mm¸I applied CTOD (7.2.6) mm¸ix crack opening displacement corresponding to initiation of creep crack

growth of extent x (Clause 9)mm

¸m CTOD at first attainment of maximum force plateau mm¸mat material toughness measured by CTOD method mm¸0.2BL resistance to crack extension expressed in terms of CTOD at 0.2 mm

crack extension offset to the blunting line (Clause 7)mm

¸r fracture ratio using CTOD parameters (7.2.6)¸u CTOD at either: mm

a) unstable fracture; orb) onset of arrested brittle crack or pop-in.This term only applies where %a0 > 0.2 mm offset to the blunting line

¼ strain¼c accumulated creep strain (Annex T)¼e elastic strain at the reference stress (Öref/E) (Annex F)¼f strain to failure of material, as measured in uniaxial creep test (Annex T)¼ij elastic-plastic mechanical strains; ij = x, y, z (Annex R)¼max maximum tensile strain (7.2.8)¼ref reference strain (7.3.2.2)¼Y yield strain, i.e. strain at ÖY (7.2.8)%¼c increment of creep strain (Annex T)á dimensionless geometrical parameter used in collapse analysis of flawed

cylinders (Annex P)Ú parametric angle to identify position along an elliptic flaw front radiansÄ constant depending on boundary conditions (Annex D)Æ, Æ1, Æ2, etc. constants used in calculating stress intensity factors (Annex M)Ær ratio to give the structural cut-off (Annex P)Æs factor used in collapse analysis of cylinders (Annex P)Æ¾ scaling factor on stress intensity factor, used to define ¾½ (Annex R)È constant in calculating the failure pressure of a corroded sphere

(Annex G)É Poisson’s ratioß constant in calculating the failure pressure of a corroded sphere

(Annex G)Ô plasticity correction factor (Annex R)Ô1 a parameter used in determining Ô (Annex R)Ôf fluid density (Annex F) kg/mm3 or

g/mm3 [see footnote5)]

× ratio of flow strengths at re-load and pre-load conditions (Annex O)Öa applied stress (Annex O) N/mm2 (MPa)Öb linearized bending stress (Clause 9) N/mm2 (MPa)

5) The units for Ôf may be kg/mm3 or g/mm3, but it is essential that they are consistent with those used for Qmf.

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Öbc hot spot bending stress for a cracked tubular joint (Annex B) N/mm2 (MPa)Öf flow strength (assumed to be the average of the yield and the tensile

strengths, limited to 1.2Öy for Level 1 analyses) (7.2.7)N/mm2 (MPa)

Öf½ flow strength of the material in the vicinity of the flaw (7.3.4.2 and Annex O)

N/mm2 (MPa)

Öm linearized membrane stress (Clause 9) N/mm2 (MPa)Ömax maximum tensile stress for Level 1 analyses (7.2.3) N/mm2 (MPa)Ön,b bending component of collapse stress (Annex P) N/mm2 (MPa)Ön,m membrane component of collapse stress (Annex P) N/mm2 (MPa)

Öp stress arising from loads which contribute to plastic collapse (Clause 9) N/mm2 (MPa)ÖR residual stress N/mm2 (MPa)

Örmax surface value of self-balancing residual stress for through-wall crack

(Annex R)N/mm2 (MPa)

ÖRL longitudinal residual stress (Annex Q) N/mm2 (MPa)

ÖRT transverse residual stress (Annex Q) N/mm2 (MPa)

ÖRL,B longitudinal residual stress at bore (Annex Q) N/mm2 (MPa)

ÖRT,B transverse residual stress at the bore (Annex Q) N/mm2 (MPa)

ÖRT,O transverse residual stress on the outer surface (Annex Q) N/mm2 (MPa)

Öref reference stress used for creep and plastic collapse considerations N/mm2 (MPa)Öref,b reference stress for pure bending (Annex P) N/mm2 (MPa)Öref,m reference stress for pure membrane loading (Annex P) N/mm2 (MPa)

Ös stress arising from loads which do not contribute to plastic collapse (Clause 9)

N/mm2 (MPa)

Ös bending stress due to misalignment (Annex D) N/mm2 (MPa)Öu tensile strength N/mm2 (MPa)ÖY lower yield strength or 0.2 % proof strength N/mm2 (MPa)Ö½Y yield strength of the material in the vicinity of the flaw, as defined in

7.2.4 (7.2.4, 7.3.4, Annex O)N/mm2 (MPa)

ÖY1 yield strength at pre-load conditions (Annex O) N/mm2 (MPa)ÖY2 yield strength at re-load conditions (Annex O) N/mm2 (MPa)Öyy stress distribution normal to crack plane (Annex R) N/mm2 (MPa)

pseudo-stress distribution normal to crack plane (Annex R) N/mm2 (MPa)

Öw applied stress on weld throat N/mm2 (MPa)Ö0.2 0.2 % proof strength N/mm2 (MPa)%Ö applied stress range (Clause 8) N/mm2 (MPa)%Öb bending component of stress range (Clause 8) N/mm2 (MPa)%Öm membrane component of stress range (Clause 8) N/mm2 (MPa)%ÖAx axial stress range in tubular joint (Annex B) N/mm2 (MPa)%ÖIPB, %ÖOPB in and out of plane bending stress ranges in tubular joint (Annex B) N/mm2 (MPa)%Önom nominal stress range in tubular joint (Annex B) N/mm2 (MPa)%ÖHs.Tot total hot spot stress range in tubular joint (Annex B) N/mm2 (MPa)

Ö̃yy

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4 Types of flawThe effects of the following flaws may be assessed by use of this document.

a) Planar flaws:

1) cracks;

2) lack of fusion or penetration;

3) undercut, root undercut, concavity and overlap (on some occasions, undercut and root undercut in welds are treated as shape imperfections).

b) Non-planar flaws:

1) cavities;

2) solid inclusions (on some occasions cavities and solid inclusions are treated as planar flaws);

3) local thinning (e.g. due to corrosion).

c) Shape imperfections:

1) misalignment;

2) imperfect profile.

Flaws of the type known as “imperfect shape” include some which may be treated as planar flaws which are listed as such in a) and others which give rise to stress concentration effects. A comprehensive classification of the various types of weld flaw which may be encountered is given in BS EN ISO 6520-1.


%ÖHs.Ax, %ÖHs.IPB, %ÖHs.OPB

axial, in and out of plane hot spot stress ranges in tubular joint (Annex B) N/mm2 (MPa)

%Ön.Ax, %Ön.IPB, %Ön.OPB

nominal axial, in and out of plane stress ranges in tubular joint (Annex B) N/mm2 (MPa)

%Ö½b bending stress range excluding the effects of misalignment (Clause 8) N/mm2 (MPa)%Öj stress range in variable amplitude fatigue spectrum which is applied nj

times (Clause 8)N/mm2 (MPa)

Ù ratio of brace wall thickness to chord wall thickness in tubular joints (Annex B)

Ù½ factor used in collapse analysis of cylinders (Annex P)Í complete elliptic integral of the second kind (Annex M)Î parameter used in defining Ô (Annex R)Ìs factor used in the collapse analysis of spheres (Annex P) radiansÌ circumferential angular spacing between adjacent corrosion flaws

(Annex G)degrees

· factor used in collapse analysis of bolts (Annex P)Ó parameter used in defining Ô (Annex R)Ë degree of bending in tubular joints (Annex B)ËTot, ËAx, ËIPB, ËOPB

total, axial, in plane and out of plane degrees of bending in tubular joints (Annex B)

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5 Modes of failure and material damage mechanisms

5.1 The influence of the flaws listed in Clause 4 may be assessed, using this document, for the modes of failure and damage mechanisms listed below:

— failure by fracture and plastic collapse (see Clause 7);— damage by fatigue (see Clause 8);— damage by creep and creep fatigue (see Clause 9);— failure by leakage of containment vessels (see 10.2);— damage by corrosion and/or erosion (see 10.3.2);— damage by environmentally assisted cracking (see 10.3.3);— failure by instability (buckling) (see 10.4).

For each flaw or flaw type consideration should be given to the following points:

a) the potential modes of final failure; and

b) any possible material damage mechanisms leading to property degradation or sub-critical flaw growth.

Material damage and sub-critical flaw growth can be affected by the material itself, design features, stress levels, time, cyclic loading, composition and concentration of process fluids and additives, flow rates, operating temperatures, external environment, etc., though not all these considerations apply to any given material damage mechanism. The following are examples of some of the most common material damage mechanisms.

1) Embrittlement. This type of damage can be caused in some materials by irradiation, temper-embrittlement, or by caustic, hydrogen or hydrogen sulphide rich environments.

2) Fatigue. This is a damage process whereby embedded or surface cracks can initiate and grow under fluctuating stress (e.g. due to applied loads, thermal stress variations and vibrations). Members containing stress concentrations (e.g. flaws, geometric discontinuities) are particularly susceptible. For these reasons, welded components can give much lower fatigue lives than plain material under the same loading.

3) Corrosion fatigue. This is a type of damage similar to fatigue, but the onset of cracking and crack growth rates are accelerated by the corrosive medium.

4) Creep cracking. This is internal and/or external cracking due to operating temperatures greater than the creep threshold temperature, which is a function of the material. Components subjected to creep conditions have a finite life and the damage rate is a function of temperature, stress and time. For this reason, the finite life of highly stressed components and welds within a structure can be much lower than the plain areas subject to membrane stress alone.

5) Internal Corrosion. Material loss can take many forms, such as pitting corrosion, crevice corrosion, localized corrosion, general corrosion, etc., and is mainly due to the contents of the system, including possible impurities.

6) External corrosion and under lagging corrosion. Depending on the material, its loss from exposed areas can be similar to internal corrosion. This damage mechanism is mainly caused by a wet and dry environmental sequence such as exposure to rain, local environment surrounding the component (e.g. leaking fluids, emissions from surrounding plant).

7) Stress corrosion cracking (SCC). In some materials internal and/or external cracking can occur due to chemical action on a stressed component. Generally as-welded components are more susceptible than those which have been post-weld heat-treated. Crack initiation and propagation rates are a function of material, stress, temperature, and the concentration of the corrosive medium.

8) Hydrogen and hydrogen sulphide related cracking. The damage rate is a function of material, pressure, temperature, concentration of H2 or H2S, etc.

9) Erosion. The internal loss of material is mainly due to rapid flow of process fluid and to abrupt changes in fluid flow direction or the presence of other liquid or solid impurities.

10) Cavitation. The most common areas affected are pump impellers and components where high flow rates occur with significant pressure drop, such as may occur across control valves in process fluid piping or pipelines.

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For a particular application, some of these failure modes and damage mechanisms will not be relevant. However, it is necessary, at the outset, to consider all operating conditions including start-up, shut-down, process upset, and external environment to establish which are relevant to the particular component under consideration. It is also necessary to take account of possible interaction between the various damage mechanisms. Reference should be made to Clauses 7, 8, 9 and 10 dealing with the detailed assessment of the various modes of failure and material damage mechanisms.

The likelihood of failure from the operation of these failure modes and damage mechanisms can be predicted with varying degrees of confidence and accuracy. The behaviour of components subject to fatigue loading, creep and brittle fracture is well understood. It is not practical, at this time, to attempt to provide treatments for the other mechanisms listed in the same depth and generality as can be provided for failure by fracture, fatigue or creep. However, they all need to be to be considered in an ECA, since failure can arise through their operation. Brief guidelines are offered in Clause 10 for the assessment of the possible risk of operation of these mechanisms. A specific assessment should be undertaken, if it is established that a risk of failure from these modes exists. This should incorporate the assumptions and approaches used in these circumstances, which should be fully documented and agreed by all parties.

5.2 The following is the recommended sequence of operations for carrying out an assessment for a known flaw.

a) Identify the flaw type, i.e. planar, non-planar or shape (Clause 4).

b) Establish the essential data, relevant to the particular structure (see 6.2).

c) Determine the size of the flaw.

d) Assess possible material damage mechanisms and damage rates.

e) Determine the limiting size for the final modes of failure.

f) Based on the damage rate, assess whether the flaw would grow to this final size within the remaining life of the structure or the in-service inspection interval, by sub-critical crack growth.

g) Assess the consequences of failure.

h) Carry out sensitivity analysis.

i) If the flaw would not grow to the limiting size, including appropriate factors of safety, it is acceptable. Ideally the safety factors should take account both of the confidence in the assessment and of the consequences of failure.

Estimation of tolerable planar flaw sizes may be made by starting from a series of limiting flaw shapes as determined in e) and determining the initial flaw sizes which would grow to these within the remaining life as in f). Procedures for calculating such tolerable initial flaw sizes are given in Clauses 7, 8, 9 and 10.

5.3 Several levels of treatment of flaws are possible, depending on the application and materials data available. Three levels of dealing with fracture are included in Clause 7. Level 1 is a conservative preliminary procedure which is simple to employ. Level 2 is the normal procedure and comprises a number of options. Level 3 is an advanced procedure which allows for ductile tearing, permitting greater accuracy when sufficient materials data are obtainable. Level 3 also includes a number of options. Procedures are given in Clauses 8 and 9, respectively, for estimating fatigue and creep crack growth when specific materials data are provided. Guidance is also given in these clauses for making assessments when specific information is not available. Where appropriate, comments are included on the probability of survival and on the desirability of conducting a sensitivity analysis.

6 Information required for assessment

6.1 General

It is inevitable that the ECA will require assumptions to be made about input parameters. Therefore, if there is any likelihood that an ECA will be required during the life of a structure, it is advisable to generate relevant material properties at the construction stage, or to retain appropriate materials for later testing. In particular, the desirability of having accurate fracture toughness data cannot be emphasized too strongly and tests on weld procedure test samples are advisable. Similarly, fatigue crack growth, creep and stress corrosion cracking data may be obtained from the actual materials of construction. Any such tests should be performed in accordance with the appropriate standard from the following list.

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The information required should take account of the material strain and thermal history and the appropriate environment. The assessment should cover all loadings, including, as appropriate, those arising during transport, erection and testing. In some cases, it is necessary to take account of fault and accident conditions. The effects of local loads and misalignment should also be considered. Any assumptions should be justified to the satisfaction of all parties and appropriate documentation, including material specification and details of actual material used, should be appended to the ECA.

6.2 Essential data

Relevant data from the following list will be required:

a) nature, position and orientation of flaw;

b) structural and weld geometry, fabrication procedure;

c) stresses (pressure, thermal, residual or resulting from any other type of mechanical loading) and temperatures including transients;

d) yield or 0.2 % proof strength, tensile strength and elastic modulus (in certain cases, a complete engineering stress/strain curve is required);

e) fatigue/corrosion fatigue S-N and crack propagation data;

f) fracture toughness (KIc or J values or CTOD) data (in certain cases fracture toughness may be estimated from relevant Charpy V-notch data [see Annex J]);

g) creep rupture, creep crack propagation and creep fatigue data;

h) bulk corrosion and stress corrosion cracking (KISCC) data.

6.3 Non-destructive testing

6.3.1 Non-destructive testing (NDT) is an essential aspect of a fitness for purpose assessment. The NDT technique(s) used for flaw evaluation should be chosen to provide the type of information required to an acceptable degree of accuracy. Such information should include some or all of the following items:

a) flaw length;

b) flaw height;

c) flaw position;

d) flaw orientation with respect to the principal stress direction;

e) whether the flaw cross section is planar or non-planar.

6.3.2 For the detection of surface-breaking flaws the following methods (in no order of preference) are suitable:

a) visual;

b) liquid penetrant;

c) magnetic particle (for ferromagnetic materials);

d) eddy current (including a.c. field measurement [ACFM]). Note that there are difficulties in applying these methods to ferro-magnetic materials because of variations in magnetic permeability. Only systems developed to overcome these problems can be used with any measure of success for such materials;

e) electrical potential drop (a.c. or d.c.);

f) radiography;

g) ultrasonics.

All the above methods are also suitable for measuring the surface length of such flaws, but only ultrasonic, eddy current (including ACFM) and potential drop methods are capable of providing a measurement of their height.

— Fatique crack growth BS ISO 12108. — Fatique crack growth threshold BS ISO 12108. — Fracture toughness BS 7448 and BS EN ISO 12737. — Stress corrosion cracking BS EN ISO 7539.

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6.3.3 For the detection of embedded flaws the following methods (in no order of preference) are suitable:

a) radiography;

b) ultrasonics;

c) eddy current (including ACFM). Note that the comments in 6.3.2d) concerning the application of these techniques to ferro-magnetic materials apply;

d) electrical potential drop (d.c. only).

Of these, both radiography and ultrasonics are capable of providing a measurement of flaw length, but only ultrasonics can provide a measurement of flaw height. Eddy current, ACFM and potential drop methods will tend to provide a measurement of the cross-sectional area of the flaw. However, these latter techniques are only capable of detecting flaws that lie close to the scanned surface.

6.3.4 Non-destructive testing to an agreed extent (not necessarily 100 %) should be carried out in accordance with the appropriate standards from the following list:

Any inspection procedure, adopted by agreement, which deviates from or is not covered by an appropriate standard, should be appended to the ECA. Suitable allowances should be incorporated in the assessment of flaw sizes to cover intrinsic and measurement errors involved and thereby ensure conservative assessment of flaw severity. These allowances and their bases should be quoted in the ECA.

Standard inspection techniques, which are suitable and economically viable for examining long lengths of weld, will not necessarily be appropriate for the accurate flaw measurement required for an ECA. In such cases, supplementary techniques or additional test methods should be employed.

6.3.5 Where a region of a structure cannot be inspected, appropriate judgement should be made, based on flaw distributions in areas of the structure which could be inspected, to estimate the size of flaw that could potentially exist in the uninspectable region. When assessing the likelihood of the presence of such flaws, account may be taken of knowledge of the weld preparations, the welding process and procedures, and the general quality of welding attained. Account may also be taken of the operating applied loads, process fluid parameters and any significant external environment relevant to the region.

6.4 Stresses to be considered

6.4.1 General

The stresses to be considered in the assessment are those which would be calculated by a stress analysis of the unflawed structure. The actual stress distributions may be used or the stresses may be linearized, as shown in Figure 1. The latter method will normally provide overestimates but has the advantage that linearization does not need to be repeated with crack growth. It is essential that account is taken of the primary membrane and bending stresses, the secondary stresses and the magnification of the primary stresses caused by local or gross discontinuities or by misalignment, as described in 6.4.2, 6.4.3 and 6.4.4. Typical schematic representations of these are given in Figure 2. In an assessment of the effect of a single or steady state applied load, it is important to distinguish between primary and secondary stresses, since only the former contribute to plastic collapse. In a fatigue assessment, the important distinction is between static and fluctuating stresses and all fluctuating stresses are treated in the same way as primary stresses. In the special case when allowance is made for R (e.g. 8.2.1.4), steady state primary stresses and secondary stresses also need to be considered, in order to determine the actual values of the maximum and minimum applied stresses. It should be noted that the stress categories described below do not necessarily coincide with those used in other standards (e.g. PD 5500). In the fracture assessment routes described in Clause 7, shear stresses are not included. If shear stresses are significant, reference should be made to Annex A.

— Ultrasonics BS EN 1712 and BS EN 1714.— Radiography BS EN 1435 and BS EN 12517.— Magnetic particle BS EN 1290 and BS EN 1291.— Liquid penetrant BS EN 571-1 and BS EN 1289.

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i) Examples of linearization of primary or secondary stress distributions for surface flaws

ii) Examples of linearization of primary or secondary stress distributions for embedded flaws

Pm,Qm and Pb,Qb can be determined from the distributions in i) and ii) using the following equations:

NOTE Any linearized distribution of stress is acceptable provided that it is greater than or equal to the magnitude of the real distribution over the flaw surface.

a) Linearization of stress distributions in fracture assessments

i) Examples of linearization of stress range distribtuions for surface flaws

ii) Examples of linearization of stress range distribtuions for embedded flaws

%Öm and %Öb can be determined from the distributions in i) and ii) using the following equations:

b) Linearization of stress range distributions in fatique assessments

Figure 1 — Linearization of stress distributions

a

B

0 B

a

0 B

a

0 B

a

σσ

σ σ

1

σ1

σ1

σ2

σ2

σ2

2a

B

0 B2a

0 B2a

0 B2a

σ

σσ σ1

σ1 σ1

σ2

σ2σ2

Pm Qm,Ö1 Ö2+

2------------------= Pb Qb,

Ö1 Ö2–2

------------------=

a

B 0 B

a

0 B

a

0 B

a

∆ 1∆ 1

∆

∆

∆ 2∆ 2

∆ 1

∆

∆ 2

σ σ σ σ

σ

σ

σσ

σ

2a

B 0 B

2a

0 B

2a

0 B

2a

∆ 2∆

∆ 1σ ∆ 1σ∆ 1σ

σ

∆ 2σ ∆ 2σσ

∆σ∆σ

%Öm

%Ö1 %Ö2+2

----------------------------= %Öb

%Ö1 %Ö2–2

---------------------------=

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6.4.2 Primary stress (P)

These are stresses that could (if sufficiently high) contribute to plastic collapse, as distinct from secondary stresses, which do not (see 6.4.3). They can also contribute to failure by fracture, fatigue, creep or stress corrosion cracking. They include all stresses arising from internal pressure and external loads. Some stresses classified as secondary by ASME Section III [2] and PD 5500:2003, Annex A are regarded as primary in this guide, e.g. certain thermal and residual stresses (see 7.3.3). The primary stresses are divided into membrane, Pm, and bending, Pb, components as follows.

a) Membrane stress (Pm ) is the mean stress through the section thickness that is necessary to ensure the equilibrium of the component or structure.

b) Bending stress (Pb) is the component of stress due to imposed loading that varies linearly across the section thickness. The bending stresses are in equilibrium with the local bending moment applied to the component. For the purpose of this document, Pb is regarded as a stress superimposed upon Pm.

6.4.3 Secondary stress (Q)

The secondary stresses, Q, are self-equilibrating stresses necessary to satisfy compatibility in the structure. An alternative description is that they can be relieved by local yielding, heat treatment, etc. Thermal and residual stresses are usually secondary (but note that fluctuating thermal stresses are treated as primary in a fatigue assessment). A significant feature of secondary stresses is that they do not, of themselves, cause plastic collapse, since they arise from strain/displacement limited phenomena. They contribute to the severity of local conditions at a crack tip, however, and, when it is necessary to include them in an assessment, they have to be included in calculations of KI, ¸I and %KI. Note that the thermal stresses (primary and secondary) should also be multiplied by appropriate stress concentration and misalignment factors, kt and km.

The secondary stresses may be divided into membrane, Qm, and bending, Qb, components as for primary stresses (see 7.3.3).

6.4.4 Stresses at structural discontinuities

Stress concentrations occur at structural discontinuities under applied primary or thermal stresses. Secondary stresses are not influenced by structural discontinuities except that thermal stresses, when considered secondary (see 7.3.3), are affected by structural discontinuities. There are three basic categories of such discontinuities:

— gross discontinuities;— misalignment and deviation from intended shape;— local discontinuities such as welds, holes, notches, etc.

These are described further in a), b) and c). Their effects are quantified by calculating peak stresses at the discontinuities, as shown in a), b) and c). The bending component may be obtained by subtracting the membrane component from the peak stress.

a) Gross structural discontinuities. Typical gross structural discontinuities are those occurring at pressure vessel nozzles and at the major intersections in tubular structures. For such situations, the peak stress at the discontinuity is calculated by multiplying the applied stress by the appropriate stress concentration factor. For nominal stress, membrane stress and bending stress, these are kt, ktm, and ktb, respectively.

In Level 1 analyses, the applied stress (which is usually the nominal membrane stress) is multiplied by a single kt to give the peak stress comprising membrane plus bending stresses. In analyses to Levels 2 and 3, the individual membrane and bending components of the applied stress are available, as shown in Figure 2, and separate factors ktm and ktb are applied to each.

Further guidance for tubular joints and for pressure vessel nozzles is given in Annex B and Annex C respectively.

This type of stress concentration usually decays over distances greater than the section thickness, and may lead to a plastic hinge across the full section thickness over local regions.

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b) Discontinuities due to misalignment or deviation from intended shape. These cause bending stresses. The additional bending stress is calculated by multiplying the applied membrane stress by a stress magnification factor km (see for example Annex D).

This type of stress magnification also decays over distances greater than the section thickness and may lead to a plastic hinge across the full thickness over local regions. If additional bending stresses due to misalignment occur within a region of stress concentration due to a gross structural discontinuity, both effects have to be considered and this is included in the relevant formulae (7.2.3 and 7.3.5.1).

c) Local structural discontinuities, such as holes, notches or sharp corners. The stress concentration due to this type of discontinuity usually decays over distances less than about 20 % of the hole or notch radius, or 20 % of the thickness. If the flaw lies within this region, then the effect of stress concentration on plastic collapse should be considered and the peak stress may be calculated by multiplying the applied stress by kt.

Stress concentration effects due to weld toes do not contribute to plastic collapse (see M.5).

For sharp corners, the theoretical stress concentration factor is infinite, and it is preferable that cracks at such regions be treated by a stress intensity magnification factor (see 7.2.5 and 7.3.5.1). Local structural discontinuities may be located within zones of stress concentration caused by gross discontinuities and/or by misalignment, and all these effects should be taken into account in the stress analysis.

Different methods of incorporating peak stresses are used in various different assessment methods within this document, as detailed in 7.1.6, 7.2.3 and Clauses 8 and 9.

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6.4.5 Stresses used in the ECA should be justified and tabulated and form an integral part of the assessment. When complete stress information is not available, the basis for any estimate should be agreed with all parties and be included in the assessment.

Where the plane of the flaw is not aligned with a plane of principal stress, further consideration is needed. The first step is to project the flaw on to each of the three planes normal to the principal stresses and to evaluate each of the three projected flaws. Often one of these projections will lead to a stress intensity factor and a reference stress that are both significantly higher than those for the other two projections. The assessment is then carried out, taking a and 2c as the projected dimensions on that plane. This for example is the method often applicable to near circumferential flaws in the wall of a pipe, where the flaw is projected on to the circumferential plane (see Figure 3). There are however restrictions on proceeding in this way. Specialist advice should be sought when the following situations arise.

a) Primary membrane stress, Pm

b) Membrane stress multiplied by stress concentration factor,

ktmPm

c) Primary bending stress, Pb d) Bending stress multiplied by stress concentration factor

ktbPb

e) Bending stress due to misalignment, kmPm

f) Secondary stress, Q g) Total stress, ktmPm + ktb[Pb + (km – 1)Pm] + Q

Figure 2 — Schematic representation of stress distribution across section

B

0

Pm

0

B

ktmPm

0

B

Pb

0

B

ktb Pb

B(-km -1)Pm

0

(km - 1)Pm

0

B

0

B

maxσ

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a) There is a large angle (greater than about 20°) between the plane of the actual flaw and the principal plane on which the stress intensity factor and reference stress are greatest.

b) There is only a small difference between the stress intensity factors on two or more planes of projection.

c) The maximum stress intensity factor occurs for the flaw projected onto one plane and the maximum reference stress occurs for the flaw projected onto another plane.

d) One of the principal stresses is significantly compressive, i.e. of a similar magnitude to the maximum principal tensile stress.

In these circumstances significant mode II and/or III loading may be present. Annex A provides guidance on the treatment of these modes of loading.

Key

1 Resolved flaw (normal to principal stress) 3 Principal stress

2 Actual flaw

a) Butt weld example

Key

1 Resolved flaw (resolved to maximize significance) 3 Principal axial stress

2 Actual flaw 4 Principal hoop stress

b) Spiral weld pipe example

Figure 3 — Procedure for resolving flaws normal to principal stress

1

2

3

12

3

4

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7 Assessment for fracture resistance

7.1 Background

7.1.1 General

There are three levels of fracture assessment in this guide, but similar methods are used in each. The choice of level depends on the materials involved, the input data available and the conservatism required. The three levels are as follows.

a) Level 1 is a simplified assessment method applicable when the information on materials properties is limited.

b) Level 2 is the normal assessment route.

c) Level 3 is appropriate for ductile materials and enables a tearing resistance analysis to be performed.

Levels 1, 2 and 3 are described in 7.2, 7.3 and 7.4 respectively.

Assessment is generally made by means of a failure assessment diagram (FAD) based on the principles of fracture mechanics. The vertical axis of the FAD is a ratio of the applied conditions, in fracture mechanics terms, to the conditions required to cause fracture, measured in the same terms. The horizontal axis is the ratio of the applied load to that required to cause plastic collapse. An assessment line is plotted on the diagram. Calculations for a flaw provide either the co-ordinates of an assessment point or a locus of points. The positions of these are compared with the assessment line to determine the acceptability of the flaw.

A general flow diagram of the procedures is shown in Figure 4 and detailed flow diagrams of each level are given in Figure 5 to Figure 7.

It is possible that acceptability can still be demonstrated, even if an initial assessment shows a flaw to be unacceptable. This may require improving the quality of the input data and/or applying a higher assessment level, if appropriate. This is discussed in 7.5.1 and 7.5.2.

In some cases surface-breaking or embedded flaws might initially be found to be unacceptable because of predicted ligament failure. However, in some circumstances this prediction of ligament failure may not be critical. The flaw may be re-characterized as a through-thickness or surface-breaking flaw, and re-assessed. The procedure for flaw re-characterization is given in Annex E.

For pressurised applications, a leak-before-break analysis (see Annex F) may show that a stable leak would occur rather than a break.

At each level, either the acceptability of a flaw may be assessed directly or the calculation may be iterated in order to determine the limiting value of a parameter such as flaw size, applied stress or fracture toughness. The limiting value may be obtained analytically or alternatively by plotting on the FAD the results from the iterations in order to determine the point at which first contact is made with the assessment line.

The material properties required for an assessment are generally those for the region in which the flaw is present, i.e. parent metal, weld metal or heat affected zone (HAZ).

All FAD assessments relate to planar flaws. Guidance on the assessment of other flaw types is given in 7.5.3. Locally thinned areas may be assessed solely against plastic collapse. Methods of assessing such areas are given in Annex G.

The assessments in this clause refer to tensile mode I loading only. Mixed mode loading is addressed in Annex A.

Annex B provides guidance on specific aspects of the assessment of offshore structures. Annex C applies similarly to pressure vessels and pipelines. Annex H gives requirements when reporting an assessment.

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Fig

ure

4 —

Flo

w c

ha

rts

— G

ener

al

met

ho

ds

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Figure 5 — Flowchart — Level 1

Level 1Simplified assessment

Y NAre fracture toughness data(K, J or δ ) available?

Determine material tensileproperties

7.1.3

Characterize flaw

7.1.2

Select analysis method

Main procedure7.2

Calculate Sr7.2.7

Calculate Kr or r7.2.5, 7.2.6

Plot assessment point(Sr , Kr or r ) on FAD

7.2.2.1

Assess significance of resultsAnnex K

Flaw tolerable? Can flaw be recharacterized?

Can stress analysis berefined?

Structure cannot bedemonstrated to be safe at

Level 1

Estimate Kmat from Cv

Annex J

Recharacterize flawAnnex E

N

N

Y

N

Y

Graphical procedureAnnex N

Calculate a and am

Check for plastic collapse

Y

Structure has beendemonstrated to be safe at

Level 1

δDetermine Kmat, mat7.1.5, Annex L

Define stresses6.4

δ

δ

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Y Are fracture toughness data(K, J or δ ) available?

Estimate Kmat from Cv

Annex J

Determine Kmat , mat7.1.5, Annex L

Level 2Normal assessment

Define stresses6.4, 7.3.3


7.1.3

Characterize flaw7.1.2


Select FAD7.3.1

Calculate Lr7.3.8

Calculate Kr or r7.3.5, 7.3.6

Plot assessment pointon FAD7.3.1

Assess significance of resultsAnnex K

7.3.1, 7.1.1.2

Flaw tolerable?Y N

Can a material specificFAD be used?

7.3.2.3

N

N

N

Structure cannot be demonstrated to be safe at

Level 2

Y

Can flaw be recharacterized?

Can stress analysis be refined?

Structure has been demonstrated to be safe at

Level 2

Y

Y

N

δ

δ

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Level 3 Ductile tearing instability assessment

Define stresses7.3.3


7.1.3

Characterize flaw7.1.2


Select FAD7.4.2

Calculate Lr for all ao , ag , aj7.3.7

Calculate Kr or r for all ao, ag, aj7.3.5, 7.3.6

Assess significance of results Annex K, 7.4.1, 7.1.1.2

Flaw tolerable?Y N

Can a higher option FAD be used?

7.4.1

N

N

N

Structure cannot be demonstrated to be safe at

Level 3

Y

Can flaw be recharacterized?

Can stress analysis be refined?

Structure has been demonstrated to be safe at

Level 3

Y

Y

Define ao , aj , ag7.4.7.2

Plot assessment points (Lr, Kror r ) on FAD

7.4.1, 7.4.2

Determine Kmat , mat ( a)7.1.5, Annex L

∆δ

δ

δ

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7.1.2 Flaw dimensions and interaction

7.1.2.1 Planar flaws should be characterized by the height and length of their containment rectangles. These dimensions [see Figure 8a), b) and c)] are as follows: 2a for through thickness flaws; a and 2c for surface flaws; and 2a and 2c for embedded flaws.

7.1.2.2 Multiple flaws on the same cross-section may lead to an interaction and to more severe effects than single flaws alone. Simple criteria for interaction are given in Figure 9, together with the dimensions of the effective flaws after interaction. If multiple flaws exist, each flaw should be checked for interaction with each of its neighbours using the original flaw dimensions in each case. It is not normally necessary to consider further interaction of effective flaws.

7.1.3 Tensile test properties

The material yield strength, ÖY, tensile strength, Öu, and modulus of elasticity, E, are required for assessment of fracture resistance. They can be determined from tests in accordance with BS EN 10002-1 or BS EN 10002-5 at the appropriate temperature. The material yield strength should be taken as either the lower yield or the 0.2 % proof strength depending on the material type. Unless specific solutions are available to assess the effect of weld strength mismatch (see I.4), safe assessments will be made of flaws located in welded regions (weld metal and HAZ) if the tensile properties assumed are the lower of the parent metal, weld metal or HAZ.NOTE Unless HAZ softening is present, the yield strength and tensile strength of the HAZ does not need to be determined.

a) Through thickness flaw[Required dimensions: 2a, B]

b) Embedded flaw[Required dimensions: 2c, p, 2a, B]

c) Surface flaw[Required dimensions: a, 2c, B]

d) Flaw at toe of fillet weld[Required dimensions: 2c, a, B]

e) Flaw at hole[Required dimensions: c, a, B]

Figure 8 — Flaw dimensions

2a

B B

2c

p2a

2c

p2a 2ca 2ca

B

L

a

B

2c

aB

c

cr

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Schematic flaws Criteria for interaction Effective dimensions after interaction

s k 2c1 for a1/c1 or a2/c2 > 1 s = 0 for a1/c1 and a2/c2 < 1 (c1 < c2)

a = max {a1, a2} 2c = 2c1 + 2c2 + s

i) Coplanar surface flaws

s k a1 + a2

2a = 2a1 + 2a2 + s 2c = max {2c1, 2c2}

ii) Coplanar embedded flaws (interaction in thickness direction)

s k 2c1 for a1/c1 or a2/c2 > 1 s = 0 for a1/c1 and a2/c2 < 1 (c1 < c2)

2a = 2a2 2c = 2c1 + 2c2 + s

iii) Coplanar embedded flaws (interaction in width direction)

a) Coplanar

Figure 9 — Planar flaw interactions

2c

2c1 2c2

a2

a1

2ca2

a1

s

2c1

2a

2a1

2a2

2c2

2c1

2a

2a1

2a2

s

2c22c1

2c

2a

2a1

2a2

2c22c1

2c

2a

2a1

2a2

s

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Schematic flaws Criteria for interaction Effective dimensions after interaction

s k a1 + a2

a = 2a1 + a2 + s 2c = max {2c1, 2c2}

iv) Coplanar surface and embedded flaws (interaction in thickness direction)

s1k 2c1 for a1/c1 or a2/c2 > 1 s1 = 0 for a1/c1 and a2/c2 < 1 and s2 k a1 + a2 (c1 < c2)

2a = 2a1 + 2a2 + s2 2c = 2c1 + 2c2 + s1

v) Coplanar embedded flaws (interaction in both thickness and width direction)

s1k 2c1 for a1/c1 or a2/c2 > 1 s1 = 0 for a1/c1 and a2/c2 < 1 and s2 k a1 + a2 (c1 < c2)

a = a1 + 2a2 + s2 2c = 2c1 + 2c2 + s1

vi) Coplanar surface and embedded flaws (interaction in both thickness and width direction)

a) Coplanar (continued)

Figure 9 — Planar flaw interactions (continued)

2a1

2c1

a

a2

2c2

2a1

2c1

sa

a2

2c22c1 s1

2c

2a1

2a2

2a

2c22c1 s1

2c

2a1

2a2

s22a

s1

2c

2c1 2c2

2a2

a1

s2a

2c

2a2

a1

s2a

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Sch

ema

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fla

ws

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teri

on

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s 1 k

a1

+ a

2

and

s 2 k

2c 1

for

a1/

c 1 o

r a 2

/c2

> 1

s 2

= 0

for

a1/

c 1 o

r a 2

/c2

< 1

w

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< c

2

(2c 1

an

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max

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m

prin

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in t

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wel

d 2c

= 2

c 1+

2c 2

+ s

2

1) P

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fla

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s 1 k

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s 2 k

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for

a1/

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w

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d 2c

= 2

c 1+

2c 2

+ s

2

1) P

rin

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m

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2) P

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onto

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ii)

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b) N

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opla

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Fig

ure

9 —

Pla

na

r fl

aw

in

tera

ctio

ns

(con

tin

ued

)

2c2

2c1

2c s 22a

2a1

2a2

2a

s 12c

22c

1

2c s 22a

Prin

cipa

l pla

ne

a 2

2a1

s 1

a

2c1

2c2

s 22c

a

2c1

2c2

s 22c

a

Prin

cipa

lpla

ne

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Sch

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s 1 k

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for

a1/

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> 1

s 1

= 0

for

a1/

c 1 o

r a 2

/c2

< 1

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1 +

a2

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ere

c 1 <

c2

(2a 1

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(co

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Fig

ure

9 —

Pla

na

r fl

aw

in

tera

ctio

ns

(con

tin

ued

)

2c1

s1

2c2

2c2a

2

2a1

2c

s 22a

Prin

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l pla

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7.1.4 Stress intensity factor (K) and CTOD (¸) assessment routes

7.1.4.1 Two routes are given in each method to determine the tendency to fracture. They appear as the ordinate on the FAD and are based either on the stress intensity factor, K, or on the crack tip opening displacement (CTOD), ¸. (They appear as Kr, the fracture ratio based on K, and as Æ¸r, the square root of the fracture ratio based on CTOD). The use of the square root of ¸r enables both Kr, and ¸r to be plotted on the same axis.

In any assessment, it is essential that one route is used consistently throughout.

7.1.4.2 The K route should be followed if Kmat is determined from one of the following:

— measured linear-elastic plane strain fracture toughness KIc; or— correlations from Charpy V-notch impact test data (see Annex J); or— conversion from J (see 7.1.5.4) using the following equation:

7.1.4.3 If valid KIc data are not obtained, CTOD test data and the CTOD assessment route should be used, or equivalent Kmat values should be derived from J-based tests.

It is not intended that CTOD toughness data should be transformed to equivalent K data.

Because of the uncertainties in the effects of crack tip constraint, differences may occur in results of assessments using K-based or CTOD-based data from the same source. However, identical results will be achieved if equation (21) is used (see 7.3.6.1).

7.1.5 Fracture toughness

7.1.5.1 Where parent and weld yield strengths are subject to mismatch of more than 25 %, special consideration should be given to the fracture toughness data being used. Annex I gives a definition of mismatch and additional guidance on fracture toughness testing and flaw assessment under conditions of mismatch.

7.1.5.2 KIc should be established following the methods specified in BS 7448 and BS EN ISO 12737. If a valid KIc is available, Kmat should be taken as KIc. Tests should be carried out on full thickness specimens.

7.1.5.3 CTOD values, ¸, should be established following the methods specified in BS 7448. Tests should be carried out on full thickness, rectangular (W = 2B) specimens wherever possible. However, where assessments involve certain types of flaw and flaw orientation (e.g. shallow surface flaws or HAZ regions), specimens of square section or of an alternative width to thickness ratio, as specified in BS 7448-1 and BS 7488-2, may be appropriate.

7.1.5.4 J-based methods of fracture toughness testing may be used in accordance with BS 7448. Full thickness tests should be employed. For J tests on welded joints, it is essential that the measurement of J take account of differences in properties between weld and parent material and also of the deformation pattern that actually occurs.

7.1.5.5 In this guide, the critical ¸ or J value from a test in accordance with BS 7448 is termed ¸mat or Jmat respectively. It should be taken as the lowest of ¸c, ¸u or ¸m, or Jc, Ju or Jm respectively; or, where no significant tearing is permitted, as ¸0.2BL or J0.2BL respectively.

For Levels 1 and 2 assessment procedures, stable tearing using full thickness laboratory test pieces in accordance with BS 7448 may be accepted up to ¸m or Jm respectively.

For a tearing analysis at Level 3, a full tearing resistance curve derived from either ¸ or J measurements is necessary.

At all levels, equivalence between CTOD and J or K procedures can be achieved by using a constraint factor, X, as described in 7.3.6.1.

(1)K2

matEJmat

1 Ý2–

------------------=

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7.1.5.6 At Levels 1 and 2, the fracture toughness value, Kmat or ̧ mat, may be taken as the minimum of three similar test results, either all showing brittle fracture, or all showing tearing up to maximum load. For ̧ mat, caution should be exercised when the minimum CTOD result is less than 50 % of the average of three, or when the maximum is more than twice the average of three. Similarly, for Kmat, caution should be exercised when the minimum result is less than 70 % of the average of three, or when the maximum is more than 1.4 times the average of three. Such variations of the minimum or maximum from the average indicate excessive scatter and the need for more data.

When the scatter is large, and for Levels 2 and 3 assessments, it is recommended that additional tests be made. Guidance on the value to be used in the assessment, when more than three tests are conducted, is given in K.2.3.2. Annex K also gives guidance on statistical treatments. Particular attention is drawn to the importance of ensuring that sets of HAZ specimens have the crack tip in similar microstructures when carrying out statistical analyses (see BS 7448-2).

When statistical analyses of sets of fracture toughness data are carried out (see Annex K) it is important that the analyses acknowledge possible differences in fracture mechanisms and materials.

With fracture toughness tests on HAZ regions, considerable variability can occur due to location of the crack tip in different microstructural regions. It is sometimes necessary to carry out sectioning of specimens for tests on HAZ regions after testing to determine the precise location of the crack tip. Results analysed as a set should include only data from tests in which the crack tip was located in microstructure of similar type and grain size (see Annex L).

7.1.5.7 Fracture toughness tests should take account of the orientation of flaws in the structure relative to welded joints, and of the constraint (if non-standard specimens are used), temperature, rate of loading and environment (particularly for materials exposed to hydrogen) experienced in service. The tests should be carried out on samples welded with the same consumables and procedures as were or are to be used for the service application and should take account of restraint during welding and of PWHT, if applicable.

7.1.5.8 Test results in which “pop-in” behaviour is observed should be analysed using the procedures in BS 7448. It should be noted that, although an individual “pop-in” may be ignored on the basis of the criteria described in BS 7448, this does not necessarily mean that the lower bound of fracture toughness has been measured. For instance, in an inhomogeneous material such as a weldment, a small “pop-in” may be recorded because of fortuitous positioning of the fatigue crack tip. Thus a slightly different fatigue crack tip position may give a larger “pop-in”, which could not be ignored. In such circumstances, the specimens should be sectioned after testing and examined to ensure that the crack tips have sampled the maximum amount of brittle microstructure in the weld or parent metal region of interest (see BS 7448-2).

7.1.5.9 Standard testing methods (e.g. BS 7448 and BS EN ISO 12737) used to derive fracture toughness data are necessarily conservative and represent high constraint applications. In specialized circumstances, full scale or model tests (e.g. wide plate tests, pressure vessel tests and tests on specimen geometries modelling structural constraint and/or containing shallow cracks) may be adopted to give more appropriate values of the data to be used in the fracture assessments.

7.1.6 Stresses

The direct stress components perpendicular to the plane of the flaw should be used in an assessment, but, when the flaw is not aligned with the direction of the principal stress, the procedures described in 6.4.5 should be followed.

The magnitude of the stresses shall be obtained in accordance with 6.4.1.

7.1.7 Large flaws

Special provision should be made when the flaw area is greater than 10 % of the load bearing cross-sectional area and no finite width correction has already been included (see Annex M).

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7.1.8 Sr and Lr

The parameter for plastic collapse appears as the abscissa on the FAD. In Level 1, it is Sr and is the reference stress divided by the flow strength (see 7.2.7). In Levels 2 and 3, it is Lr and is the reference stress divided by yield strength (see 7.3.7). The reason for the difference is that the assessment line for Level 1 is based on the assumption of an elastic-perfectly plastic stress-strain curve with no strain hardening. This is conservative and to compensate for this conservatism, it is permissible to use in the denominator of Sr the flow strength rather than the yield strength. Levels 2 and 3 allow more accurately for the actual shape of the material stress-strain curve and so no such concession can be made.

7.1.9 Peak stress at weld toe

There is no simple upper bound limit for the peak stress at a shallow surface flaw (a/B < 0.2) located within the stress concentration zone at the toe of a weld. Thus such flaws are most accurately assessed at Levels 2 or 3. However, Level 1 assessments can be performed for surface flaws at the toes of fillet or butt welds (see Figure 8) where the stress concentration factor kt is taken as 3 at the weld toe decreasing linearly to 1.0 as a increases from 0 to 0.15B)6). If a is greater than 0.15B then kt = 1.

Flaws at the toe of a fillet or T butt weld, which is itself in a geometric stress concentration (e.g. a nozzle/pad combination), should be considered to lie in the combined geometric and fillet weld stress concentration fields for a depth up to 0.15B.

7.1.10 Sensitivity analysis

If the result is marginal, an analysis to determine the sensitivity of the results should be performed. This will reveal the main factors determining likelihood of fracture. Guidance is given in Annex K.

7.2 Level 1 — Simplified assessment

7.2.1 Main features

This is a simplified assessment route applicable where there is limited information on material properties or applied stresses. It contains two methods, Levels 1A and 1B. Conservative estimates of applied stress, residual stress and fracture toughness are employed. Additional partial safety factors are not used.

7.2.2 Assessment methods

7.2.2.1 Level 1A: general

The FAD is shown in Figure 10. The area bounded by the axes and by the assessment line is a rectangle. The flaw is acceptable if Kr or Æ¸r is less than 1/Æ2 (i.e. 0.707) and Sr is less than 0.8. The FAD contains an in-built safety factor (which approximates to a factor of 2 on flaw size).

A single FAD is used. If the assessment point lies in the area within the assessment line, the flaw is acceptable; if it lies on or outside the line, the flaw is not acceptable.

Where a measured fracture toughness (as given by Kmat or ¸mat) is not available, an estimate of Kmat determined from Charpy V-notch impact test data (see Annex J) may be used.

Values of Kmat derived from J or from “invalid” K tests may have to be adjusted to take account of the different constraint conditions in the test piece compared with those of plane strain (see 7.1.5.5 and 7.3.6.1).

Relaxation of the FAD for strain controlled loading is described in 7.2.8.

7.2.2.2 Level 1B: manual estimation

A manual estimation method, which does not involve a FAD, is given in Annex N.

6) The stress concentration factor, kt, used at Level 1, is equivalent to the factor Mk, used at Levels 2 and 3.

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7.2.3 Maximum stress

The stress used is the maximum tensile stress, Ömax, which is taken to be equal to the sum of the values of the stress components. If only nominal membrane stresses, Snom, are known, Ömax = ktSnom + (km – 1)Snom + Q. If membrane and bending components are known, Ömax = ktmPm + ktb[Pb + (km – 1)Pm] + Q (see Figure 2). The variation in the stress components across the section is not taken into account and this leads to a conservative estimate of the total applied stress. Annex A should be used if shear stresses are significant.

7.2.4 Residual stress

7.2.4.1 In a structure in the as-welded condition, with a flaw lying in a plane transverse to the welding direction (i.e. the stresses to be considered are parallel to the weld), the tensile residual stress should be assumed to be a uniform membrane stress contributing to Qm. This stress should be assumed to be equal to the room temperature yield strength of the material in which the flaw is located.

For a flaw lying in a plane parallel to the welding direction (i.e. the stresses to be considered are perpendicular to the weld), the residual stress should be assumed to be equal to the lesser of the room temperature yield strengths of the weld or parent metal.

7.2.4.2 In a structure subject to PWHT, the residual stresses will not in general be reduced to zero. The level of residual stress remaining in welds after PWHT may be estimated on the basis of stress relaxation tests for all-weld or parent metal specimens, as appropriate. Where these data are not available, it may be assumed, in carbon manganese and low alloy steels, that the stresses after heat treatment in an enclosed furnace within the range 580 °C to 620 °C (in accordance with procedures such as those of PD 5500) are as follows:

— parallel to the weld, the residual stress (Qm) should be assumed to be equal to 30 % of the room temperature yield strength of the material in which the flaw is located; — transverse to the weld, the residual stress (Qm) should be assumed to be 20 % of the lesser of the yield strengths of the weld or parent material.

Figure 10 — Level 1A FAD

1.0

0.8

0.6

0.4

0.2

0.707

Sr

0.0 0.2 0.4 0.6 0.8 1.0

Acceptable

Assessmentpoint

Unacceptable

Assessmentline

Kr

or

rδ

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7.2.4.3 Uncontrolled local heat treatment may leave significantly higher residual stresses and as-welded values should be assumed.Increased levels of residual stresses may be experienced with local heat treatments to code requirements (e.g. PD 5500) and specific assessments should be made.

7.2.4.4 Advantage may be taken of the reduction in residual stresses due to the application of an initial pressure test or other form of mechanical pre-loading, for structures of satisfactory design and construction (see Annex O). No advantage can be taken if the stress distribution can reverse in sign compared to the pre-load.It is not, in general, permissible to assume that the level of residual stresses to be used in a flaw assessment will be reduced by the application of a vibratory “stress relief ” treatment.If an assessment is carried out on a structure that received a proof test prior to entering service, but which has subsequently experienced an extensive period of operation, the potential benefits of the proof test may be reduced by the occurrence of in-service crack growth or the effects of embrittlement.

7.2.5 Fracture ratio (Kr) The applied stress intensity factor, KI, has the following general form:

(2)

where(3)7)

and whereM and fw are bulging correction and finite width correction factors respectively;Ömax is the maximum tensile stress (see 7.2.3);Mm is a stress intensity magnification factor.

Specific solutions for various geometries are given in Annex M, including flat plates, curved shells, welded joints and round bars.Kr is the ratio of the stress intensity factor, KI, to the fracture toughness Kmat, i.e.

7.2.6 Fracture ratio (¸r)The applied CTOD, ¸I, is determined from KI as follows:

a) for steels (including stainless steels) and aluminium alloys where Ömax /ÖY k 0.5, and for all Ömax /ÖY ratios with other materials:

b) for steels (including stainless steels) and aluminium alloys where Ömax /ÖY > 0.5:

and where¸r is the ratio of ¸I to the fracture toughness, ¸mat; andthe square root of ¸r is calculated from the following equation:

7) The equations in this document differ from those found, for example, in the publications of Newman and Raju and in PD 6493, which is now withdrawn from publication. For surface, embedded and corner flaws, Mm and Mb have been modified here by dividing by the complete integral, Í. By making this change, it has been possible to write one set of equations that apply to all geometries.

(4)

(5)

(6)

(7)

KI YÖ( ) Ïa( )=

YÖ MfwMmÖmax=

KrKI

Kmat-------------=

¸IK 2

IÖYE-----------=

¸I

K I2

ÖYE---------

ÖY

Ömax-----------⎝ ⎠⎛ ⎞

2 Ömax

ÖY----------- 0.25–⎝ ⎠⎛ ⎞=

¸r ¸I ¸⁄ mat=

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7.2.7 Load ratio (Sr)

The load ratio, Sr, is calculated from the following equation:

where

Öref is obtained from an appropriate reference stress solution given in Annex P.

The flow strength, Öf, should be assumed to be the arithmetic mean of the yield strength and the tensile strength up to a maximum of 1.2ÖY.

7.2.8 Strain controlled loading

In cases where the loading conditions are strain-controlled or where there is contained plastic deformation, the stress-based plastic collapse solutions in Annex P may be unnecessarily restrictive.

Where this is judged to apply, and hence where there is no risk of structural plastic collapse, the restriction on the load ratio (Sr k 0.8) can be ignored and the FAD (see Figure 10) can be extended, provided that the following conditions apply.

Pm + Pb k ÖY or Snom k ÖY; and

ktmPm + ktbPb k 2ÖY or ktSnom k 2ÖY

Alternatively, if the same strain-controlled conditions apply and the strain local to the crack tip is known or can be estimated, the strain ratio (¼max /¼Y ) can be used in place of the stress ratio, (Ömax /ÖY), in equation (7) to determine ¸I. From ¸I, the ratio Æ¸r can be calculated. Assessments can then be performed to Level 1A, using the strain-based Æ¸r ratio. Once again, the Sr requirement is ignored. These calculations can also be performed to Level 1B, applying the procedures of Annex N to assess a known flaw or to calculate the tolerable flaw size, , using the strain ratio (¼max /¼Y ) in equations (N.2) and (N.3).

For high strain ratios (i.e. ¼max /¼Y > 4) an elastic-plastic stress analysis is recommended. One method of estimating plastic strains at strain concentration regions is to use the Neuber hypothesis that the product of plastic stress and strain concentration factors is equal to the square of the elastic stress concentration factor. Alternatively, Level 2 or 3 assessment procedures for global collapse may be considered (see Annex P).

7.3 Level 2 — Normal assessment

7.3.1 Main features

This is the normal assessment route for general application. It has two methods.

Each method has an assessment line given by the equation of a curve and a cut-off. If the assessment point lies within the area bounded by the axes and the assessment line, the flaw is acceptable; if it lies on or outside the line, the flaw is unacceptable.

The cut-off is to prevent localized plastic collapse and it is set at the point at which Lr = Lrmax where:

For the purposes of defining the cut-off, mean rather than minimum properties may be used.

(8)

(9)

Sr

ÖrefÖf

---------=

am

Lrmax

ÖY Öu+2ÖY

--------------------=

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No inherent safety factors are included. To obtain the required reliability, appropriate partial safety factors (see Annex K) may be applied to the flaw dimensions, stresses, yield strength and fracture toughness. For the flaw dimensions, either the size of the individual flaws (see Figure 8) or the effective dimensions after interaction (see Figure 9) should be multiplied by the partial safety factor. Stresses are similarly multiplied (by the appropriate partial safety factor), but fracture toughness and yield strength are divided.

Assessments are based on a single value of toughness. This may be a value associated with limited ductile tearing, but, for a full analysis of ductile tearing, a Level 3 approach is required.

Where a measured fracture toughness (as given by Kmat or ¸mat) is not available, an estimate of Kmat determined from Charpy V-notch impact test data (see Annex J) may be used.

Margins of safety can be assessed using reserve factors and probabilistic approaches as described in Annex K.

7.3.2 FADs

7.3.2.1 Level 2A: generalized FAD, not requiring stress/strain data

The equations describing the assessment line are the following:

a) for Lr k Lrmax:

b) for Lr > Lrmax:

The FAD is shown in Figure 11a) with different cut-offs for different materials.

For materials which exhibit a yield discontinuity (often referred to as Lüders plateau) in the stress-strain curve (i.e. any curve which is not monotonically increasing), or for which it cannot be assumed with confidence that no discontinuities exist, either a cut-off value for Lr of 1.0 should be applied or Level 2B should be used. If it is impractical to determine a Level 2B FAD, the FAD at and beyond Lr = 1.0 can be estimated [238] using:

where

¼L = 0.0375( /1000) is the estimated length of the Lüders plateau (this relation is restricted to < 800 N/mm2);

is the upper yield strength (if this is unavailable, it is safe to use the lower yield strength or 0.2 % proof strength, ÖY);

and

or

where

N = 0.3(1 – ÖuY/Öu) is the lower bound strain hardening exponent estimated from the yield to tensile

strength ratio, ÖuY/Öu [238].

(10)

(11)

(10a)

(10b)

(10c)

¸r or Kr 1 0.14–(= Lr2) 0.3 0.7exp 0.65Lr

6i–( )+{ }

¸r or Kr 0=

¸r Lr 1=( ) or Kr Lr 1=( ) =

1E¼L

ÖYu

--------- 12 1 E¼L ÖY

u⁄+( )-----------------------------------+ +

0.5–

1 ÖYu–

ÖYu

ÖYu

¸r Lr 1>( ) ¸r Lr 1=( )LrN 1–( ) 2N⁄=

Kr(Lr 1)> Kr Lr 1=( )LrN 1 ) 2⁄ N–(=

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NO

TE

Lev

el 2

FA

D w

ith

typ

ical

cu

t-of

fs o

n t

he

Lr a

xis,

i.e.

Lrm

ax, f

or t

he

mat

eria

l bei

ng

asse

ssed

. How

ever

, th

ese

cut

offs

do

not

app

ly u

nde

r gl

obal

col

laps

e, a

s de

fin

ed in

A

nn

ex P

. For

Lrm

ax s

ee e

quat

ion

(9)

. a) L

evel

2A

FA

Db)

Lev

el 2

B F

AD

[der

ived

from

mat

eria

l str

ess/

stra

in d

ata,

e.g

. as

show

n in

Fig

ure

11c

)]

c) A

ppro

xim

ate

stre

ss/s

trai

n c

urv

e fo

r m

ater

ial r

esu

ltin

g in

Lev

el 2

B F

AD

as

show

n in

Fig

ure

11b

)

Fig

ure

11

— L

evel

2 F

AD

s

1.2

1.0

0.8

0.6

0.4

0.2 0.

00.

40.

81.

21.

62.

0

Acce

ptab

le

2.4

Cut-

off a

t 1.1

5 (ty

pica

l of

low

allo

y st

eels

and

wel

ds)

Cut-

off a

t 1.2

5 (ty

pica

l of

mild

ste

el a

nd a

uste

nitic

weld

s)

Cut-

off a

t 1.8

(typ

ical

of

aust

eniti

c par

ent s

teel

s)

L r

Krorr

Una

ccep

tabl

e

δ

1.4

1.2

1.0

0.8

0.6

0.4

0.2

L r0.

00.

20.

40.

60.

81.

0

Acce

ptab

le

Una

ccep

tabl

e

L rm

ax

Asse

ssm

ent

line

1.4

1.6

Krorr δ

Stre

ss

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7.3.2.2 Level 2B: material-specific curve

This method is suitable for parent material and weld metal of all types. It will generally give more accurate results than Level 2A but requires significantly more data. It requires a specific stress-strain curve; therefore it is not suitable for HAZs, for which Level 2A is appropriate. Stress-strain data are required at the appropriate temperature for parent material and/or weld metal. The lower yield or 0.2 % proof strength, tensile strength, and modulus of elasticity should be determined together with sufficient co-ordinate stress/strain points to define the curve. Particular attention should be paid to defining the shape of the stress/strain curve for strains below 1 %. It is recommended that the engineering stress/strain curve should be accurately defined at the following ratios of applied stress, Ö, to yield strength, ÖY:

Ö/ÖY = 0.7, 0.9, 0.98, 1.0, 1.02, 1.1, 1.2 and intervals of 0.1 up to Öu.

The equations describing the assessment line are the following:

a) for Lr k Lr max:

b) for Lr > Lr max:

where

¼ref is the true strain8) obtained from the uniaxial tensile stress-strain curve at a true stress, LrÖY. For most applications it is acceptable to use engineering stress-strain data, but it is important to concentrate calculation points around ÖY. A typical FAD and the associated stress-strain curve are shown in Figure 11b) and c) respectively.

7.3.3 Stress components

The assessments take account of the actual distributions of stress in the vicinity of the flaws, where they are known. The stresses required are the membrane and bending components of the primary and secondary stresses, i.e. Pm, Pb, Qm and Qb. They can be obtained by linearization as illustrated in Figure 1 and should be multiplied by the appropriate partial safety factor, if required (see K.2). If the resultant total stress intensity factor calculated is negative, the value used in assessments should be taken as zero.

In certain situations, thermal and residual stresses, which may be self-balancing throughout a structure, may act as primary stresses on an individual component (see Annex Q). This occurs when the flaw is small compared with the zone of influence of the thermal or residual stress, for example in the case of large elastic follow-up or when the spatial extent of the stress is large compared with the flaw size. In these circumstances, such thermal and residual stresses should be treated as primary stresses and be incorporated in the Æ¸r or Kr and Lr calculations.

7.3.4 Residual stresses

7.3.4.1 The residual stresses may in general be assumed to be uniform, as in 7.2.4 for Level 1, or non-uniform. Annex Q contains guidance on appropriate non-uniform residual stress distributions for specific weld geometries. The secondary stress components Qm and Qb may be obtained from non-uniform distributions using the linearization method illustrated in Figure 1.

The residual stress distributions in Annex Q are upper bound profiles to data on residual stresses in as-welded joints at room temperature. They may be used in assessments of welded joints at any temperature, but may not be modified to take account of stress relaxation caused by elevated temperature, prior overload or interaction with applied stresses.

(13a)

(13b)

8) True stress, Öt, and true strain ¼t, may be derived from engineering stress-strain data using Öt = (1 + ¼)Ö and ¼t = ln(1 + ¼).

¸r or Kr

E¼ref

LrÖY

-----------Lr

3ÖY

2E¼ref

--------------⎠⎞

0.5–+⎝

⎛=

¸r or Kr 0=

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7.3.4.2 Where the residual stresses are assumed to be uniform, the residual stress component, Qm, may be assumed to be equal to the lower of the following values:

or

where

Ö½Y is the appropriate material yield strength at the assessment temperature, except that for temperatures below ambient, the room temperature value of Ö½Y is used in equation (14a);

Ö½f is the appropriate flow strength (assumed to be the average of the yield and the tensile strengths) at the assessment temperature.9)

Note that, if secondary stresses are treated as primary in the above derivation of residual stresses, they should be treated as primary in the overall assessment.

7.3.4.3 Where the structure is subject to PWHT and/or pressure test, 7.2.4.2 to 7.2.4.4 and Annex O apply.

7.3.4.4 Note that, in cases where the reference stress, Öref, is high, the application of 7.3.4.2 may predict lower residual stresses than values determined by actual measurements or those assumed for PWHT conditions, where appropriate. In such cases, the assumed value of 7.3.4.2 may still be used, as it has been found to provide a conservative assessment.

7.3.5 Fracture ratio (Kr)

7.3.5.1 For Level 2 and 3, KI has the general form given in equation (2) (see 7.2.5), where Y(Ö) is given by:

where (YÖ)p and (YÖ)s represent contributions from primary and secondary stresses, respectively.

(17)10)

In the above equations, expressions for M, fw, Mm and Mb are given in Table M.2a) to Table M.4 and Table M.6 for different types of flaw in different configurations. Mkm and Mkb apply when the flaw or crack is in a region of local stress concentration and are given in Table M.5 and Table M.6. For ktm, ktb and km, reference should be made to 6.4 and Annex D.

Annex M contains specific solutions for various geometries, including flat plates, curved shells, welded joints and round bars. Alternatively, handbook solutions, numerical modelling or weight function methods may be used to derive stress intensity factors. The procedure adopted should be fully documented.

Kr is calculated from the following equation:

(14a)

(14b)

9) For the purposes of determining the residual stress, the flow stress is not restricted to a maximum of 1.2 times the yield strength, as it is elsewhere in this guide.

(15)

(16)

10) Equations (16) and (17) differ in appearance from those to be found, for example, in the publications of Newman and Raju and in PD 6493, which is now withdrawn from publication. For surface, embedded and corner flaws, Mm and Mb have been modified here by dividing by the complete integral, Í. By making this change it has been possible to write one set of equations that apply to all geometries.

(18)

Qm Ö′Y=

Qm 1.4Öref

Ö′f-------–⎝ ⎠

⎛ ⎞ Ö′Y=

YÖ( ) YÖ( )p YÖ( )s+=

YÖ( )p Mfw ktm[ MkmMmPm ktbMkbMb Pb km( 1 )–+{+ Pm }]=

YÖ( )s MmQm MbQb+=

Kr

KIKmat-------------=

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Where secondary stresses are present, a plasticity correction factor, Ô, is necessary to allow for interaction of the primary (YÖ)p and secondary (YÖ)s stress contributions, such that:

where

Ô is as defined in Annex R.

7.3.5.2 Note that, for surface breaking and embedded flaws, the calculated value of stress intensity factor KI will vary around the crack front. The maximum value of KI will frequently occur at the deepest point (for surface breaking flaws) or the point closest to the surface (for embedded flaws) where, in both cases, the parametric angle, Ú, equals Ï/2 (see Figure M.2 and Figure M.7). However, this is not always the case. The location of the point of maximum KI round a crack front can be influenced by a number of factors including the following:

— flaw aspect ratio (a/2c);— surface stress concentrations (e.g. weld toes);— thermal shock;— residual stress variation.

Therefore, in the case of surface breaking and embedded flaws, KI should be calculated at a number of points along the crack front.

Similarly, it is possible for Kmat to vary with depth either due to a lack of homogeneity in the material in which the flaw is located, or due to variation in constraint (see 7.4.1).

To ensure conservatism, the fracture assessment should use the maximum value of Kr that is calculated around the crack front.

7.3.6 Fracture ratio (¸r)

7.3.6.1 The applied CTOD, ¸I, is determined from the appropriate KI solution using the following equation:

where

X is a factor (generally of value between 1 and 2) influenced by crack tip and geometric constraint and the work hardening capability of the material.

Appropriate values of X may be determined from elastic analyses which model structural constraint. The value of X will also be affected by work hardening and this may be allowed for by appropriate elastic-plastic analyses. If values of X are not quantified by structural analyses, use X = 1.

When fracture assessments are performed using Kmat determined via Jmat, identical predictions will be achieved using ̧ mat results derived from the same tests when X is determined using the following equation:

7.3.6.2 For assessments without secondary stresses, the parameter ¸r is the ratio of the applied CTOD ¸I to the fracture toughness ̧ mat, including partial safety factors from Annex K. To facilitate plotting the FAD, the square root of ¸r is calculated using the following equation:

(19)

(20)

(21)

(22a)

Kr

KIKmat------------- Ô+=

¸I

KI2

XÖYE′------------------=

XJmat

ÖY¸mat 1 v2–( )----------------------------------------=

¸r ¸I ¸mat⁄=

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Where secondary stresses are present, an additional adjustment, Ô, is necessary to allow for plasticity interactions of the primary (YÖ)p and secondary (YÖ)s stress contributions. In such circumstances the following equation is applicable:

where

Ô is as defined in Annex R.

7.3.6.3 As explained in 7.3.5.2, for surface breaking and embedded flaws, KI varies around the crack front. The value of ¸I from equation (20) will similarly vary and its maximum will be determined by the factors listed in 7.3.5.2. Therefore, KI should be calculated at a number of points along the crack front in the same manner.

Similarly, it is possible for ¸mat to vary with depth either due to a lack of homogeneity in the material in which the flaw is located, or due to variation in constraint.

To ensure conservatism, the fracture assessment should use the maximum value of Æ¸r that is calculated around the crack front.

7.3.7 Estimate of Lr

For Level 2 and 3, the load ratio Lr is calculated from the following equation:

where

Öref is obtained from an appropriate reference stress solution as outlined in Annex P, with partial safety factors applied as appropriate.

