Introduction to RPV Structural Integrity Procedures to RPV Structural Integrity Procedures ... Fracture mechanics has been used as the basis for ASME ... The basic concept:

Introduction to RPV Structural Integrity Procedures

William Server ATI Consulting

Assessment of Degradation Mechanisms of Primary Components in Water Cooled Nuclear Reactors: Current Issues and

Future Challenges 29 September – 2 October 2014

CIEMAT, Madrid (Spain)

Main Topics

• Fracture mechanics as applied to structural integrity of RPVs

• Material property requirements for operating RPVs (including surveillance programs)

2

1

What is Fracture Mechanics?

Fracture is a deformation process whereby regions of a

material body separate and load-carrying capacity decreases

significantly, approaching zero for brittle materials

Fracture can be viewed at different levels: macro to nano

(atomistic) scale

Fracture is defined when the applied loading of a cracked

body (crack driving force) exceeds the material’s resistance to

failure (fracture toughness)

Fracture toughness is a material property for a given material

condition (including environmental exposure)

Fracture mechanics is an engineering discipline which

evaluates the behavior of crack-like defects in structures or

components and their effect on integrity

3

1

Brief Overview of Fracture Mechanics

Fracture mechanics was conceived by A.A. Griffith during

World War I

Early applications were limited to fracture in very brittle cracked bodies,

such as glass

Interest intensified when approximately 25% of the all-welded U.S.

Liberty ships in WW II experienced brittle fracture, exposing the urgent

need to understand failure in ferritic structural steels and weldments

First use of fracture mechanics in mid-1950’s for missile and

rocket motor cases

Brittle fracture in these high strength materials

U.S. Sec of Defense requested assistance from the American Society

for Testing and Materials (ASTM)

4

1


ASTM formed a special committee in 1959 to develop

technology and test methods for brittle fracture

Linear Elastic Fracture Mechanics (LEFM) technology

developed rapidly

LEFM first applied to fatigue crack growth 1963 and to stress

corrosion crack growth in 1965

In 1965, the special committee changed to standing Committee

E24 on Fracture Testing of Materials (now part of E08

Committee on Fatigue and Fracture)

Power generation equipment manufacturers and utilities also

became interested since brittle fracture was unacceptable

5

1


Fracture mechanics has been used as the basis for ASME

Boiler & Pressure Vessel Code, Section III, Appendix G, fracture

prevention criteria dating back to about 1970 – provides the

methodology for development of pressure-temperature (P-T)

operating curves, ASME Section XI flaw evaluation, etc.

For LEFM, EPFM, and HTTDFM, the crack driving force is a

function of the applied stresses, the size of the crack in the

subject body, and body geometry factors

The basic concept: if a material's resistance to failure in the

presence of a sharp crack in a structure is less than the crack-

tip stress-strain conditions imposed by the loading and

geometry conditions, failure will occur

To avoid failure:

Material Resistance (MR) > Crack Driving Force (CDF)

6

1

Elements of Fracture Mechanics

7

1

Variables Affecting Material Fracture Toughness

External and mechanical variables

Temperature

Loading rate

Environment (neutron irradiation, corrosive, etc.)

Material variables

Chemical composition/impurities

Heat treatment

Microstructure

Strength level

Fabrication (welding method, rolling practice, etc.)

Time-temperature metallurgical changes (temper embrittlement)

8

1

Generalized Categories of Fracture Mechanics

9

1

Linear Elastic Fracture Mechanics (LEFM)

LEFM is based on elastic stress analysis of relatively brittle

materials containing infinitely sharp cracks

The intensity of the localized, elastic, stress-strain field in the

vicinity near the crack-tip is described in terms of a singular

term called the stress intensity factor, K

K parameter usually includes a subscript (I, II, or III) which

refers to the 3 different modes of loading a cracked body

Mode I: the opening mode where the cracked body is loaded by normal

stresses (technically the most important loading mode)

