Section 6 - Stress Analysis in FFS Assessment

Fitness-for-Service (FFS) Assessment based on API RP579

Section 6 - Stress Analysis in FFS Assessment

Copyright 2005, TWI Ltd 1

Copyright © 2005, TWI Ltd World Centre for Materials Joining TechnologyWorld Centre for Materials Joining Technology

Stress Analysis for FFS Assessment

Stress Analysis for FFS Assessment


IntroductionIntroduction

Essential in a FFS assessment to know the Essential in a FFS assessment to know the actual stresses applied to any damage:actual stresses applied to any damage:

•• What loads are applied?What loads are applied?•• Manufacturing residual or direct stress?Manufacturing residual or direct stress?•• Operation loads lower than design?Operation loads lower than design?•• Linear elastic or elastic plastic?Linear elastic or elastic plastic?•• Stress increase at local discontinuity?Stress increase at local discontinuity?•• Determining stresses and strain ?Determining stresses and strain ?•• InIn--situ measurement ?situ measurement ?





Session agendaSession agenda

•• DefinitionsDefinitions•• StressStress--strain response of materialsstrain response of materials•• Stresses in pressure equipmentStresses in pressure equipment•• Stresses in ASME PV and piping Stresses in ASME PV and piping

standardsstandards•• Residual stressesResidual stresses•• Finite element analysisFinite element analysis•• Strain measurementStrain measurement•• Stresses for a FFS assessmentStresses for a FFS assessment


Definition of stressDefinition of stress

Stress: Internal force exerted by either of Stress: Internal force exerted by either of two adjacent parts upon the other across two adjacent parts upon the other across an imagined plane of separation.an imagined plane of separation.

The bar, subjected to tension, has been cut perpendicular to theThe bar, subjected to tension, has been cut perpendicular to the axis axis into two free bodies to show the normal stress, into two free bodies to show the normal stress, σσxx, This multiplied by , This multiplied by the area (A) on which it acts must be in equilibrium with the apthe area (A) on which it acts must be in equilibrium with the applied plied force (F) hence:force (F) hence:

σσxx

FF FF

σσx x A = FA = F σσxx = F / A= F / A





Definition stress termsDefinition stress terms•• Shear stress: when Shear stress: when

the force is parallel the force is parallel to the planeto the plane

•• Normal stress: when Normal stress: when the force is normal the force is normal to the planeto the plane

•• Compressive stress: Compressive stress: when the normal when the normal stress is directed stress is directed toward the planetoward the plane

•• Tensile stress: when Tensile stress: when the normal stress is the normal stress is acting away from acting away from the planethe plane

FF

FF

FF FF9090oo

FF FF9090oo

FF FF9090oo


Definition stress termsDefinition stress terms

•• Bending Bending stress: when a stress: when a bending bending moment acts moment acts normal to the normal to the planeplane

•• Torsion stress: Torsion stress: when a torque when a torque acts parallel acts parallel to the plane to the plane

Point load on a beamPoint load on a beam

Through beam bending stressThrough beam bending stressTensileTensile

CompressiveCompressive

Solid cylinder with applied torqueSolid cylinder with applied torque

Through cylinder torsion stressThrough cylinder torsion stress





Definition principal stressesDefinition principal stresses

•• At a point in a stressed body there pass At a point in a stressed body there pass 3 mutually perpendicular planes, the 3 mutually perpendicular planes, the stress on the planes are purely normal, stress on the planes are purely normal, tension or compression. These are tension or compression. These are termed the principal planes for that termed the principal planes for that point. The stresses on the planes are point. The stresses on the planes are principal stresses of which:principal stresses of which:–– One is the maximum stress at the point (σOne is the maximum stress at the point (σ11))–– One is the medium stress at the point (σOne is the medium stress at the point (σ22))–– One is the minimum stress at the point (σOne is the minimum stress at the point (σ33))


Definition principal stressesDefinition principal stresses

θθ θθ

σσyy

σσyy

σσxxσσxx

ττxyxy

ττxyxy

ττyxyx

ττyxyxΤΤs s = 0= 0

σσ1 1 or σor σ22

Element subjected to general two Element subjected to general two dimensional stress systemdimensional stress system





Definition strainDefinition strain

•• Strain: Any forced change in the Strain: Any forced change in the dimensions of a body. A stretch is a dimensions of a body. A stretch is a tensile strain; a shortening is a tensile strain; a shortening is a compressive strain; and an angular compressive strain; and an angular distortion is a shear strain.distortion is a shear strain.