7.4 Level 3 — Ductile tearing assessment

7.4.1 Main features

This is appropriate for ductile materials that exhibit stable tearing (e.g. austenitic steels and ferritic steels on the upper shelf). However, Level 3 assessments may also be applied to materials exhibiting a brittle failure mechanism, after pure ductile tearing, provided toughness data are obtained from specimens of adequate constraint. There are three assessment methods: Levels 3A, 3B and 3C.

Each method uses a different assessment line and applies a ductile tearing analysis. The analysis results in a plot of either a single assessment point or a locus of assessment points. If either the point or any part of the locus lies within the area bounded by the axes and the assessment line, the flaw is acceptable; if it does not, the flaw is not acceptable.

The Lr cut-off is as given in 7.3.1.

No inherent safety factor is included. Partial safety factors may be applied, as described in 7.3.1. Margins of safety can be assessed using reserve factors and probabilistic approaches as described in Annex K.

The FADs presented in 7.4.2 represent high structural constraint applications. When toughness is measured using standard procedures, it is possible to modify the FAD to account for lower constraint [3]. Alternatively, it is possible to maintain the use of a high constraint FAD and account for lower structural constraints using appropriate test geometries, as described in 7.1.5.9. These two approaches have been shown to be equivalent [4]. The effect of geometry on constraint is described further by Anderson and Dodds [5], O’Dowd et al [6] and Sumpter and Hancock [7].

For the ductile tearing analysis, the fracture toughness is required in the form of a ¸ or J resistance curve (see 7.4.7).

(22b)

(23)

¸r

¸I¸mat------------⎝ ⎠⎛ ⎞ Ô+=

Lr

ÖrefÖY---------=

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Strictly speaking, the shape of the FAD should be modified when performing a tearing instability analysis dependent on the extent of stable crack extension [8]. This effect is small, however, and it is conservative to ignore it.

The FADs have been validated for a wide range of metallic structures [9].

7.4.2 FADs

7.4.2.1 Level 3A: generalized FAD of Level 2A (not requiring stress-strain data)

The FAD is the same as that for Level 2A and as described by equations (10), (11), (12a), (12b) and (12c) (see 7.3.2.1). This FAD provides a reasonable underestimate of the flaw tolerance of a structure but the underestimate may be excessive in cases where the initial rate of hardening in the stress-strain curve is high (such as materials operating in the strain ageing régime). In those cases, Level 3B should be considered.

7.4.2.2 Level 3B: material-specific curve

The material-specific FAD is derived as for Level 2B (see 7.3.2.2). Stress-strain data for the material are needed, especially at strains below 1 %.

This diagram is suitable for all metals, regardless of their stress-strain behaviour.

7.4.2.3 Level 3C: J-integral

A FAD specific to a particular material and geometry is obtained by determining the J-integral using both elastic and elastic-plastic analyses of the flawed structure under the loads of interest. Determination of the respective values, Je and J, for a range of loads (i.e. a range of values of Lr) leads to the assessment line being described by the following equations:

Kr = (Je/J)½ for Lr k Lr max

Kr = 0 for Lr > Lr max

where

Je and J are values corresponding to the same load (same Lr) and Kr is plotted as a function of Lr.

All analyses to determine Je or J should be performed using validated computer codes. An accurate description of the true uniaxial stress-strain curve should be used in the analysis.

7.4.3 Stress components

The procedures for determining the stress components and related factors are identical to those for Level 2 described in 7.3.3.

7.4.4 Residual stress

Calculation of residual stress is identical to that in 7.3.4 for Level 2.

7.4.5 Applied stress intensity factor (KI)

The calculation of KI should follow the same procedure as outlined in 7.3.5.1 for Level 2. However, because of the increased accuracy required for this level, consideration should be given to the use of specific numerical solutions.

7.4.6 Applied CTOD (¸I)

The calculation of ¸I should follow the same procedure as given in 7.3.6.1 for Level 2. However, because of the increased accuracy required for this level, consideration should be given to the use of specific numerical solutions for the calculation of KI.

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7.4.7 Ductile tearing analysis

7.4.7.1 For a ductile tearing analysis, the fracture tearing resistance, Kmat, Jmat or ¸mat, is defined as a function of the amount of ductile crack extension or tearing, %a. R-curve testing should be carried out in accordance with BS 7448-4. The test method employed will produce a resistance curve of toughness as a function of %a, from either a single specimen or a set of specimens. The toughness may be determined as a series of values of one of two parameters, ¸mat or Kmat derived from J.

When the single specimen method is used, data should be obtained from at least three single specimen tests. A lower bound curve to these data should be adopted. Where a set of specimens is used, at least six specimens are needed and a lower bound curve should be used. In both cases, where there is considerable scatter in the data, increased confidence in the main curve can be obtained by increasing the number of tests.

The crack plane and direction of propagation in the test specimen should be consistent with those in the structure.

In the transition temperature régime for ferritic steels, specimens of full thickness may fail by cleavage fracture whereas specimens that are less than the full thickness may fail by shear fracture, and not give representative toughness values. Therefore, where there is a risk of brittle fracture, the test specimens should preferably be equal in thickness to the structure. For thick structures this is not always possible, either because of geometry effects or because of limitations of available testing machine capacity. In such instances, data should be obtained from the thickest practicable specimens and use of the results for application to the full section thickness should be fully justified after assessment for the possible effects of increasing section size. Guidance on these effects may be obtained from evidence in the literature and from data banks, e.g. [10].

Where there is no risk of brittle fracture, e.g. for non-ferritic materials, or for ferritic steels at temperatures well above the ductile/brittle transition, it is permissible to use data from test specimens that are thinner than the structure. In such cases the data should be restricted to a valid range up to a limiting value of the crack extension %ag. NOTE This is the same quantity as %amax given in BS 7448-4.

The parameters involved are the following:

a) %ag is the limit of tearing crack extension over which the analysis may be performed, and is defined as follows:

1) for specimens equal in thickness to the structure, the limit of the experimental data;

2) for specimens which are thinner than the structure, the limit for J-validity for the particular specimen geometry.

b) Kg or ¸g, is the value of Kmat or ¸mat at %ag.

c) Kmat or ¸mat may then be defined by an equation dependent on the crack extension, %a, between %ao and %ag, or as point to point values at discrete quantities of %a between the same limits. For ferritic steels, %ao may be taken as 0.2 mm.

7.4.7.2 The tearing analysis is made in accordance with the following procedure:

a) Define the size of known flaw, ao.

b) Define Kmat or ¸mat [see 7.4.7.1c)].

c) Define %ag [see 7.4.7.1a)]; read off Kg or ¸g.

d) If %ag < 1.0 mm, calculate Lr using 7.3.7 and Kr or ¸r using the following equation:

see equation (19)

KI is defined in 7.4.5.

¸I is defined in 7.4.6.

KI, ¸I and Öref are determined at a flaw length of a = ao + %ag, including partial safety factors on stress and flaw size if appropriate.

see equation (22b)

KrKI

Kg

------ Ô+=

¸r¸I

¸g

----- Ô+=

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e) If 1.0 mm < %ag < 5.0 mm, define intervals of flaw extension, %aj, as follows:

%a0 = 0

%a1 = 1.0 mm

%a2 = 2.0 mm, etc.

If %ag > 5.0 mm, define intervals of flaw extension, %aj, as follows:

%a0 = 0

%a1 = 1.0 mm

%a2 = 0.2%ag

%a3 = 0.4%ag, etc.

Calculate Lr using 7.3.7 and Kr or ¸r using equations (19) and (22a) or (22b) respectively.

KI, ¸I, Kmat, ¸mat and Öref are determined at flaw lengths a = a0, a0 + %a1, a0 + %a2, etc.

f) Plot all pairs of Lr, Kr or Lr, Æ¸r as co-ordinate points on the FAD to derive the locus of the assessment points (see Figure 12). If the locus lies completely outside the assessment line, the flaw is unacceptable. If it crosses the assessment line, some ductile tearing may occur. However, this is predicted to stabilize, and the flaw is deemed acceptable.

7.5 Further points

7.5.1 Comparison of the levels

Although conservatism generally reduces with increasing level of analysis, the assessment levels each provide a self-contained procedure and there are situations where this does not occur. In particular, when assessing flaws subject to high residual stresses using CTOD toughness as input to a Level 1 analysis, there may be little or no advantage in moving to a Level 2 analysis.

Figure 12 — Level 3A FAD with assessment locus for a known flaw

Kr

or

r

Lr

0.0 0.2 0.4 0.6 0.8 1.0

Acceptable

Unacceptable

Assessmentline

1.4 1.6

Locus of assessmentpoints

Lrmax

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

δ

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7.5.2 Non-unique solutions

Because of the mathematical form of solutions used in the procedures, and the interaction of the input data, it is possible that a flaw of one size is acceptable but that a flaw of smaller size is unacceptable (see Figure 13). Such conditions [11], are most likely to occur where stress distributions decrease through the section (for example, due to bending stresses or the stress raising effect of weld toes), or where increasing primary stresses result in increased relaxation of assumed residual stresses (see 7.3.4.2). Sensitivity analyses should be employed to check for possible non-unique solutions (see Annex K).

7.5.3 Fracture assessment for non-planar flaws, imperfect shape, locally thinned regions and fillet welds

7.5.3.1 Non-planar flaws

It is conservative to treat non-planar flaws as if they are planar, using 7.1.2 to determine the appropriate dimensions and the relevant solution in Annex M to determine the stress intensity factor. Otherwise, the limits of Table 1 are acceptable for non-planar flaws in steels that meet the following requirements:

— minimum specified yield strength <450 N/mm2;— average Charpy V-notch energy at the minimum service temperature U40 J for three tests;— minimum individual Charpy V-notch energy at the minimum service temperature of 28 J.

For other materials, the limits of Table 1 are acceptable provided the fracture toughness (KIc) of the material in which the flaw lies exceeds 1 250 N/mm3/2 (40 MPaÆm). For materials of lower toughness, these flaws should be assessed on the basis of their dimensions as planar flaws.

Table 1 — Limits for slag inclusions and porosity

Figure 13 — Example of non-unique solutions (schematic)

Slag inclusions Porosity

Percentage of projected area on

radiograph

%

Individual pore diameter

No limit on length; maximum height or width 3 mm

5 B/4 or 6 mm, whichever is smaller

1.0

0.8

0.6

0.4

0.2

Lr0.0 0.2 0.4 0.6 0.8 1.0

Acceptable

Unacceptable

Kr

or

r

Locus ofassessmentpoint

Assessmentline

1 2

3Increasingflaw size

Lrmax

δ

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7.5.3.2 Imperfect shape (including undercut)

Variations in weld profile from that specified, which could give a weld throat dimension below that needed to carry the maximum allowable design stresses, are unacceptable.

Undercut may prevent detection of other flaws by non-destructive testing. If it can be shown that no planar flaws exist other than undercut, then undercut is acceptable to a maximum depth of 1 mm or 10 % of the thickness, whichever is the lesser, under the following circumstances:

— the structure or component is made of steel;— the minimum specified yield strength is <450 N/mm2;— the average for three tests of the Charpy V-notch energy absorption at the minimum service temperature is U40 J;— the minimum individual value Charpy V-notch energy absorption at the minimum service temperature is U28 J.

All other cases of undercut should be assessed as planar flaws.

7.5.3.3 Locally-thinned regions (corrosion/erosion/pits)

It is conservative to assess local thinning, due for example to pitting corrosion or erosion, as a planar flaw of the same depth and shape. However, if the thinning does not create a sharp discontinuity, the likelihood of failure is likely to be controlled by plastic collapse considerations (see Annex G).

7.5.3.4 Fillet welds

It is not normally necessary to consider the effects of flaws contained within the weld metal of fillet welds in relation to fracture behaviour in normal structural applications, except for low service temperatures or impact loading, in tension. In such cases, it is possible, in principle, to calculate stress intensity factors for the particular geometry, and apply the general methods of the fracture assessment clauses, although there will be considerable uncertainties about the toughness, residual stresses and flaw dimensions.

Flaws in fillet welds, which may affect the static strength of the weld, do so through their effect on the cross-sectional area. The real stressing situation in fillet welds is complex, particularly under combined loading situations. It is recommended that the maximum shear stress should be calculated on the net minimum throat area, by combining the normal, parallel shear and perpendicular shear components as in the IIW method [12]. This maximum shear stress should not exceed 0.48 times the minimum tensile yield strength of the weld metal used.

There will be a significant effect of flaws in fillet welds on fatigue performance for potential failure in the weld throat (see Clause 8).

7.5.4 Fabrication test pieces

The desirability of having appropriate accurate toughness data cannot be emphasised too strongly. It is vital that toughness data be obtained from weld procedure test samples at the time of construction and that the tests be recorded. Without these, in-service flaw assessment of a high accuracy is not possible.

8 Assessment for fatigue

8.1 Assessment procedures

8.1.1 General

Procedures are given for assessing the acceptability of flaws found in service in relation to their effects on fatigue strength, both in welded or unwelded parts (see 8.4 to 8.6), or for the estimation of tolerable flaw sizes based on fitness for purpose (see 8.7). Planar and non-planar flaws are considered in a fatigue assessment. Fracture mechanics principles are used to describe the behaviour of planar flaws (see 8.1.2) whilst the assessment of non-planar flaws is based on experimental S-N data (see 8.1.3). Guidance is also given on the assessment of shape imperfections (see 8.1.4). The assessment methods are summarized in Table 2. Results should be reported in accordance with Annex H.

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Table 2 — Procedure for assessment of known flaws

Quite apart from weld flaws, the presence of a weld will reduce the fatigue strength to levels below the fatigue strength of unwelded parent material due to the geometric stress concentration it introduces. The reduction depends on the weld detail under consideration. Fatigue S-N curves for typical weld details are given in BS 7608. When considering the acceptance level for a weld flaw in a fatigue-loaded structure, it should be recognized that it will only be of significance if it causes a greater reduction in fatigue strength than that caused by the weld detail.

Step Relevant clause reference(s)

Relevant figure(s) and table(s)

1 Determine cyclic stress range from Pm, ktm, Pb, ktb, Q 6.4.1, 6.4.5, 8.2.1 Figure 1b), Figure 2 and Table 3

2 Resolve flaw normal to maximum principal stress 6.4.5 Figure 3

3 Define flaw dimensions 7.1.2 Figure 8

4 Assess uninspectable regions 7.1.2.3

5 Define limit to crack growth:

a) for unstable fracture

Level 1 7.2 Figure 10, Figure N.1 and Figure N.2

Level 2 7.3 Figure 11

Level 3 7.4 Figure 11 and Figure 12

b) other failure modes Clause 10

Planar flaws (general procedure)

6 Select values of A, m and %K0 8.2.3 Table 4 to Table 6

7 Determine %K for cyclic stress range and flaw height and shape

8.4.3, Annex M

8 Calculate crack growth increments %a and %c for one stress cycle

8.4.4

9 Repeat steps 7 and 8 for crack height a + %a and continue until the limit to crack growth (step 5) or the specified design life is reached. The flaw is acceptable if the limit to crack growth is not exceeded in the design life

8.4.4, 8.4.5, 8.4.6 (or Annex S)

Planar flaws (using quality categories)

10 Select quality category required 8.5.3.1 or 8.5.3.2 Figure 16 and Table 7

11 From flaw dimensions, determine initial flaw parameter Œi

8.6.2 Figure 17a) to Figure 21a)

12 Determine limit to crack growth (step 5) See also 8.6.2

13 Determine Si and Sm from Œi and Œm 8.6.2 Figure 17b) to Figure 21b)

14 Determine quality category for flaw under consideration from S = (Si

3 – Sm3)1/3. If this is equal to or better than

quality required, flaw is acceptable

8.6.2 Figure 16

Non-planar and shape imperfections

15 Confirm that flaw does not need to be treated as planar Clause 4, 8.2.2

16 Calculate km for misalignment 8.8.1, Annex D Table D.1 and Table D.2

17 Determine required quality category 8.5.3 Figure 16

18 Determine allowable flaw sizes or shape imperfections 8.7, 8.8 Table 8 to Table 11

19 Compare detected with allowable flaws or imperfections 8.7, 8.8

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8.1.2 Fracture mechanics analysis of planar flaws

Two methods are outlined for assessing planar flaws. A general procedure is given in 8.4, while a simplified procedure related to S-N curves is given in 8.5. Both methods are based on the fracture mechanics analysis of cracks under fatigue loading and estimate the fatigue life by integrating the crack growth law. The general procedure permits the use of accurate expressions for the cyclic stress intensity factor and specific fatigue crack growth data. The simplified procedure entails the use of the results of fracture mechanics calculations already performed and presented graphically.

In a fracture mechanics assessment it is usual to adopt conservative estimates of the various parameters required. Recommendations in the present clause are based on this philosophy. However, another approach is to use reliability methods to allow for uncertainties in the parameters.

The fracture mechanics approach assumes that a flaw may be idealized as a sharp tipped crack which propagates in accordance with the law relating the crack growth rate, da/dN, and the range of stress intensity factor, %K, for the material containing the flaw. The crack growth law is determined experimentally, and might be generated specifically for the ECA (see 4.1). However, crack growth laws are recommended in 8.2.3, and the use of appropriate published data is also permitted. The overall relationship between da/dN and %K is normally observed to be a sigmoidal curve in a log(da/dN) versus log(%K) plot. There is a central portion for which it may be reasonable to assume a linear relationship (i.e. the Paris law) or, for greater precision, to represent the data by two or more straight lines (see Figure 14). At low values of %K, the rate of growth falls off rapidly, such that, below a threshold stress intensity factor range, %K0, crack growth is insignificant. At high values of %K, when the maximum stress intensity factor in the cycle, Kmax, approaches the critical stress intensity factor for failure under static load, Kc, the rate of crack growth accelerates rapidly. A number of crack growth laws are available which describe the entire sigmoidal relationship [13] and [14]. However, it is often sufficient to assume that the central portion applies for all values of %K from %K0 up to failure. See, for example, Paris and Erdogan [15], Maddox [16], Griffiths and Richards [17], Richards and Lindley [18]. Assuming, for illustration purposes, the Paris law, the relevant equation is as follows:

where

For %K < %K0, da/dN is assumed to be zero.

The stress intensity factor range, %K, is a function of structural geometry, stress range and instantaneous crack size and is calculated from the following equation:

The overall life is calculated by substituting equation (26) into equation (25) and integrating the following equation:

The acceptability of a crack of initial size ai then depends on whether the calculated cyclic life, N, is greater or less than the required life.

For situations in which crack growth near the threshold is significant, a less conservative form of equation (25) based on the effective value of %K, %Keff, may be justified. In these circumstances, the relevant equation is the following:

da/dN = A(%Keff)m (28a)

where the default value of %Keff is %K.

da/dN = A(%K)m (25)

A and m are constants which depend on the material and the applied conditions, including environment and cyclic frequency.

(26)

(27)

%K Y %Ö( ) Ïa( )=

daYm Ïa( )m 2⁄----------------------------

ai

af

∫ A %Ö( )mN=

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At temperatures up to 100 °C, advantage can be taken of the proximity to the threshold, %K0, such that for %K < %K0/R:

%Keff = (%K – %K0)/(1 – R) (28b)

where

R is the stress ratio (or effective stress ratio for welded joints, [see 8.2.1.4]).

The values of the material constants m and A in equation (28a) will usually be different from those in equation (25). Substituting %Keff, equation (27) becomes:

8.1.3 Assessment of non-planar flaws

It is conservative to treat non-planar flaws as if they are planar and to assess them using fracture mechanics (see 8.1). However, in some cases (see 8.5) they can be assessed as standard weld details in terms of S-N curves obtained by statistical analysis of test data. The resulting acceptance limits, given in 8.7, are founded on fatigue test results obtained from specimens containing naturally and artificially flawed butt welds.

8.1.4 Assessment of shape imperfections

8.1.4.1 General

Shape imperfections increase the severity of existing regions of stress concentration in the welded joint, chiefly at the weld toe.

Guidance is given in 8.8 on the assessment of the two shape imperfections that are most significant for fatigue, namely misalignment and weld toe undercut.

8.1.4.2 Misalignment

Misalignment in an axially loaded joint introduces bending stresses, increasing the total stress range near the joint. It is found that fatigue test results from aligned and misaligned butt welded and cruciform joints are correlated in terms of the sum of the applied axial stress and the induced bending stress in the region of crack initiation. Thus, the bending stress due to misalignment is added to the applied stress when calculating the total stress in the fatigue assessment (see 6.4 and Annex D). This stress can be used in conjunction with the design S-N curve for the (aligned) joint to assess the effect of misalignment. Alternatively, it can be used in the assessment of a planar or non-planar flaw in a misaligned joint.

8.1.4.3 Undercut

The acceptance limits for weld toe undercut in 8.8.2 are based on fatigue test results from butt and fillet-welded joints containing natural undercut or undercut artificially manufactured for the purposes of the fatigue test programme, often by machining. Thus, as in the case of non-planar flaws, they relate directly to the design S-N curves.

8.1.4.4 Local thinning

It is conservative to assess local thinning, due for example to corrosion pitting or erosion, as a planar flaw of the same depth and shape (see 8.1.2). Alternatively, within the limits prescribed in 8.8.2, the acceptance levels for undercut in butt welds may be used.

8.2 Data required for assessment

8.2.1 Stress

8.2.1.1 Fluctuating stresses

Assessments use the nominal applied stress range acting on the section containing the flaw, resulting from the fluctuating components of load. Thus, residual stresses are not included, but fluctuating thermal

(29)

1 R–( )

Y Ïa( )i i%K0%Ö

-----------–------------------------------------------

⎩⎪⎨⎪⎧

⎭⎪⎬⎪⎫m

da A %Ö( )mN=

ai

af

∫

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stresses are. The stresses may be treated either directly or after resolution into the components described in 6.4.1.

8.2.1.2 Stress concentrations

Only stress concentrations due to gross structural discontinuities and misalignment are included when calculating the applied stress. The stress concentration effect of a local structural discontinuity, due for example to welded joint geometry, is only taken into account in a fracture mechanics assessment as part of the calculation of the stress intensity factor (see 8.4.3).

The peak stress due to misalignment depends only on the membrane component of applied stress. If a misaligned joint is within the stress concentration field due to a gross structural discontinuity, this membrane stress has to include the effect of the gross structural discontinuity.

8.2.1.3 Determination of stress ranges when resolved into components P and QNOTE See Figure 2.

The procedure for determining the stress ranges when resolved into components P and Q is as follows.

a) Identify the extreme maximum and minimum algebraic values of the primary plus secondary stresses [(P + Q)max and (P + Q)min], and their through-thickness distributions if possible, throughout the loading cycle under consideration. Applied tensile and compressive stresses are considered to be positive and negative respectively.

b) Calculate the peak stress, taking into account any gross structural discontinuities [see Figure 2b) and Figure 2d)].

c) At the two extremes in the loading cycle, determine ktm(Pm + Qm) + ktb(Pb + Qb). Separate the membrane and bending stress components Öm and Ö½b, if necessary, by linearizing the through-thickness stress distribution in a conservative way. In particular, linearization should not underestimate the surface stresses or, as far as possible, the stress acting in the region of the flaw being assessed [see Figure 1b)].

d) Calculate the maximum changes in Öm and Ö½b, to give stress ranges %Öm and %Ö½b.e) Calculate the additional stress range due to misalignment under the membrane stress range, %Öm[(km – 1)%Öm]. Add this to %Ö½b to give the total bending stress range, %Öb.

%Öb = %Ö½b + (km – 1)%Öm

If misalignment alone is being assessed, it is neglected at this stage (km = 1), so that %Öb = %Ö½b. The effect of misalignment is then assessed using 8.8.1.

f) Membrane or bending stress ranges may be used separately or together, depending on the type of assessment being performed (see Table 3).

Table 3 — Stress ranges used in fatigue assessments

Application Stress Comments

1. Assessment of embedded non-planar flaws (see 8.7) or undercut (see 8.8.2) using quality category S-N curves

(%Öm + %Öb) S-N curves do not distinguish between membrane and bending stresses

2. Assessment of misalignment (%Öm + %Öb) with km = 1 S-N curves do not distinguish between membrane and bending stresses

3. Assessment of planar flaws using quality category S-N curves (see 8.6)

(%Öm + %Öb) Used with Figure 17, Figure 19 or Figure 20, or, if %Öm k 0.25%Öb, Figure 18 or Figure 21

4. Assessment of planar flaws using fracture mechanics

%Öm and %Öb

(%Öm + %Öb)

Used separately if stress intensity factor (K) solution differentiates between membrane and bending stress (see Annex M), but sum used if K solution does not

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8.2.1.4 Effect of applied stress ratio

The use of the full stress range regardless of applied stress ratio (R) is the established approach to the fatigue design of welded joints (e.g. BS 7608). It is based on the fact that yield strength magnitude tensile residual stresses usually exist in weld regions, [19]. Therefore, it is recommended that as-welded and PWHT welds be dealt with similarly. If it is required to take account of stress ratio (e.g. when considering unwelded components or using 8.2.3.6), the effective value obtained by superimposing applied and residual stresses should be used.

8.2.1.5 Variable amplitude loading

Where the stress range varies during the life, knowledge of these variations is required. A stress spectrum should be converted to identifiable stress ranges using a cycle counting method (e.g. rainflow or reservoir). The stress spectrum should then be represented as a distribution of stress ranges versus numbers of occurrences. If this is further reduced to a histogram, any convenient number of stress intervals can be used, but, for conservatism, each block of cycles should be assumed to experience the maximum stress range in that block.

8.2.2 Flaw type and dimensions

The flaw type should be established from Clause 4 except that the following should be assessed as planar flaws:

a) surface breaking non-planar flaws;

b) weld toe undercut deeper than 1 mm;

c) embedded flaws that cannot be positively identified as non-planar;

d) any flaw, if it is necessary to assess fatigue crack growth from the flaw (e.g. to estimate inspection intervals).

The definitions of flaw dimensions are given in 7.1.2. It is not necessary to apply the flaw interaction criteria in 7.1.2.2 in a fatigue assessment. However, if there is any doubt that multiple flaws are separate, they should be assumed to be combined. Embedded planar flaws should be idealized as having an elliptical shape and surface planar flaws a semi-elliptical shape.

8.2.3 Fatigue crack growth law

8.2.3.1 General

The rate of fatigue crack growth assumed in this subclause is given by equation (25) for values of %K above a threshold value, %K0. For %K less than %K0, da/dN is assumed to be zero. Values of A and m depend on material and applied conditions.

Recommendations [20] are available in the form of simple laws [see Figure 14a)] and more precise two-stage relationships [Figure 14b)]. For the latter, both the mean and mean plus two standard deviations (mean + 2SD) of log(da/dN) versus log(%K) relationships for R < 0.5 and R U 0.5 are given. However, for conservatism (see 8.3) and to allow for the influence of residual stresses (see 8.2.1.4 ), the mean + 2SD laws for R U 0.5 should normally be used to assess welded components.

8.2.3.2 Specific fatigue crack growth and crack growth threshold data

Where specific fatigue crack growth and, if applicable, threshold data are available for the material and service conditions, they may be used in the general procedure for planar flaw assessment given in 8.4. A number of reviews are available of published fatigue crack growth data for a range of materials and environments [21], [22], [23], [24], [25], [26], [27], [28], [29] and [30], and of threshold data [24], [25], [30], [31], [32], [33] and [34]. Marine environments have received particular attention [26], [27] and [28], but there have been few studies of “sweet” (oxygen-free brine with CO2) and “sour” (oxygen-free brine with H2S) production conditions [230]. Special care is needed for the assessment of flaws in aggressive environments, particularly with respect to the effects of testing frequency and waveform on the rate of crack growth. Where any doubt exists concerning the relevance of available data for the particular assessment being performed, specific data should be obtained using the methods given in BS ISO 12108 (see also 10.3.3.4).

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8.2.3.3 Recommended fatigue crack growth laws for steels in air

Values of the constants A and m in equation (25), given in Table 4, are recommended for assessing low strength steels. They are applicable:

— to steels (ferritic, austenitic or duplex ferritic-austenitic) with yield or 0.2 % proof strengths k700 N/mm2;— when operating in air or other non-aggressive environments at temperatures up to 100 °C.

Unless justification is provided, the upper bound (mean + 2SD) values for R U 0.5 should be used for all assessments of flaws in welded joints. These laws are shown in Figure 15a) and Figure 15b).

a) Simple “Paris law” crack growth relationship b) Two stage crack growth relationship

Figure 14 — Schematic crack growth relationships

Kmax = Kc

Paris law:da/dN = A(K)m

K = K0

Log

(rat

e of

crac

k gr

owth

, da/

dN)

Log (stress intesity factor range, K)

Kmax = Kc

Stage B:da/dN = A2(K)m2

K = K0

Log

(rat

e of

crac

k gr

owth

, da/

dN)

Stage A:da/dN = A1(K)m1

Log (stress intensity factor range, K)

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Table 4 — Recommended fatigue crack growth laws for steels in aira

8.2.3.4 Recommended fatigue crack growth laws for steels, excluding austenitic and duplex stainless steels, in a marine environment

Values of the constants A and m in equation (25) given in Table 5 are recommended for assessing low strength steels. They are applicable:

— to steels (excluding austenitic and duplex stainless steels) with yield or 0.2 % proof strengths k600 N/mm2;— when operating in marine environments at temperatures up to 20 °C.

a) Operation in air or other non-aggressive environments b) Welded steels (excluding austenitics) in marine environments

Figure 15 — Recommended fatigue crack growth laws

R Stage A Stage B Stage A/Stage Btransition point %K

N/mm3/2Mean curve Mean + 2SD Mean curve Mean + 2SD

Ab m Ab m Ab m Ab m Mean curve

Mean + 2SD

<0.5 1.21 × 10–26 8.16 4.37 × 10–26 8.16 3.98 × 10–13 2.88 6.77 × 10–13 2.88 363 315

U0.5 4.80 × 10–18 5.10 2.10 × 10–17 5.10 5.86 × 10–13 2.88 1.29 × 10–12 2.88 196 144

a Mean + 2SD for RU0.5 values recommended for assessing welded joints. b For da/dN in mm/cycle and %K in N/mm3/2.

10 20 50 100 200 500 1 000 2 000

Rat

e of

crac

k gr

owth

, da/

dNm

m/c

ycle

Simplified law forwelded aluminiumalloys

Simplified law forwelded steels

2-stage law forwelded steels

10-7

10-8

10-6

10-5

10-4

10-3

10-2

Stress intensity factor range, K N/mm3/210 20 50 100 200 500 1 000 2 000

Rat

e of

crac

k gr

owth

, da/

dNm

m/c

ycle

With cathodic protection(–850 or –1 100 mV)

2-stage law forfree corrosion

Simplified law forfree corrosion

–1 100 mV cathodicprotection

–850 mV cathodicprotection

10-2

10-3

10-4

10-5

10-6

10-7

10-8

Stress intensity factor range, K N/mm3/2

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Table 5 — Recommended fatigue crack growth laws for steels in a marine environmenta

The values in Table 5 are based on data obtained either in artificial seawater or in 3 % NaCl solution at temperatures in the range 5 °C to 20 °C and cyclic frequencies in the range of 0.17 Hz to 0.5 Hz [20]. Use of the recommended crack growth laws for operating conditions outside these ranges requires justification. Note in particular that significantly higher crack growth rates have been observed in certain steel HAZ microstructures tested in seawater with cathodic protection under long duration loading cycles due to combined fatigue and stress corrosion [239].

8.2.3.5 Simplified fatigue crack growth laws for steels

For preliminary screening assessments, hand-calculations or assessments that can be compared directly with calculations based on fatigue design rules for welded steels (e.g. BS 7608), simple and conservative laws are recommended for steels with yield or 0.2 % proof strengths up to 600 N/mm2. These correspond to the upper bounds to the data used to derive the crack growth laws presented in 8.2.3.3 drawn with a slope of m = 3, consistent with the slope of the design S-N curves.

For steels, including austenitics, operating in air or other non-aggressive environments at temperatures up to 100 °C, the recommended values of the constants m and A in equation (25) are as follows:

m = 3

A = 5.21 × 10–13

for da/dN in mm/cycle and %K in N/mm3/2.

This law is included in Figure 15a).

For elevated temperatures, up to 600 °C, the following values are recommended:

m = 3

A = 5.21 × 10–13 (ERT/EET)3

where

ERT is the elastic modulus at room temperature (say 20 °C); and

EET is the elastic modulus at the elevated temperature.

For steels (excluding austenitic stainless steels) operating in marine environments at temperatures up to 20 °C, with or without cathodic protection the following values are recommended:

m = 3

A = 2.3 × 10-12

This law is included in Figure 15b).

R Stage A Stage B Stage A/Stage Btransition point %K

N/mm3/2Mean curve Mean + 2SD Mean curve Mean + 2SD

Ab m Ab m Ab m Ab m Mean curve

Mean + 2SD

Steel freely corroding in a marine environment

< 0.5 3.0 × 10–14 3.42 8.55 × 10–14 3.42 1.27 × 10–7 1.30 1.93 × 10–7 1.30 1336 993

U0.5 5.37 × 10–14 3.42 1.72 × 10–13 3.42 5.67 × 10–7 1.11 7.48 × 10–7 1.11 1098 748

Steel in a marine environment with cathodic protection at –850 mV (Ag/AgCl)

<0.5 1.21 × 10–26 8.16 4.37 × 10–26 8.16 5.16 × 10–12 2.67 1.32 × 10–11 2.67 462 434

U0.5 4.80 × 10–18 5.10 2.10 × 10–17 5.10 6.0 × 10–12 2.67 2.02 × 10–11 2.67 323 290

Steel in a marine environment with cathodic protection at –1 100 mV (Ag/AgCl)

<0.5 1.21 × 10–26 8.16 4.37 × 10–26 8.16 5.51 × 10–8 1.40 9.24 × 10–8 1.40 576 514

U0.5 4.80 × 10–18 5.10 2.10 × 10–17 5.10 5.25 × 10–8 1.40 1.02 × 10–7 1.40 517 415

a Mean + 2SD values for R U 0.5 recommended for assessing welded joints. b For da/dN in mm/cycle and %K in N/mm3/2.

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8.2.3.6 Recommended fatigue crack growth thresholds for steels

Threshold stress intensity factor, %K0, values are strongly dependent on environment and R [24], [25], [31], [32] and [33]. %K0 is found to increase with decrease in R. Recommended values for some conditions are given in Table 6. It is recommended that the lower bound value obtained at high R values in the relevant environment is adopted for all assessments of flaws in welded joints.

Table 6 — Recommended fatigue crack growth threshold, %K0, values for assessing welded joints

The values of %K0 in Table 6 for austenitic steels and unprotected steels operating in a marine environment are also applicable for assessing unwelded components. However, for unwelded steel components, account may be taken of R. Based on published data for steels (excluding austenitic) in air and with cathodic protection in marine environments at temperatures up to 20 °C, the following values of %K0 (in N/mm3/2) are recommended:

However, the value used should not exceed 63 N/mm3/2 (2 MPaÆm) for assessments of surface-breaking flaws less than 1 mm deep.

8.2.3.7 Fatigue crack growth and crack growth threshold in non-ferrous metals

Whenever possible, specific crack growth data for the material being considered should be used. For aluminium alloys, multi-branch crack growth relationships for a range of alloys are given by Jaccard [34]. However, for approximate assessments [22], [35], [37] and [38], the recommended crack growth constants of m = 3 and A = 5.21 × 10-13 for steels could be applied to another material with elastic modulus E by using m = 3 and the following value for A:

Similarly, the threshold stress intensity factor can be obtained from equation (30a–c) as follows:

8.2.4 Limits to crack propagation

In the fatigue assessment of planar flaws, an upper limit should be set to the extent of crack propagation that may be allowed without failure occurring during operation by any of the modes listed in Clause 5. The maximum total stress should be used to determine the maximum acceptable crack size as referred to in 5.2e).

Material Environment %K0

N/mm3/2

(MPaÆm)

Steels, including austenitic Air or other non-aggressive environments up to 100 °C 63 (2)

Steels, excluding austenitic Marine with cathodic protection, up to 20 °C 63 (2)

Steels, including austenitic Marine, unprotected 0 (0)

Aluminium alloys Air or other non-aggressive environments up to 20 °C 21 (0.7)

%K0 = 63 for R U 0.5 (30a)

%K0 = 170 – 214R for 0 k R < 0.5 (30b)

%K0 = 170 for R < 0 (30c)

(31)

(32)

A 5.21 10 13– Esteel

E-------------⎝ ⎠⎛ ⎞

3

×=

%K0 %K0,steelE

Esteel-------------⎝ ⎠⎛ ⎞=

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8.3 Probability of survival

The simplified procedure outlined in 8.5 and the procedures for non-planar flaws and undercut given in 8.7 and 8.8, respectively, are based on the results of large numbers of laboratory fatigue tests. These were analysed statistically assuming a log-normal distribution of fatigue life to obtain the lower 95 % confidence limit, corresponding to 97.7 % probability of survival.

Similarly, use of the recommended (mean + 2SD) fatigue crack growth rate laws and crack growth thresholds (see 8.2.3) corresponds to this probability of survival in fatigue life calculations. Other survival probabilities could be adopted from the information given in Table 4 and Table 5 or from the original data [20]. Alternatively, if the assessment is related to the quality categories (see 8.5), use can be made of the fact that differences in fatigue life between the categories are approximately equivalent to one standard deviation.

8.4 General procedure for fracture mechanics assessment of planar flaws

8.4.1 The crack propagation relationship and relevant value of %K0 should be determined as described in 8.2.3. For elliptical flaws, it can normally be assumed that the same relationship applies for crack growth in both the a and c directions.

8.4.2 The relevant stress range should be determined (see 8.2.1). For spectrum loading, unless the order of application of cycles is known, cycles, or blocks of cycles should be assumed to occur in the most damaging order. This is not always clear. It may be necessary to perform the calculations for various orders to determine the worst case.

8.4.3 For the actual or assumed flaw dimensions and position (see 8.2.2), the stress intensity factor range, %K, corresponding to the applied stress range should be estimated. Stress intensity factor solutions are provided in Annex M. Alternatively, published solutions (e.g. Tada et al [40], Murakami [41], Hobbacher [36], Oore and Burns [42]), numerical analysis methods or weight function techniques [43] may be used, but the basis of the method and the results should be documented.

For partial-thickness surface or embedded flaws, %K should be determined at the ends of both the minor and major axes of the elliptical idealization of the flaw (see 8.2.2).

8.4.4 The growth of the crack, %a, should be estimated for one cycle from the value of %K calculated in 8.4.3 using the crack growth relationship determined in 8.4.1. The dimension, a, should be increased by %a. Similarly, the growth, %c, at the ends of a part wall surface breaking or embedded flaw should be estimated for one cycle from the value of %K calculated for those flaw ends. The length of the flaw 2c should be increased by 2%c.

8.4.5 Taking the peak value of the tensile stress in the stress cycle, the stress intensity factor corresponding to the new size and shape should be estimated using 8.4.3. For fatigue loading, the solutions in 8.4.3 can still be assumed to be applicable for stresses exceeding yield.

8.4.6 The incremented crack dimension or stress intensity factor calculated in 8.4.5 should be compared with the limiting value with regard to other failure modes (see 8.2.4).

If acceptable, the next stress cycle should be considered and the procedure from 8.4.2 repeated. If the specified fatigue design life is reached and the limit to growth is not exceeded, the flaw should be regarded as acceptable.

For elliptical and semi-elliptical flaws, the crack front shape changes as a increases. This analysis should be continued until one of the following occurs:

a) For embedded flaws

When the crack breaks through to one surface, it should be treated as a surface crack of length 2c and, unless failure may be deemed to have occurred, for example by leakage caused by breakthrough, the analysis continued.

b) For surface flaws

When the crack breaks through to the far surface it should be treated as a through-thickness crack of length 2c and the process of incremental growth can then be continued unless failure may be deemed to have occurred, for example by leakage.

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8.4.7 The procedure of 8.4.3 to 8.4.6 entails a cycle-by-cycle calculation of crack growth. In some situations, this is impracticable and an approximate numerical integration method may be preferable. Guidance on two possible approaches is given in Annex S.

8.5 Basis of procedure for assessing flaws using quality categories

8.5.1 General

In this procedure, flaws are assessed on the basis of a comparison of the S-N curves that represent the actual and required fatigue strengths of the flawed weld. A grid of S-N curves is used, each curve representing a particular quality category. The flaw is acceptable if its actual quality category is the same as or higher than the required quality category.

The required quality category is determined for the service conditions to be experienced by the flawed weld. This can be fixed on the basis of the stress ranges and the total number of cycles of fatigue loading anticipated in the life of the component (see 8.5.3.1). Alternatively, the quality category can be selected by reference to adjacent design details. This should include the weld being assessed (e.g. the toe of a butt weld in which an embedded flaw is being assessed). The quality category S-N curve need be no higher than the S-N curve for the design detail (see 8.5.3.2).

The actual quality category for the flaw being assessed is determined from 8.6, 8.7 or 8.8, as appropriate.

8.5.2 Quality categories

8.5.2.1 Quality category S-N curves

The quality categories refer to particular fatigue design requirements or the actual fatigue strengths of flaws and are defined in terms of the ten S-N curves in Figure 16 labelled Q1 to Q10. These are described by the following equation:

%Ö 3N = constant (33)

Values of the constant are given in Table 7. It is convenient to characterize each curve in terms of the stress range, S, corresponding to a particular fatigue life and Table 7 includes values of S corresponding to a life of 2 × 106 cycles.

Table 7 — Details of quality category S-N curves

Qualitycategory

Constant in equationof curve %Ö3N = constant

(values for steel)

EquivalentBS 7608 design

class

Stress range, S, for 2 × 106 cycles

Steels Aluminium alloys

N/mm2 N/mm2

Q1 1.52 × 1012 D 91 30

Q2 1.04 × 1012 E 80 27

Q3 6.33 × 1011 F 68 23

Q4 4.31 × 1011 F2 60 20

Q5 2.50 × 1011 G 50 17

Q6 1.58 × 1011 W 43 14

Q7 1.00 × 1011 — 37 12

Q8 6.14 × 1010 — 32 10

Q9 3.89 × 1010 — 27 9

Q10 2.38 × 1010 — 23 8

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Fig

ure

16

— Q

ua

lity

ca

teg

ory

S-N

cu

rves

fo

r u

se i

n s

imp

lifi

ed f

ati

gu

e a

sses

smen

ts

104

105

106

107

210

8

Oper

atio

nal e

ndur

ance

N, c

ycle

s

300

200

100 90 80 70 60 50 40 30 20 15 10

Operational stress range, ∆ C and CMn steels, N/mm2

100

90 80 70 60 50 40 30 1020 15 8 7 6 5 4

Operational stress range, ∆ aluminium alloys, N/mm2

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

Eff

ectiv

e fa

tigue

lim

its fo

r as

sess

men

t of

non

-pla

nar

flaw

s in

C a

nd C

-Mn

stee

ls

a

nd a

lum

iniu

m a

lloys

in p

assi

ve e

nvir

onm

ents

.

F

or o

ther

cond

ition

s, co

ntin

ue li

near

ext

rapo

latio

n

σ

σ

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To facilitate comparisons of the fatigue lives of flaws with those of weld design details in steels (see 8.5.3.2), quality category S-N curves Q1 to Q6 are identical to the design S-N curves11) corresponding to 97.7 % survival limits, for classes D to W in British Standard fatigue design specifications BS 5400, PD 5500 and BS 7608 (see Table 7). Furthermore they are directly comparable with the design S-N curves in DD ENV 1993, Eurocode 3 for welded steels. The flaw acceptance levels given also ensure 97.7 % probability of survival when related to the quality category S-N curves. However, in the assessment of planar flaws, they can be adapted to consider other probabilities of survival (see 8.6.4), for example if a higher probability of survival is required for flaws than for design details.

8.5.2.2 Effect of material type

The majority of the data on which the procedures of 8.6 and 8.7 are based are from fatigue tests on welds containing flaws and from fatigue crack propagation studies on ferritic steels (some data for aluminium alloys were also analysed). It is, however, generally observed that, in dry air environments, fatigue cracks grow at closely similar rates in a wide range of steels, including austenitic stainless steels.

The curves in Figure 16 and the corresponding values of S in Table 7 for quality categories in aluminium alloy welds are identical to those for steel, but with the stress range divided by 3. Furthermore, they are directly comparable with some of the design S-N curves in BS 8118 and in DD ENV 1999, Eurocode 9 for welded aluminium.

For steels, the quality category S-N curves are identical in this guide to those for various weld details in BS 5400, PD 5500 and BS 7608. The quality category S-N curves for aluminium alloys do not necessarily coincide with the fatigue design S-N curves for welded aluminium alloys in BS 8118. This is particularly true for high design class details where the correlation between steel and aluminium based on their elastic moduli (see 8.2.3.7) does not always hold, and fatigue design stresses for aluminium exceed one-third of those for steel. Account should be taken of this when selecting the required quality category by reference to adjacent design details (see 8.5.3.2).

8.5.2.3 Stress relieved welds

In view of the effect of residual stresses in welded joints (see 8.2.1), the procedures for assessing flaws by reference to quality categories and the associated S-N curves are based on the use of the full stress range. This applies both to as-welded and to stress relieved weldments, regardless of R. However, thermal stress relief has the beneficial effect of removing hydrogen from embedded slag inclusions and account is taken of this in deriving the permissible lengths of inclusions (see 8.7.3).

8.5.3 Required quality category

8.5.3.1 Identifying the quality category by reference to service loading

The quality categories are identified as follows.

a) Constant amplitude loading

A quality category S-N curve lying above the point fixed by the required stress range and cyclic life.

b) Variable amplitude loading

Suppose the fatigue loading comprises k blocks with n1 cycles at an applied stress range %Ö1, n2 cycles at %Ö2, nj cycles at %Öj, etc. Using Miner’s rule, the equivalent constant amplitude stress range, S, corresponding to 2 × 106 cycles is then calculated using the following equation:

The required quality category is that corresponding to the stress range in Table 7 that is next above the calculated S value.

11) The equivalent curves in PD 5500 and BS 7608 use the notation Sr – N, while BS 5400 uses %Ör – N.

(34)

S

%Ö n3j j

j = 1

j = k

∑2 106×

------------------------

⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

1 3⁄

=

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8.5.3.2 Identifying the quality category by comparison with design details

One rationale for the acceptance of a flaw is that its fatigue life is no lower than that of an adjacent standard detail, which is known to have an adequate life. This provides a basis for selecting the quality category required for the flaw. For example, a flaw in a transverse butt weld would be acceptable if its quality category S-N curve coincided with the design S-N curve for the (flaw-free) butt weld for failure from the weld toe. To facilitate the selection of quality category by such means for steels, Q1 to Q6 S-N curves coincide, respectively, with those for standard weld detail classes D to W in other British Standards.

The presence of, say, a nominal Class D detail, does not, of course, imply that the fatigue design stresses and lives will necessarily be the maximum allowable for such a detail. In particular, this Class D detail may be adjacent to one of Class F, in which case the fatigue design would be fixed by the latter. In such a case, the quality category to which the nominal Class D weld should be inspected would be category Q3 and not Q1. Additional lower quality categories, Q7 to Q10, have been included to allow for those cases where fatigue loading is not the controlling criterion in determining the types of joint detail to be used in a weldment, but where fatigue cannot be ignored in an assessment of flaws. These do not relate to any specific joint classification and have been arbitrarily chosen with the stress following the same geometric progression as Q1 to Q6.

There will be cases where the designer does not have a good knowledge of the fatigue loadings for the weldment. Whilst this is, of course, undesirable from the design point of view, the quality categories can still be used. In this case, the required category can be matched to the lowest design detail in the same part of the weldment and subjected to the same stress ranges as the weld under consideration. This can be done in the knowledge that there will then be an equal probability of failure from the design detail as from any weld flaws assessed by these methods.

8.6 Assessment of planar flaws using quality categories

8.6.1 General

The procedure described in this subclause makes use of the results of fracture mechanics calculations already performed and presented graphically. The calculations were carried out using the general procedure given in 8.4 for selected geometries of welded joints containing planar flaws, subjected to either axial or bending loading, with the recommended Paris crack growth law for steels, i.e. m = 3 and A = 5.21 × 10–13, in equation (25). However, application of the graphs for other values of A is also described. The appropriate stress intensity factor solutions from Annex M were used and therefore the change in crack front shape as the crack propagated was automatically incorporated in the calculations.

8.6.2 Quality category for flaw

The actual quality categories for a range of planar flaws are determined using Figure 17 to Figure 21 depending on the type of flaw (surface or embedded), its location, the geometry of the weld detail containing the flaw and the loading. The first step is to convert actual flaw dimensions, a and 2c, to an effective initial flaw parameter, Œi, corresponding to a straight-fronted crack (a/2c = 0), using Figure 17a) to Figure 21a), as appropriate.

A tolerable value of the flaw parameter, Œmax, to which fatigue crack growth is permitted, should be specified. Again, this is an equivalent straight-fronted crack. It might refer to failure (see 8.2.4), or to some other criterion (e.g. detectability of the fatigue crack), in which case Œmax will be lower. It is obtained directly from Annex N (Figure N.1 and Figure N.2) if it results from a Level 1 fracture assessment, being the equivalent part thickness crack corresponding to a/2c = 0. However, if the tolerable flaw size does not refer to failure, Œmax may be specified directly as the tolerable height of straight-fronted flaw. Alternatively, if the tolerable flaw is specified in terms of an elliptical shape (e.g. minimum size of crack of a specified shape which is detectable in service), it may be specified as the straight-fronted flaw which is equivalent to the actual tolerable flaw in terms of the remaining fatigue life. Thus, Œmax is obtained in the same way as Œi using Figure 17a) to Figure 21a), as appropriate. The corresponding quality category is found from Figure 17b) to Figure 21b), as appropriate, as follows.

a) Entering the figures at Œmax on the ordinate axes and, interpolating as necessary, for the given thickness, B, a value of S should be read off, namely Sm.

b) Entering the figures at Œi on the ordinate axes and, interpolating as necessary, for the given thickness, B, a value of S should be read off, namely Si.

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Then

S = (Si3 x Sm

3) 1/3

If Œmax Œi, then S . Si. The actual quality category for the flaw in question is the next below S in Table 7. If this is the same as or higher than the required quality category, the flaw is acceptable.

8.6.3 Background to simplified assessment of planar flaws

The simplified procedure is based on the integration of the crack propagation law for a constant stress range from an initial flaw size either until the crack penetrates through the thickness or until some other failure mode intervenes. The integration was performed using equation (25) with A = 5.21 × 10–13 and m = 3, which results in 97.7 % probability of survival.

The method of calculation was similar to that recommended in S.2 using a block size in which the number of cycles was less than 0.5 % of total life. For each welded joint geometry and material thickness from 5 mm to 100 mm, calculations were performed for a range of flaw sizes and shapes ranging from straight-fronted (i.e. a/2c = 0) to semi-circular (a/2c = 0.5) surface flaws or circular (2a/2c = 1) buried flaws. The stress intensity factor solutions from Annex M were used. The crack front shape was automatically adjusted after each increment of crack growth. In the case of weld toe flaws, the assumption was made that, for surface crack growth, Mk was constant and corresponded to the value for a crack height a = 0.15 mm. Straight-fronted cracks were assumed to remain straight-fronted throughout their fatigue lives. In this way, flaw sizes corresponding to the quality category S-N curves were determined as a function of material thickness and flaw shape for each joint geometry. The results for straight-fronted flaws are presented in Figure 17b) to Figure 21b). Comparison of the results for straight-fronted and elliptical flaws for each quality category enabled the height of a straight-fronted crack that was equivalent in terms of fatigue strength to an elliptical flaw to be established. This is the effective initial flaw parameter Œi, which is plotted as a function of equivalent elliptical flaw shape and material thickness in Figure 17a) to Figure 21a). The use of these figures in conjunction with Figure 17b) to Figure 21b) enables any initial flaw shape to be considered.

The application of equation (35) is equivalent to the subtraction of the integral of equation (27), for crack growth from Œmax to B, from that for growth from Œi to B, thus deducting the fatigue life lost as a result of the intervention of an alternative failure mode.12)

12) It will be seen from Figure 20 that it is virtually impossible to detect the size of flaw which would be considered acceptable at the toes of fillet welds for design to Classes F or F2 (categories Q3 and Q4). This is not surprising. The bases for the S-N curves for the various joint classes are test data for nominally sound welds made under laboratory conditions [44]. It is almost certain that none of the test welds had flaws of normally detectable size at the weld toe. However, they will have had, in this position, the small slag intrusions observed by Signes et al [45]. Watkinson et al [46] showed these to vary in size between 0.15 mm and 0.4 mm and it is interesting to observe that this range lies between quality categories Q3 and Q5 for a material thickness of about 10 mm in Figure 20b)iii). These are the equivalent categories to the fillet-welded details Classes F and G.

The curves of Figure 20 also highlight the thickness effect [47] whereby, after an initial rise, the allowable initial flaw size tends to drop rapidly as thickness increases. The physical explanation for this is that the depth below the surface over which the stress concentration effect of a fillet weld is active is proportional to thickness. Thus, in thick material, the fatigue crack will be influenced over much more of its growth by this stress concentration. Almost all of the work surveyed by Gurney and Maddox [44] was on specimens 10 mm to 12 mm thick. Experimental work on thicker material [48], [49] indicates that the trend shown in Figure 20 is reasonable.

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a) Relation between actual flaw dimensions and effective flaw parameter

Figure 17 — Assessment of surface flaws in axially-loaded material for simplified procedure

1.0

0.5

0.2

0.3

0.4

0.1

0.05

0.04

0.03

0.02

0.01

0.005

0.001

0.002

0.003

0.004

0.01 0.02 0.03 0.05 0.1 0.3 1.00.50.2

Actual flaw size, a/B

Effe

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aw p

aram

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, a/B

2c

aB

0.4

Initial a/2c

0.1

0.2

0.050.01

-

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NOTE Values of S are for steel. For aluminium alloys, divide by 3.

b) Relation between effective flaw parameter, section thickness and quality category

Figure 17 — Assessment of surface flaws in axially-loaded material for simplified procedure (continued)

100

20

10

5.0

3.0

2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200

Section thickness, B mm

a max

ora i

, mm

S = 0

B

ai

(S, N/mm2)

Q10 (23)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)

Q5 (50)

Q4 (60)

Q3 (68)

Q2 (80)

50

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Figure 18 — Assessment of surface flaws in flat material (no weld toe or other stress raiser) in bending for simplified procedure

1.0

0.5

0.2

0.3

0.4

0.1

0.05

0.04

0.03

0.02

0.01

0.005

0.001

0.002

0.003

0.004

0.01 0.02 0.03 0.05 0.1 0.3 1.00.50.2


Effe

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aw p

aram

eter

, a/B

Initial a/2c0.002 50.0050.010

0.025

0.05

0.1

0.2

0.4

2c

aB

_

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Figure 18 — Assessment of surface flaws in flat material (no weld toe or other stress raiser) in bending for simplified procedure (continued)

100

20

10

5.0

3.0

2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


(S, N/mm2)

Q10 (62)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)

Q5 (50)

Q4 (60)

Q3 (68)

Q2 (80)

S = 0ai

50

40

B

a max

ora i, m

m_

_

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Figure 19 — Assessment of embedded flaws in axially-loaded joints for simplified procedure

1.0

0.5

0.2

0.3

0.4

0.1

0.05

0.04

0.03

0.02

0.01

0.005

0.001

0.002

0.003

0.004

0.01 0.02 0.03 0.05 0.1 0.3 1.00.50.2

Actual flaw size, 2a/B, or 2a/B' for non-central flaws

Effe

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aw p

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, 2a/

B, o

r 2a

/B'f

or n

on-c

entr

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aws

Initial a/2c0.010.050.1

0.2

0.4

p

B2a

2c

For non-central flaws, useeffective thickness, B' = 2a + 2p

__

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Figure 19 — Assessment of embedded flaws in axially-loaded joints for simplified procedure (continued)

100

20

10

5.0

3.0

2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


2am

axor

2a i

, mm

B

2ai

(S, N/mm2)

Q10 (23)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)

Q5 (50)

Q4 (60)

Q3 (68)

Q2 (80)

Q1 (91)

p

S = 0

50

40 _

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Figure 20 — Assessment of weld toe flaws in axially-loaded joints for simplified procedure

1.0

0.5

0.2

0.3

0.4

0.1

0.05

0.04

0.03

0.02

0.01

0.005

0.001

0.002

0.003

0.004

0.01 0.02 0.03 0.05 0.1 0.3 1.00.50.2


Effe

ctiv

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aw p

aram

eter

, a/B

2c

aB

0.1

Initial a/2c0.010.030.05

0.20.4

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i) L/B = 0.5

b) Relation between effective flaw parameter, welded joint geometry and quality category (continued)

Figure 20 — Assessment of weld toe flaws in axially-loaded joints for simplified procedure (continued)

100

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5.0

3.0

2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


a max

ora i

, mm

Q5 (50)

Q4 (60)

B

ai

(S, N/mm2)

Q10 (23)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)

S = 0

50

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ii) L/B = 0.75



a max

or

a i, m

m

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2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


S = 0

(S, N/mm2)

Q10 (23)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)Q5 (50)

B

ai

Q4 (60)

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iii) L/B = 1.0



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0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


am

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ai,

mm

S = 0

(S, N/mm2)

Q10 (23)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)

Q5 (50)

B

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Q4 (60)

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iv) L/B = 1.8



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2.0

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0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


a max

ora i

, mm

S = 0

(S, N/mm2)

Q10 (23)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)

B

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Q5 (50)

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v) L/B U 5.3



100

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3.0

2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


a max

ora i

, mm

S = 0

(S, N/mm2)

Q10 (23)

Q9 (27)

Q8 (32)

Q7 (37)

Q6 (43)

B

a

Q5 (50)

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Figure 21 — Assessment of weld toe flaws in joints loaded in bending for simplified procedure

1.0

0.5

0.2

0.3

0.4

0.1

0.05

0.04

0.03

0.02

0.01

0.005

0.001

0.002

0.003

0.004

0.01 0.02 0.03 0.05 0.1 0.3 1.00.50.2


2c

aB

Initial a/2c0.0030.01

0.03

0.10.2 to 0.5

Effe

ctiv

e fl

aw p

aram

eter

, a/B

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i) L/B < 1.0

b) Relation between effective flaw parameter, welded joint geometry and quality category)

Figure 21 — Assessment of weld toe flaws in joints loaded in bending for simplified procedure (continued)

100

20

10

5.0

3.0

2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


a max

ora i

, mm

S = 0

(S, N/mm2)

Q10 (23)

Q9 (27)

Q6 (43)

Q5 (50)Q4 (60)

B

a

Q3 (68)

Q8 (32)

Q7 (37)

50

40

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ii) L/B U 1.0


Figure 21 — Assessment of weld toe flaws in joints loaded in bending for simplified procedure (continued)

100

20

10

5.0

3.0

2.0

1.0

0.5

0.4

0.3

0.2

0.15 10 20 30 5040 100 200


S = 0

(S, N/mm2)

Q10 (23)

Q7 (37)

Q6 (43)

Q5 (50)

Q4 (60)

B

a

Q3 (68)

Q9 (27)

Q8 (32)

a max

ora i, m

m

50

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8.6.4 Quality categories for different crack growth rate assumptions

The curves in Figure 17 to Figure 21 have been calculated using m = 3 and A = 5.21 × 10–13. They are only applicable for m = 3 but, since fatigue life is directly proportional to A, they can be used for other values of A by establishing an effective quality category.

Expressed in terms of S, the stress range S1 corresponding to this effective quality category for a crack growth constant A1 is as follows:

Thus, for example, in order to assess a surface flaw in a steel structure in seawater using the values of m and A recommended in 8.2, the flaw is first assessed using 8.6.2 and a quality category determined. Suppose this is Q4, so that S = 60 N/mm2. Then,

giving an effective quality category of Q8. This effective quality category is compared with the required quality category to assess the acceptability of the flaw.

The same procedure could be used to consider a different probability of survival to that embodied in the curves in Figure 17 to Figure 21, that is 97.7 % (approximately two standard deviations from the mean), by defining the appropriate value of A. Alternatively, one step in the quality categories is approximately equivalent to one standard deviation of log(life) or log(crack growth rate). Thus, for example, for 99.9 % probability of survival (approximately three standard deviations from the mean) only flaws compatible with Q3 would be acceptable in order to achieve a required quality category of Q4.

8.7 Assessment of embedded non-planar flaws using quality categories

8.7.1 General

Only flaws that can be shown to be embedded and non-planar in accordance with 4b) should be considered for acceptability according to the criteria contained in this subclause. If any doubt exists, flaws should be considered as planar and treated in accordance with the procedures in 8.5 or 8.7.

As is the case with the S-N curves for design details, fatigue failure in this subclause corresponds to the attainment of through-thickness fatigue cracking. Therefore, if it is required to consider other failure criteria (e.g. fracture from a part-through-thickness crack), the flaw has to be assessed as planar.

Since it will usually be difficult to determine the distance between multiple slag inclusions occurring in the same cross section, they should be treated as a single planar flaw of height 2a equal to the total height of material containing inclusions. If, however, it can be demonstrated that the separation between such flaws is >1.25 times the height of the larger flaw, they may be assessed as separate slag inclusions, in accordance with Table 10 or Table 11, as appropriate.

The treatment can be applied to carbon and carbon manganese steels and to low alloy pressure vessel steels operating at temperatures up to 375 °C. It can also be applied to austenitic stainless steels up to 430 °C and to aluminium alloys up to 100 °C, in all cases for material thicknesses of at least 10 mm.

8.7.2 Required quality category

The quality category required should be determined in accordance with 8.5.2. However, if equation (34) is used, an effective fatigue limit may be assumed, such that all values of %Öj below those given in Table 8 can be ignored in deriving the equivalent constant amplitude stress range, S.

(36)

(37)

S1 S 5.21 10 13–×A1

-------------------------------⎝ ⎠⎛ ⎞

1 3⁄=

S1 60 5.21 10 13–×2.3 10 12–×

-------------------------------⎝ ⎠⎛ ⎞

1 3⁄37 N/mm2==

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Table 8 — Minimum values of %Öj for assessing non-planar flaws and shape imperfections

Since the stress ranges that may be ignored depend on the quality category required and this in turn depends on S, it may be necessary to iterate to arrive at the final quality category required.

8.7.3 Quality category for flaws

If the detected non-planar flaw is smaller than that given in Table 9 or Table 10 (whichever is appropriate) it should be regarded as acceptable. In assessing porosity, the area of radiograph to be considered should be the length of weld affected by porosity times the maximum width of the weld. Individual pores larger in diameter than B/4 or 6 mm, whichever is the lesser, should be repaired.

8.7.4 Background to the assessment of embedded non-planar flaws

The method for assessing embedded non-planar flaws outlined in this subclause is based on a very large volume of data, giving results of fatigue tests on butt welds in steel containing slag inclusions [50] and [51] and in steel and aluminium alloys containing porosity [44] and [52].

Table 9 and Table 10 give different limits for slag inclusions in as-welded and stress relieved welds. Larger inclusions are tolerable in stress relieved welds and it is believed that this is entirely due to the elimination of hydrogen from the voids as a result of PWHT. For weldments where an effective stress relief can be shown to have been achieved mechanically but where PWHT has not been performed, the limits of Table 9 should be applied.

The limits for porosity that could be permitted purely from a fatigue point of view are very large. The levels given in Table 9 and Table 10 are based on the density of porosity that might interfere with radiographic inspection and mask other flaws. Reasonable judgement has to be exercised in interpreting the condition given in 8.7.3 that the area of radiograph to be considered should be the length of weld affected by porosity times the maximum width of the weld. Clearly, if a small area of weld contains dense porosity with a much larger surrounding area containing sparse porosity, the area of radiograph to be assessed should be that incorporating the dense porosity. The tolerable porosity levels for an effective ultrasonic inspection may be considerably less, particularly for thinner sections.

Quality category

Minimum value of %Öj for inclusion in calculation of S

Steels Aluminium alloys

N/mm2 N/mm2

Q1 42 14

Q2 37 12

Q3 32 11

Q4 28 9

Q5 23 8

Q6 20 7

Q7 17 6

Q8 15 5

Q9 12 4

Q10 11 4

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Table 9 — Limits for non-planar flaws in as-welded steel and aluminium alloy weldments

Table 10 — Limits for non-planar flaws in steel weldments stress relieved by PWHT

8.8 Assessment of shape imperfections using quality categories

8.8.1 Assessment of misalignment

The presence of misalignment in a welded joint can reduce the fatigue life because it leads to an increase in stress at the joint when it is loaded, due to the introduction of bending stresses. Assessment of the effect of misalignment on fatigue life involves calculation of the bending stress (see Annex D). Bending stresses are not induced as a result of misalignment in continuous welds loaded longitudinally or in joints subjected only to bending. Thus, there is no limit to the allowable extent of misalignment in such cases, from a fitness for purpose viewpoint.

In the assessment of weldments in which the only imperfection is misalignment, the quality category required should be determined in accordance with 8.5.3, or, if equation (34) is used, 8.7.2. The misalignment is acceptable if the total stress range resulting from the sum of the applied stress, %Ö, and the bending stress due to misalignment, %Ös, does not exceed S in Table 8 for the required quality category. %Ö is the cyclic stress range from 8.2.1, calculated excluding the effect of misalignment.

As an alternative approach, the acceptance limits are summarized in Table 11 in terms of the magnification factor, km, where:

(see Annex D).

Quality category

Maximum length ofslag inclusiona

mm

Limits for porosity expressed as a percentage of area on radiograph

%

Q1 2.5 3

Q2 4 3

Q3 10 5

Q4 35 5

Q5 and lower No maximum 5

a Tungsten inclusions in aluminium alloy welds do not affect fatigue behaviour and need not be considered as flaws under this heading.

Quality category

Maximum length ofslag inclusion

mm

Limits for porosity expressed as a percentage of area on radiograph

%

Q1 19 3

Q2 58 3

Q3 and lower No maximum 5

(38)km 1%Ös

%Ö----------+=

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Table 11 — Acceptance levels for misalignment expressed in terms of stress magnification factor, km

8.8.2 sessment of undercut

The quality category required should be determined in accordance with 8.5.3 or, if equation (34) is used, 8.7.2.

Acceptance levels for weld toe undercut in butt and fillet welds stressed in the transverse direction for the various quality categories are given in Table 12. The maximum acceptable depth of undercut in any thickness of material is 1 mm. Undercut that exceeds these limits or undercut in material thicker than 40 mm should be assessed as a planar flaw using 8.4 or 8.6.

Table 12 — Acceptance levels for weld toe undercut in material thicknesses from 10 mm to 40 mm

Undercut in continuous welds stressed in the longitudinal direction will not affect the fatigue life of the joint. Hence, there is no limit to its size from the fitness for purpose viewpoint.

Quality category

Allowable km in accordance with BS class of (aligned) weld detail

D E F F2 W

Q1 1.0 — — — —

Q2 1.14 1.0 — — —

Q3 1.34 1.18 1.0 — —

Q4 1.52 1.34 1.13 1.0 —

Q5 1.84 1.61 1.37 1.21 —

Q6 2.16 1.88 1.61 1.42 1.0

Q7 2.48 2.18 1.85 1.63 1.15

Q8 2.92 2.56 2.18 1.92 1.35

Q9 3.40 2.99 2.53 2.23 1.58

Q10 4.00 3.52 2.98 2.63 1.85

NOTE 1 km is the magnification factor due to any type of misalignment, including combinations of more than one type.

NOTE 2 Assessment of Class W joints refers to possible fatigue cracking in the weld throat and is based on the stress range on the weld throat.

NOTE 3 km values are not given for cases in which the basic fatigue strength of the aligned joint is less than the quality category.