Mode II: sliding or in-plane shearing mode

Mode III: tearing mode caused by out-of-plane shear

10

1

Modes of Crack Opening

11

1


12

1


13

1

Stress Intensity Factor, K

14

KI is the LEFM parameter of concern for RPV integrity

1


15

1


Continuum mechanics solutions for prescribed applied

loadings and geometries permit characterization of stress (and

deformation) fields near a crack tip

Functional form of the local asymptotic field includes a scalar

amplitude value of K that can be expressed in Mode I loading

for crack opening in the yy-direction as

16

1


17

1


The variables of which K is a function are given in the following

equation:

where KI is the applied fracture driving force, or the

fracture toughness,

is the stress,

a is the flaw size, and

F(a/W) is the geometry factor

18

1

Plane-Strain Fracture Toughness, KIc

KIc is a measure of the plane-strain, brittle fracture resistance

of a material and is commonly referred to as plane strain

fracture toughness

Unstable, rapid crack extension is predicted to occur when the

applied structural K reaches KIc

KIc is a unique material property for a given material condition,

temperature, and loading rate

KIc can be measured in the laboratory using the specimen(s) and test

procedures described in ASTM Standard Test Method E 399 for “Plane-

Strain Fracture Toughness of Metallic Materials” or using the unified

ASTM Standard Test Method E 1820 for “Measurement of Fracture

Toughness” which covers both potential LEFM and EPFM conditions

KIc can be used to evaluate the brittle fracture conditions in any other

linear-elastic loaded cracked body of practical interest so long as it

contains the same material and environmental condition, is loaded at

the same rate, and is at the same temperature as the laboratory test

19

1

Plane Strain vs. Plane Stress

20

Transverse contractions in z-direction are opposed by unyielding faces of crack area resulting in transverse stresses xx and zz ahead of the crack

Plane strain occurs when ezz = 0

Plane stress occurs when zz = 0

Generally, most cracks in structures/components are loaded somewhere in between plane strain and plane stress

1

Static Fracture Toughness of RPV (bcc) Steel

21

1

Crack Arrest Fracture Toughness, KIa

KIa is a measure of the plane-strain crack-arrest toughness of

ferritic steels and represents the level of K at which a rapidly

running crack can be arrested

A crack can initiate in a local region of a structure due to a combination

of factors (e.g., low temp., high stresses, embrittled material, and high

loading rates)

The fast running crack may eventually run into a region of higher

temperature, lower stress, or greater toughness. The crack will arrest

only when the applied K (crack driving force) is less than KIa

KIa is a material property that has a unique value for a given

material at a given temperature – ASTM Standard Test Method

E 1221 for “Determining Plane-Strain Crack-Arrest Fracture

Toughness, KIa, of Ferritic Steels”

22

1 ASME Code KIC Curve

23

1

Normalized KIa and Dynamic KIC Fracture

Toughness Data – ASME Code KIR = KIa Curve

24

1

Comparison of KIa and KIc for RPV Steels

25

1

Material Resistance to Crack Growth

Termination of the life of a component may be based on the

applied stress intensity factor reaching a critical value (KIc),

representing the material's brittle fracture resistance

Useful life of a component depends on the rate of growth of

flaws (cracks) from some subcritical size to the critical size

when K reaches KIc

Recall that K is a function of the applied stress (σ), the cracked

body geometry, and the crack size (a)

In order to utilize LEFM concepts it is necessary to characterize

the material resistance to crack growth in terms of K under

cyclic loading (e.g., fatigue) and/or static loading (e.g., stress

corrosion) conditions

26

1

Fatigue Crack Growth

The rate of crack growth expressed as da/dN (change in crack

size, a, with respect to elapsed cycles of loading, N) depends

primarily on the cyclic range of the applied stress intensity

factor, ΔK, above a threshold ΔKth

ΔK is analogous to Δσ as commonly used in conventional

fatigue analyses

Select a K expression applicable to the geometry and loading

method of practical interest and substitute Δσ for σ in order to

compute ΔK rather than K

For Mode I loading (simple tensile opening of a crack):