•• Strain is generally used to denote unit Strain is generally used to denote unit strain (ε)strain (ε)

ε = ε = Change in length (δ)Change in length (δ)Original length (L)Original length (L)

•• As with stress there are principal As with stress there are principal strainsstrains


Geometric stress concentrationsGeometric stress concentrations•• Stress concentration: Stress concentration:

Discontinuities of form may Discontinuities of form may produce high localised stressproduce high localised stress

•• Stress concentration factors Stress concentration factors (SCF) have been developed (SCF) have been developed to predict the stress at the to predict the stress at the discontinuitydiscontinuity

Plate with a hole showing stress trajectoriesPlate with a hole showing stress trajectories ( )tdw=AAF

=σ

σσ

=K

0

0nom

nom

maxt

-





SCF exampleSCF example•• Determine the maximum stress Determine the maximum stress

at a sphere/nozzle junction for at a sphere/nozzle junction for a flush nozzle at the start and a flush nozzle at the start and end of end of life.end of end of life.

•• Nozzle OD = 170mmNozzle OD = 170mm•• Nozzle thickness = 7.2mmNozzle thickness = 7.2mm•• Sphere OD = 2500mmSphere OD = 2500mm•• Sphere thickness = 57.15mmSphere thickness = 57.15mm•• Pressure = 40barPressure = 40bar•• Future corrosion allowance = Future corrosion allowance =

2mm2mm

•• σσmaxmax = s.c.f x (PR/(2T’))= s.c.f x (PR/(2T’))Maximum stress in sphere for internal pressure (flush nozzle)Maximum stress in sphere for internal pressure (flush nozzle)

Where,Where,

P = pressure (MPa)P = pressure (MPa)R = mean radius of spherical shell (mm)R = mean radius of spherical shell (mm)r = mean radius of nozzle (mm)r = mean radius of nozzle (mm)t = wall thickness of nozzle (mm)t = wall thickness of nozzle (mm)T’ = wall thickness of spherical shell (mm)T’ = wall thickness of spherical shell (mm)


Stress strain material responseStress strain material response

•• For most metallic For most metallic materials at 0.002 materials at 0.002 strain (or a defined strain (or a defined yielding point) the yielding point) the material is no longer material is no longer fully elastic and fully elastic and starts to plastically starts to plastically deform, which is deform, which is none recoverablenone recoverable

•• While in the elastic While in the elastic region stress and region stress and strain are strain are proportional proportional ((Hooke’sHooke’s law)law)





Stress strain material responseStress strain material response•• The rate of change of The rate of change of

stress with respect to stress with respect to strain in the elastic strain in the elastic region is termed the region is termed the modulus of elasticity modulus of elasticity (or Young’s modulus) (or Young’s modulus) and is denoted as Eand is denoted as E

•• Most engineering Most engineering design codes and design codes and standards aim to limit standards aim to limit the normal stress in a the normal stress in a component to below component to below yield levels.yield levels.

Ultimate tensile strength (UTS)Ultimate tensile strength (UTS)


Yielding criteriaYielding criteria•• Real structures have Real structures have

complex stress complex stress systems.systems.