Quality category Depth of undercut/material thickness

Butt welds Fillet welds

Q1 0.025 —

Q2 0.05 —

Q3 0.075 0.05

Q4 0.10 0.075

Q5 0.10 0.10

Q6 to Q10 0.10 0.10

NOTE Maximum depth of undercut in any thickness is 1 mm.

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8.8.3 Background to assessment of shape imperfections

The method of assessing misalignment is based on the successful correlation of a large body of fatigue test data obtained from aligned and misaligned joints in terms of the local stress range equal to the sum of the applied stress and the bending stress due to misalignment. The fatigue data considered were obtained from transversely loaded butt and cruciform joints containing axial and/or angular misalignment and from vessels with misaligned seams, mainly in steel [53] and [54] but supported by limited data for aluminium alloys [55]. For convenience, the magnification factor, km, [see equation (38)] is used to enable the influence of misalignment to be expressed as a factor on fatigue design stresses.

The acceptance limits for undercut were derived from published fatigue data for transversely-loaded steel butt and fillet welds containing either natural or artificial undercut [56]. By comparing these data with data for similar joints without undercut, the depths of undercut corresponding to reductions in fatigue strength equivalent to steps in the grid of quality category S-N curves (Figure 16) were determined. Representation of undercut size in terms of depth to material thickness ratio reduced the scatter in the data. The limitations on material thickness and maximum undercut depth are necessary because of the restricted database available.

8.9 Estimation of tolerable sizes of flaws

The estimation of the size of hypothetical flaws which could be present in a welded joint and grow to an appropriate limiting size (see 8.2.4) by fatigue during the required lifetime provides a quantitative basis for specifying quality control levels. Similarly, rational acceptance levels could be based on knowledge of the type and extent of shape imperfections whose presence would not increase the stress at the weld sufficiently to reduce the fatigue life below that required. In determining a tolerable flaw level in a weld, the most severe combination of cyclic stress, flaw position and flaw orientation should be assumed. In the context of the cyclic stress to be assumed, the possible presence of misalignment may need to be considered and hence acceptance levels for both flaws and misalignment have to be established. The degree of conservatism that should be in-built into a general estimate of tolerable flaw size will result in a size below that which could be demonstrated to be acceptable as an individual flaw in accordance with 8.4 to 8.8.

For planar flaws, the step-by-step procedure of 8.4 may be used. However, in this case the calculation should be carried out in the reverse order, starting with the final crack size as determined in 8.2.4 and working backwards until all the design fatigue cycles have been accounted for. The crack size at this stage is the tolerable initial flaw size.

Tolerable flaw sizes and shape imperfection levels can also be determined using the procedure given in 8.5. The required quality category is established from 8.5 to 8.7, as appropriate, and the corresponding acceptance levels are determined from 8.6.2 (planar flaws), 8.7.1 (embedded non-planar flaws) or 8.8 (shape imperfections).

9 Assessment of flaws under creep conditions

9.1 General

This clause gives guidelines for assessing the significance of flaws in components that operate in the creep range. Procedures are presented for describing failure by net section rupture, crack growth or some combination of both processes. The influence of fatigue and the onset of brittle or ductile fracture in determining tolerable flaw size are also considered. The calculations make use of limit analysis methods, continuum damage mechanics and fracture mechanics concepts. Several levels of complexity are discussed depending on the criticality of the problem and the materials property data. Approximations are presented for dealing with cracked components when only stress rupture data are available. The information required for making creep assessments is described in Annex T. A worked example which takes the user through the procedure step by step, is provided in Annex U. This clause provides a method of assessing the significance of flaws when time dependent creep effects have to be taken into account. It is based on the R5 Procedure [57], but simplified where appropriate. It is intended for use when assessing components made in ferritic and austenitic steels since most information is available on these materials. The same principles are applicable to other metallic components, provided the user can obtain the relevant materials data.

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The assessment procedure may be applied at the design stage to components containing planar flaws, including cracking or lack of fusion. It may be applied, subject to the restrictions given below, to hypothetical flaws, in order to set inspection sensitivity or to check that a proposed component is tolerant to flaws. In the design assessment of components that may be allowed to enter service with permissible pre-existing flaws, it may be appropriate to allow for any creep crack incubation time in the determination of flaw tolerance.

The procedure may also be applied, subject to the same restrictions to flaws that are actually discovered during pre-service or in-service inspection. The objective is to decide whether the flaw is innocuous and will never affect the integrity of the plant, whether remedial action can be deferred until some time in the future or whether repairs are needed immediately. It would normally be inappropriate to allow for a creep crack incubation time when determining the tolerance of flaws discovered during in-service inspection.

The procedure is not applicable to flaws that are caused by stress corrosion and similar environmental phenomena.

Initially a creep exemption criterion is established to determine the lowest temperature at which creep effects need to be considered. Next the procedures for assessing damage formation and cracking in the presence of creep are presented.

Annex H gives requirements when reporting an assessment.

9.2 Creep exemption criteria

9.2.1 General

For plant operating at high temperatures, the first factor to be established is whether the component will operate in the creep régime. Guidance is given in 9.2.2 for determining whether the component can be considered as being exempt from the possibility of creep failure. The guidelines rely on the use of the creep results for the actual material of interest or minimum property data for the alloy type. In circumstances where only mean data are available, a suitable safety factor should be adopted. It is particularly important to ensure that due consideration is given to the creep properties of all constituent microstructures of a welded joint (see 9.2.3). If the component/temperature/service life combination fulfils the exemption criteria of 9.2.2, no further consideration need be given to creep.

If the exemption criteria are not met, the possibility of creep failure cannot be ruled out. Provided it can be shown by reference to previous experience that the material is not sensitive to creep crack propagation, flaws may be assessed using calculations based on creep rupture of the remaining net section. Existing design standards (e.g. BS EN 13480 or PD 5500) may assist in this respect.

For situations where creep crack propagation is possible, the remaining procedures in this clause should be employed. If cyclic loading is involved, consideration should be given to the possibility of creep fatigue interaction.

9.2.2 Temperature limits

For a component, or part of a component, creep may be discounted if one or other of the conditions in a) or b) below are met.

a) The maximum temperature during the total operating period is less than the temperature, Tc; Tc being specific to the material of construction and the period of operation.

For materials with uniaxial creep rupture ductilities >10 % in the time/temperature régime of interest, Tc is the temperature at which 0.2 % creep strain is accumulated at a stress level equal to the proof strength over the period of operation of the component (see Figure 22). The proof strength is equal to Ö0.2 at the service temperature for Level 1 assessments (i.e. when Lr is restricted to 1) and to (Ö0.2 + Öu )/2 at the service temperature for Level 2 and 3 assessments.

Examples of values for Tc are given in Table 13 for a range of steels, based on published lower bound data (e.g. see BS 6525-1, ASME Case N-47 [58] and Institution of Mechanical Engineers, the Creep of Steels Working Party [59]) and a lifetime of 200 000 h. It may be possible to demonstrate higher temperature limits when use of mean data can be justified or when a maximum stress of LrÖ0.2 cannot be exceeded (see Figure 22) for Lr < 1. For other steels and/or longer lifetimes, the value of Tc has to be derived from data obtained from creep tests on relevant material.

For materials with uniaxial creep rupture ductilities <10 % in the time/temperature régime of interest, Tc should be determined on the basis of the stress associated with a creep strain having a magnitude of 1/50th of the actual rupture ductility.

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Table 13 — Temperature below which creep is negligible in 200 000 h

Figure 22 — Determination of the temperature Tc at which 0.2 % creep strain is accumulated at a stress level equal to the proof strength

Type of steel Tc

Level 1 Levels 2 and 3

°C °C

Carbon manganese steel (see PD 6525-1) 330 310

Ferritic steels (see PD 6525-1 and reference [57]) ("CR"Mo!V, 1Cr"Mo, 2!Cr1Mo, 9Cr1Mo,12CrMoV(W)

420 400

Type 316 austenitic stainless steel (see reference [58]) 485 Note

NOTE Data inadequate for extrapolation to such high stress levels.

Stress to give 0.2 % creepstrain over the period ofoperation of the plant

t1 t2 t3

0.2 + u 2

0.2

Stre

ss,

t1> t2>t3

Temperature, T

Tc

Levels 2 and 3 Level 1

All levels ε0.2

Lr 0.2

σ

σ

σ

σ

σ

σ

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b) The total operating period/temperature history of the component satisfies the life-fraction rule based inequality:

where t(T) for materials with creep rupture ductilities >10 %, is the time required, at a constant temperature, T, to achieve an accumulated creep strain of 0.2 % at a stress level equal to the proof strength (see Figure 23), proof strength being defined in 9.2.2a).

The time, t(T), should be derived using relevant creep rupture properties for the material, and published data may be considered suitable for this purpose.

For ductilities <10 %, t(T) should be determined on the basis of creep strains with a magnitude 1/50th of the creep rupture ductility.

9.2.3 Constituent weldment microstructures

The consideration of both Tc and t(T) requires a knowledge of the creep rupture properties of the material in which the flaw to be assessed is located. Such information is rarely available for real HAZs but has been determined for simulated microstructures in certain circumstances [57]. It may be possible to base Tc and t(T) on the properties of the parent material, if it can be demonstrated that its creep resistance is no better than that of the HAZ.

9.3 General restrictions and information requirements

Where cracks are discovered in material that has suffered extensive creep damage, it is essential to use material data that relate to the material in its end-of-life condition. Creep rupture data and fracture toughness are particularly sensitive in this respect.

Cracks in welds need special treatment. The properties of the heat affected zone and the weld metal usually differ from those of the parent material and local residual stress may need to be taken into account. Particular care is needed in situations that involve reheat cracking.

Figure 23 — Determination of the time t(T) to achieve an accumulated creep strain of 0.2 % at a stress level equal to the proof strength

dtt T( )----------- 1<∫

Stre

ss to

giv

e 0.

2 %

cree

p st

rain

, ε 0

.2

Lr 0.2

Levels 2 and 3

Level 1 All levels

T1>T2>T3

T1

T2

T3

t(T)3 t(T)1,2 Time, t

0.2

0.2 + u

2

σ σ σ

σ

σ

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The document does not suggest the factor of safety that should be applied to predictions of crack growth and final failure. The decision about this has to be left to the discretion of the assessor. The value chosen will depend on the degree of pessimism introduced into the input data and on the results of sensitivity analyses. Further guidance will be found in Annex K, although the factors of safety given there may need to be adjusted to suit the circumstances of the case under investigation.

9.4 Crack beheaviour at high temperature

The behaviour of a crack in a component subject to steady loading at elevated temperature is shown schematically in Figure 24. Following the initial loading of the component, the crack may blunt and, in these circumstances, there will be an incubation period before a further short crack forms and propagation initiates. Where such blunting does not occur, crack propagation may be assumed to start immediately on loading. The crack grows, in all cases, by a fracture mechanics controlled mechanism.

Crack propagation can theoretically continue until structural failure takes place. Creep damage may build up ahead of the crack and creep rupture of the remaining material may occur. Alternatively, the net section may fail through a short-term phenomenon, such as plastic collapse or fast fracture. These conditions are shown diagrammatically in Figure 25.

In some circumstances, additional confidence may be obtained by demonstrating leak-before-break (Annex F).

Figure 24 — Schematic behaviour of crack subjected to steady loading at elevated temperature

Incubation Growth

Time, t

tix

Crac

k si

ze (a

, c)

a0 , c0

0

ix

t > tix

t = tix

t < tix

t = 0 Initial sharp crack

Crack blunting

Formation of a short crackwhen the crack openingreaches a critical value

Creep crack growth

δ

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Where new plant is under consideration, it may be possible to benefit from the incubation period, starting the crack growth calculations at the end of this period. The incubation time should be calculated by the methods described in T.1.8.

When a flaw has been discovered after the component has been in service, the conservative assumption should be made that the crack initiated earlier in life, unless there is strong evidence to the contrary.

The assessment of a flaw in an actual component is carried out in a series of well-defined steps as follows.

a) 9.5 describes the initial work that needs to be undertaken to decide whether the procedure is applicable. It shows what needs to be done to establish service loads and temperatures, to characterize the dimensions of the flaws and to define materials properties and stress levels.

b) The calculations needed to predict flaw growth are outlined in 9.5 and given in detail in T.2. These also describe the checks that are made to establish margins against creep rupture and fast fracture.

c) The materials data required for the assessment are discussed in T.1 and examples are quoted for the most commonly used materials. T.1 also provides a means of estimating materials properties when test data are not available.

It should be noted that only the basic procedures needed for flaw assessment have been included in this clause and these necessarily contain an element of conservatism. Background information can be obtained from Nuclear Electric [60], Ainsworth [3], Ainsworth [61], Ainsworth and Goodall [62], Nibkin et al [63], Nishida et al [64], Nishida and Webster [65] and Webster and Ainsworth [66].

It may be appropriate to use less conservative procedures where economic circumstances justify such a course of action. These, however, involve more complex analysis than that described here and a certain amount of materials testing will also usually be necessary. In these situations it is desirable to take specialist advice.

If td > tcd and td < tff then remedial action is not needed.

If td > tcd and td > tff then remedial action is needed.

Figure 25 — Schematic representation of crack propagation and failure conditions

a0 , c0

Crac

k si

ze (a

, c )

tff

Crack size forfast fracture

Required life is td

tcd

Time, t

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9.5 Assessment procedures

9.5.1 General

The procedure for creep assessment is implemented in a series of well-defined steps, which are shown in the flow chart in Figure 26. The flow chart and the detailed descriptions of the individual steps given in 9.5.2 to 9.5.11 relate to a flaw that has been discovered after a component has been in service for a period of time.

When considering a component before it enters service, containing either a postulated flaw or one discovered during inspection, some modifications are needed. These are noted in the text, as appropriate.

9.5.2 Initial investigations to establish cause of in-service cracking

Prior to performing calculations, an initial investigation should be carried out to identify the most likely cause of cracking. This may include a combination of non-destructive testing and visual and/or metallurgical examination, as appropriate. Also, if possible, a dimensional check should be carried out on the component to establish if there has been any significant distortion.

Often the cause of cracking will be obvious and, in these cases, only a relatively straightforward confirmatory metallurgical examination is required. When the reasons for the cracking cannot be established unequivocally in this way, a more detailed metallurgical study will be needed [67]. Specialist advice should be sought, as a discussion of all the relevant metallurgical factors is outside the scope of this guide.

Where there is evidence of stress corrosion and environmentally assisted cracking, for example multiple intergranular cracking without cavitation, the methods given in this clause should not be applied. However, it may not always be necessary to replace the component, provided it can be shown that the cracks will not propagate significantly. Advice is given in Clause 10.

Significant bulk creep damage away from the crack tip, particularly if accompanied by distortion of the component, is often an indication that there has been local overheating or some form of over-stressing and that the material is nearing the end of its safe working life. Any crack propagation and failure calculations that are carried out should take into account the properties of the material in its damaged state.

Leaving aside overheating, over-stressing and environmental effects, crack growth in high temperature plant is most likely to be associated with a pre-existing flaw which has not been detected by pre-service inspection or with a crack which has been initiated by some form of fatigue loading. In both situations, the guidance given in this document is applicable.

Pre-existing flaws often occur in welds and certain precautions, described in T.3, are necessary when applying the assessment procedure.

9.5.3 Define previous plant history and future operational requirements

The service loads and service temperatures for the component should be established for each operating condition. The previous history of the plant can usually be obtained from operating records. Where service loadings and temperatures depend on plant output, the previous history should be broken down into a series of blocks, during which the stress and temperature are sensibly constant.

Where sufficiently detailed records are not available, an initial assumption may be made that the total period of operation has been under the most onerous conditions. Where this leads to an unduly pessimistic prediction about remaining life, a more detailed investigation should be undertaken.

In addition to tabulating the total time at each of the steady operating conditions, any events likely to contribute to fatigue damage need also to be taken into account. Where vibration or thermal fluctuations occur during periods of nominally constant load operation, an estimate of the frequency and magnitude of the fluctuations is required.

Where transient thermal or mechanical loads occur at start up or shut down or with change in plant output, the number of load cycles and their magnitude should be established.

In defining the future life that is required from the plant, predictions have to be made about the way in which the plant is likely to be operated. Where transient load conditions are likely to occur, it is important to consider future operating régimes which may involve more frequent output changes than previously.

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a) Flow chart for overall creep assessment

Figure 26 — Procedure for creep assessment

Establish cause of cracking.Is there evidence of stress corrosion

cracking, environmentally assisted cracking or bulk creep damage? 9.5.2

Specialconsiderations

Define plant history and future operational requirements; steady service loads, temperatures; other loadings; life to date, t0; future life

required, td9.5.3

Is creep exemption criterion satisfied?

No further calculations needed

Y

Y

N

Establish stresses9.5.4

Characterize initial flaw dimensions a0, c0

9.5.5

Obtain material properties9.5.6/T.1

N

Is fatigue significant?9.5.7

Y

N

Perform defect assessment9.5.8/T.2

Perform sensitivity studies9.5.10/Annex K

Clause 8/T.4

Are margins satisfactory?Y Future service acceptable

for time, td

N

Can more precise calculations be performed?

Y

N

Can more precise materials data be obtained?

N

Can service parameters be defined more accurately?

Take remedial action9.5.11

N

Y

Y

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b) Flow chart of detailed flaw assessment procedure

Figure 26 — Procedure for creep assessment (continued)

Calculate margin against time-independent fracture for initial defect size

T.2

Margin acceptable?

Calculate rupture life, tcd for initial defect size

T.2.2

tcd > t0 + td ?

Calculate incubation time, tixT.1.8

Make modifications for non-steady state creep

N

Have steady state creep conditions been established?

N

YY

tix > t0?

Crack will grow in service,calculate crack size after growth in

time td or t0 – tix – td

tix > t0 + td ?

No crack growth in service

Have modifications for non-steady state creep been made?

Make modifications fornon-steady state creep

T.2.4.6

Have steady state creepconditions been established?

Y

N

Y

Recalculate rupture life, tcd , for final defect size

T.2.3

Recalculate margin against time-independent fracture for final defect size

T.2.2

Proceed to next step in flow chart Figure 26a)

9.5.10

Y

N

Have modifications for non-steady state creep been made?

N

N

Y

N

Y

N

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9.5.4 Establish stresses

The relevant stresses to be used in the assessment should be those which would exist in the neighbourhood of the flaw if the body were uncracked. They should not include stress intensification effects due to the flaw itself, as these are naturally taken into account by the assessment procedure.

At all stages in the assessment it is necessary to distinguish between those stresses arising from loads which contribute to plastic collapse and those stresses arising from loads which do not do so. In the terminology of the Nuclear Electric/Magnox Electric R5 [57] and R6 [60] procedures, these are defined as primary stress and secondary stress, respectively. The primary stresses are used in calculating the stress intensity factor KI

p and the secondary stresses plus the primary stresses are used in calculating the stress intensity factor KI

(p+s) as described in Annex A.

It is necessary, when following the procedures described in this clause, to separate the stresses into different categories. All stresses which are induced by internal pressure and external loads need to be categorized as primary despite the fact that, in many instances, PD 5500 and ASME Section III [2] would classify them as secondary. In the case of peak stresses, it is necessary to distinguish between those that are due to internal pressure and external load and those that are brought about by thermal loading or residual stresses in welds.

In carrying out the stress categorization, it is important to take into account any elastic follow up effect due to the spring action of adjacent parts of the structure. Unless it can be demonstrated to the contrary, long range thermal and residual stresses should be categorized as primary. Credit may be taken for reduction in short range thermal and residual stresses due to creep relaxation.

Therefore the stress intensity factor KIp is calculated using the stresses which are categorized as P. The

portion of the peak stresses which are induced by internal pressure and external loads are added to the P stresses if the crack tip is situated in the stress concentration region.

The stress intensity factor KI(p+s) is calculated using the sum of the P and the Q stresses. The effects of

stress concentrations arising from all causes are added if the crack tip is situated in the stress concentration region.

If the method of Annex M is used to determine stress intensity factors, it is necessary to linearize the stresses and obtain membrane and bending components. Two ways of doing this are shown in Figure 1. One involves linearizing across the flaw [Figure 1a)] and the other linearization over the cross-section of the component [Figure 1b)]. The former will produce the most realistic estimates of the stress intensity factor, but linearization will usually have to be repeated as the crack extends. The latter method will normally provide overestimates but has the advantage that linearization does not need to be repeated with crack growth.

It is necessary to emphasize that many of the difficulties inherent in stress categorization and in linearization can be avoided if the finite element method is used to calculate the stresses in the vicinity of the flaw. Stress intensity factors can be determined using a weight function method or by using a post processor program. Two calculations will generally be required. In the first, used to determine KI

p, the component is subjected only to those loads that could contribute to plastic collapse, including, where necessary, long range thermal and residual stresses. In the second, in order to determine KI

(p+s), the calculation is carried out for the total loading to which the structure is subjected, i.e. internal pressure and external loads plus both long range and localized thermal and residual stresses.

9.5.5 Characterize flaws

Flaws are generally of irregular shape. The maximum height and maximum length are used in this instance. The method of determining the size and circumscribing rectangle should be that given in 7.1.2.1, which also provides the method for characterizing and assessing the interaction of multiple flaws and crack orientations.

Where there is doubt about the accuracy of the size of flaw established by the inspection procedure, it may be necessary to assume a larger flaw in order to ensure a safe assessment. It is the intention of this clause that upper bound sizes for flaws should always be used.

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9.5.6 Establish material properties

The basic materials data required for the assessment comprise the following, which need to be in the relevant range of stresses and temperatures:

a) yield strength or 0.2 % proof strength;

b) ultimate tensile strength;

c) creep strain versus time curves or creep strain rate data;

d) stress to rupture versus time to rupture curves;

e) creep crack propagation rates;

f) fatigue crack propagation rates;

g) fracture toughness properties.

Allowance should be made for any deterioration that may occur during service, due to thermal ageing and environmental effects. Allowance should also be made for any reduction in fracture toughness and any increase in creep and fatigue crack propagation rates that may occur in material which has suffered significant bulk creep damage; that is in material in which Dc is greater than about 0.8. Further information may be found in Nishida et al [64], Nishida and Webster [65], Webster and Ainsworth [66].

It is preferable to use data which are derived from the material actually used in the component. Often these are not available and T.1 provides some information on the more commonly used materials. It is important to undertake a sensitivity analysis, when using the data of T.1, to allow for the possible presence of material with inferior properties in the component.

Worst case material data can be used in making a preliminary assessment; for example, upper bound data for crack growth rate and lower bound data for fracture toughness. However, care needs to be taken to guard against excessive pessimism; materials with a low creep ductility tend to have low creep strain rates but high crack growth rates and the reverse is true for materials with a high creep ductility. When the worst case assumption does not provide satisfactory margins, a more thorough investigation may be carried out.

9.5.7 Check on fatigue

In general, a creep-fatigue crack growth assessment requires stress analysis that allows for the effects of cyclic loading, and data that allow for the creep-fatigue interactions, leading to enhanced fatigue crack growth rates. However, in many cases these complexities can be avoided by performing simple checks to assess the severity of the fatigue loading.

The first check is to establish that the change in crack size due to fatigue crack growth is sufficiently small so as not to influence fracture mechanics calculations. Fatigue crack growth may be calculated using the methods in Clause 8 in terms of the stress intensity factor range, %K, where both P and Q stresses have to be included when appropriate. If the crack tip is located in a stress concentration region then the stresses arising from that stress concentration should also be incorporated into calculations of %K.

A second check is required to demonstrate that cyclic loading does not prevent steady state creep conditions applying during dwell periods at high temperature. This check is performed both for the overall structural response and for the stresses local to the crack tip.

For the small cracks usually assessed, the overall structural response can be determined from uncracked body elastically calculated stress changes due to cyclic loadings. These, when added to steady state creep stresses, should not lead to the yield strength being exceeded. The steady state creep stresses can often be represented by a reference stress based on limit analysis, as in T.2.3.1, and this simplifies the calculations. If this check is not satisfied, then a shakedown analysis is needed to establish the stresses acting during the dwell periods [57].

The check on stresses local to the crack tip can be made by demonstrating that the cyclic plastic zone size is small. Under cyclic loading, the allowable elastic stress range is 2ÖY in the absence of cyclic hardening or softening and the cyclic plastic zone size is:

rp = ¶¾(%K/2ÖY)2

where ¶¾ is typically 1/2; in plane stress and 1/6; in plane strain. The cyclic plastic zone size should be much less than the crack size or any other dimension characteristic of the structure, such as section thickness or remaining ligament ahead of the crack.

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If the above checks are satisfied, fatigue can be neglected, provided that the fatigue crack growth does not exceed 1/10th of the creep crack growth. This requires creep crack growth to be determined as described in T.2. However, at the start of an assessment, approximate calculations can be performed using the simplified materials data and simplified assessment approaches described in T.1. These approximate calculations can be refined when the results of a detailed assessment become available. If fatigue cannot be neglected, then the total crack growth should be calculated as the sum of the fatigue and creep contributions as described in T.4.

9.5.8 Perform flaw assessment

Flaw assessment should be performed using the following principal steps.

a) Assess fracture by the elastic-plastic methods of Clause 7, using initial flaw dimensions.

b) Determine the creep rupture life of the component, using initial flaw dimensions.

c) Determine the crack propagation rates and estimate the amount of crack growth at intervals during the future life of a component.

d) Check that steady creep conditions apply at the crack tip; if not, revise crack growth estimates.

e) Determine the crack dimensions at the end of each interval.

f) Assess fast fracture by the elastic-plastic methods of Clause 7, using crack dimensions at the end of each interval.

g) If the end of life margin against fast fracture is satisfactory, no remedial action is needed.

h) If the end of life margin against fast fracture is unsatisfactory, the intermediate calculations can be used to establish the time at which this margin ceases to be acceptable and to define when remedial action is necessary.

Calculations should be performed in accordance with T.2.

It is often possible to demonstrate that the component has adequate future life by making conservative assumptions about stress level, temperatures and material properties. Where such calculations do not give satisfactory margins, a more thorough investigation should be performed.

9.5.9 Special considerations for welds

The properties of the weld metal and heat affected zone usually differ considerably from those of the parent material in terms of creep strength, crack propagation rate and fracture toughness. It is important to identify the part of the weld in which the crack is situated and then use properties appropriate to that location.

Residual stresses in the vicinity of a weld can have a significant influence on crack propagation and failure and should be considered in the assessment.

Typical residual stress distributions in some commonly used types of weld are provided in Annex Q. For other configurations, in the absence of data to the contrary, it should be assumed that a tensile membrane stress of yield point magnitude is present.

Where it can be confirmed that the component has been subjected to PWHT that reduces the residual stresses to a negligible level, they can be ignored in the assessment. It may also be possible to take credit for a reduction in residual stress when a component has been in service for a sufficiently long period at a sufficiently high temperature.

Special care is needed in dealing with situations involving reheat cracking, particularly in welds which have not been stress relieved or which have been subjected to inadequate PWHT. Although such cracking is likely to occur during manufacture and will be identified during pre-service inspection, it sometimes occurs after the plant has been in service for a period of time. When assessing cracks of this type, which have been discovered in service, it is important to take full account of the residual stresses and also to make full allowance for the degraded material in the heat affected zone and weld metal.

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9.5.10 Sensitivity analysis

Assuming the final flaw size gives an acceptable end-of-life safety margin, a sensitivity analysis should now be conducted. The analysis given in Annex K, which describes the principles in the context of low temperature fracture, should be used. The sensitivity analysis should consider the effects of different assumptions (e.g. stress levels, material properties and flaw size).

For example, there may be uncertainties in the service loading conditions, the extrapolation of material data to service conditions, the nature, size and shape of the flaw and the calculation inputs. For flaws found in service, the sensitivity of the assessment to any assumption about whether the crack is already growing may be tested by performing assessments both with and without the incubation stage.

Confidence in an assessment is gained when it is possible to demonstrate that small changes in the input parameters do not lead to dramatic reductions in the end-of-life safety margin. Further confidence in the assessment is gained when the predictions at the end of an appropriate inspection period indicate that crack growth is not accelerating in such a way as to lead to imminent failure. Details of the sensitivity analysis should be reported with the assessment results.

9.5.11 Remedial action

If failure by excessive crack growth is indicated within the required service life, or if the sensitivity analysis gives unacceptable results, then remedial action is required, such as repair of the component or removal of the flaw.

Alternatively, a change in service parameters (load, temperature, desired service life) may be made and the assessment procedure repeated either to demonstrate acceptability or to estimate at what time repair will be necessary. Finally, it may be possible to obtain data on the material actually used in the component to remove pessimism in the assessment resulting from the use of bounding data.

The sensitivity analysis is particularly useful for indicating which material properties may significantly influence the assessment. For example, if remedial action is required because the desired service life exceeds the rupture life calculated, there is no point in generating creep crack growth data in an attempt to improve the assessment.

9.5.12 Worked example

Annex U gives a worked example of the use of the procedures described in 9.5.1 to 9.5.11.

10 Assessment for other modes of failure

10.1 Yielding due to overloading of remaining cross section

In practice, the need for critical assessment of this failure mode is most likely to arise in small structural sections. A detailed assessment for tensile loading can be carried out using the formulae given in Annex P to calculate reference stress Öref, and limiting the maximum value of Öref to the material flow strength. For shear loading the maximum shear stress should be calculated on the net area and this value limited to 0.48 times the material yield strength. Assessment for this failure mode is automatically performed when using the procedures given in Clause 7.

10.2 Leakage in pressure, liquid or vacuum containing equipment

In equipment for containing fluids under pressure or vacuum, no flaws should be regarded as acceptable which provide a path from interior to exterior of such equipment.

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10.3 Environmental effects

10.3.1 General

Whenever aggressive environments are present these have to be taken into account in any ECA. Since environmental effects are frequently highly specific, it is only possible to give general guidance. However, such effects can be extremely sensitive to small variations in material and operating conditions. Thus, any assessment or experimental measurements should take into account variations of heat treatment, chemical compositions, etc., within a given material specification. Equally, in-service conditions can change susceptibility to environmental effects due, for example, to temper embrittlement or sensitization of material and, for such cases, assessments or measurements have to be made for materials for which the appropriate in-service conditions have been simulated.

10.3.2 Corrosion and/or erosion

Avoidance of failure due to corrosion and/or erosion is mainly influenced by the suitable choice of materials for the particular environment. However, the following recommendations should be applied:

— for flaws not open at either surface, the recommendations of 10.1 should be followed with any corrosion/erosion allowance removed;— for crevices of any sort exposed at the surface to a corrosive or erosive environment, including cracks, lack of fusion or penetration, pores and pits, an estimate should be made of the maximum rate of crevice corrosion and time to grow to a size that is regarded as unacceptable.

A conservative treatment for assessing the significance of pitting can be obtained by taking the envelope containing a group of pits and treating this as a planar flaw of the same height and surface length, using the methods of assessment in Clauses 7, 8 and 9 as appropriate. A more detailed and less conservative approach to the treatment of locally thinned areas in pipes and pressure vessels is given in Annex G.

An assessment should take account of any possibility of failure by yielding, leakage, fracture or other modes of failure from the increased flaw size resulting from crevice corrosion. In the absence of sufficient information where crevice corrosion is relevant, no exposed crevices should be regarded as acceptable.

10.3.3 Environmentally assisted cracking

10.3.3.1 General

When assessing the integrity of a structure containing a flaw or flaws, it is necessary to consider whether subcritical crack growth can occur under service conditions by environmentally assisted cracking. The latter is a collective description for stress corrosion, corrosion fatigue, and combinations thereof. The interactions between these failure mechanisms can be complex. For example, apparent stress corrosion thresholds and growth rates can be profoundly influenced by minor cyclic forces or very slow monotonically increasing forces. The term corrosion does not necessarily imply gross surface oxidation or dissolution but may be, and often is, the very mild form of general corrosion associated with the formation of passive and largely protective oxide films. Because of its complexity, the assessment of flaws in structures where environmentally assisted crack extension might occur should only be undertaken by engineers with a high level of appropriate knowledge.

Because of the potential complexity of these interactions and because they are specific to particular material/environment combinations, only data obtained under conditions resembling as closely as possible the practical situation should be used in the assessment of environmentally assisted cracking. General guidance on testing procedures for determining stress corrosion threshold stress intensity factors, KISCC, and crack propagation rates is given in 10.3.3.2.2, 10.3.3.2.3 and 10.3.3.3.2. Where necessary, tests should be conducted on representative materials (parent metals, weld metals and/or heat affected zones, as appropriate). Attention should be given to the simulation of environmental chemistry and temperature and to the use of appropriate loading conditions, including any possible influence of dynamic forces that invariably act on real structures. The extent and duration of chemical transients, the high probability of environmental chemistry modification in cracks and crevices and a probability that hydrogen embrittlement processes can affect buried flaws should also be taken into account.

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The procedures presented here use a linear elastic fracture mechanics approach to describe crack growth due to environmentally assisted cracking. These techniques are specific to assessing subcritical crack growth, either from original welding flaws (which are idealized as sharp cracks) or from cracks formed in service by other mechanisms. It is important to appreciate that subcritical growth from existing flaws or cracks is only one part of an overall assessment of susceptibility to environmentally assisted cracking. It is strongly recommended that, in addition to the stability of existing cracks or flaws, an assessment should always be made of the risk of crack initiation from plain surfaces or blunt stress concentrations. This is required to ensure that the total stress (ktmPm + ktbPb + Q) is less than the appropriate threshold stress for environmentally assisted crack initiation. Alternatively, it may be possible to demonstrate that the environment is effectively benign.

10.3.3.2 Stress corrosion cracking

10.3.3.2.1 General

Stress corrosion cracking results from the conjoint action of an aggressive environment and a static applied or residual stress. It includes cracking due both to metal dissolution and to hydrogen embrittlement. An apparently benign environment may be corrosive locally due to concentrations of chemical species. Once initiated, stress corrosion cracks usually attain an approximately uniform velocity, provided that the driving force is maintained and that the local environment remains unchanged. This velocity depends on the particular metal and environment. Typical behaviour is shown in Figure 27 in terms of the crack growth rate, da/dt, plotted against the stress intensity factor, K.

a) b)

Figure 27 — Schematic diagrams of typical relationships between crack velocity and stress intensity factor during stress corrosion cracking

K =

KIS

CC

Stress intensity factor, K

K=

KIC

Stre

ss co

rros

ion

crac

k ve

loci

ty, d

a/dt

K =

KIS

CC

Stress intensity factor, K

K =

KIC

Stre

ss co

rros

ion

crac

k ve

loci

ty, d

a/dt

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In order to assess the significance of a known flaw, the applied stress intensity factor, KI, should be estimated following procedures laid down in 7.2.5 and 7.3.5. Residual stresses may be of overriding importance. This applied value should then be compared with the threshold stress intensity factor for susceptibility to stress corrosion cracking, KISCC. If KI is less than (1/fscc)KISCC, the flaw is acceptable. The factor of safety, fscc (fscc > 1.0), should be agreed between the parties and appropriately documented. Under these conditions, the data required are confined to values of KISCC which is defined as the stress intensity factor at which stress corrosion cracks will initiate and grow for the specified condition (metal, environment, exposure time, etc.) under predominantly plane strain conditions. Advice on the determination of KISCC is given in 10.3.3.2.2.

If the applied value of KI exceeds (1/fscc)KISCC, the possibility of stress corrosion crack growth should be recognized. In this case, careful consideration should be given to the advisability of taking appropriate remedial action, such as modification of the environment, elimination of the flaw(s) or stress relief. However, an assessment may be made to determine whether the flaws would grow to an unacceptable size within the design life of the structure or within the appropriate inspection interval. This assessment should be based on available stress corrosion crack velocity data, extrapolated, where necessary, to stress intensity factors below KISCC. Extrapolation is necessary if (1/fscc)KISCC < KI < KISCC. The method of extrapolation should be agreed between the parties. Advice on the determination of stress corrosion crack velocity is given in 10.3.3.2.3.

10.3.3.2.2 KISCC determination

When determining KISCC, it should be noted that stress corrosion processes can be very sensitive to small changes in test conditions. In particular, the environment itself is an important variable, and considerable care is necessary to ensure that the service conditions are adequately simulated. Detailed guidance on this topic is given in BS EN ISO 7539-1. It is normal to conduct KISCC tests under static load conditions. However, it should be noted that structures are seldom subjected to purely static loading and it is well known that the value of KISCC can be considerably reduced if a cyclic component, even of very small magnitude, is superimposed on the static loading. For these reasons, it may often be more appropriate to assess the significance of flaws in terms of the threshold range in stress intensity factor, %K0, for the growth of fatigue cracks under the environmental and loading conditions of interest.

Should it be decided that KISCC values are appropriate, these can be determined for the weldments of interest using the procedures described in BS EN ISO 7539-6. This document describes both crack initiation and crack arrest methods using fatigue pre-cracked, fracture mechanics type specimens tested under constant load or constant displacement.

10.3.3.2.3 Stress corrosion crack velocity determination

Data on the weldments of interest can be obtained by monitoring the crack velocity during stress corrosion testing of pre-cracked fracture mechanics specimens using the procedures given in BS EN ISO 7539-6 and the crack monitoring methods given in Nuclear Electric [57]. These techniques enable the stress corrosion crack velocity, da/dt, to be determined as a function of the stress intensity factor, K, as illustrated in Figure 27. One or more expressions of the following form:

da/dt = C1Kn(scc) (39)

can be fitted to the data, where C1 and n(scc) are constants.

Alternatively, in instances where a stress corrosion mechanism prevails in service, it may be possible to estimate crack velocity conservatively by appropriate inspection of the equipment at suitable intervals. This involves careful determination of the size of service flaws, either from samples taken from the equipment or in situ using suitable metallographic techniques. Clearly considerable skill and care are necessary in making such measurements.

If it is decided that it is necessary to assess the growth of flaws by a stress corrosion cracking mechanism, these expressions can be integrated numerically to predict the anticipated amount of growth during the design life of the structure or the relevant inspection period, whichever is appropriate. If, as a result of this growth, the flaws do not reach the maximum tolerable size for other failure mechanisms (brittle or ductile fracture, see Clause 7) the flaws are acceptable. If, on the other hand, the calculated crack size at the end of the design life or inspection interval exceeds the tolerable size for other failure mechanisms, the flaws are unacceptable.

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10.3.3.3 Corrosion fatigue

10.3.3.3.1 General

Fatigue crack growth in aggressive environments may be greater than in inert ones. A number of types of corrosion fatigue relationship have been observed in different metal/environment systems, as summarized in Figure 28. This complex behaviour means that, if reliable corrosion fatigue crack growth data are not available for the material, environment and loading conditions of interest, it is essential to determine such data as described in 10.3.3.3.2. Equations describing fatigue crack growth in aggressive environments are available in only a very limited number of instances. Crack growth parameters are given in 8.2.3.5 and 8.2.3.6 for the special case of crack growth in ferritic steels in a marine environment.

10.3.3.3.2 Determination of corrosion fatigue data

The determination of corrosion fatigue data with pre-cracked specimens is similar to that described in BS ISO 12108 for normal fatigue data, but it is vital to employ environmental conditions and a loading cycle and test frequency which are representative of those encountered in service. In addition to temperature and chemical composition (including degree of aeration), factors such as flow rate, crack length and shape, contact with dissimilar metals or electrochemical polarization, can influence growth rates and should be reproduced during testing. In the absence of national or international standards for corrosion fatigue testing, the following approach is recommended.

For the determination of threshold %K0 values, above which corrosion fatigue cracks will initiate and grow under the specified test conditions, similar pre-cracked specimens geometries and procedures can be used as in the fatigue threshold testing to BS ISO 12108, provided that the appropriate environmental conditions are adequately simulated.

Similar specimens and methods can also be used to determine the relationship between da/dN and %K for corrosion fatigue. When practical applications involve random loading cycles or well defined periodic changes in cyclic loading conditions, it is preferable to simulate service conditions, particularly with respect to stress ratio, cyclic frequency and cyclic wave form.

Environmental influences may be incorrectly estimated if the imposed cyclic frequencies are either too high and there is insufficient time for corrosion/diffusion processes to occur or too low, allowing, for example, for re-passivation. The rise time over which the application of stress occurs during the fatigue cycle can also strongly influence the corrosion fatigue process and appropriate cyclic wave forms should be employed in any testing. Sinusoidal, triangular, saw-tooth and square wave forms are often employed to simulate service loading conditions and, where appropriate, representative hold times should be imposed during the cycle.

a) b) c)

Figure 28 — Types of corrosion fatigue crack growth behaviour

Inert

Aggressive

log (∆K)

log

(da

/dN

)

Inert

Aggressive

log

(da/

dN)

log (∆K)

Inert

Aggressive

log

(da/

dN)

log (∆K)

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Having determined the appropriate crack growth relationship, the flaw should be assessed using the procedure outlined in Clause 8.

10.4 Instability (buckling)

10.4.1 General

In members loaded in compression, flaws should be assessed with regard to their possible effects on the buckling resistance of the component or structure. In this regard, flaws are divided into three broad categories:

a) those that reduce the effective local cross section, i.e. planar and non-planar flaws [see 4a) and 4b)];

b) laminations or lamellar flaws lying parallel to the component surfaces;

c) flaws involving failure to conform to the design form (misalignment, angular and out of plane distortion, etc.).

In any assessment of flaws with regard to instability, account should be taken of the possibility of crack growth by fatigue, corrosion-fatigue, stress corrosion cracking and creep. Guidance on these aspects is given elsewhere in this document. The instability assessment should be performed for the flaw size at the end of design life. Some structures operate in a post-buckled mode. Whilst many flaws may not affect the initial buckling strength, they may reduce the post-buckled deformation capacity. No specific guidance can be given here on this aspect, but it should be borne in mind for structures required to operate in such conditions.

10.4.2 Flaws that reduce the local cross-section

At any cross section, the total aggregate area and position of any flaws should be such that the factored buckling strength of the component is not reduced below the factored maximum applied loading effects. The effect on buckling of flaws that reduce the local cross section will depend on the loss of section area as well as on the position of the flaw both overall within the member and within the thickness of the member. An assessment of the significance of a flaw with regard to buckling should take these aspects into account. The buckling strength should be checked using the second moment of area for the affected cross section, calculated by omitting the flaw area projected onto a plane perpendicular to the compressive stress (Pm + Pb + Q) and taking into account any eccentricity in loading due to the presence of the flaw.

If a flaw occurs parallel to the surface under the weld attaching a stiffener to a plate loaded in compression, it will reduce the effective length over which the stiffener is attached to the plate. Such flaws may take the form of laminations or lamellar tears or of underbead cracks. If a flaw of this type is located, it should be assessed assuming that the stiffener is intermittently welded to the plate and that the flaw forms a “space” between two welds. Rules for determining the allowable “weld/space” ratio for intermittent fillet welds are given in BS 5400-3:1982, 14.6.3.1.

10.4.3 Flaws parallel to plate surfaces

The significance of planar flaws parallel to a plate surface and in the direction of compressive stress (laminations, lamellar tears, etc.) should be assessed by checking the buckling strength of each part of the material between the flaw and the component surface. This should be done by calculation as if the individual parts of the material are separate plates of the same area as the flaw using the distance between the flaw and the surface as an effective thickness. In this calculation it should be assumed that the plate is simply supported around its boundaries defined by the boundaries of the flaw.

10.4.4 Failure to conform to the design form

Flaws involving failure to conform to the design form at welds can have serious implications with regard to the buckling strength of members or components loaded in compression. Realistic limits for flaws of misalignment, out of plane, and angular distortion have been determined for pressure vessels subjected to external pressure and for structural members loaded in compression. These are given in the following standards: PD 5500:2003, 3.6 and PD 5500:2003, Annex M and BS 5400-6:1999, 4.2. Concerning pressure vessels, reference should also be made to the PD 5500 Enquiry Case No. 5500/33 dealing with the verification of shape of vessels subject to external pressure. If the structure under consideration is not built to one or other of these standards, care should be taken in applying the allowable tolerances from these standards, to ensure that these tolerances are consistent with the assumptions inherent in the actual design method used for the structure.

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Annex A (normative) Evaluation under combined direct and shear stresses or mode I, II and III loads

A.1 Introduction

This annex gives guidance on evaluation under combined direct and shear stresses, i.e. for mixed mode loading under tensile (mode I), in-plane shear (mode II) and out-of-plane shear (mode III) loadings. Such situations may arise, for example, in cracked joints subject to out-of-plane loading or in fillet welded joints.

The basis of any fracture mechanics assessment is a comparison of the material’s resistance to fracture with the severity of conditions at the crack tip under the applied loading. The presence of mixed mode loading will affect the severity of crack tip loading conditions [68]. The procedures outlined in this annex are only applicable to homogenous materials or at the interface between materials of similar elastic moduli. They can be applied to materials for which Kmat/ÖY U 6.3 ( units). For materials with Kmat/ÖY k 6.3 ( units) see Budden and Jones [69].

A.2 Outline of methodology

This annex recommends an assessment route based upon mode I material property values, Kmat and ÖY (7.1.4.2, 7.1.3), and mode I failure analysis diagrams. The mode II and III contributions are incorporated in the calculation of the applied stress intensity factors, Keff, and the plastic yield load [70] and [71].

The procedures are those outlined in Clause 7. For ductile tearing, it is recommended that the approach is restricted to a Level 2 analysis using initiation toughness (e.g. J0.2) unless it is known that tearing follows a clearly defined path.

The Lr based generalized Level 2A FAD [Figure 11a)] in particular is recommended for use in mixed mode loading assessments.

A.3 Determination of Kr

A.3.1 General

In 7.3.3, the applied stresses are resolved into primary and secondary type stresses. Under mode I loading the value of Kr is the sum of two components, Kr

p and Krs, corresponding to the primary and secondary

stress categories (see 7.3.3). Under combined mode I, II and III loading, this simple addition is no longer valid and the linear dependence of Kr on applied load is lost.

As stated in A.2, this annex recommends the use of mode I fracture toughness values. In most cases mode I tests will yield the lower bound value of toughness, though it is recommended that tests be performed to confirm this. However, it should be noted that, for high strength/low toughness materials (Kmat/ÖY < 6.3 units), this may not be the case and unconservative assessments may result (see Budden and Jones [69]).

For the case of ductile tearing, it is recommended that the lower of mode I and mode II R-curves be used in the assessment.

It should be noted that standard fracture toughness testing methods are not yet available other than for mode I. Hence mode II test results are open to interpretation. In mode II testing, resistance may occur due to friction at the crack surface. A small level of mode I loading or careful specimen design may be required to eliminate this.

A.3.2 Linear elastic stress intensity factor

Stress intensity factors may be determined using the general procedures given in Annex M. Mixed mode solutions for a limited range of geometries are available [72], [73] and [74]. In the absence of accurate compliance functions for mixed mode loading, mode I values can be used to provide pessimistic estimates.

When dealing with flaws subject to mixed mode loading, one can analyse the situation directly or project the flaw onto a reference plane, see 6.4.5. In the latter case, however, unless the principal planes are chosen, shear stresses should be taken into account in determining stress intensity factors.

In general, the stress intensity factors (SIF) for tensile (mode I), in-plane shear (mode II) and out-of-plane shear (mode III) loadings are required in the calculation of Kr.

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These are designated as follows:

In addition, it is necessary to determine the parameter Ô(a), which takes account of plasticity corrections required to allow for interaction between primary and secondary stresses (see 7.3.5.1 and 7.3.6.2). A method of determining Ô is given in A.3.5.

A.3.3 The effective stress intensity factor

Determine the three SIF components KI, KII and KIII as follows:

KI = KIp + KI

s

KII = KIIp + KII

s

KIII = KIIIp + KIII

s

Hence, calculate the effective SIF, Keff, as follows:

a) If Kmat/ÖY U 6.3 units;

Keff = {KI2 + KII

2 + KIII2/(1 – Ý)}" (A.1)

b) If Kmat/ÖY < 6.3 units;

refer to Budden and Jones [69].

A.3.4 Determination of Kr for a Level 2 analysis

(A.2)

where Ô is defined in A.3.5.

A.3.5 Procedure for determining Ô

The procedure of 7.3 is adopted with an effective SIF replacing the mode I SIF as follows.

a) For the elastically calculated secondary stresses for the crack size of interest, define Keffs from

equation (A.1), using only the secondary components, i.e. with KI, KII or KIII in equation (A.1) replaced by KI

s, KIIs and KIII

s, respectively.

b) For the primary stresses, define Keffp from equation (A.1), using only the primary components, i.e. with

KI, KII or KIII in equation (A.1) replaced by KIp, KII

p and KIIIp, respectively.

Determine the ratio (Keffp/Lr). For multiple loading systems in which the various primary loads increase

independently (non-proportionally), both Keffp and Lr depend on the ratios of the independent loads. Thus

the value of (Keffp/Lr) should be calculated for each load combination of interest when, for example,

assessing individual load factors (see Annex K).

c) Determine Keffs/(Keff

p/Lr) from the results of a) and b).

d) Determine Ô in accordance with the procedures of Annex R, replacing KI by Keff.

A.4 Determination of Lr and Sr

As in 7.1.8, the parameters Lr and Sr are a measure of how close the structure containing the flaw is to plastic yielding or collapse. The applied loads to be used in determining Lr or Sr are those that give rise to primary stresses. Lr is defined as the ratio of the loading condition being assessed to that required to cause plastic yielding of the structure (7.3.1, 7.3.7):

KIp(a) and KI

s(a) The linear elastic SIFs for the flaw size, a, for loads giving rise respectively to primary and secondary stress components which are normal to the plane of the crack.

KIIp(a) and KII

s(a) The linear elastic SIFs for the flaw size, a, for loads giving rise respectively to primary and secondary stress components which are in-plane shear.

KIIIp(a) and KIII

s(a) The linear elastic SIFs for the flaw size, a, for loads giving rise respectively to primary and secondary stress components which are out-of-plane shear (torsion).

mm

mm

Kr

Keff(a0)

Kmat--------------------- Ô(a0)+=

Lrtotal applied load giving rise to primary stresses

plastic yield load of the flawed structures--------------------------------------------------------------------------------------------------------------------------------------=

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Sr is defined similarly, but in terms of plastic collapse load, based on (ÖY + Öu)/2, rather than plastic yield load, based on ÖY.

The value of ÖY used in determining Lr is that obtained from uniaxial tensile data, as indicated in 7.3.7. The von Mises yield criterion is recommended for shear or multiaxial stress fields.

The limit load review of Miller [72] contains a number of solutions that involve multiaxial and shear loadings. In addition, Ewing [73] and [74] has presented a number of solutions for extended flaws under mixed mode I/mode II and mixed mode I/mode III loadings.

Annex B (informative) Assessment procedures for tubular joints in offshore structures

B.1 Overview

B.1.1 Introduction

This annex presents guidance on specific procedures for the assessment of flaws in offshore structures. The assessment of fatigue crack growth and fracture in tubular joints requires specialist guidance due to the complexity of the joint geometry and the applied loading and this annex provides supplementary guidance on the application of the procedures described in Clauses 7 and 8 to tubular joints. Its scope is limited to the assessment of known or assumed weld toe flaws, including fatigue cracks found in service, in brace or chord members of T, Y, K, or KT joints between circular section tubes under axial and/or bending loads. The annex describes one specific analysis route. Others are possible, in general accordance with this document.

B.1.2 General procedure

The basic components of the fatigue crack growth and fracture assessment procedure for tubular joints, which is outlined in Figure B.1, are as follows.

a) Global structural analysis — determination of components of brace nominal stress corresponding to fatigue and storm loads generated by wave loading.

b) Local joint stress analysis — determination of the hot-spot stress concentration factors and the degree of bending, Ë, i.e. the proportion of the bending to total stress through the wall thickness, relevant to the crack location.

c) Determination of stress spectrum — generation of the hot-spot stress range histogram for the joint (see 8.2.1.5).

d) Fatigue crack growth analysis — integration of the appropriate fatigue crack growth law (see 8.1.2) to determine the remaining fatigue life.

e) Fracture analysis — determination of Kr and Lr after each increment of crack growth, use of the Level 2 FADs.

B.2 Stress analysis

B.2.1 General

Results of structural analysis of the overall frame under the chosen critical loading conditions should be available to give the forces and moments in the members in the region being assessed. These should be provided as axial force, in-plane and out-of-plane bending moments. Both maximum load and fatigue load ranges are required.

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Figure B.1 — Assessment methodology for fatigue crack growth in tubular joints

Cracklocation

Jointgeometry

Fatiguewave

spectra

Globalgeometry

Local jointstress

analysis

Stressconcn. factor and degreeof bending

Globalstructuralanalysis

Nominalstresses dueto each wave

Waveexceedance

Total hot spot stress and

overalldegree of

Fatigueload history

Throughthickness stressrange and no.of occurrences

AppropriateY-calibration

Crack growthparameters

A, m

Calculate SIF for each increment

of growth, ∆K

Initial and finalcrack size

ai, af

Integrate crackgrowth law

aida=A(∆K)mN

Remainingfatigue life

Assessment step

Input and output forkey step of assessment

∫ af

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B.2.2 Global structural analysis

A global finite element analysis of the complete structure is performed to determine the stress spectrum corresponding to the wave loading at the flaw location. The wave exceedance curve is used to construct a histogram of wave height versus the number of occurrences. The stress range due to each wave height is then determined in the global structural analysis. The latter gives the nominal brace loading due to the action of the fatigue and storm wave loading. From this the axial, in-plane bending and out-of-plane bending brace stress ranges (%ÖAx, %ÖIPB and %ÖOPB respectively) are computed for each wave height. Further details are given in Health and Safety Executive [75], American Petroleum Institute [76], Det Norske Veritas [77], Graff [78] and Barltrop and Adams [79].

B.2.3 Local joint stress analysis

The local joint stress ranges are generated by the nominal brace axial and bending loads, which are reacted by the chord. High secondary bending stresses are developed due to the local deformation of the tubular walls. This leads to high stress concentrations and through-thickness stress gradients at the brace/chord intersection. The variation of stress range around the joint periphery needs to be determined and stress range histograms are evaluated for a minimum of eight equally spaced positions, including the saddle and crown locations.

Each hot-spot stress range component is determined from the nominal stress range, %Önom, and the appropriate stress concentration factor [75] and [80], i.e.

%ÖHS = %Önomkt,HS (B.1)

The hot-spot stress range component is sub-divided into axial and bending components, thus:

%Öm = (1 – Ë)%ÖHS (B.2)

%Öb = Ë%ÖHS (B.3)

The local stress field can be based on published parametric equations for kt,HS and Ë [81]. Alternatively, more accurate predictions can be obtained by performing a finite element analysis.

The nominal stresses obtained from the global analysis and the stress field parameters at the crack location, kt,HS and Ë, obtained from the local joint stress analysis are used to calculate the total hot-spot stress and total degree of bending for each wave:

%ÖHS.Tot = %ÖHS.Ax + %ÖHS.IPB + %ÖHS.OPB

= %Ön.Axkt.Ax + %Ön.IPBkt.IPB + %Ön.OPBkt.OPB (B.4)

The degree of bending for the total hot-spot stress range is determined from the following expression:

B.3 Stress intensity factor solutions

B.3.1 Evaluation methods

The principal methods used to determine stress intensity factors for tubular joints are the following:

a) numerical (i.e. finite element or boundary element) analysis of tubular joints;

b) standard and analytical (e.g. weight function) solutions for semi-elliptical cracks in plates.

B.3.2 Numerical solutions for tubular joints

Numerical methods provide the most realistic predictions of stress intensity factors. However, the determination of stress intensity factors for cracks in tubular joints by numerical methods requires complex modelling and stress analysis and consequently only a limited number of solutions are available [82], [83], [84] and [85].

(B.5)ËTot

ËAx%ÖHS.Ax ËIPB+ %ÖHS.IPB ËOPB+ %ÖHS.OPB

%ÖHS.Tot------------------------------------------------------------------------------------------------------=

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B.3.3 Plate solutions

The application of plate solutions to the assessment of tubular joints provides stress intensity factors for a very wide range of geometries. Stress intensity factors for the deepest and the surface points can be determined using the Newman and Raju [164], [165] solution in conjunction with magnification factors determined either by 2-D finite element analysis (see M.5) or by the weight function solution for surface cracks. The use of the 2-D magnification factor solutions tends to be conservative, particularly for the evaluation of the stress intensity factor at the surface point. The weight function solutions may be more appropriate for the surface point, though validation of these solutions is limited.

More realistic estimates of the stress intensity factor in a tubular joint can sometimes be obtained from plate solutions, if allowance is made for load shedding resulting from the reduction of member stiffness with crack growth. The moment release model proposed by Aaghaakouchak et al [87] can be used in conjunction with plate solutions to reduce the excessive conservatism inherent in the application of stress intensity factor solutions of plate joints to tubular joints. The moment release model assumes that load shedding reduces the net moment acting across the cross section of a cracked tubular member, and hence also reduces the stress intensity factor. The linear moment release model involves the reduction of the bending stress components using the following simple expression:

Öbc = Öb(1 – a/b) (B.6)

where

Öbc and Öb are the bending hot-spot stress components for the cracked and uncracked joint, respectively. (Limited studies have indicated that application of this equation may lead to an underestimate of K up to 30 % [87] and [89].)

B.4 Fatigue assessment

B.4.1 Stress range

The variation of damage at the joint periphery should be determined and the stress range histogram corresponding to the maximum damage in the region corresponding to the crack location selected. The stress range histogram is then applied on a block by block basis, as described in Annex S.

B.4.2 Stress intensity factor range

The stress intensity factor range is calculated from the following general expression:

%K = %Km + %Kb

If the plate stress intensity factor solution is used, equation (B.7) can be expressed as follows:

B.4.3 Initial flaw dimensions

Careful consideration should be given to the estimation of the initial flaw size – it is important that this is not underestimated. The methods given in this guide can be used to assess the integrity of a structure containing an initial hypothetical flaw. The size of this assumed flaw should be the estimated maximum size, considering the reliability of the chosen inspection method(s) and of the welding procedure applied.

B.4.4 Limit to fatigue crack propagation

For cracking in the chord, failure is generally considered to occur when the crack penetrates the wall thickness, though the possibility of brittle fracture or plastic collapse should be taken into consideration for cracks in the weld region. This may be significant to greater depths for brace cracks than for chord cracks, due to the possibility of crack propagation in the vicinity of the weld fusion line.

(B.7)

(B.8)

Y{ w,m 1( ËTot ) Yw,bËTot }%ÖHS Ïa+–=

%K MkmY{ m 1( ËTot ) MkbYbËTot }%ÖHS Ïa+–=

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B.5 Fracture assessment

B.5.1 Introduction

Tubular joints can be assessed using the general procedure described in 7.3, with the modifications presented below. The fracture assessment procedure for offshore structures is a modification of the Level 2B FAD for low work hardening materials. All loading effects should be determined in the first instance for best estimates of the maximum loading, excluding load factors prescribed by limit state design codes. Where a probabilistic assessment is required, estimates of the variability and distributions of the loading and other input parameters are necessary.

B.5.2 Primary stresses

For the selected wave, the maximum applied nominal forces and moments in the joint containing the flaw need to be determined. The maximum applied nominal forces and moments are then converted into maximum applied axial, in-plane, and out-of plane nominal stresses from which the local joint stresses are determined, as described in B.1.

B.5.3 Residual stresses

General guidance on the treatment of residual stresses is given in 7.3.4. This is supplemented by recommendations on residual stress distributions in Annex Q.

B.5.4 Determination of Kr or

The fracture parameter, Kr or , is determined using the procedure in 7.3.

B.5.5 Collapse parameter Lr

B.5.5.1 Introduction

General guidance and recommendations on the prediction of plastic collapse are given in Annex P. The collapse parameter Lr for tubular joints may be calculated using either local or global collapse analyses [85]. The local collapse approach will usually be very conservative whilst the use of the global approach tends to give more realistic predictions of plastic collapse in tubular joints.

B.5.5.2 Local collapse analysis for part-thickness flaws

For the deepest point of part-thickness flaws in circumferential butt welds, the standard solution in Annex P should be used to calculate the reference stress, Öref, across the remaining ligament, using as the effective width the length of the joint subjected to tensile stresses.

For the surface point at the ends of surface-breaking flaws in circumferential butt welds, the standard solutions in Annex P should be used to calculate the reference stress, Öref, for a through-thickness flaw having a length equal to the surface length of the part thickness flaw, 2c. The effective width should be taken as the length of the joint subject to tensile stresses.

B.5.5.3 Global collapse analysis

B.5.5.3.1 For circumferential butt welds or tubular nodal joints containing a flaw in the brace, lower bound collapse loads should be calculated separately for axial loading, in-plane bending and out-of-plane bending for the overall cross-section of the member containing the flaw based on net area and yield strength.

The net area for axial loading should be taken as the full area of the cross-section of the joint minus the area of rectangle containing the flaw. The collapse load Pc is the load to raise the average stress on the net area to the yield strength.

The fully plastic moment of the cross-section of the joint should be calculated for in-plane or out-of-plane loads, allowing for the cross-sectional area of the rectangle containing the flaw. The net fully plastic moments, Mci and Mco, based on the yield strength, are the collapse moments.

B.5.5.3.2 For tubular nodal joints containing a part-thickness or through-thickness flaw in the chord, parametric equations for the design strength of the uncracked geometry are available, see Health and Safety Executive (HSE) [75] and American Petroleum Institute (API) [76]. The lower bound characteristic ultimate strength for the geometry concerned should be calculated using the equations for the uncracked geometry from the above references, together with the specified minimum yield strength. The ultimate strengths for axial, in-plane and out-of-plane bending loads should be calculated separately.

¸r

¸r

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For T joints subjected to compression or tension loading, the ultimate strength should be calculated from the HSE characteristic strength or API RP 2A formulae for the relevant loading mode. For K joints, the HSE characteristic strength or API RP 2A compression strength should be used, even when the flaw is located in the tension brace/chord joint.

The plastic collapse loads for the cracked geometry are determined by reducing the plastic collapse loads for the corresponding uncracked geometry on the basis of the net load-bearing area for axial loading and the effect of the flaw area on the plastic collapse modulus for bending loads. The correction factor for axial loading is given [88] by the equation:

where

FAR is the reduction factor to allow for the loss of load-bearing cross-sectional area due to the presence of the flaw;

Q¶ allows for the increased strength observed at ¶ values above 0.6;

Ac = crack area = 2aB for a through thickness flaw; or

Ac = crack area = (½);ac for a surface breaking flaw;

lw = weld length = entire length of weld toe along brace/chord intersection on the chord side;

Q¶ = 1 for ¶ k 0.6;

Q¶ = 0.3/{¶(1 – 0.833¶)} for ¶ > 0.6;

For tubular joints containing part-thickness flaws, mq = 0.

For tubular joints containing through-thickness flaws, validation of equation (B.9) is at present limited to joints with ¶ ratios less than 0.8 and the following configurations:

— K-joint with a through-thickness crack at the crown subjected to balanced axial loading;— tension axially loaded T and DT joint with a through-thickness crack at the saddle.

For K joints, use either of the following:

— the HSE characteristic compression design strength with mq = 1; or— the API RP 2A compression design strength with mq = 0.

For T and DT joints, use either of the following:

— the HSE characteristic tension design strength with mq = 1; or— the API RP 2A tension design strength with mq = 0.

B.5.5.3.3 For tubular nodal joints containing a part thickness or through thickness flaw in the chord, the parameter Lr is calculated from the following:

where

Pc, Mci and Mco are plastic collapse loads in the cracked condition for axial loading, in-plane bending and out-of-plane bending respectively. For example Pc is equal to FAR times the plastic collapse load in the uncracked condition for axial loading.

(B.9)

(B.10)

Pa, Mai and Mao are the applied axial load, and the in-plane and out-of-plane moments, respectively.

The vertical lines in and mean the absolute values (moduli) of these ratios.

FAR 1Ac

lw

-----⎠⎞ 1

Q¶

-----⎝ ⎠⎛ ⎞

mq

–⎝⎛=

LrÖf

ÖY

-----⎝ ⎠⎛ ⎞ Pa

Pc

----- Mai

Mci

-------⎝ ⎠⎛ ⎞

2Mao

Mco

--------+ +⎩ ⎭⎨ ⎬⎧ ⎫

=

Pa

Pc

----- Mao

Mco

--------

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B.5.5.3.4 If conservative assumptions lead to the global collapse value of Lr being lower than the local collapse value of Lr, the local value may be used.

B.5.6 Flaw assessment

As an initial assessment, the co-ordinates relating to the deepest point and surface point positions should be plotted on the Level 2B FAD for low work hardening materials. If the points lie within the locus the flaw may be acceptable. If any of the points lie on or outside the locus the flaw is unacceptable.

If all points lie within the FAD, the co-ordinates should be re-evaluated using the partial safety factors appropriate to the required level of reliability as described in B.5.7. If all the reassessed points lie within the locus the flaw is acceptable for the level of the reliability selected. If any of the points lie on or outside the locus, the flaw is unacceptable for the level of reliability selected.

Partial safety factors should be applied, as described in Annex K.

Annex C (informative) Fracture assessment procedures for pressure vessels and pipelines

C.1 General

Advice is given in this annex on how this guide should be applied to pressure vessels and pipelines as part of a fitness for purpose assessment. Many types of engineering plant can be classified as pressure vessels. These range from very thick walled reactor vessels to thin walled storage vessels, and pipelines. Rather than attempting to give industry prescriptive guidelines, this annex suggests a general methodology for performing fitness for purpose assessments of pressure vessels and pipelines. Guidelines are also given on the type of input data that are required. The special case of local thinning of pressure vessels and pipelines, due for example to corrosion, is treated in Annex G.

C.2 Suggested methodology for the fitness for purpose assessment of flaws in pressure vessels and pipelines

C.2.1 Pressure vessels

A methodology for the fitness for purpose assessment of flaws in pressure vessels is given in Figure C.1. This algorithm emphasizes that assessing fitness for purpose requires more than a consideration of the significance of the flaw. It is also necessary to consider the previous history of the vessel in order to establish the cause of the flaw. Information about the behaviour of similar plant or flaws, if available, may be valuable, as this can indicate whether the plant has a poor or good safety record.

Flaws associated with poor repairs have often resulted in failures. Any weld repair or grind repair has to be carefully designed, such that it will not crack or deteriorate during service. A repair weld or grind repair that does contain cracks is unsatisfactory and indicates both poor design and unsatisfactory repair procedures. In these situations, a complete reappraisal of the repaired region is necessary. Redesign of the problem area and an alternative, improved repair method may be necessary.

Surface breaking flaws are commonly ground out. This grinding serves the dual purpose of accurately “sizing” the flaw and removing it. However, the grinding groove is itself a flaw and should be assessed accordingly. Grind repairs in vessels require a detailed consideration of the stress acting on the grind, particularly at stiffened regions in the vessel, which may be associated with welds and may also be acting as stress raisers.

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Figure C.1 — Algorithm for pressure vessel flaw assessment

Competent persondetects flaw

in pressure vessel

Meet/Liaise withvessel user

Has flaw beenreported on a

previous inspection

Report of flawreferred to

responsible engineer

No

NoYesHave containing

areas beeninspected before

Determine the reason for missing

the flaw

No Yes

Yes

Yes

No

Has any flawdimension increased ?

Is the flaw within thelimits set in the design code or to a previous

assessment ?

YesNo

Accept and record

Can all the areabe inspected ?

YesNo

No Yes

YesNo

Repair and record or seek expert advice

Does flaw coincide with a

previous repair ?

Can weld/parentmaterial beidentified ?

Repair using procedure designed to ensure no flaws are

reintroduced, taking account of material PWHT requirements, etc.,

reinspect and record OR seek expert advice

Is value of toughnessavailable or

can it be estimated/measured ?

Record

Reject

Accept

Use this guide to

assess defect

YesNo

Are stresses known or

readily calculated ?