KI = σ(πa)½

For fatigue analysis: ΔKI = Δσ(πa)½

27

1

Schematic of Fatigue Crack Growth Behavior

28

1

Stress Corrosion Crack Growth

For some combinations of materials and environments, it is

possible for cracks to grow under sustained (constant) loading

conditions

Two characterization parameters:

Material behavior under constant loading conditions in an aggressive

environment can be characterized in terms of KIscc, a threshold level of K

below which a crack will not grow for a given material and environment

if the applied K level is greater than the KIscc threshold, the material crack

growth rate behavior can be characterized in terms of da/dt versus K

(crack growth rate per unit time as a function of the applied K)

29

1

Stress Corrosion Crack Growth Behavior

30

1

LEFM Material Parameters and Test Methods

31

Parameter Characterizes Comments ASTM Test Method

KIc Plane strain, brittle fracture toughness

Material property, static & dynamic

E 399-09

E 1820-09 (unified)

KIa Plane strain, crack arrest toughness

KI when running crack is arrested

E 1221-06

KIscc Threshold for SCC propagation

Sustained loading and environment

E 1681-03 (2008)

da/dt vs. K Growth rate for SCC Sustained loading and environment

Under development

Kth Fatigue crack growth threshold

Region I crack growth Under development

da/dn vs. K Fatigue crack growth rates Region II crack growth E 647-08

1

General Approach for Applying LEFM

32

1

Limitation of LEFM Concepts

The entire concept of LEFM is based on elastic stress analysis

of cracked bodies and is therefore limited to small-scale local

yielding at the crack tip

The most significant limitation of LEFM is that the amount of

local crack-tip plasticity prior to and/or during the crack growth

or fracture processes must be small by comparison to the K

zone in which the elastic-stress field equations apply

33

1

Limitations of LEFM Led to EPFM

Since LEFM is applicable only when the plastic zone is small, it

is commonly used for some limited situations involving:

High strength

Relatively brittle materials

Mechanical restraint

Heavy section thicknesses

Low temperatures

Extremely high rates of loading

Factors that cause embrittlement of materials (i.e., irradiation damage

and temper embrittlement)

When there is too much local crack-tip plasticity, EPFM is used

34

1

Elastic Plastic Fracture Mechanics (EPFM)

EPFM was developed to address common situations in nuclear

systems:

Sections not sufficiently thick to satisfy very conservative LEFM size

requirements

Temperature range sufficiently high, resulting in much higher levels of

toughness than at lower temperatures

Test specimen size limited as in surveillance capsules (specimen sizes

large enough to meet LEFM requirements would impractical)

The fracture mode of structural steels change from a brittle to a ductile

fracture type with increasing temperature

Austenitic stainless steels that are much too tough for LEFM to be

applicable

35

1


J-integral approach to EPFM is most popular although others

can be utilized, such as crack tip opening displacement (CTOD)

J is a field parameter that defines the plastic stress and strain

intensity in the region around a crack tip

J is a function of stress, strain, crack size, and geometry of the

crack and body

J is directly analogous to K used in LEFM

36

1


JIc defines the level of applied J at the onset of ductile, stable

crack extension during monotonic loading of a precracked

specimen at a temperature within the ductile behavior regime

(i.e., the ductile upper shelf for ferritic materials)

JIc is a basic material property representing a lower-bound

measure of ductile fracture toughness in the presence of an

initial sharp crack (fatigue precrack)

Tearing modulus, T, accounts for sustained stable crack growth

and is treated as a material parameter:

T = [E / o2] (dJ/da)

37

1

Stages of Ductile J-Resistance Curve

38

1

EPFM Material Parameters and Test Methods

39

Parameter Characterizes Comments ASTM Test Method

JIc or Jc Initiation J for ductile

crack extension Material property, static & dynamic

Old E 813, now E 1820-09 (unified); also E 1921-09ce2 for ferritic

steels

J-R Curve Resistance to stable, ductile crack growth

J-a under monotonic loading

Old E 1152, now E 1820-09 (unified)