•• A number of A number of different yielding different yielding criteria have been criteria have been developed, the two developed, the two most common are;most common are;TrescaTresca (maximum (maximum shear stress) or Vonshear stress) or Von--mises mises (shear strain (shear strain energy)energy)Yielding criteria envelope (2D) with Yielding criteria envelope (2D) with

actual test dataactual test data





Stresses in pressure equipmentStresses in pressure equipment•• Stresses in pressure equipment are generally Stresses in pressure equipment are generally

produced from the following loads:produced from the following loads:–– Internal and external pressureInternal and external pressure–– Weight of equipment, including contents, live and Weight of equipment, including contents, live and

dead loadsdead loads–– Loads from attached equipment e.g. pipingLoads from attached equipment e.g. piping–– Attachment of internals (trays etc.), lugs, supports, Attachment of internals (trays etc.), lugs, supports,

skirts etc.skirts etc.–– Temperature gradients and differential thermal Temperature gradients and differential thermal

expansionexpansion–– Wind, snow, seismic reactionsWind, snow, seismic reactions–– Impact or shock loadingImpact or shock loading


Pressure equipment stressesPressure equipment stresses

σσCC

σσLL

σσRR

•• Circumferential Circumferential stress (σstress (σCC), also ), also termed hooptermed hoop

•• Longitudinal stress Longitudinal stress (σ(σLL), also termed ), also termed axialaxial

•• Radial stress (σRadial stress (σRR), in ), in thin wall cylinders thin wall cylinders this value is small this value is small





Pressure equipment stressesPressure equipment stresses•• For the internal pressure only case for the For the internal pressure only case for the

circumferential (hoop) stress, in thinned circumferential (hoop) stress, in thinned walled cylinders:walled cylinders:

•• The corresponding longitudinal (axial) stress The corresponding longitudinal (axial) stress is:is:

•• Which is also the equation for a spherical Which is also the equation for a spherical shell in both directionsshell in both directions

P = pressure P = pressure

D = Outside diameterD = Outside diameter

t = wall thicknesst = wall thicknesst2PD

=σh

t4PD

=σ l


Pressure equipment designPressure equipment design

•• Pressure equipment is usually designed Pressure equipment is usually designed to construction standards requirements to construction standards requirements by either:by either:–– Design by rule (DBR): engineering formulas Design by rule (DBR): engineering formulas

to produce simple calculations to derive to produce simple calculations to derive sizes etc. utilising an allowable standardised sizes etc. utilising an allowable standardised design stress followed by strict adherence design stress followed by strict adherence to specific rules. Does not provide the to specific rules. Does not provide the designer with a value of the stress. designer with a value of the stress. This is the philosophy of many national pressure vessel design standards

–– Design by analysis (DBA): usually finite Design by analysis (DBA): usually finite element analysis and stress categorisationelement analysis and stress categorisation





Pressure equipment DBAPressure equipment DBA•• Most of the design by analysis guidelines given Most of the design by analysis guidelines given

in the codes relates to design based on elastic in the codes relates to design based on elastic analysis (1960’s). analysis (1960’s).

•• The rules were developed to guard against The rules were developed to guard against elastic failure mechanisms. Thus guidelines elastic failure mechanisms. Thus guidelines guard against three specific failure modes:guard against three specific failure modes:–– gross plastic deformation, incremental plastic gross plastic deformation, incremental plastic

collapse (collapse (ratchettingratchetting) and fatigue.) and fatigue.•• In this approach the designer is required to In this approach the designer is required to

classify the stress into primary, secondary and classify the stress into primary, secondary and peak categories and apply allowable stress peak categories and apply allowable stress limits. limits.

•• See appendix B in API RP 579See appendix B in API RP 579


ASME standardsASME standards

•• The most widely used standards in the The most widely used standards in the world.world.

•• ASME section VIII division 1 “Rules for ASME section VIII division 1 “Rules for the construction of pressure vessels”the construction of pressure vessels”

•• ASME section VIII division 2 ASME section VIII division 2 “Alternative rules for the construction of “Alternative rules for the construction of pressure vessels”pressure vessels”

•• ASME B31.3 “Process piping”ASME B31.3 “Process piping”





Cylindrical shell formulae (ASME)Cylindrical shell formulae (ASME)•• S is the allowable stress for the S is the allowable stress for the

materialmaterial•• E is the weld joint efficiencyE is the weld joint efficiency•• P is the internal pressureP is the internal pressure•• RRcc is the internal radius adjusted for is the internal radius adjusted for

future corrosion future corrosion ectect..•• ttslsl is the extra material required for is the extra material required for

other loads (e.g. bending due to other loads (e.g. bending due to wind)wind)