Repair using procedure designed to ensure no flaws are

reintroduced, taking account of material PWHT requirements, etc.,

reinspect and record OR seek expert advice

Repair using procedure designed to ensure no flaws are reintroduced, taking account of material PWHT requirements, etc., reinspect and record OR seek

expert advice

Repair using procedure designed to ensure no flaws are reintroduced, taking account of material PWHT requirements, etc., reinspect and record OR seek

expert advice

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Service-induced flaws usually take the form of structural damage, for example a dent, or cracks. Cracks, particularly surface breaking cracks, have to be viewed with special caution as they are likely to be indicative of one or more of the following:

a) poor quality welding/construction;

b) stresses in excess of design;

c) poor inspection methods at time of construction;

d) stress corrosion, fatigue, corrosion fatigue.

Some cracks can be shown to be benign fabrication flaws using methods such as metallographic replicas or “boat samples” (shallow removal of the crack and neighbouring material). All other cracks should be thoroughly investigated and their cause established before conducting an assessment. Where the cause is poor design or excessive loading, a flaw assessment may not be appropriate; repair and redesign is required.

C.2.2 Pipelines

Transmission pipelines transport gases and liquids at high pressures. They can be subjected to a variety of loads ranging from internal pressure to external ground loading. They can also sustain various forms of damage ranging from environmentally induced cracks to impact damage from third parties.

Because of these variables, prescriptive guidelines are not presented in this annex. However, the following sequence should be followed when reviewing a pipeline.

a) Establish the cause and nature of the pipeline damage/flaw.

b) Establish the quality and properties of the associated pipeline material.

c) Identify and calculate all stresses acting on the damaged or flawed region.

d) Establish the size of the flaw or damage zone, and quantify any associated tolerances and reliabilities.

e) Identify all possible failure modes, and consider the consequences of the release of the pipeline’s product from the damage/flaw.

C.3 Guidance for pressure vessels

C.3.1 General

The type of engineering critical assessment required depends on the flaw in question. Most pressure vessel flaws are associated with welds. However, gouges in parent material, flaws resulting in a loss of wall thickness in the pressure vessel material, and flaws in weldments can be assessed using this document. (See C.3.3.4.) Dents and flaws within dents require special consideration due to the geometric stress concentration of the dent and to its potential “instability” (popping out). If these effects can be quantified, the techniques described in this guide may be applied. Otherwise specialist advice should be sought [90].

The fitness for purpose assessment requires three inputs: the flaw size, the stress field in which the flaw is located, and the material fracture toughness. It is necessary to ensure that all data used are relevant. In some assessments, testing, stress analysis, further inspection or metallurgical work may be required to generate suitable data. Obtaining all relevant data can be difficult, particularly values of toughness for older or second-hand equipment.

The fitness for purpose assessment should take into account all possible failure modes (creep, buckling, etc.) and carefully consider the effect of environment (for example stress corrosion) and duty (for example fatigue) to which the pressure vessel is subjected.

C.3.2 Toughness data

In a very limited number of cases, operators may have obtained representative fracture toughness data at the construction stage. Often, however, this is not the case. Charpy impact data may be available from the original construction records, in which case, the correlations given in Annex J may be used. Other alternatives are to use cut-out material, if available, or to adopt a conservative lower bound established from the literature for similar steel and weldments.

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C.3.3 Flaw size data

Flaw size data are obtained by non-destructive testing (NDT). It is essential that the operator and organization inspecting the vessel are thoroughly qualified and experienced to a specified level. All NDT should be conducted in accordance with recognized and appropriate standards. These standards (and any deviation) should be specified in the ECA.

Ultrasonics is the major inspection method used in measuring flaw sizes for fitness for purpose assessments. This is because it is generally the flaw height (through-thickness) that is the critical dimension in an assessment, with flaw length being of secondary importance. Ultrasonic inspections are prone to inaccuracies and unreliability. An ultrasonic inspection can reliably detect a weld flaw, but sizing can be subject to inaccuracy. Therefore, safety factors should be applied to flaw sizes reported by ultrasonics.

C.3.4 Flaw type

C.3.4.1 Orientation

A relatively simple but basic requirement is that the possible extension of a crack like flaw should be assessed by application of the total stress tending to open the crack, i.e. the stress perpendicular to the centre line bisecting the crack tip. The method advised in this guide is to establish the angle at the crack centre line relative to the principal stress direction and then to use the projected length of the flaw in the principal stress direction as the length for calculating purposes. (See 6.4.5.)

C.3.4.2 Discontinuous flaws

Flaws classified as discontinuous should be assessed by means of the interaction criteria of 7.1.2.

C.3.4.3 Visible cracks

Cracks may be indicative of poor design features or workmanship and therefore the cause should be ascertained before proceeding with an assessment. In older vessels, surface cracks may be caused by plate laminations appearing after being opened up by the tension resulting from welds cooling down. Such cases require further investigation of the vessel parent plate in that area in order to establish the true nature of the problem.

C.3.4.4 Flaws removed by grinding

Any reductions in wall thickness require assessment. Grind-outs may be associated with large geometric discontinuities, such as saddles, and may be extensive. Grind-outs may have a significant effect on the stress levels around the discontinuity, in which case a full structural analysis may be necessary to establish realistic stress values in such areas, especially if new flaws appear adjacent to previous grind-outs.

The procedures adopted for the analysis of grind-outs caused by removal of flaws are outside the procedures given in the pressure vessel and piping codes and need individual treatment.

However, if the grind-out is smooth and free from surface breaking flaws it can be treated as follows. For static failure (provided that there is no risk of failure by brittle fracture and that the sole potential final failure mode is plastic collapse), treat as a reduction in cross sectional area (refer to Annex G). For fatigue, give consideration to the stress concentration arising as a result of the grind-out profile.

C.3.5 Stress analysis

In many cases stress analysis may be relatively simple, but more difficult cases can arise, particularly with flaws associated with branch or fillet weld connections. Flaws in these locations are subject to stress concentrations. For the stress analysis of flaws at nozzles, the stress concentration factors given in PD 5500:2003, Annex G can be used for guidance. Where standard solutions are not available, numerical analysis may be required.

C.4 Guidance for oil and gas transmission pipelines

Oil and gas transmission pipelines can contain flaws in the parent material or in the weldments. These flaws can occur during fabrication or construction; or in service by mechanical damage, corrosion, etc. The significance of these flaws can be assessed using appropriate fitness for purpose methods, including the methods in this document

The assessment should take into account all the stresses that can act on a pipeline. These include static and cyclic stresses for internal pressure, external forces [e.g. due to work on the pipeline, ground movement, free spanning (offshore lines)], construction stresses, thermal stresses, etc.

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The assessment should confirm that all pipeline parent materials have adequate ductility to prevent brittle fracture initiation. Additionally, gas pipelines should be designed to avoid fracture propagation. This is generally achieved by specifying pipe body Charpy V and DWTT requirements [91] which also prevent brittle fracture initiation.

The significance of flaws in the parent pipe material can be assessed using one of the following methods:

a) the methods detailed in this document;

b) another recognized standard e.g. American Society of Mechanical Engineers [92];

c) specialist methods, e.g. Kiefner et al [93] or Hopkins and Jones [94].

Gouges, flaws resulting in a loss of wall thickness in the pipe material, and flaws in weldments can be assessed using this document. Dents and flaws within dents require special consideration due to the geometric stress concentration of the dent and to its potential “instability” (popping out). If these effects can be quantified, the techniques described in this guide may be applied. Otherwise specialist advice should be sought, e.g. Hopkins and Cosham [90]. Flaws in pipeline girth welds can be assessed using this standard, or specialist methods detailed in the literature, e.g. Knauf and Hopkins [95].

Transmission pipelines are increasingly being inspected using on-line inspection vehicles. Some of these vehicles can detect and size flaws in a pipeline. Any assessment of a pipeline flaw which has been detected and sized by an on-line inspection vehicle should take into account the capability, reliability and accuracy of the vehicle’s inspection technology. Additionally, the assessment should take into account any potential further growth of the flaw following the inspection.

Annex D (normative) Stress due to misalignment

D.1 Calculation of stress magnification factor

The presence of misalignment, axial (eccentricity) or angular, or both, at a welded joint can cause an increase or decrease in stress at the joint when it is loaded, due to the introduction of local bending stresses [53], [54] and [96]. These will influence both stress intensity factors (Annex M) and reference stresses (Annex P) (see 6.4.4). This applies to both butt and fillet welded joints, but only under loading which results in membrane stresses transverse to the line of misalignment. Bending stresses do not occur as a result of misalignment in continuous welds loaded longitudinally or at joints in plates subjected only to bending. However, misaligned joints in sections (e.g. beams, tubes) subjected to overall bending will experience combined membrane and bending stresses and additional bending stresses may arise due to the membrane stress component.

If more than one type of misalignment exists, the total induced bending stress is the sum of the bending stresses due to each type. Both tensile (positive) and compressive (negative) stresses will arise as a result of misalignment, depending on the surface or through-thickness position being considered. Account should be taken of the relevant sign when calculating the net effect of combined misalignments (combined axial and angular misalignment might act together, e.g. both tensile, or in opposition) and when calculating the total stress due to applied and induced stresses.

The bending stress due to misalignment depends not only on its type and extent, but also on factors that influence the ability of the welded joint to rotate under the induced bending moment. These factors include loading and boundary conditions, section shape and the presence of other members which provide local stiffening. Special analysis (e.g. finite element stress analysis) is usually required to quantify their effects. Unless it can be demonstrated that restraint on the joint reduces the influence of misalignment, the induced bending stress should be calculated assuming no restraint.

Formulae for calculating the bending stress, Ös, as a function of applied membrane stress, Pm, for a number of cases of misalignment are given in Table D.1 and Table D.2 [53], [54] and [96]. For joints that experience combined membrane and bending stresses, the formulae are used in conjunction with the membrane stress component only. Apart from the weld root in a cruciform fillet weld, all the formulae give Ös at the weld toe. If the stress is required at a different position through the thickness, for example when assessing buried flaws, the bending stress due to misalignment can be assumed to vary linearly through the material thickness to zero at its neutral axis.

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It is sometimes convenient (see 8.8.1) to express the effect of misalignment in terms of the maximum factor by which the applied stress (Pm) or stress range (%Pm) is magnified as a result of its presence. This magnification factor, km, is defined as:

(D.1)

(D.2)

where

Ös is the maximum induced bending stress due to the misalignment, which has the same sign as Pm (i.e. Ös/Pm is positive).

For combined misalignments (e.g. axial and angular):

km = 1 + (km – 1)axial + (km – 1)angular (D.3)

It may be noted that the guidance given in this annex may be unduly conservative if applied to through-thickness flaws. This is because the presence of such flaws will serve to reduce local bending stresses resulting from misalignment. In fact, the magnitude of local bending due to misalignment will decrease with increasing crack length for through-thickness flaws.

kmPm Bs+

Pm

------------------- 1Bs

Pm

-------+==

km%Pm %Bs+

%Pm

---------------------------- 1 %Bs

%Pm

-----------+==

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Ta

ble

D.1

— F

orm

ula

e fo

r ca

lcu

lati

ng

th

e b

end

ing

str

ess

du

e to

mis

ali

gn

men

t in

bu

tt j

oin

ts

Ty

pe

Det

ail

Ben

din

g s

tres

s, Ö

sR

ema

rks

a) A

xial

mis

alig

nm

ent

betw

een

fla

t pl

ates

wh

ere Ä

is a

fac

tor

depe

nde

nt

on r

estr

ain

t

Ä =

6 f

or u

nre

stra

ined

join

t F

or r

emot

ely

load

ed jo

ints

, ass

um

e l 1

= l 2

b) A

xial

mis

alig

nm

ent

betw

een

fla

t pl

ates

of

diff

eren

t th

ickn

ess

Rel

ates

to

rem

otel

y lo

aded

, un

rest

rain

ed

join

ts

Use

n =

1.5

su

ppor

ted

by t

ests

c) A

xial

mis

alig

nm

ent

at

lon

gitu

din

al s

eam

wel

ds

in t

ube

s, p

ipes

an

d ve

ssel

s, w

ith

or

wit

hou

t th

ickn

ess

chan

ge

—

d) A

xial

mis

alig

nm

ent

at

girt

h w

elds

in t

ube

s,

pipe

s, v

esse

ls a

nd

at

seam

s in

sph

eres

, wit

h o

r w

ith

out

thic

knes

s ch

ange

s

If Ö

s/Pm <

1:

If Ö

s/Pm U

1:

(Con

nel

ly a

nd

Zet

tlem

oyer

[24

0])

—

l 2l 1

Be

Bs

Pm

-------

Äel

1

Bl 1

l 2+

()

--------

--------

--------

⎩⎭

⎨⎬

⎧⎫

=

B2

B2

> B

1

eB

1Ö

s

Pm

-------

6e

B1

------

Bn 1

Bn 1

Bn 2

+----

--------

--------

⎝⎠

⎜⎟

⎛⎞

=

B1

B2

e

B2

> B

1-

s

mP

e

BB

B

=−

()

+(

)⎛ ⎝⎜ ⎜

⎞ ⎠⎟ ⎟6

1

1

11

2

21

06

.

B1

B2 >

B1

B2

e

_

Ös

Pm

-------

6e

B1

1v2

–(

)----

--------

--------

------

11

B2

B1

⁄(

)1.5

+----

--------

--------

--------

---------

⎩⎭

⎨⎬

⎧⎫

=

Ös

Pm

-------

2.6

eB

1

--------

---1

10.

7B

2B

1⁄

()1

.4+

--------

--------

--------

--------

--------

-----⎩

⎭⎨

⎬⎧

⎫=

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e) A

ngu

lar

mis

alig

nm

ent

betw

een

fla

t pl

ates

µ in

rad

ius

Ass

um

ing

bou

nda

ry c

ondi

tion

s eq

uiv

alen

t to

: —

fix

ed e

nds

:

— p

inn

ed e

nds

:

wh

ere,

in e

ach

cas

e

Th

e ta

nh

cor

rect

ion

(in

cu

rly

brac

kets

) al

low

s fo

r re

duct

ion

in a

ngu

lar

mis

alig

nm

ent

due

to s

trai

ghte

nin

g of

jo

int

un

der

ten

sile

load

ing.

It

is a

lway

s k1

and

ther

efor

e it

is u

sual

ly

con

serv

ativ

e to

ign

ore

it. T

he

exce

ptio

n

is if

, wh

en c

ombi

ned

wit

h a

xial

m

isal

ign

men

t, t

he

angu

lar

com

pon

ent

has

th

e ef

fect

of

redu

cin

g th

e ov

eral

l st

ress

. Its

eff

ect

is n

egli

gibl

e fo

r 2l

/B <

10

and

it is

inde

pen

den

t of

th

e as

sum

ed e

nd

fixi

ng

con

diti

on f

or

2l/B

> 1

00. N

ote,

for

com

pres

sive

lo

adin

g, w

ith

out

any

late

ral r

estr

ain

t,

the

“tan

h”

term

bec

omes

a “

tan

” te

rm

and

it is

no

lon

ger

con

serv

ativ

e to

ign

ore

it.

Ty

pe

Det

ail

Ben

din

g s

tres

s, Ö

sR

ema

rks

B

y 2l

α

Ös

Pm

-------

3y ¶------

tan

h¶

2⁄(

)¶

2⁄----

--------

--------

--------

⎩⎭

⎨⎬

⎧⎫

=

3a 4-------

2l B-----

tan

h¶

2⁄(

)¶

2⁄----

--------

--------

--------

⎩⎭

⎨⎬

⎧⎫

=

Ös

Pm

-------

6y B------

tan

h¶(

)¶

--------

--------

-----⎩

⎭⎨

⎬⎧

⎫=

3a 2-------2

l B-----ta

nh

¶()

¶----

--------

---------

⎩⎭

⎨⎬

⎧⎫

=

¶2

l B-----3Ö

m

E--------

--⎝

⎠⎛

⎞0.5

=

Ta

ble

D.1

— F

orm

ula

e fo

r ca

lcu

lati

ng

th

e b

end

ing

str

ess

du

e to

mis

ali

gn

men

t in

bu

tt j

oin

ts (

con

tin

ued

)

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f) A

ngu

lar

mis

alig

nm

ent

at lo

ngi

tudi

nal

or

circ

um

fere

nti

al s

eam

s in

tu

bes

or v

esse

ls

Ass

um

ing

bou

nda

ry c

ondi

tion

s eq

uiv

alen

t to

: —

fix

ed e

nds

:

— p

inn

ed e

nds

:

wh

ere,

in e

ach

cas

e

Ass

um

ing

an id

eali

zed

geom

etry

,

g) O

vali

ty in

pre

ssu

rize

d pi

pes

or v

esse

ls

Ú in

deg

rees

wh

ere

D is

th

e m

ean

dia

met

er

p m is

th

e m

axim

um

pre

ssu

re a

t th

e op

erat

ing

con

diti

on b

ein

g as

sess

ed.

For

mu

la t

akes

acc

oun

t of

exa

ct lo

cati

on

of w

eld

seam

an

d be

nef

icia

l ch

ange

in

shap

e of

ves

sel d

ue

to p

ress

uri

zati

on. I

f,

un

der

fati

gue

load

ing,

pm

var

ies,

use

th

e m

ean

val

ue

duri

ng

the

tim

e in

terv

al

con

side

red.

A c

onse

rvat

ive

esti

mat

e of

Ös

is:

Ty

pe

Det

ail

Ben

din

g s

tres

s, Ö

sR

ema

rks

α

yd

2lÖ

s

Pm

-------

3d

B1

v2–

()

--------

--------

--------

tan

h¶

2⁄(

)¶

2⁄----

--------

--------

--------

⎩⎭

⎨⎬

⎧⎫

=

Ös

Pm

-------

6d

B1

v2–

()

--------

--------

--------

tan

h¶(

)¶

--------

--------

-----⎩

⎭⎨

⎬⎧

⎫=

¶2

l B-----3

1v2

–(

)Pm

E----

--------

--------

--------

---⎩

⎭⎨

⎬⎧

⎫0.5

=

dy 2---

or µ

l 2------

=

θ

Wel

d

B

Dm

in

Dm

ax

Ös

Pm

-------

1.5

Dm

axD

min

–(

)cos

2Ú

B1

0.5

+P

m1

v2–

()

E----

--------

--------

-------

⎝⎠

⎛⎞

D B---- ⎝⎠

⎛⎞3

⎩⎭

⎨⎬

⎧⎫

--------

--------

--------

--------

--------

--------

--------

--------

--------

----=

Ös

Pm

-------

1.5

Dm

axD

min

–(

)B

--------

--------

--------

--------

--------

---=

Ta

ble

D.1

— F

orm

ula

e fo

r ca

lcu

lati

ng

th

e b

end

ing

str

ess

du

e to

mis

ali

gn

men

t in

bu

tt j

oin

ts (

con

tin

ued

)

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Ta

ble

D.2

— F

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Annex E (normative) Flaw recharacterization

When an embedded or a surface flaw cannot be assessed as tolerable according to any of the three levels of Clause 7, it is possible that, in some circumstances, the prediction of failure of a ligament may not be critical to the overall integrity of the structure or component. In such cases, a further assessment step may be carried out, in which the ligament concerned is assumed not to be present and the initial flaw is re-characterized as a surface or through thickness flaw, as appropriate. The resulting flaw may require an allowance to be made for dynamic conditions and for possible crack growth at the ends if ligament failure actually occurred.

a) When ligament failure is predicted to occur by local yielding or it is known that ligament failure will be by a ductile mechanism (upper shelf operation) an allowance should be made for possible crack growth at the ends during ligament breakthrough. The size of the recharacterized flaw is calculated by increasing the total length of the original flaw, as shown in Figure E.1. It should be noted that re-characterization of flaws is also required for leak before break assessments (Annex F) but the latter are primarily to assess leak rates. The general effect of bending as opposed to tension stresses on re-characterization can be seen between Figure F.7a) and Figure F.6a) in the leak before break analysis.

b) When an assessment to Levels 1, 2 or 3 indicates that ligament failure may occur and where this failure may be by a brittle mechanism (lower shelf or transition régime) an allowance should be made for possible dynamic conditions at the moving crack tip. The dimensions of the recharacterized flaw should be made as for a) (Figure E.1), but the fracture toughness used in the assessment of the recharacterized flaw should be a dynamic or crack arrest toughness, appropriate for the material and temperature.

The recharacterized flaw may then be assessed according to the procedures of Clause 7. This procedure will only be of benefit if local conditions in the ligament are more severe than those of the recharacterized flaw. If the re-characterized flaw also fails the assessment, the initial flaw is not acceptable.

a) Embedded flaws b) Surface flaws

Figure E.1 — Rules for recharacterization of flaws

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Annex F (informative) A procedure for leak-before-break assessment

F.1 General

Clause 7 suggests several options by which it may still be possible to demonstrate the safety of a structure containing flaws when an initial analysis has failed to show that adequate margins exist (see flow chart in Figure 4). For pressurised components one of these options is to make a leak-before-break case by demonstrating that a flaw will grow in such a way as to cause, in the first instance, a stable leak of the pressure boundary rather than a sudden disruptive break.

The various stages in the development of a leak-before-break argument may be explained with the aid of the diagram shown in Figure F.1 [97]. This diagram has axes of crack height, a, and crack length, l½, (for nomenclature see footnote to l½ in Clause 3) normalized to the pipe or vessel wall thickness, B. An initial part-through crack is represented by a point on the diagram. The crack may grow by fatigue, tearing or any other process until it reaches some critical height at which the remaining ligament ahead of the crack breaks through the wall. The crack then continues growing in surface length until there is sufficient opening to cause a detectable leak or until the crack becomes unstable. A leak-before-break argument is aimed at demonstrating that leakage of fluid through a crack in the wall of a pipe or vessel can be detected prior to the crack attaining conditions of instability at which rapid crack extension occurs.

lc½ is the critical length of a fully penetrating through-wall crack

Figure F.1 — The leak-before-break diagram

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This annex sets out two alternative procedures for making a leak-before-break case and recommends methods for carrying out each of the steps involved. The first is a simplified detectable leakage approach, based on a postulated through-wall crack. The second sets out a more rigorous approach, which considers the development of a part-penetrating flaw. The alternative procedures are as follows.

a) Detectable leakage approach

This simplified type of leak-before-break argument aims to demonstrate that a leaking through-wall crack is detectable well before it grows to a limiting length. Such “detectable leakage” arguments are increasingly being used for leak-before-break assessments. An example of this is the leak-before-break procedure for light water reactor pipework published by the US Nuclear Regulatory Commission in NUREG 1061 [60]. The starting point for this type of assessment is to postulate a fully-penetrating crack and show that, should such a crack arise, the leakage would be detectable before the crack grew to a limiting length. However, for this simplified approach to be valid, there should be a mechanism for developing localized damage, and no risk of the development of long surface cracks. The detailed procedure for performing this kind of assessment is set out in F.2.

b) Full leak-before-break approach

The starting point for the full leak-before-break procedure is usually a surface flaw that has yet to break through the pipe or vessel wall. In order to make a leak-before-break case for this type of flaw, it is necessary to show that:

1) the flaw penetrates the pressure boundary before it can lead to a disruptive failure;

2) the resulting through-wall crack leaks at a sufficient rate to ensure its detection before it grows to a critical length at which disruptive failure occurs.

Several steps are involved in establishing each of these requirements. First, the flaw should be characterized and the mechanisms by which it can grow identified. The next step is to calculate the length of the through-wall crack formed as the initial flaw penetrates the pressure boundary; this is then compared with the critical length of a fully-penetrating crack. Finally, it is necessary to estimate the crack-opening area, the rate at which fluid leaks from the crack and whether or not the leak will be detected before the crack grows to a critical length. These steps form the basis of the full leak-before-break procedure described in F.3.

It is important that additional calculations are carried out to assess the sensitivity of the results to likely variations in the input data. Guidance on this and on other aspects of the analysis is given in F.4. It is important that this is read before using the procedure.

Where possible, the leak-before-break procedures make use of methods and guidance already contained in the main document or its other annexes. Where this is the case, for example, in the crack growth and critical crack size calculations, reference is made to the appropriate clauses of the document. Methods other than those recommended in this procedure may be used, but it is the responsibility of the user to ensure that such methods can be justified and appropriate validation exists.

In contrast to the procedures of the main document, which are concerned with failure avoidance, part of the leak-before-break case involves failure prediction. It is therefore recommended that best-estimate values of stresses and material properties, rather than pessimistic values, be used to estimate the crack length at breakthrough when part-through flaws are being considered. However, to ensure conservatism, pessimistic values should be used to calculate the critical length of the resulting through-wall crack, in accordance with the procedures of the main document. For the purpose of the leak-before-break procedure, the critical length is therefore synonymous with, and should be taken to be equal to, the limiting length as defined in the main document. The term “limiting length” is therefore used in this annex.

Leak-before-break assessments for a pressure boundary should be conducted for locations judged to be most at risk. Some guidance on the selection of assessment sites is given in Table F.1. It may be necessary to examine several locations to demonstrate that the worst case has been found. Any postulated flaws should be oriented in the most onerous direction to ensure that they experience the highest stresses and worst material properties at that location.

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Table F.1 — Guidance on selection of assessment sites around a pipe system

The procedures are primarily aimed at the assessment of discrete flaws, either postulated or known to exist in a component, for which breakthrough would occur in a ductile manner. In principle, the procedures can be used when the ligament beneath the flaw fails in a brittle manner. However, the re-characterization rules following brittle ligament failure are such that it may not be possible to make a leak-before-break case without recourse to crack-arrest arguments. These are beyond the scope of this document. The route based on detectable leakage starts with a postulated through-wall crack, and avoids the difficulties of recharacterization following breakthrough.

A leak-before-break case may not be tenable in plant that is prone to cracking mechanisms which may lead to very long surface flaws. Also, the risk of transient water hammer loading in piping containing high-energy fluid can preclude leak-before-break arguments, unless the peak loads are considered in the limiting crack size evaluation. Where there is significant risk of damage to piping from impacting (missiles or dropped loads), other whipping pipes or arising from equipment failure, then such considerations should override any leak-before-break case.

F.2 Detectable leakage procedure

The simplified detectable leakage procedure [see Figure F.2a)] is similar in concept to NUREG-1061 [60]. Because NUREG-1061 is intended for light water reactor piping, some of its recommendations and safety margins are rather specific. Here, in keeping with the approach in the present guide, margins are left to the judgement of the user with due regard to the methodology used, assumptions made, sensitivity studies and the specific application.

Consideration Influence on leak-before-break arguments

Pipe size For given operating conditions and operating stresses, leak rate will be less for smaller pipes.

Welds and castings

Flaws are more likely to occur in these features than in straight forged pipe made to modern standards.

Components (elbows, tees, valves, etc.)

Likely to have start of life flaws (especially if cast). Geometric stress raisers can promote in-service degradation. Complex stress fields complicate leak-before-break arguments.

Material properties

Low yield strength and fracture toughness and poor creep ductility make it more difficult to demonstrate a leak-before-break case.

Susceptibility to degradation

Locations should be ranked against mechanisms such as fatigue, continuum damage, ageing, etc. Other mechanisms such as stress corrosion cracking, erosion, corrosion, etc. may preclude a leak-before-break case.

Stresses High stresses may result in an inability to make a leak-before-break case. Comparison of uncracked combined loading reference stress is usually a reasonable criterion for ranking locations having similar material properties.

Inspection History or feasibility of future inspections may be a crucial factor in choosing locations for assessment.

Consequences Acceptability of guillotine failure may determine which locations should be assessed.

Leak detection The detection system used may have to change for different potential crack locations.

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a) Flow chart of assessment assuming a through-wall flaw

Figure F.2 — Leak-before-break procedure

Determine limiting length of through-wall crack

Calculate the crackopening area (COA)

Can part penetration flawsarise that could grow into

through-wall flaws greaterthan the LCL or can

non-penetrating critical flaws arise?

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crack length (LCL)

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Refine calculations

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b) Flow chart of full assessment

Figure F.2 — Leak-before-break procedure (continued)

Charaterize flaw

Determine limiting length

pf through-wall flaw

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at breakthrough

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Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

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area of flaw

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system

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Refine calculations

Refine calculations

Refine calculations

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Can limiting crack length

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Leak-before-break case

cannot be made

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Can leak rate calculations

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Can crack-opening area

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cannot be made

Can margins be refined?


cannot be made

No

No

No

No

No

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No

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A detectable leakage analysis is usually carried out in speculative (that is, design or safety) studies, where through-wall cracks are postulated in welds and other features. However, care should be taken in the use of this strategy. The user should ensure that the appropriate mechanisms exist for the development of a detectable through-wall crack, and that a surface crack cannot arise which would lead to gross failure of the pressure boundary. The role of welding residual stresses in particular needs to be considered; these will influence crack propagation, COA and critical crack length.

To make a detectable leakage case at each location, the following steps should be taken:

a) Determine limiting length of through-wall crack, l½c.The limiting length, l½c, is found under extreme loading conditions, using procedures from Clause 7 and with the minimum material properties. Stable tearing can be allowed for in the calculation of l½c.

b) Calculate the length, l½L, of a penetrating crack that leaks at the minimum detectable rate, under normal operating conditions.

The leak rate is determined from the COA, as in steps 4 and 5 of the full procedure in F.3. Normal operating loads, rather than peak loads, should be assessed to avoid under-predicting the detectable leakage crack length. The length of the postulated through-wall crack is adjusted until the leak rate just becomes detectable; the minimum detectable leak rate depends on the detection apparatus (see F.4.7). An appropriate margin on leak detection should be included.

c) Assess results.

The length, l½L, should be less than l½c with a suitable margin on length. If this is satisfied, a detectable leakage case is made. Implicit in this case is the assumption that the leak can be detected very quickly once the fluid loss exceeds a certain rate. When plant is only monitored at intervals, perhaps by personnel on scheduled inspections, allowance should be made for any fatigue or creep crack growth that might occur between inspections. The minimum detectable crack size, l½L, in step 1 should be replaced by an enhanced size, l½L*, which includes growth over the full interval between inspections and step 2. The increment (l½L* – l½L) can be estimated using the fatigue crack growth procedure of Clause 8, or the creep crack growth procedure in Clause 9.

It is recommended that a sensitivity analysis be carried out to determine the extent to which changes in the input data affect the results of the calculations.

F.3 Full leak-before-break procedure

The leak-before-break procedure is set out as a series of steps below. These are summarized in the form of a flow-chart in Figure F.2b). More detailed guidance on carrying out each of the steps is given in F.5, the number in brackets after each step indicating the appropriate subclause.

a) Characterize the flaw (F.4.2).

To use this procedure, the flaw dimensions should be characterized as a surface or through-wall flaw in accordance with 7.1.2.1. For extended, irregular flaws, where a narrow ligament exists over only a small fraction of the overall flaw length, the characterization may be based on that part of the flaw where the narrowest ligament exists. Embedded flaws should first be re-characterized as surface flaws in order to use the procedure.

b) Determine limiting length of through-wall flaw (F.4.3).

The limiting length at which a through-wall flaw at the position of the initial flaw would become unstable should be determined using the procedures contained in 7.3 or 7.4. The limiting length should be determined for the most onerous loading condition using lower-bound values for materials properties. A stable tearing (Level 3) assessment can be invoked in this part of the assessment.

c) Estimate flaw length at breakthrough (F.4.4).

The flaw length at breakthrough can be estimated using the procedures of Clause 7 and the re-characterization rules in Annex E. To determine the length at breakthrough:

1) calculate the flaw length at which ligament failure is predicted to occur using the procedures in 7.3 or 7.4;

2) re-characterize the flaw for which ligament failure is predicted to occur as a through-wall flaw using the rules of Annex E.

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The flaw length at breakthrough is given by the length of the through-wall flaw resulting from this recharacterization. Ligament failure should be assessed under normal operating conditions unless some other loading condition could result in a larger flaw length at breakthrough. Best estimate material properties and loads should be used, together with local collapse solutions and ductile tearing. This provides a best estimate of the breakthrough length. Use of minimum material properties, and failure based on initiation, reduces the breakthrough length and enhances the margin on crack stability. The calculated leak rate is, however, reduced by this means. Because it is not clear which factor dominates, the use of best estimate data is advocated. The mechanisms of crack growth (fatigue, creep, etc.) should be identified; if necessary, the surface length of the flaw should be increased with the height, until the ligament fails. When assessing ligament failure, the stability of the surface points should be assessed, along with that of the deepest point on the crack front. If the flaw becomes unstable at the surface, a leak-before-break case cannot be made.

d) Calculate crack-opening area (COA) of flaw (F.4.5).

The COA of a potential through-wall flaw is required to estimate leakage flow rates. The COA depends on the crack geometry (effective length, shape, orientation, etc.), the component geometry, the material properties and the loading conditions. In addition, if operating at high temperature, the COA changes with time owing to creep (see H.6).

A best estimate approach to calculating COA is advocated to establish the viability of a leak-before-break case and provide a basis for the assessment of margins. However, COA calculations are not simple and a bounding approach that minimizes flow rates can offer alleviation of effort.

Advice on the calculation of COA for idealized flaws in flat plates, pipe-work components and spheres is given in F.4.5.

e) Calculate leak rate from flaw (F.4.6).

Several computer codes are available to predict leakage rates for single and two-phase flows through a wide range of through-wall cracks. Details of these codes and approximate analytical solutions for isothermal and polytropic flow of gasses are given in F.4.6. An alternative means of estimating the leakage rate would be to use relevant experimental data if these are available.

f) Estimate time to detect leak from flaw (F.4.7).

The leak detection system should be selected with due regard to the nature of the leaking fluid and the calculated leak rate. The detection time is then assessed from knowledge of the sensitivity of the equipment and of its response time, with due allowance for the need, if any, to check that the signal is not spurious.

The time for detection and the execution of the subsequently required actions should be less than that required for the crack to grow to the limiting length.

g) Calculate time to grow to limiting length (F.4.7).

If the through-wall crack can continue to grow in length as a result of fatigue or other mechanisms then the time required for the flaw to grow to a limiting length should be calculated by integrating growth law for any applicable sub-critical growth mechanism. The forms of these laws are given in Clauses 8, 9 and 10 for fatigue, creep crack growth and environmentally assisted cracking respectively. Due account should be taken of potential interactions between these mechanisms themselves and between them and ductile tearing.

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h) Assess results (F.4.8).

In principle, a leak-before-break case has been made provided that the calculations carried out in the preceding steps show that:

1) the flaw length at breakthrough is less than the limiting length of a through-wall flaw.

2) the time to detect the leak is less than the time for the flaw to grow to a limiting length.

However, it is recommended that a sensitivity analysis be carried out in order to determine the extent to which changes in the input data affect the results of the calculations. Only if the above two conditions can be satisfied with adequate margins throughout the range of variations likely to occur in the input data can a satisfactory leak-before-break case be claimed. One type of sensitivity study uses the detailed type of leak-before-break diagram depicted in Figure F.3, where critical flaw size envelopes are plotted for failure based on initiation (with allowable tearing) and on instability. Upper bound material properties can be used, if known. These envelopes are sensible extremes to the possible flaw break-through shape. Critical crack lengths based on initiation (with allowable tearing) and on instability are also included in Figure F.3.

It should be noted that an initial failure to demonstrate that the flaw length at breakthrough is less than the limiting length, that the leak will be detectable before the flaw could grow to a limiting length, or that adequate margins exist, does not necessarily mean a leak-before-break case cannot be made. As indicated in the flow-chart of Figure F.2, it may be possible to refine either the margins or the calculations of limiting crack length, flaw length at breakthrough, crack-opening area, leak rate or leak detection system and as a result make a satisfactory leak-before-break case.

F.4 Background notes and guidance on using the procedure

F.4.1 General

F.4.2 to F.4.8 are intended to provide more detailed guidance on the methods recommended for carrying out the various steps in the leak-before-break procedure. It is recommended that these be read before using either procedure. Where it is relevant, background information on various aspects of the procedure is also included.

Whilst several of the following subclauses are relevant to both the “detectable leakage” and “full leak-before-break” procedures, F.4.2 and F.4.4 are only appropriate to the latter.

F.4.2 Flaw characterization

The aim of flaw characterization is to represent a known or postulated flaw by a relatively simple shape that adequately models the flaw and can be readily analysed. It is recommended that the flaw characterization rules of 7.1.2 or Annex E be used for this purpose.

It is recognized that, for extended irregular flaws, where a narrow ligament may exist over only a small fraction of the overall flaw length, the characterization rules of 7.1.2 are likely to be unnecessarily pessimistic when making a leak-before-break case. For flaws of this nature it may be more realistic to base the initial characterization on that part of the flaw where the narrow ligament exists. If this is done, however, it will be necessary to characterize and separately assess the remainder of the flaw to ensure that a critical part-penetrating flaw cannot arise that would lead to a double-edged guillotine break.

Figure F.4 illustrates such an example where a complex flaw has been separately characterized as the superposition of an extended, part-through flaw and a semi-elliptical flaw in a section of reduced thickness. Provided the extended flaw cannot grow to penetrate the wall before the semi-elliptical flaw breaks through, it is acceptable in this example to assess the leak-before-break behaviour of the complex flaw in terms of the behaviour of the simpler semi-elliptical flaw.

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Fig

ure

F.3

— D

eta

iled

lea

k-b

efo

re-b

rea

k d

iag

ram

Det

ecta

ble

leak

age

zone

Grow

th to

failu

rewi

ll no

t occ

ur

Flaw

s be

low

dete

ctab

le li

mit

1 00

A'B'

C'A

BC

Crac

k le

ngth

Critical crack length based on initiation

Critical crack length based on enhancedtoughness (say 2 mm tearing )

Critical crack length based on instability

"Bre

akth

roug

h" cu

rve

base

d on

inst

abili

ty

"Bre

akth

roug

h" cu

rve

base

d on

enh

ance

dto

ughn

ess

(say

2 m

m o

f te

arin

g)

"Bre

akth

roug

h" cu

rve

base

d on

initi

atio

n

Lim

it of

det

ectio

n cu

rve

Leak

age

rate

=x

l/m

inLe

akag

e ra

te=

nx

x l /

min

Leak

age

rate

=m

xx

l/m

in

Mar

gins

on

criti

cal c

rack

leng

thto

allo

w fo

r le

akag

e de

tect

ion

or cr

ack

grow

th co

nsid

erat

ions

a t

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If this approach is adopted, care will be needed in several areas to ensure that the leak-before-break case remains conservative. In reducing the section thickness for example, the stresses in the remaining section should be increased to compensate for the loss of load-bearing area. Although this is conservative when calculating the limiting length of a through-wall crack, the flaw length at breakthrough could be under-predicted as a result of the increased stresses. In this example, it is therefore recommended that the breakthrough length be also calculated for a semi-elliptical flaw of length 2c and height a having the same aspect ratio but based on the full section thickness; the larger of the two breakthrough lengths should be used in the subsequent calculations. In practice Lr (or Sr) is unlikely to vary significantly and it may only be necessary to compare the Kr or values at the deepest points of the two semi-ellipses to determine which will have the greater length at breakthrough. The crack-opening area is proportional to the applied stress. Also any flow reduction due to friction is proportional to the flow path length (and therefore the wall thickness). Therefore the crack-opening area and leak rate calculations should be based on a through-wall crack in the full section thickness in order to ensure that the predicted leakage remains conservative.

The flaw discussed above is just one example of a whole class of possible complex flaws that might require analysis. Other flaws may well need to be characterized in different ways in order to make satisfactory leak-before-break cases.

a)

b)

c)

The complex flaw in a) may be separately assessed as the two simple flaws in b) and c).

Figure F.4 — Example characterization of a complex flaw

l

d

a'

B

a'

B

l

d

BB – a'

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F.4.3 Calculation of limiting crack lengths

As part of the leak-before-break procedure, the limiting length of a through-wall flaw at the position of the initial surface flaw should be calculated. It is recommended that this be done using the procedures of 7.3 or 7.4.

It is important that the limiting length is calculated for the most onerous loading condition anticipated and with minimum material properties. Ductile tearing (Level 3 assessment) can be invoked within the validity limits defined in 7.4.

In determining the most onerous loading conditions, secondary stresses need to be considered using the procedures outlined in Annex Q and Annex R. The treatment in Annex Q includes stress distributions for completely self balancing through-wall residual stresses, representative of those which might arise from some welding processes. These depend on wall thickness rather than on crack length. Results of an experimental programme designed to investigate the influence of in-plane self-balancing residual stress fields on the limiting crack length for through thickness flaws are reported in Sharples et al [98].

F.4.4 Calculation of flaw length at breakthrough (only required for the full leak-before-break procedure)

Since the flaw length at breakthrough determines whether the initial failure results in a leak or a break, it is important to predict the crack shape development correctly as the crack grows to penetration.

Where growth occurs by fatigue, the methods described in Clause 8 can be used to predict the increases in both the height and length of a flaw. A procedure for the treatment of creep effects is included in Clause 9. Annex M gives guidance on determining stress intensity factors. Ligament failure should be assessed using the stresses associated with normal operating conditions unless some other operating régime (prolonged operation at reduced pressure for example) would lead to an increased flaw length at breakthrough. In calculating the breakthrough length, it is assumed that ligament failure is not preceded by instability at the surface-breaking points of the crack. However, the growth calculations may indicate that unstable growth in the length direction can occur before the flaw has grown fully through the wall. This result may be an artefact of the assumed crack shape (e.g. a semi-circular flaw), or the use of limited ductile tearing. These aspects should be considered before concluding that a leak-before-break case cannot be made.

To ensure that a leak can be detected, it is important that crack lengths (and hence COAs) at, and following, breakthrough are not over predicted. It is recognized that, when ligament failure first occurs, the flaw may not penetrate the wall along its entire length with a rectangular shape, as shown in Figure F.5a). Furthermore, it is recognized that the crack length at breakthrough, defined in terms of the flaw re-characterization rules of Annex E, is itself likely to be an over-estimate of the actual flaw length. Immediately following breakthrough, therefore, a cross-section of the crack might appear, as shown in Figure F.5b) for example. As a consequence, the initial rate of leakage from the crack may be significantly less than predicted on the assumption of a uniform crack length equal to the crack length at breakthrough, as determined by ligament instability and flaw recharacterization rules. In general, this is not of concern, since, before the flaw can grow to a limiting length, it will first grow to the breakthrough length, as determined by ligament instability and re-characterization rules. This argument though relies on the fact that, if the crack extends in length, it will grow in such a way as to tend towards a rectangular shape. However, the stress distribution may be such that the crack can increase in length whilst not tending towards a rectangular shape, but rather maintaining the crack shape at breakthrough, as shown in Figure F.5b) without recharacterization. The above argument no longer holds for such cases and estimates of COA based on a rectangular shape are unconservative.

Experimental evidence [99] suggests that, for cases where stress distributions are predominantly tensile, cracks do tend towards a rectangular shape. For such cases therefore, the re-characterization rules of Annex E should be followed.

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However, the leak-before-break procedure recognizes that these rules have been written to assure failure avoidance and are likely to be extremely pessimistic when the ligament thickness at failure is relatively small and failure occurs in a ductile manner. For thin ligaments, less than about 20 % of the wall thickness (which fail in a ductile manner), a more realistic length for the re-characterized through-wall flaw can be used given by its length at failure, 2c, plus the ligament thickness p.

The recommended re-characterization rules for predominantly tensile loading and where failure would occur in a ductile manner are summarized in Figure F.6.

Where through-wall bending stresses predominate, cracks do not tend to a rectangular shape and different crack shape development rules are required. A reasonable assumption is that, with crack growth after breakthrough, the crack front profile remains from that at breakthrough. Breakthrough is also assumed to occur without re-characterization, as shown, for example, in Figure F.5b). Then, following breakthrough, the crack lengths at the two surfaces increase by the same amount, as shown in Figure F.7, as at the initiation surface. This approach has been adopted for the calculation of COAs in the leak-before-break method developed for the European Fast Reactor [100], where it is assumed that penetration is achieved by continuing fatigue and without re-characterization. However, in order to extend the approach for more general applications, it may be necessary to re-characterize the flaw to allow for possible lengthways crack growth as the ligament breaks through. The recommended re-characterization rules for predominantly through-wall bending, and where failure occurs in a ductile manner are summarized in Figure F.7.

a) Assumed crack

b) Possible actual crack

Figure F.5 — Schematic crack profiles at breakthrough

Crack length at breakthrough

B

Crack length at breakthrough

B

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i) Flaw size at ligament failure ii) Re-characterized through thickness flaw

a) d > 20 % B


b) d k 20 % B

Figure F.6 — Recommended re-characterization of flaws at breakthrough for predominantly tensile loading

lbd

B B

lb lb+B

B/2

B/2

lbd

B

d/2

d/2

lb lb+d

B

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a) d > 20 % B


b) d k 20 % B

Figure F.7 — Recommended re-characterization of flaws at breakthrough for predominantly through-wall bend

lbd

B

B/2

B/2

lbB

B

lbd

B

d/2

d/2

lb d

B

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F.4.5 Calculation of crack-opening areas

Crack opening area (COA) estimates for postulated through-wall cracks can vary widely depending on how the crack is idealized, which crack opening model is used and what material properties are assumed. This subclause provides outline advice on the factors that should be considered, and will influence whether or not the simplified procedure of assuming a through-wall crack can be used. For example, the methods for calculating COA in the presence of residual stress fields will show the feasibility, or otherwise, of developing a detectable through-wall crack.

Estimation methods for COA can be classified into three categories:

a) linear elastic models;

b) elastic models incorporating a small scale plasticity correction;

c) elastic-plastic models.

A wide range of published solutions are available for idealized slot-like cracks in simple geometries subject to basic loadings (pressure, membrane and bending). Their accuracy varies with geometry (e.g. r/B ratio), crack size and type and magnitude of load. Generally the models, except for results based on detailed finite element analysis, estimate COA at the mid-thickness position; that is they do not account for crack taper arising from through-wall bending loads.

If through-wall bending stresses are absent or can be ignored, a conservative approximation for the COA can be calculated from the following equation:

where

l½ is the through-wall crack length;

the term in brackets represents a first-order correction for the effects of crack tip plasticity;

µ(Æ½) is a correction to allow for bulging in terms of the shell parameter, Æ½;and where

For axial cracks in cylinders:

µ(Æ½) = 1 + 0.1Æ½ + 0.16Æ½2For circumferential cracks in cylinders:

µ(Æ½) = (1 + 0.117Æ½2)1/2

For meridional cracks in spheres:

µ(Æ½) = 1 + 0.02Æ½ + 0.22Æ½2The first expression is valid for Æ½ k 8, the second and third expressions for Æ½ k 5.

These expressions for the crack-opening area were derived using thin-walled, shallow-shell theory and are strictly valid only when DSM/B U 20 and crack lengths do not exceed the least radius of curvature of the shell. Some alternative COA models in Langston [101], Knowles and Kemp [102], Miller [103], Westergaard [104], Kumar and German [105], Wuthrich [106], France and Sharples [107] for plates, cylinders and spheres are summarized in Table F.2. Background to and validation of these models, specifically for cylinders with circumferential cracks, is given by Sharples and Kemp [108]. The more accurate elastic-plastic model of Langston [101] is recommended for best estimate leak-before-break calculations where stress levels are high enough to induce significant plasticity (i.e. Lr greater than about 0.4). However, this method requires a description of the material stress-strain curve. For bounding calculations, the linear elastic finite element results presented by Knowles and Kemp [102] and France and Sharples [107] are recommended. These results cover a wide range of cylinder

(F.1)A

P l

E

P P

OA

m m

2

f

m

f

= ′( )′( )′

+⎛

⎝⎜⎜

⎞

⎠⎟⎟ −

⎛

⎝⎜⎜

⎞

⎠⎟⎟

π 2

2

3 22

2

3

2

1

2 2

/ / 22⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

′ =−( ){ }

( )

2 12 12

1 4

1 2

c v

rB

/

/

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geometries (rSM/B from 5 to 100) and crack lengths. Where high accuracy elastic estimates are required it should be noted that non-linear geometric deformation effects can be important in some circumstances [108]. The solutions for plates and cylinders effectively assume that the cracks are in the centre of an “infinite” body. For many geometries this will be a reasonable approximation. However, if the crack is close to a significant geometric constraint (e.g. a pipe nozzle intersection) then local effects can influence COA (see for example, France [109] and Rahman et al [110]).

Table F.2 — Crack opening area methods for simple geometrics and loadings

Where the estimation model gives centre crack opening displacement rather than area, an elliptical crack opening shape should be assumed (i.e. COA = ¸l½;/2).

For complex geometries (such as elbows and branch junctions), unusual crack configurations, or for high confidence calculations, it is necessary to use finite element methodology to give accurate COA results.

Mean material properties should be used to provide a best estimate of COA. These properties should be relevant to the condition of the plant; that is, time dependent changes in properties, such as degradation, relaxation and redistribution processes should be allowed for.

The plant loading conditions used for COA and leakage rate estimates are usually those associated with normal operation. If creep deformations at high temperature are being considered, details of plant loading history may be required.

For pipe-work subjected to global transverse bending, the orientation of the resultant bending moment with respect to the potential through-wall crack should be considered. Off centre loads can cause asymmetric (and hence non elliptical) crack opening or partial or complete closure, if the crack lies totally on the compressive side (see Rahman et al [110], May et al [111]).

Geometry Primary loading Elastic or small-scale yielding Elastic-plastic

Elastic model Plasticity model

Plates Membrane Westergaard [104] Wuthrich [106] —

Through wall bending

Miller [103] — —

Spheres Pressure Wuthrich [106] rSM/B k 10, Æ½ k 5

Wuthrich [106] —


Miller [103] — —

Cylinders with axial cracks

Pressure Knowles and Kemp [102] 5 k rSM/B k 100

Wuthrich [106] —


Knowles and Kemp [102] 5 k rSM/B k 100

— —

Cylinders with circumferential cracks

Pressure Knowles and Kemp [102] 5 k rSM/B k 100

Wuthrich [106] Langston [101] 5 k r/B k 20

Global bending France and Sharples [107] 5 k r/B k 100

Wuthrich [106] Langston [101] 5 k r/B k 20

Pressure and global bending

Add elastic components Wuthrich [106] Kumar and German [105] 5 k rSM/B k 20


Knowles and Kemp [102] 5 k rSM/B k 100

— —

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For thick-walled geometries the effect of crack-face pressure, which acts to open the crack, will be a function of crack opening; for tight cracks the mean pressure will be lower than for wide cracks. To assess the significance of such effects it is recommended that 50 % of the internal pressure should be added to the membrane stress on the crack face. This value should then be reassessed when undertaking the leakage flow calculations (which usually output exit pressures), and the results iterated if necessary.

Local through-wall bending stresses can induce elastic crack face rotations that reduce effective COA. If complete crack closure occurs, no leak-before-break case can be made. Significant local through-wall bending stresses may be present in thick-walled shells under internal pressure, or be associated with weld residual stresses, geometric discontinuities, or thermal gradients. References for estimating elastic crack face rotations in simple geometries are included in Table F.2.

Most leak-before-break assessments are likely to be concerned with the existence or potential existence of cracks at welds. The variation in material properties at welds, the influence of the weld preparation angle and the presence of residual welding stresses all affect the COA (see for example Dong et al [112]).

The initial leakage rate through a flaw, which has just broken through the pressure boundary, may be significantly less than that predicted, assuming a uniform crack length equal to the re-characterized flaw length [see discussion in F.4.4 and Figure F.5b)]. This is because, when ligament failure first occurs, the flaw may not penetrate the wall along its entire length, and because the re-characterization rules may over-estimate the actual flaw length. In general this is not of concern, since, before the flaw can grow to a limiting length, it should first extend to the break-through length in the COA calculations. However, for cases where through-wall bending stresses predominate and development of a rectangular shape is unlikely, COA can be estimated using the approximation given by Hodgson and Leggatt [113].

F.4.6 Leak rate calculations

The calculation of the fluid flow or leak rate through a crack is in general a complex problem, involving the crack geometry, the flow path length, friction effects and the thermodynamics of the flow through the crack. Several computer codes have been written to predict leakage rates for a variety of fluids through cracks. Some of the more readily available codes are described below. The codes are of necessity complex and may have physical limitations as to their use: care should be taken to ensure that codes are not used to solve problems for which they are not valid.

For single-phase flow, the program DAFTCAT [114] and [115] calculates flow rates through rectangular-section cracks including the effects of friction. The COA should be input as a rectangular planform. For a diverging or converging crack, such as might occur if significant through-wall bending were present, the program uses the approximations given by Ewing [116]. A lower bound to flow rate can be calculated based on the smaller of the COAs. In addition, Ewing [116] presents simple, approximate solutions for isothermal or polytropic flows of gases in the following form:

Qmf = CD(Pf Ô f ) 1/2WCl½ (F.2)

The above formulation can also be used for tapered cracks.

For two-phase flow of steam/water mixtures PICEP [117] and SQUIRT [118] can be used to calculate leak rates through a variety of cracks. The two programs are similar and use the same thermal-hydraulic model for the flow. In PICEP the leaking fluid can be wet steam or initially sub-cooled or saturated water: SQUIRT requires initially sub-cooled or saturated water. Both programs allow the crack shape to be elliptical or rectangular and the COA to vary linearly through the wall thickness if required. Friction losses are included and additional losses due to path tortuosity are included in an indirect manner.

All of these programs have been validated to some extent against a variety of experimental data and reasonable agreement obtained [114], [117] and [118]. In the case of the two-phase flow programs, the validation included comparisons with flow rates through artificial cracks in the form of machined slots or parallel plates and flow rates through circular pipes.

Whilst flow rate measurements have been made on real cracks [119], [120], [121], [122] and [123], the extent of validation for such cracks is relatively small and the agreement with theory generally less good. The likely accuracy of the leak rate predictions for both single and two-phase flows depends on a variety of factors and should be judged by examining the available validation data.

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Friction effects are important and there is a difference in approach between the various codes. For example, PICEP and SQUIRT use an established correlation between sand roughness (but converted to surface roughness, Ra) and friction factor, ff, based on pipe experiments, together with an empirical tortuosity term. However, relevant information on tortuosity is limited. In DAFTCAT, an empirically derived relationship between surface roughness and friction factor is used. In principle, the latter type of approach is simpler, as only one parameter, Ra, is required. It should be noted that expert guidance may be required in interpretation, as roughness measurements depend on a number of parameters; in particular the measured Ra value increases as the sampling length over which it is measured increases. This is illustrated by Wilkowski et al [124], who present data for surface roughness for a number of different crack types. In the absence of specific Ra data, the lower values quoted, corresponding to the shorter traverse length measurements, can be used as indicative values for flow rate calculations. These values are reproduced in Table F.3 which includes, where appropriate, mean values and standard deviations. These data enable sensitivity studies to be undertaken.

Table F.3 — Summary of surface roughness values from Wilkowski et al [124]

Formulations for friction factor, ff, show it to increase continuously as roughness increases or crack width reduces. However, flow rate experiments show that ff does not increase continuously, but reaches an effective maximum. The effective maximum friction factor, ffmax, is dependent upon surface geometry. Gardner and Tyrrell [125] advance a theory justifying the existence of ffmax and this is assessed against experiments using relatively large-scale conforming surfaces (i.e. one surface is manufactured and the opposing one is a replica). For the surface of most relevance to structural flaws, the random roughness, ffmax was approximately 0.2. For a very regular and stepped surface, ffmax was unity. This range of values has been confirmed by experimental data on flow through real cracks: Sharples et al [119] and Gardner et al [122] report experiments on fatigue cracks; Rawlings [126] reports measurements of flow through a crack in a defective weld. These results are discussed collectively by Chivers [127]. It should be noted that the above discussion on ff values relates to fully developed turbulent flow: higher values can occur in laminar flow, but, in general, these are of little interest in leak-before-break.

Finally, in assessing flow rate calculations, consideration should be given to the potential for flow reduction mechanisms such as blocking of the crack by oxide growth or by particle or debris entrapment. No firm advice can be offered on how to assess such effects, and any judgements will have to be based on knowledge of the particulate and/or oxidation mechanisms and the calculated COA.

F.4.7 Leak detection and crack stability following breakthrough

Any leak-before-break procedure should show that the leaking crack remains stable for a sufficient time to allow the leak to be detected. The stability of the leaking crack needs to be assessed in terms of the margins to criticality and the potential for further crack growth.

If further time dependent crack growth can occur, then margins on length and time to failure need to be demonstrated. The assessed time to failure, in conjunction with the estimated flow rate, permits a suitable leak detection system to be selected.

Mitchell [128] and Chivers [129] give some information and guidance on the wide range of leak detection systems that are available; here only a brief outline is given in terms of two broad categories: global and local. In the former category are leak detection systems that monitor large areas of plant or segregated regions. Examples include sump pumps, pumps for water systems, humidity detection for steam leaks, gas levels in air for gaseous systems and radiation monitors for nuclear systems. All global systems detect all leaks (including, for example, valve glands, seals), and hence any leakage identified by the monitoring equipment needs to be investigated and the source established. The response times for such systems are relatively long and depend on plant segregation.

Crack mechanism Material Ra range

4m

Average Ra

4m

Standard deviation

4m

IGSCC Stainless steel 0.64 to 10.5 4.7 3.9

Fatigue (air) Stainless steel 8.1 — —

Fatigue (air) Carbon steel 3 to 8.5 6.5 3

Corrosion fatigue Carbon steel 3 to 11 8.8 3

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Local leak detection systems monitor specific plant features (e.g. a weld) or a well-defined area (e.g. length of pipe). Some detectors are medium or plant specific. For example, moisture sensitive tapes only work in water or steam systems where condensation can take place on the outer surface.

Leakage through cracks generates acoustic emission that is transmitted through the structure, and, in some circumstances, through the air. Wave guide and microphone systems have been developed which offer flexible and sensitive leak detection capabilities for a wide range of fluids. Details of design and deployment depend on applications.

F.4.8 Assessment of results

The final step in a leak-before-break assessment is a sensitivity analysis. This should take into account the range of likely variations in the main parameters used in the calculations. It is particularly important to ensure that the sensitivity of the results to variations in material properties, applied loads and the predicted COAs and leak rates are investigated.

In a sensitivity analysis of a leak-before-break case, it is important to realize that the use of upper-bound loads and stress-intensity factors together with lower-bound material properties and collapse solutions would not necessarily lead to a conservative result. In this, leak-before-break analyses differ from those in the main document, where use of such upper and lower-bound data help to ensure that the integrity assessment is always conservative. Although these bounding values provide conservative estimates of critical crack length and are therefore recommended for calculating limiting lengths, they minimize the flaw length at breakthrough and maximize the crack-opening displacement, both of which are unconservative when making a leak-before-break case. Best-estimate values should therefore be used to calculate the flaw length at breakthrough and the COA. The effect of varying each input parameter in turn should then be examined.

When considering crack stability at breakthrough, maximum conservatism is ensured by using lower bound material properties for the calculation of crack growth in the surface direction, and upper bound material properties for the calculation of through-thickness crack growth and ligament instability. For conservatism in the prediction of COA, however, the reverse conditions could be adopted, i.e. the use of upper bound material properties for the calculation of crack growth in the surface direction and the use of lower bound material properties for the calculation of through-thickness crack growth and ligament instability. The sensitivity of results to methods used for determining crack length at breakthrough (such as the use of local or global limit load solutions) should also be examined separately for stability and COA considerations.

Care should be taken to account properly for all loadings that may be imposed. Residual welding stresses and fit-up stresses for example are often not known to the same degree of precision as thermal, pressure and other operational stresses. It is important, therefore, that the sensitivity calculations reflect this uncertainty by allowing a suitably wide range of variation for these parameters.

The requirement to use best-estimate data should be borne in mind when choosing both assessment level and FAD. The general Lr based failure assessment curves (Levels 2A and 3A) contain small but real pessimisms and will tend to under predict both limiting and breakthrough crack lengths. The material specific Lr based curves (Levels 2B and 3B) are also pessimistic although in general to a lesser extent. The Level 3C curve represents a best-estimate locus of failure assessment points and so the use of this curve or the material specific Lr based curve is preferable if this is possible. Similarly, where ductile tearing is likely to occur, the use of a Level 3 analysis will provide more accurate estimates of limiting and breakthrough crack lengths than a Level 2 analysis based on initiation toughness. In practice the choice both of failure assessment curve and of analysis level is likely to depend on other factors such as the availability of materials data or whether a particular assessment curve or level of analysis is appropriate to the case in question. Nevertheless it is important from the point of view of assessing appropriate margins that any excessive conservatisms or possible unconservatisms in the analysis are recognized and accounted for.

In common with the main procedure, prescribed margins are not advocated in this annex, and it is for the user to determine what margins are acceptable. It also needs to be recognized that what constitutes an adequate margin in one particular application may not be appropriate in another. Thus, whether or not the margins demonstrated by the sensitivity analysis are deemed adequate is left to the judgement of the user. Although no direct guidance is given on quantifying what constitutes an adequate margin, there are certain factors which should be taken into account when assessing the adequacy or otherwise of margins. These include the levels of confidence in the input data used in the calculations, any simplifying assumptions or approximations that may have been necessary, and whether or not the consequences of a sudden break failure are tolerable.

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When the procedure is used to assess discrete flaws, a possible result is that ligament failure may not be predicted under the prescribed loading conditions and neither a leak nor a break occurs. In such a case the sensitivity analysis should be used to determine the limiting conditions for ligament failure and whether the failure would result in leak or a break.

F.5 Inclusion of creep effects

F.5.1 General

F.5 describes how the leak-before-break procedures given in F.2 and F.3 are modified by creep effects. The additional advice given here is based on the principles of a high temperature leak-before-break methodology, as outlined in Jones [130], Budden and Hooton [131] and Ainsworth and Chivers [132].

For cracked components operating within the creep range, creep rupture due to continuum damage mechanisms and creep crack growth needs to be considered both before and following flaw breakthrough. The methods for treating these effects are set out below and are based on Clause 9.

A high-temperature leak-before-break case can be made if it is possible to demonstrate:

a) that the crack length at breakthrough is less than the limiting crack length; and

b) that creep rupture of the entire section has not occurred prior to breakthrough; and

c) that the through-wall crack leaks fluid at a rate which is detectable before the crack grows to the limiting length and before creep rupture of the section occurs.

F.5.2 Limiting length of through-wall crack, l½cThis is determined as described in F.2a) and F.3b). However, tensile properties and fracture toughness should both be appropriate to a material that has experienced creep damage.

F.5.3 Crack length at breakthrough, 2cb

For postulated through-thickness cracks as part of a detectable leakage argument, the crack length at breakthrough, 2cb, is prescribed (see F.2).

When flaw growth through the wall is considered as part of a full leak-before-break case, creep crack growth of the flaw prior to breakthrough should be estimated using the methods described in Clause 9. It is assumed that the shape of the surface-breaking flaw at the start of high temperature service has been characterized as semi-elliptical with height a and surface length 2c, respectively. The instantaneous crack growth rates at the surface, 2c. , and at the deepest point of the flaw, a., should be calculated using reference stress estimates of C* together with an appropriate best estimate creep crack growth law. The latter is usually given in the form:

a. = C(C*)q

where

C and q are constants (T.1.6).

In the absence of specific crack growth rate data on the material, methods are given in Table T.1 and Nuclear Electric [57] for estimating crack growth rates in terms of rupture or creep ductility data only. The growing flaw is then continuously re-characterized as a semi-elliptical surface crack. Specifically, the increments in crack height and surface crack length between times t and t + %t are given by the following equation:

(F.3)

and

(F.4)

Details of how these calculations are made are given in T.2.

Crack growth due to fatigue and other sub-critical mechanisms should be separately accounted for using the methods given in Clauses 8 and 10.

%a a·t

t %t+∫ t( )dt=

% 2c( ) 2c·t

t %t+∫ t( )dt=

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Ligament failure of the growing crack, and the crack length at breakthrough, are characterized using the methods described in F.3c). The crack length at breakthrough is insensitive to the constant C in the creep crack growth law:

a. = C(C*)q

as a. and 2c. are affected equally. The time to breakthrough is, however, affected by the choice of constants.

Welding residual stresses should be taken into account, although their magnitude reduces with time due to creep straining. The effect of residual stresses on creep crack growth rates is described in Clause 9. Estimates are also given there which enable the timescales over which these stresses relax to be quantified. It may then be possible to justify considering only part or none of the initial residual stresses when considering further crack growth.

The time at which breakthrough occurs is denoted t(2cb). If the through wall crack is assumed to be present at the start of high temperature operation, t(2cb) = 0.

F.5.4 Time required to detect leak, ¹td

The time required to detect a leak depends both on the leak rate and on the sensitivity of the detection system, and is discussed in F.3d) to F.3f). The time, %td, is to be compared with the time to grow the crack to the limiting length, t(2cc), and with the time to creep rupture, tcd, as discussed below.

It should be noted that the COA, H, in general changes with time due to creep. In primarily membrane loading situations, the COA increases and hence it is conservative to use the elastic opening, He, as this leads to an underestimate of leak rate and hence both to a greater predicted detection time, %td, and to lower margins in a leak-before-break case. An approximate expression for estimating the rate of change of the creep component of COA, H

.c = H

. – H

.c, with time is found in Jones [130] and Budden and Hooton [133]:

H.c = Hc ¼

.c/¼e with Hc(0) = 0 (F.5)

where

¼e = Öref /E is the elastic strain at the reference stress, LrÖY;

¼.c is the corresponding creep strain rate at time t;

E is the elastic modulus.

For thick walled vessels (r/B k 5), the effect of crack face pressure may be significant and F.4.4 recommends that initially 50 % of the internal pressure should be added to the membrane stresses. It is then necessary to integrate equation (F.5) in conjunction with the flaw growth and leak rate calculations in order to determine a less conservative estimate of leakage detection time. F.4.5 gives advice on treating crack flow path characteristics in the leak rate calculations. For strain controlled situations, the elastic opening should be used. In cases involving significant through-wall bending the effects of crack face rotation and taper should be taken into account (see F.4.5).

F.5.5 Time, t(l½c), for the flaw to grow to the limiting length, l½c

In some instances, at the start of life it may be possible to justify a period, ti, of crack incubation prior to creep crack growth (T.1.8). In general, it is prudent to introduce a measure of conservatism by assuming that creep crack growth follows immediately on commencement of high temperature operation subsequent to breakthrough.

The time, t(l½c), for the flaw to grow to the limiting crack length is then obtained by integrating a creep crack growth law between the crack length at breakthrough, 2cb, and the limiting length l½c. The creep crack growth law should be relevant to the material in which the flaw is growing. Advice on calculating creep crack growth in weldments is given in Clause 9.

The creep crack growth parameter, C*, is estimated by reference stress methods as described in Annex T. Solutions for the stress intensity factor, K, for fully penetrating cracks are required to estimate C* and advice is included in Annex M.

Best estimate creep strain and creep crack growth data for the material containing the crack tip should be used in estimating C* and the amount of creep crack growth, respectively.

Residual stresses do not need to be considered following breakthrough if they are considered to have relaxed due to creep straining prior to breakthrough.

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F.5.6 Calculate times to creep rupture at crack sizes 2cb and l½cThe times to continuum damage failure of the cracked component should be calculated assuming fully-penetrating cracks of length 2cb and l½c. These times are given by:

tcd (2cb) = tr {Öref (2cb)} (F.6)

tcd (l½c) = tr {Öref (l½c)} (F.7)

where Öref (l½) is the reference stress assuming a fully penetrating crack of length 2c; Öref follows for a homogeneous component from Öref = LrÖY (7.3.7), where ÖY is the yield strength. Here tr(Ö) is the rupture time at the appropriate temperature and stress, Ö, from stress rupture data. For conservatism, lower bound rupture data should be used, as these lead to reduced estimates of rupture time and hence lower margins in a leak-before-break case.