T0 Ductile-cleavage

transition temperature for ferritic steels

Master Curve application

E 1921-09ce2

da/dn vs. J Fatigue crack growth

rates

Crack extension per

cycle of J Under consideration

HTTDM: da/dt vs. C* Creep crack growth

rate High temperature, time-dependent

E 1457-07e2

1

Two Common Test Specimens for J Testing

40

1

Fracture Behavior of Ferritic RPV Steels

41

1

Master Curve for Ferritic Steels

Master Curve technology is a direct method of determining

cleavage fracture toughness of ferritic steels, as opposed to

the traditional methods of inferring toughness from RTNDT,

reference curves, and Charpy shifts

“Master Curve methodology” refers to a method of

characterizing the cleavage fracture toughness of all ferritic

steels using a universal curve shape

For a ferritic steel, the spread of fracture toughness values

around the median value at any temperature in the transition

region follows a consistent statistical pattern that can be

described using a Weibull three parameter equation

The statistical consistency of a Weibull distribution provides a

means to calculate confidence bounds on cleavage data

Ferritic steels also exhibit a common variation of cleavage

fracture toughness with temperature

42

1

The Master Curve Is Defined Using T0

43

-80 -60 -40 -20 0 20 40 60 800

50

100

150

200

KJc [

MP

am

]

T - T0 [

oC]

Master Curve

KJc

= 30 + 70 exp [0.019 (T-T0)]

1

Master Curve Methodology

Master Curve technology was first incorporated into ASTM Test

Method in 1997

ASTM Standard Test Method E 1921 describes how to measure

the index temperature, T0, for the Master Curve

T0 positions the Master Curve on the temperature scale in

terms of (T – T0) for the steel of interest

ASTM E 1921 permits determination of T0 using specimens as

small as a pre-cracked Charpy V-notch geometry single-edged

notched bend, SE(B) – i.e., irradiated surveillance specimens

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1

ASTM E 1921 Test Method for Determining T0

45

VG 3

Relation Between KJc Measurements and To

Test 6-10 toughness

specimens at one

temperature

Convert to 1T

equivalence

Calculate median 1T

equivalent KJc from

data

Using the Master

Curve, extrapolate till

median 1T equivalent

KJc is 91 ksi*in0.5

This temperature is To

To

1

2 5

4

2

1

3

4

5

3

0

50

100

150

200

-100 -50 0 50 100

T - T o [oF]

1T

Eq

uiv

. K

Jc

[k

si*

in0.5

]

1

Effect of Specimen Size Adjustment

46

1

Application to Irradiated RPVs

ASME Boiler and Pressure Vessel Code Cases N-629 and N-631

published in 1998 permit use of a Master Curve-based index

temperature as an alternative to RTNDT:

RTTo = T0 + 35ºF [19.4ºC]

Code Case N-629 is for Section XI applications for both

irradiated and non-irradiated RPV steels; Code Case N-631 is

essentially the same for Section III design applications for only

non-irradiated RPV steels

RTTo is a direct measure of reference temperature for irradiated

materials, but application often requires some normalization to

project to slightly different fluences

Other uncertainties and margins can be applied as needed for

the specific application – eg., see IAEA TRS 429 (2005),

Guidelines for Application of The Master Curve Approach to

Reactor Pressure Vessel Integrity in Nuclear Power Plants

47

1

Normalized Fracture Toughness Data

48

No Index RTNDT RTTo

0

100

200

300

400

500

-300 -150 0 150 300

T [oF]

KJ

c

[ksi*

in0

.5]

CVN

1/2T

1T

1.25T

2T

3T

4T

6T

8T

9T

10T

11T

0

100

200

300

400

500

-300 -150 0 150 300

T - RT NDT [oF]

KJ

c

[ksi*

in0

.5]

0

100

200

300

400

500

-300 -150 0 150 300

T - RT To [oF]

KJ

c

[ksi*

in0

.5]