•• ttminmin is the minimum required wall is the minimum required wall thicknessthickness

•• MWAP is the maximum allowable MWAP is the maximum allowable wall thicknesswall thickness

•• σσm m is the nominal membrane stressis the nominal membrane stress•• Formulae summarised in the Formulae summarised in the

appendix of API RP 579 for various appendix of API RP 579 for various pressure equipment and sectionspressure equipment and sections


Allowable stress (ASME)Allowable stress (ASME)•• The maximum allowable stress value to be The maximum allowable stress value to be

used in any construction code is defined in the used in any construction code is defined in the pressure vessel standard. pressure vessel standard.

•• For ASME VIII division 1 the listing of For ASME VIII division 1 the listing of materials and allowable stress values are given materials and allowable stress values are given in ASME section II, Part Din ASME section II, Part D

•• For the piping standard B31.3 the allowable For the piping standard B31.3 the allowable stresses are given in its Appendix Astresses are given in its Appendix A

•• The allowable stresses are given for various The allowable stresses are given for various temperaturestemperatures

•• The materials are grouped by general alloying The materials are grouped by general alloying contentcontent





Extract ASME II, Part D, Table 1A Extract ASME II, Part D, Table 1A

ImportantImportant


Allowable stress basis (ASME)Allowable stress basis (ASME)

•• ASME VIII division 1 pre 1999 the allowable ASME VIII division 1 pre 1999 the allowable room temperature stress was defined as:room temperature stress was defined as:•• Minimum of 2/3 yield or ¼ of UTSMinimum of 2/3 yield or ¼ of UTS

•• ASME VIII division 1 post 1999 the allowable ASME VIII division 1 post 1999 the allowable room temperature stress is defined as:room temperature stress is defined as:•• Minimum of 2/3 yield or UTS/3.5Minimum of 2/3 yield or UTS/3.5

•• ASME VIII division 2 the allowable room ASME VIII division 2 the allowable room temperature stress is defined as:temperature stress is defined as:•• Minimum of 2/3 yield or UTS/3Minimum of 2/3 yield or UTS/3





ASME joint efficiencies (E)ASME joint efficiencies (E)

•• Table UWTable UW--12 in ASME VIII division 1, efficiencies based 12 in ASME VIII division 1, efficiencies based on:on:–– Joint type i.e. butt single or double sidedJoint type i.e. butt single or double sided–– Level of radiography i.e. 100%, spot or noneLevel of radiography i.e. 100%, spot or none

•• For example:For example:–– A double V seam weld with 100% radiography E=1.A double V seam weld with 100% radiography E=1.–– A double V seam weld with spot radiography E=0.85.A double V seam weld with spot radiography E=0.85.


Extract table UW-12Extract table UW-12





Example problemExample problemVessel has full radiography applied to all joints. Determine theVessel has full radiography applied to all joints. Determine theminimum require thickness for the shell. Material of constructiominimum require thickness for the shell. Material of construction n is A516 grade 65is A516 grade 65

Design pressureDesign pressure

Design temperatureDesign temperature

Corrosion allowanceCorrosion allowance


Residual stresses causesResidual stresses causesMaterial ManufactureMaterial Manufacture–– castingcasting–– forgingforging–– rollingrolling–– heat treatmentsheat treatments–– quenchingquenching–– straighteningstraightening

FabricationFabrication–– cuttingcutting–– formingforming–– bendingbending–– jigging, fit upjigging, fit up–– weldingwelding–– claddingcladding–– PWHTPWHT–– case hardeningcase hardening–– machiningmachining–– peaningpeaning–– auto auto frettagefrettage

Service lifeService life–– proof loadproof load–– service loadservice load–– service temperatureservice temperature





Rolling & cooling residual stresses Rolling & cooling residual stresses

AC

Heatingfurnace

slabs

4-High Primaryleveler

Cooling bed Trimming

Discrete plate product

Reverse Mill Process

Thermal cooling controlled


Residual stresses due to weldingResidual stresses due to welding

•• Tensile residual stresses in weld metal Tensile residual stresses in weld metal are caused by the contraction of the are caused by the contraction of the weld metal from softening temperatureweld metal from softening temperature