Equations (F.6) and (F.7) assume a crack of length 2cb or (l½c) from the start of high temperature operation. This is conservative as it ignores flaw growth to that size. During that growth period, the reference stress, and hence the rate of accumulation of creep damage, is lower. Advice is given in Clause 9 for calculating improved estimates of tcd, which account for the flaw growth stage; these calculations need to be performed simultaneously with the crack growth calculations described above. In cases where a high temperature leak-before-break case cannot be made due to creep rupture prior to leak detection [see inequalities given by equations (F.8) to (F.11)], it may be possible to increase the predicted rupture times by following this route. However, in cases where a fully penetrating initial flaw is postulated at the start of high temperature operation, this decrease in conservatism is relevant to equation (F.7) only.

Advice on calculating creep rupture in welded joints is given in Clause 9. Then tcd is the minimum from equations (F.6) and (F.7) over the discrete metallurgical regions of the weldment. Definition of the reference stress appropriate to each region depends on materials and geometry, however, and reference [57] should be consulted for advice for specific material combinations. Note that this requires rupture data for each weld region.

F.5.7 Assess results

The time required to detect the leak, %td, following breakthrough should be compared with the time, t(l½c), for the crack to grow to the limiting length and with the times to creep rupture, tcd(2cb) and tcd(l½c). If t(l½c) k tcd(l½c), then the remaining life of the component is limited by unstable crack growth prior to creep rupture (see Figure F.8). Conversely, if tcd(l½c) < t(l½c) then creep rupture limits life (see Figure F.9).

A high temperature leak-before-break case can be made if each of the following inequalities is satisfied:

2cb < l½c (F.8)

t(2cb) < tcd(2cb) (F.9)

%td < t(l½c) – t(2cb) (F.10)

%td < tcd(l½c) – t(2cb) (F.11)

Inequalities given by equations (F.8) and (F.10) are identical to those given in textual form in F.3h)i) and F.3h)ii) in the context of low temperature leak-before-break. They ensure that failure by fast fracture does not occur either prior to breakthrough or before the leak can be detected, respectively. The time t(l½c) is, however, affected by creep crack growth as described below. Inequalities given by equations (F.9) and (F.11) stipulate that creep rupture has not occurred prior to breakthrough and that sufficient time is available following breakthrough to detect the leak before creep rupture occurs, respectively.

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[t(l½c) k t(l½c)]

Figure F.8 — Unstable crack growth before creep rupture

[tCD (lc) < t(lc)]

Figure F.9 — Rupture before unstable crack growth

t (lb ) t (lc ) tcd (lr) tcd (lb )

Time

∆ td

Creep rupture tCD (l)

Creep crack growth t (c)

lc

lb

Surf

ace

crac

k le

ngth

t (lb ) tcd (lr ) tcd (lb )Time

Creep rupture tcd (l)

Creep crack growth t (l)

lr

lb

lc

∆ td

tcd (lc ) t (lc )

Surf

ace

crac

k le

ngth

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If the case fails due to the inequality given by equation (F.11) alone not being satisfied, or if insufficient margins exist, then that inequality may be replaced by the following expression:

%td < tcd(l½c) – t(2cb) (F.12)

Here, l½r and tcd(l½r) are the crack length and corresponding time to rupture and are obtained by solving the following equation:

tcd(l½) = t(l½) for l½ = l½rwhere

t(l½) is the time to reach crack size l½ (Figure F.9).Note that from the inequalities given by equations (F.9) and (F.11), l½r satisfies 2cb < l½r < l½c.

F.5.8 Sensitivity studies

In general, the effect of varying the various materials and flow parameters should be examined in turn to identify those to which the results of the leak-before-break arguments are sensitive. It is conservative, in the context of leak-before-break assessments, to use lower bound tensile and fracture toughness data and lower bound creep rupture data. The effect of creep crack growth, however, is such that increasing growth rates lead to reductions both in the time to attain the limiting length and in that to leak detection. The procedure therefore recommends best estimate creep strain and creep crack growth data in the initial leak-before-break assessment. Further advice on realistic data combinations in creep crack growth assessments is given in Clause 9. Similarly, advice on friction factors and flow paths is given in F.4.6.

Margins on the detection time compared with the times to failure of the component by fast fracture or creep rupture are not specified in this procedure and are left to the discretion of the user to argue on a case-by-case basis. Further advice on this is given in F.3h) and in F.4.7 (see also Budden and Hooton [131]).

Annex G (normative) The assessment of corrosion in pipes and pressure vessels

G.1 Background

The purpose of this annex is to provide guidance for determining the acceptability of areas of loss of wall thickness caused by internal or external corrosion in internally pressurized pipes or pressure vessels.

Guidance is given on assessment methods, the data required and the accuracy that can be achieved. The single flaw method in G.4 has been extensively validated against small-scale testing, full-scale testing and extensive finite element analysis (Batte et al [133] and [134], Fu and Kirkwood [135]). The interaction rules in G.5 and assessment method in G.6 have only been checked against a limited range of burst tests involving equally sized flaws, and may not be appropriate for multiple flaws of widely differing size.

G.2 Applicability

G.2.1 General

The methods specified in this annex may be used to assess corrosion damage in pipes and pressure vessels that have been designed to a recognized design code. The annex deals in detail with corrosion flaws in pipes and cylindrical vessels in G.4 to G.6. Spherical vessels are treated in less detail in G.7.

This guidance does not cover every situation that requires a fitness for purpose assessment and further methods may be required (Sims et al [136]). Alternatively non-linear stress analysis such as finite element modelling may be used. Such analysis may be required for complex corrosion geometries and where external loadings are significant. Guidance on analysis methods is given in G.9.

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G.2.2 Applicable flaws

The following types of corrosion flaw can be assessed using this annex:

a) internal corrosion;

b) external corrosion;

c) corrosion in parent material;

d) corrosion in or adjacent to longitudinal and circumferential welds;

e) colonies of interacting corrosion flaws.

All procedures apply to either internal or external corrosion flaws. They can be applied to corrosion flaws in longitudinal and circumferential welds, with the following provisos:

— There should be no significant weld flaw present that may interact with the corrosion flaw. — The weld should not undermatch the parent steel in strength. — Brittle fracture should be unlikely to occur (see G.2.3).

It should be noted that the limiting condition might not be failure due to the applied hoop stress. This can occur in cases where there is significant additional external loading (axial and/or bending), and/or when the circumferential extent of the corrosion is greater than the longitudinal extent (e.g. preferential girth weld corrosion).

When assessing corrosion flaws, due consideration should be given to the measurement uncertainty of the flaw dimensions and the structural geometry. The limitations of the measurement techniques (e.g. intelligent pigs, ultrasonic testing) should be taken into account (see 6.3).

G.2.3 Exclusions

The following are outside the applicability of this annex:

a) materials with specified minimum yield strengths exceeding 550 N/mm2 or values of ÖY/Öu exceeding 0.9;

b) loading other than internal pressure above atmospheric;

c) cyclic loading;

d) sharp flaws (i.e. cracks);

e) combined corrosion and cracks;

f) corrosion in association with mechanical damage;

g) metal loss flaws attributable to mechanical damage (i.e. gouges)13);

h) fabrication flaws in welds;

i) environmentally induced cracking14);

j) flaw depths greater than 85 % of the original (i.e. not corroded) wall thickness (i.e. remaining ligament less than 15 % of the original wall thickness);

k) corrosion at regions of stress concentration such as nozzles, tees and the knuckle region of vessel heads.

13) Metal loss flaws due to mechanical damage may contain a work hardened layer at their base and may also contain cracking.14) Environmentally induced cracking, such as SCC (stress corrosion cracking), is not considered here. Guidance on the assessment of crack like corrosion flaws is given in 10.3.3.

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The assessment procedure is only applicable to ductile linepipe and pressure vessel steels that are expected to fail through plastic collapse. The procedure is not recommended for applications where brittle fracture is likely to occur. These may include the following:

1) any material that has been shown to have a full-scale fracture initiation transition temperature above the operating temperature;

2) material of thickness 13 mm and greater, unless the full scale initiation transition temperature is below the operating temperature;

3) flaws in mechanical joints, fabricated, forged, formed or cast fittings and attached appurtenances;

4) flaws in bond lines of flash welded (FW) or low frequency electric resistance welded (ERW) butt-welded pipe;

5) lap welded or furnace butt-welded pipe.

In such materials, fracture toughness tests should be carried out to confirm that they are operating above their brittle to ductile transition temperature. If they are, the procedures of this annex may be used. If they are not, the corrosion flaws should be treated as cracks and should be assessed according to the procedures of Clause 7.

G.2.4 Factors of safety

The factors of safety to be applied in determining the safe working pressure have the following two components.

fc1 which is the modelling factor15) which is based on the accuracy of the equations when compared against the database of burst tests.

fc2 which is the original design factor which is introduced to ensure a safe margin between the operating pressure and the failure pressure of the corrosion flaw.

The total factor of safety (fc) to be applied to determine the safe working pressure is calculated from the following:

fc = fc1 × fc2 (G.1)

G.2.5 Assessment Procedure

A flow chart describing the assessment procedure is shown in Figure G.1.

G.3 Terminology

A single flaw is one that does not interact with a neighbouring flaw, see G.5. The failure pressure for a single flaw is independent of other flaws in the pipe or vessel.

An interacting flaw is one that interacts with neighbouring flaws in an axial or circumferential direction.

A complex shaped flaw is either one that results from combining colonies of interacting flaws, or a single flaw for which a depth profile is available.

15) fc1 = 0.9 if the measured ultimate tensile strength is used. The measured UTS can be obtained from the results of standardtensile tests on representative specimens or from mill certificates.

fc1 = 1.0 if the minimum specified tensile strength is used.

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Figure G.1 — Flow chart of assessment procedure

START

Analyse all Corrosion DamageSites as Isolated Single Flawsusing G.4

Check for Possible InteractionsBetween Sites using G.5

Analyse Damage Sites as aColony of Interacting Flawsusing G.6

Are Failure PressuresAcceptable?

Continue operation at currentsafe working pressure

Revise safe working pressure orreassess using finite elementanalysis or full scale testing

No Interaction

Interaction

Yes

No

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G.4 Safe working pressure estimate for a single flaw

The safe working pressure of a single flaw can be estimated by the following procedure (see Figure G.2):

a) Calculate the failure pressure of the unflawed pipe or vessel cylinder (Po):

b) Calculate the length correction factor (Qc):

c) Calculate the reserve strength factor (Rs):

d) Calculate the failure pressure of the corroded pipe or vessel (Pf):

Pf = P0 × Rs (G.5)

e) Calculate the safe working pressure of the corroded pipe or vessel (Psw):

Psw = fc × Pf (G.6)

(G.2)

(G.3)

(G.4)

Figure G.2 — Single flaw dimensions

PB

D B0

0

0

=−( )

2u

Ql

DBc

c= +⎛

⎝⎜⎜

⎞

⎠⎟⎟1 0 31

2

.

0

R

d

B

d

B Q

s

c

0

c

0 c

=−

⎛

⎝⎜

⎞

⎠⎟

−⎛

⎝⎜

⎞

⎠⎟

1

1

1

dc lc

B0

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G.5 Interaction rules

The interaction rules given below apply solely to corrosion flaws. Rules for cracks and other non-planar flaws are given in Clauses 7 and 8. Adjacent corrosion flaws can interact to produce a failure pressure that is lower than that due to either of the isolated flaws (if they were treated as single flaws). For the case where interaction occurs, the single flaw equation is no longer valid and the rules given in G.6 should be applied.

A flaw can be treated as isolated if:

a) its depth is less than 20 % of the wall thickness; andb) the circumferential spacing between adjacent flaws, Ì, exceeds the angle given by the following:

c) the axial spacing between adjacent flaws, s, exceeds the value given by the following:

Two adjacent flaws within (axial spacing) will interact if:

or

where

and

Figure G.3 shows the key dimensions for flaw interaction.

(in degrees); and

(G.7a)

(G.7b)

Ì 3603;---

B0D

------->

s 2.0 DB0>

2.0 DB0

1

1

1

11

1

1

1 1 2 2

1 2

−

−

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

>−

⎛

⎝⎜

⎞

⎠⎟

++ +

⎛

⎝⎜

⎞d

B

d

B Q

B

d l d l

l l s0

0

0 ⎠⎠⎟

−⎛

⎝⎜

⎞

⎠⎟

++ +

⎛

⎝⎜

⎞

⎠⎟

⎧

⎨⎪⎪

⎩⎪⎪

⎫

⎬⎪⎪

⎭⎪⎪1

1

12

1 1 2 2

1 2B Q

d l d l

l l s0

1

1

1

12

2

2

1 1 2 2

1 2

−

−

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

>−

⎛

⎝⎜

⎞

⎠⎟

++ +

⎛

⎝⎜

⎞d

B

d

B Q

B

d l d l

l l s0

0

0 ⎠⎠⎟

−⎛

⎝⎜

⎞

⎠⎟

++ +

⎛

⎝⎜

⎞

⎠⎟

⎧

⎨⎪⎪

⎩⎪⎪

⎫

⎬⎪⎪

⎭⎪⎪1

1

12

1 1 2 2

1 2B Q

d l d l

l l s0

Ql

DB1

11 0 31= +

⎛

⎝⎜⎜

⎞

⎠⎟⎟.

0

2

Ql

DB2

2

2

1 0 31= +⎛

⎝⎜⎜

⎞

⎠⎟⎟.

0

Ql l s

DB12

1 2

2

1 0 31= ++ +⎛

⎝⎜⎜

⎞

⎠⎟⎟.

0

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G.6 Interacting flaws

G.6.1 General

The minimum information required for an assessment comprises the following:

a) the angular position of each flaw around the circumference;

b) the axial spacing between adjacent flaws;

c) the length of each individual flaw;

d) the depth of each individual flaw;

e) the width of each individual flaw.

G.6.2 Safe working pressure estimate

The safe working pressure of a colony of interacting flaws can be estimated from the following procedure16).

a) For regions where there is general metal loss (less than 10 % of the wall thickness), the local wall thickness and flaw depths should be used (see Figure G.4).

Figure G.3 — Interacting flaw dimensions

16) Within the colony of interacting flaws, all single flaws, and all combinations of adjacent flaws, are considered in order to determine the minimum predicted failure pressure.

Combined flaws (i.e. those that are deemed to interact) are assessed with the single flaw equation (see G.4), using the total length (including spacing) and the effective depth (based on the total length and a rectangular approximation to the corroded area of each flaw within the combined flaw).

Flaw 1

Flaw 2

Axis

d1 d2

l1 l2s

φ

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c) Construct a series of axial projection lines with a circumferential spacing calculated from the following:

d) Consider each projection line in turn. If flaws lie within ±Ì, they should be projected onto the current projection line (see Figure G.5).

e) Where flaws overlap, they should be combined to form a composite flaw. This is formed by taking the combined length, and the depth of the deepest flaw (see Figure G.6).

f) Calculate the failure pressures (P1, P2, …, PN) for each flaw, to the Nth flaw, treating each flaw, or composite flaw, as a single flaw (see G.4):

where

and

Pi = (P1, P2, …, PN)

g)17) Calculate the combined length of all combinations of interacting flaws (see Figure G.7 and Figure G.8). For flaws n to m the total length is given by the following equation:

h) Calculate the effective depth of the combined flaw formed from all of the interacting flaws from n to m, as follows (see Figure G.7):

b) The corroded section of the pipe or vessel should be divided into sections of a minimum length of , with a minimum overlap of . Steps c) to l) should be repeated for each sectioned length to assess all possible interactions.

(G.8)

17) The calculations described in g) to i) are to estimate the failure pressures of all combinations of adjacent flaws. The failure pressure for the combined flaw nm (i.e. defined by single flaw n to single flaw m, where n = 1 … Nc and m = n … Nc) is denoted Pnm.

When n equals m, the failure pressure is identical to that for an individual flaw, as calculated in f).

Mathematically, the process is to estimate the failure pressure along the generator as:

where Xnm equals unity if the value of Pnm is the minimum of all estimates, else Xnm equals zero.

(G.9)

(G.10)

5.0 DB0 2.5 DB0

Ì 3603;---

B0D

------- (in degrees)=

P P

d

B

d

B Q

i

i

i

i

=−

⎛

⎝⎜

⎞

⎠⎟

−⎛

⎝⎜

⎞

⎠⎟

0

0

0

1

1

Ql

DBi

i= +⎛

⎝⎜⎜

⎞

⎠⎟⎟1 0 31

2

.

0

P X P

m n

m N

n

N

f

1

==

=

=∑∑ nm nm.

l l l snm m i i

i n

i m

= + +( )=

= −∑

1

d

d l

lnm

n

m

nm

= =

=∑ i i

i

i

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Figure G.4 — Corrosion depth adjustment for flaws with background corrosion

Figure G.5 — Projection of circumferentially interacting flaws

l

d

>0.1B0

B0

Axial projection linesBox enclosing flaw

Project onto line

z

z

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Figure G.6 — Projection of overlapping sites onto a single projection line

Figure G.7 — Combining interacting flaws

di

li si

Projection line

Section through projection l0ine

ln

dn

sn lm

dm

ln + 1

dn + 1dn dmdn + 1

sm - 1

l l l snm m i i

i n

i m

= + +=

−∑ ( )

= 1

d

d l

lnm

i i

i n

i m

nm

= =

−∑

= 1

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Figure G.8 — Example of the grouping of adjacent flaws for interaction to find the grouping which gives the lowest estimated failure pressure

1

1-2

1-3

1-4

2

2-3

2-4

3

3-4

4

GROUP

Flaw 1 Flaw 2 Flaw 3 Flaw 4

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i) Calculate the failure pressure for the combined flaw from n to m (Pnm), (see Figure G.7), using lnm and dnm in the single flaw equation (see G.4):

where

j) The failure pressure, for the current projection line, is taken as the minimum of the failure pressures for all of the individual flaws (P1 to PN) and for all the combinations of individual flaws (Pnm), on the current projection line:

Pf = min{P1, P2, … PN, Pnm} (G.12)

k) Calculate the safe working pressure (Psw) for the interacting flaws on the current projection line:

Psw = fc × Pf (G.13)

l) The safe working pressure for the section of corroded pipe or vessel is taken as the minimum of the safe working pressures calculated for each of the projection lines around the circumference.

m) Repeat steps c) to m) for the next adjacent section of the corroded component.

G.7 Circular locally thinned areas in uncracked spherical shells (Sims et al [136])

A lower bound failure pressure of a locally thinned spherical shell, Pf, can be estimated from:

where

where

NOTE Sims et al [136] use finite element models of elastic linear-hardening-plastic materials with failure defined as 2 % plastic strain. Equation (G.14) is a fit to the finite element results. Hence, the use of yield strength (as opposed to the use of the ultimate tensile strength in other parts of this annex) in equation (G.14) is consistent with the analysis by Sims et al [136].

(G.11)

(G.14)

dLTA is the diameter of a circle circumscribing the locally thinned area (see Figure G.9);È being given by the following:

Range of application: 0.25 < Bmin/B < 1 0 < dLTA/D < 0.95

P P

d

B

d

B Q

nm

nm

nm

nm

=−

⎛

⎝⎜

⎞

⎠⎟

−⎛

⎝⎜

⎞

⎠⎟

0

0

0

1

1

Ql

DBnm

nm= +⎛

⎝⎜⎜

⎞

⎠⎟⎟1 0 31

2

.

0

Pf4ÖY

D----------

Bmin

1 1ß--- 1

Bmin

B------------–⎝ ⎠

⎛ ⎞–----------------------------------------×≥

= . B

B

d

D1 2 3

2 3

+min LTA

⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

.

B

B

B

B

B

B= 55 168 + 189

4

min

3

min

2

min⎛⎝⎜

⎞⎠⎟ − ⎛

⎝⎜⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

−− ⎛⎝⎜

⎞⎠⎟

B

B100 + 25

min

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G.8 Further assessment

The intent of this guidance is to provide simplified conservative procedures for the assessment of corroded pipes or vessels. If the corrosion flaws are not found to be acceptable using the procedures given in this guidance, then the user has the option of considering an alternative course of action to assess the remaining strength of the corroded pipe or vessel more accurately. This could include, but is not limited to detailed finite element analysis and/or full scale testing. The use of finite element analysis to analyse corrosion flaws is discussed in G.9.

G.9 Recommendations for conducting non-linear finite element analysis of corrosion flaws in pipes and pressure vessels

G.9.1 General

The failure pressure of an internally pressurized ductile steel pipe or pressure vessel with either local or general metal loss flaws, such as corrosion, can be predicted by numerical analysis using the non-linear finite element method with a validated failure criterion (Fu and Kirkwood [135]). Complex flaw shapes and combined loading conditions can be considered in the analysis.

Figure G.9 — Cross section of locally thinned area geometry on spherical shell

dLTA diameter (length)of local thin area

Top viewActual thin area

BB min

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The analysis consists of four major steps (see G.9.2 to G.9.5), which are as follows.

a) Create a finite element model of the corroded pipe or vessel, using information on the flaws detected, the measured material properties and the structural constraints and loads applied.

b) Perform a non-linear large-deformation stress analysis using a validated finite element analysis software package and an appropriate analysis procedure.

c) Examine analysis results obtained from the stress analysis.

d) Determine the failure or critical pressure value based on the variation of local stress or strain states with reference to a validated criterion.

Accuracy of the failure prediction depends on a number of factors. At every step of the analysis, judgement is required. Knowledge of structural analysis and materials behaviour, and experience in non-linear finite element analysis, are essential.

A method for predicting the failure pressure has been developed and validated against 93 ring tension and vessel burst test results (Batte et al [133] and [134]).

A narrow flaw may experience a high stress gradient across the remaining ligament, which can result in crack initiation well before the gross yield of the remaining ligament. This may consequently lead to failure by crack growth without significant necking deformation. Therefore, the failure criterion given in G.9.5 may not be applicable. Examples of such flaws are those with circumferential widths less than the wall thickness and 10 % of the flaw axial length.

G.9.2 Modelling

The use of actual pipe or vessel and flaw sizes is preferable but it is not always necessary. A flaw shape can be simplified, but its maximum dimensions (length, width and depth) need to be retained. Account should also be taken of possible uncertainty in the measurement of the flaw shape and dimensions.

The minimum value of the wall thickness measured in a local region around the flaw should be used.

The flaw simulated in the finite element model can be placed in a convenient position around the circumference of the pipe or vessel if the actual flaw is not likely to be affected by any specific supporting condition or constraint.

The analyst should use experience and judgement on the flaw shape simplification, the mesh density through the flaw ligament and the extent of the mesh refinement area. In general, the use of a coarse element mesh will reduce the computational costs as well as the effort in flaw modelling, but it will give less accurate stress analysis results with generally lower magnitudes. Consequently a coarse element mesh will result in a higher predicted, and possibly unconservative, failure pressure value. Sensitivity and convergence studies may be required to demonstrate that adequate mesh design and analysis procedures have been used.

A coarse finite element mesh can be used for the pipe or vessel wall away from the flaw. The mesh density should be gradually increased towards the local area containing the flaw. It is recommended that two to four layers of elements are provided through the minimum ligament of the flaw. The longer the circumferential length of the flaw, the fewer the element layers required. Solid, second-order elements, such as 20-node hexahedra, should be used. Severe element distortions, especially at the minimum ligament of the flaw, should be avoided.

The length of pipe or vessel section simulated should be at least five times the pipe diameter or the flaw axial length, whichever is the longer.

To apply appropriate boundary conditions to the pipe or vessel section needs an understanding of the general deformation of the damaged pipe under its specific operating condition and the experience in idealization of structural supporting conditions. For buried or anchored straight pipeline sections, the boundary conditions should be such as to restrict axial displacement of the pipe.

A non-linear, large-deformation finite element analysis requires the use of a true stress/true strain relationship. This should extend at least to the point corresponding to the material’s ultimate tensile strength. A true stress/true strain curve can be constructed from true stresses and strains measured from a tensile test on a round bar specimen. The test specimen(s) should be taken from the pipe or vessel transverse direction and the tensile tests should be conducted at a temperature relevant to the operating condition. The true stress value corresponding to the material’s ultimate tensile strength is used when determining failure pressure.

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Alternatively, an approximation to a true stress/true strain curve can be obtained by converting an engineering stress-strain curve and linearly extrapolating the curve from the point at its tensile strength in a log-log plot. Such replacement generally gives lower stress values, particularly at a high strain level. It will lead to a more conservative failure prediction.

G.9.3 Finite element stress analysis

The finite element stress analysis should be performed using validated software, with a non-linear analysis procedure that incorporates both incremental plasticity and large displacement theory18).

It is recommended that the von Mises yield criterion and associated flow rule be used in the non-linear stress analysis. If the pipe is subjected to quasi-static loading, isotropic hardening should be selected if this option is available. Severe cyclic loading requiring consideration of the cyclic stress-strain behaviour and more complex hardening rules is outside the applicability of this annex (see G.2.3).

Static stress analysis procedures (ignoring dynamic or inertia effects) should be used. In the static stress analysis, the increment of the pressure load applied to the pipe wall has to be sufficiently small. Alternatively automatic load incrementation algorithms may be used.

G.9.4 Assessment of analysis results

Results of von Mises equivalent stress variations and/or equivalent plastic strain variations against pressure values should be obtained from the finite element stress analysis. The stress and/or strain values from one or more positions within the flaw, at which high von Mises equivalent stresses are experienced, should be examined.

In general, the stress variations with increased pressure load will show three distinct stages. The first is a linear response progressing to a point when the elastic limit is reached. At this point a second stage is evident, i.e. a stage where plasticity spreads through the ligament while the maximum von Mises equivalent stress remains approximately constant or increases slowly. This is due to constraint from the surrounding pipe wall. The third stage is dominated by material hardening and begins when the von Mises equivalent stress in the entire ligament exceeds the material’s yield strength. Once this stage is reached, the whole ligament deforms plastically but failure does not occur immediately due to strain hardening.

The overall stress and deformation responses in the model should be carefully checked. Errors may occur due to the application of incorrect constraints or the use of inappropriate elements.

G.9.5 Prediction of failure pressure

Batte et al [133] and [134] have shown that the failure pressure can be determined from the von Mises equivalent stress through the minimum ligament of the flaw. The failure pressure is considered to be the pressure that causes the averaged stress in the ligament to be equal to the material’s tensile strength from a uniaxial tensile test.

The accuracy of the above failure prediction relies on the accuracy of the stress analysis. The analyst should justify the adequacy of the analysis methods and the computer software, and that the pipe modelling and stress analysis results are correct.

18) Detailed numerical and experimental studies show that the stresses do not vary in proportion to the internal pressure load. At the state close to failure, localized but large deformation is evident leading to necking and outward bulging.

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Annex H (normative) Reporting of fracture, fatigue or creep assessments

H.1 General

When reporting the results of an assessment carried out in accordance with the procedures described in this guide, it should be noted that the report forms part of the quality audit. Reference should be made to the standards and quality systems used. The following information should be listed together with comment on uncertainties and reliability.

H.2 Fracture assessments

H.2.1 Analysis details

Level of analysis (1A, 1B, 2A, 2B, 3A, 3B or 3C), K or CTOD route through procedure and consideration of lower yield plateau.

H.2.2 Input data

a) Loading conditions

Normal operation, fault or transient conditions, 100 year storm, etc.; additional loads and stresses considered (e.g. system stresses, residual stresses); categorization of loads and stresses; stress analysis method (finite element, photo-elastic, classical analysis); temperature.

Input parameters: Pm, Pb, Qm, Qb, SCF.

b) Material properties

Material specification, weld procedure; tensile properties, weld metal and/or parent material yield strength and ultimate strengths at temperature of interest, stress-strain data for Levels 3B and C assessments; fracture toughness at temperature of interest; whether data obtained by direct testing or indirect means; source and validity of all data.

Input parameters: ÖY, Öu, E, ¸mat, Kmat.

c) Definition of flaw

Flaw type, location, orientation, shape and size; allowance for sizing errors; whether recharacterization of flaw undertaken.

d) Flaw growth

Whether any allowance made for crack extension by sub-critical crack growth mechanism (e.g. ductile tearing, fatigue, creep, stress corrosion); the crack growth laws employed.

e) Plastic limit load

Source of limit load and net section stress solutions (e.g. established analysis, non-linear finite element analysis, scale model testing); whether local and/or global collapse considered.

f) Stress intensity factor solution

Reference in Annex M: source of K solution not included in Annex M (e.g. published solution, finite element analysis).

H.2.3 Results

Results for each assessment undertaken, assessment points (Sr, Kr or Æ¸r) for Level 1, (Lr, Kr or Æ¸r) for Level 2, assessment loci (Lr, Kr or Æ¸r) for Level 3; assessment points/loci should be displayed on the appropriate failure assessment diagram; reserve factors.

H.2.4 Sensitivity analysis

Input parameters against which sensitivity studies undertaken (e.g. flaw size, material properties, loading conditions); results of each individual study.

Known conservatisms incorporated in the assessment route should be listed. In addition, all departures from the recommendations laid down in this guide should be reported and justified. A separate statement should be made about the significance of potential failure mechanisms remote from the flawed areas and failures of the flawed area by mechanisms other than fracture (see Clauses 8, 9 and 10).

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H.3 Fatigue assessments

H.3.1 Method and criterion of acceptance

General procedure using fracture mechanics (e.g. to show that a flaw will not grow to a critical size in a specified time) or simplified procedure using quality category S-N curves (e.g. to show that a flaw has a longer fatigue life than an adjacent standard weld detail), in which case the required quality category should be stated.

H.3.2 Input data


Load spectrum, additional loads and stresses considered (e.g. misalignment, residual stresses), categorization of loads and stresses; stress analysis method (e.g. elastic theory, finite element analysis, experimental); cyclic frequency.

Input parameters: %Pm, %Pb, %Qm, %Qb, km.

b) Operating conditions

Temperature, environment, etc.

c) Material properties

Material specification, tensile properties.

Input parameters: ÖY, E.

d) Definition of flaw

Flaw type, location, orientation, shape and size; allowance for sizing errors; whether recategorization of flaw undertaken.

e) Planar flaw growth

Fatigue crack growth law; fatigue crack growth threshold.

f) Limit to crack growth

Critical crack size and shape (in which case state criterion); plate thickness, etc.

g) Stress intensity factor solution

Reference in Annex M: source of K solution not included in Annex M (e.g. published solution, finite element analysis).

H.3.3 Results

Provide full details of the results, including any relevant graphs (e.g. crack length versus number of cycles) and conclusions drawn.

Reference should be included to any other assessment (e.g. fracture assessment) of the flaw being considered.


Input parameters against which sensitivity studies undertaken (e.g. flaw size, material properties, loading conditions); results of each individual study.

Known conservatisms incorporated in the assessment should be listed. In addition, any departures from the recommendations laid down in this guide should be reported and justified.

H.4 Creep assessments

H.4.1 Analysis details

In the analysis, any incubation period, the extent of crack growth and damage accumulation in the ligament ahead of the crack tip are estimated for a component which undergoes creep.

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H.4.2 Input data


These should include those specified in H.2.2 and H.3.2, together with the relevant temperature history.

b) Material properties

Creep deformation, creep rupture and creep crack growth properties of weld metal, HAZ and/or parent material as appropriate; source and validity of all data.

Input parameters: C, D½, n, b, q, Tr, ¸ix, ¼f.

c) Definition of flaws

As for H.2.2.

d) Flaw growth

Crack growth laws employed, to include all mechanisms of sub-critical crack extension (see H.2.2 and H.3.2).

e) Creep fracture parameter, C*

Source of solution for C* (e.g. Annex T, published solution, finite element analysis); values of K, Öref, tR(ref) used to estimate C*.

H.4.3 Results

Results for loading and temperature conditions assessed to include: incubation period tix, plots of creep damage Dc and crack size versus time; checks on extent of fatigue crack growth and risk of fracture; assessment of margins against failure.


Input parameters against which sensitivity studies undertaken (e.g. flaw size, loading conditions, material properties, safety factor ¾c for use with creep data); results of each individual study.

Known conservatisms incorporated into the assessment should be listed. In addition, any departures from the recommendations laid down in this guide should be reported and justified.

Annex I (informative) The significance of weld strength mismatch on the fracture behaviour of welded joints

I.1 General

Welded joints, by their very nature, are highly inhomogeneous in both microstructural and mechanical property characteristics. The microstructure varies in different regions of the joint, both in the weld metal and in the heat-affected zone (HAZ). The overall yielding behaviour of a complete joint is governed by the properties of the relevant structural cross-section, taking account of the direction of loading relative to the joint and of the effects of constraint on yielding criteria. The fracture behaviour is controlled by microstructural effects (the local microstructure at the crack tip) and by physical effects (the applied stress intensity factor at the crack tip). The constraint conditions for the particular geometry further affect the relationship between loading and the resultant potential for fracture.

Differences in yield strength between the parent material and the weld metal can influence the joint behaviour such that the definition of toughness requirements for different service conditions is difficult. The effect of mismatch both on fracture toughness measurement and on flaw assessment procedures is addressed in the following sections. Where the state of present knowledge permits, specific recommendations are given, whereas for areas currently under investigation the potential problem areas are highlighted. In the following subclauses, mismatch is defined as a percentage, by the following expression:

(I.1)ÖY weld ÖY base metal–

ÖY base metal---------------------------------------------------------- 100×

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I.2 Effect of mismatch on fracture toughness measurement

I.2.1 General

Fracture toughness values in accordance with BS 7448 and BS EN ISO 12737 can be determined using both compact tension and bend specimens and the resultant value expressed in terms of K, CTOD or J. Further general guidance on fracture toughness determination for welds is given in Annex L.

I.2.2 KIC measurement in weld metal and HAZs

KIC values measured in weld metals are unaffected by the degree of yield strength mismatch, provided that yielding does not occur in the arms of the specimen. A similar situation is expected to hold for HAZs, provided that the width of the HAZ is greater than the plastic zone size and that the degree of yield strength mismatch is less than ±50 %.

I.2.3 CTOD and J measurements in weld metal

The greater potential influence of mismatch is on CTOD and J data, since these parameters often represent toughness measurements beyond the onset of plasticity. For standard deeply notched specimens, the range of mismatch conditions (in terms of strength and weld width), over which standard fracture toughness estimation procedures are valid, are given in BS 7448-2. For mismatch conditions outside this range and when non-standard, shallow notched specimens are employed, fracture toughness estimation methods may not be valid and alternative procedures may be necessary. These have not yet been standardized, but guidance can be found in Schwalbe and Koçak eds. [137] and Schwalbe et al [138].

I.2.4 CTOD and J measurements in HAZs (see also Annex L)

The comments in I.2.3 cannot be assumed to be applicable to HAZ notch locations. In such locations in mismatched joints the plastic deformation associated with the crack tip is not symmetrical. It is recommended that the test conditions (specimen thickness, constraint, degree of weld strength mismatch) be representative of the structural component being assessed.

Research work is ongoing to help define remaining areas of concern. These include shallow cracks, narrow welds, and the correct definition of weld width for practical welds for through-thickness and surface notched specimens.

I.3 Effect of mismatch on flaw assessment procedures

I.3.1 General aspects

Weld strength mismatch effects should not influence flaw assessment procedures using stress-based methods, if these are limited to purely elastic conditions. Mismatch, because of its effect on applied fracture mechanics parameters and the possible effect on material fracture toughness, Jmat or ¸mat, will influence assessments conducted for situations in which plasticity is developed at the crack tip.

The effect of weld strength mismatch in service applications depends on the type of weld and on its orientation relative to the applied stresses. It also depends on the dimensions of any crack-like flaws present relative to the width of the weld and to the width and thickness of the whole joint.

I.3.2 Effect of crack size and material work hardening rate

Crack size and material work hardening rate can have a strong influence on the fracture of welded joints and can therefore alter the extent to which mismatch effects are apparent. Deep cracks located in regions having low work hardening rates tend to favour net section yielding (NSY) behaviour, in which strain is concentrated into the plane of the flaw. Conversely, shallow cracks located in regions having high work hardening rates will tend to favour gross section yielding (GSY). In view of these effects, there may be some situations in which the mismatch effects seem to be more significant than others. There are likely to be situations where the fracture behaviour is close to the GSY condition and can be changed from NSY to GSY by weld metal strength over-match. Such situations are likely to be those in which shallow surface cracks are present in weld metal or HAZ regions.

I.3.3 Assessment of butt welds perpendicular to the applied tensile stress

The general effect of strength mismatch in flaw-free transverse butt welds, if the loading exceeds that necessary to cause yielding in whichever is the lower strength material, is to concentrate plastic strains into that material. If the loading does not reach this level, the only effect of the strength mismatch is on the level of residual stress present. The presence of flaws in the joint complicates this situation.

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The effect of planar flaws in butt welds that are transverse to the direction of stressing depends on their overall dimensions relative to the joint geometry. For through-thickness cracks at the centre line of the weld and contained wholly within weld metal of different strength from the parent material, the resultant yielding behaviour depends on the ratios of crack length to weld width, and crack length to plate width. Results from experimental and finite element analyses show that, for through-thickness cracks which are short compared to the plate width and shorter than the weld width, over-matching weld metal strength can protect the crack plane against net section yielding. This is because a yielding cross section may be available through the parent plate, which therefore yields first.

For through-thickness cracks, research has shown that adopting a homogeneous approximation of the lower strength material, all base metal for over-matched welds and all weld metal for under-matched welds, will always produce a conservative result for the assessment of welded structures.

With part-thickness cracks in transverse butt welds, the possibility of yielding has to be considered on the remaining ligament of the thickness as well as on the weld width and the net section width of the plate. In general, shallow part thickness flaws in over-matching weld metal will receive substantial protection against yielding, but they will be vulnerable in under-matching welds and the extent of this vulnerability cannot be accurately defined at present.

I.3.4 Assessment of butt welds parallel to the applied tensile stresses

The effects of weld strength mismatch in butt welds parallel to the direction of stressing are different from those for transverse butt welds. Flaws normal to the stress should be analysed using the lowest yield strength of the combination for conservatism, unless it can be shown that the flaw size is such that the plastic zone is wholly contained in a region of known strength level. It should also be noted that, in the as-welded condition, residual stress parallel to the weld would usually be of magnitude equal to the yield strength of the weld metal. Higher residual stress will therefore be present in over-matching welds and account may need to be taken of this in any flaw assessment.

I.3.5 Assessment of fillet welds

Very little account is usually taken of the effects of mismatch in fillet welds. The real stress state in such welds is very complex, but normal design procedures make simplified assumptions. Design strengths are often set significantly less than the corresponding ones for parent material of the same tensile yield strength, because fillet welds are considered to be subjected to a high shear stress component. Furthermore, very little account is taken of fracture toughness in fillet welds. It is usually found that failure of fillet welds is governed by yielding/ultimate strength on the minimum cross sectional area. In considering the effects of mismatch in strength, account should be taken of alternative failure paths through weld and parent material along the lines described above. Benefit for over-matching in transverse fillets should only be claimed if it can be demonstrated that failure will not occur at unacceptably low loads on a path through the parent material around the weld.

The strength of under-matching transverse fillet welds should be based on the weld metal strength and it should be noted that such welds cannot be expected to be able to absorb any significant structural deformation because of the short gauge lengths involved at the welds compared to the parent material.

I.4 Specific procedures for assessing effects of mismatch

The basic procedure for assessing the effect of flaws on fracture/plastic collapse under mismatch conditions is basically the same as the standard procedures given in Clause 7, except that the collapse load used to calculate Lr should be a mismatch limit load. In general the mismatch limit load, PL mis, depends on geometry, flaw size, flaw position and degree of strength mismatch. PL mis cannot be less than the limit load calculated assuming that the structure is homogeneous and made of the weakest material in the vicinity of the flaw. Solutions for limit load for mismatched components may be obtained from slip-line field analysis or using finite element methods. Some solutions have been published by Lei and Ainsworth [139], [140] and [141].

The procedure is implemented by using the following equation:

LrP

PL mis---------------=

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Annex J (informative) Use of Charpy V-notch impact tests to estimate fracture toughness

J.1 Introduction

Direct determination of fracture toughness by testing is always preferable, but where this is not possible an estimate of Kmat may be obtained from correlations with Charpy V-notch impact test data taken from material of the same general microstructural type (e.g. weld metal, HAZ, parent material) in which the flaw is situated. The orientation of the Charpy V-notch specimens should be such as to reproduce the fracture path that would result from the flaw under consideration.

Three correlations are described in J.2, each one is appropriate for ferritic steels and provides estimates of Kmat under quasi-static loading conditions. The three correlations are as follows.

a) A lower bound relation for lower shelf/transitional behaviour, where Charpy energy has been obtained at a single temperature (see J.2.1).

b) A relation for lower shelf/transitional behaviour based upon the master curve approach [144], where the Charpy temperature for an energy of 27 J (T27 J) or 40 J (T40 J) has been established (see J.2.2).

c) A relation that limits Kmat (estimated according to J.2.1 and J.2.2) to ensure that materials with low upper shelf Charpy energy are not assumed to have high fracture toughness (see J.2.3).

To ensure conservative estimates of fracture toughness, especially in steels with potentially low upper shelf fracture toughness, fracture toughness estimates shall be the lower of a) and c), or b) and c), as appropriate, at the service temperature.

Figure J.1 shows a flowchart for the selection of an appropriate correlation based on available data. All correlations described are between Charpy impact energy (measured on standard 10 mm × 10 mm, 2 mm deep V-notched specimens) and fracture toughness values in terms of Kmat. Where impact energy is from sub-sized Charpy specimens, the procedures described in J.3 should be used.NOTE 1 The units for Kmat in this annex are MPaÆm, in order to convert this into N.mm–3/2 units, multiply by 31.63.

NOTE 2 BS 7910:1999, Annex J (including Amendment 1:2000) provided a method of estimating T27 J from Charpy data obtained at other temperatures. This has been omitted from BS 7910:2005 because the procedure was found to be potentially unconservative owing to uncertainty in the shapes of Charpy transition curves [243].

J.2 Charpy/fracture toughness correlations

J.2.1 Lower shelf and transitional behaviour

Where Charpy results are available at the temperature at which Kmat is required, equation (J.1) [142] can be used to estimate fracture toughness.

(J.1)

where

NOTE Equation (J.1) is conservative with respect to equation (J.4) for temperatures below T27 J or T40 J but can be unconservative (at Pf = 0.05) at higher temperatures. However, the range of temperatures over which the unconservatism is present is minimized by the limit imposed by equation (J.5).

Kmat is the estimate of the fracture toughness (in MPaÆm);B is the thickness of the material for which an estimate of Kmat is required (in mm);Cv is the lower bound Charpy V-notch impact energy at the service temperature (in joules).

Kmat 12 Cv( 20 ) 2( 5 B⁄ )–[ 0.25 ] 20+=

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J.2.2 Lower shelf transitional behaviour based on the master curve

For ferritic steels, a correlation between the 27 J and 40 J Charpy transition temperatures (T27 J and T40 J) and the 100 MPaÆm fracture toughness transition temperature (T0) in 25 mm thick specimens is described by equations (J.2) and (J.3) [154].

T0 = T27 J – 18 °C (standard deviation = 15 °C) (J.2)

T0 = T40 J – 24 °C (standard deviation = 15 °C) (J.3)

where

T0 is the temperature for a median toughness of 100 MPaÆm in 25 mm thick specimens;

T27 J and T40 J are the temperatures for energies of 27 J and 40 J, respectively, measured in a standard 10 mm × 10 mm Charpy V specimen.

T0 is used to define the transition curve in the master curve approach [144]. The master curve approach allows for the following factors:

— thickness effect;— fracture toughness distribution;— shape of fracture toughness transition curve for ferritic steels and welds;— required probability of achieving a particular value of Kmat.

The fracture toughness transition curve is described by the master curve as follows:

where

NOTE 1 Equations (J.2), (J.3) and (J.4) are not applicable to ductile behaviour. Consequently, Charpy specimen fracture appearance at T27 J or T40 J needs to show a high crystallinity (~70 %).

NOTE 2 T27 J and T40 J are derived from the Charpy energy versus temperature transition curve. It is recommended that T27 J or T40 J be derived from a lower bound to the transition curve data because of scatter and the need to ensure a conservative estimate of Kmat.

NOTE 3 Reference Charpy energies of 27 J and 40 J have been chosen as they correspond to typical requirements in steel specifications. The original correlations were based on reference energies of 28 J and 41 J, but the difference is considered have an insignificant impact on the estimation of toughness according to the procedures described here.

(J.4)

Kmat is in MPaÆm;T is the temperature at which Kmat is to be determined (in °C);T0 is estimated from equations (J.2) or (J.3);TK is the temperature term that describes the scatter in the Charpy versus fracture toughness

correlation given by equations (J.2) and (J.3). For a standard deviation of 15 °C and 90 % confidence TK = +25 °C. A lower value for TK may be used if supported by experimental data for the material of interest;

B is the thickness of the material for which an estimate of Kmat is required (in mm);Pf is the probability of Kmat being less than estimated. The use of Pf = 0.05 (5 %) is recommended

unless experimental evidence supports the use of a higher probability for a given material.

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J.2.3 Validity limits

The validity of the correlation based upon the master curve approach for pressure vessel-type steels and structural steels is well established. Further examples of its application have been demonstrated [145] with data sets from parent plates, sections, linepipe, weld metals and HAZs.

A number of situations have been identified which could result in unconservative predictions. These include:

— cases where Charpy specimens exhibit unusual fracture behaviour, such as fracture path deviation (where the fracture propagates out of the region being tested). This has been observed in narrow welds such as those made by laser and electron beam welding);— presence of splits on the fracture surface;— through-thickness variation of microstructure and properties such that the Charpy specimen does not test the region of lowest toughness. This is more likely to be a problem in inhomogeneous materials such as weld metals and HAZs. This can be minimized by ensuring that the Charpy specimens test regions of suspected low toughness. Expert advice may be necessary to select such regions;— severely cold worked material.

In these instances, equation (J.4) may be inappropriate and expert advice should be sought.

J.2.4 Upper limit for Kmat

To avoid overestimating fracture toughness at the service temperature in materials with potentially low upper shelf Charpy energy, Kmat (estimated in accordance with J.2.1 and J.2.2) shall not exceed the value given by the following equation.

Kmat = 0.54Cv + 55 (J.5)

where

NOTE 1 Equation (J.5) is derived from PD 6493:1991, Appendix B which is now withdrawn from publication. This restricts the use of equation (J.5) to ferritic steels with yield strengths <480 MPa.

NOTE 2 An example of the use of equations (J.2), (J4) and (J.5) is as follows. A 60 mm thick ferritic steel with a yield strength of less than 480 MPa has a T27 J of –50 °C and a Charpy energy of 60 J at the service temperature of 0 °C. From equation (J.2), T0 is estimated as –68 °C. From equation (J.4), TK is 25 °C and Kmat is estimated as 90.8 MPaÆm at 0 °C for Pf = 0.05. Equation (J.5) provides an estimate of 87.4 MPaÆm at 0 °C. Therefore the best estimate for Kmat in accordance with this annex is 87.4 MPaÆm at 0 °C.

Kmat is the estimated fracture toughness (in MPaÆm);Cv is the lower bound Charpy V-notch impact energy at the service temperature for which Kmat is

required (in joules).

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J.3 Treatment of sub-size Charpy data

When Charpy data have been obtained from sub-size specimens (i.e. specimens which are identical to standard 10 mm × 10 mm specimens except in terms of thickness) because either:

a) the material being tested is less than 10 mm thick; or

b) the product shape does not permit full size specimens to be extracted;

the following procedure can be used to determine T27 J required in equation (J.2).

Compared with a full sized Charpy specimen, the sub-size specimen will have a lower transition temperature and lower impact energy capacity. The energy of 27 J in the full size specimen corresponds to a normalized energy in the net section of 34 J/cm2. The corresponding energy in the sub-size specimen is obtained by assuming that the normalized energy in the net section is 34 J/cm2. The temperature at which this energy is measured is shifted upwards by %Tss to correspond to a full size specimen.

%Tss = –51.4 ln{2(Bss/10)1/4 – 1} (J.6)

where

Bss is the sub-size Charpy specimen thickness (in mm).NOTE An example of the use of this procedure is as follows. A 5 mm thick sub-size Charpy specimen is removed from a 7 mm thick component. The equivalent to a normalized energy in the net section of 34 J/cm2 is 14 J. The temperature at which this energy is measured in the sub-size Charpy specimen is shifted upwards by 20 °C to give the equivalent T27 J in a full sized specimen. Equations (J.2) and (J.4) are then used to estimate Kmat. The dimension B in equation (J.4) is 7 mm.

Annex K (normative) Reliability, partial safety factors, number of tests and reserve factors

K.1 General

The application of deterministic fracture mechanics assessment procedures to the prediction of fitness for purpose requires the use of data that are often subject to considerable uncertainty. The use of extreme bounding values for the relevant parameters can lead, in some circumstances, to unacceptably over-conservative predictions of structural integrity. An alternative approach is to use structural reliability methods to allow for the uncertainties in the parameters and to assess the probability of failure of structures containing flaws. It should be noted that the question of the required reliability or safety margin for a particular application depends on the consequences of the failure and requires an overall risk assessment to be carried out.

Because of the increasing trend in industry towards this approach, guidance is included on the use both of partial safety factors aimed at different target reliability levels and of conventional reserve factors for the fitness for purpose assessment of engineering structures in design, fabrication and in-service inspection. However, adequate data may not always be available and extreme care should therefore be exercised before assumptions and approximations are made. The procedures described in this annex are given as a guide and are subject to the above limitations.

The equations used in Clause 7 (fracture assessment) and Clause 8 (fatigue assessment) should be regarded as modelling the occurrence of failure, if the input conditions and data are representative of real values. It is necessary, therefore, to consider whether additional safety factors are necessary to allow for uncertainties in input data and to have a means of assessing reliability.

The following subclauses offer the alternative of a partial safety factor treatment to achieve a given target probability of failure or a treatment to assess reserve factors for fracture assessment. It should be noted that there is no unique relationship between reliability and partial safety factors or reserve factors; the values given in this annex provide general guidance.

The application of appropriate partial safety factors to the relevant input quantities in a deterministic assessment of structural integrity provides a means of relating the deterministic analysis to a specific (target) probability of failure. If, after applying the partial safety factors, the resulting assessment is found to be acceptable with respect to the FAD, then, in principle, it may be inferred that the probability of failure of the component is at least as low as the target value. In the context of this document, the probability of failure refers to the probability of an assessment point falling outside the assessment line and not necessarily to the failure of the component or structure.

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The partial safety factors recommended in K.2 were derived after making certain assumptions about the FAD, the number of variables and their statistical distribution. Where these are considered to be inappropriate (for example, where the statistical distribution and/or the coefficient of variation is different from that specified in Table K.2, or where other variables need to be considered), an alternative is to carry out a probabilistic fracture mechanics analysis. Such an analysis should employ a limit state function based on the Level 2 or 3 assessment procedures and can be conducted using Monte Carlo simulation, first or second order reliability methods or integration methods, as considered appropriate. In using such procedures, special care needs to be taken to ensure that the statistical distributions employed are derived from data representative of the materials and conditions in the structure being assessed. Guidance on deriving the fracture toughness distribution is given in K.2.3.3.

K.2 Use of partial safety factors for fracture assessment

K.2.1 Partial safety factors — General

No additional partial safety factors are required for the screening assessment of Level 1, since the assumptions of uniform tension stress at the peak value and of full yield welding residual stress, together with the assessment diagram for Level 1, will provide conservative results. However, worst case estimates of stress level, flaw size and toughness should be used for Level 1 fracture assessments.

For Levels 2 and 3, no additional partial safety factors are required where worst case estimates are taken for stress level, flaw size and toughness, i.e. all partial safety factors should be taken as unity. This does not give a quantitative assessment of safety, however, and the partial safety factor approach given below may be adopted where the assessment is to Level 2A or 3A (for high work-hardening materials).

K.2.2 Partial safety factors on stress, flaw size, toughness and yield strength

The partial safety factors to be applied in assessments depend on the acceptable probability of failure with respect to fracture and plastic collapse. The partial safety factors described here are not appropriate when the expected mode of failure is creep. The acceptable probability of failure depends on the consequences of failure of the component being considered and on the variability and accuracy of the estimates of the main input data, namely fracture toughness, yield strength, stress level and measurement of flaw size.

For the purposes of this document, three failure consequences have been defined for redundant and non-redundant components, as shown in Table K.1 following the general principles recommended by the Nordic Committee on Building Regulations [148] and ISO Draft Guidelines for General Principles on Reliability for Structures [149].

Table K.1 — Target probability of failure (events/year)

All values in Table K.1 refer to probability of failure of individual components. The overall objective is to protect the complete structure against failure, accepting that it may be possible to tolerate local damage in some locations of redundant structures.19)

Partial safety factors on stress level, flaw size, toughness and yield strength to achieve the required probability of failure have been derived, using first order second moment reliability analysis methods, with the Level 2A FAD [150].

Failure consequences Redundant component

Non-redundant component

Moderate 2.3 × 10–1 10–3

Severe 10–3 7 × 10–5

Very severe 7 × 10–5 10–5

19) In redundant structures, failure of a single component may be accommodated by alternative load paths and, although undesirable and expensive, it may be possible to make a case for a higher target probability of failure for such a component compared to a critical one which would cause complete failure. “Moderate” consequences should be interpreted as potential financial costs without threat to life. If failure is predicted to be by fracture which may be brittle (Lr < 1) the consequences should be interpreted as “severe” or “very severe”. In other respects, “severe” consequences should be interpreted as any potential threat to human life and “very severe” consequences as a potential threat to multiple lives. If failure is expected to be by plastic collapse and provided that there is no threat to human life, the consequences may be interpreted as “'moderate”.

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The partial safety factors depend both on the target probability of failure required and on the scatter or uncertainty of the input data, as reflected by the coefficient of variation (COV) of the distribution representing the data. Results have been derived for different coefficients of variation of stresses, flaw sizes, fracture toughness and yield strength. The partial safety factors on stress and on yield strength match existing requirements for DD ENV 1993-1-1, EuroCode 3 at its target probability of failure of 7 × 10–5. These requirements assume COVs of 0.2 and 0.3 on dead and live load stresses respectively and of 0.1 on yield strength. The partial safety factors on flaw size and on fracture toughness have then been calibrated to give the target probability of failure for the worst combination of input data considered. Where it is required to make assessments for structures or components for which design codes have been used with different sets of load factors on stress, *Ö, and/or yield strength, *Y, from the DD ENV 1993-1-1, EuroCode 3 values assumed here, these factors should be retained for the assessment. The partial safety factor on fracture toughness from Table K.2 should be adopted, but a different partial safety factor on flaw size should be used. The flaw size factor should be determined by maintaining the product of *ÖÆ*a to have the same value as for the appropriate combinations of COV and target probability of failure in Table K.2.

The resulting recommendations for partial safety factors to be applied to the best estimate (mean) values of maximum tensile stresses and flaw sizes, and to the characteristic value of toughness (taken as mean minus one standard deviation) and yield strength (mean minus two standard deviations), are given in Table K.2. The stress levels and flaw sizes should be multiplied by the appropriate partial safety factor, whereas toughness and yield strength should be divided by the partial safety factor.

The partial safety factors in Table K.2 have been derived over a range of flaw sizes and fracture toughness values. The flaw sizes range from small surface flaws up to through thickness flaws of 200 mm length, with the restriction that the reduction in cross sectional area should not exceed 20 %. Fracture toughness values cover the range from 800 Nmm–3/2 to 6 000 Nmm–3/2. The most critical cases are those for large flaws and low toughness. The actual notional probability of failure will be less than the target value (i.e. safer) for other combinations of flaw size and toughness [150]. It should be noted that, in order for the partial safety factor approach to be used, it is considered that sufficient fracture toughness tests must be carried out to establish parameters of the underlying statistical distribution with confidence; the number of tests required is described in K.2.3.

Experimental validation studies (mainly based on wide plate testing) indicate that failure does not necessarily occur on the assessment line of the failure analysis diagram, but outside it. However, the partial safety factors in Table K.2 were derived assuming that the assessment line defines a failure condition. Consequently, the partial safety factors given in Table K.2 are likely to be conservative, i.e. they will give lower target notional probabilities of failure than those indicated in the table [151]. Since the degree of conservatism between the failure assessment diagram and actual failure conditions will depend on a number of factors, it is not considered appropriate to give general guidance on reductions here. Any case for reductions in partial safety factors on this basis must be calculated using reliability analysis methods and justified in any written submission.

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Table K.2 — Recommended partial factors for different target probabilities of failure

K.2.3 Fracture toughness values: number of tests

K.2.3.1 General

The number of fracture toughness tests necessary for an assessment depends on the scatter and on the type of assessment required. When a deterministic assessment is conducted, the characteristic fracture toughness value is usually taken as the minimum value obtained from three tests, or the equivalent to the minimum of three as described in 7.1.5.6 and K.2.3.2. When there is a sufficient number of test results available, a characteristic toughness value can be derived from a statistical treatment of the data, as described in K.2.3.2 and K.2.3.3. Analyses may then be conducted with these data either by the use, in the assessment, of worst case estimates of stress level, flaw size and strength or by the use of partial safety factors.

Where there is a requirement to estimate reliability either using the partial safety factor approach, as described in K.2, or using a probabilistic approach, as outlined in K.1, the fracture toughness values used need to be derived from a statistical distribution fitted to the data. Procedures for fitting statistical distributions are described in K.2.3.3. The distribution is then used either to select a characteristic value for which a partial safety factor is applied, or to select parameters for a probabilistic assessment.

p(F) 2.3 × 10–1 p(F) 10–3 p(F)7 × 10–5 p(F)10–5

¶r = 0.739 ¶r = 3.09 ¶r = 3.8 ¶r = 4.27

Stress, Ö (COV)Ö *Ö *Ö *Ö *Ö

0.1 1.05 1.2 1.25 1.3

0.2 1.1 1.25 1.35 1.4

0.3 1.12 1.4 1.5 1.6

Flaw size, a (COV)a *a *a *a *a

0.1 1.0 1.4 1.5 1.7

0.2 1.05 1.45 1.55 1.8

0.3 1.08 1.5 1.65 1.9

0.5 1.15 1.7 1.85 2.1

Toughness, K (COV)K *K *K *K *K

0.1 1 1.3 1.5 1.7

0.2 1 1.8 2.6 3.2

0.3 1 2.85 NP NP

Toughness, ¸ (COV)¸ *¸ *¸ *¸ *¸

0.2 1 1.69 2.25 2.89

0.4 1 3.2 6.75 10

0.6 1 8 NP NP

Yield strength (COV)Y *Y *Y *Y *Y

0.1 1 1.05 1.1 1.2

NOTE 1 ¾Ö is a multiplier to the mean stress of a normal distribution.

NOTE 2 ¾a is a multiplier to the mean flaw height of a normal distribution.

NOTE 3 ¾ K or ¾ ̧ are dividers to the mean minus one standard deviation value of fracture toughness of a Weibull distribution.

NOTE 4 ¾Y is a divider to the mean minus two standard deviation value of yield strength of a log-normal distribution.

NOTE 5 These partial safety factors may not be appropriate for other statistical distributions or coefficients of variation (COV), see Nordic Committee on Building Regulations [148].

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K.2.3.2 Deterministic assessment

For the screening assessment of Level 1, as described in 7.2, the lowest of three test results may be used, subject to the overall recommendations of 7.1.5 and particularly 7.1.5.6 on scatter. If the scatter limits of 7.1.5.6 are not satisfied for a Level 1 assessment, it is recommended that a further three tests on samples from the same source should be carried out. The second lowest of the full set of six results should be used for the assessment [152].

For the normal and tearing instability assessment methods of Levels 2 and 3 respectively, the lowest of three test results may also be used (subject to the scatter limits of 7.1.5.6).

Where additional test results are available, and the assessment is to be conducted to Level 2, the equivalent to the minimum of three tests may be used, as given in Table K.3 [152]. These have not been shown to be applicable to tearing instability analyses carried out to Level 3.

If more than 15 results are available, a statistical distribution is fitted to the data, as described in K.2.3.3, and the mean minus one standard deviation value is the ¸mat or Kmat used in the assessment. Where there is sufficient confidence in the data, the statistical distribution may be fitted to less than 15 results.

These statistical analyses assume that all the data represent one homogeneous group, and that all available results are included in the group. It is recommended that checks be made to satisfy these two conditions. In particular, attention is drawn to the variability of results in HAZs (see 7.2.5.1, 7.2.6 and Annex L) and additional tests may be necessary to allow for this.

Table K.3 — Equivalent fracture toughness values to the minimum of three results [152]

K.2.3.3 Fracture toughness to be used with partial safety factors and probabilistic assessment

For the normal assessment method to Level 2, either where the partial safety factors are applied, or where a probabilistic approach is used, fracture toughness values are derived from a statistical distribution fitted to the data. In order to fit a distribution with confidence, it is usually necessary to have at least 10 results [153]. The results should represent one homogeneous group, as required in K.2.3.2. Standard statistical methods may be employed to obtain the parameters for the best fit to the data. Experience indicates that most fracture toughness data follow either a log-normal or a Weibull distribution. If the data set includes maximum load fracture toughness values or results from prematurely terminated tests, these should not be excluded but should be treated as censored non-failures in the statistical analysis. In such cases it is recommended that maximum likelihood statistical methods be used.

Procedures for fitting K fracture toughness data to a Weibull distribution are described in ASTM E1921 [154]. These may be used, provided that the data fit the Weibull model described.

The mean minus one standard deviation, derived from the best fit to the data, is the characteristic value (¸mat or Kmat) for deterministic analyses and analyses using partial safety factors. If the coefficient of variation (standard deviation divided by the mean) is out of the range of values given in Table K.2, consideration should be given to one or other of the following:

a) conduct more tests (to characterize the distribution and mean better); or

b) carry out a probabilistic analysis to estimate the probability of failure.

Number of fracture toughness results Equivalent value

3 to 5 Lowest

6 to 10 Second lowest

11 to 15 Third lowest

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K.3 Sensitivity analyses for fracture assessments

K.3.1 General

Confidence in assessments performed in accordance with this standard can also be gained in two stages by the use of reserve factors. The use of lower bound material data and collapse load equations, together with upper bound loads, flaw sizes and stress intensity factor values, provides the initial confidence. This should then be reinforced by investigating the sensitivity of the assessment point to variations of appropriate input parameters. Sensitivity analyses are facilitated by considering the effect that such variations have on reserve factors.

K.3.2 Reserve factors

Reserve factors are used to illustrate safety margins between the cases being assessed and the limiting conditions for fracture assessments. Reserve factors will be influenced by the treatment of input data and by the use of partial safety factors and, as such, can be used to assess the results of sensitivity analyses. This is discussed below for reserve load factors.

Reserve factors for a component may be expressed with respect to any input parameter. Frequently, the most significant parameter considered is the applied load. The load factor, FL, is defined as the ratio of the load that would produce a limiting condition to the applied load in the assessed condition.

For a given assessment point (or locus for a Level 3 tearing analysis), (Lr, Kr or Æ¸r), the limiting load is determined by changing the value of the specified load until the assessment point lies on the failure assessment line. When the structure is subjected to one primary (P) stress only, this may be done by scaling the assessment point linearly along a radius from the origin, as shown in Figure K.1. When the structure is subjected to more than one stress, only the stress of interest should be changed. If both primary (P) and secondary (Q) stresses exist, allowance should be made for the change in the value of the parameter Ô (Annex R) with Lr. A simple graphical method for this is shown in Figure K.2.

Figure K.1 — Evaluation of FL for a single primary stress

1.0

00 1.0 Lrmax

Lr

Kr

A

B

FL = 0B0A

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a) b)

c)

FL can be determined from a), b) and c) using the following equation:

FL = LrC/LrB.

NOTE If LrC < 0.8 or LrB > 1.05 this reduces to FL = AC/AB

LrC and LrB can be determined from the graphical constructions illustrated in examples a), b) and c). The following is a description of how to construct the graphs.

i) ii) iii) iv) v) vi) vii)

B is the assessment point of interest. A is the assessment point for zero applied load but plotted for Ô having the value appropriate to the load at point B. Draw line ABM on which X has an Lr value of 0.8 and Z has an Lr value of 1.05. Point Y is vertically below Z at a distance equal to the Ô contribution to the assessment point B. Draw YN parallel to ZM. Connect Y to B or X whichever has the higher Lr value. C is the point where ABXYN or AXBYN crosses the assessment curve.

These graphical constructions work for the situation of a single primary stress application which results in an assessment point B lying inside the failure assessment line.

Figure K.2 — Three scenarios for the graphical determination of FL in the presence of Ös loads

MZ

X

CY

NBA

1.0

1.0

00Lrmax

Kr

or

r

LrC

Lr

LrB

ρ

δ

MZ

XC

Y

N

B

A

1.0

1.0

00

Lr

Lrmax

ρ

Kr

or

rδ

MZX CY NBA

1.0

1.0

00

Lr

= O

Lrmax

ρKr

or

rδ

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Similar methods may be used to calculate reserve factors on other parameters, sample definitions being the following:

a) Reserve on flaw size, Fa, is the ratio of the limiting flaw size to the flaw size of interest.

b) Reserve on fracture toughness, FK, is the ratio of the fracture toughness of the material being assessed to the fracture toughness to produce a limiting condition.

c) Reserve on yield strength, FY, is the ratio of the yield strength of the material being assessed to the yield strength to produce a limiting condition.

K.3.3 Level 2 assessments — Sensitivity analysis using reserve load factors

The reserve load factor, FL, can be plotted against the variables of interest as shown in Figure K.3. The sensitivity of FL to the variables, taking into account the range of uncertainty, can then be assessed to determine the safe loading conditions, as discussed in K.3.5.

K.3.4 Level 3 assessment — Sensitivity analysis using reserve load factors

A sensitivity analysis using reserve load factors can be carried out as follows.

a) The reserve factor on load, FL, can be plotted as a function of postulated crack growth, ¹a, keeping all other variables constant [Figure K.4a)]. Note that the extent of this plot will depend upon the crack growth range of the toughness resistance curve. If this is sufficiently extensive, a maximum will be obtained in the FL-¹a plot, Figure K.4b). This corresponds to the limiting condition being a tangency condition.

b) The analysis for different values of ao should be repeated to establish the sensitivity of the results to initial crack size and plot these on the same graph. Connect equivalent points on each plot to construct loci of FL as a function of initial crack size for different values of %a, see Figure K.4c).

c) The effects of changing the other variables should be explored. In judging what reserve factors are required, account needs to be taken of the range of J or ¸ controlled crack growth, and the significance of exceeding it. Guidance is given in 7.6.

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Figure K.3 — Typical load factor variation graphs

1.0

0Flaw size, a

Limitingcrack size

A

B

1.0

00 1.0 Lr

a

FL = 0B0A

Kr

or

r

1.0

0

Limitingvalue

Fracture toughness

A

B

1.0

00 1.0 Lr

FL = 0B0A

Res

erve

load

fact

or F

LR

eser

ve lo

ad fa

ctor

FL

δ

Kr

or

rδ

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a) Limited toughness resistance b) More extensive resistance

c) Graph of load factor as a function of flaw growth for various initial flaw sizes

Figure K.4 — Load factor variation with flaw size Level 3 analysis

a0

Crack size, a

∆a1Res

erve

load

fact

or, F

L

∆a1

a0

Crack size, a

Res

erve

load

fact

or, F

L

∆a1

∆a1

∆a1Initiation

Crack size, a

1.0

Res

erve

load

fact

or, F

L

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K.3.5 Sensitivity analyses

To establish confidence that a specified loading condition is acceptable, it is advisable to perform a sensitivity analysis. Such an analysis should evaluate the sensitivity of the results to variations in the input parameters, taking into account all uncertainties and known variations. The parameters of interest are the following:

— applied loads;— thermal and residual stresses;— flaw size and characterization, including possible changes in aspect ratio during ductile tearing;— material properties data, as used in the fracture assessment, residual stress estimate, etc.