1

Probabilistic/Deterministic Fracture Mechanics

Fracture mechanics analyses can be performed either

deterministically or probabilistically

Deterministic methodology is used when all the input

information to the analysis is considered to be known with

certainty or when conservative estimates provide acceptable

results

Probabilistic fracture mechanics (PFM) has evolved from the

need to provide results more representative of actual situations

rather than conservative lower bound analyses

PFM has been used for reliability analyses of components such

as reactor pressure vessels, piping, steam turbine generator

rotors and gas turbine disks and blades

49

1

Probabilistic/Deterministic Fracture Mechanics

Purpose of PFM is to estimate or bound the reliability [1 -

(probability of failure)] of a component subject to cracking, and

to quantify the influence of engineering and management

decisions on component reliability

The probability of failure is typically defined as the number of

simulations that resulted in failure divided by the total number

of simulations

Deterministic methods assume inputs are known or use

conservative or “worst-case,” estimates which can lead to

multiple, compounded conservatisms giving overly pessimistic

results

PFM combines conventional fracture mechanics calculations

with appropriate statistical methods to minimize stacking of

conservatisms

Monte Carlo sampling techniques are widely used in PFM

50

1

FAVOR Computer Code

The FAVOR computer code (Fracture Analysis of Vessels – Oak

Ridge) was developed at Oak Ridge National Laboratory

(ORNL) under NRC Research funding and has been used for

the reassessment of pressurized thermal shock (PTS) and for

risk-informed approach for RPV operating curves in the USA

The FAVOR PFM model uses Monte Carlo techniques

Deterministic fracture analyses are performed on a large

number of stochastically generated RPV trials or realizations

Each trial considers the uncertainties of the vessel’s properties and the

postulated flaw population, which are described by statistical

distributions

Trials propagate the input uncertainties (with associated interactions)

through the model and determine probability of crack initiation and

through-wall cracking

51

USA Reactor Vessel Integrity Rules

Low Upper Shelf

Toughness

10CFR50 Appendix G

Reg. Guide 1.99 Rev. 2 (for calculating embrittlement

effects)

ASME Section XI Appendix K

Pressure-Temperature

Limits

10CFR50 Appendix G

Reg. Guide 1.99 Rev. 2 (for calculating embrittlement

effects)

ASME Section XI Appendices

G & E

Reactor Vessel Material

Surveillance

10CFR50 Appendix H

ASTM E 185 (-73, -79, or -82; testing &

reporting procedures should

meet E 185-82)

Pressurized Thermal Shock

10CFR50.61 •(use Reg. Guide 1.99 Rev. 2

methods to calculate embrittlement effects)

10CFR50.61a •(specifies own methods to

calculate embrittlement effects)

52

Monitoring of Vessel Irradiation Effects

• Variables that can influence the rate and degree of vessel embrittlement: – Number and energy level of neutrons impacting the

vessel wall – Temperature of the vessel wall during irradiation

(essentially, coolant inlet temperature during power operations)

– Correlation of neutron impact rate to material damage

• Surveillance programs obtain data on these variables by placing capsules near the pressure vessel wall

53

Surveillance Capsules Placed Near RPV Wall to Monitor Embrittlement

54

Typical Placement of Capsules in a PWR

55


• RPV surveillance programs are administered to accurately assess actual material embrittlement levels and to provide a physical correlation to predictive techniques

• Capsules contain material specimens, temperature monitors and dosimetry to measure the level of neutron bombardment

• Periodic withdrawal and testing of capsules allows for verification of analytical predictions of vessel embrittlement

• In some cases - depending on the quality of the data – surveillance data may be used to change the estimate/prediction of vessel embrittlement

56


• In July 1973, 10 CFR Part 50, Appendix H, “Reactor Vessel Material Surveillance Program Requirements,” established the first legal requirements for a comprehensive surveillance program – Plants already licensed had generally installed irradiation

test samples (usually Charpy V-notch specimens) of RPV material per ASTM E 185, “Surveillance Tests on Structural Materials in Nuclear Reactors”

• ASTM E 185 (1961, 1966, 1970, 1973, 1979, 1982, 1994, 1998….2010) plus Standard E 2215 (2002….2010)