•• The maximum residual stresses are The maximum residual stresses are usually approximately equal to the yield usually approximately equal to the yield strength strength if if there is restraint against there is restraint against contraction and the contraction strain is contraction and the contraction strain is greater than the yield straingreater than the yield strain

•• i.e. i.e. ifif αα(T(Tss--TT00) > ) > σσy y /E/E





Typical residual stressesTypical residual stresses

Residual stresses in an Residual stresses in an ““as weldedas welded”” thick section Vthick section V--butt butt


Standard residual stress profilesStandard residual stress profiles

•• BS 7910:1999 Amendment 1, BS 7910:1999 Amendment 1, October 2000, Annex QOctober 2000, Annex Q

•• R6 Revision 4, September 2000, R6 Revision 4, September 2000, Chapter IV.4Chapter IV.4

•• API 579, January 2000, Appendix EAPI 579, January 2000, Appendix E





Finite Element AnalysisFinite Element Analysis•• The finite element method was first introduced The finite element method was first introduced

in the 1950in the 1950’’s s •• It is a mathematical technique which models a It is a mathematical technique which models a

structure as thousands of small pieces structure as thousands of small pieces (elements)(elements)

•• For each element, calculations can be For each element, calculations can be performed simulating various loads to performed simulating various loads to determine the structure's response (e.g. determine the structure's response (e.g. deflection, strain, stress, etc.) deflection, strain, stress, etc.)

•• The technique requires large computational The technique requires large computational resources, thus it has become more accessible resources, thus it has become more accessible over the last twenty years.over the last twenty years.


Finite Element AnalysisFinite Element Analysis•• FEA shows results for FEA shows results for

whole structurewhole structure•• Strain measurement only Strain measurement only

provides the material provides the material response at the surface response at the surface location of measurementlocation of measurement

•• FEA only as good as the FEA only as good as the analyst conducting the analyst conducting the assessment (validation)assessment (validation)

•• Hand calculations Hand calculations provide accurate results provide accurate results but are typically useful but are typically useful for only simple for only simple geometries.geometries.

•• See appendix B of API RP See appendix B of API RP 579 for the use of FEA in 579 for the use of FEA in a FFSa FFS

FEA results of a 2:1 elliptical head with FEA results of a 2:1 elliptical head with nozzles, under pressurenozzles, under pressure





Strain measurementStrain measurement•• While there are While there are

several methods of several methods of measuring strain, the measuring strain, the most common is with most common is with a strain gaugea strain gauge

•• A stain gauges A stain gauges electrical resistance electrical resistance varies in proportion varies in proportion to the amount of to the amount of strainstrain


Strain measurementStrain measurement•• Surface only stresses Surface only stresses

from the structure under from the structure under assessmentassessment

•• Limited number of Limited number of readingsreadings

•• Can become detachedCan become detached•• Requires good bonding Requires good bonding

between the gauge and between the gauge and structurestructure

•• FEA and strain gauge FEA and strain gauge combination excellent for combination excellent for accurate determination accurate determination of structure stressesof structure stresses





Stresses required for FFSStresses required for FFS

•• Depending on the assessment type, two Depending on the assessment type, two components of stress may be required:components of stress may be required:–– Primary stresses are developed by loads to Primary stresses are developed by loads to

satisfy the laws of equilibrium of external satisfy the laws of equilibrium of external and internal forces and moments (e.g. and internal forces and moments (e.g. pressure)pressure)

–– Secondary stress distribution is developed Secondary stress distribution is developed by the constraint of adjacent parts or by by the constraint of adjacent parts or by selfself--constraint of a structure (e.g. thermal constraint of a structure (e.g. thermal expansion stresses)expansion stresses)

–– If it is uncertain whether a given stress is a If it is uncertain whether a given stress is a primary or secondary stress, it is more primary or secondary stress, it is more conservative to treat it as primaryconservative to treat it as primary


Stresses required for FFSStresses required for FFS•• Stresses required for Stresses required for

assessment generally assessment generally based on a damage typebased on a damage type

•• Most complex is possibly Most complex is possibly for crackfor crack--like flaws like flaws –– The through wall stress The through wall stress

distribution is required distribution is required to be knownto be known

–– The distribution may be The distribution may be linear (made up of linear (made up of membrane and/or membrane and/or bending distributions) or bending distributions) or highly nonhighly non--linear based linear based on the component on the component geometry and loading geometry and loading conditions.conditions.