Sensitivity analyses may be performed in the way most convenient for the user, but will be somewhat dependent on whether the analysis is Level 1, 2 or 3.

K.3.6 Guidance on determination of safe loading conditions

The required factor of safety or reserve factor depends on each individual situation and the conditions for which a component is being assessed. As a general guide, the reserve factor needs to be at least sufficient to prevent realistic variations in parameters or analysis methods, whether singly or combined, leading to assessment points that violate the limiting conditions.

If an assessment is particularly sensitive to any parameter in the region of interest, then the required safety factor should be large enough to avoid this condition. When the graphical procedures suggested in K.3.2 are used, this state is recognized by steep gradients in the region of interest. Figure K.5 compares qualitatively the preferred and non-preferred conditions.

When a genuine lower bound assessment has been performed, i.e. all contributing parameters have been bounded, including the failure assessment line itself (as in Levels 2B, 3B or 3C), any uncertainty in individual contributions can only move an assessment point in one direction. That is to provide higher factors and therefore increased confidence in the component. Under such circumstances, a factor of one against the selected limiting conditions will be sufficient to avoid failure, although a sensitivity analysis is still recommended to demonstrate this and to establish the level of confidence.

A common reason for requiring high values of reserve factor is uncertainty in material properties. Bounded values are estimated from a finite number of tests and are thus associated with a particular statistical significance. The lower this is, the higher the required reserve factor. In addition to this type of material variability, the assessed state may be close to a mode change that could drastically alter material properties. In particular, the ductile-brittle transition may induce cleavage in an otherwise ductile process, and higher factors may be required in these conditions.

When fracture toughness values are obtained from Charpy correlations (see Annex J), a distinction needs to be made between lower bound and best estimate correlations, and whether the correlation is directly applicable or was obtained only for a similar material.

In a Level 3 analysis, there is doubt about using toughness data beyond the range of J or ̧ -controlled crack growth and, in general, the reserve factor of interest is that at the limit of valid data (7.6). However, analysis beyond this limit may give confidence in the adequacy of reserve factors by demonstrating that the factors are not sensitive to the imposition of this limit, or that the factors would be expected to increase by considering larger crack extensions.

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a) Sensitivity analyses with respect to flaw size, a

b) Sensitivity analyses with respect to toughness

NOTE In both a) and b), the load factors in the “preferred” and “non-preferred” situations are the same, but the margin against limiting flaw size in a) or toughness in b) is smaller in the “non-preferred” situation.

Figure K.5 — Preferred sensitivity curves

FL

1.4

1.0

Assessedcondition Limiting

condition

FL

1.4

1.0

Assessedcondition

Limitingcondition

a a

Preferred Non-preferred

FL

1.3 1.3

1.0

Assessedcondition

Limitingcondition

FL

1.0

Assessedcondition

Preferred Non-preferred

Toughness Toughness

Limitingcondition

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There are many other circumstances that might lead to the requirement for increased reserve factors. Some are listed below.

— The true loading system has to be simplified or assumptions have to be made in order to analyse the component unless these can be clearly shown to result in upper bound values.— The non-destructive examination capabilities are indistinct. — Flaw characterization is difficult or uncertain.— The assessed loading condition is frequently applied or approached.— Little pre-warning of failure is expected. Forewarning is more likely in cases of ductile failure and in particular a leak before break condition may provide a great deal of confidence.— There is a possibility of time dependent effects.— Changes of operational requirements are possible in the future.— The consequences of failure are unacceptable.

It should be remembered that reserve factors are dependent on each other and should not be considered in isolation. There can be no generally applicable value of acceptable reserve factor. Each case or class of problem has to be judged on its own merits.

Annex L (normative) Fracture toughness determination for welds

L.1 General

Weldment fracture toughness data are required for the fracture assessment of flaws in welds. The assessment of flaws such as heat affected zone (HAZ) hydrogen cracking, lack of side wall fusion flaws and in-service fatigue cracks which may propagate through the HAZ require a knowledge of HAZ toughness data, whilst weld metal toughness data are necessary for assessing weld metal hydrogen cracks, solidification cracks, lack of root fusion flaws, etc.

This annex gives guidance on the formulation of test programmes and test procedures suitable for the assessment of flaws in welds in steel. The fracture toughness test procedures should be in accordance with BS 7448-2.

The determination of HAZ toughness presents particular problems owing to the small size and heterogeneous nature of the HAZ. Care should be taken to ensure that the test has sampled the correct HAZ microstructure at the crack tip. Furthermore, fracture toughness tests on HAZ material generally show a higher degree of scatter than tests on parent metal or weld metal. This is due to the inherent variability of the HAZ microstructures, the different proportions of each microstructure sampled in each test and the formation of low toughness microstructures termed local brittle zones (LBZs) in some welds. Apart from the practical consideration that several tests may be required to sample the HAZ microstructure of interest, the higher degree of scatter may necessitate carrying out a greater number of tests and employing statistical methods in order to characterize HAZ toughness effectively.

There are also problems associated with determining weld metal toughness. These arise because weld metals are also heterogeneous. In particular root toughness may differ markedly from that remote from the root.

L.2 Test philosophy

Fracture toughness tests can be carried out to provide data for general purpose assessments of unspecified flaws or to provide data for the assessment of specified flaws.

Fracture toughness tests on welding procedure qualification plates are normally used to characterize weldment toughness. Such data may be used for assessments where the dimensions and location of the flaws in the structure are not known (e.g. assessments of post-weld heat treatment or inspection requirements). For major construction projects involving large numbers of welding procedures, it may be preferable to plan a programme of tests covering specific material variables and welding parameters (detailed in L.4.1 and L.4.2) rather than test individual welding procedures. Where appropriate, results already obtained from earlier test programmes can be used instead of generating new data. The results of test programmes are often more amenable to statistical analysis and may give a higher degree of confidence for critical applications where the consequences of failure are severe.

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Non-standard, shallow crack fracture toughness tests can also be used to provide data for a specific assessment, where the dimensions and location of the flaw are known. However, appropriate fracture toughness assessment procedures should be used because those given in BS 7448 and BS EN ISO 12737 are only appropriate for deeply notched specimens. Further guidance is provided in [157] and [158].

L.3 Microstructures in steel weldments

L.3.1 Heat affected zones

The base metal adjacent to the weld fusion line is subject to complex thermo-mechanical cycles during welding, which vary with the distance from the fusion line and the sequence in which individual weld beads are deposited. The base material is transformed into a range of different HAZ microstructures, which change with increasing distance from the fusion line and through the thickness of the joint. Immediately adjacent to the fusion line, the HAZ microstructure consists of a grain coarsened region (GCHAZ) which may be partially transformed by subsequent welding passes into grain refined (GRHAZ), intercritically reheated grain coarsened (ICGCHAZ), or subcritically reheated grain coarsened (SCGCHAZ) regions. Further from the fusion boundary, the HAZ microstructure changes to grain refined (GRHAZ), intercritical (ICHAZ), and subcritical (SCHAZ) regions, each of which is modified by subsequent welding passes.

For structural steels with minimum specified yield strengths up to 450 N/mm2, the lowest toughness regions of the HAZ are believed to be the grain coarsened HAZ (GCHAZ) adjacent to the fusion line and the boundary of the intercritical HAZ (ICHAZ) and the subcritical HAZ (SCHAZ). Both in these materials and in other steels, selection of the appropriate HAZ microstructure(s) to be tested should take account of available fracture toughness data and other relevant information.

L.3.2 Weld metals

There are similar variations in microstructures in weld metals. After the first run of a multi-pass weld has been deposited, each subsequent run creates heat-affected zones in the runs that precede it. However, the testing problems are generally less severe compared to HAZs, because it is easier to ensure that the various regions have been sampled by the fatigue crack tip. An important feature is that the roots of multi-pass welds are subjected to straining and ageing (see L.4.2) and, for this reason, the root tends to be the region of lowest toughness. In order to assess this, tests on non-standard shallow crack fracture toughness specimens may be necessary to characterize weld root regions in welds made from one side only, e.g. V welds.

L.4 Test requirements

L.4.1 Materials

The chemical composition, manufacturing route and heat treatment of the parent material can affect HAZ and weld metal toughness. Fracture toughness data are only applicable to a particular assessment, if the test material is representative of that used in the structure. As a general rule, the chemical composition of the steel used to make the test specimen should lie within the actual composition range for the particular grade and material thickness used in the structure or the target composition range proposed by the steel maker. For some applications, more stringent requirements may be necessary and, in particular circumstances, it may be appropriate to test material from the same heat or plate as that in which the flaw is located. When weld metal toughness is to be determined, it is important that the consumables used be the same as those used for the structure to be assessed.

L.4.2 Welding

Where possible, the test panel should be welded with the same welding procedure as that used in the structure. However, minor differences in procedure may be acceptable. Procedural variables that affect HAZ and weld metal toughness are listed below:

a) welding heat input;b) bead overlap (bead size, weave technique, bevel angle);c) welding consumable (for the weld metal);d) weld metal strength (for the HAZ);e) welding process;f) joint preparation;g) back-gouging/grinding to weld root;h) degree of restraint (for the weld metal);i) PWHT.

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It should be noted that the relative importance of these variables may vary considerably and more precise information can often be obtained by examining trends in available fracture toughness data.

In some circumstances, it may be necessary for test welds to differ from structural welds in order to facilitate testing. In particular, for full thickness tests on heat-affected zones, a square weld bevel (K or half K) is recommended. This helps to ensure that the crack plane is parallel to the plane of the HAZ, thereby maximizing the amount of HAZ microstructure sampled by the crack tip (see BS 7448-2).

Special specimen preparation and testing requirements may be necessary to determine the fracture toughness of SCHAZs in older coarse grained as-rolled steels, and also old and modern weld metals that are susceptible to strain ageing. Further information is given by Dolby and Saunders [155] and Dawes [156].

L.4.3 Specimen geometry

Specimens for fracture tests should normally conform to the requirements of BS 7448-2. Full thickness, rectangular (B × 2B) or square section (B × B) specimens are recommended.

Tests may also be carried using square section (B × B) specimens that model the actual orientation and height of the flaw, if this information is available. Non-standard specimens, which fall outside the scope of BS 7448-2, may be required to simulate shallow cracks in weld metals (such as the weld root region in single V welds) or in the HAZs of attachment welds or capping passes [157], [158].

L.5 Test procedure

Fracture toughness tests on standard specimens should be conducted in accordance with BS 7448-2. It should be recognized that strength mismatch between the parent material and weld can influence the fracture toughness of the weld metal and HAZ. For deeply notched specimens, guidance on the validity of the fracture toughness estimation procedures is given in BS 7448-2 and by Schwalbe and Koçak, eds. [159]. The test procedures described by Dolby and Saunders [155], Dawes [156], Dawes et al [157] and Wang et al [158] should be used as a basis for tests on non-standard shallow crack specimens. However, yield strength mismatch effects are more likely to affect fracture toughness measurement of shallow notched specimens than with deeply notched specimens. Guidance on estimation procedures is given by Schwalbe and Koçak, eds. [159]. See also Annex I concerning the significance of strength mismatch.

L.6 Metallographic validation

Metallographic examinations should be undertaken, as specified in BS 7448-2. For weld positional testing, a detailed microstructural examination is not required. However, for microstructure specific tests it is necessary to show that the crack tip has sampled the type and proportion of the specified microstructure. Experimental evidence indicates that the exact location of the crack tip, and the amount of the relevant microstructure at the crack tip, affect toughness values. Toyoda and Thaulow [160] and Francois and Burdekin [161] suggest that lower bound toughness values will be obtained if metallographic examination shows that regions of the specified microstructure are located within 0.5 mm from the appropriate microstructural boundary in the central 75 % of the specimen. In addition, the crack tip should sample either 15 % [161] or at least 7 mm [160] of the specified microstructure within the central 75 % of the crack front. Clearly these criteria will not apply if the maximum amount of the specified microstructure present in the weld is less than these limiting values. In such cases, alternative criteria should be developed based on available test data.

L.7 Number of tests required

The number of valid test results (i.e. results from specimens where the fatigue crack has been shown to sample the type and proportion of specified microstructure) required to characterize the HAZ toughness will depend on the degree of scatter in the results. If the HAZ exhibits upper shelf behaviour and scatter is limited, then three valid test results may be sufficient (see 7.1.5.6). If the HAZ is operating in the ductile/brittle transition region or excessive scatter is anticipated, a larger number of test results may be required to characterize HAZ toughness, see K.2.3. For example, experience has shown that a minimum of 12 valid test results is normally required to characterize HAZ toughness distribution in structural steels with yield strengths up to 450 N/mm2 and typical North Sea operating temperatures, see K.2.3.

It should be noted that additional tests may be required to fulfil the metallographic validation criteria given in L.6 and consideration should be given to providing sufficient material for re-tests.

L.8 Analysis of test results

Test results should be analysed in accordance with Annex K.

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Annex M (normative) Stress intensity factor solutions

M.1 General

This annex contains stress intensity factor, KI, solutions for a range of flaw types that are likely to arise in welded joints. Additional stress intensity factor solutions have been published in the form of handbooks [41], [39], [162], [40] and [163], for a wide range of geometry and loading configurations. Alternatively, numerical analysis methods (e.g. finite elements) or weight function techniques [42] can be used to derive stress intensity factors, but the basis of the method and the results should be fully documented.

The solutions provided in this annex are as follows:

For information on tubular joints, see Annex B.

Where stated, the validity of the solutions given in this annex is limited strictly to the ranges stated; no extrapolation outside these limits should be carried out.

Matching sets of reference stress (Öref) solutions are provided in Annex P, for assessing plastic collapse.

The general form of the stress intensity factor solutions in this annex is:

(M.1)

and for fatigue assessments, the corresponding stress intensity factor range is:

(M.2)

Net area, misalignment, stress concentration and bulging effects M.2Flat plates M.3

Through-thickness flaws in plates M.3.1Surface flaws in plates M.3.2Long surface flaws in plates M.3.3Embedded flaws in plates M.3.4Edge flaws in plates M.3.5Corner flaws in plates M.3.6Corner flaws at hole M.3.7Single corner flaw at hole M.3.8

Curved shells M.4Through thickness flaws M.4.2Surface flaws M.4.3Embedded flaws M.4.4Flaws at nozzles M.4.5

Welded joints M.5Surface flaws at weld toes M.5.1Weld root flaws in cruciform joints M.5.2

Round bars/bolts M.6Straight-fronted flaw in round bar M.6.1Semi-circular surface flaws in round bars M.6.2Semi-circular surface flaws in bolts M.6.3Circumferential flaws in round bars M.6.4

KI YÖ( ) ;µ=

%KI Y %Ö( ) ;µ=

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For fracture assessments at Level 1 the following equation applies:

(M.3)20)

For fracture assessments at Levels 2 and 3 the following equation applies:

(M.4)

where

(YÖ)p and (YÖ)s represent contributions from primary and secondary stresses, respectively. They are calculated as follows:

(YÖ)p = Mfw [ktmMkmMmPm + ktbMkbMb {Pb + (km – 1)Pm}] (M.5)

(YÖ)s = MmQm + MbQb (M.6)

For fatigue assessments the following equation applies:

(Y%Ö)p = Mfw [ktmMkmMm%Bm + ktbMkbMb {%Bb + (km – 1)%Bm}] (M.7)

In the above equations, expressions for M, fw, Mm and Mb are given in M.2 to M.4 and M.6 for different types of flaw in different configurations. Mkm and Mkb apply when the flaw or crack is in a region of local stress concentration and are given in M.5. For kt, ktm, ktb and km, reference should be made to 6.4.4 and Annex D.

All solutions exclude the possible effects of crack face pressure for pressurized components. Whilst the effect is likely to be small it should be considered when appropriate.

M.2 Net area, misalignment, stress concentration and bulging effects

The estimation methods for stress intensity factor KI do not always allow for situations where the flaw area is significant compared to the load bearing cross-section area, where misalignment or angular distortion occurs, or for long flaws in curved shells subject to internal pressure where bulging effects may occur.

Where the actual flaw area is greater than 10 % of the load bearing cross-section area (generally BW), KI should be multiplied by the fw factor. Formulae for fw are given in Annex M for different geometries, but if one is not specified for the geometry under consideration, the following should be used.

fw = {sec (;A1/2A2)}0.5 (see Newman and Raju [164])

where generally, A2 = BW, and A1 = 2ac, 4ac and 2aB for surface, embedded and through-thickness flaws, respectively.

M.3 Flat plates

M.3.1 Through-thickness flaws in plates

See Figure M.1 for the definition of the geometry. The stress intensity factor is given by equations (M.1) to (M.7), where M = Mm = Mb = 1, and fw = {sec(;a/W)}0.5.

M.3.2 Surface flaws in plates (Raju and Newman [165])

M.3.2.1 General

See Figure M.2 for the definition of the geometry. The stress intensity factor solution presented in this subclause is applicable to both normal restraint and pin-jointed boundary conditions (see P.3.2). The stress intensity factor is given by equations (M.1) to (M.7), where M = 1:

fw = {sec [(;c/W)(a/B)0.5]}0.5

which equals 1.0 if a/2c equals 0.NOTE This equation for fw is safe up to 2c/W = 0.8.

Mm and Mb are defined in M.3.2.2 and M.3.2.3, respectively.

20) The equations in this document differ in apearance from those to be found, for example, in the publications of Newman and Raju and in the original PD 6493. For surface, embedded and corner flaws, Mm and Mb have been modified here by dividing by the complete integral, Í. By making this change it has been possible to write one set of equations that apply to all geometries.

YÖ MfwMmÖmax=

YÖ YÖ( )p YÖ( )s+=

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M.3.2.2 Membrane loading

M.3.2.2.1 Conditions

The following conditions apply:

0 k a/2c k 1.0

0 k Ú k ;and

a/B < 1.25 (a/c + 0.6) for 0 k a/2c k 0.1a/B < 1.0 for 0.1 k a/2c k 1.0

Figure M.1 — Through-thickness flaw geometry

Figure M.2 — Surface flaw

W

2a

BX X

Axis for planeof bending

B

2c

θ

a

X X


In equations, maximumtensile bending stressis at this surface

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M.3.2.2.2 Solution

Mm = {M1 + M2(a/B)2 + M3(a/B)4}gfÚ/ (M.8)

where

, the complete elliptic integral of the second kind, may be determined from standard tables or from the following solution, which is sufficiently accurate:

A graphical solution for Í is given in Figure M.3.

Graphical solutions for Mm are given in Figure M.4a) and Figure M.4b).

M.3.2.2.3 Simplifications

The following simplifications may be used as indicated.

a) At the deepest point on the crack front:

b) At the ends of the crack, Ú = 0, so that:

c) If a/2c > 1.0 use solution for a/2c = 1.0.

M1 = 1.13 – 0.09(a/c) for 0 k a/2c k 0.5M1 = (c/a)0.5{1 + 0.04(c/a)} for 0.5 < a/2c k 1.0M2 = [0.89/{0.2 + (a/c)}] – 0.54 for 0 k a/2c k 0.5M2 = 0.2(c/a)4 for 0.5 < a/2c k 1.0M3 = 0.5 – 1/{0.65 + (a/c)} + 14{1 – (a/c)}24 for a/2c k 0.5M3 = –0.11 (c/a)4 for 0.5 < a/2c k 1.0g = 1 + {0.1 + 0.35(a/B)2}(1 – sinÚ)2 for a/2c k 0.5g = 1 + {0.1 + 0.35(c/a)(a/B)2}(1 – sinÚ)2 for 0.5 < a/2c k 1.0fÚ = {(a/c)2 cos2Ú + sin2Ú}0.25 for 0 k a/2c k 0.5

fÚ = {(c/a)2 sin2Ú + cos2Ú}0.25 for 0.5 < a/2c k 1.0

= {1 + 1.464(a/c)1.65}0.5 for 0 k a/2c k 0.5

= {1 + 1.464(c/a)1.65}0.5 for 0.5 < a/2c k 1.0 (M.9)

g = 1

fÚ = 1 for 0 k a/2c k 0.5

fÚ = (c/a)0.5 for 0.5 < a/2c k 1

g = 1.1 + 0.35 (a/B)2 for 0 k a/2c k 0.5

g = 1.1 + 0.35 (c/a)(a/B)2 for 0.5 < a/2c k 1.0

fÚ = (a/c)0.5 for 0 ka/2c k 0.5

fÚ = 1.0 for 0.5 < a/2c k 1.0

Í

Í

Í

Í

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Fig

ure

M.3

— E

llip

tica

l in

teg

ral Í

as

a f

un

ctio

n o

f a

/2c

use

d f

or

the

calc

ula

tio

n o

f K

1 fo

r su

rfa

ce a

nd

em

bed

ded

fla

ws

1.6

1.5

1.4

1.3

1.2

1.1

1.0

Φ

a/2c

00.

10.

20.

30.

40.

5

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a) A

t de

epes

t po

int

alon

g fl

aw f

ron

t, i.

e. Ú

= ;

/2ra

d

Fig

ure

M.4

— S

tres

s in

ten

sity

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gn

ific

ati

on

fa

cto

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m f

or

surf

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fla

ws

in t

ensi

on

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

3.0

2.5

2.0

2c

1.5

1.0

0.5 0

00.

10.

20.

30.

40.

50.

60.

70.

80.

9

Mm

a/B

a/2c

= 0

a/2c

= 0

.05

a/2c

=

a

B

0.10

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b) A

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i.e.

Ú =

0

Fig

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M.4

— S

tres

s in

ten

sity

ma

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ati

on

fa

cto

r M

m f

or

surf

ace

fla

ws

in t

ensi

on

(co

nti

nu

ed)

a/2c

=

0.1

0 0

.15

0.0

5

0.20

0.2

5 0

.30

0.3

5 0

.40

0.4

5 0

.50

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

a/B

1.6

1.4

1.2

1.0

0.8

0.50

0.25 0.

6

0.4

0.05

0.20

0.15

0.10

Mm

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M.3.2.3 Bending loading


The conditions are as given in M.3.2.2.1.

M.3.2.3.2 Solutions

Mb = HMm (M.10)

where

Mm is calculated from equation (M.8).

H = H1 + (H2 – H1)sinqÚ

where

where

Graphical solutions for Mb are given in Figure M.5.



a) At the deepest point on the crack front, Ú = ;/2 so that H = H2 and:

b) At the ends of the crack, Ú = 0, so that:

and

H = H1.

c) If a/2c > 1.0, use solution for a/2c = 1.0.

q = 0.2 + (a/c) + 0.6(a/B) for 0 k a/2c k 0.5q = 0.2 + (c/a) + 0.6(a/B) for 0.5 < a/2c k 1.0H1 = 1 – 0.34(a/B) – 0.11(a/c)(a/B) for 0 k a/2c k 0.5H1 = 1 – {0.04 + 0.41(c/a)}(a/B) + {0.55 – 1.93(c/a)0.75 + 1.38(c/a)1.5}(a/B)2 for 0.5 < a/2c k 1.0H2 = 1 + G1(a/B) + G2(a/B)2

G1 = –1.22 – 0.12(a/c) for 0 k a/2c k 0.5G1 = –2.11 + 0.77(c/a) for 0.5 < a/2ck 1.0G2 = 0.55 – 1.05(a/c)0.75 + 0.47(a/c)1.5 for 0 k a/2c k 0.5G2 = 0.55 – 0.72(c/a)0.75 + 0.14 (c/a)1.5 for 0.5 < a/2c k 1.0

g = 1

fÚ = 1 for 0 k a/2c k 0.5

fÚ = (c/a)0.5 for 0.5 < a/2c k 1

g = 1.1 + 0.35 (a/B)2 for 0 k a/2c k 0.5g = 1.1 + 0.35 (c/a) (a/B)2 for 0.5 < a/2c k 1

fÚ = (a/c)0.5 for 0 k a/2c k 0.5

fÚ = 1.0 for 0.5 < a/2c k 1

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a) A

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aw f

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= ;

/2ra

d

Fig

ure

M.5

— S

tres

s in

ten

sity

ma

gn

ific

ati

on

fa

cto

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b f

or

surf

ace

fla

ws

in b

end

ing

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2 0

00.

10.

20.

30.

40.

50.

60.

70.

80.

9

a/B

Mb

a/2c

= 0

0.05 0.

1

0.2

0.3

0.35

0.4

0.45

0.50.15

2c

a

B

0.25

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b) A

t fl

aw t

ip o

n m

ater

ial s

urf

ace,

i.e.

Ú =

0

Fig

ure

M.5

— S

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s in

ten

sity

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on

fa

cto

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b f

or

surf

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fla

ws

in b

end

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(co

nti

nu

ed)

1.2

1.0

0.8

0.50

0.30 0.6

0.4

0.2 0

0.25

0.20

0.10

0.05

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Mb

00.

10.

20.

30.

40.

50.

60.

70.

80.

9

a/B

a/2c

= 0

.50

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M.3.3 Long surface flaws in plates [39]

See Figure M.6 for the definition of the geometry. The stress intensity factor is given by equations (M.1) to (M.7), where fw = 1, and Mm and Mb are given below for a/B k 0.6:

Mm = 1.12 – 0.23(a/B) + 10.6(a/B)2 – 21.7(a/B)3 + 30.4(a/B)4 (M.11)

Mb = 1.12 – 1.39(a/B) + 7.32(a/B)2 – 13.1(a/B)3 + 14(a/B)4 (M.12)

M.3.4 Embedded flaws in plates [165]

M.3.4.1 General

See Figure M.7 for the definition of the geometry. The stress intensity factor is given by equations (M.1) to (M.7), where M = 1, fw = {sec[(;c/W)(2a/B½)0.5]}0.5 and solutions for Mm and Mb are given in M.3.4.2 and M.3.4.3 respectively, where B is the effective thickness, equal to 2a + 2p.NOTE This equation for fw is safe up to 2c/W = 0.8.

Figure M.6 — Long surface flaw geometry

Figure M.7 — Embedded flaw

W

B

a

X X


W

B

p

θ

2c

X X

Axis forplaneof bending

2a

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The conditions for membrane loading are as follows:

0 k a/2c k 1.0

2c/W < 0.5

–; k Ú k ;

a/B½ < 0.625(a/c + 0.6) for 0 k a/2c k 0.1

where

B½ is the effective thickness, equal to 2a + 2p.

M.3.4.2.2 Solution

Mm = {M1 + M2(2a/B½)2 + M3(2a/B½)4}g fÚ/Í (M.13)

where

Í is defined in equation (M.9)

A graphical solution for Mm is given in Figure M.8.

M1 = 1 for 0 k a/2c k 0.5M1 = (c/a)0.5 for 0.5 k a/2c k 1.0

fÚ = {(a/c)2cos2Ú + sin2Ú}0.25 for 0 k a/2c k 0.5

fÚ = {(c/a)2sin2Ú + cos2Ú}0.25 for 0.5 < a/2c k 1.0

M =

+ a c2

1 5

0 05

0 11

.

..

/( )

M =

+ a c3

1 5

0 29

0 23

.

..

/( )

g = a B a B

a c1

2 2 6 4

1 4

4 0 5

−′( ) − ′( ){ }

+ ( )⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

/ /

/

.

cos

.

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Fig

ure

M.8

— S

tres

s in

ten

sity

ma

gn

ific

ati

on

fa

cto

r M

m f

or

emb

edd

ed f

law

s in

ten

sio

n (

at

po

int

nea

rest

ma

teri

al

surf

ace

)

B2c

2.5

2.0

1.5

1.0

0.5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mm

2a/2

c=

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

p2a

B2c

2a/(

2a +

2p

)

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a) At the point on the crack front closest to the material surface, Ú = ;/2 so that:

b) At the ends of the crack, Ú = 0 so that:

and

c) If a/2c > 1.0, use solution for a/2c = 1.0.



The conditions for bending loading are as follows:

0 k a/2c k 0.5

Ú = ;/2

(i.e. solution only refers to the ends of the minor axis of the elliptical crack).

A graphical solution for Mb is given in Figure M.9.

g = 1fÚ = 1 for a/2c k 0.5fÚ = (c/a)0.5 for 0.5 < a/2c k 1

fÚ = (a/c)0.5 for 0 k a/2c k 0.5

fÚ = 1 for 0.5 < a/2c k 1.0

g = a B a B

a c1

2 2 6 4

1 4

4 0 5

−′( ) − ′( ){ }

( )⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

/ /

+ /

.

.

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Fig

ure

M.9

— S

tres

s in

ten

sity

ma

gn

ific

ati

on

fa

cto

r M

b f

or

emb

edd

ed f

law

s in

ben

din

g

1.0

0.8

0.6

0.4

0.2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2ap

2c

B

Mbp

/B =

0.0

5

p/B

= 0

.10

p/B

= 0

.15

p/B

= 0

.2

p/B

= 0

.25

p/B

= 0

.3

p/B

= 0

.35

p/B

= 0

.4

2a/B

Φ.

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M.3.4.3.2 Solution

Mb = [Æ1 + Æ2(p/B) + Æ3(a/B) + Æ4(pa/B2)]/Í (M.14)

where

— for p/B k 0.184 1:Æ1 = 1.044

Æ2 = –2.44

Æ3 = 0

Æ4 = –3.166

— for p/B > 0.184 1 and a/B k 0.125:

Æ1 = 0.94

Æ2 = –1.875

Æ3 = –0.114 6

Æ4 = –1.844

— for p/B > 0.184 1 and a/B > 0.125:

Æ1 = 1.06

Æ2 = –2.20

Æ3 = Æ4 = –0.666 6

M.3.5 Edge flaws in plates [165]

See Figure M.10 for the definition of the geometry. The stress intensity factor is given by equations (M.1) to (M.7), where, for a/W k 0.6, M = 1, fw = 1 and:

Mm = Mb = 1.12 – 0.23(a/W) + 10.6(a/W)2 – 21.7(a/W)3 + 30.4(a/W)4 (M.15)NOTE This solution has the same form as that for long surface flaws (M.3.3), equation (M.11), although the plate membrane and bending stresses have been superimposed. Equation (M.15) does not account for in-plane bending (e.g. SENB specimen). In such cases, a modified form of the long surface flaw solution may be used.

Figure M.10 — Edge flaw geometry

W

B

a

X X

Axis for plane of bending

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M.3.6 Corner flaws in plates [165]

M.3.6.1 General

See Figure M.11 for the definition of the geometry. The stress intensity factor is given by equations (M.1) to (M.7), where M = 1, with fw given by:

where

Solutions for Mm and Mb are given in M.3.6.2 and M.3.6.3 respectively.



0.2 k a/c k 2, a/B < 1, 0 k Ú k ;/2 and c/W < 0.5.

M.3.6.2.2 Solution

Mm = {M1 + M2(a/B)2 + M3(a/B)4}g1g2 fÚ/Í (M.16)

where

Figure M.11 — Corner flaw geometry

fw = 1 – 0.2Æ + 9.4Æ2 – 19.4Æ3 + 27.1Æ4 for c/W k 0.5

Í is defined in equation (M.9);M1 = 1.08 – 0.03(a/c) for 0.2 k a/c k 1M1 = {1.08 – 0.03(c/a)}(c/a)0.5 for 1 < a/c k 2M2 = {1.06/(0.3 + a/c)} – 0.44 for 0.2 k a/c k 1M2 = 0.375(c/a)2 for 1 < a/c k 2M3 = –0.5 + 0.25(a/c) + 14.8(1 – a/c)15 for 0.2 k a/c k 1M3 = –0.25(c/a)2 for 1 < a/c k 2g1 = 1 + {0.08 + 0.4(a/B)2} (1 – sinÚ)3 for 0.2 k a/c k 1g1 = 1 + {0.08 + 0.4(c/B)2} (1 – sinÚ)3 for 1 < a/c k 2g2 = 1 + {0.08 + 0.15(a/B)2} (1 – cosÚ)3 for 0.2 k a/c k 1g2 = 1 + {0.08 + 0.15(c/B)2} (1 – cosÚ)3 for 1 k a/c k 2fÚ = {(a/c)2cos2Ú + sin2Ú}0.25 for 0.2 k a/c k 1fÚ = {(c/a)2sin2Ú + cos2Ú}0.25 for 1 < a/c k 2

W

a

B

c

θ

X

In equation, maximum tensile bending stress is at this surface

X


= ( ) ( )c W a B

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See M.3.6.2.1.

M.3.6.3.2 Solution

Mb = HMm (M.17)

where

Mm is given by equation (M.16)

where

M.3.7 Corner flaws at hole [164]

M.3.7.1 General

See Figure M.12 for the definition of the geometry. Equations (M.1) to (M.7) give the stress intensity factor, where M = 1 and:

where n = 1 for a single flaw and n = 2 for two symmetric flaws. This equation accounts for finite width effects, together with the stress concentrating effect of the hole. Solutions for Mm and Mb are given in M.3.7.2 and M.3.7.3 respectively.

H = H1 + (H2 – H1)sinqÚq = 0.2 + (a/c) + 0.6(a/B) for 0.2 k a/c k 1

q = 0.2 + (c/a) + 0.6(a/B) for 1 < a/c k 2H1 = 1 – 0.34(a/B) – 0.11(a/c)(a/B) for 0.2 k a/c k 1

H1 = 1 – {0.04 + 0.41(c/a)}(a/B) + {0.55 – 1.93(c/a)0.75 + 1.38(c/a)1.5}(a/B)2 for 1 < a/c k 2

H2 = 1 + G1(a/B) + G2(a/B)2

G1 = –1.22 – 0.12(a/c) for 0.2 k a/c k 1G1 = –2.11 + 0.77(c/a) for 1 < a/c k 2

G2 = 0.64 – 1.05(a/c)0.75 + 0.47(a/c)1.5 for 0.2 k a/c k 1

G2 = 0.64 – 0.72(c/a)0.75 + 0.14(c/a)1.5 for 1 < a/c k 2

Figure M.12 — Corner flaw at hole geometry

f r Wr nc

W c nca Bw = ( ) +( )

−( ) +( )

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

⎡

⎣⎢⎢

⎤

⎦⎥⎥

sec / secππ 2

4 2 2/

/

00 5.

W

B

c

θ

a

2r

X X


In equation, maximum tensile bending stress is at this surface

Size of circumscribing flaw forSize of circumscribing flaw forsimplified analysissimplified analysis

Size of circumscribing flaw forsimplified analysis

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0.2 k 2

a/B < 1

0.5 k r/B k 2

2(r + c)/W k 0.5

0 k Ú k ;/2

M.3.7.2.2 Solution

Mm = {M1 + M2 (a/B)2 + M3(a/B)4}g1g2g3g4fÚ/Í (M.18)

where

where



See M.3.7.2.1.

M.3.7.3.2 Solution

Mb = HMm (M.19)

where

Í is defined in equation (M.9)M1 = 1.13 – 0.09(a/c) for 0.2 k a/c k 1M1 = {1 + 0.04(c/a)}Æ(c/a) for 1 < a/c k 2M2 = –0.54 + 0.89/(0.2 + a/c) for 0.2 k a/c k 1

M2 = 0.2(c/a)4 for 1 < a/c k 2

M3 = 0.5 – 1/(0.65 + a/c) + 14(1 – a/c)24 for 0.2 k a/c k 1

M3 = –0.11(c/a)4 for 1 < a/c k 2g1 = 1 + {0.1 + 0.35(a/B)2}(1 – sinÚ)2 for 0.2 k a/c k 1g1 = 1 + {0.1 + 0.35(c/a)(a/B)2}(1 – sinÚ)2 for 1 < a/c k 2g2 = (1 + 0.358Æ + 1.425Æ2 – 1.578Æ3 + 2.156Æ4)/(1 + 0.13Æ2)

Æ = 1/{1 + (c/r)cos(ÈÚ)}È = 0.85

g3 = (1 + 0.04a/c) {1 + 0.1( 1 – cosÚ)2}{0.85 + 0.15(a/B)0.25} for 0.2 k a/c k 1g3 = (1.13 – 0.09c/a) {1 + 0.1(1 – cos Ú)2}{0.85 + 0.15(a/B)0.25} for 1 < a/c k g4 = 1 – 0.7(1 – a/B)(a/c – 0.2)(1 – a/c) for 0.2 k a/c k 1g4 = 1 for 1 < a/c U 2fÚ = {(a/c)2cos2Ú + sin2Ú}0.25 for 0.2 k a/c k 1

fÚ = {(c/a)2sin2Ú + cos2Ú}0.25 for 1 < a/c k 2

Mm is given in equation (M.18)

È = 0.85 – 0.25(a/B)0.25

H = H1 + (H2 – H1)sinqÚ

q = 0.1 + 1.3a/B + 1.1a/c – 0.7(a/c)(a/B) for 0.2 k a/c k 1q = 0.2 + c/a + 0.6a/B for 1 < a/c k 2

H1 = 1 + G11(a/B) + G12(a/B)2 + G13(a/B)3

H2 = 1 + G21(a/B) + G22(a/B)2 + G23(a/B)3

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where

M.3.8 Single corner crack at holeThe stress intensity factor for a single corner crack at a hole (Ksingle crack) may be estimated from Ksymmetric crack using the following expression:

Ksymmetric crack is found from equations (M.1) to (M.7) with Mm and Mb from equations (M.18) and (M.19) and the modified finite width correction factor, fw, defined in M.3.7.1.

M.4 Curved shells

M.4.1 GeneralTwo methods are given in Annex M for the calculation of M, fw, Mm and Mb.For curved shells under internal pressure, the formulae in M.4.2 may be used.For curved shells under combined internal pressure and mechanical loads, the formulae in M.4.3 may be used.

M.4.2 Curved shells under internal pressure

M.4.2.1 GeneralThe finite width correction factor, fw, is given in M.2.Unless justified otherwise, for curved shells under internal pressure the bulging correction factor, M, is calculated from the following expressions.

a) For through-thickness flaws in spheres, and for axial through-thickness flaws in pipes and cylinders:M = {1 + 3.2(a2/2rB)}0.5 (M.20)

b) For surface flaws in spheres, and for axial surface flaws in cylinders:

(M.21)

whereMT = {1 + 3.2(c2/2rB)}0.5

See Kiefner et al [93] and Willoughby and Davey [166].c) For other cases, e.g. embedded flaws, circumferential flaws in cylinders or for flaws at nozzles in pressure vessels, the bulging correction factor M = 1.

In equations (M.20) and (M.21), r and B are the mean shell radius and thickness, respectively.

G11 = –0.43 – 0.74(a/c) – 0.84(a/c)2 for 0.2 k a/c k 1

G11 = –2.07 + 0.06(c/a) for 1 < a/c k 2G12 = 1.25 – 1.19(a/c) + 4.39(a/c)2 for 0.2 U a/c k 1

G12 = 4.35 + 0.16(c/a) for 1 < a/c k 2

G13 = –1.94 + 4.22(a/c) – 5.51(a/c)2 for 0.2 k a/c k 1G13 = –2.93 – 0.3(c/a) for 1 < a/c k 2G21 = –1.5 – 0.04(a/c) – 1.73(a/c)2 for 0.2 k a/c k 1G21 = –3.64 + 0.37(c/a) for 1 < a/c k 2G22 = 1.71 – 3.17(a/c) + 6.84(a/c)2 for 0.2 k a/c k 1

G22 = 5.87 – 0.49(c/a) for 1 < a/c k 2

G23 = –1.28 + 2.71(a/c) – 5.22(a/c)2 for 0.2 k a/c k 1

G23 = –4.32 + 0.53(c/a) for 1 < a/c k 2

Ksingle crack = Ksymmetric crack

+ ac

Br

+ac

Br

0 5

4

2

4

.

π

π

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

M1 a BMT( )⁄{ }–

1 a B⁄( )–-----------------------------------------=

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M.4.2.2 Surface flaws

Solutions for Mm are given in M.3.2.2 and for Mb in M.3.2.3.

M.4.2.3 Embedded flaws

Solutions for Mm are given in M.3.4.2 and for Mb in M.3.4.4.

M.4.3 Curved shells under internal pressure and mechanical loads

M.4.3.1 General

The finite width correction, fw, is as given in M.2.Table M.1a) to Table M.8 may be used to determine the applied stress intensity factor for combined internal pressure and mechanical loads, within the specified range of application. Interpolation is permitted for values falling between those quoted. When Mm* and Mb* are used from Table M.1a) to Table M.8 these include any bulging effect and the general bulging factor M from M.2 should be taken as 1.

M.4.3.2 Through-thickness flaws

M.4.3.2.1 Through-thickness flaws in cylinders oriented axially [167]

See Figure M.13 for the definition of the geometry. The stress intensity factor solution is calculated from equation (M.1) to (M.7):where

KI = KIpressure + KI

bending

M = 1 [Note, bulging is taken into account by the parameter Æ: see equation (M.22)]Mm = Mb = Mm* ± Mb*

whereKI

pressure and KIbending are calculated from equations (M.1) to (M.7) and represent, respectively,

contributions to KI of pressure-induced membrane stresses and through-wall bending stresses.Mm* and Mb* are given in Table M.1a) to Table M.1d) for pressure and bending loading, in terms of Æ.

(M.22)

NOTE The stress intensity magnification factors at the outside (o) and inside (i) surfaces are given by Mm* + Mb*, and Mm* – Mb* respectively. These solutions are valid for long cylinders, or pressure vessels with closed ends.

Range of application: 0 k Æ k 12.2115 k r/B k 100

Figure M.13 — Through-thickness flaw in cylinder oriented axially

Æ 12 1( É2 )–{ }0.25 arB

-----------=

B

riror

CL

W

o

i

2a

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Table M.1a) — Mm* for axial through-thickness flaws in cylinders — Pressure loading

Parameter, Æ r/B = 5 r/B = 10 r/B = 20 r/B = 50 r/B = 100

0.000 1.000 1.000 1.000 1.000 1.000

0.862 1.158

0.910 1.264

1.016 1.433 1.249

1.285 1.383

1.818 1.609

1.928 1.663

2.012 1.636

2.032 1.912 1.691

3.636 2.543

3.856 2.642

4.024 2.604

4.065 3.133 2.709

5.784 3.613

6.036 3.527

6.097 4.116 3.369

6.362 3.927

7.712 4.534

7.926 4.980

8.048 4.377

8.130 4.605

8.186 4.799

9.959 5.873

9.998 5.628

10.162 5.463

10.283 5.688

11.816 6.416

11.991 6.687

12.072 5.874

12.194 6.257

12.211 6.503

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Table M.1b) — Mb* for axial through-thickness flaws in cylinders — Pressure loading


0.000 0.000 0.000 0.000 0.000 0.000

0.862 0.093

0.910 0.143

1.016 0.098 0.125

1.285 0.165

1.818 0.229

1.928 0.205

2.012 0.156

2.032 0.143 0.182

3.636 0.218

3.856 0.161

4.024 0.041

4.065 –0.030 0.089

5.784 –0.077

6.036 –0.264

6.097 –0.419 –0.399

6.362 –0.126

7.712 –0.436

7.926 –0.851

8.048 –0.684

8.130 –0.622

8.186 –0.475

9.959 –1.358

9.998 –0.884

10.162 –1.122

10.283 –1.034

11.816 –1.339

11.991 –1.829

12.072 –1.718

12.194 –1.700

12.211 –1.543

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Table M.1c) — Mm* for axial through-thickness flaws in cylinders — Bending loading


0.000 0.000 0.000 0.000 0.000 0.000

0.862 0.040

0.910 0.025

1.016 0.053 0.040

1.285 0.042

1.818 0.055

1.928 0.060

2.012 0.075

2.032 0.083 0.068

3.636 0.095

3.856 0.097

4.024 0.109

4.065 0.121 0.103

5.784 0.119

6.036 0.128

6.097 0.139 0.123

6.362 0.127

7.712 0.134

7.926 0.150

8.048 0.138

8.130 0.135

8.186 0.139

9.959 0.161

9.998 0.147

10.162 0.143

10.283 0.145

11.816 0.151

11.991 0.171

12.072 0.150

12.194 0.146

12.211 0.150

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Table M.1d) — Mb* for axial through-thickness flaws in cylinders — Bending loading


0.000 1.000 1.000 1.000 1.000 1.000

0.862 0.694

0.910 0.637

1.016 0.701 0.659

1.285 0.629

1.818 0.598

1.928 0.600

2.012 0.608

2.032 0.604 0.602

3.636 0.527

3.856 0.529

4.024 0.517

4.065 0.493 0.524

5.784 0.474

6.036 0.453

6.097 0.417 0.467

6.362 0.448

7.712 0.430

7.926 0.364

8.048 0.403

8.130 0.421

8.186 0.407

9.959 0.314

9.998 0.374

10.162 0.382

10.283 0.381

11.816 0.348

11.991 0.276

12.072 0.328

12.194 0.355

12.211 0.353

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M.4.3.2.2 Through-thickness flaws in cylinders oriented circumferentially [167]

See Figure M.14 for the definition of the geometry. The stress intensity factor solution is calculated from equations (M.1) to (M.7):

where

KI = KIpressure + KI

bending;

M = 1;

Mm = Mb = Mm* ± Mb*

where

KIpressure and KI

bending are calculated from equations (M.1) to (M.7) and represent, respectively, contributions to KI of pressure-induced membrane stresses and through-wall bending stresses.

Mm* and Mb* are given in Table M.2a) to Table M.2d) for pressure and bending loading, in terms of the parameter Æ referred to in equation (M.22). For pressure loading, Pm should be multiplied by a factor of ¶, where:

(M.23)

NOTE The stress intensity magnification factors at the outside (o) and inside (i) surfaces are given by Mm* + Mb*, and Mm* – Mb* respectively. These solutions are valid for long cylinders, or pressure vessels with closed ends.

Range of application: 0 k Æ k 15.1435 k r/B k 100

Figure M.14 — Through-thickness flaw in cylinder oriented cicumferentially

¶2ra------tan a

2r------⎝ ⎠⎛ ⎞

⎩ ⎭⎨ ⎬⎧ ⎫

0.5

=

o

r

B

2a

Circumferential lengthof flaw measured atmid-thickness

i

X X


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Table M.2a) — Mm* for circumferential through-thickness flaws in cylinders — Pressure loading


0.000 1.000 1.000 1.000 1.000 1.000

0.177 1.248

0.251 1.032

0.355 1.290 1.050

0.502 1.066

0.561 1.061

0.709 1.085

0.793 1.088

1.064 1.406

1.122 1.096

1.505 1.192

1.586 1.139

1.596 1.522

2.128 1.276

2.257 1.324

2.306 1.723

3.193 2.044 1.469

3.261 1.545

3.365 1.378

3.902 2.367

4.515 1.864

4.612 1.752

4.759 1.425

4.789 2.883

5.498 3.414

5.518 2.164

6.385 4.301 2.140

6.772 2.641

7.139 1.732

7.776 3.117

7.804 2.495

9.032 3.917

9.578 3.040

10.096 2.588

10.997 3.580

12.770 4.502

15.143 3.623

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Table M.2b) — Mb* for circumferential through-thickness flaws in cylinders — Pressure loading


0.000 0.000 0.000 0.000 0.000 0.000

0.177 0.069

0.251 0.035

0.355 0.077 0.034

0.502 0.057

0.561 0.045

0.709 0.069

0.793 0.063

1.064 0.140

1.122 0.087

1.505 0.121

1.586 0.102

1.596 0.153

2.128 0.116

2.257 0.108

2.306 0.112

3.193 –0.014 0.041

3.261 0.019

3.365 0.043

3.902 –0.158

4.515 –0.153

4.612 –0.119

4.759 –0.082

4.789 –0.385

5.498 –0.622

5.518 –0.328

6.385 –1.015 –0.318

6.772 –0.528

7.139 –0.277

7.776 –0.747

7.804 –0.485

9.032 –1.071

9.578 –0.762

10.096 –0.585

10.997 –0.944

12.770 –1.281

15.143 –1.126

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Table M.2c) — Mm* for circumferential through-thickness flaws in cylinders — Bending loading


0.000 0.000 0.000 0.000 0.000 0.000

0.177 0.023

0.251 0.021

0.355 0.037 0.015

0.502 0.028

0.561 0.013

0.709 0.025

0.793 0.012

1.064 0.064

1.122 0.026

1.505 0.054

1.586 0.025

1.596 0.079

2.128 0.048

2.257 0.063

2.306 0.092

3.193 0.106 0.052

3.261 0.069

3.365 0.043

3.902 0.117

4.515 0.074

4.612 0.052

4.759 0.032

4.789 0.135

5.498 0.156

5.518 0.079

6.385 0.191 0.054

6.772 0.088

7.139 0.033

7.776 0.100

7.804 0.059

9.032 0.119

9.578 0.065

10.096 0.046

10.997 0.068

12.770 0.078

15.143 0.029

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Table M.2d) — Mb* for circumferential through-thickness flaws in cylinders — Bending loading


0.000 1.000 1.000 1.000 1.000 1.000

0.177 0.918

0.251 0.828

0.355 0.816 0.750

0.502 0.733

0.561 0.673

0.709 0.666

0.793 0.633

1.064 0.624

1.122 0.587

1.505 0.544

1.586 0.544

1.596 0.533

2.128 0.465

2.257 0.450

2.306 0.441

3.193 0.361 0.373

3.261 0.364

3.365 0.364

3.902 0.315

4.515 0.299

4.612 0.301

4.759 0.293

4.789 0.270

5.498 0.239

5.518 0.264

6.385 0.203 0.249

6.772 0.230

7.139 0.228

7.776 0.205

7.804 0.218

9.032 0.179

9.578 0.187

10.096 0.184

10.997 0.182

12.770 0.161

15.143 0.205

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M.4.3.2.3 Through-thickness flaws in spheres [168]


where

M = fw = 1;

Mm and Mb are given in Table M.3.

Range of application: 0 k 2a/B k 20

0.05 k B/ri k 0.1

Table M.3 — Mm and Mb for through-thickness flaw in spherical shell

B/ri = 0.05 B/ri = 0.1

2a/B Mm(o) Mb(o) Mm(i) Mb(i) 2a/B Mm(o) Mb(o) Mm(i) Mb(i)

0.0 1.000 1.000 1.000 –1.000 0.0 1.000 1.000 1.000 –1.000

2.0 1.144 1.020 0.941 –0.995 2.0 1.240 1.031 0.919 –0.993

4.0 1.401 1.050 0.897 –0.992 4.0 1.637 1.074 0.894 –0.993

6.0 1.700 1.080 0.895 –0.993 6.0 2.083 1.111 0.944 –0.997

8.0 2.020 1.106 0.932 –0.996 8.0 2.549 1.143 1.059 –1.003

10.0 2.351 1.130 1.003 –1.001 10.0 3.016 1.170 1.231 –1.011

15.0 3.186 1.180 1.309 –1.014 15.0 4.124 1.226 1.915 –1.031

20.0 3.981 1.219 1.799 –1.028 20.0 5.084 1.272 2.968 –1.050NOTE (o) is for the intersection of the flaw with the outside surface, and (i) the inner.

Figure M.15 — Through-thickness flaw in spherical shell

o

B

2a

i

ri

r0

Circumferential lengthof flaw measured atmid-thickness

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M.4.3.3 Surface flaws

M.4.3.3.1 Internal surface flaws in cylinders oriented axially [169], [170] and [171]


where

M = fw = 1;

Mm and Mb for the deepest point in the flaw (d) and for the points where the flaw intersects the free surface (s) are given in Table M.4.

Range of application: 0 k a/B k 0.80.05 k a/c k 10.1 k B/ri k 0.252c/W k 0.15

Table M.4 — Mm and Mb for axial internal surface flaw in cylinder

a/c = 1.0, B/ri = 0.1 a/c = 1.0, B/ri = 0.25

a/B Mm(d) Mb(d) Mm(s) Mb(s) a/B Mm(d) Mb(d) Mm(s) Mb(s)

0.0 0.663 0.663 0.729 0.729 0.0 0.663 0.663 0.729 0.729

0.2 0.647 0.464 0.726 0.676 0.2 0.643 0.461 0.719 0.669

0.4 0.661 0.291 0.760 0.649 0.4 0.656 0.288 0.745 0.638

0.6 0.677 0.110 0.804 0.623 0.6 0.677 0.107 0.785 0.610

0.8 0.694 –0.080 0.859 0.599 0.8 0.704 –0.079 0.838 0.585

a/c = 0.4, B/ri = 0.1 a/c = 0.4, B/ri = 0.25

0.0 0.951 0.951 0.662 0.662 0.0 0.951 0.951 0.662 0.662

0.2 0.932 0.698 0.676 0.632 0.2 0.919 0.688 0.669 0.627

0.4 1.016 0.519 0.768 0.651 0.4 0.998 0.506 0.759 0.644

0.6 1.109 0.316 0.896 0.674 0.6 1.110 0.311 0.889 0.666

0.8 1.211 0.090 1.060 0.700 0.8 1.255 0.103 1.060 0.694

a/c = 0.2, B/ri = 0.1 a/c = 0.2, B/ri = 0.25

0.0 1.059 1.059 0.521 0.521 0.0 1.059 1.059 0.521 0.521

0.2 1.062 0.806 0.578 0.548 0.2 1.045 0.791 0.577 0.547

0.4 1.260 0.677 0.695 0.597 0.4 1.240 0.663 0.698 0.599

0.6 1.500 0.515 0.876 0.660 0.6 1.514 0.515 0.887 0.665

0.8 1.783 0.320 1.123 0.737 0.8 1.865 0.348 1.144 0.745

a/c = 0.1, B/ri = 0.1 a/c = 0.1, B/ri = 0.25

0.0 1.103 1.103 0.384 0.384 0.0 1.103 1.103 0.384 0.384

0.2 1.172 0.897 0.451 0.429 0.2 1.153 0.881 0.451 0.428

0.4 1.494 0.834 0.582 0.503 0.4 1.470 0.816 0.585 0.504

0.6 1.985 0.765 0.820 0.623 0.6 2.003 0.765 0.830 0.627

0.8 2.737 0.689 1.219 0.810 0.8 2.864 0.749 1.242 0.819

a/c = 0.05, B/ri = 0.1 a/c = 0.05, B/ri = 0.25

0.0 1.120 1.120 0.275 0.275 0.0 1.120 1.120 0.275 0.275

0.2 1.231 0.946 0.335 0.318 0.2 1.211 0.929 0.334 0.318

0.4 1.701 0.971 0.469 0.406 0.4 1.674 0.950 0.471 0.407

0.6 2.619 1.080 0.765 0.584 0.6 2.285 1.079 0.774 0.587

0.8 4.364 1.301 1.374 0.919 0.8 3.163 1.081 1.400 0.928

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M.4.3.3.2 Internal surface flaws in cylinders oriented circumferentially [169], [170], [172] and [173]


where

M = fw = 1;

Mm and Mb for the deepest point in the flaw (d) and for the points where the flaw intersects the free surface(s) are given in Table M.5.

A global bending moment on the cylinder can be included by adding the following stress to Pm:

Mglobal(ri + a)/;{(ri + B)4 – ri4} (M.24)

Range of application: 0 k a/B k 0.80.1 k a/c k 10.1 k B/ri k 0.2

Figure M.16 — Internal surface flaw in cylinder oriented axially

Figure M.17 — Internal surface flaw in cylinder oriented circumferentially

B

ri

CL

W

2c

ds

a

o

s

B

d

a

2c

X X


ri r

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Table M.5 — Mm and Mb for circumferential internal surface flaw in cylinder

M.4.3.3.3 Long internal surface flaws in cylinders oriented axially [169], [170] and [171]


where

M = fw = 1;

Mm and Mb are given in Table M.6 for the deepest point in the flaw.

Range of application: 0 k a/B k 0.80.1 k B/ri k 0.25

Table M.6 — Mm and Mb for long axial surface flaw in cylinder

a/c = 1.0, B/ri = 0.1 a/c = 1.0, B/r = 0.2


0.0 0.663 0.663 0.729 0.729 0.0 0.663 0.663 0.729 0.7290.2 0.667 0.574 0.681 0.623 0.2 0.667 0.582 0.681 0.6230.4 0.670 0.327 0.706 0.528 0.4 0.670 0.334 0.706 0.5280.6 0.686 0.140 0.733 0.431 0.6 0.686 0.117 0.733 0.4310.8 0.702 –0.105 0.764 0.332 0.8 0.702 –0.099 0.764 0.332

a/c = 0.5, B/ri = 0.1 a/c = 0.5, B/ri = 0.2

0.0 0.896 0.896 0.697 0.697 0.0 0.896 0.896 0.697 0.6970.2 0.999 0.731 0.731 0.628 0.2 1.004 0.735 0.731 0.6280.4 1.031 0.504 0.801 0.563 0.4 1.030 0.503 0.801 0.5630.6 1.121 0.306 0.889 0.502 0.6 1.124 0.305 0.889 0.5020.8 1.148 0.014 0.993 0.445 0.8 1.192 0.027 0.993 0.445

a/c = 0.2, B/ri = 0.1 a/c = 0.2, B/ri = 0.2

0.0 1.059 1.059 0.521 0.521 0.0 1.059 1.059 0.521 0.5210.2 1.168 0.870 0.617 0.623 0.2 1.144 0.851 0.617 0.6230.4 1.375 0.736 0.835 0.591 0.4 1.318 0.698 0.835 0.5910.6 1.599 0.561 1.048 0.556 0.6 1.517 0.515 1.048 0.5560.8 1.803 0.269 1.255 0.519 0.8 1.782 0.253 1.255 0.519

a/c = 0.1, B/ri = 0.1 a/c = 0.1, B/ri = 0.2

0.0 1.103 1.103 0.384 0.384 0.0 1.103 1.103 0.384 0.3840.2 1.219 0.921 0.482 0.487 0.2 1.214 0.903 0.482 0.4870.4 1.529 0.829 0.700 0.498 0.4 1.382 0.776 0.700 0.4980.6 1.939 0.677 0.981 0.525 0.6 1.661 0.624 0.981 0.5250.8 2.411 0.479 1.363 0.570 0.8 2.031 0.386 1.363 0.570

B/ri = 0.1 B/ri = 0.25

a/B Mm Mb a/B Mm Mb

0.0 1.122 1.122 0.0 1.122 1.1220.2 1.380 1.018 0.2 1.304 1.0020.4 1.930 1.143 0.4 1.784 1.0330.6 2.960 1.484 0.6 2.566 1.0940.8 4.820 1.990 0.8 3.461 0.949

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M.4.3.3.4 Long internal flaws in cylinders oriented circumferentially [172], [174] and [175]


where

M = fw = 1;


Loading in terms of a global moment Mglobal can be accounted for by adding the term in equation (M.23) to the primary stress, Pm.

Range of application: 0 k a/B k 0.80.1 k B/ri k 0.2

Figure M.18 — Long internal surface flaw in cylinder oriented axially

Figure M.19 — Long internal surface flaw in cylinder oriented circumferentially

B

ri

CL

W

a

a

ri

B

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Table M.7 — Mm and Mb for long circumferential internal surface flaw in cylindrical shell

M.4.3.3.5 External surface flaws in cylinders oriented axially [169], [170] and [171]


where

M = fw = 1;

Mm and Mb for the deepest point in the flaw (d) and for the points where the flaw intersects the free surface (s) are given in Table M.8.

Range of application: 0 k a/B k 0.80.05 k a/c k 10.1 k B/ri k 0.252c/W k 0.15

B/ri = 0.1 B/ri = 0.2

a/B Mm Mb a/B Mm Mb

0.0 1.122 1.122 0.0 1.122 1.122

0.2 1.261 0.954 0.2 1.215 0.933

0.4 1.582 0.909 0.4 1.446 0.810

0.6 2.091 0.810 0.6 1.804 0.650

0.8 2.599 0.600 0.8 2.280 0.411

Figure M.20 — External surface flaw in cylinder oriented axially

B

ri

CL

W

2c

d

sa

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Table M.8 — Mm and Mb for axial external surface flaw in cylinder

M.4.3.3.6 Circumferential external surface flaws in cylinders

The flat plate solution in M.3.2 can be applied to circumferential external surface flaws in cylinders.

M.4.3.3.7 Long external surface flaws in cylinders oriented axially [174] and [176]


where

M = fw = 1;


a/c = 1.0, B/ri = 0.1 a/c = 1.0, B/ri = 0.25


0.0 0.663 0.663 0.729 0.729 0.0 0.663 0.663 0.729 0.729

0.2 0.653 0.470 0.736 0.685 0.2 0.656 0.473 0.741 0.689

0.4 0.675 0.301 0.783 0.666 0.4 0.683 0.307 0.793 0.673

0.6 0.695 0.122 0.846 0.649 0.6 0.710 0.131 0.864 0.659

0.8 0.712 –0.068 0.926 0.634 0.8 0.736 –0.055 0.954 0.647a/c = 0.4, B/ri = 0.1 a/c = 0.4, B/ri = 0.25

0.0 0.951 0.951 0.662 0.662 0.0 0.951 0.951 0.662 0.662

0.2 0.953 0.716 0.685 0.641 0.2 0.964 0.726 0.689 0.644

0.4 1.077 0.561 0.799 0.673 0.4 1.110 0.582 0.806 0.678

0.6 1.213 0.377 0.970 0.715 0.6 1.289 0.417 0.982 0.721

0.8 1.361 0.167 1.198 0.769 0.8 1.502 0.230 1.217 0.775

a/c = 0.2, B/ri = 0.1 a/c 0.2, B/ri = 0.25

0.0 1.059 1.059 0.521 0.521 0.0 1.059 1.059 0.521 0.521

0.2 1.092 0.831 0.583 0.552 0.2 1.106 0.844 0.583 0.552

0.4 1.370 0.750 0.706 0.606 0.4 1.410 0.776 0.693 0.598

0.6 1.735 0.644 0.912 0.681 0.6 1.838 0.693 0.867 0.659

0.8 2.188 0.514 1.202 0.780 0.8 2.390 0.595 1.105 0.736

a/c = 0.1, B/ri = 0.1 a/c = 0.1, B/ri = 0.25

0.0 1.103 1.103 0.384 0.384 0.0 1.103 1.103 0.384 0.384

0.2 1.206 0.926 0.455 0.432 0.2 1.222 0.939 0.455 0.432

0.4 1.624 0.923 0.592 0.510 0.4 1.672 0.955 0.581 0.504

0.6 2.295 0.957 0.853 0.643 0.6 2.432 1.029 0.811 0.622

0.8 3.360 1.108 1.305 0.857 0.8 3.670 1.128 1.199 0.809

a/c = 0.05, B/ri = 0.1 a/c = 0.05, B/ri = 0.25

0.0 1.120 1.120 0.275 0.275 0.0 1.120 1.120 0.275 0.275

0.2 1.266 0.976 0.338 0.321 0.2 1.282 0.991 0.338 0.321

0.4 1.849 1.075 0.477 0.412 0.4 1.753 1.011 0.468 0.407

0.6 2.628 1.349 0.796 0.602 0.6 2.581 1.107 0.757 0.583

0.8 4.090 1.549 1.471 0.972 0.8 3.839 1.153 1.352 0.918

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© BSI 27 July 2005 221

M.4.3.3.8 Long external surface flaws in cylinders oriented circumferentially [39]

See Figure M.22 for the definition of the geometry (note, this solution is appropriate for membrane loading only; bending stresses Pb and Qb should be added to Pm and Qm for assessment purposes). The stress intensity factor solution is calculated from equations (M.1) to (M.7)

where

M = fw = 1;

(M.25)

where

Æ = ri/ro;

È = a/B.

Figure M.21 — Long axial external surface flaw in cylinder

Figure M.22 — Long circumferential external surface flaw in cylinder

B

ri

CL

W

a

Mb Mm1 Æ2–

1 1 Æ–( )–{ È }2 iÆ2–[ ]--------------------------------------------------- 0.8 1 Æ–( )È

1 1 Æ–( )È–------------------------------+ 4 1.08Æ

1 Æ–( ) 1 È–( )-----------------------------------+

⎩ ⎭⎨ ⎬⎧ ⎫

0.5–

= =

ri

B

a

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M.4.4 Embedded flaws in shells

The flat plate solution in M.3.4 can be applied to embedded flaws in shells

M.4.5 Flaws in nozzles

The flat plate solution in M.3.7 can be applied to radial internal corner flaws in nozzles, together with appropriate stress concentration factors.

M.5 Welded joints

M.5.1 Surface cracks at weld toes [see Figure 23a) to Figure 23c)]

M.5.1.1 General

When a flaw or crack is situated in a region of local stress concentration, such as the weld toe, it is necessary to include the effect of the field of stress concentration when calculating KI

21). Unless the KI solution being used already incorporates the influence of the stress concentration, it is necessary to introduce the correction factor Mk, which is a function of crack size, geometry and loading. In general, the correction factor, Mk, is the product of the ratio of the K for a crack in material with stress concentration to the K for the same crack in material without stress concentration.

Thus, Mk normally decreases with increases in through-thickness distance z from the weld toe to unity at crack heights of typically 30 % of material thickness. For butt welds, T-butt welds, full penetration cruciform joints and members with fillet or butt-welded attachments, Mk has been found to be a function of z, B and L. Here z is the height, measured from the weld toe, and L is the overall length of the attachment measured from weld toe to weld toe [177], as illustrated in Figure M.23a) to Figure M.23c).

The Mkm and Mkb stress intensity factor magnification factors, for membrane and bending loading, are required for the general stress intensity factor solutions in equations (M.1) to (M.7). The resulting relationships are given in M.5.1.2 and M.5.1.3.

Mk has been calculated by 2D finite element analysis for profiles representing sections of the welded joint geometry. Thus, Mk is directly applicable to the case of a straight-fronted weld toe surface crack (i.e. a/2c = 0). However, experience indicates that it can also be applied to semi-elliptical cracks (0 k a/2c k 0.5) and other flaw types. The nature of the finite element model used to calculate Mk is such that the solutions produced are not applicable for z = 0, and near-surface Mk values should be used (z = 0.15 mm) for the intersection of surface flaws with the weld toe and through-thickness flaws at weld toes.

The solutions presented apply for 45° weld profiles: Mk is slightly lower for lower angles and vice versa [36].

More accurate solutions based on 3D-stress analysis of semi-elliptical cracks at weld toes are available [178], [179] and [180]. One such solution [178], is presented in M.5.1.3.

For fillet or partial penetration welded load-carrying T-joints or cruciform joints (Figure M.24), L/B is not relevant, but the weld throat thickness, tw, is [36]. The resulting Mk solutions are given in M.5.1.2.

M.5.1.2 Solution based on 2D finite element analysis [177]

In general the following solutions apply:

Mk = v(z/B)w (M.26)

down to Mk = 1

where

v and w have the values given in Table M.9 for flaws at the toes of full penetration or attachment welds.

For flaws at the toes of fillet or partial penetration load-carrying welds (see Figure M.24), the values of v and w are those corresponding to L/B > 2 for axial loading or L/B U1 for bending and the resulting value of v is multiplied by (B/tw)0.5.

21) This approach contrasts with that used in the application of the fatigue design rules (e.g. BS 7608). In applying such rules, the design data, obtained from fatigue tests on welded specimens, already incorporate the influence of the weld stress concentration factor and are therefore used in conjunction with the nominal stress range near the weld.

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a)

b)

c)

Figure M.23 — Crack and welded joint geometries

zB

L

zB

L

z

L

B

αtw

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Table M.9 — Values of v and w for axial and bending loading

M.5.1.3 Solution based on 3D finite element modelling [178]

M.5.1.3.1 General

Alternative stress intensity magnification factor solutions (Mk) for the deepest and surface points of a semi-elliptical weld-toe flaw (see Figure M.23) are given in M.5.1.3.2 and M.5.1.3.3. The solutions were obtained by curve fitting to individual finite element analyses [178]. They include the weld profile angle as variables, but the following simplified solutions are valid for 45º weld profiles with sharp radii (less than 0.1B) and for the following parametric ranges:

0.005 < a/B < 1.0

0.1 k a/c k 1.0

0.5 k L/B k 2.75 (for L/B > 2.75, use the value for L/B = 2.75)

Figure M.24 — Transverse load-carrying cruciform joint

Loading mode L/B z/B v w

Axial k2 k0.05(L/B)0.55 0.51(L/B)0.27 –0.31

>0.05(L/B)0.55 0.83 –0.15(L/B)0.46

>2 k0.073 0.615 –0.31

>0.073 0.83 –0.20

Bending k1 k0.03(L/B)0.55 0.45(L/B)0.21 –0.31

>0.03(L/B)0.55 0.68 –0.19(L/B)0.21

>1 k0.03 0.45 –0.31

>0.03 0.68 –0.19

aB

h

w

L

tw

2a

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M.5.1.3.2 Deepest point

a) Axial

(M.27)

where

where

g1 = –1.034 3(a/c) – 0.156(a/c) + 1.340 9;

g2 = 1.321 8(a/c)–0.61153;

g3 = –0.872 38(a/c) + 1.278 8;

g4 = –0.461 90 (a/c)3 – 0.670 90(a/c)2 – 0.375 71(a/c) + 4.6511;

and where

where

g5 = –0.015 647(L/B)3 + 0.090 889(L/B)2 – 0.171 80(L/B) – 0.245 87;

g6 = –0.201 36(L/B)2 + 0.93311(L/B) – 0.414 96;

g7 = 0.201 88(L/B)2 – 0.978 57(L/B) + 0.068 225;

g8 = –0.027 338(L/B)2 + 0.125 51(L/B) – 11.218.

NOTE If equation (M.27) gives a value of Mk < 1.0 assume that Mk = 1.0.

b) Bending

If 0.005 k a/B k 0.5, then the following expression applies:

(M.28)

where

where

g1 = –0.014 992(a/c)2 – 0.021 401(a/c) – 0238 51;

g2 = 0.617 75(a/c)–1.027 8;

g3 = 0.000132 42(a/c) – 1.474 4;

g4 = –0.287 83 (a/c)3 + 0.587 06(a/c)2 – 0.371 98(a/c) – 0.898 87;

;

;

4;

Mkm f1aB----⎝⎛ a

c---⎠⎞, f2

aB----⎝ ⎠⎛ ⎞ f3+ + a

B----⎝⎛ L

B---- ⎠⎞,=

fa

B

a

ca B a B

g g a Bg

1

0

0 433 58 0 931 631 2

3

,( ) ( ) ( )+ ( ){ }⎡⎣⎢

⎤⎦⎥

−= . + . exp

.0050 966

4{ } + g

fa

Ba B a B

a B

2

176 419 9 0 107 40

1( ) − − ( ){ } ( )− ( )= 0.215 21 + 2.814 1

.. /

fa

B

L

Ba B a B g a B g a B

g

3

0 230 03

6

2

70

5,

.( ) ( ) ( ) ( ) + ( )( )= .339 94 + 1.949 3 + ++{ }g

8

Mkb f1aB----⎝⎛ a

c---⎠⎞, f2

aB----⎝ ⎠⎛ ⎞ f3+ + a

B----⎝⎛ L

B----⎠⎞,=

fa

B

a

ca B a B

g g a Bg

1

1 2, exp( ) ( ) ( )( ){ }⎡

⎣⎢⎤⎦⎥

−= 0.065 916 + 0.520 86

+ 03

..103 64

+{ } g

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and where

;

where

g5 = –17.195(a/B)2 + 12.468(a/B) – 0.516 62;

and where

where

g6 = –0.059 798 (L/B)3 + 0.380 91 (L/B)2 – 0.802 20 20 (L/B) + 0.319 06;

g7 = –0.358 48(L/B)2 + 1.397 5(L/B) – 1.753 5;

g8 = 0.312 88(L/B)2 – 1.359 9(L/B) + 1.661 1;

g9 = –0.001 470(L/B)2 – 0.002 507 4(L/B) – 0.008 984 6.NOTE If equation (M.28) gives a value of Mk < 1.0 assume that Mk = 1.0.

M.5.1.3.3 Surface point

a) Axial

(M.29)

where

where

g1 = 0.007 815(c/a)2 – 0.070 664(c/a) + 1.850 8

g2 = –0.000 054 546(L/B)2 + 0.000 136 51(L/B) – 0.000 478 44;

g3 = 0.000 491(L/B)2 x 0.001 359(L/B) + 0.011 400;

g4 = 0.007 165 4(L/B)2 – 0.033 399(L/B) – 0.250 64;

g5 = 0.018 640(c/a)2 + 0.243 11(c/a) – 1.764 4;

g6 = –0.001 671 3(L/B)2 + 0.009 062 0(L/B) – 0.016 479;

g7 = –0.003 161 5(L/B)2 – 0.010 944(L/B) + 0.139 67;

g8 = –0.045 206(L/B)3 + 0.323 80(L/B)2 – 0.689 35(L/B) + 1.495 4;

and where

where

g9 = –0.254 73(a/c)2 + 0.409 28(a/c) + 0.002 189 2;

g10 = 37.423(a/c)2 – 15.741(a/c) + 64.903;

;

;

fa

Ba B a B

g

2

2 808 6

0 1 05( ) − −( ) ( )= .219 950 + .021 403

.

fa

B

L

Ba B a B g a B g

g

3

0 200 77

7

26

7,.( ) ( ) − ( ) ( ) +( ) −

= 0.233 44 / 0.148 2 / + /88 9

a B g/( ) +{ }

Mkm f1aB----⎝⎛ c

a--- L

B----⎠⎞, , f2

aT----⎝⎛ a

c---⎠⎞, f3

aB----⎝⎛ a

c--- L

B----⎠⎞, ,××=

fa

B

c

a

L

Bg a B g

gc

ag

c

ag

1 1 5

2

2

3 41, ,( ) ( )

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪= ++ + −− ( ){ }

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪a Bg

c

ag

c

ag

6

2

7 8+ +

fa

B

a

ca c a c a B

g

2

2

0 286 39 0 1 0 99

, .( ) − ( ) ( ){ }( )= + .354 11 + .643 0 + .274 4 1110− ( ){ }a B

g

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and where

whereg11 = –0.105 53(L/B)3 + 0.598 94(L/B)2 – 1.094 2(L/B) – 1.265 0;

g12 = 0.043 891(L/B)3 – 0.248 98(L/B)2 + 0.447 32(L/B) + 0.601 36;

g13 = –0.011 411(a/c)2 + 0.004 369(a/c) + 0.517 32.

b) Bending

(M.30)

where

where g1 = 0.002 323 2(c/a)2 – 0.000 371 56(c/a) + 4598 5;

g2 = –0.000 044 010(L/B)2 + 0.000 144 25(L/B) x 0.000 867 06;

g3 = 0.000 399 51(L/B)2 – 0.001 371 5(L/B) + 0.014 251;

g4 = 0.004 616 9(L/B)2 – 0.017 917(L/B) – 0163 35;

g5 = –0.018 524(c/a)2 + 0.278 10(c/a) – 5.425 3;

g6 = –0.000 379 81(L/B)2 + 0.002 507 8(L/B) + 0.000 146 93;

g7 = –0.003 850 8(L/B)2 + 0.002 321 2(L/B) – 0.026 862;

g8 = –0.011 911(L/B)3 + 0.082 625(L/B)2 – 0.160 86(L/B) + 1.230 2;

g9 = 0.277 98(a/B)3 – 1.214 4(a/B)2 – 2.468 0(a/B) + 0.099 981.

and where

whereg10 = –0.259 22(a/c)2 + 0.395 66(a/c) + 0.011 759;

g11 = 6.596 4(a/c)2 + 55.787(a/c) + 37.053;

and where

whereg12 = –0.148 95(L/B)3 + 0.815(L/B)2 – 1.479 5(L/B) – 0.898 08;

g13 = 0.055 459(L/B)3 – 0.301 80(L/B) + 0.541 54(L/B) + 0.534 33;

g14 = –0.013 43(a/c)2 + 0.006 670 2(a/c) – 0.759 39.

;

;

;

fa

B

a

c

L

Bg a B g a B

g

3 11

0 754 29

12

13, ,

.( ) = ( ) + ( ){ }exp

Mkb f1aB----⎝⎛ c

a--- L

B----⎠⎞, , f2

aB----⎝⎛ a

c---⎠⎞, f3

aB----⎝⎛ a

c--- L

B----⎠⎞, ,××=

fa

B

c

a

L

Bg a B g

gc

ag

c

ag

1 1 5

2

2

3 41, ,( ) ( )

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪= ++ + −− ( ){ } +

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪a B gg

c

ag

c

ag

6

2

7 8

9

+ +

fa

B

a

ca c a c a B

g

2

2

0 350 06 0 1 010

, .( ) − ( ) ( ){ }( )= + .407 68 + .705 3 + .249 888 111− ( ){ }a B

g

fa

B

a

c

L

Bg a B g a B

g

3 12

0 947 61

13

14, , / /

.( ) = ( ) + ( ){ }exp

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M.5.2 Weld root flaws in cruciform joints [181]

M.5.2.1 General

See Figure M.24 for the definition of the geometry. (Note that this refers only to straight fronted cracks [a/2c = 0].) The stress intensity solution is calculated from equations (M.1), (M.2) and (M.4) to (M.7):

where

M = Mm = Mb = 1;

Ö is the stress in the loaded member.

The influence of joint geometry on stress intensity factors for root flaws in fillet and partial penetration welds is accounted for by the application of modified finite width correction and stress intensity factor magnification factors, fwm, fwb, Mkm and Mkb, for membrane and bending loading.


where

Æo = 0.956 – 0.343(h/B)

Æ1 = –1.219 + 6.210(h/B) – 12.220(h/B)2 + 9.704(h/B)3 – 2.741(h/B)4

Æ2 = 1.954 – 7.938(h/B) + 13.299(h/B)2 – 9.541(h/B)3 + 2.513(h/B)4

Range of application: 0.1 k 2a/W k 0.7;0.2 k h/B k 1.2.


where

= 2a/W.

where

Æ0 = 0.792 – 3.560(h/B) + 1.276(h/B)2

Æ1 = 1.064 – 4.898(h/B) + 3.670(h/B)2

Æ2 = 0.496 – 1.328(h/B) + 1.012(h/B)2

È0 = 0.285(h/B)2 – 1.866(h/B)

È1 = 0.028(h/B) – 0.761

Range of application: 0.1 k 2a/W k 0.7.

(M.31)

(M.32)

(M.33)

for 0.2 k h/B k 0.7 (M.34)

for 0.7 k h/B k h/B k 0.7

wmf = 2

2a

W

0 5.

sec⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

⎛

⎝⎜

⎞

⎠⎟

km o 1 2/ /M = + a W + a W2 2

2( ) ( )

wb =

2

1

1

1 +

1

2

+

3

8

11

16

+ 0.464f−( )−

−⎡⎣⎢

⎤⎦⎥

0 5

3

2 3 4

.

kb

2 /

exp 2 / 2 /M = a W a Wa W

0

1 2( )( ) ( ) ( )ln

kb2 /M = a Wexp

0

1( )( )

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M.6 Round bars/bolts

M.6.1 Straight-fronted flaws in round bars [182]

See Figure M.25a) for the definition of the geometry. The stress intensity factor is calculated from equations (M.1) to (M.7):

where

M = Mkm = Mkb = fw = 1, with Mm and Mb as follows:

Range of application: 0.062 5 k a/2r k 0.625.

M.6.2 Semi-circular surface flaws in round bars [182]

See Figure M.25a) for the definition of the geometry. The stress intensity factor solution is calculated from equations (M.1) to (M.7):

where


where

Range of application: a/2r < 0.6.NOTE K solutions for straight fronted flaws in round bars (M.6.1) are generally conservative compared to semi-circular surface flaws.

(M.35)

(M.36)

(M.37)

m

2 3

0.926 1.771

2

26.421

1

2

78.481

1

2

M = a

r r r− ⎛

⎝⎜⎞⎠⎟

− ⎛⎝⎜

⎞⎠⎟

− ⎛⎝⎜

⎞⎠⎟⎟

⎛⎝⎜

⎞⎠⎟

+a

r87.911

2

4

b

2 3

= 1.04 3.64

2

16.86

2

32.59

2

Ma

r +

a

r

a

r− ⎛

⎝⎜⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

− ⎛⎝⎜

⎞⎠⎟

++a

r28.41

2

4⎛⎝⎜

⎞⎠⎟

M ga

r

a

rm

sin= + ⎛⎝⎜

⎞⎠⎟

+ − ⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

⎡

⎣⎢⎢

⎤

⎦⎥⎥

0 752 2 02

2

0 37 1

4

3

. . .

π

M ga

rb

sin= + − ⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

⎡

⎣⎢⎢

⎤

⎦⎥⎥

0 923 0 199 1

4

4

. .

π

g

a

r

a

r

a

r

=

1 84

4 4

4

0 5

.

.

ππ π

π

tan

cos

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

⎛⎝⎜

⎞⎠⎟

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M.6.3 Semi-circular surface flaws in bolts

M.6.3.1 Solution 1 [175]

See Figure M.25b) for the definition of the geometry. This solution has been developed for the ISO M8 × 1.0 bolt geometry. The stress intensity factor is calculated from equations (M.1) to (M.7):where


where the following apply for the conditions indicated:a) Tension loading (Mm), at the deepest point in the flaw:

Æ0 = 1.015 5 – 0.237 5(a/c);Æ1 = –0.584 + 0.015(a/c);Æ2 = 6.455 75 – 3.348 75(a/c).

Intersection of the flaw with the free surface:Æ0 = 0.469 5 + 0.822 5(a/c);Æ1 = 0.377 75 – 1.478 75(a/c);Æ2 = –0.160 25 + 2.946 25(a/c).

b) Bending loading (Mb), at the deepest point in the flaw:Æ0 = 0.893 75 – 0.363 75(a/c);Æ1 = –0.559 25 + 0.366 25(a/c);Æ2 = 2.379 – 1.88(a/c).

Intersection of the flaw with the free surface:Æ0 = 0.653 5 – 0.092 5(a/c);Æ1 = –1.148 75 + 1.558 75(a/c);Æ2 = 3.028 – 1.855(a/c).

Range of application: 0.2 k a/c k 1;0.1 k a/2r k 0.5.

a) In round bar b) In bolt

Figure M.25 — Surface flaw

(M.39)

a

r

2c

a)

b)

M = M = + a r + a rm b 0 1 2

2

2 2/ /( ) ( )

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M.6.3.2 Solution 2 [182]

An alternative solution for semi-circular surface flaws in threaded bolts (UNF) in tension is calculated from equations (M.1) to (M.7):

where

M = Mkm = Mkb = fw = 1 with Mm as follows:NOTE This solution is based on a combination of solutions for semi-circular surface flaws (M.6.2) and straight-fronted flaws in round bars for a/2r > 0.4 (M.6.1), together with thread effects for a/2r < 0.1.

Mm = 2.043exp{–31.332(a/2r)} + 0.650 7 + 0.536 7(a/2r) + 3.046 9(a/2r)2 – 19.504(a/2r)3 + 45.647(a/2r)4 (M.40)

Range of application: 0.004 k a/2r k 0.65.

Equation (M.40) can be used for flaws in smooth bars if the exponential term is set to zero. Equation (M.41) is a similar expression given for bending loading (this solution does not include thread effects).

M.6.4 Circumferential flaws in round bars [40]


where


(M.43)

M.7 Tubular joints (not nozzles)

See B.3.2 for guidance on the determination of appropriate stress intensity factors.

(M.41)

(M.42)

Figure M.26 — Circumferential flaw in bolt

M =a

r

a

r+

a

rb

2 3

0.630 1 + 0.034 88

2

3.336 5

2

13.406

2

⎛⎝⎜

⎞⎠⎟

− ⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎠⎟

− ⎛⎝⎜

⎞⎠⎟

6.002 1

2

4

a

r

m

1.52 3

2

1 0.5 0.375 0.363M =r

r a

+r a

r+

r a

r

r

−( )−⎛

⎝⎜⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

− −1 5.

aa

r+

r a

r

⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪0.731

4

Mr

r a

r a

r

r a

rb

=−( )

+ −⎛⎝⎜

⎞⎠⎟

+ −⎛⎝⎜

⎞⎠⎟

−0 375

1 0 5 0 375 0 313

2 5

2 5

2

..

.

. . .

rr a

r

r a

r

r a

r

−⎛⎝⎜

⎞⎠⎟

+ −⎛⎝⎜

⎞⎠⎟

+ −⎛⎝⎜

⎞⎠⎟

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

3 4 5

0 273 0 537. .

a

r

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Annex N (normative) Simplified procedures for determining the acceptability of a known flaw or estimating the acceptable flaw size using Level 1 fracture procedures

N.1 Estimation of acceptable flaw sizes

N.1.1 General

An equivalent flaw parameter, , is defined as the half-length of a through-thickness flaw in an infinite plate subject to remote tension loading. A preliminary estimate of acceptable flaw sizes can then be obtained by calculating the maximum tolerable value, .

The limiting flaw parameter, , may be used to represent a variety of different flaw shapes and dimensions of equivalent severity. Equivalent part thickness flaw dimensions can be obtained using the simplified graphical solutions of Figure N.1 and Figure N.2. Finite width corrections may be required (see N.1.4). The resulting flaw dimension has to be checked as acceptable for plastic collapse considerations by calculating the associated Sr value. If Sr is less than 0.8 the flaw is acceptable. If Sr is greater than 0.8, the flaw dimensions have to be reduced to give an Sr value not exceeding 0.8. However, under certain conditions of strain controlled loading where it can be shown that structural plastic collapse is not possible, this restriction on Sr can be ignored (see 7.2.8).

The equivalent tolerable flaw parameter, , is calculated from the expressions outlined in N.1.2 and N.1.2, which include a variable safety factor, averaging about 2. (See Annex K for general guidance on safety factors. However, no additional partial safety factors are required for Level 1.)

N.1.2 Calculation of when estimates of Kmat are available

When toughness estimates are available in terms of Kmat, can be calculated using the following equation:

N.1.3 Calculation of when estimates of $mat are available

When toughness estimates are available in terms of ̧ mat, can be calculated using either of the following equations, as appropriate:

— for steels (including stainless steels) and aluminium alloys, where Ömax/ÖY k 0.5 and for all other materials for all Ömax/ÖY ratios:

— for steels (including stainless steels) and aluminium alloys where Ömax/ÖY > 0.5:

(N.1)

(N.2)

(N.3)

a

am

am

am

am

am

aK

m =

1

2

2

mat

maxπ

⎡

⎣⎢

⎤

⎦⎥

am

am

aE

m =

2

mat

2

max

Y

Yπ⎛

⎝⎜

⎞⎠⎟

aE

m

mat

Y

Y

=

2 .maxπ −

⎛

⎝⎜

⎞

⎠⎟0 25

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N.1.4 Finite width correction

In applications where the component under consideration has a finite width and the calculated value exceeds one-twentieth of the total width, then the calculated value should be multiplied by the following factor:

where

W is the width of the component [183].

It should be noted that the graphical solutions of Figure N.1 and Figure N.2, although based on Annex M solutions, represent simplified versions of the mathematical forms. Also, the finite width correction is only an estimate. Furthermore, other effects such as bulging have not been allowed for. Because of these factors, the manual treatment will not necessarily give the same answers as those achieved by following the procedures described in 7.2.

N.2 Estimation of the acceptability of a known flaw

When the dimensions of a flaw are known the equivalent flaw parameter defined in N.1.1 can be obtained using Figure N.1 or Figure N.2. The acceptability of the flaw can then be assessed by comparing the value of with the maximum tolerable value, , as determined from equation (N.1) or (N.2).

amam

1

(2 ) + 1a Wm

/

a

a am

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Fig

ure

N.1

— R

ela

tio

nsh

ip b

etw

een

act

ua

l fl

aw

dim

ensi

on

s a

nd

th

e p

ara

met

er

fo

r su

rfa

ce f

law

s

1

0.1

0.01

0.00

10.

010.

110

1

a/B

a/B

_

a/2c

= 0

.5

a/2c

= 0

.4

a/2c

= 0

.3

a/2c

= 0

.2

a/2c

= 0

.1

a/2c

= 0

a

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N

OT

E

can

be

use

d to

est

imat

e ac

cept

able

cen

tral

em

bedd

ed f

law

.

Fig

ure

N.2

— R

ela

tio

nsh

ip b

etw

een

act

ua

l fl

aw

dim

ensi

on

s a

nd

th

e p

ara

met

er

fo

r em

bed

ded

fla

ws

2c2a

B

0.01

0.05

0.1

0.5

1.0

5.0

10.0

1.0

0.1

=0.

990.

80.

60.

40.

2

p

a/2c

a/2(

p+a

)

a/(p

+a)

0

a B----

a

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Annex O (informative) Consideration of proof testing and warm prestressing

O.1 General

This annex describes how the loading history due to i) proof or overload tests or ii) warm prestressing of a structure containing flaws may be taken into account when performing an integrity assessment using the procedures described in Clause 7. The effect of loading history is considered with regard to mechanical relaxation of residual stresses and enhancement of lower shelf fracture resistance. The latter is only applicable where the pre-load constitutes a warm prestress. (See 7.2.4.4.)

Procedures are set out in this annex which enable these effects to be quantified. In practice, the different phenomena may interact and it may not be possible to separate the different effects simply. This annex does not cover sub-critical crack growth in service.

O.2 Proof or overload testing

In the assessment of a cracked component that has been proof tested, the residual stress level assumed in the fracture analysis may be taken [184] as a uniform stress equal to the lower of the following factors:

either or (O.1)

where

is the maximum reference stress under the proof load conditions (see 7.2.7, 7.3.7 and Annex P). Here, the upper limit for should be and the lower limit 0.4 ;

is the appropriate material yield strength at the proof test temperature;

is the flow strength (assumed to be the average of the yield and the tensile strengths) at the proof test temperature. Here, is not limited to 1.2 times the yield strength.

Equation (O.1) is also used in 7.3.4.2 to account for mechanical relief of residual stresses caused by the interaction of primary and residual stresses under loads [184]. It is used here to account for mechanical stress relief under proof test or prior overload, on the assumption that the same equation is equally applicable under any loading conditions and that the reduction in residual stress due to a proof load or prior overload remains after the load is removed.

Note that the assumed residual stress level should always be U0.

Where a crack in a proof loaded structure is believed to have initiated in service, after the proof loading, the residual stress level in fracture analysis should be taken as a uniform stress equal to the lower of the following factors:

either or (1.1 – 0.8 ) (O.2)

where

is the appropriate material yield strength at the proof test temperature;

is the applied stress due to the proof loads at the location of interest [185]. Here the upper limit for should be and the lower limit 0.3 .

The applied stress, , should be taken as the lower of the membrane stress in the section, or the total stress including membrane, bending and stress concentration effects. The total stress may be lower than the membrane stress if the bending stress is negative or if there is a stress de-concentration effect, such as the convex side of a welded joint with angular misalignment.

O.3 Warm prestressing

A warm prestress (WPS) is an initial pre-load applied to a ferritic steel structure containing a pre-existing flaw, which is carried out at a temperature above the ductile-brittle transition temperature, and at a higher temperature or in a less-embrittled state than that corresponding to the subsequent service assessment. A WPS argument differs from a proof-test argument in conferring added resistance to fracture under the assessment conditions; that is, it is considered to elevate the stress intensity factor at failure, Kf, above the corresponding fracture toughness, Kmat, in the absence of the WPS [186], [187], [188], [189], [190] and [191].

Ö′Y 1 4. −′

⎛

⎝⎜

⎞

⎠⎟ ′ref

f

Y

ÖrefÖref Ö′f Ö′f

Ö′YÖ′f

Ö′f

Ö′Y Ö′Y Öa

Ö′YÖa

Öa Ö′Y Ö′YÖa

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Although there is some evidence [185] and [191] that warm prestressing may produce benefits in terms of both residual stress relaxation [186] and improvement in fracture resistance, the evidence is not conclusive. It is therefore recommended that, where some relaxation in residual stress has been adopted in accordance with O.2, no improvement in fracture toughness should be claimed in the same assessment through the WPS argument.

The WPS review presented by Muhammed [185] suggests that repeated prestressing does not significantly increase fracture resistance above the level achieved following a single prestress. It is recommended that no extra benefit above that obtained from a single prestress should be claimed in such cases.

The WPS effect is most beneficial at low values of Kmat. Hence, this procedure is most effective for material exhibiting toughness values determined using KIc and KQ values directly and not where Jmat or ̧ mat values are applicable due to the extent of plasticity exhibited at the service temperature.

In service assessments using the procedure of the main document, the fracture toughness used in determining Kr is then taken as the enhanced value, Kf.

Warm prestressing can involve three types of cycle (Figure O.1). T1 and T2 denote the temperatures at which the pre-load and re-load to failure occur, respectively, in each case. Similarly, the stress intensity factors due to the pre-load and following the unload are denoted K1 and K2, respectively. The three types of cycle are as follows:

a) Load-Unload-Cool-Fracture (LUCF), where the structure is pre-loaded at temperature T1 to stress intensity factor K1, unloaded to stress intensity factor K2, cooled to temperature T2 and re-loaded to fracture. The case where T2 = T1 is permissible if hardening mechanisms have occurred prior to the re-load to fracture.

b) Load-Cool-Unload-Fracture (LCUF), where cooling to T2 takes place prior to unloading and re-loading to fracture.

c) Load-Cool-Fracture (LCF). This is similar to the LUCF cycle except that no unloading occurs prior to the imposition of extra load to fracture.

a) b) c)

Figure O.1 — Typical warm pre-stress cycles

Stre

ss in

tens

ity fa

ctor

K1

Temperature

(LUCF)

Kf

(LCUF) (LCF)Kf

Kf

K2

T2 T1 T2 T1 T2 T1

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The greatest benefit in terms of maximizing Kf is given by the LCF cycle: the least by the LUCF cycle with full unloading. Intermediate forms of cycle, where partial unloading occurs prior to re-loading to failure, and where the temperature and pressure are simultaneously reduced, give benefits lying between these two limits.

This annex gives advice on quantifying the benefit of a WPS. Two levels of argument are set out: firstly, a simplified lower-bound approach; and secondly, a more detailed route based on calculations, which may be of value when the simplified route is insufficient. The detailed route is consistent with a best-estimate prediction of fracture load.

For a WPS argument to be made in accordance with the procedure of this annex, the following conditions should be met.

1) The failure mechanism at the service condition should be by cleavage.

2) The flow properties of the material should increase between the WPS and the service failure condition.

3) There should be no significant sub-critical crack growth between the WPS and the service failure condition.

4) The stress intensity factor K1 due to the WPS loading should exceed the baseline fracture toughness Kmat at the re-load condition.

5) Small-scale yielding conditions hold, that is (K1/ÖY1)2/2¶; is much less than the size of the uncracked ligament and any relevant structural dimensions. Here ÖY1 is the yield strength at the pre-load and ¶ = 1 or 3 in plane stress or plane strain, respectively. As defined in Clause 7, the stress intensity factor, K1, is based on the elastic loads induced by the WPS only. No account should be taken of any plasticity induced in the preload by using J or CTOD approaches for the applied conditions.

There is evidence [185] and [188] that, for increasing pre-loads, the benefits on the apparent re-load fracture toughness lessen. Indeed, in the limit of extensive plasticity, the toughness determined in terms of CTOD or J after WPS loading may actually be reduced compared to its value in the absence of the WPS. Muhammed [185] and Chell [188] should be consulted for further advice in cases of large pre-loads.

6) The pre-load and re-load should be in the same direction; that is, both tensile or both compressive at the crack tip. A compressive pre-load followed by a tensile re-load may reduce the apparent fracture toughness.

O.4 Simplified WPS argument

Failure is avoided if the stress intensity factor during cooling is constant or monotonically falling to a value K2. This corresponds to a benefit if K2 exceeds Kmat, the fracture toughness in the absence of a WPS, and is consistent with maximum benefit from an LCF cycle. Margins against failure are not in general given by this simplified argument. In order to quantify margins it is necessary to use the detailed approach of O.5.

A particular example of this simplified WPS argument is in the assessment of thermal transients (e.g. downshocks or blow-down conditions), where cleavage fracture would otherwise be predicted. The loading history during the thermal shock event is regarded as a WPS. It is argued that failure does not occur when the instantaneous stress intensity factor, KI, exceeds the corresponding Kmat if KI is then reducing with temperature. The maximum size of flaw that satisfies this criterion can be compared with the size of the largest flaw that may have escaped detection to derive a margin on crack size. Any sub-critical growth of the latter flaw between inspection and the service assessment time should be allowed for.

O.5 Full WPS procedure

The argument is based on the LUCF cycle, allowing for partial unloading. This provides a conservative prediction of the stress intensity factor at failure, Kf, during the re-load compared with the other forms of WPS cycle. The fracture toughness used in service assessments using the fracture procedures of Clause 7 is then Kf .

The following steps should be carried out in quantifying the effect of the WPS on Kf for a given structural geometry and flaw dimensions:

a) Determine the temperature and pressure corresponding to the WPS.

b) Determine the stress intensity factor decrement due to the unload, K1 – K2. It follows that K1 – K2 is independent of the magnitude of any system or residual stresses incorporated in the total stress intensity factors K1 and K2 at the pre-load and unload phases, and depends on the contribution due to the varying load only.

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c) Determine the fracture toughness, Kmat, of the material at the assessment time, but neglecting the effects of the WPS. The effects of any degrading mechanisms, such as strain ageing or irradiation/hydrogen embrittlement that may have occurred between the time of the WPS and the subsequent assessment, should be taken into account. A lower bound value of Kmat should be adopted here both for consistency with the procedures of Clause 7 and to predict the elevation of Kf conservatively [see equation (O.3)].

d) Determine the stress intensity factor at failure from the following equation:

Kf = K2 + 0.2(K1 – K2) + 0.87Kmat (O.3)

The value Kf – K2 is the additional stress intensity factor due to the re-load. Equation (O.3) holds provided that the following applies:

Kf – K2 k (1 + ×) (K1 – K2)/2 (O.4)

where × is the ratio of the flow strengths (defined as the mean of the yield and ultimate tensile strengths) at the failure and pre-load conditions. Then × exceeds unity in the cases of either a fall in temperature between the pre-load and re-load or when hardening mechanisms have occurred. If inequality equation (O.4) fails to hold then it is conservative to assume that Kf – K2 = 0.

Smith and Garwood [183] give an alternative expression to equation (O.3) under the same conditions (for K2 = 0):

where ÖY2 is the yield strength corresponding to the final fracture condition. Then ÖY2 U ÖY1. This equation satisfies Kf = Kmat when K1 = Kmat and Kf U Kmat for K1 U Kmat, as expected. Equations (O.3) and (O.5) are shown by Smith and Garwood [186] to give similar results on a plot of Kf /Kmat against K1/Kmat, with each equation predicting results within the scatter band of experimental data.

Work reported by Muhammed [192] confirms that equations (O.3) and (O.4) give a conservative prediction of fracture toughness, even after exposure to hydrogen. However, it was also noted in the same reference that the safety margins on the predictions may be slightly reduced when compared to cases without the effects of hydrogen. Therefore, for components that have been exposed to hydrogen, the value of Kmat and ÖY2 used in equations (O.3) and (O.4) should be those appropriate to the hydrogen embrittled state.

Annex P (normative) Calculation of reference stress

P.1 Purpose

In carrying out a failure assessment, it is necessary to determine the reference stress, Öref, for the flawed structure or component. For Level 1 assessment, this is divided by the flow strength to determine Sr and for Levels 2 and 3, it is divided by yield strength to obtain Lr. Sr and Lr are measures of the amount of plasticity at the crack tip.

Three potential collapse modes can be identified (see also P.9):

— collapse of the remaining ligament adjacent to the flaw being assessed — local collapse;— collapse of the structural section containing the flaw — net section collapse;— collapse of the structure by gross straining — gross section collapse. This occurs when collapse takes place away from the flawed section or is unaffected by the presence of the flaw.

This annex provides formulae for the calculation of Öref for local or net section collapse for various structural configurations. Gross section collapse is not dealt with here, it being outside the scope of this guide and being preventable by attention to normal good design practices.

In redundant structures, it may be excessively conservative to consider solely local collapse. Global collapse may be more relevant and limits are given for which an additional check on global collapse should be made. Methods are provided for the evaluation of global collapse.

(O.5)K KK

Kf mat

Y

Y Y

Y1

Y mat

=+

⎛

⎝⎜

⎞

⎠⎟ +⎛

⎝⎜

⎞

⎠⎟2

1 2

1

2

1

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P.2 General

A check on local collapse should be made for all flaws. This annex provides formulae to determine Öref in order to make such a check. Where stated, the validity of the solutions given in this annex is limited strictly to the ranges stated; no extrapolation outside these limits should be carried out. If stresses due to stress concentration or stress magnification effects are considered primary, then they contribute to plastic collapse and have to be added to the reference stress solutions given below. Thus, additional bending stresses due to misalignment (see Annex D), if considered primary, are included by adding the term (km – 1)Pm to Pb in the relevant Annex P equations.

Multiple flaws should be assessed for interaction in accordance with 7.1.2 and Figure 9. The area of all flaws should be included in the formulae for Öref given in P.4.

If, in an initial check to a FAD a flaw is unacceptable because of plastic collapse of the remaining ligament (Lr > Lrmax or Sr > 1), a further check should be made applying recharacterization of the flaw (see 7.1.1.2 and Annex E).

P.3 Formulae for flat plates [166]

P.3.1 Through-thickness flaw (see Figure M.1)

The reference stress is calculated from the following equation:

P.3.2 Surface flaw (see Figure M.2)

The reference stress is calculated from either of the following equations as appropriate:

a) normal bending restraint (e.g. uniform remote stress plus bending):

b) negligible bending restraint (e.g. pin jointed):

where

µ¾ = (a/B)/{1 + (B/c)} for W U 2(c + B);

µ¾ = (2a/B)(c/W)} for W < 2(c + B).

P.3.3 Long surface flaws in plates (see Figure M.6)

The reference stress is calculated from equations (P.2) and (P.3) where µ¾ = a/B.

(P.1)

(P.2)

(P.3)

ref

b b

2

m

2

=+ +( )

− ⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

P P P

a

W

9

3 1

2

0 5.

ref

b b

2

m

=+ + − ′′( ){ }

− ′′( )

P P P9 1

3 1

2 20 5

2

.

ref

b m b m m

=+ ′′ + + ′′( ) + − ′′( ){ }

− ′′( )

P P P P P3 3 9 1

3 1

2 2 20 5

2

.

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P.3.4 Embedded flaw (see Figure M.7)


where

µ¾ = (2a/B)/{1 + (B/c)} for W U 2(c + B);

µ¾ = (4a/B)(c/W) for W < 2(c + B).

P.3.5 Edge flaw (see Figure M.10)


where

µ¾ = (a/W).

P.3.6 Corner flaws in plates (see Figure M.11)

The reference stress can be estimated from equations (P.2) and (P.3):

where

NOTE 1 Equations (P.2) and (P.3) are valid where local collapse would occur in the ligament, B-a, and peak bending stresses occur on the edge remote from the flaw.

NOTE 2 Local collapse of the ligament W-c is not described by equations (P.2) and (P.3). Where this is considered a possible failure mechanism, the flaw should be recharacterized as an edge flaw circumscribing the corner flaw.

P.3.7 Corner flaws at hole (see Figure M.12)

A conservative estimate of Öref can be made by recharacterizing the flaw as a through-thickness flaw circumscribing the corner flaws and applying equation (P.1). (See Figure M.12.)

Alternatively, the reference stress can be estimated by multiplying the Öref calculated using equations (P.2) and (P.3) by a magnification factor, kt, for the hole, adapting the values of µ¾ and net section stress to account for the loss of section area due to the hole. This is expressed by equation (P.6).

kt is obtained by taking the mean value of the SCF at the edge of the hole and the SCF at a distance c from the hole which results in the following equation:

where

kt, the SCF for a hole in a plate is calculated from the Kirsch [193] solution.

(P.4)

(P.5)

for W U c + 2B;

for W < c + 2B.

(P.6)

(P.7)

ref

b mP P P P Pp

B=

+b m m

23 3 9 1 4

2 2′′ + + ′′( ) + − ′′( ) +′′⎛

⎝⎜⎞⎠⎟

⎧⎨⎨⎩

⎫⎬⎭

⎡

⎣⎢

⎤

⎦⎥

− ′′( ) +′′⎛

⎝⎜⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

0 5

2

4

.

3 1

p

B

ref

b b

2

m

2

=+ +( )

− ′′( )P P P9

3 1

0 5.

′′ ⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

= a

B +

2B

c1

′′ ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟

= a

B

c

W

ref, hole ref, no hole=

−⎛

⎝⎜

⎞

⎠⎟

W

W rk

2h

t

t

h h

k = +r

r + c

+r

r + c

1

2

4

2

3

2

h

2

h

2

2

1

( ) ( )

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

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In these circumstances the values of µ¾ are as follows.

It should be noted that the equations in P.3.7 are only valid where local collapse occurs in the ligament (B–a) and peak bending stresses occur on the edge remote from the flaw.

P.3.8 Single corner flaw at hole

A conservative estimate of the net section stress can be made by recharacterizing the flaw as a through-thickness flaw circumscribing the corner flaw.

Alternatively, the reference stress can be estimated by multiplying the net section stress calculated using equations (P.2) and (P.3) by a magnification factor, kt, calculated from equation (P.7) and adapting the solution to account for the loss of section area due to the hole. This is expressed by the following equation.

where

kt is calculated from equation (P.7);

It should be noted that the equations in P.3.8 are valid where local collapse occurs in the ligament (B–a) and peak bending stresses occur on the edge remote from the flaw.

P.3.9 Other geometries

For most other geometries the local collapse and net section collapse stress formulae for plates will be conservative, sometimes excessively so. This includes embedded flaws in shells, flaws at nozzles in pressure vessels, surface flaws and short (2c < 0.2;r) surface flaws, circumferentially oriented, in nozzles or pipes under tension or bending.

In cases where the plastic collapse solution for a particular flaw geometry is unknown, a conservative estimate of the net section stress can be made by assuming that the flaw is equivalent to a simplified square cross section flaw circumscribing the existing flaw.

In cases where the plastic collapse loads are known for tension and bending applied separately, Öref under combined tension and bending can be conservatively estimated from the following expression:

where

Öref,m is the reference stress for pure membrane loading;

Öref,b is the reference stress for pure bending.

for W – 2rh U 2(c + B)

for W – 2rh < 2(c + B)

for W – 2Rh U 2(c + B);

for W – 2Rh < 2(c + B).

′′ ⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

= a

B +

B

c1

′′ ⎛⎝⎜

⎞⎠⎟ −⎛

⎝⎜

⎞

⎠⎟ =

a

B

c

W r

2

2h

ref, hole ref corner crack, no hole=

−⎛

⎝⎜

⎞

⎠⎟

W

W Rk

2h

t

′′ ⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

= a

B +

2B

c1

′′ ⎛⎝⎜

⎞⎠⎟ −⎛

⎝⎜

⎞

⎠⎟ =

a

B

c

W R2h

ref ref,b ref,m≤ +

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P.4 Formulae for curved shells

P.4.1 General

The formulae in P.4.2, P.4.3 and P.4.4 relate to flaws in spheres and cylinders. They are based on the solutions of Folias [194], Miller [195] and Kastner et al [196].

P.4.2 Through-thickness flaws

P.4.2.1 Through-thickness flaws in cylinders oriented axially (see Figure M.13) [194], [166]


where

MT = {1 + 1.6(a2/riB)}0.5;

Pm is the hoop (membrane) stress;

Pb is the bending stress transverse to the flaw.NOTE The multiplier of 1.2 is introduced for Öref to achieve approximately the same level of conservatism as that in P.3.1.

P.4.2.2 Through-thickness flaws in cylinders oriented circumferentially (Figure M.14) [196], [197]


where

Pm is the total primary membrane stress and equals Pm,a + Pm,p + Pm,b

Range of application: 0.0 k 2a/;r k 0.5;

0.0 < B/ri k 0.2.

22)

(P.8)

(P.9)22)

22) Where the cylinder under consideration is part of a pin-jointed structure and where the flaw length is greater than ( of the circumference, equation (P.9) may be unconservative and secondary bending should be taken into account by calculating the true position of the neutral axis.

ref T m

3 1

= +−⎛

⎝⎜⎞⎠⎟

1 2

2

2

. M PP

a

W

b

ref

m,a m,p

i

1

i

m,b o i

sin sin

=+( )

− −⎛

⎝⎜

⎞

⎠⎟

+−( )

−

π

π

πP P

a

r

a

r

P r r

2

1

2

4 4

πππ

− −

⎛

⎝⎜

⎞

⎠⎟

−⎛

⎝⎜

⎞

⎠⎟

−

⎛

⎝⎜

⎞

⎠⎟

⎧

⎨⎪⎪

⎩⎪⎪

⎫

⎬⎪⎪a

r

a

r

a

r

a

r

i

2sin sin

2

2

2

i

i

i

⎭⎭⎪⎪

( )

+−

⎛

⎝⎜

⎞

⎠⎟

4

2

2r r B

P

a

r

o

i

3 1

2

b,1

π

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P.4.2.3 Through-thickness flaws in spheres (Figure M.15) [197], [166]


where

Range of application: 0.0 k B/ri k 0.1

0.0 < 2a/;(ri + B/2) < 1.0

P.4.3 Surface flaws in cylinders

P.4.3.1 Internal surface flaws in cylinders oriented axially (see Figure M.16) [195], [166]


where

NOTE Equation (P.11) is based on the original Folias solution for thin walled cylinders [194]. The multiplier of 1.2 is introduced to give similar levels of conservatism to those for flat plates in P.3.2.

(P.10)

(P.11)

for W U 2(c + B)

for W < 2(c + B)

ref

m

scos

=

+ +⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

+−

⎛

⎝⎜

⎞

⎠⎟

P

P

a

r

1 1

8

2

2

3 1

2

2

s

b

iπ

s

2

=a

B r +B

i

⎛⎝⎜

⎞⎠⎟

s

2

= a

r + B

i

ref s m= +

− ′′( )1 2

2

3 12

. M PP

b

Ma BM

a Bs

=− ( ){ }

− ( )1

T

1

′′ ⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

= a

B +

B

c1

′′ ⎛⎝⎜

⎞⎠⎟⎛

⎝⎜

⎞

⎠⎟ =

a

B

c

r2

πi

Mc

r BT

= +⎛

⎝⎜⎜

⎞

⎠⎟⎟1 1 6

2

.

i

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P.4.3.2 Internal surface flaws in cylinders oriented circumferentially (see Figure M.17) [196], [166]


where

Pm is the total membrane stress due to external bending, axial loads and pressure;

Pb is the total through-wall bending stress due to external bending or local misalignment.

P.4.3.3 Long internal surface flaws in cylinders oriented axially (see Figure M.18)

The reference stress is calculated from equation (P.11):

where

P.4.3.4 Long internal surface flaws in cylinders oriented circumferentially (see Figure M.19) [195], [197]


where

c is set equal to ;r.

P.4.3.5 External surface flaws in cylinders oriented axially (see Figure M.20) [195], [197]

The reference stress is calculated from equation (P.11).

P.4.3.6 External surface flaws in cylinders oriented circumferentially

Equation (P.12) may be applied in order to calculate the reference stress relating to circumferential external flaws in cylinders.

P.4.3.7 Long external flaws in cylinders oriented axially (Figure M.21)

The reference stress may be calculated from equation (P.11):

where

(P.12)

for r U c + B

for r < c + B

;

c is set equal to .

;

;

.

ref

msin

=

Pa

B+

a

B

c

r

a

B

π 1 2

1

−⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

−⎛⎝⎜

⎞⎠⎟

ππ − ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

+− ′′( )c

r

a

B

P2

3 12

b

′′ =+ ⎛

⎝⎜⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

a

B

B

c1

π

′′ = ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟

a

B

c

rππ

′′ = a

B

W

2

′′ = a

B

M = a

B

s

1

1 −

′′ = a

B

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P.4.3.8 Long external surface flaws in cylinders oriented circumferentially (see Figure M.22)


where

c is set equal to ;r.

P.4.4 Embedded flaws in shells

The flat plate solutions of equation (P.4) may be applied to embedded flaws in shells.

P.5 Formulae for weld toe cracks [see Figure M.23a) to c)]

The flat plate solutions of equations (P.2) and (P.3) can be applied to surface cracks at weld toes. No allowance should be made for any stress concentrating effects at the weld toes.

P.6 Formulae for round bars and bolts [195]

P.6.1 Semi-elliptical surface flaws in bolts/chordal surface flaws in bolts (see Figure M.25)

The reference stress for a semi-elliptical flaw in a bolt or a bar can be conservatively estimated by assuming the flaw is equivalent to a chordal surface flaw in a bolt or bar where the chordal flaw encompasses the semi-elliptical flaw. The reference stress may be calculated from the following equation.

where

where

and where

where · has the values given in Table P.1 [195].NOTE Ön,m is conservative for a/2r k 0.4 with negligible or normal bending restraint.

Table P.1 — Values of · for bending loading

;

(P.13)

a/2r 0 0.05 0.1 0.15 0.2 0.25 0.3

#, lower bound 1 0.958 0.889 0.810 0.725 0.640 0.556

a/2r 0.35 0.4 0.45 0.5 0.55 0.6 0.65

#, lower bound 0.475 0.400 0.329 0.265 0.208 0.158 0.116

a/2r 0.7 0.75 0.8 0.85 0.9 0.95 1.0

#, lower bound 0.080 0 0.051 6 0.030 0 0.014 8 0.005 5 0.001 0 0

′′ = a

B

ref n,m n,b= +

n,m

2

1

2

sin2

= P

+ +

πm

= r a

rarc sin

−⎛⎝⎜

⎞⎠⎟

n,b b

3= π16

P

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P.6.2 Circumferential flaw in round bar (see Figure M.26)

The reference stress can be conservatively estimated from the following equation:

P.7 Plastic collapse of tubular joints

See Annex B for guidance on the determination of the appropriate treatment for Öref.

P.8 Plastic collapse from volumetric flaws

Volumetric flaws may be treated as embedded flaws using the expression for Öref given in equation (P.4).

P.9 Global collapse

P.9.1 Conditions for which a check on global collapse should be made

In redundant structures, global collapse cannot develop until sufficient plastic hinges have formed for a mechanism to occur. If a crack is present at the location of one such plastic hinge, the amount of plasticity that can develop at this location depends on the behaviour of the rest of the structure and how plastic hinges form elsewhere. For redundant cases, the use of local collapse of the first hinge as the basis for calculating Lr may be unduly conservative. Thus if an assessment of a redundant structure or component fails because of local collapse of a ligament the procedures in P.9.2 may be followed.

It is also possible that global collapse may occur at a different cross section which is inherently weaker than that containing the flaw being assessed and care should be taken to ensure that loadings are limited to those permitted by normal design procedures for the structure as a whole.

If the structure lies within the following limits, a check on local collapse is always adequate and no additional check of global collapse is needed. The limits are:

— minimum specified tensile strength of the weld metal is within 10 % of that of the parent material;— maximum levels of primary stress other than at and perpendicular to the flaw, do not exceed those at the flaw by more than 20 %.

Beyond these limits, a check on global collapse should be made as described in P.9.2.

P.9.2 Methods

P.9.2.1 General

Global collapse may take place away from the cracked section due to the presence of thinned areas or because of the stress distribution in the structure. It may also occur at a load which is unaffected by the presence of the crack. A check should be made as to whether or not global collapse may intervene at loads below local or net section collapse for the region containing the assessed flaw. A method for assessing corroded pressure vessels, pipework and pipelines is described in Annex G.

P.9.2.2 Use of lower bound global collapse load

As noted above, where there is a high degree of redundancy, global collapse cannot develop until sufficient plastic hinges have formed for a mechanism to occur. (A particular example is tubular joints — see Annex B). For this approach to be adopted, it is essential that validation studies be carried out to confirm that the plasticity at the cracked section is contained sufficiently by the remaining structure, so that the use of the standard FAD gives safe results. This requires finite element analyses of the cracked body to determine both the elastic (Jel) and elastic-plastic (Jep) J values at load levels of interest. A safe lower bound collapse load is one that ensures that the ratio Æ(Jel/Jep) at a given value of Lr lies on or above the standard assessment diagram value of Kr. In ferritic steels, care should be exercised to ensure that local constraint conditions are not sufficient to induce fracture by a cleavage mechanism.

(P.14)ref

b=

−⎛⎝⎜

⎞⎠⎟

+

−⎛⎝⎜

⎞⎠⎟

P

a

r

P

a

r

m

1

3

16 1

2 3

π

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Annex Q (informative) Residual stress distributions in as-welded joints

Q.1 General

In some situations the recommendations in 7.2.4.1 and 7.3.4 on residual stresses for as-welded joints may be too conservative and more precise information on the residual stress distribution is required. The residual stress distribution can consist of local welding and long-range components and both categories need to be taken into account in a fracture assessment. Long-range stresses are balanced between major structural components and can give rise to net sectional forces and moments. These residual stresses will behave as primary stresses due to elastic follow-up and contribute to both Kr and Sr or Lr. The local welding residual stress distribution contributes to Kr but not to Sr or Lr.

This annex gives information on typical through-thickness welding residual stress distributions for a range of common welded joint geometries, i.e.

a) plate butt welds;

b) pipe circumferential butt welds;

c) pipe axial seam welds;

d) T-butt and fillet welds;

e) repair welds.

Schematic diagrams of the distributions are illustrated in Figure Q.1. The recommended residual stress distributions for plate butt welds and pipe welds are based on reviews of experimental data [198], [199], [200], [201] and [202] and are valid for the parametric ranges listed in Table Q.1.

Table Q.1 — Parametric ranges for recommended residual stress distributions

The user should confirm that the residual stress distributions are representative of the welded joint being assessed. The distributions for T-butt, fillet and repair welds are based either on simple models for heat flow and stress generation at welds described by Leggatt [203] or on parametric formulae derived from curve fitting experimental data [198], [199], [200], [201] and [202].

It should be noted that:

— the use of this annex is for Level 2 and 3 assessments only;— the distributions are upper bound profiles to data and are not necessarily self-equilibrating;— the directions of stress in this annex are given relative to the welding direction;— the residual stress distribution is sensitive to the restraint conditions. The distributions are not applicable for welds such as closure welds where there is restraint against transverse shrinkage;— the effect on the distributions of assessment temperature, post weld heat treatment and residual stress relaxation due to prior overload or applied loads is not covered in this annex. Under these circumstances, the user has the option of either using the present room temperature distributions or assuming uniform residual stress and invoke the relaxation rules as outlined in 7.3.4.2 and Annex O.

Geometry Thickness

mm

Proof stress

N/mm2

Electrical energy per unit length

kJ/mm

Plate butt welds 24 to 300 310 to 740 1.6 to 4.9

Pipe circumferential butt welds 9 to 84 225 to 780 0.35 to 1.9

Pipe axial seam welds 50 to 85 345 to 780 Not known

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Joint geometry Longitudinal residual stress distribution

Transverse residual strees distribution

a) Plate butt weld and axial seam welds

i) ii)

b) Pipe circumferential butt welds

i) ii)

c) T-butt and fillet welds

i) ii)

d) Repair welds

i) ii)

Figure Q.1 — Typical residual stress distribution in welded joints

- Y + Y0

z

σ σ - Y + Y0

z

σ σ

- Y 0

z

σ σ

0

0.2

0.4

0.6

0.8

1

-0.5 0 0.5 1

z/B

Low heat input Medium heat inputHigh heat input

zT/ Yσ σ

z

z0

σ

z0

Y

z

σ

0

z0

zr

σ 0 Y

z0

zr

σ

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Equations for transverse and longitudinal residual stresses in ferritic and austenitic steel joints are given in Q.2 to Q.6. The distributions are expressed in terms of the depth, z, through the wall thickness and the yield strength, ÖY. The depth, z, is measured from the surface on which the last weld bead is deposited, except where specified otherwise. For the purpose of this annex, ÖY is the 0.2 % proof stress for ferritic steels and the 1 % proof stress for austenitic steels. ÖY should be based on an average (or typical) value of the appropriate proof stress (i.e. 0.2 % or 1 %) as opposed to, for example, a lower bound value. For transverse residual stresses, ÖY should be taken to be the lesser of the yield strengths of the parent and weld material. The greater value of the two yield strengths should be used for longitudinal residual stresses.

In some cases, the residual stress profiles are expressed as a function of E1, the electric energy per unit length of one weld run, which is equal to (welding current) × (welding voltage)/(welding travel speed). In other cases data are available to enable residual stress profiles to be fitted by empirical polynomial distributions within the limits for which the data were obtained. The expressions given have been chosen to give an upper bound to residual stress distributions and either form of distribution may be used where the data are available. If data on welding energy parameters are not available, it may be possible for an experienced welding engineer to advise on the likely weld energy range on the basis of weld bead dimensions, welding process, procedure and position. An upper bound estimate for the weld energy per unit length should be used.

Several of the residual stress distributions presented in Q.2, Q.3, Q.4 and Q.5 are represented by polynomial equations up to the fourth order. Stress intensity factor solutions for flaws situated in such stress fields have been developed [241] and [242].

Q.2 Plate butt welds — Figure Q.1a)

Q.2.1 Longitudinal residual stresses (i.e. parallel to the weld length)

For both ferritic and austenitic steels the following equation applies.

The effect of structural restraint on the longitudinal residual stress is expected to be negligible.

Q.2.2 Transverse residual stresses (i.e. perpendicular to the weld length)

Transverse residual stresses can be highly variable, as shown in Figure Q.1a). The upper bound transverse residual stress distribution for ferritic and austenitic steels, under minimum restraint, is calculated from the following equation:

ÖRT = ÖY{0.9415 – 0.0319(z/B) – 8.3394(z/B)2 + 8.660(z/B)3} (Q.2)

This distribution is applicable to welds with no restraint or with bending restraint, but not to welds with membrane restraint (i.e. restraint against transverse shrinkage).

Q.3 Pipe circumferential butt welds23) — Figure Q.1b)

Q.3.1 Longitudinal residual stresses (i.e. parallel to the weld length and circumferential to the pipe)

The longitudinal residual stress distribution for ferritic and austenitic steel pipe butt welds is represented conservatively by a linear profile defined by a stress equal to ÖY at the outer surface and ÖR

L,B at the bore, and is calculated from the following equation:

where

for B k 15 (in mm) ÖRL,B = ÖY (Q.3b)

for 15 < B k 85 (in mm) ÖRL,B = ÖY {1 – 0.014 3(B – 15)} (Q.3c)

z is measured from the outer surface and is given in millimetres.

(Q.1)

23) The distributions in this subclause are for single sided welds made from the outside.

(Q.3a)

R

L =Y

R

L

R

L,B= + ( ) ( ) −{ }⎡⎣⎢

⎤⎦⎥Y Y

1 1z B

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Q.3.2 Transverse residual stresses (i.e. perpendicular to the weld length and parallel to the axis of the pipe)

The transverse residual stress profile for pipe butt-welded joints is influenced by the electrical energy per unit length of weld, E1, and the wall thickness. Distributions are given below as a function of z/B and E1/B, where z is measured from the bore and E1 is the electrical energy per unit length of the largest weld run in J/mm.

a) Low heat input, E1/B k 50 J/mm2

b) Medium heat input, 50 < E1/B k 120 J/mm2

c) High heat input, E1/B > 120 J/mm2

Q.4 Pipe axial seam welds

The recommendations for plate butt welds in Q.2 are applicable to pipe axial seam welds.

Q.5 T-butt and fillet welds — Figure Q.1c)

Q.5.1 General

All residual stress distributions given in this subclause refer to residual stresses in the main plate under the welds. The treatments in Q.5.2 and Q.5.3 may be regarded as alternatives.

Q.5.2 Electrical energy (heat input) based

The distributions in this subclause, based on the electrical energy of the largest weld run at the weld toe, are applicable for T-butt and fillet welds at plate-to-plate, tube-to-plate and tube-to-tube joints. The distributions are only valid for flaws emanating from the welded side.

For ferritic and austenitic steels, the longitudinal and transverse residual stresses in the main plate in the plane of the weld toe can be obtained from the following expressions.

a) If zo < B,

b) If zo > B,

Ö RT = ÖY (Q.6)

where

ÖY is in N/mm2;

z, zo and B are in mm;

E1 is the electrical energy per unit length of the largest weld run at the toe (in J/mm);

z is the distance into the plate measured from the surface at the weld toe.

(Q.4a)

(Q.4b)

(Q.4c)

for z k zo (Q.5a)

for z U zo (Q.5b)

in ferritic steels and in austenitic steels (Q.7)

R

T

Y= − ( ) − ( ) + ( ) − ( ){ }1 6 80 24 30 28 68 11 18

2 3 4

. . . .z B z B z B z B

R

T = − ( ) + ( ) − ( ) + ( ){ }Y1 4 43 13 53 16 93 7 03

2 3 4

. . . .z B z B z B z B

R

T = − ( ) − ( ) + ( ){ }Y1 0 22 3 06 1 88

2 3

. . .z B z B z B

R

T = − ( ){ }Y1 z zo

R

T = 0

zE

o

Y

=122

1 zE

o

Y

=161

1

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Q.5.3 Parametric formulae based on experimental data

Q.5.3.1 Plate to plate T-butt welds

For longitudinal stresses (ferritic steels) the following equation applies.

For transverse stresses (ferritic steels) equation (Q.6) applies.

Q.5.3.2 Tubular T-butt welds

For longitudinal stresses (ferritic steels) the following equation applies.

For transverse stresses (ferritic steels) the following equation applies.

Q.6 Repair welds — Figure Q.1d)

The transverse and longitudinal residual stresses in repair welds should be taken to be of yield magnitude throughout the depth of the repair. For part-depth repairs of depth zr, the residual stresses may be assumed to decrease from yield magnitude at the bottom of the repair to zero at depth zo below the repair weld, where zo is defined by equation (Q.7), as follows.

where z is measured from the face of the component from which the repair was made.

The distribution given by equations (Q.11a), (Q.11b) and (Q.11c) is only valid for flaws emanating from the repaired side.

(Q.8)

(Q.9)

(Q.10)

For z k zr (Q.11a)

For zr k z k zr + zo (Q.11b)

For z U zr + zo (Q.11c)

R

L = + ( ) − ( ) + ( ) − ( ){ }Y0 75 4 766 26 696 38 11 16 82

2 3 4

. . . . .z B z B z B z B

R

L = + ( ) − ( ) + ( ) − ( ){Y1 025 3 478 27 861 45 788 21 799

2 3 4

. . . . .z B z B z B z B }}

R

T = + ( ) − ( ) + ( ) − ( ){Y0 97 2 326 7 24 125 42 485 21 087

2 3 4

. . . . .z B z B z B z B }}

R

T

R

L= =Y

R

T

R

L= =+ −⎛

⎝⎜

⎞

⎠⎟Y

o r

o

z z z

z

R

T

R

L= = 0

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Annex R (normative) Determination of plasticity interaction effects with combined primary and secondary loading

R.1 General

When structures are loaded by a combination of primary and secondary stresses, plasticity effects occur which cannot be evaluated by a simple linear addition of the effects resulting from the two independent stress systems. In 7.3.5.1 and 7.3.6.2 a term Ô is included in the definitions of Kr and to cover interaction between these two stress systems. This annex gives methods for the determination of Ô. The case of through-wall cracks subject to a self-balancing through-wall residual stress field is included as a special case. The determination of Kr when secondary stresses act alone is also included.

R.2 gives a simplified method for the determination of Ô when secondary loads are small. This method [204] is the same approach as was incorporated in previous versions of the current document. R.3 gives a detailed procedure [205] and [206] for calculating Ô for situations in which the simplified route is not applicable or when it leads to over-conservative assessments. These situations are identified in R.2. The detailed route requires an estimate of the inelastic response of the structure and includes methods based on analysing the uncracked body under the secondary loadings alone. Advice on calculating the effective secondary stress intensity factor for use in R.3 is given in R.4. The limits of the different procedures are clearly stated at the start of each subclause.

Alternative approaches for assessing combined primary and secondary stresses are discussed in R.5. Finally, the special case of a through-wall crack subjected to a self-balancing through-wall residual stress field is addressed in R.6.

The value of Kr and determined using the methods of this annex in conjunction with 7.3 is independent of the order of application of the primary and secondary stresses. Where primary stresses are applied after secondary stresses, this may lead to some conservatism, which may be removed by following the detailed analysis approach of R.5.1.

R.2 Simplified procedure for the determination of Ô when KIs/(KI

p/Lr)k4

This procedure recognizes that plasticity corrections for secondary stresses become unimportant at large mechanical loads, and the value of Ô is reduced to zero beyond the yield load of the structure. The value of Ô depends on Lr and on the ratio KI

s/(KIp/Lr). The procedure should not be applied when there are secondary

stresses only, as the geometric parameter KIp/Lr, and hence KI

s/(KIp/Lr), is undefined. For large secondary

stresses (KIs/(KI

p/Lr) > 4), plastic redistribution of stress is likely to be important and the value of Ô given below will be over-conservative. Over-conservatism may also result for the case of small primary stresses combined with secondary stresses, as the value of Ô determined using the method of this clause does not tend to zero in the limit of negligible primary stress loads. In these cases, and in the case of secondary stresses alone, the more detailed approach of R.3 is recommended. Alternatively Ô = 0.1 may be assumed for such cases. Similarly, when elastic follow-up is judged to be significant in the cracked section, the approach of R.3 should also be used.

The procedure for determining Ô is as follows.

a) Determine KIs, the linear elastic stress intensity factor for the flaw size of interest, using the

elastically-calculated secondary stresses (Annex Q). KIs is positive when it tends to open the crack.

If KIs is negative or zero, then Ô is set to zero and the remainder of this annex does not apply.

b) Determine the ratio KIp/Lr. Note that, since both KI

p and Lr are directly proportional to load, the level of primary stresses is irrelevant, provided it is common to the calculations of both KI

p and Lr. Only the nature and distribution of the applied primary stresses need to be considered when calculating the ratio.

c) Determine KIs/(KI

p/Lr) from the results of a) and b). If KIs/(KI

p/Lr) > 4 then R.3 should be used to evaluate Ô.

d) Determine Ô1 from Figure R.1.

e) Determine Ô.

Ô = Ô1 Lr k 0.8;

Ô = 4Ô1 (1.05 – Lr) 0.8 < Lr < 1.05;

Ô = 0 1.05 k Lr.

¸r

¸r

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R.3 Detailed procedure for the determination of Ô

This procedure should be followed when the ratio KIs/(KI

p/Lr) determined in R.2 exceeds 4 and in the case of secondary stresses alone. It should also be applied when primary stresses are low and the conservatism given by the method of R.2 is excessive. Similarly, this procedure may be used to remove any unconservatism that follows from the simplified approach in the case of large amounts of elastic follow-up in the cracked section.

The steps in the procedure are as follows.

a) Calculate the parameters KIs and Kp

s. Advice on determining the effective stress intensity factor Kps

is given in R.4.

If KIs is negative or zero, then Ô is set equal to zero and the remainder of this annex does not apply.

If secondary stresses act alone, Ô is set to zero and KIs is set equal to Kp

s. The remainder of this annex is then omitted.

b) Determine the ratio Kps/(KI

p/Lr) where KIp and Lr are calculated as in 7.3 and 7.4.

c) Obtain the parameter Ò from Table R.1 in terms of Lr and the parameter Kps/(KI

p/Lr) calculated in step b). Linear interpolation should be used for values not given in the table. If Kp

s = KIs, then Ô is set

equal to Ò and the remainder of this annex does not apply.

Figure R.1 — Values of Ô1 for defining Kr

0.25

0.20

0.15

0.10

0.05

00 1.0 2.0 3.0 4.0

1 = 0.1χ0.714 – 0.007 χ2 + 3 x 10–5χ5

χ =K I Lr

K I

S

P

1

ρ

ρ

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d) Obtain the parameter Î from Table R.2 in terms of Lr and the parameter Kps/(KI

p/Lr) from step b). Linear interpolation should be used for values not given in the table.

e) Determine Ô from the following equation.

If this results in a negative value for Ô then Ô is re-defined to be zero.

Table R.1 — Tabulation of Ò as a function of Lr and Kps/(KI

p/Lr)

Lr Kps/(KI

p/Lr)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0 0 0 0 0 0 0 0 0 0 0 0

0.1 0 0.020 0.043 0.063 0.074 0.081 0.086 0.090 0.095 0.100 0.107

0.2 0 0.028 0.052 0.076 0.091 0.100 0.107 0.113 0.120 0.127 0.137

0.3 0 0.033 0.057 0.085 0.102 0.114 0.122 0.130 0.138 0.147 0.160

0.4 0 0.037 0.064 0.094 0.113 0.126 0.136 0.145 0.156 0.167 0.182

0.5 0 0.043 0.074 0.105 0.124 0.138 0.149 0.160 0.172 0.185 0.201

0.6 0 0.051 0.085 0.114 0.133 0.147 0.159 0.170 0.184 0.200 0.215

0.7 0 0.058 0.091 0.117 0.134 0.147 0.158 0.171 0.186 0.202 0.214

0.8 0 0.057 0.085 0.105 0.119 0.130 0.141 0.155 0.169 0.182 0.190

0.9 0 0.043 0.060 0.073 0.082 0.090 0.101 0.113 0.123 0.129 0.132

1.0 0 0.016 0.019 0.022 0.025 0.031 0.039 0.043 0.044 0.041 0.033

1.1 0 –0.013 –0.025 –0.033 –0.036 –0.037 –0.042 –0.050 –0.061 –0.073 –0.084

1.2 0 –0.034 –0.058 –0.075 –0.090 –0.106 –0.122 –0.137 –0.151 –0.164 –0.175

1.3 0 –0.043 –0.075 –0.102 –0.126 –0.147 –0.166 –0.181 –0.196 –0.209 –0.220

1.4 0 –0.044 –0.080 –0.109 –0.134 –0.155 –0.173 –0.189 –0.203 –0.215 –0.227

1.5 0 –0.041 –0.075 –0.103 –0.127 –0.147 –0.164 –0.180 –0.194 –0.206 –0.217

1.6 0 –0.037 –0.069 –0.095 –0.117 –0.136 –0.153 –0.168 –0.181 –0.194 –0.205

1.7 0 –0.033 –0.062 –0.086 –0.107 –0.125 –0.141 –0.155 –0.168 –0.180 –0.191

1.8 0 –0.030 –0.055 –0.077 –0.096 –0.114 –0.129 –0.142 –0.155 –0.166 –0.177

1.9 0 –0.026 –0.049 –0.069 –0.086 –0.102 –0.116 –0.129 –0.141 –0.152 –0.162

2.0 0 –0.023 –0.043 –0.061 –0.076 –0.091 –0.104 –0.116 –0.126 –0.137 –0.146

=K

K

− −⎛

⎝⎜⎜

⎞

⎠⎟⎟

I

s

p

s

1

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Table R.2 — Tabulation of Î as a function of Lr and Kps/(KI

p/Lr)

R.4 Advice on calculating Kps

R.4.1 General

The procedure of R.3 requires the calculation of the effective stress intensity factor, Kps, for the secondary

loading alone. Kps is defined in terms of the value, J s, of the J-integral for the secondary loading alone, and

at the flaw size of interest, from the following equation:

There are three options for determining Kps. Firstly, an inelastic stress analysis of the cracked body may

be performed to calculate J s explicitly and hence Kps. Advice on the use of finite element analysis is given

in R.5.1. Secondly, an approximation to Kps may be calculated from an inelastic analysis of the uncracked

body under the same secondary stress loads [205], [206], [207] and [208]. Uncracked-body analyses are quicker and cheaper to perform and a method of calculating Kp

s using such an approach is given in R.4.2. Thirdly, a simple but conservative linear elastic calculation of Kp

s is presented in R.4.3.

When secondary stresses are low and elastic follow-up is judged not to be significant, KIs may replace Kp

s in R.3. This reduces the conservatism of the simplified route of R.2 for small primary stresses.

R.4.2 Determination of Kps from uncracked-body analysis

Kps may be determined from steps a) to e). It is assumed that the stress Öyy and mechanical strains ¼xx, ¼yy

and ¼zz across the plane of the flaw have been determined from an elastic-plastic analysis of the uncracked body. Here the y-axis is normal to the plane of the flaw and x, z are in-plane. The strains are the mechanical components: that is, any strain due to uniform thermal expansion has been subtracted from the total strain values.

Lr Kps/(KI

p/Lr)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0 0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.1 0 0.815 0.869 0.877 0.880 0.882 0.883 0.883 0.882 0.879 0.874

0.2 0 0.690 0.786 0.810 0.821 0.828 0.832 0.833 0.833 0.831 0.825

0.3 0 0.596 0.715 0.752 0.769 0.780 0.786 0.789 0.789 0.787 0.780

0.4 0 0.521 0.651 0.696 0.718 0.732 0.740 0.744 0.745 0.743 0.735

0.5 0 0.457 0.589 0.640 0.666 0.683 0.693 0.698 0.698 0.695 0.688

0.6 0 0.399 0.528 0.582 0.612 0.631 0.642 0.647 0.648 0.644 0.638

0.7 0 0.344 0.466 0.522 0.554 0.575 0.587 0.593 0.593 0.589 0.587

0.8 0 0.290 0.403 0.460 0.493 0.516 0.528 0.533 0.534 0.534 0.535

0.9 0 0.236 0.339 0.395 0.430 0.452 0.464 0.470 0.475 0.480 0.486

1.0 0 0.185 0.276 0.330 0.364 0.386 0.400 0.411 0.423 0.435 0.449

1.1 0 0.139 0.218 0.269 0.302 0.326 0.347 0.367 0.387 0.406 0.423

1.2 0 0.104 0.172 0.219 0.256 0.287 0.315 0.340 0.362 0.382 0.399

1.3 0 0.082 0.142 0.190 0.229 0.263 0.291 0.316 0.338 0.357 0.375

1.4 0 0.070 0.126 0.171 0.209 0.241 0.269 0.293 0.314 0.333 0.350

1.5 0 0.062 0.112 0.155 0.190 0.220 0.247 0.270 0.290 0.309 0.325

1.6 0 0.055 0.100 0.139 0.172 0.200 0.225 0.247 0.267 0.285 0.301

1.7 0 0.048 0.089 0.124 0.154 0.181 0.204 0.224 0.243 0.260 0.276

1.8 0 0.042 0.078 0.110 0.137 0.161 0.183 0.202 0.220 0.236 0.250

1.9 0 0.036 0.068 0.096 0.120 0.142 0.162 0.180 0.196 0.211 0.225

2.0 0 0.031 0.058 0.082 0.104 0.124 0.141 0.157 0.172 0.186 0.198

K = E Jp

s ′ s

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In steps c) and d), effective crack sizes are calculated. These crack sizes may exceed the section thickness in some cases. The calculated values should be used in all cases in step e).

a) Determine an effective stress intensity factor KÖs(a) from the uncracked-body stress, Öyy, normal to the

crack plane. Note that KÖs(a) will generally differ from the elastic stress intensity factor, KI

s(a).

b) Determine an effective stress intensity factor, K¼s(a), from the stress, , normal to the crack plane

defined in terms of the elastic-plastic, uncracked-body mechanical strains as if the material response were linear elastic. Specifically, yy is calculated from the following equation:

c) Define an effective crack size from the following equation:

where

¶½ = 1 or 3 for plane stress or plane strain, respectively.

d) Define an effective crack size aeff¼ from the following equation:

where

¶½ = 1 or 3 in plane stress or plane strain, respectively.

e) Determine Kps from the following equation:

R.4.3 Linear elastic calculation of Kps

In the absence of an elastic-plastic analysis, a conservative estimate of Kps is given by the following

equation.

where

the effective crack size, aeff, is calculated from the following equation:

(See Hooton [205] and Takahashi [208]).

This may however be over-conservative for elastic stresses not much greater than yield, but provides a simple first approximation. Note that aeff may exceed the section thickness in some cases.

Ö̃yy

Ö̃

yy=

+( ) −( ) −( ) + +( ){ }E

1 1 2

1yy xx zz

a aK a

eff

s

Y

= +′

( )⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

1

2

2

π

effa = a +

K a1

2

2

π ′( )⎧

⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

s

Y

K a =a a

a

K a K a

//

p

s eff eff s s( )⎛

⎝⎜⎜

⎞

⎠⎟⎟ ( ) ( ){ }1 4

2

1 2

K = a

aK a

/

p

s

I

s

1 2

eff⎛⎝⎜

⎞⎠⎟

( )

effa = a +K a1

2

2

π ′( )⎧

⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪I

s

Y

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R.5 Alternative approaches for assessing combined primary and secondary stresses

R.5.1 The finite element method

The finite element method provides a versatile means of calculating the J-integral. Firstly, J can be found directly by calculating the energy release associated with an increase in crack size. Alternatively, a single elastic-plastic analysis can be carried out and J obtained by the non-linear virtual crack extension (VCE) technique, or following the analysis, by use of contour integrals. The non-linear VCE method is discussed by Hellen [209]. The contour integration should be done using a validated program, which produces a value that is path independent in the presence of thermal and residual stresses [210] and [211]. Guidance on the specific integral to use and on the choice of contour to obtain numerical accuracy is given by Hellen [212]. The stress/strain curve used in the analysis should provide an accurate description of material behaviour.

There are a number of examples of finite element analysis solutions for thermal and residual stresses. These include: centre-cracked plates with parabolic temperature gradients [207], [210], [211], [213] and [214]; single-edge cracked plates with parabolic temperature gradients [214]; a single-edge cracked plate with an exponential temperature gradient [215]; axially-cracked cylinders with parabolic temperature gradients [214]; an axially cracked cylinder under centrifugal and thermal shock loading [216]; circumferentially cracked cylinders with a variety of thermal and displacement loadings [214], [217], [218], [219], [220] and [221]; and a sandwich plate model with temperature difference between the two plates [222].

The above finite element analysis solutions have been performed for mechanical loading combined with thermal loading as well as for thermal loading alone. They provide guidance for the assessment of cases of secondary stresses acting alone and for the assessment of large secondary stresses. The finite element analyses are useful for providing additional confidence for assessments on critical components or for providing a close definition of margins in specific cases. However, where solutions are required for a range of loadings and crack sizes, a simplified form of analysis such as that of R.2 and R.3 may be preferable.

R.5.2 The EPRI-GE J-estimation scheme

This approach, developed by workers at General Electric in the USA, involves an explicit determination of the J-integral from a compendium of solutions [223] for particular geometries and loadings. Incorporation of secondary stresses into the procedure was addressed [214]. Care should be taken that the material stress/strain curve is closely fitted by a Ramberg-Osgood law when using the procedure (see, for example Ainsworth et al [224]). Application of the procedure is limited to geometries contained in the compendium and this can lead to considerable idealization of the actual geometry and interpolation/extrapolation for geometric variables such as crack size.

R.6 Through-thickness cracks with completely self-balancing residual stress fields

The case of through-wall cracks with completely self-balancing through-wall stress distributions is considered in this subclause, and is of particular interest for leak-before-break assessments (Annex F). Figure R.2 gives examples of such stress distributions. The estimates [205] and [225] of Kr

s are based on linear elastic methods. Therefore application of this subclause is limited to the range 0 < KI

s/(KIp/Lr) < 4 as

discussed in R.2. Secondary loads outside this range will require individual consideration.

Finite element analyses [225] have shown that the stress intensity factor and the net section load are independent of crack length and hence these stresses do not contribute to Lr or to Ô. However, neglect of these stresses can be unconservative. The finite element analyses by Green and Knowles [225] have shown that, for crack lengths greater than about half the wall thickness, the stress intensity factor at the surface is approximately constant, the mid-thickness value being equal and opposite. It is therefore recommended that, for the cases of triangular, sinusoidal and square through-wall self-balancing stress distributions (Figure R.2), the value of Kr

s in 7.3 should be set equal to ¾½ where ¾½ is defined by the following equation.

where

Ö rmax is the surface value of the self-balancing through-wall stress;

B is the thickness of the cracked section;

′′′

=B

K

max

r

mat

π

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Æ¾ is a constant equal to 0.38, 0.43 and 0.48 for the triangular, sinusoidal and square stress distributions, respectively.

These values are for surface assessments; for mid-surface assessments it is conservative to set Krs equal to

zero. Other self-balancing through-wall distributions will require to be individually assessed in comparison with the particular solutions discussed above. It is conservative to use these values for very short cracks; in this case Figure R.2 [205] and [225] should be consulted to determine the variation of non-dimensional stress intensity factor, Æ¾, with crack length.

In general, residual stress fields may not be completely self-balancing through the wall thickness. The part of the stress distribution which is not self-balancing should then be assessed separately, using the methods of R.3 to R.5 to determine Ô and hence Kr

s for that part. The term ¾½ due to the self-balancing stress field is then added to define the total Kr

s for use in 7.3.

Annex S (normative) Approximate numerical integration methods for fatigue life estimation

S.1 The use of finite crack growth increments

A conservative approach is to choose small increments of crack growth and to calculate the number of cycles used extending the crack over each increment, basing the calculations on %K at the end of the increment. However, in the case of surface or embedded elliptical flaws, this requires knowledge of the flaw length 2c at the end of the increment, which is not known in advance. A possible approach is to assume the crack-front shape, for example on the basis of experimental observations in laboratory specimens, but any assumption should be justified in the ECA. Alternatively, assuming equation (S.1), the crack shape can be estimated using %K at the beginning of the increment. This is on the basis that, for small increments, the following equation applies:

%c/%a = (%Kc/%Ka)m

where

Figure R.2 — Stress intensity factor for through-thickness cracks with through-wall self-balancing stress distributions

0.5

0.4

0.3

0.2

0.1

0 0.5 1.0 1.5 2.0 2.5a/B

Square

Cosine

Triangular

0 BThickness

1.0

0Stre

ss, M

Pa

λ"

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%Kc and %Ka are the values of %K at the ends of the major and minor axes of the elliptical crack respectively (see 8.4).

Using the solutions in Annex M [164], the following expressions are obtained.

1) For surface flaws (axial or bending):

where

Mk,c and Mk,a are the appropriate Mk values (i.e. for axial or bending loading) at the ends of the major and minor axes respectively.

2) For embedded flaws (axial loading):

The accuracy of the finite crack growth increments method increases with the number of increments chosen. If the analysis is performed by computer, a large number (e.g. 1 000) can be used. Alternatively, different numbers of increments can be tried and the final results obtained by convergence.

If a small number of increments is used, it is recommended that they should be logarithmic.

For example, for 20 increments from a flaw height ao to a tolerable crack height af, the logarithmic increment x is calculated from the following equation:

Then, the crack height at the end of the jth increment is calculated as follows:

The procedure for calculating the fatigue life for a given flaw is then as follows.

a) Estimate the tolerable size of fatigue crack (af), and hence the total permissible extent of fatigue crack growth, and other limiting values corresponding to the definition of failure (see 8.2.4). If relevant, assume that the final crack shape is circular or semicircular (i.e. a = c).

b) Divide the total extent of crack growth into increments.

c) Taking each increment in turn, calculate %K from 8.4.3 at the end of the increment. In the case of surface or embedded elliptical shaped flaws, it will first be necessary to estimate the crack-front shape at the end of the increment. For spectrum loading account may need to be taken of changes in stress range during an increment. One approach would be to terminate the increment when the stress changes, but otherwise %K should be calculated on the basis of the stress range corresponding to the current crack size, together with the crack size and shape at the end of the increment.

d) Check to ensure that failure will not occur due to the presence of the incremented crack (see 8.4.6).

e) For the relevant fatigue crack growth law (see 8.4.1) and stress range (see 8.4.2) calculate the number of cycles %Nj consumed in the increment, where:

f) Continuing this analysis, the flaw is acceptable if the limiting conditions corresponding to the definition of failure are not reached during a number of cycles equivalent to the required fatigue life, that number of cycles being the sum of the numbers of cycles consumed in each increment of crack growth.

(S.1)

(S.2)

(S.3)

(S.4)

(S.5)

∆∆

K

K

M

Ma B a c

c

a

k,c

k,a

= + ( ){ }( )1 1 0 352 0 5

. ..

∆∆

K

K

a B a B

a ca c

c

a

= −( ) − ( ){ }

+ ( ){ }⎡

⎣

⎢⎢

⎤

⎦

⎥⎥ ( )1

2 2 6 4

1 4

0 5

0 5.

.

.

xa a

=( ) − ( )log log

f o

20

aj

log a jxo= ( )+

10

∆N

a a

a Nj

j j

j

=−

( )−( )1

d d

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S.2 The use of blocks of stress cycles

An alternative approach to fixed increments of crack growth is to consider the applied stress spectrum to be divided into blocks and to calculate the extent of crack growth in each block, assuming that the rate of crack growth is constant. This method has advantages over the fixed crack growth increment method. A spectrum of stress ranges, reduced to the form of a histogram, can be accommodated more easily. For example the block size can be varied, depending on the stress range or crack size; finally the correct crack-front shape is automatically obtained during the analysis. The main disadvantage of the method is that it is necessary to relate crack growth rate to the crack size and shape at the beginning of the block, so that the method is non-conservative. However, this can be overcome if the block length is relatively short, or if the increment of crack growth is small. Experience indicates that the result will be close to that obtained by the cycle-by-cycle method, if the block length is less than 0.1 % of the total fatigue life or if the increment in crack growth is less than 0.5 % of the crack height at the start of a block.

The procedure is as follows.

a) Assemble the stress spectrum in the form of a histogram of stress ranges versus number of cycles of occurrence, the stress range being constant in a block. Ideally, the number of cycles in each block should be a convenient multiple of the block length chosen for the analysis (see 8.4.2).

b) Establish the limiting values corresponding to the definition of failure (see 8.2.4).

c) Taking each block of stress cycles in turn, calculate %K from 8.4.3 at the beginning of the block.

d) Check to ensure that failure will not occur at this stage (see 8.4.5).

e) For the relevant fatigue crack growth law (see 8.4.1) and block length NB, calculate the increments of crack growth in the height (%a) and length (%c) directions, where:

%a = (da/dN)jNB (S.6)

%c = (dc/dN)jNB (S.7)

f) Check any conditions imposed on the extent of crack extension and, if necessary, repeat step for a shorter block length.

g) Continuing this analysis, the flaw is acceptable if the limiting conditions corresponding to the definition of failure are not reached during a number of cycles equivalent to the required fatigue life.

Annex T (informative) Information for making high temperature crack growth assessments

T.1 Materials data

T.1.1 Tensile properties

For certain materials, stress-strain data, including yield strength and ultimate tensile strength, can be obtained from PD 6525-1 and references [226], [227] and [228].

T.1.2 Creep strain versus time curves

Strain versus time curves for certain materials can be obtained from published information. For a number of austenitic and alloy ferritic steels, creep strain versus time data are available directly in tabular form in Appendix A3 of sub-section A, of RCC-MR [226].

Where strain versus time data are not available explicitly, they can be derived from iso-strain curves, such as those shown in Figure T.1a), by cross plotting as shown in Figure T.1b).

Iso-strain curves are presented in High Temperature Design Data for Ferritic Steels [227] for the following materials over the temperature range given:

Carbon-manganese steel 400 °C to 500 °C;½Cr½MoV steel 475 °C to 600 °C;1Cr½Mo steel 475 °C to 600 °C;2¼Cr1Mo steel 475 °C to 600 °C;9Cr1Mo steel 475 °C to 625 °C;12Cr1MoV(W) steel 500 °C to 625 °C.

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Where iso-strain curves are not available, it is sometimes possible to derive the strain versus time curves from a cross plot of isochronous curves. These are given, for certain materials, in references [226], [227] and [58].

a) Typical iso-strain curve

KeyA Limit of creep strain dataB Limit of rupture curvesC Limit of extended extrapolation

b) Strain versus time curve drawn by cross-plotting [i.e. <1>, <2> and <3> from a)]

Figure T.1 — Derivation of strain versus time curves from iso-strain curves

300

250

200180160140

120

100

80

60

40

30103 104 105 106

Duration, hr

0.1 %

0.2 %

0.5 % 1 % 2 % 5 %

Rupture

1 3

B C

A

Stre

ss, N

/mm

2

2

1.0

0.8

0.6

0.4

0.2

0100 000 200 000

1

3

2

Stra

in, %

Time, hr

60 N/mm255 50 45

4035

30

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T.1.3 Derivation of incremental creep strains

The strain hardening procedure is recommended. This means that the increment in creep strain is read off from the creep strain versus time curve, relevant to the current reference stress and temperature, starting from a point on the curves where the strain equals the accumulated strain to date. It is important to note that these curves need to be plotted in terms of fractional strain, not percentage strain.

The procedure is shown in Figure T.2 where the calculations are shown diagrammatically for a hypothetical set of blocks of loading 10, 11 and 12.

The strain versus time curve relevant to Öref10 and T10 is entered at a strain level of ¼c9. The strain at the end of block 10, ¼c10, is estimated by following the creep curve for a time interval of %t10.

The strain versus time curve relevant to Öref 11 and T11 is entered at a strain level of ¼c10. The strain at the end of block 11, ¼c11, is estimated by following the creep curve for a time interval of %t11.

The strain versus time curve relevant to Öref 12 and T12 is entered at a strain level of ¼c11. The strain at the end of block 12, ¼c12, is estimated by following the creep curve for a time interval of %t12.

T.1.4 Stress to rupture

Stress rupture data for certain carbon, alloy ferritic and austenitic steels are given in references [226], [227], [228] and [58].

The construction to obtain the accumulated creep damage in a block, %Dc is shown in Figure T.3.

NOTE The curves are plotted in terms of fractional strain not percentage strain.

Figure T.2 — Strain hardening construction to obtain incremental strains

∆t12

∆t10

∆t11

εc11εc10

εc12

εc9

εref.11,T11

σref.10,T10

∆ref.12,T12

Time, h

Frac

tiona

l str

ain

∆εc11

∆εc12

∆εc10

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T.1.5 Fatigue crack propagation rate

In the absence of plasticity, the fatigue crack propagation rate at high temperatures is defined by the following equation:

(da/dN)f = A(qo%K)m (T.1)

where

(da/dN)f is the crack extension per cycle due to fatigue (in mm);qo is the fraction of the total load range for which a crack is judged to be open [229].

For a structure, qo may be estimated conservatively from the following:

qo = 1 for R U 0 (T.2)

qo = (1 – 0.5R)/(1-R) for R < 0 (T.3)

An upper bound to fatigue crack propagation data for ferritic and austenitic steels and for cyclic frequencies greater than 1 Hz can be obtained by setting the following values:

m = 3;

A = (ERT/ET)mAo.

Ao is 5.21 × 10–13 for steels, including austenitic steels, operating in air or other non aggressive environments at temperatures up to 100 °C. The relationship has been validated by the results of tests at the following temperatures:

Carbon manganese steels 400 °C;

Chromium ferritic steels 500 °C to 550 °C;

Austenitic steels 550 °C to 650 °C.

Further data can be found in Hudson et al [23], Waterman and Ashby [231], Engineering Sciences Data Unit [21] and Holdsworth [232].

The rate of growth in the height a of the crack (for which Ì = ;/2) may differ from the rate of growth of the crack along the surface (Ì = 0). This arises because of a possible difference in %K in the two positions.

Figure T.3 — Construction to estimate creep damage in block

Stre

ss to

rup

ture

∆t tR(ref)

ref

∆Dc = ∆t/tR(ref)

Time to rupture

σ

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Where cracks are propagated by fatigue through material heavily damaged by prior creep (i.e. with a Dc greater than about 0.8) propagation rates are likely to be increased. In these circumstances, a factor should be applied to the data, depending on the amount of prior creep damage. This should be determined experimentally.

T.1.6 Creep crack propagation rate

Where crack propagation data are not available for the material used in the component, estimates can be obtained from the following equations, using the data given in Table T.1. Depending upon the material, further information may be available in the published literature (see for example Hollstein et al [233], Dimopulos et al [234], Winstone et al [235], Nikbin et al [236]).

The constants in Table T.1 lead to growth rates in mm/h if C* is in units N/(mm/h).

Both mean and upper bound data are presented; use of the upper bound data results in lower estimates of remaining life. For components more than about 100 mm thick, crack propagation rates may be higher; specialist advice should be sought about the appropriate values to be used.

The rate of growth in the height a of the crack (for which Ì = ;/2) may differ from the rate of growth (along the surface Ì = 0). This arises because of a possible difference in C* in the two positions.

For materials not covered by Table T.1 two methods are available to estimate crack propagation rates, although the results may not be upper bound.

Table T.1 — Constants used to derive creep crack propagation rates in mm/h

(T.4)

Material Temp. range of data Upper bound Mean

°C C q C q

Plain C steels 482 to 538 0.015 1.00 0.006 1.0

½Cr Mo V — wrought and cast 500 to 600 0.24 0.80 0.024 0.80

½Cr Mo V — type IV 540 to 565 0.6 0.80 0.028 0.80

½Cr Mo V — coarse HAZ 565 1.2 0.80 0.4 0.80

1Cr Mo 450 to 600 0.06 0.84 0.018 0.84

2¼ Cr 1 Mo weld metal 540 to 565 0.139 0.674 0.027 0.674

AISI type 304 and 304H 650 to 760 0.035 1.00 0.007 1.00

AISI type 304 (service exposed) 760 0.28 0.85 0.14 0.85

AISI type 321 (wrought) inc HAZ and ageing

650 0.04 0.90 0.0094 0.90

AISI type 316 and 316H (wrought) 500 to 550 0.085 0.81 0.011 0.81

(inc HAZ) 625 0.042 0.89 0.0041 0.89

AISI type 316 weld (as welded, stress relieved and aged)

600 to 650 0.134 0.876 0.0236 0.876

AISI type 316 weld (solution treated) 550 0.085 0.81 0.011 0.81

Inconel 800H 800 0.16 0.9 0.05 0.9

Mod 9Cr steel 580 to 593 0.05 0.65 0.024 0.7

Mod 9Cr 1C-HAZ 580 0.091 0.78 0.046 0.78

2¼ Cr1 Mo 550 to 600 0.024 0.8 0.012 0.83

Aluminium alloy RR 58 150 7.0 0.85 4.23 0.85

Aluminium alloy 2519 — T851 135 0.7 0.9 0.35 0.9

Astroloy API 700 0.57 0.78 0.23 0.79

In 939 850 0.2 1.0 0.04 1.0

1Cr Mo V steel 538 to 594 0.084 0.75 0.02 0.79

a = C Cc

*( )q

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Where the creep rupture ductility of the material is known, a guide to crack propagation rates can be obtained by taking q as 0.85 and deriving C from the following equation:

C = 0.0085/¼f (T.5)

where ¼f is the creep rupture ductility of the material in a uniaxial test at Öref with the fractional strain used and not the percentage strain. Creep rupture ductilities for certain steels are given by the Institution of Mechanical Engineers; Creep of Steels Working Party [227] and the British Iron and Steel Research Assoc./Iron and Steel Institute [228].

When the creep rupture ductility is not known, a guide to propagation rates can be obtained from the following equations:

where

Kp is the elastically calculated stress intensity factor at Ì = ;/2 for growth in the height direction and at Ì = 0 for growth along the surface;

Öref is the reference stress;

tR(ref) is the time to rupture at the reference stress.

These latter two terms are not sensitive to Ì (see 9.5.4 and T.2).

T.1.7 Fracture toughness

Data should preferably be obtained on the materials actually used in the component. Where these are not available, the typical values that are provided in Table T.2 for a range of temperatures may be used. It is necessary to check that these are applicable to the heat treatment and manufacturing procedure used for the component. A check should also be made regarding any allowances for ageing of the material, for creep damage and for the presence of welds.

Further information on fracture toughness values is provided by Hudson et al [23] and Waterman and Ashby [231].

Table T.2 — Typical values of fracture toughness (based on the value of KI at 0.2 mm crack extension)

T.1.8 Incubation period

An incubation period is frequently observed prior to the onset of creep crack growth.

Where data are not available for the material used in the component, the incubation period can be estimated from the following equation:

(T.6)

Material Temperature range Mean, KIc Lower bound, KIc

°C N/mm3/2 N/mm3/2

Si killed CMn steel 300 to 380 5 185 3 130

A1 killed CMn steel 300 to 380 6 200 4 615

Wrought AISI type 316 steel 300 to 600 4 430 3 320

2¼C1Mo steel 100 to 500 4 740 3 160

(T.7)

a

K

tc

p

ref R ref

=( )⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪( )

0 014

20 85

.

.

t =

t

K

ix

R ref

0 892

0 85

.

.

ref

p

( )

( )

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

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Where experimental data are available and the following conditions are met:

a) the crack opening displacement at initiation of creep crack growth, ¸ix, is known;

b) the creep strain versus time curve for the material, at the relevant stress and temperature, can be represented by an equation of the form:

¼c = D½Bntb

then tix can be obtained from the following equation:

where

It should be noted that a variety of criteria can be used to define creep incubation and hence incubation time, tix. The criteria employed should be stated. The criterion of 0.05 mm growth quoted with respect to equation (T.7) is an example.

Where incubation time data are available from test specimens, the incubation time for the component can be obtained from the following equations, provided that both specimen and component are in the secondary stage of creep:

where

subscript “comp” refers to the component;

subscript “spec” refers to the specimen.

It should also be noted that, in the expressions given in this subclause for estimating incubation periods, no allowance has been made for the presence of secondary stresses. When these are present a conservative assessment will be obtained by replacing Kp by K(p + s) in equations (T.7) and (T.10). For cracks in un-stress relieved welds, ti should be taken as zero.

T.2 Calculation procedure

T.2.1 Step 1: Plot past operating history and future operating requirements

This is done as shown schematically in Figure T.4 in which periods of operation at various stress levels and temperatures are indicated. In those cases where it can be assumed that the component operates under steady conditions, it is still necessary to divide the life into a series of blocks, to prevent cumulative errors in the predictions. P and Q are as defined in 6.4. It is assumed in what follows, for the purpose of illustrating the method, that a flaw is discovered at the end of block 5, having dimensions of height a5 and length c5. The flaw is considered to have been present from the date that the plant entered service, unless there is evidence to the contrary.

If a flaw in new plant is being assessed, the calculations are similar, but start at t0. In new plant it may be permissible to make allowance for the incubation period of the crack (see 9.4 and T.1.8).

(T.9)

(T.10)

(T.11)

tix

¸ix R′⁄( )n n 1+( )⁄Öref E⁄–

D′Önref

-------------------------------------------------------------------⎩ ⎭⎨ ⎬⎧ ⎫

1 b⁄( )

=

′ ⎛⎝⎜

⎞⎠⎟

R K=

p

ref

2

icomp

ispec

n n+1

spec

comp

t

t

= C*

C*

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

( )

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T.2.2 Step 2: Calculate margin against fracture

These calculations should be carried out for the most onerous loadings likely to occur, including accidental overloads, for a crack characterized by the dimensions a5 and c5. Material properties should be appropriate to the age of the component and the temperature should be that associated with the loading condition being assessed.

The elastic-plastic methods of Clause 7 may be used to assess the margin against fast fracture. The values of Kp and K(p + s) can be calculated using any suitable procedure, taking into account the recommendations of Clause 7. The calculation of the reference stress is given in T.2.3.

Further information about the determination of the stress intensity factors will be found in references [39], [40], [41], [60] and [164]. Where residual or thermal stresses are large compared with the stresses due to internal pressure and external loads, it is recommended that the methods given in Annex R should be followed.

If the margin against fast fracture is unsatisfactory, refined calculations should be carried out. If the margin is still unsatisfactory, remedial action is required.

Figure T.4 — Division of operating history into blocks of constant stress and constant temperature

Stre

ss a

nd te

mpe

ratu

re

Block2

Block1

Block4

Block5

Block7

Block8

Block6

∆t6

Block3

∆t3

∆t1 ∆t2 ∆t4 ∆t5 ∆t7 ∆t8

t8t7t6t5t4t3t2t1t0 Time

Expected future operationPast history

k t.P

k t.P

Q

T

Q

T

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T.2.3 Step 3: Calculate the effect of previous history

T.2.3.1 Calculate reference stress

Calculate the reference stress, Öref1, for block 1, taking a = a5 and c = c5.

Repeat blocks 2, 3, 4 and 5 to obtain Öref2, Öref3, Öref4 and Öref5, again taking a = a5 and c = c5.

In general, the reference stress to be used can be obtained from the limit load of the structure by the following equation:

Öref = LrÖY (T.12)

The determination of reference stress is carried out using the loads acting on the structure which give rise to P stresses and includes any long range thermal and residual stresses classified as P. The internal loads giving rise to Q stresses are ignored.

Where a combination of loads acts on the component, the reference stress to be used in the calculations may be determined using the limit load for the combined loading or conservatively by summing the reference stresses due to the individual loads.

For components of simple shape subject only to primary membrane and primary bending stress, information will be found in Annex N.

For more complex situations, information will be found in references [60] and [237].

T.2.3.2 Calculate creep damage in ligament

Calculate %Dc1 for block 1 from the stress to rupture versus time to rupture curve for the material at a temperature of T1. The time to rupture, tR(ref 1) is read off at a stress level of Öref 1. The creep damage is calculated from the following equation (see Figure T.3):

%Dc1 = %t1/tR(ref1) (T.13)

where

%t1 = t1 – t0.

Repeat for blocks 2, 3, 4 and 5 to obtain %Dc1, %Dc2, %Dc3, %Dc4 and %Dc5.

Calculate accumulated creep damage up to the end of block 5 from the following equation:

Dc5 = %Dc1 + %Dc2 + %Dc5 (T.14)

T.2.3.3 Check margins against creep rupture

Check that Dc5 is less than unity by an adequate margin [see 9.3c)]. If this is satisfactory proceed with calculations. If not take remedial action (see 9.5.11).


Read off %¼c1 for block 1 from the strain against time curve at Öref1, calculated as in T.2.3.1, using a = a5 and c = c5 and temperature T1.

Repeat for blocks 2, 3, 4 and 5 at Öref2, Öref3, Öref4 and Öref5 and temperatures T2, T3, T4 and T5, respectively to obtain %¼c2, %¼c3, %¼c4 and %¼c5, again using a = a5 and c = c5. The strain hardening construction of T.1.3 should be used.

Calculate ¼c5 using the following equation:

¼c5 = %¼c1 + %¼c2 + %¼c3 + %¼c4 + %¼c5 (T.15)

T.2.4 Step 4: Assess future performance in block 6

T.2.4.1 Calculate reference stress in block 6

Calculate Öref 6 for block 6, using the method of T.2.3.1 taking a = a5 and c = c5.

T.2.4.2 Calculate accumulated creep strain to end of block 6

Read off %¼c6 for block 6 from the strain against time curve at Öref 6, using a = a5 and c = c5 and temperature T6. The strain hardening construction of T.1.3 should be used.

Calculate ¼c6 using the following equation:

¼c6 = %¼c5 + %¼c6 (T.16)

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T.2.4.3 Calculate creep damage in ligament up to end of block 6

Calculate %Dc6 for block 6, using the method of T.2.3.2 taking a = a5 and c = c5. Calculate accumulated creep damage up to the end of block 6 from the following equation:

Dc6 = Dc5 + %Dc6 (T.17)

T.2.4.4 Calculate C* parameters for block 6

Calculate C*a6 for block 6 taking a = a5 and c = c5 from the following equation:

C*a6 = Öref 6 (%Dc6/%t6)R½ (T.18)

where

R½ = (Kp/Öref 6)2; (T.19)

Kp is the elastic stress intensity factor at Ì = ;/2 for crack growth in the height direction and Ì = 0 for growth along the surface.

See 9.5.4 for the stresses to be included, T.2.2 for methods of calculation of stress intensity factor and T.2.3.1 for methods of calculation of reference stress.

T.2.4.5 Calculate increment of crack growth in block 6

Use T.1 or experimental data to establish the creep crack propagation rate at temperature T6 as a function of C*. Calculate the creep crack growth rate, c6, in the height direction (Ì = ;/2) using the procedure of T.1.6 to obtain the increment of crack extension %ac6 in the block from the following equation:

Calculate the new crack height from the following equation:

a6 = a5 + %ac6 (T.21)

Repeat the procedure for Ì = 0 to determine the creep crack extension on the surface and the new surface crack length from the following equation:

c6 = c5 + %cc6 (T.22)

T.2.4.6 Check that steady creep conditions have been achieved at the crack tip

Calculate the elastic strain, ¼c6, from the following equation:

where

E is the elastic modulus of the material;

K(p + s) and Kp are the elastically calculated stress intensity factors, appropriate to block 6.

See 9.5.4 for the stresses to be included, T.2.2 for methods of calculation of stress intensity factor and T.2.3.1 for methods of calculation of reference stress.

The procedure should be repeated for the deepest point (Ì = ;/2) and at the surface (Ì = 0) and the largest value of ¼c6 chosen.

If ¼c6 < ¼e6, stress redistribution is incomplete and the creep crack propagation rate calculated in T.2.4.5 should be doubled. It should also be doubled in subsequent blocks until ¼c U ¼e.

In materials of low creep rupture ductility, such as occur in certain types of weld, the additional creep damage due to non-steady creep conditions at the crack tip may lead to a reduction in rupture life. In these circumstances specialist advice should be sought.

T.2.4.7 Check convergence of results

Repeat calculations of Öref6, %¼c6, %Dc6, %ac6 and %cc6 using a = a6 to check that c = c6 predictions are not significantly changed.

If they are, subdivide block 6 and repeat the calculations, or repeat using some suitable predictor-corrector interpolation.

(T.20)

(T.23)

a·

∆ ∆a = a tc6 c6 6

e

ref

p s

p6

6

2

=⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+( )

E

K

K

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If they are not, proceed to T.2.4.8.

Usually a discrepancy of a few per cent is acceptable. However, where the total life is divided into a large number of time steps, greater accuracy may be needed to prevent an accumulation of errors.

T.2.4.8 Check margins against fast fracture

Check the margin against fracture at the end of block 6 by using the procedure of setting a = a6 and c = c6.

If this is satisfactory, then proceed to T.2.4.9.


Check that Dc6 is less than unity by an adequate margin (see 9.3).

If this is satisfactory proceed to T.2.5. If not, take remedial action (see 9.5.11).

T.2.5 Step 5: Assess performance during future life

Repeat T.2.4 for block 7, setting a = a6 and c = c6, using the stresses and temperatures appropriate to block 7.

Repeat T.2.4 for each remaining block in turn, setting a and c dimensions at the beginning of each block.

It is important to check, at each stage, that steady creep conditions have been achieved at the crack tip (see T.2.4.6) and that the calculations converge (see T.2.4.7).

If either the margin against fast fracture or the margin against creep rupture becomes too small at the end of an intermediate step, then repair or replacement will be necessary before the point is reached.

T.2.6 Modifications to allow for incubation period

When a flaw is discovered before a component goes into service, or when a hypothetical flaw is assumed in order to check the flaw sensitivity of a proposed design, it may be possible to benefit from an incubation period before the crack starts to grow.

When a flaw has been discovered after a component has been in service, the conservative assumption should be made that the crack initiated early in life, unless there is strong evidence to the contrary.

Where it is legitimate to allow for the incubation period, for example when considering whether a crack in a new component should be repaired, the following modifications are made to the procedure. Where data are not available for the materials used in the component, an estimate of incubation period can be obtained from T.1.8. The lower value of incubation period at maximum height and at the surface should be used.

For the purpose of illustration, it is assumed that the incubation period occupies blocks 1 to 3 of the loading history.

The calculation of Öref, %¼c, and %Dc in blocks 1 to 3 are carried out as described in T.2.3, taking a = a0 and c = c0.

For block 4, Öref, %¼c, %Dc, C*, %ac and %cc are calculated with a = a0 and c = c0.

For block 5, Öref, %¼c, %Dc, C*, %ac and %cc are calculated with a = a4 and c = c4 and so on for the remaining blocks.

T.3 The assessment of flaws in weldments

T.3.1 General

Many of the flaws found in high temperature plant are associated with weldments. They may arise during fabrication, post-weld heat treatment or in service. Furthermore, since weldments contain wide metallurgical and mechanical property variations, the flaws are often located in non-homogeneous material, which has a significant effect on crack growth.

Flaws in austenitic and ferritic weldments, including type IV (see T.3.2.4) cracking can be assessed using the methods described in this standard, provided that the special requirements of this annex are taken into account.

However, where cracking occurs at the interface between the austenitic weld metal and ferritic parent metal in dissimilar metal weldments, special consideration is necessary. Such weldments are excluded from the scope of this document and specialist advice should be sought when assessing them.

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T.3.2 Plant experience

T.3.2.1 General

It is important to recognize that weldments may fail by a number of different modes that involve creep crack growth. A basic understanding of these failure modes enables the appropriate materials properties and stresses to be identified and brought together in the procedure in order to carry out an assessment. To assist in this respect, the following are some commonly encountered failure modes in pipe to pipe weldments.

T.3.2.2 Reheat cracking in ferritic weldments

In pressure vessels, etc., circumferential heat-affected zone (HAZ) and transverse weld metal cracking arise during post weld stress relief heat treatment or very early in the plant operating life. Initiation of cracking is highly dependent on the material’s composition, weldment microstructure and residual stress; the last two factors depend critically on welding and heat treatment procedures. Crack growth depends on welding and heat treatment procedures and on microstructure and stress. Both of the latter vary initially as a function of position and change further as a function of time and temperature as the weldment is exposed to plant conditions.

T.3.2.3 Reheat or stress-relief cracking in austenitic weldments

Stress-relief or reheat cracking similar to that described above for ferritic steels can also occur in austenitic steels.

This brittle intergranular cracking occurs in the HAZ close to the fusion line as a result of the concentration onto grain boundaries of relaxation strains associated with stress relief, or the concentration of creep strain during extended service. This strain concentration is due to strengthening within the matrix of the grains resulting from fine precipitate dispersions on dislocation networks. The mechanism appears able to operate in service at temperatures as low as 500 °C, given sufficiently long times.

The propensity for this type of cracking is greatest in the Nb stabilized AISI type 347 steel, but it is also encountered in the Ti stabilized AISI type 321 steel. Dependent upon operating temperature and the level of residual or applied stress, a similar mechanism might also occur in AISI type 316 steel, particularly high carbon varieties. It is, however, less likely to occur in nitrogen strengthened low carbon varieties, due to the greater solubility of nitrogen as compared with carbon.

T.3.2.4 Type IV cracking in ferritic weldments

This mode of failure in pressure vessels, etc., involves the initiation and growth of circumferential creep cracks in the low temperature extremity of the HAZ adjacent to the untransformed parent material. It has been observed from times midway through the design life onwards. Axial loading over and above the nominal axial stress due to internal pressure is significant in promoting this mode of cracking.

T.3.2.5 Transverse weld metal cracking in ferritic weldments.

This is the dominant mode of cracking encountered in pipe to pipe weldments subjected to predominantly internal pressure loading. Under these conditions, the weldments invariably reach or exceed their design lives, by which time the hoop strain accumulation initiates axial cracks, transverse to the weldment, in the more coarse-grained columnar regions of the weldments. This crack initiation is generally multiple, leading eventually to excessive deformation, bulging and the formation of secondary circumferential cracks in the weld metal, which result in eventual failure.

T.3.3 Advice on structural calculations for weldments

Flaws may arise in weldments for a number of different reasons and extend by creep crack growth until they cause failure. Furthermore, creep deformation alone can lead to the initiation of discrete cracks in weldments even in the absence of pre-existing flaws. Crack growth may also involve periods of fast and slow propagation as cracking traverses regions of different microstructure. The flaw assessment procedure needs to take account of these factors in applying this document to the assessment of pre-existing weldment flaws and growing creep cracks.

It is often sufficient to carry out a simplified analysis as described below, although in some circumstances this can be over conservative. For a more detailed investigation, the user should refer to [57] or seek specialist advice.

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For fracture, bulk creep damage and crack growth, the following points should be considered.

a) Fracture analysis.

— Assume that the weldment is homogeneous.— Use the yield and ultimate tensile strength of the weakest constituent of the weldment.— If it can be shown that the flaw cannot propagate into another region of the weldment, use the value of KIc appropriate to the region in which it is situated. If this cannot be shown, use the lowest value of KIc that occurs anywhere in the weldment.

b) Analysis of bulk creep damage.

— Calculate Öref assuming the weldment to be homogenous.— Calculate tR(ref) for the region of the weldment with the shortest rupture life, but also check that there is adequate margin against failure, if stronger regions are present that have a low creep rupture ductility.

c) Creep crack growth analysis.

— Calculate C*, assuming that the weldment is homogenous. Use the strain rate data of the fastest creeping constituent.— If it can be shown that the flaw cannot propagate into another region of the weldment, use the value of c appropriate to the region in which it is situated. If this cannot be shown, use a value of c appropriate to the region with the highest crack propagation rate.— In making a preliminary assessment, worst case materials data can be used in the analysis: for example, upper bound crack propagation rate and upper bound strain rates. However, care needs to be taken to guard against excessive pessimism — for different casts of steel to the same specification, there is an approximate proportionality between crack propagation rate and strain rate.

T.3.4 Residual stresses

A particular problem with weldments is the presence of residual welding stresses. Although these relax as creep strains accumulate, they may reduce the creep life by initiating crack growth at shorter times and by increasing crack growth rates. However, often the effect is small, particularly in the case of stress-relieved welded joints made from creep ductile materials.

Residual stresses are incorporated into the calculations as follows.

— In fracture assessments, the value of the stress intensity factor, K(p + s), is derived from the total stress acting in the region of the crack, including local residual stresses.— In determining Kp for post yield fracture assessment and for the calculation of C*, local residual stresses are ignored but long range residual stresses, classified as P, are included.— For post yield fracture assessment, Ks is calculated as K(p + s) – Kp.— In calculating Öref, local residual stresses are ignored, but loads associated with long range residual stress are included in the total applied loads.

T.4 Assessment to include creep-fatigue loading

T.4.1 General

The crack growth per cycle for creep-fatigue loading is estimated by summing the independently calculated crack propagation due to creep and that due to fatigue. Separate calculations, as in T.2 are needed to predict growth in the height (Ì = ;/2) and the surface (Ì = 0) directions.

The procedure described in T.4 replaces that described in T.2.4.5.

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T.4.2 Crack growth due to creep

The crack growth rate due to creep, c, is calculated, as in T.1.6 from the following equation:

c = C(C*)q (T.24)

The crack extension due to creep in a single fatigue cycle (da/dN)c, is thus calculated from the following equation:

where the calculation is made for both the height and surface directions.

T.4.3 Crack growth due to fatigue

The crack growth per cycle due to fatigue is calculated from the following equation:

where qo%K is the effective range of stress intensity factor at the crack tip due to cyclic loading (see T.1.5).

The value of %K is calculated using the methods described in T.2.2.

The same linearization procedure can be applied to the range of the cyclically variable stresses, as is described in 9.5.4 for the non-variable stresses. The ranges in P and Q stresses should be included, together with the effect of any stress concentration.

The predictions made using these equations may be over conservative if qo is not set to less than unity, where the stresses at one end of the cycle are compressive (T.1.5). The corrections for compressive stress, given in Clause 8, should not be used as these are inapplicable when creep occurs. In situations where plasticity occurs, the appropriate parameter for characterizing fatigue crack growth is %J. Guidance for the use of %J in such circumstances is given by Nuclear Electric [57].

Where data for the material used in the component are not available, advice on the values to be taken for A and m is provided in T.1.5. Where cracks are propagated by fatigue through material heavily damaged by prior creep (i.e. with a Dc greater than about 0.8), propagation rates are likely to be increased. In these circumstances, a factor should be applied to the data, depending on the amount of prior creep damage. This should be determined experimentally.

The rate of growth in the height of the crack may differ from the rate of growth in the surface length. This arises because of a possible difference in %K in the two positions.

T.4.4 Total crack growth in block

The total crack growth per cycle, (da/dN), is calculated from the following equation:

(da/dN) = (da/dN)c + (da/dN)f (T.27)

The total growth in crack height in block n, %an, is calculated from the following equation:

%an = 3 600f%tn (da/dN) (T.28)

The total growth in surface crack length in block n, %cn is obtained in a similar way.

The assessment procedure is identical to that described in 9.5 and in T.2, except that, in T.2.4.5, the values of %a6 and %c6 etc., are calculated as described above.

T.4.5 Incubation period

Where fatigue must be taken into account under the provisions of 9.5.7, the incubation period should be ignored, unless experimental data are available for the material under the appropriate conditions.

(T.25)

(T.26)

a·

a·

d da Na

f( ) = ( )c

c

3 600

d da N A q K( ) = ( )f T o

m∆

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Annex U (informative) Worked example to demonstrate high temperature failure assessment procedure

U.1 General

This example is provided to indicate how the procedure for predicting high temperature crack growth can be applied.

Initially the problem is specified and relevant materials data are identified. An example has been chosen that includes non-steady primary and secondary stresses to illustrate how these conditions are handled. The assessment procedure is then outlined in sequence. Checks are made to determine the magnitude of any fatigue crack growth, the proximity to fast fracture and the amount of creep damage that takes place as creep crack growth occurs. Finally a sensitivity analysis is included to determine the effect of allowing for an incubation period prior to the onset of crack propagation and for using average rather than lower bound rupture data.

U.2 Problem specification

A plant operates for 28 days each month. The material of the plant is AISI Type 316 stainless steel. At the end of the 28th day it is shut down and is restarted at the beginning of the 1st day of the succeeding month. The monthly operating schedule is given in Table U.1.

Table U.1 — Operating conditions

The plant was put into operation at the beginning of April 1985 and during the July 1990 shutdown, a crack was discovered in a component. A crack was located in parent material, well away from any welds. There was no evidence that the crack had grown during the first five years of service. There was also no evidence of stress corrosion cracking or of widespread creep damage.

The owners wish to use the plant until mid 2005 under the same operating régime.

Will it be necessary to take remedial action? If so, when?

The crack was located at the outer surface of a cylindrical vessel of internal diameter 1 050 mm and wall thickness 35 mm. It was oriented in an axial-radial direction normal to the surface with the dimensions (in mm) shown in Figure U.1.

No residual stresses are present in the vicinity of the flaw and there is no discontinuity causing a stress concentration. However, during start up, transient thermal stresses are superimposed on the pressure stresses for a period of 15 min. The distribution of these thermal stresses is as shown in Figure U.2.

Temperature

ºC

Pressure bara Temperature

ºC

April, May, June, 40 575

August,

September,

October, January,

February, March

November, December 60 550

July Shut down Shut downa 1 bar = 0.1 N/mm2.

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Apart from the transient thermal stresses, there is no accidental overload or other abnormal loading which has to be taken into account.

It may be assumed that the material creep strain properties can be described by the following relation:

where

It may also be assumed that the creep rupture data can be calculated from the following equation:

where

When the safety factor is chosen to equal 10, the expression corresponds with lower bound data given in the French Code RCC-MR. The elastic modulus E, lower-bound yield strength ÖY and tensile strength Öu are also taken from that code, as given in Table U.2.

Other data can be taken from Annex T.

Dimensions in millimeters

Figure U.1 — Flaw dimensions

Figure U.2 — Thermal stress distribution in the region of the flaw

(U.1)

¼c is the fractional accumulated creep strain;

Ö is stress (in N/mm2);

T is the absolute temperature (K);

t is time (h).

(U.2)

tR is rupture life (h);¾c is a safety factor.

40

7

35

50 N/mm2

50 N/mm2

0

c= × × + × ×( )− − −4 19 700 3 0 333 6

4 0 10 5 21 10e t tT

. ..

T tlogc R10

4 2 222 0 2 686 5 10 25 320 1 9748 10+( ) = × − + ×( )−

. . . .

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Table U.2 — Selected materials data

U.3 Assessment procedure

U.3.1 Step 1: General (see 9.5.1)

The solution procedure is given in 9.5 and Annex T. The same clause headings are used here as in the main text.

The assessment procedure is represented by the flow chart in Figure 26. It is followed step by step.

U.3.2 Step 2: Initial investigations to establish cause of cracking (see 9.5.2)

From the information provided in the problem specification, the possibility of stress corrosion cracking can be neglected. Also, there was no evidence of widespread creep damage so that property data for new material can be employed in the assessment.

U.3.3 Step 3: Define previous plant history and future operational requirements (see 9.5.3)

These have been specified in U.2. The plant operates for 11 months each year; nine of these months are at low pressure and two at high pressure. During each of the 11 months the plant operates for 28 days (i.e. 672 h). Transient conditions exist for 15 min (0.25 h) after each start up, so that thermal stresses should be superimposed on the steady loading conditions for this period.

U.3.4 Step 4: Establish stresses (see 9.5.4)

It is necessary to separate the stresses into their primary (P) and secondary (Q) components to determine stress intensity factors. For this purpose, the steady operational stresses are classified as primary stresses, the thermal as secondary stresses and km equals 1 in this problem. The primary stresses are those that result from the internal pressure. A non-linear thermal stress distribution is indicated. In principle, it is possible to integrate any stress distribution experienced. Consequently, linearization is adopted to calculate the secondary component of K(p + s). Linearization over the whole cross section is employed, as illustrated in Figure 1b), as this procedure is simple to apply and provides a conservative assessment. The resulting mean and bending components of stress are listed in Table U.3 for each loading condition.

It is assumed that any stresses present during a shut down are negligible. It is not necessary to consider residual stresses due to welding as the flaw is remote from any weld.

Table U.3 — Stress category

U.3.5 Step 5: Characterize flaws (see 9.5.5)

Only one flaw is to be considered. From the method of characterization shown in Figure 8, it is described as a surface flaw of height a = 7 mm and length c = 20 mm.

Temperature

ºC

ÖY

N/mm2

Öu

N/mm2

E

kN/mm2

550 113 395 149.23

575 112 384 147.195

Condition Stress values

N/mm2

Pm Pb Qm Qb km

Low pressure start up 60 0 0 50 1

Low pressure 60 0 0 0 1

High pressure start up 90 0 0 50 1

High pressure 90 0 0 0 1

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U.3.6 Step 6: Establish material properties (see 9.5.6)

Tensile, creep strain and rupture data are provided for the stainless steel in U.2. No other materials specific information is supplied. However, guidance can be obtained from T.1. An upper bound on fatigue crack growth rate for steels is given in T.1.5, coefficients to describe mean and upper bound creep crack growth rates for stainless steel are listed in Table T.1 and lower bound fracture toughness properties are given in Table T.2.

No allowance for bulk material damage is necessary since none was observed. Worst case data are assumed initially in making the assessment. The significance of altering some of the material properties is discussed in U.3.10. The most reliable predictions are obtained when actual data for a particular batch of materials are employed.

U.3.7 Step 7: Check on fatigue (see 9.5.7)

The P and Q stresses listed in Table U.3 and the fatigue crack propagation properties given in T.5 are used in this estimate. Guidance on making fatigue crack growth assessments is provided in Clause 8. The largest fatigue cycle will occur during start up when transient conditions apply to this example. Therefore %K is given by:

This term has to be determined at the deepest point of the crack and where it intersects the vessel surface. The formulae given in Clause 8 are used to calculate %K. In general %K is given in terms of a geometry factor Y and the stress range %Ö by:

which can be expressed in the absence of stress concentrations as:

where

For the crack dimensions given in U.2, the following values for Mm and Mb are obtained.

Hence, for the worst loading conditions represented by a high pressure start up, the following values of %K(p + s) are calculated.

%K(p + s) = 610 N/mm3/2

at the deepest point and

%K(p + s) = 430 N/mm3/2

at the surface giving the following values:

(da/dN)f = 5.74 × 10–4 mm/cycle;

(dc/dN)f = 2.01 × 10–4 mm/cycle.

Relative to the initial crack dimensions, this amount of growth during a start up cycle is small and will not influence calculations of K and %K for each loading period.

%K = K(p + s) – 0 = K(p + s) (U.3)

(U.4)

(U.5)

Mm and Mb are dimensionless magnification factors obtained from Table M.8;

%Pm, %Pb, %Qm and %Qb are the corresponding ranges of the mean and bending components of the primary and secondary stresses.

Mm Mb

At surface 0.67 0.62Deepest point 1.017 0.767

∆ ∆K Y a= π

∆ ∆ ∆ ∆ ∆K a M P Q M P Q= +( ) + +( ){ }πm m m b b b

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U.3.8 Step 8: Perform flaw assessment24) (see 9.5.8)

U.3.8.1 This step requires the operational conditions for each month and these are given in Table U.2 (see T.2.1).

U.3.8.2 It is first necessary to determine the margin against fast fracture. As this should be done for the most severe loading conditions, the high-pressure start up is considered (see U.2.2). The method given in Clause 7 is used. Three levels of treatment are identified: Level 1 for initial screening, Level 2 for normal assessments and Level 3 for a tearing instability analysis. The Level 2 treatment given in 7.3.2.1 is employed as it is most appropriate for a high work-hardening material like stainless steel.

It is necessary to calculate Kr and Lr as described in Clause 7, from the following equations:

In this example, Öref is calculated from P.4.3.5. K(p + s) is determined in U.3.7. The term Ô is a plasticity correction factor that depends on the ratio of the secondary and primary stresses. It can be obtained from Annex R. Hence, assuming lower bound properties for stainless steel from Table U.2, Kmat = KIc = 3 320 Nmm–3/2, so that, for the most severe loading conditions the following values apply:

The maximum acceptable value of Lr from 7.3.1 is calculated as follows:

Lrmax = (ÖY + Öu)/2ÖY = 2.248

When the assessment points are superimposed on the failure assessment diagram (Figure U.3) an adequate margin of safety is demonstrated.

U.3.8.3 This step determines the effects of the previous history up to July 1990 (see T.2.3). All calculations are based on the crack dimensions at July 1990, as it is conservative to assume that the crack was present in April 1985 but was not discovered.

The reference stresses for the high and low-pressure conditions Öref1 and Öref2 are 108.5 N/mm2 and 72.3 N/mm2 respectively.

The creep damage in the ligament is obtained by summation over each 28-day period from T.2.3.2 using the following equation:

where from the creep rupture data:

tR(ref1) = 3.87 × 106 h under the high pressure conditions, and

tR(ref2) = 4.40 × 106 h for low-pressure operation.

Therefore, between April 1985 and July 1990, the value of Dc is as follows:

Dc = 0.009 07

Since Dc < 1, there is an adequate margin against creep rupture and calculations to determine the amount of crack growth can continue.

24) This detailed procedure follows the steps given in T.2.

and

K(p + s) Ô Kr Lr

N/mm–3/2

At surface 430 0.021 2 0.151 0.96Deepest point 610 0.018 4 0.202 0.96

KK

Kr

p s

mat

= ++( )

Lr

ref

y

=

Dt t

c

R ref1 R ref2

= × + ×

( ) ( )

10 672 48 672

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Fig

ure

U.3

— M

arg

in a

ga

inst

fra

ctu

re f

or

hig

h p

ress

ure

sta

rt u

p

1.0

0.5 0

0.5

1.0

1.5

2.0

L rm

axL r

Kr

Surf

ace

poin

t 1

990

Dee

pest

poi

nt

199

0

Surf

ace

poin

t

2004

Dee

pest

poi

nt

200

4

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The creep strain accumulated to July 1990 can be determined from T.2.3.4 using the strain hardening equation of state:

U.3.8.4 This step predicts future performance from August 1990 onwards using the same procedures as T.2.4. For each month a new amount of damage Dc, and creep strain %¼c are calculated using updated estimates of Öref for each new crack length. For example, for August 1990 the following values apply:

At the deepest point:

At the surface:

Hence, assuming that the upper bound creep crack growth constants at 550 °C for AISI type 316 stainless steel from Table T.1 apply at both 550 °C and 575 °C, then C = 0.085, q = 0.81 and the creep crack extension at the deepest point from T.2.4.5 becomes the following:

%a = 672 c = 7.3 × 10–3 mm

and the corresponding extension on the surface becomes the following:

%c = 3.7 × 10–3 mm

This magnitude of crack growth is sufficiently small that it is not necessary to divide the time steps into less than a month.

A check for the elastic strain using the procedure of T.2.4.6 gives ¼e = 1.303 × 10–3 which is greater than the creep strain of 1.01 × 10–3 from step U.3.8.3d). This indicates that the steady state creep conditions have not yet been reached at the crack tip and the creep crack growth rates calculated above need to be doubled as described in T.2.4.6. Further checks at the end of the month reveal adequate margins against fast fracture and creep rupture. The calculations also show the creep component of cracking is more than 10 times the fatigue component so that the fatigue contribution can be neglected (see 9.5.8).

U.3.8.5 The steps of U.3.8.4 are repeated for each successive month (see T.2.5). Some sample results are given in Table U.4 and Table U.5. Non-steady state conditions persist until August 1992. The amounts of creep crack growth obtained at the deepest point and on the surface are shown in Figure U.4. It is apparent that the crack is expected to grow by creep to a = 9.0 mm and c = 21.1 mm by June 2005. Figure U.5 shows the accumulation of creep damage Dc up to this time. It is clear that there is a satisfactory margin against creep rupture.

Figure U.3 indicates also that there is still no likelihood of fast fracture by the end of life. These calculations demonstrate, therefore, that the plant is safe to operate to the year 2005 without risk of failure by creep rupture or fracture.

Table U.4 — Data at beginning of each month for deepest point of crack

Öref = 72.3 N/mm2;%¼c = 9.17 × 10–6;%Dc = 1.53 × 10–4.

KP = 286 Nmm–3/2;C* = 1.54 × 10–5 N/(mmh).

KP = 188 Nmm–3/2;C* = 6.69 × 10–6 N/(mmh).

Month Year Kp

Nmm–3/2

Öref

N/mm2

C*

N/mmh

Dc ¼c

× 10–3

ta

mm

August 1990 286 72.306 1.541 × 10–5 0.009 07 1.006 2 0.014 53

November 1990 430 108.463 6.929 × 10–5 0.009 53 1.033 4 0.049 10

August 2004 313 72.461 1.706 × 10–5 0.033 31 2.768 5 0.007 89

November 2004 470 108.696 6.897 × 10–5 0.033 77 2.793 5 0.024 46

June 2005 314 72.472 1.719 × 10–5 0.034 90 2.880 5 0.007 94

c c= = × −∑∆ 1 01 10

3.

a·

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Table U.5 — Data at beginning of each month for crack growth along surface

U.3.8.6 It is stated in U.2.6 that, when a flaw is discovered after a component has been in service, the conservative assumption should be made that the crack growth has already initiated. No allowance has been made, therefore, in the calculations for an incubation period.

U.3.9 Step 9: Special considerations for welds (see 9.5.9)

This is not required in this example, since the flaw is remote from any weld.

Month Year Kp

Nmm–3/2

Öref

N/mm2

C*

N/mmh

Dc ¼c

× 10–3

%c

mm

August 1990 189 72.306 6.692 × 10–6 0.009 07 1.006 2 0.007 39

November 1990 248 108.463 3.026 × 10–6 0.009 53 1.033 4 0.025 10

August 2004 229 72.461 9.096 × 10–6 0.033 31 2.768 5 0.004 74

November 2004 344 108.696 3.686 × 10–6 0.033 77 2.793 5 0.014 72

June 2005 231 72.472 9.261 × 10–6 0.034 90 2.880 5 0.004 81

Figure U.4 — Creep crack growth for period August 1990 to July 2005

2.0

1.5

1.0

0.5

1985 1990 1995 2000Year

2005 2010

Crac

k ex

tens

ion,

mm

Surface point ∆c

Deepest point ∆a

0

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U.3.10 Step 10: Sensitivity analysis (see 9.5.10)

Worst case material properties have been used and the most conservative assumptions made. Allowance for an incubation period prior to the onset of cracking can be incorporated into the assessment by reference to T.1.8, which gives the following equation:

where

tix is the initiation period for 0.05 mm of crack growth.

Because of the short duration of the secondary stresses in this example, only the primary stresses are included in K. Initiation will occur first at the site where K is largest. For this example this is at the deepest point. For high-pressure operation tix equals 625 h and for the low pressure conditions it equals 987 h. Hence allowance for an incubation period will not significantly affect the predictions.

Figure U.5 — Increase in creep damage from start of operation in April 1985 to July 2005

1985 1990 1995 2000Year

2005 2010

0.04

0.03

0.02

0.01

0

Cree

p da

mag

e, D

c

t

t

Kix

ref R ref

=( ){ }⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

( )0 89

2

0 85

.

.

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Use of average creep rupture data (with ¾c = 1) rather than lower bound estimates will cause the incubation periods to increase by about seven times so that cracking will not initiate until tix equals 4 440 h for the high pressure conditions and tix equals 6 990 h for low pressure use. Since more than one operating régime is being examined, a life fraction summation approach should be employed to calculate the incubation period. With this method, crack initiation is predicted to have taken place in February 1986. Use of the average creep rupture data will also cause the damage fraction Dc to accumulate at only a tenth of the lower bound rate. Alteration of the rupture data, whilst keeping the creep strain relation unchanged, will cause no change in creep crack propagation.

U.3.11 Step 11: Remedial action (see 9.5.11)

No remedial action is required as the plant can continue to be operated safely until mid-2005, even when the most conservative assumptions are made.

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Bibliography

Standards publications

BS EN 13480 (all parts), Metallic industrial piping.

PD 6493:1991, Guidance on methods for assessing the acceptability of flaws in fusion welded structures.

PD 6525-1:1990, Elevated temperature properties for steels for pressure purposes.

DD ENV 1993-1-1:1992, Eurocode 3: Design of steel structures — Part 1.1: General rules and rules for buildings (together with United Kingdom National Application Document).

DD ENV 1993-1-2:2001, Eurocode 3: Design of steel structures — Part 1.2: General rules — Structural fire design (together with United Kingdom National Application Document).

DD ENV 1993-1-3:2001, Eurocode 3: Design of steel structures — Part 1.3: General rules — Supplementary rules for cold formed thin gauge members and sheeting (together with United Kingdom National Application Document).

DD ENV 1999-1-1:2000, Eurocode 9: Design of aluminium structures — Part 1.1: General rules — General rules and rules for buildings.

DD ENV 1999-1-2:2000, Eurocode 9: Design of aluminium structures — Part 1.2: General rules — Structural fire design.

DD ENV 1999-2:2000, Eurocode 9: Design of aluminium structures — Part 2: Structures susceptible to fatigue.

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[3] AINSWORTH, R.A., 1989. Defect assessment procedures at high temperatures. In: Structural Mechanics in Reactor Technology, 10th International Conference of the International Association for Structural Mechanics in Reactor Technology. Anaheim, CA, 1989, Division L. Los Angeles, CA: American Association for Structural Mechanics in Reactor Technology. ISBN 0 962 33060 4 (set).

[4] MacLENNAN, I. and J.W. HANCOCK, 1995. Constraint-based failure assessment diagrams. International Journal of Pressure Vessels and Piping. 64 (3) 287–298. ISSN 0308-0161.

[5] ANDERSON, T.L. and R.H. DODDS, 1991. Specimen size requirements for fracture toughness testing in the ductile-brittle transition region. ASTM Journal of Testing and Evaluation. 19 (2) 123–124. ISSN 0090-3973.

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[7] SUMPTER, J.D.G. and J.W. HANCOCK, 1994. Status revision of the J plus T stress fracture analysis method. In: Structural integrity: experiments — models — applications. Proc. 10th bi-annual European conference on fracture [ECF-10], Berlin, 20–23 Sept. 1994. Warley, UK: EMAS. 1 617–623. ISBN 0947817743.

[8] BILBY, B.A., I.C., HOWARD, LI,, Z.H., and SHEIKH, M.A. 1995. Some experience in the use of damage mechanics to simulate crack behaviour in specimens and structures. International Journal of Pressure Vessels and Piping. 64 (3) 213–223. ISSN 0308-0161.

[9] CHALLENGER, N.V., R. PHAAL, and S.J. GARWOOD, 1995. Appraisal of PD6493:1991 fracture assessment procedures. Parts I, II and III. Abington, Cambs.: TWI. Research Report No. 512/1995.

[10] UK ATOMIC ENERGY AUTHORITY, 1987. An assessment of the integrity of PWR pressure vessels. Addendum to the second report of the Study Group under the chairmanship of Prof. Sir P.B. HIRSCH. Report HL 87/1018. Abingdon, Oxon.: UKAEA. ISBN 0705811557.

[11] PHAAL, R., 1993. Non-unique solutions in PD6493:1991 fracture assessment procedures. In: H.S. MEHTA, ed. Fracture mechanics: applications and new materials. Presented at the pressure vessels and piping conference, Denver, Co., 25–29 July 1993. New York: ASME. PVP-260 149–155. ISBN 0791809870.

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[18] RICHARDS, C.E. and T.C. LINDLEY, 1972. The influence of stress intensity and microstructure on fatigue crack propagation in ferritic materials. Engineering Fracture Mechanics. 4 (4) 951–978. ISSN 0013-7944.

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[24] CIRIA: UNDERWATER ENGINEERING GROUP, 1985. Design of tubular joints for offshore structures. 3 volumes. London: Underwater Engineering Group. UEG Publication UR33. ISBN 0860172317.

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[34] JACCARD, R., 1990. Fatigue crack propagation in aluminium. Abington, Cambs.: International Institute of Welding. IIW Document XIII-1377-90. [Unpublished.]

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Other reading

AINSWORTH, R.A., 1995. A constraint-based failure assessment diagram for fracture assessment. International Journal of Pressure Vessels and Piping. 64 (3) 277–285. ISSN 0308-0161.

SCHWALBE, K.H., R.A. AINSWORTH, C. ERIPRET, C.H. FRANCES, P.H. GILLIES, M. KOÇAK, H.G. PISARSKI, and Y.Y. YANG, 1997. Common views on the effects of yield strength mismatch on testing and structural assessment. Proceedings of the Second International Symposium on Mismatching of Interfaces and Welds, eds. K.H. SCHWALBE and M. KOCAK, GKSS Research Center: Germany, 99–132.

BURDEKIN, F.M., J.G. YOUNG, and J.D. HARRISON, 1967. The effect of weld defects with special reference to BWRA research. In: Proc. first conference on the significance of defects in welds, London, 23–24 Feb. 1967. London: Institute of Welding. 63–74.

DAVIES, R., S. HEWERDINE, and J.S. SHIPMAN, 1995. Fatigue cracking of an absorber on a hydrogen PSA unit. Proc. Symposium on ammonia plant safety and related facilities. Tucson, Ariz. 18–20 Sept. 1995. New York: AIChE. ISBN 0816907080.

KANNINEN, M.F., D. BROEK, C.W. MARSCHALL, E.F. RYBICKI, S.G. SAMPATH, F.A. SIMONEN, and G.M. WILKOWSKI, 1976. Mechanical fracture predictions for sensitized stainless steel piping with circumferential cracks. Final Report EPRI NP-192. Palo Alto, CA: EPRI.

MADDOX, S.J., 1991. Fatigue strength of welded structures. Abington, Cambs.: Abington Publishing. ISBN 1855730138

SHARPLES, J.K. and P.J. BOUCHARD, 1995. Assessment of crack opening area for leak rates. In: Proceedings of the seminar on leak-before-break in reactor piping and vessels (LBB ’95), Lyon, France, October 1995. United States Nuclear Regulatory Commission, Proceedings of conferences, NUREG/CP-0155, 1997, 267–276.

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Documents

Guide to methods for assessing the acceptability of flaws ... 7910-2005... · curves 262 Figure T.2 Strain hardening cons truction to obtain incremental strains 263 Figure T.3 Construction