57

Appendix H to 10 CFR 50

• Design of surveillance program and capsule withdrawal schedule must meet requirements of ASTM E 185, “Standard Practice for Conducting Surveillance Tests for Light-Water Cooled Nuclear Power Reactor Vessels” – ASTM E 185-73, -79, or -82, depending on which was in

effect on date the RPV was purchased

• Proposed capsule withdrawal schedule must be approved by NRC

• Capsule test report must be submitted to NRC within one year of capsule withdrawal

• Appendix H also provides the requirements for integrated surveillance programs (e.g., B&W, BWRVIP)

58


• Specific requirements for surveillance program design have evolved over time and are very detailed – Each vessel program is designed to “...the edition of ASTM

E 185 that is current on the issue date of the ASME Code to which the reactor vessel was purchased.”

• Later editions may be used, but only those editions through 1982

• RPVs which have peak neutron fluence greater than 1017 n/cm2 (E > 1 MeV) at end of design life must have the beltline materials (base metal and weld metal) monitored

59

Requirements for Materials in RVSP

• Actual material used in the construction of the beltline • Include at least one heat of base metal, weld metal, and

heat-affected-zone (HAZ) material – current status is that it is not recommended to test HAZ

• Selection of materials based on materials predicted to be most limiting, with regard to setting P-T limits at end-of-license (e.g., those with highest projected ART); any material projected to be < 68 J (50 ft-lb) at ¼-T also included

• Fabrication history of surveillance specimens is to be fully representative of fabrication history of the vessel materials (e.g., thermal annealing, austenitizing treatment, quenching and tempering, and PWHT)

60

Test Specimen Requirements

• CVN and tension specimens • Fracture toughness specimens included if surveillance

materials are predicted to exhibit marginal properties • Tension and CVN specimens for base metal & HAZ shall be

from ¼- thickness (¼-T) locations; weld specimens may be from any thickness except near root or surface of weld

• Base metal tension & CVN specimens: major axis normal to principal rolling direction of the plate, normal to the major working direction for forgings – Charpy specimens should have the transverse (T-L) orientation

(weak direction) – Older plants may have L-T or both orientation specimens

61

Specimen Requirements

62

Specimen Orientation Issues

• Prior to 1973, the specification required Charpy specimens to be longitudinal (L-T), so older plants will have L-T, not T-L, specimens in their capsules

• Branch Technical Position 5-3 provides conservative guidance (but now being questioned):

“If transversely-oriented Charpy V-notch specimens were not tested, the temperature at which 68 J (50 ft-lbs) and 0.89 mm (35 mils) LE would have been obtained on transverse specimens may be estimated by one of the following criteria:

(a) Test results from longitudinally-oriented specimens reduced to 65% of their value to provide conservative estimates of values expected from transversely oriented specimens.

(b) Temperatures at which 68 J (50 ft-lbs) and 0.89 mm (35 mils) LE were obtained on longitudinally-oriented specimens increased 11°C (20°F) to provide a conservative estimate of the temperature that would have been necessary to obtain the same values on transversely-oriented specimens.”

63

Minimum Number of Test Specimens Required by ASTM E185-82

1Number of test specimens per exposure set (capsule) 2A minimum of 15 shall be tested 3Later versions of ASTM E185 (e.g., ASTM E185-92) require 6, not 3, unirradiated tension specimens

64

Capsule Dosimetry

• Dosimeters are placed in the surveillance capsules when the capsules are fabricated during reactor construction – Because each dosimeter reacts to neutrons of a

particular energy in the spectrum, a set of dosimeters are used in each capsule to provide adequate spectrum coverage

– Most are thin circular activation foils, although other shapes are available

– In addition to fast-neutron threshold monitors, a thermal monitor such as 59Co is typically included to determine thermal neutron fluence

65

Coiled Dosimetry Wire

66

Temperature Monitors

• Mechanical and impact properties of irradiated specimens depend on the temperature at which the material is irradiated