Stresses required for crack-like flawsStresses required for crack-like flaws

•• The stress distribution normal to the crack face The stress distribution normal to the crack face should be determined for the primary, should be determined for the primary, secondary, and residual loading conditions secondary, and residual loading conditions based for an uncracked componentbased for an uncracked component

•• For linear stress distributions and less For linear stress distributions and less complicated noncomplicated non--linear stress distributions the linear stress distributions the membrane and bending components can be membrane and bending components can be found using the found using the linearisationlinearisation process.process.

•• For highly nonFor highly non--linear stress distributions API linear stress distributions API 579 appendix C gives a Fourth Order 579 appendix C gives a Fourth Order Polynomial Stress Distribution method for Polynomial Stress Distribution method for determining the membrane and bending determining the membrane and bending components.components.


Stress linearisationStress linearisation•• Stress distribution Stress distribution

broken down into broken down into membrane, bending membrane, bending componentscomponents

•• Needed for both primary Needed for both primary and secondary stressesand secondary stresses

•• LinearisationLinearisation can be over can be over the cross section or just the cross section or just the flaw, depends on the flaw, depends on assessment typeassessment type

LinearisedLinearised membrane stress is:membrane stress is:σσmm = = σσ11 + σ+ σ22

22LinearizedLinearized bending stress is:bending stress is:σσbb = = σσ11 -- σσ22

22





Stress linearisation exampleStress linearisation example

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30 35 40 45

Distance through section, mm

Perp

endi

cula

r str

ess

to fl

aw, M

Pa

Surface breaking flaw 10mm deep

310MPa at surface

100MPa at surface

Wall thickness of section 45mm

•• Linearise Linearise the stresses over the flaw the stresses over the flaw


•• The fourth order polynomial stress distribution The fourth order polynomial stress distribution can be obtained by curvecan be obtained by curve--fitting the general fitting the general stress distribution. The general form of the stress distribution. The general form of the fourth order polynomial stress distribution is fourth order polynomial stress distribution is as follows:as follows:

•• The equivalent membrane and bending stress The equivalent membrane and bending stress distributions for the fourth order polynomial distributions for the fourth order polynomial stress distribution are:stress distribution are:

Fourth Order Polynomial Stress Distribution








Best fit 4th order polynomial equation y = 1394.3x4 + 625.24x3 - 2131.9x2 - 22.318x + 240

-400

-300

-200

-100

0

100

200

300

0 0.2 0.4 0.6 0.8 1

Stress, MPa

Dis

tanc

e th

roug

h w

all (

x/t)

Stress data Membrane Bending 4th Order polynominal


Stresses in FFSStresses in FFS•• Most level 3 assessment methods in API RP Most level 3 assessment methods in API RP

579 allow the use of a detailed stress analysis 579 allow the use of a detailed stress analysis to determine the acceptability of the flawto determine the acceptability of the flaw

•• The stress analysis techniques discussed in The stress analysis techniques discussed in Appendix B of API RP 579 can be utilized Appendix B of API RP 579 can be utilized

•• FEA is typically usedFEA is typically used•• Handbook solutions may also be used if the Handbook solutions may also be used if the

solution is an exact match. solution is an exact match. •• The evaluation based on a linear stress The evaluation based on a linear stress

analysis and stress categorization, or a nonanalysis and stress categorization, or a non--linear stress with plastic collapse. linear stress with plastic collapse.

•• NonNon--linear stress analysis techniques are linear stress analysis techniques are recommended, if data is availablerecommended, if data is available

Documents

Section 6 - Stress Analysis in FFS Assessment