• ASTM E 185 requires temperature monitors in capsules • Low-melting alloys or pure metals are inserted inside

of the capsules to monitor peak temperature – Including different detectors of varying composition of the

alloys allows for a range of temperatures to be monitored – Provide indication of the maximum temperature

experienced by the capsule specimens (and RPV wall) – Value is limited since they do not give temperature history,

especially at lower operating temperatures

67

Other Material Requirements

• Chemical Analysis – available chemical composition information for the surveillance materials should documented for at least P, S, Cu, V, Si, Mn, Ni

• Archive materials

– Full-thickness sections of the original materials (plates, forgings and welds) should be retained

– Enough material to fill six additional capsules should be available

– Heat-affected-zone (HAZ) associated with archive weld material should also be retained

68

ASTM E 185-82 Reporting Requirements

• Administrative: Both conventional and SI units reported • Surveillance Program Description • Surveillance Material Selection & Characterization • Test results

– Tension Tests – Charpy Tests – Hardness tests (optional) – Other Fracture Toughness Tests (if performed) – Temperature & neutron radiation environment

• Application of Test Results (compare with predicted) • Deviations

69

Charpy V-notch Testing: Measured Parameters

• Impact energy (CVE) - the energy needed to fracture the test specimen – Determined directly from the impact test machine scale

(corrected for windage and friction losses)

• Lateral expansion (LE) - the amount of deformation caused by the pendulum striking the specimen resulting in the expansion of the specimen thickness

• Shear fracture (% Shear) - the percent area on the face of the fractured specimen that is attributed to brittle failure – Not commonly used as a specification – Plays important role in determination of Upper Shelf Energy

(USE)

70

Set of Tested CVN Specimens (broken faces)

GF 009

GF 004

GF 005

GF 006

GF 001

GF 003

GF 010

GF 008

GF 007

GF 002

Ductile-to-Brittle Transition Behavior

72

CVN Lateral Expansion

CVN Specimen Fracture Appearance

Illustration of digital optical measurement of shear fracture area. First,

the brittle fracture area is outlined within green line. Next, the outer

ductile fracture area is outlined in red. Software integrates the areas and

calculates the percent shear fracture area.

Summary – Output of Charpy Test Results

Index temperature shifts and USE

decreases for a surveillance material

irradiated in four capsules; each capsule has

a unique fluence (not listed here) 75

Charpy Data Curve Fitting Technical Description

• ASTM E 185-82 requires that irradiation effects be determined from Charpy data by measuring the differences in the 30 ft-lb (41 J) energy, 50 ft-lb (68 J) energy, and 35 mil (0.89 mm) lateral expansion index temperatures before and after irradiation

• “The index temperatures shall be obtained from the average curves.” – The guide does not specify how the average

curves are to be determined

76

Charpy Data Curve Fitting Technical Description • The general shape of Charpy test data (energy

versus temperature, or lateral expansion versus temperature) is that of an "S”

• The hyperbolic tangent (tanh) function is used as a simple statistical curve-fit tool to describe the "S"-shaped response – The tanh curve fit parameters defining the "S" shape

have physical meaning relative to what is generally evaluated from the test results

– The tanh curve fitting of Charpy V-notch data is a standard practice within the industry

• Mager, T. R., Server, W. L., and Beaudoin, B. F., “Use of the Hyperbolic Tangent Function for Fitting Transition Temperature Toughness Data,” WCAP-14370, Westinghouse Electric Corporation, May 1995.

77

Charpy Data Curve Fitting Technical Description

• The general tanh model often used for modeling Charpy curves: Cv = A + B tanh [(T – To) / C] where

Cv = Charpy impact energy, lateral expansion, or fracture appearance

T = test temperature

A = the mean energy level between the upper and lower shelves

B = the + or – deviation from the mean

To = a parameter that represents the mid-energy transition temperature

C = the + or – deviation of the intercepts of the tangent to the transition of To and the upper and lower shelves

78

Mathematical Interpretation of the Tanh Curve

79

Tanh Fit of Actual Charpy Test Data using CVGRAPH

80

Documents

Introduction to RPV Structural Integrity Procedures to RPV Structural Integrity Procedures ... Fracture mechanics has been used as the basis for ASME ... The basic concept: