Fitness-for-Service Fracture Assessment of Structures Containing Cracks: A Workbook based on the European SINTAP FITNET procedure (Advances in Structural Integrity)

Fitness-for-Service Fracture Assessment of Structures Containing Cracks A Workbook based on the European SINTAP/FITNET ...

Author: Uwe Zerbst | Manfred Schodel | Stephen Webster | Robert Ainsworth

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Fitness-for-Service Fracture Assessment of Structures Containing Cracks A Workbook based on the European SINTAP/FITNET Procedure

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Fitness-for-Service Fracture Assessment of Structures Containing Cracks A Workbook based on the European SINTAP/FITNET Procedure Uwe Zerbst Manfred Schödel Stephen Webster Robert A. Ainsworth

Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo Academic Press is an imprint of Elsevier

Academic Press is an imprint of Elsevier 84 Theobald’s Road, London WC1X 8RR, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands Linacre House, Jordan Hill, Oxford OX2 8DP, UK 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA First edition 2007 Copyright © 2007 Elsevier Ltd. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice While the authors believe that the information and guidance given in this book are correct, all parties making use of it must rely on their own skill and judgement. The authors cannot assume any liability for loss or damage caused by any error or omission in the application of the SINTAP/FITNET procedure. Any and all such liability is disclaimed. The authors do not give any warranty or guarantee whatsoever that the information and guidance given in this book does not infringe the rights of any third party or can be used for any particular purpose at all. Any person intending to use the same should satisfy himself as to accuracy and the suitability for the purpose for which it is intended to be used. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-08-044947-0 For information on all Elsevier Science publications visit our web site at books.elsevier.com Printed and bound in Great Britain 07 08 09 10 11

10 9 8 7 6 5 4 3 2 1

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Contents

Nomenclature

ix

1. Introduction 1.1. SINTAP 1.2. FITNET 1.3. The Topic of the Present Book

1 1 3 3

2. Brief Overview on the Development of Flaw Assessment 2.1. General Aspects 2.2. Ligament Yielding 2.3. The TWI (The Welding Institute) Design Curve Approach 2.4. The Early FAD Approach of CEGB (Central Electricity Generating Board) 2.5. The EPRI (Electric Power Research Institute) Approach 2.6. The Reference Stress Method of CEGB 2.7. The R6-Revision 3 Approach of CEGB 2.8. The Engineering Treatment Model (ETM) Approach of GKSS 2.9. The SINTAP Approach

7 7 8 9 10 11 12 13 15 16

3. Basic Features of SINTAP/FITNET 3.1. Fitness-for-Service 3.2. Potential Tasks of a SINTAP/FITNET Analysis 3.3. Multi-Optional Concept 3.4. FAD versus CDF Analyses 3.5. Integrated Concept

19 19 20 21 24 25

4. The Input Parameters 4.1. Loading Input Parameters 4.1.1. General Considerations 4.1.2. Primary and Secondary Stresses 4.1.3. Definition of the Stress Profile for Use with the K-Factor 4.1.4. Definition of the Stress Profile for Yield Load Determination 4.2. Flaw Characterisation 4.2.1. Planar and Volumetric Flaws 4.2.2. Basic Crack Types

29 29 29 29 30 35 36 36 36

vi

Contents

4.2.3. Crack Shape Idealisation 4.2.4. Interaction Effects of Multiple Cracks 4.2.5. Crack Re-characterisation 4.2.6. Crack Orientation and Projected Crack Depth 4.3. Deformation Characteristics of the Material 4.3.1. General Remarks 4.3.2. Engineering and True Stress-Strain Curve 4.3.3. Modulus of Elasticity (Young’s Modulus) and Poisson’s Ratio 4.3.4. Yield Strength and Tensile Strength 4.3.5. Flow Stress 4.3.6. Strain Hardening Coefficient 4.3.7. Yield Strain (Lüders’ Strain) 4.3.8. Tensile Data Relevant to Welds 4.3.9. Temperature and Strain Rate Dependency 4.4. Toughness Characteristics of the Material 4.4.1. General Remarks 4.4.2. The Fracture Toughness Transition Curve 4.4.3. Lower Shelf Fracture Toughness 4.4.4. Upper Shelf Fracture Toughness 4.4.5. Ductile-to-Brittle Transition 4.4.6. Constraint Dependency of Fracture Toughness 4.4.7. Reference Toughness Based on Charpy Data 5. The Model Parameters 5.1. The Stress Intensity Factor (K-Factor) 5.1.1. Sources for Analytical K-Factor Solutions 5.1.2. Types of Analytical K-Factor Solutions 5.1.3. Superposition of K-Factors 5.1.4. Treatment of Geometry Factor Solutions Available in Table Format 5.1.5. Individual Determination of K-Factors by Finite Element or Comparable Methods 5.2. Net Section Yield Load FY , Reference Stress ref and Ligament Yielding Lr 5.2.1. Methods for the Generation of Yield Load Solutions 5.2.2. Global vs. Local Yield Load 5.2.3. Conservatism in Yield Load Determination 5.2.4. Sources for Analytical Yield Load Solutions 5.2.5. Types of Analytical Yield Load Solutions for Homogenous Components 5.2.6. Equivalent Yield Load Solutions for Strength Mismatch Components

36 38 40 41 43 43 44 44 45 46 46 47 48 50 50 50 51 53 54 56 74 85 89 89 89 90 110 110 111 112 112 113 114 115 116 129

Contents vii

6. Structural Assessment 6.1. Acceptable or Critical Conditions of a Component 6.2. Assessment Based on the FAD Philosophy 6.2.1. The FAD 6.2.2. The Assessment Point (or Path) 6.2.3. Types of FAD Analysis 6.2.4. Non-unique Solutions 6.3. Assessment Based on the CDF Philosophy 6.3.1. The CDF Functions 6.3.2. The Determination of the Critical Condition 6.4. The f(Lr ) Function According to the Different Analysis Levels 6.4.1. General Remarks 6.4.2. Option 0 (“Basic Option”) 6.4.3. Option 1 (“Standard Option”) 6.4.4. Option 3 (“Stress–Strain Defined Option”) 6.5. Examples for SINTAP/FITNET Analysis 6.5.1. Determination of the Critical Load 6.5.2. Determination of the Critical Crack Size 6.5.3. Determination of the Required Minimum Toughness 6.5.4. Determination of the Instability Load (R-Curve Analysis) 6.6. Combined Primary and Secondary Stresses 6.6.1. General Remarks 6.6.2. The Correction Term V in the FAD and CDF Approaches 6.6.3. The Determination of V 6.6.4. Welding Residual Stress Profiles 6.6.5. Examples of Analysis for Combined Primary and Secondary Stresses 6.6.6. Further Remarks on Welding Residual Stress Profiles 6.7. Constraint Effects 6.7.1. Consideration in the FAD and CDF Approaches 6.7.2. Example of an Assessment Including Constraint Effects 6.8. Mixed Mode Loading 6.8.1. General Aspects 6.8.2. FAD Analysis 6.8.3. CDF Analysis 6.9. Rapid Loading and Crack Arrest 6.9.1. General Aspects 6.9.2. Quasi-Static vs. Dynamic Analysis 6.9.3. Crack Arrest 6.10. Thin Wall Structures 6.10.1. General Aspects

137 137 139 139 139 141 142 143 143 144 147 147 147 148 151 153 153 157 158 159 162 162 163 164 165 172 185 188 188 188 191 191 193 194 194 194 196 197 198 198

viii Contents

6.11.

6.12.

6.13.

6.14.

6.10.2. Thin Wall Assessment Module 6.10.3. Examples of Thin Wall Assessments Strength Mismatch 6.11.1. The Strength Mismatch Phenomenon 6.11.2. The Strength Mismatch Options 6.11.3. Examples of Option 2 Analysis 6.11.4. The Option 3 Mismatch Module 6.11.5. Further Aspects of Strength Mismatch Weld Shape Imperfections 6.12.1. Weldment Specific K-Solutions 6.12.2. Misalignment 6.12.3. Example of an Assessment Taking into Account Misalignment Reliability Aspects and Significance of the Results 6.13.1. General Aspects 6.13.2. Reserve Factors and Sensitivity Analysis 6.13.3. Reliability Analysis 6.13.4. Example of a Simplified Reliability Analysis 6.13.5. Partial Safety Factors Potential Benefit of Applying Advanced Options and Modules

200 202 208 208 210 214 219 220 224 224 225 226 229 229 230 230 231 235 238

7. Validation Examples 7.1. Introduction 7.2. Pipelines and Pressurised Tubes 7.3. Thin Wall Structures 7.4. Strength Mismatched Configurations 7.5. Failure Investigation

241 241 241 244 247 248

References

251

Appendix: “Fracture Toughness Test Standards”

265

Glossary

269

Index

289

Nomenclature

(Remark: Not every symbol used in this book could be included in this nomenclature list. Symbols that are only used in specific contexts will be explained in the corresponding sections of the text.)

(a) Frequently used symbols a

amax ao A b B B c cgsY co CV CVus E E’ F fc Fc Fpc

Crack depth (embedded or surface cracks), sometimes also crack length in surface direction of through wall cracks (2a for tension geometries) Deepest of a population of adjacent coplanar cracks (in the context of combination criteria, Section 4.2.4.2) Original or initial crack depth before extension Cross section area of the section containing the crack Ligament length (W-a) Specimen thickness (refers to t in components) Normalised T stress (constraint correction of fracture toughness, Section 4.4.6.2) Crack length in surface direction (through wall, embedded or surface cracks), for tension geometries 2c Half maximum length of an idealised surface crack under plastic collapse conditions in a tension plate (Section 4.2.4.2) Original or initial crack length before extension Charpy energy Upper shelf Charpy energy Modulus of elasticity (Young’s modulus) Effective Young’s modulus (= E for plane-stress; = E/(1-2 for plane-strain) Load (general term), also tensile force Probability density function (bi-modal Master Curve approach, Section 4.4.5.3.4) Critical load Plastic collapse load

x

Nomenclature

fs FY FYB FYW FYM f(Lr fi , Fi h h H H J JBL Jc , Ju , Juc Jcen JLB Jmat Jmed Jp Jssy Jo J02/BL , J02 , Ji K Kcen Keq

Dynamic stress enhancement factor for crack arrest events (Section 6.9) Net-section yield load (general term, also tensile yield force) Yield load of base plate material (weldments) Yield load of weld metal (weldments) Equivalent mismatch corrected yield load (strength mismatch joints) Correction function for ligament yielding given for different assessment options Tabulated geometry functions of K-factor solutions Fit function to finite element results in the EPRI approach (Section 2.5) Stress triaxiality parameter (= h /e , sometimes also h /Y , Section 4.4.6.2) Spacing between cracks for alignment criteria (Section 4.2.4.1) Height of the weld strip (Sections 5.2.6 and 6.11), for tension geometries 2H J-integral (for its different interpretations see the Glossary “J-integral”) J-integral referring to the blunting range before crack initiation Fracture toughness in J-integral terms determined at the point of instability (for definition see Section 4.4.2) Census criterion of the alternative two-parameter Weibull distribution according to Eqn 4.40 (Section 4.4.5.2.2) Engineering lower-bound toughness of the alternative two-parameter Weibull distribution according to Eqn 4.41 (Section 4.4.5.2.2) General term of fracture toughness expressed in terms of the J-integral Average toughness value of the alternative two-parameter Weibull distribution according to Eqn 4.41 (Section 4.4.5.2.2) Plastic component of the J-integral Elastic or small-scale yielding component of the J-integral Scale parameter of the two-parameter Weibull distribution (Section 4.4.5.2.2) Resistance against stable crack initiation in J-integral terms (for definition see Section 4.4.2) Stress intensity factor (K-factor) Census criterion of the Master Curve approach (Section 4.4.5.2.2) Equivalent K-factor for mixed mode loading (Section 6.8)

Nomenclature

KJ K km Kmat c Kmat

Kmed Kmin Kr KIp KIs Kps Ko KI , KII , KIII KIA KIB KIA KIB KIC KIc

L Lr Lmax r m

xi

K-factor formally determined from the J-integral (Eqn 6.4) K-factor formally determined from the CTOD (Eqn 6.5) Misalignment magnification factor for K-factor determination (Section 6.12) General term of fracture toughness expressed in terms of the K-factor Constraint corrected fracture toughness (Sections 4.4.6.3 and 6.7) Mean toughness value of the three-parameter Weibull distribution (Master Curve approach, Section 4.4.5.2.2) Shift parameter of the three-parameter Weibull distribution (Master Curve approach (= 20 MPa · m1/2 for ferritic steels with yield strengths between 275 and 825 MPa) Ordinate of the Failure Assessment Diagram (FAD) (= K/Kmat Mode I stress intensity factor for primary loading (Section 6.6) Mode I stress intensity factor for secondary loading (Section 6.6) Plasticity corrected mode I stress intensity factor for secondary loading (Section 6.6) Scale parameter of the three-parameter Weibull distribution (Section 4.4.5.2) Mode I, II and III stress intensity factors (Section 6.8) K-factor at the deepest point of a semi-elliptical surface crack K-factor at the surface points of a semi-elliptical surface crack K-factor at the surface points and the centre point of a quarter-elliptical surface crack (Example 5.5) Plane strain fracture toughness (small-scale yielding) Crack front length in the component (for statistical size correction of the scale parameter of the Weibull distribution in the ductile-to-brittle transition, Section 4.4.5.2) Likelihood (bi-modal Master Curve approach, Section 4.4.5.3.4) Ligament yielding parameter (= F/FY = ref /Y , abscissa of the FAD and CDF diagrams Plastic collapse limit Lr value Constraint factors in various equations (for specific meanings consult the text)

xii Nomenclature

m

M Mb Mk n N

N NB NM NW p p P P Pf pY Po Q r r o , yo ReL ReH

Shape parameter of the Weibull distribution (= 4 in the Master Curve approach; = 2 in the alternative two parameter Weibull distribution of Eqn 4.39) Mismatch factor (= YW /YB Global bending moment Magnification factor for K-factor determination of weldments (Section 6.12) Ramberg-Osgood strain hardening exponent (see the Glossary “crack tip opening displacement”, Eqn G3) Strain hardening exponent used in SINTAP/FITNET; slope of the plastic branch of the true stress-strain curve in double-logarithmic scales. SINTAP/FITNET uses, however, an empirical lower bound to experimental data that were obtained by the general definition. In the ETM approach (Section 2.8) N refers to the engineering stress-strain curve Number of tests of a data set for statistical analysis in the ductile-to-brittle transition (Section 4.4.5.2) Strain hardening exponent of the base plate material (weldments) Equivalent strain hardening exponent of the strength mismatched configurations Strain hardening exponent of the weld metal (weldments) Number of invalid or censored data in the statistical analysis of ductile-to-brittle transition (Section 4.4.5.2) Internal pressure (pressurised components) Load (general) in EPRI terminology (Section 2.5) Failure probability of test specimens (e.g. in the Master Curve approach; Section 4.4.5.2) Failure probability of the component (Section 6.13) Yield internal pressure Reference load (quantitatively close to the yield load FY in the EPRI approach (Section 2.5) Q-stress (constraint parameter, Section 4.4.6.2) Number of valid or uncensored data in the statistical analysis of ductile-to-brittle transition (Section 4.4.5.2) Parameters for describing surface welding residual stress profiles (Section 6.6) Lower yield strength of a material displaying a yield plateau (Lüders’ plateau) Upper yield strength of a material displaying a yield plateau (Lüders’ plateau)

Nomenclature

Rm Ri , Ro , R s Sc Sr t,T tr T T To

T27J , T28J u

V

W Wb x

Y

xiii

Uniaxial tensile strength Inner, outer and mean radius of hollow cylinders Spacing between cracks for combination criteria (Section 4.2.4.2) Survival function (bi-modal Master Curve approach, Section 4.4.5.3.4) Abscissa of the original R6 Rev. 1-FAD (= F/Fpc Wall thickness of the component Rise time (rapid loading, Section 6.9) T stress (constraint parameter, Section 4.4.6.2) Temperature (in C) Transition temperature of the Master Curve approach (the temperature at which the mean value of the fracture toughness, Kmed , equals 100 MPa · m1/2 for 1T specimens) (of thickness of 25 mm) Transition temperature based on Charpy test data Distance from one surface (usually at the crack location) through the thickness. (in some applications also designated by x; see also the comments for x. If the distance is required in two directions this can be described by u and v coordinates (e.g. Example 5.5)) Correction factor for primary and secondary stresses interaction (replacement for the -factor in older versions of FAD procedures) Specimen thickness, for tension geometries 2W Section modulus of the component Distance from one surface (usually at the crack location) through the thickness of the component (in some applications also designated by u); Care has to be exercised since x (or u) refers in some applications to the wall thickness and in others to the crack depth (for specific applications consult the text). Geometry function of K-factor solutions (General term) Angle of inclination with respect to the applied stress direction(s) (Section 4.2.6), also designated by in Section 6.10 Component constraint factor (Section 4.4.6.3) Partial safety factor (Section 6.13) Crack tip opening displacement (CTOD) (for its different specifications see the Glossary “crack tip opening displacement”)

xiv

Nomenclature

c , u , uc i mat 02/BL 02 I 5

a, c

aBL

Tss p ref t Y pl r

Fracture toughness in CTOD terms determined at the point of instability (for definition see Section 4.4.2) Census factor of the Master Curve approach (= 1 for uncensored and = 0 for censored data) General term of fracture toughness expressed in terms of the CTOD Resistance against stable crack initiation in CTOD terms (for definition see Section 4.4.2) Definition of the CTOD measured at the surfaces of the specimen or component, used in SINTAP/FITNET for the Thin Wall Module (Section 6.10) Stable crack extension in depth and surface directions Crack extension due to blunting Lüders’ strain, refers to the portion of the stress-strain curve beyond yield and before strain hardening where the stress stays nearly constant with increasing strain (length of the yield plateau) Shift in the Charpy data based transition temperature due to the use of sub-sized Charpy specimens (Section 4.4.7.5) Strain Plastic strain Reference strain (Reference stress method, Section 2.6, also used in SINTAP/FITNET; obtained for any ref = Lr · Y as the corresponding strain on the true stress-strain curve) True strain (up to curve maximum of the engineering stress-strain curve = ln (1+ with being the engineering strain) Yield strain Shape function for determining the J-integral in test specimens Coordinate for describing points at the front of semi-elliptical cracks Polar coordinates used to describe the stress-strain field ahead of a crack Biaxial tension loading parameter (= x /y Parameter used in conjunction with Option 1 and 2 analyses for modelling the yield plateau effect at Lr = 1 for materials displaying such a yield plateau (Section 6.4) Mean value of a given statistical distribution (general term)

Nomenclature

a b e f gb h Kmat m p p R RL RT ref s s t t x (xx

xv

Parameter used in conjunction with Option 1 and 2 analyses for correcting the f(Lr function at, and slightly below, Lr = 1 for materials without yield plateau (Section 6.4) Poisson’s ratio Function for determining the correction factor V (effect of secondary stresses on the crack driving force) (Section 6.6) Standard deviation of a given statistical distribution (general term) Proof test load (Section 6.6.6.2) Bending stress component (linear stress distribution across the wall). Note that different definitions have to be applied for use in K-factor and yield load determination. Equivalent stress (Section 4.4.6.2) Flow stress, equivalent yield strength taking into account strain hardening in a simplified way, in SINTAP/FITNET = 0.5(Y + Rm Global bending stress (= Mb /Wb Hydrostatic stress (Section 4.4.6.2) Standard deviation of fracture toughness in terms of the K-factor Membrane stress component (uniform stress distribution across the wall). Note that different definitions have to be applied for use in K-factor and yield load determination. Stress due to internal pressure Primary stresses Residual stresses (general term) Residual stresses in longitudinal direction (in weldments, parallel to the fusion line) Residual stresses in transverse direction (in weldments, normal to the fusion line) Net section reference stress (= Lr · Y Maximum induced bending stress due to misalignment (Section 6.12) Secondary stresses True stess (up to curve maximum of the engineering stress-strain curve = 1 + with being the engineering stress and the engineering strain) Stress due to thermal loading (Example 5.3) Normal stress in x direction (Fig. 4.23; refers to the in-plane or ligament direction)

xvi

Nomenclature

y (yy z (zz Y YB YW YM w 1 2 1 2 i

ij

Normal stress in y direction (Figure 4.23) Normal stress in z direction (Figure 4.23; refers to the out-of-plane direction) Yield strength (general term; for its different meanings see Section 4.3.4) Yield strength of the base plate material (weldments, general term) Yield strength of the weld metal (weldments, general term) Equivalent mismatch corrected yield strength of mismatched joints (Mismatch module of Option 3, Section 6.11.4) Weibull stress (Beremin model, Section 4.4.6.3) Principal stresses Stresses from a linear stress profile extrapolated to the front and back surface (definition for K-factor determination, Section 4.1.3) Stress coefficients (1 , 2 , …, n for modelling stress profiles across the wall of the un-cracked section (n = order of the polynomial, Section 4.1). Note that in some applications re-calculations of i are necessary before being applied to K-factor determination. Fundamental period of a component subjected to rapid loading (referring to its period of oscillation, Section 6.9) Shear stresses (Fig. 4.23; i and j = x, y or z) Angle of inclination with respect to the applied stress direction(s) (Section 6.10, in Section 4.2.6 also designated by ß) Angle to the rolling direction in anisotropic sheets Geometry parameter for describing mismatched configurations (= (W-a)/H)

(b) Frequently used subscripts A, B

ax i i; o i L mat

Deepest point and surfaces points of a semi-elliptical surface crack. In the case of quarter-elliptical corner cracks A and C mark the surface points and B the inner point Axial Original, initial Inner, internal and outer Number (counting variable) Longitudinal Material (referring to toughness)

Nomenclature

max B c T W us Y

Maximum Base plate material (weldments) Critical Transverse Weld metal Upper shelf Yield

(c) Frequently used abbreviations CDF CMOD COV CTOA CTOD C(T) FAD HRR HS LS M(T) OM PSF R-curve RT SSC UM 1T

Crack driving force Crack mouth opening displacement Coefficient of variation (ratio of standard deviation go mean value of a given statistical distribution) Crack tip opening angle Crack tip opening displacement ( Compact tension specimen Failure assessment diagram Hutchinson-Rice-Rosengreen field (stress-strain field the magnitude of which is defined by J or Higher strength (material of bi-material joints) Lower strength (material of bi-material joints) Middle cracked tension specimen Overmatching Partial safety factor Crack (extension) resistance curve Room temperature Small scale yielding Undermatching Specimen with a thickness of one inch (∼25 mm)

xvii


Chapter 1

Introduction This chapter briefly describes the European SINTAP and FITNET projects and the aim of this book.

1.1. SINTAP SINTAP (Structural INTegrity Assessment Procedure) was a multidisciplinary collaborative project, part-funded by the European Union, with the aim of devising a unified procedure for the assessment of fracture behaviour, offering a range of assessment routes with maximum applicability from the smallest SME (small and medium-sized enterprise) to major industrial users. The project commenced in April 1996 and was completed in April 1999. Although many fracture assessment methods were in existence when the SINTAP project commenced, as will be outlined in Chapter 2, there were conflicting approaches and unspecified levels of empiricism. These approaches did not fully reflect either the performance of modern materials or the current state of knowledge. SINTAP covered both modelling and experimental work, and a large part of the project was concerned with the transfer of knowledge and data between industries and scientific organisations together with its compilation and interpretation to provide the required solutions. The culmination of this project was a procedure that is applicable to a wide cross-section of users because of its ability to offer routes of varying complexity, reflecting data quality and the scope for a final interpretation reflecting the preference of the user. In view of the comprehensive nature of the project and the necessity to consider carefully the requirements of the end user, a wide-ranging consortium was established for the project. This comprised a material supplier (British Steel, now part of the Corus Group), an electricity generator (British Energy), an oil and gas supplier (Shell), a chemical processor (EXXON), safety assessors (Health & Safety Executive and SAQ Inspection Ltd., now part of DnV), research institutes (GKSS, Fraunhoffer IWM, lnstitut de Soudure, TWI, VTT, JRC (IAM), two universities (Cantabria and Gent), a software developer (Marine Computation Services) and a consultancy (Integrity Management Services). The project was co-ordinated by Swinden Technology Centre, Corus (UK), with the five principal areas of study being led by Task Leaders as summarised below.

2

Fitness-for-Service Fracture Assessment of Structures Containing Cracks

Task 1: Mismatch – Leader: GKSS To quantify the behaviour of strength mismatched welded joints and to provide recommendations for their treatment in a procedure. Task 2: Failure of Cracked Components – Leader: British Energy To extend the understanding of the behaviour of cracked components in the specific areas of constraint, influence of yield strength (YS) to tensile strength (UTS) ratio, prior overload, leak-before-break, and stress intensity factor (SIF) and yield load (YL) solutions. Task 3: Optimised Treatment of Data – Leader: VTT To provide an industriallyapplicable method for a reliability-based defect assessment procedure. Task 4: Secondary Stress. – Leader: IdS The determination and validation of the most appropriate method of accounting for residual stress, including a compendium of residual stress profiles. Task 5: Procedure Development – Leader: Corus Development and validation of the procedure. Each task comprised a number of sub-tasks, (see Table 1.1), and was structured into three basic steps: As a first step a comprehensive collation of existing data,

Table 1.1: Sub-tasks in project Task 1: Mismatch

Task 2: Cracked Components

1.1 Review 2.1 Review 1.2 Bi-Materials 2.2 Constraint 1.3 Multipass Weld 1.4 Modelling 1.5 Procedure

Task 3: Optimised Data Treatment 3.1 Review 3.2 Toughness

Task 4: Secondary Stress

4.1 Review 4.2 Collate Profiles 2.3 YS/UTS 3.3 Charpy 4.3 Experiment Ratio Correlations & Modelling 2.4 Prior 3.4 NDI 4.4 Profiles Overload Guidance Library 2.5 Leak-before- 3.5 Probabilistics 4.5 Procedure break 2.6 SIF & YL 3.6 Procedure Solutions 2.7 Procedure

Task 5: Procedure Development 5.1 Review 5.2 Procedure 5.3 Software 5.4 Validation 5.5 Documentation

Introduction

3

procedures and codes was completed and then experimental work was carried out to cover omissions and to validate the approaches and assumptions relevant to the particular study area. The best practice approach within each task was finally collated within Task 5, with consideration of the needs of the practising engineer in order to formulate the procedure itself.

1.2. FITNET FITNET (Fitness-for-Service Network) was a European thematic network, which ran for four years from February 2002 to May 2006. The overall objective of the group was to develop and extend the use of fitness-for-service (FFS) procedures for welded and non-welded metallic structures throughout Europe. It was partly funded by the European Commission within the fifth framework programme and comprised about 50 organisations from 17 European countries but also included contributions from organisations in the USA, Japan and Korea. The FITNET FFS procedure is built up in four major analysis modules, namely: Fracture, Fatigue, Creep and Corrosion and the full procedures, together with background information on this is given in [1.1]. The procedures were developed in parallel as a CEN (Comit´e Europ´een de Normalisation) Workshop Agreement (a CEN document). The overall structure of the FITNET-FFS procedure is given in Fig. 1.1. The Fracture Module of the FITNET FFS procedure was mainly based on the previous developments carried out within the SINTAP project as well as later advances in other documents such as the Revision 4 of the British Energy R6 procedure [1.2] and amendments to the British Standard BS 7910 [1.3]. In addition, the results from other European Union projects were used to extend the treatment of several problem areas, such as the effects of constraint and the treatment of thin walled structures.

1.3. The Topic of the Present Book The emphasis of the present book is on the practical application of FFS tools for predicting the fracture behaviour of structures with real or potential cracks. The content is mainly based on the SINTAP procedure, which is basically the same as the fracture module of FITNET in many aspects, but complemented by additional topics such as mixed mode loading, the treatment of thin-walled structures and some further items. Since the name “SINTAP” has now been in use for more than seven years and has become quite widespread, the name is retained here but modified to “SINTAP/FITNET” to reflect the inclusion of elements of FITNET,

4


Application Areas of FITNET FFS Procedure Design of new structures

Fabrication support

Failure analysis

In-service assessment

Information required for Assessment (Inputs) Flaw Information

Material properties

Stresses

Assessment Modules Fracture

Fatigue

Creep

Corrosion

Assessment and Reporting of Results

Alternative Approaches and Specific Applications (Leak-before-break, Local approach, Crack arrest, Mixed Mode . . .)

Additional Information Compendia (K solutions etc.)

Validation and case studies

Figure 1.1: Overall flowchart of the FITNET FSS procedure.

which did not belong to the original SINTAP document. On the other hand, the concentration on fracture, i.e., only the fracture module of FITNET, implies a restriction to the end-of-life conditions of a damaged component whereas FITNET actually covers a wider range; containing further modules for fatigue life, fatigue crack extension, creep and corrosion, as illustrated in Fig. 1.1. The intention of the present book is not to provide the reader with the SINTAP or FITNET procedure itself. The latter is available as a CEN document, as mentioned above. Instead the intention is to provide the potential user with detailed guidance on how to use the procedure in practical applications, complemented with background information that needs to be considered to avoid mistakes. The book is intended to be useful for training by containing a wider range of practical information than the procedural documents. For this purpose, additional details

Introduction

5

on the scientific background, alternative approaches in the FFS literature and practical tips are given in the text and in the Glossary. A large range of worked examples are included as tutorials. However, it should be recognised that the book does not contain all elements of the SINTAP/FITNET documents, such as the extended annexes of K-factor solutions, yield load solutions etc. which by themselves constitute a complete volume of FITNET. It is therefore intended to be used in conjunction with, rather than instead of, the procedural documents and in particular with the CEN-FITNET document.


Chapter 2

Brief Overview on the Development of Flaw Assessment 2.1. General Aspects Engineering design codes traditionally work on the philosophy of comparing the applied stress with some limit stress level, such as the yield strength of the material and, as long as the latter is greater than the former, the component is regarded as safe. This approach assumes two things; the material is homogeneous and is free from defects. If a structural discontinuity (e.g., a crack) is present then the principle may not apply and comparisons need to be carried out on the basis of crack tip parameters (i.e., fracture mechanics). The behaviour of the component can then be analysed in terms of the critical applied load or a critical crack size. As long as the deformation behaviour of the structural component is linear elastic then the relevant parameter is K and comprehensive compendia of K-factor solutions exist in handbooks and computer programs. If the component behaves in an elastic–plastic manner then the situation is more complex as the crack tip loading is also influenced by the deformation behaviour of the material, as dictated by the appropriate stress–strain curve. This makes handbook solutions a very difficult task although they are available for some limited configurations [2.1]. Hence analytical methods are required to answer the vast majority of structural integrity questions. These approaches have been under development for more than 30 years and comprehensive reviews of the various methods available have been provided in a special edition of the International Journal of Pressure Vessels and Piping [2.2] and in a volume of the Elsevier encyclopaedia Comprehensive Structural Integrity (CSI) [2.3]. The principles behind the various methods are discussed in state-of-the-art papers in [2.4–2.6] and developments across the world are summarised in other publications. One principle common to all the methods is that they aim to produce conservative results and, hence, if an analysis leads to an “unsafe” result this does not mean that the component will fail, just that it is necessary to examine it more closely. The drive in recent years has been to reduce this degree of uncertainty using staged levels of increasing sophistication in analysis to provide scope for simple to complex evaluations.

8


2.2. Ligament Yielding Note that, as a general rule, the crack driving force is correlated with the local strain rather than with stress. To use a simple comparison: in the elastic range of a stress–strain curve the stress and strain are simply related by Young’s modulus and it does not matter which parameter is given to reconstruct the whole curve. However, above the yield strength Y , the deformation behaviour becomes nonlinear and strain increases non-proportionally with further increase in stress. If we compare the determination of crack driving force by the linear elastic factor K with the determination of strain from a stress value using Young’s modulus we get the same effect. The crack driving force is underestimated for loads larger than approximately 60% or 70% of the net section yield load FY of the cracked component, and the greater the underestimation the lower the strain hardening exponent of the material, that is, the flatter the plastic branch of the stress–strain curve. The common flaw assessment methods are not restricted to a linear elastic deformation pattern, but cover the whole range up to elastic–plastic. Hence the yield load relevant to a cracked component plays an important role in almost all models and this marks the change from contained to net-section yielding (for a definition of these terms see the Glossary “crack tip plasticity”). In the literature the term “limit load” is frequently used instead of the term “yield load”. The reason for this is that FY is frequently determined for ideally plastic, that is, non-hardening material. In such a case the terms “yield load”, “limit load” or “collapse load” describe the same load level that is associated with the failure of the component. However, if the material work hardens beyond yield, the yield load does not correspond to failure, which may not occur until the plastic collapse load is reached. With the exception of the Design Curve approaches the concepts discussed below, independent of their different individual backgrounds, all have in common that they are based on the K-factor but “correcting” this for plasticity effects. Even if they, as in the case of the FAD (Failure Assessment Diagram) approaches, are still written in terms of K this is not in line with the original linear elastic stress intensity factor concept. Rather they describe the crack driving force in terms of a formal elastic–plastic K-factor or, alternatively, in terms of the J-integral or the crack tip opening displacement (CTOD). The underlying principle is schematically illustrated in Fig. 2.1. The advantage of this approach is that it can make use of K-factor solutions that are nowadays relatively simple to determine or are even available in compendia, thus avoiding the need for individual finite element determination of the crack driving force.

Brief Overview on the Development of Flaw Assessment

Formal elastic-plastic K (real crack driving force CDF)

Crack driving force Ligament yielding factor f(F/FY)

9

linear elastic K

CDF = K · f (F/FY)

1 0.6 – 0.7

F/FY

Figure 2.1: Schematic illustration of the effect of ligament yielding on the crack driving force.

2.3. The TWI (The Welding Institute) Design Curve Approach Burdekin and Dawes [2.7] formulated the earliest analytical methods in 1971 as the Design Curve approach, based on original ideas from Wells [2.8]. This basically relates the applied strain to the CTOD () or, latterly, the J-Integral via a quadratic equation in the contained yield region and linearly in the net-section yielding regime. Comparison of the material toughness with that necessary to withstand the applied strains gives the failure prediction. This approach was modified several times, finally, for deeper cracks, by Dawes [2.9] who also rewrote the equations in terms of stress to fit into the FAD approach that had then been adopted for the British PD 6493 procedure [2.10, 2.11]. It is still part of the current BS 7910 [2.12] and, with some modifications, is contained in US and Canadian guidelines for welded pipes, API 1104 [2.13] and CSA Z662 [2.14], and in the Chinese pressure vessel code CVDA-1984 [2.15]. A preferential application field is shallow cracks originating in notches.

10


The original TWI-CTOD Design Curve was based on a semi-empirical correlation of the crack tip opening displacement, CTOD, with the local strain at the surface of a tension plate. Today, the method has been extended for tension and bending, for including strain hardening and for the use of the J-integral as crack driving force parameter in addition to the CTOD (for an overview see [2.4] and [2.6]).

2.4. The Early FAD Approach of CEGB (Central Electricity Generating Board) In parallel with the activities at TWI, a flaw assessment concept was developed by the British nuclear power industry in the 1970s. The early R6 routine of British Energy (formerly CEGB) [2.16] introduced the concept of the so-called two-criteria approach and the Failure Assessment Diagram (for a discussion of the early development see [2.5]). Failure was assumed either when the stress intensity factor in the component exceeds the fracture toughness in terms of the linear elastic KIc or when the applied load exceeds the plastic collapse load of the net section of the component containing the crack. The advantage of this approach was that both criteria were sufficiently well understood at a time when the theories of post-yield fracture mechanics were still under development. In between the extreme cases of KIc based fracture and plastic collapse, the failure mode of elastic–plastic fracture is modelled by an interpolation line based on empirical data and a strip yield approach [2.17]. A further part of R6-Revision 1 was that the applied K-factor is normalised by the fracture toughness Kmat and the applied load F by the plastic collapse load Fpc : Kr = K/Kmat

(2.1)

Sr = F/Fpc

(2.2)

and

In this way, the interpolation line K r = Sr

−1/2 8/ 2 ln sec Sr /2

(2.3)

becomes a failure line designated as a FAD (Fig. 2.2). In the FAD approach, the assessment of the component is based on the relative location of a geometrydependent assessment point (Kr Sr ) with respect to the FAD line which is assumed


11

potentially unsafe

C

1.0

B increasing load

Kr = K/Kmat

0.8 0.6

A 0.4

C FAD line B increasing crack size

A

0.2

safe 0

0

0.2

0.4

0.6

0.8

1.0

Sr = F/Fpc

Figure 2.2: Failure Assessment Diagram approach according to R6-Revision 1.

to be a universal curve roughly independent of the component geometry and the material. In the simplest application the component is regarded as safe as long as the assessment point lies within the area below the failure line. It is regarded as potentially unsafe if it is located on the line or outside the shaded area in Fig. 2.2. An increased load or larger crack size would move the assessment point along the loading path towards the failure line, as indicated by the locus A → B → C.

2.5. The EPRI (Electric Power Research Institute) Approach At about the same time that the R6 routine was first published, the American EPRI approach was developed [2.18]. The following explanations refer to the J-integral as the crack driving force parameter. Note, however, that solutions for CTOD in terms of the 45 definition (see the Glossary “crack tip opening displacement”) are available as well. In the EPRI method the J-integral is split into small scale yielding (ssy) and widespread yielding (p) components J = Jssy + Jp

(2.4)

The small scale yielding part, Jssy , is obtained from the elastic stress intensity factor with minor adjustments based on plastic zone corrections to the crack size (see the Glossary “crack tip plasticity”). For the plastic part, the HRR (Hutchinson-Rice-Rosengreen) field equation (see the Glossary “crack tip opening

12


displacement” and “J-integral”) is solved for J. Replacing the HRR stresses by the applied load P and a reference load Po (EPRI terminology) gives an expression Jp = o o hL

P Po

n+1

(2.5)

In the EPRI approach, as in the R6 routine, the load is normalised by a reference load Po which, in principle, may be freely chosen but is usually identified with the yield load of the cracked component. The quantities o , o , and n are the fitting parameters of the Ramberg–Osgood formulation of the stress–strain curve (see the Glossary “crack tip opening displacement”, Eqn G3). L is a characteristic dimension that is commonly identified with the ligament length or crack size. In order to specify the function h for specific geometries, large sets of 2D finite element calculations were performed varying the component and crack dimensions as well as the Ramberg–Osgood strain hardening exponent n of the material. Tables of h for a range of plate and cylindrical configurations form the main items of the EPRI handbooks [2.1]. The EPRI approach was primarily developed in what in SINTAP/FITNET is called a CDF format, an acronym standing for “Crack Driving Force”. In contrast to the FAD philosophy used in R6, the CDF philosophy strictly separates the applied and material sides. The determination of the crack driving force in the component and its comparison with the fracture resistance of the material are two separate steps. It was, however, also implemented in a FAD format, see for example, [2.19]. In contrast to the CEGB-FAD, the EPRI-FAD is based on the yield load FY instead of the collapse load Fpc of the cracked component and the FAD line becomes a function of the strain hardening of the material. The advantage of the EPRI approach is that it is based on finite element analyses although the solutions in the EPRI handbook are restricted to 2D calculations. On the other hand its application is limited to only a few configurations, namely those for which tables of h factors are available. Another critical point is its use of the Ramberg–Osgood fit to the stress–strain curve since most materials do not follow this fit satisfactorily and, in particular, the important region near the yield strength is usually poorly described.

2.6. The Reference Stress Method of CEGB These limitations were overcome in the so-called Reference Stress method developed in the early 1980s at CEGB in the context of steady state creep fracture mechanics [2.20]. It was subsequently shown that the method could be interpreted as a generalisation of the EPRI approach [2.21]. In the Reference Stress approach,


13

the deformation behaviour is considered by a piece-wise introduction of the true stress–strain curve allowing an exact description of any material. In addition, it was shown in [2.21] that the dependency of h on the strain hardening coefficient n in Eqn (2.5) could be minimised by redefining the reference load Po . In this way it becomes possible to set h for any strain hardening approximately equal to the value for n = 1, the corresponding value for linear elastic material behaviour and related to the linear elastic K-factor. This gives the basic equation of the reference stress method K 2 E ref −1 (2.6) Jp = E ref with being equal to 0.75 for plane strain and 1 for plane stress. Since the modified reference load Po is found to be close to the yield load FY in many cases, the reference stress ref can be defined as ref =

F FY Y

(2.7)

The reference strain ref can be determined as the strain at the true stress–strain curve referring to ref . The term Y denotes the yield strength as a general term being ReL for materials with, and Rp02 for materials without, a Lüders’ strain. In Eqn (2.6) the second term can be interpreted as a ligament yielding correction to the linear elastic K-factor. For a more detailed discussion see [2.5] and [2.6].

2.7. The R6-Revision 3 Approach of CEGB Although it could also be applied in a CDF format the Reference Stress method was primarily developed for use in the R6-FAD. Eqn (2.3) is replaced by

E ef L3 + r Y Kr = K/Kmat = Lr Y 2E ref

−1/2 (2.8)

or in more general terms by Kr = f2 Lr

(2.9)

where f2 Lr =

E ef L3 + r Y Lr Y 2E ref

−1/2 (2.10)

14


and Lr = ref /Y = F/FY

(2.11)

in R6-Revision 3 [2.22]. The first term (E ref /Lr Y ) in Eqn (2.8) describes both the elastic and fully plastic behaviour of the component but not the intermediate region between both limiting conditions. This is modelled by the second term (Lr3 Y /2E ref ) which was originally based on EPRI considerations but modified by adapting to additional finite element results on various geometries (see [2.23]). A maximum value for Lr , Lrmax , is introduced to cover failure by plastic collapse. This is determined by Y + Rm 2 max (2.12) Lr = Y Two examples of Eqn (2.8) for different materials are shown in Fig. 2.3. The curves reflect the different shapes of the stress–strain curves of the materials. The fLr function in Eqns (2.9) and (2.10) is designated as f2 Lr with the index “2” referring to what is called “Option 2” in R6-Revision 3. In addition, the procedure contains an “Option 1” which is still applicable when only the yield and tensile strength of the material under consideration, but not its complete stress–strain curve, are available. The “Option 1” fLr , designated as f1 Lr , is derived as a fit to “Option 2” curves for a variety of materials but biased towards a lower bound. It is given by (2.13) f1 Lr = 1 − 014Lr2 · 03 + 07 exp −065Lr6 with Lrmax as defined by Eqn (2.12).

Kr = K/Kmat

1.0

C-Mn Steel

0.8 0.6

Option 1 Curve

Austenitic Steel

0.4 0.2 0

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Lr = σref /σY = F/FY

Figure 2.3: Failure Assessment Diagrams for various materials according to R6-Revision 3 (according to [2.23]).


15

The two options in R6-Revision 3 follow a principle of stepwise graded conservatism. The lower “Option 1” allows less sophisticated analyses which, nevertheless, will give satisfying results in many cases. The higher “Option 2” requires more effort, but the user is “rewarded” by less conservative results. That also means that an unacceptable “Option 1” result may provide a motivation for repeating the analysis at “Option 2” rather than claiming that the component is proven to be unsafe. The principle of stepwise graded conservatism is developed further in the SINTAP/FITNET procedure. In the 1990s the R6 routine was adopted by a number of flaw assessment procedures such as the British Standards BS 7910 [2.24], the American API document API 579 [2.25], the Swedish SAQ procedure [2.26] and others (for overviews see [2.4, 2.27, 2.28]). Note that in R6-Revision 4 [2.29], as well as in the 2005 revised BS 7910 document [2.12], elements of the SINTAP procedure have been used.

2.8. The Engineering Treatment Model (ETM) Approach of GKSS During the early 1980s, at about the same time that the EPRI approach and the Reference Stress method were under development in the US and Britain, an independent method was developed at GKSS in Germany. The basic concept of the ETM is illustrated in Fig. 2.4. The deformation behaviour of the ligament ahead of the crack is assumed to be satisfactorily described by a piece-wise power law E·

for < Y (2.14) = Y / Y N for ≥ Y fitted to tensile test data. Replacing by F, Y by FY , by 5 and Y by 5Y gives an expression 5 /5Y = F/FY N

for

F ≥ FY

The contained yielding branch, F < FY , is described by

2 1 Keff F 5 = K + E mEY FY

(2.15)

(2.16)

with 1 and m being constraint and material dependent constants, for example, for plane stress in steel 1 = 241 and m = 1. Keff is the Irwin-type


log σ/σY

16

1

1

ε/εY

log F/FY

1

1

1

1

N

N

δ5/δ5Y

Figure 2.4: Engineering Treatment Model (ETM): Basic principle.

plastic-zone-corrected stress intensity factor (see the Glossary “crack tip plasticity”). A special aspect of the ETM concept is its use of 5 , a special definition of the CTOD, that is, measured at two gauge points at the surface of the component (see the Glossary “crack tip opening displacement”). This makes the concept particularly suited to thin-walled structures. This method also includes a J-integral based approach. The ETM concept has been worked out in handbook format [2.30] and consists of a number of modules (basic module, notch module, strain-based module etc., see also [2.6, 2.31, 2.32]). Special emphasis is put on strength mismatch problems for which a specific methodology was developed and complemented by a compendium of modified yield load solutions [2.33].

2.9. The SINTAP Approach The aim of the SINTAP project was to develop a unified European procedure to combine the strengths of the methods available at the end of the 1990s. In a preinvestigation it was found that the results of these methods were very similar (see Fig. 2.5) so that the existing range of approaches was more of a handicap than an advantage to the user. In [2.34] the authors list a number of improvements and


(a)

17

(b)

1,0

f(Lr) 0.6 0.4

ETM R6-Opt.2 FEM [M(T), a/W = 0.5] FEM [SE(B), a/W = 0.25]

0.2 0

0

0.5

1

ETM R6-Opt.2 FEM [M(T), a/W = 0.5] FEM [SE(B), a/W = 0.25] 1.5

0

0.5

Lr

1

1.5

Lr

(c)

(d)

1,0

f(Lr) 0.6 0.4

ETM-MM R6-Opt.2 FEM

0.2 0

0

ETM-MM R6-Opt.2 FEM

0.5

1

Lr

1.5

0

0.5

1

1.5

2

Lr

Figure 2.5: Comparison between ETM, R6-Revision 3 Option 2 and finite element results for tension [M(T)] and bending [SE(B)] specimens ((a) and (b) [2.37], (c) and (d) [2.38]). (a) Homogeneous, material with yield plateau (e.g., ferritic steel); (b) Homogeneous, material without yield plateau (e.g., austenitic steel); (c) Weldment, strength mismatch base plate and weld metal with yield plateau (e.g., medium strength ferritic steels); (d) Weldment, strength mismatch neither base plate nor weld metal with yield plateau (e.g., austenitic steels).

novel features of the SINTAP procedure compared to the approaches available then. The most important changes are: • Extension and more detailed outline of the principle of stepwise graded conservatism • Redefined fLr functions for materials with and without yield plateau • Guidance on statistical aspects, among others with respect to the fracture toughness • A modified approach for treating combined primary and secondary stresses.

18


Note that the SINTAP procedure of 1999 [2.35] has become the major part within a module of the European FITNET method that has recently been completed [2.36]. Within this project some minor changes were made on SINTAP and the procedure was extended to include further aspects. The present book refers to the most recent development and makes this recognisable by choosing the term SINTAP/FITNET instead of SINTAP.

Chapter 3

Basic Features of SINTAP/FITNET 3.1. Fitness-for-Service SINTAP/FITNET provides a fitness-for-service (sometimes referred to as a “fitness-for-purpose” or “engineering critical assessment”) procedure. In general, a structure is fit for service when it is capable of withstanding all the loads imposed by service or, in other words, when the conditions to cause failure are not reached. It should be noted that a wide range of failure modes including fracture, corrosion damage, cavity, erosion and creep damage are encountered in industrial practice. Only the final fracture of cracked components, caused by cleavage and micro-ductile fracture mechanisms and fracture modes such as stable crack initiation and extension, unstable crack initiation and plastic collapse, is considered in this book. It should be noted that the comprehensive FITNET method also includes modules which allow fatigue, high temperature creep and corrosion damage to be considered in analyses. Frequently the term “fitness-for-service” is used in contrast to what is called a “good workmanship” or “quality control” philosophy, which also deals with critical defect sizes but on the basis of experience and the potential (and limitations) of non-destructive inspection (NDI). Defects that are less severe than permitted by a certain quality-control specification are usually regarded as acceptable without any further consideration. Obviously, good workmanship arguments – to a certain extent – are arbitrary and usually conservative, but they are, nevertheless, of irreplaceable value in monitoring and maintaining high standards during production and fitness-for-service arguments should not be used for justifying poor quality standards. However, since fitness-for-service provides individual assessment, this is much more precise than good workmanship arguments. There will be cases where a component that fails to satisfy quality-control criteria is shown to be nonetheless safe, but there might also be cases where a component which meets these criteria in reality is not safe. Good workmanship and fitness-for-service should generally be regarded as complementary approaches with each having its own benefits. Today, the latter is frequently applied “after the fact”, that is, it is used to assess a component in which a conventionally unacceptable defect was found during manufacturing or in

20


service. In addition to this important kind of application there is, however, an even more important future perspective in combining both assessment philosophies so that fitness-for-service results are used as input for specifying quality-control measures more precisely and, where required, more individually.

3.2. Potential Tasks of a SINTAP/FITNET Analysis The questions to be answered by SINTAP/FITNET follow the so-called “fracture mechanics triangle” (Fig. 3.1). The fracture behaviour of a given component is controlled by the three corners of the triangle: (a) The loading of the component. This includes the applied (or primary) loads and secondary loads such as residual stresses. (b) The crack dimensions and shape; through crack, embedded crack, surface crack, etc. (c) The fracture toughness of the material. Further parameters affecting the behaviour of a cracked component are the deformation properties of the material (its stress–strain curve) and constraint issues (geometry dependence of the toughness). All these parameters are covered by the SINTAP/FITNET procedure. The potential tasks of a SINTAP/FITNET analysis are based on the triangle. If two “corners” are known, the limiting value of the third can be determined. (a) A crack is detected or postulated (e.g., based on the NDI detection limit). With known loading, defect size and shape the question whether the component is safe or not can be answered. In conjunction with a fatigue crack extension analysis – which itself is not part of the fracture module of FITNET – the residual lifetime up to final failure can be determined as, for example, input information for establishing inspection intervals. (b) If the applied load as well as the material properties, including the fracture toughness, are known, the desired information is the critical size of a postulated crack, or – again combined with a fatigue crack extension analysis – the size of the crack that could grow to its critical size within a certain time, for example, the time up to the next inspection. This information is then used as input for the NDI, that is, what crack size has to be detectable with high confidence.

Basic Features of SINTAP/FITNET

21

Loading (primary and secondary)

Crack size and shape

Fracture toughness

Figure 3.1: The so-called “fracture mechanics triangle”.

(c) The third “edge” marks the fracture toughness. A minimum required fracture toughness can be specified for a postulated crack large enough to be reliably detected in quality control or in-service inspection. The rest of this chapter introduces some basic features of the procedure, these will be described in detail in subsequent chapters.

3.3. Multi-Optional Concept The SINTAP/FITNET flaw assessment module permits analyses at multiple levels of complexity and accuracy. Higher options are much more complex than a lower one and need improved input information; however, the user is “rewarded” by less conservative results. The various analysis options are mainly defined by the quality and completeness of the input information on the deformation and fracture behaviour of the material. SINTAP/FITNET comprises the following options (Table 3.1). (a) Option 0 – “Basic Option” This option is not recommended for general use but can be an alternative for cases of very limited knowledge of the material properties. It requires the information on yield strength and Charpy data only. The results of an Option 0 analysis can be unduly conservative. (b) Option 1 – “Standard Option” This is the minimum recommended option. It requires knowledge of the yield strength and the ultimate tensile strength of the material and of the toughness, which ideally should be available from at least three toughness tests. It can also be applied to strength mismatch components, for example, weldments, with yield-strength mismatch ratios less than 10%. In most such applications, the lower of the base and weld tensile properties have to be used.

22


Table 3.1: SINTAP/FITNET assessment options Option

FITNET designation

Original SINTAP designation

Data needed

Application range remarks

Basic Option 0

Basic Option

Default Level

Yield strength, Charpy data

When no other tensile data available

Standard Options 1

Standard Option

Basic Level

2

Mismatch Option Stress-Strain Defined Option

Mismatch Level

3

4

J-Integral Analysis

5

Constraint Option

Stress-Strain Level

Yield strength, Tensile strength, Fracture toughness Yield strength, Charpy data Complete stress-strain curve, Fracture toughness

Advanced Options J-Integral Level Complete stress-strain curve, Fracture toughness Constraint Level Geometry dependent fracture toughness

When no complete stress-strain curve available For yield strength mismatch >10% Assessment modules for homogenous & yield strength mismatched components Numerical determination of crack tip parameter, e.g., J Based on two-parameter concepts

(c) Option 2 – “Mismatch Option” This option refers to a modification of Option 1 for strength-mismatch components with yield strength mismatch ratios larger than 10% and ligament yielding Lr > 075. For the terminology see Section 5.2.


23

(d) Option 3 – “Stress–Strain Defined Option” For this option the complete stress–strain curve of the material, as well as fracture toughness data, are required. Both homogeneous and strengthmismatch components can be assessed in special assessment modules. Note that, in some cases, a complete stress–strain curve will be available in conjunction with Charpy data only instead of with fracture toughness data, or vice-versa. In such cases the options may be “mixed” but the user should always be aware of the potential conservatism of his analysis varient. In addition to these options the procedure comprises further modules that can help to reduce conservatism. (e) Option 4 – “J-Integral Analysis” This option includes the finite element determination of the crack driving force in terms of J (or crack tip opening displacement CTOD) in the frame of a general SINTAP/FITNET analysis. Only limited guidance on numerical aspects is provided in the documents and this will not be discussed in this book. (f) Option 5 – “Constraint Option” This option provides rules for the estimation of geometry dependent toughness values, in particular in low constraint geometries such as thin sections or predominantly tension-loaded plates. In this book Option 5 will not be described as a separate option but is included in Sections 4.4.6 and 6.7. No discussion will be provided on the original SINTAP Level 6 (Leak-beforebreak). The philosophy of different analysis levels enables the user to perform uncomplicated and straightforward analyses in a number of cases. If a lower-option analysis indicates safety, no further analysis is necessary. On the other hand, the application of a higher option is advisable when a more accurate, that is, a less conservative, analysis is needed. This requires more complete input information and sufficient expertise to handle the additional complexity. As a consequence of the multi-optional concept, an unacceptable result at a lower analysis option does not necessarily mean the failure of the component. Instead, it rather provides a motivation for repeating the analysis at the next higher level such as illustrated in Fig. 3.2. Note that the effect of assessment at a higher option on the final conservatism of the SINTAP/FITNET analysis does depend on the ligament yielding parameter Lr (for definition see Section 5.2). This will be discussed in Section 6.14.

24


Only σY (Re or Rp0.2) available

σY and Rm available

Option 0

yes

no

Safe service?

Strength mismatch?

no

yes

Option 1 (∗)

Option 2 (∗)

yes

Safe service? no Option 3 (∗∗)

(∗) σ and Y

Rm have to be available

(∗∗)

yes Safe service? no

Complete stress-strain curve has to be available

Complete FEM analysis yes Safe service?

Component is safe!

no

Component is not safe!

Figure 3.2: Multi-optional assessment concept of SINTAP/FITNET.

3.4. FAD Versus CDF Analyses The terms FAD and CDF analysis and their scientific and historical backgrounds have already been introduced in Sections 2.4 and 2.5. In the FAD approach, a roughly geometry-independent failure line is constructed by normalising the crack driving force by the material’s fracture resistance. The assessment of the component is then based on the relative location of a geometry-dependent assessment point with respect to this failure line. In contrast to this, in the CDF philosophy the applied and material sides are strictly separated. The determination of the


25

crack driving force in the component, and its comparison with the fracture resistance of the material, are two separate steps. Note that both analysis types are harmonised with each other in the SINTAP/FITNET procedure. In other words, FAD and CDF lead to identical results. Whether to follow an FAD or a CDF philosophy is merely a matter of personal preference and not of importance for the correctness of the results. More detailed guidance on FAD and CDF analyses including worked examples will be provided in Chapter 6.

3.5. Integrated Concept As mentioned above, the fracture of a specimen or component can occur by different mechanisms such as • cleavage fracture, • micro-ductile fracture or • plastic collapse. While these possibilities have explicitly to be taken into account in the determination of the fracture toughness of the material, they are covered by the same set of equations f(Lr ) for the crack driving force in SINTAP/FITNET, see Fig. 3.3. There is no need to determine whether a cracked component operates in small-scale yielding, net-section yielding or in the plastic-collapse regime (for a definition of these terms see the Glossary “crack tip plasticity”). This is of great benefit since this distinction would be much more complicated for a component than for a test specimen. Another aspect of the integrated concept is that the FITNET document provides a number of extensive annexes with solutions for input and model parameters Small-scale yielding 1

Contained yielding Net-section yielding Plastic collapse

f (Lr)

Lr = F/FY = σref /σY

1

Lrmax

Figure 3.3: Ligament yielding ranges covered by SINTAP/FITNET.

26


such as stress intensity factors, yield loads, welding residual stress profiles, stress magnifications due to misalignment and constraint parameters for a wide range of component geometries. These solutions make it possible, in many cases, to perform SINTAP/FITNET analyses without consulting additional sources. In Fig. 3.4 only those annexes are included which are of importance for the topic of this book. Annex A: Stress intensity factor (SIF) solutions Flat plates with and without hole Round bars and hollow cylinders Nozzles Welded joints Through thickness cracks Embedded cracks Extended and semi-elliptical surface cracks Corner cracks Annex B: Yield load solutions Flat plates with and without hole Round bars and hollow cylinders Welded joints (with and without strength mismatch) Tubular joints Through thickness cracks Embedded cracks Extended and semi-elliptical surface cracks Annex C: Welding residual stress profiles Plate and pipe butt welds Plate and pipe T-butt welds Set-in nozzles Repair welds Surface profiles Through thickness profiles Longitudinal and transverse profiles Annex I: Bending stresses due to misalignment Axial and angular misalignment Ovalisation Flat plates and hollow cylinders Butt and fillet welds Annex K: Input for constraint analysis T stress and β solutions Flat plates and hollow cylinders

Figure 3.4: FITNET annexes containing compendia of solutions needed for fracture analysis.


27

A further annex (Annex L) provides the user with literature sources in which information on material properties can be found. Tables of specific values that are required for use in conjunction with the SINTAP module, as sometimes given in industry-specific documents, are avoided. Instead, the user is referred to conservative estimates based, for example, on Charpy information. At this point a warning is advisable with respect to literature data on fracture toughness. The user should always be aware that toughness values are much more sensitive to even minor changes in the microstructure than strength properties or the Paris constants of a da/dN-K curve. An example is that structural steels of identical yield or tensile strengths, which comply with the same manufacturer’s specification, can show quite different fracture resistance and this is even the case for materials that undergo heat treatment by the final producer. Data compendia do, however, make sense in specific industries where a limited variability of materials is used and where the materials are subject to strict input quality control.


Chapter 4

The Input Parameters 4.1. Loading Input Parameters 4.1.1. General Considerations All relevant loads have to be taken into account in a SINTAP/FITNET analysis. These may include: • • • •

Applied service loads such as external forces, moments or pressure, Dead weight and inertia loads, Thermal stresses Residual stresses.

The loads can be available as forces, moments or pressure, or as stress profiles across the section of the component. The latter may be obtained by numerical analysis techniques or handbook solutions. The stress profiles used in SINTAP/FITNET analysis Options 0 to 3 refer to the uncracked geometry and are commonly available from conventional strength analyses. Note, however, that caution has to be exercised for structures with multiple load paths, as the failure of one load path will affect the stress distribution on the remaining uncracked path(s).

4.1.2. Primary and Secondary Stresses In the analyses, the stresses are categorised as primary or secondary. As a rule, primary stresses arise from the applied mechanical load, including any dead weight or inertia effects, whilst secondary stresses result from suppressed local distortions, for example during the welding process, or are due to thermal gradients. Secondary stresses are self-equilibrating across the structure, so that net force and bending moment are zero. This separation is necessary because primary stresses contribute to plastic collapse but secondary stresses do not. As a consequence, the K-factor determination is based on both primary and secondary stresses, whereas only the primary stresses are taken into account for the determination of the yield load, FY (or the reference stress ref or ligament yielding factor Lr respectively, see Section 6.6).

30


Note, however, that categorisation is not always straightforward because secondary stresses, which are self-equilibrating in the whole structure, will not always be self-equilibrating on the section containing the crack. Caution has to be exercised when the crack is small compared to the spatial extent of the secondary stress distribution, or in cases with significant elastic follow-up from the rest of the structure. If it is uncertain whether a stress is primary or secondary, its treatment as primary is conservative.

4.1.3. Definition of the Stress Profile for Use with the K-Factor The stress profile can be approximated by a polynomial expression or it can be linearized. If possible, the former method is to be preferred. However the solution that will be finally applied depends on the available K-factor expression for the case under consideration. (a) If the uncracked structure stress distribution x in the thickness direction is available, from, for example, a finite element analysis, this can be represented by a polynomial x/t =

n

i x/ ti = o + 1 x/ t + 2 x/ t2 + · · · + n x/ tn

(4.1)

i=0

with n being the order of the polynomial, t the wall thickness and x the distance from the surface through the thickness of the component (Fig. 4.1). Polynomial expressions of the stress distribution can be used, for example, in conjunction with weight function solutions to determine the K-factor. K solutions of that type are usually based on third- to sixth-order polynomials. Note that the quality of a polynomial approximation should always be tested (e.g., by eye). Example 4.1: A stress profile across the wall of a component is provided in Table 4.1. The approximation by Eqn (4.1) gives polynomials, for example, Third order:

x t

in MPa = 22883 − 68758 · + 90513 ·

x 2 t

x t

− 41958 ·

x 3 t

The Input Parameters

Sixth order:

x t

in MPa = 23009 − 59856 · + 637755 ·

x t

x 3

− 58350 ·

31

x 2

t x 4

− 12 89693 · t t x 5 x 6 + 10 86727 · − 3 36601 · t t The eye check of Fig. 4.1 shows that both expressions describe the empirical stress distribution well. In this case it is more convenient to use the lower-order polynomial for the further analysis. 300

Sixth order polynomial Third order polynomial

Stress in MPa

250

200 x t

150

100

50

0

0

0.2

0.4

0.6

0.8

1

x /t

Figure 4.1: Example 4.1: Approximation of the empirical stress profile of Table 4.1 by third and sixth order polynomials. Table 4.1: Example 4.1: Empirical stress profile across the wall of a component, for example as the result of a finite element analysis x/t

Stress perpendicular to the assumed crack plane in MPa

x/t


x/t


0.0 0.1 0.2 0.3

230 170 120 90

04 05 06 07

73 63 55 46

08 09 10

40 34 30

32


For hollow cylinders it is common to present the stress distribution as a combination of a local non-linear stress distribution and a global bending stress bg obtained as the quotient of bending moment, Mb , and section modulus, Wb x =

n

i x/ti + bg =

i=0

n

i x/ti + Mb Wb

(4.2)

i=0

An example for this type of approximation is provided in Fig. 5.3. First, the global bending stress bg has to be subtracted from the finite element distribution and then the remaining profile is fitted by the polynomial. An example will be provided in Section 5.1.2.2. If the stress profile across the wall is available from a finite element analysis, but only a K solution is available for linear stress profiles in terms of membrane and bending stress components, m and b , the stress profile has to be approximated by a straight line over the position of the crack. The principle is illustrated for surface and embedded cracks in Fig. 4.2.

Stress

Empirical stress distribution Fitted stress distribution σ1 Stress

σ1

σ2

σ2

Potential crack

Potential crack

t

t

Figure 4.2: Stress linearisation for the determination of membrane and bending stress components.


33

From the stresses at both surfaces, 1 and 2 , the membrane and bending stress components, m and b , can then be determined by m = 05 · 1 + 2

(4.3)

b = 05 · 1 − 2

(4.4)

and Example 4.2: The empirical stress profile of Example 4.1 is used to obtain the membrane and bending stress components for a relative crack size of a/t = 03. The procedure is illustrated in Fig. 4.3. With 1 = 230 MPa and 2 = −23667 MPa the stress components are determined as m = −334 MPa and b = 23334 MPa 300 250 σ1 = 230 MPa 200 x t

150

Stress in MPa

100 50

Potential crack

0 – 50 – 100 – 150 – 200 σ2 = – 236.67 MPa – 250

0

0.2

0.4

0.6

0.8

1

x /t

Figure 4.3: Example 4.2: Stress linearization. Determination of the 1 and 2 stresses.

34


Note that polynomial and linearized stress profiles will frequently be used in conjunction with substitute geometries for K-factor determination. This means that the stress profile will be determined – usually by finite element analysis – for the component section to be assessed. It can then be approximated as described above and finally used as input to a K solution for a substitute geometry, such as a plate or a cylinder (Fig. 4.4). The component to be assessed and the substitute geometry should not be too different with respect to their stiffness. If the component is stiffer than the substitute geometry the resulting K-factor will be over-estimated and, thus, conservative. According to Fig. 4.2 and Eqns (4.3) and (4.4), a special feature of the membrane and bending stress components is their dependency on the crack length. In Example 4.2, the bending stress will become smaller and the membrane stress larger for a crack size greater than the assumed a/t = 03. Note that this is in contrast to the conventional definition of the stress components m = F/A

and

b = Mb /Wb

(4.5)

Component A A t

x

t

x A

A Stress distribution in section A-A

x

x=0

x=t

x

x=0

x=t

Approximation of the stress field by a polynomial or linearly Determination of the K-factor for a substitute geometry t

t

Figure 4.4: Determination of K-factors using substitute geometries.


35

with F being the tensile force, A the cross section area, Mb the bending moment and Wb the section modulus. A number of K solutions available in the literature and in compendia are also based on the conventional definition. The type of specific K solution to be applied defines which m and b are relevant for an individual application. For a linear stress distribution across the section of a component without a geometric discontinuity, the use of the polynomial approximation (Eqn 4.1), the straight-line approximation (Eqns 4.3, 4.4) and the definition according to Eqn (4.5) will yield identical results. In this case the 0 and 1 terms of the polynomial refer to the membrane and bending stress components, m and b . For a non-linear stress distribution the linearization technique will usually tend to be more conservative than the polynomial approach, slightly overestimating the resulting K values. An example for this effect is provided in Section 5.1.2.4.

4.1.4. Definition of the Stress Profile for Yield Load Determination Yield load (FY ), reference stress (ref ), or ligament yielding parameter (Lr ) solutions are sometimes based on bending and membrane stress components. Note, however that the m and b used for determining the yield load are different from those used for determining K as described in Section 4.1.3. In general they are obtained by m =

1 t dx t 0

(4.6)

and 6 t t b = 2 − x dx t 0 2

(4.7)

If the stress profile is available as a sixth-order polynomial (Eqn 4.1), m and b , can be solved as 1 1 1 1 1 1 m = 0 + 1 + 2 + 3 + 4 + 5 + 6 2 3 4 5 6 7

(4.8)

1 1 9 2 5 9 b = − 1 − 2 − 3 − 4 − 5 − 6 2 2 20 5 14 28

(4.9)

If the polynomial is lower than sixth order, the superflous i coefficients are simply set to zero, for example, for a third degree polynomial 4 = 5 = 6 = 0.

36


Example 4.3: The empirical stress profile of Example 4.1 is used to determine m and b for yield load determination. With the polynomial coefficients of Example 4.1 the results are Third-order polynomial: m = 8185 MPa and b = 8003 MPa, Sixth-order polynomial: m = 8166 MPa and b = 8066 MPa. Note that the m and b stress components used for yield load determination deviate significantly from those used for the K-factor determination (m = −334 MPa and b = 23334 MPa) obtained in Example 4.2.

4.2. Flaw Characterisation 4.2.1. Planar and Volumetric Flaws Flaws can be planar or non-planar/volumetric. Planar flaws are cracks, laminations, lack of fusion in welds, undercuts, sharp groove-like localised corrosion, branch-type cracks due to environmental effects, etc. Volumetric flaws are, for example, cavities, aligned porosity, solid inclusions and local thinning as a consequence of corrosion. Planar flaws are generally treated as cracks, but the decision as to when a volumetric flaw should be treated as a crack is rather complicated and has to include the user’s experience of the structure under consideration. It should be taken into account that non-destructive examination might not be sensitive enough to find out whether or not microcracks have initiated from a volumetric flaw. The following discussion refers to cracks and crack-like flaws.

4.2.2. Basic Crack Types Flaw characterisation means that an existing or postulated crack is modelled by a simpler geometry such as a through crack with a straight crack front, an embedded crack with elliptical shape or a surface crack with a semi-elliptical shape. The basic types of idealised planar flaws are given in Fig. 4.5. Note that for throughwall crack configurations the nomenclature a or 2a is sometimes used instead of 2c, for example, in conjunction with strength mismatched configurations as in Sections 5.2.6 and 6.11.

4.2.3. Crack Shape Idealisation Crack shape idealisation becomes necessary when real cracks have been detected during an inspection. Idealisation means that a flaw or crack with a complex


37

shape is modelled as one of the basic crack types shown in Fig. 4.5, but with conservative dimensions, so that the idealised crack geometry should be more severe that the actual one. The principle is shown in Fig. 4.6 in which the idealised cracks are characterised by the containment rectangles of the actual cracks.

Surface crack

Through wall crack

Edge crack

a 2c

2c

c

Corner crack

Embedded crack 2a

a c

2c

Figure 4.5: Basic types of planar flaws.

a

a 2c

2c

2c

2c

c

c

a

a c

c

2a

2a 2c

2c

Figure 4.6: Idealisation of detected planar flaws for a SINTAP/FITNET analysis.

38


4.2.4. Interaction Effects of Multiple Cracks 4.2.4.1. Alignment Criteria Multiple cracks can be coplanar or non-coplanar. Non-coplanar cracks under mode I loading tend to shield one another, their K factors being reduced relative to those of the single cracks. In most cases, therefore, the interaction of noncoplanar cracks is of little concern for an assessment that has the aim of being conservative. Exceptions are closely spaced non-coplanar cracks that are aligned to the same cross section. The SINTAP/FITNET criterion for this is based on spacing between the cracks H ≤ min 2a1 2a2 for embedded cracks (Fig. 4.7a) and H ≤ min 2a1 a2 for surface and embedded cracks (Fig. 4.7b) Note that the flaw alignment criteria are based on the maximum principal stress plane. 4.2.4.2. Combination Criteria If coplanar cracks, that is, multiple cracks on the same cross section, are in close proximity to one another, they may show some interaction effects that make them more serious than the individual cracks. In such cases, rules are given (a)

(b)

Plane normal to the maximum principal stress

Plane normal to the maximum principal stress

2a1

2a1

Crack 1

Crack 1 Crack 2

Crack 2

2a2 H

a2 H

Figure 4.7: SINTAP/FITNET flaw alignment criteria – (a) Embedded cracks; (b) Surface and embedded cracks.


39

in SINTAP/FITNET to decide when they have to be combined and treated as one single crack whose dimensions encompass the individual cracks. After the correction is done, usually no further interaction between the obtained effective cracks has to be considered. If the spacing between coplanar cracks is sufficient to avoid interaction, they are treated individually. Only the worst-case crack needs to be considered in a fracture analysis. No complete overview will be given here on the SINTAP/FITNET interaction rules. Fig. 4.8 shows some examples for illustrating the principle. With the terminology of Fig. 4.8, interaction has to be assumed for s ≤ min 2c1 2c2

s ≤ max 05a1 05a2

or

for a1 /c1 or a2 /c2 > 1

otherwise s ≤ max 05a1 05a2 in Fig. 4.8 (a) and for s ≤ a1 + a2 in Fig. 4.8 (b). The reason why interaction effects have to be taken into account is that the local stress field at the tip of a crack controls the crack driving force and this can be significantly affected by adjacent cracks. In the case of coplanar cracks, the interaction criteria are defined for a maximum tolerable increase in the crack driving force. Since “maximum tolerable” is a term open to discussion, slightly different interaction criteria are adopted by various documents. An overview on the criteria of ASME, BS 7910, API 579 and SINTAP is provided in [4.1]. The interaction rules discussed so far consider only elastic behaviour. It has, however, to be expected that in the net-section and gross-section yielding regimes

(a)

a2

a1 2c1 s (b)

2c2

max(a1, a2 ) 2c1 + 2c2 + s

2c1

2a1

s

2a2 2c2

2a1 + 2a2 + s

max(2c1, 2c2 )

Figure 4.8: Interaction rules for co-planar flaws – (a) Surface cracks; (b) Embedded cracks.

40


the magnitude of the interaction effect will also be affected by the plastic deformation pattern. Therefore, SINTAP/FITNET provides a separate rule for situations where failure by brittle fracture can be excluded. A maximum crack length 2cgsY is determined for a rectangular surface crack of a depth amax which refers to the crack depth of the deepest single crack: 2cgsY =

1 − Y /Rm W · t · 1 + Y /Rm amax

(4.10)

Equation (4.10) is obtained for a flat plate of width W and thickness t and gross-section yielding conditions; the plastic deformation is not confined to the crack plane but also includes the remote cross section. For large plates (W > 300 mm), an effective W has to be specified based on experience or experiments. A correction for interaction has to be carried out for cracks the spacing of which is s≤

1 + Y /Rm 2ci − 2cgsY 2 · Y /Rm

(4.11)

where i is a counter variable for multiple cracks. For plates showing strength mismatch, the mismatch ratio M plays an additional role (for strength mismatch see Section 6.11.1). Equation (4.10) is then modified by 2Y /Rm B W·t 2cgsY = 1 − · (4.12) M · 1 + Y /Rm

amax with M being the yield strength mismatch ratio YW /YB (W = weld metal; B = base plate).

4.2.5. Crack Re-characterisation Crack re-characterisation means that an embedded or a surface crack is recharacterised as a surface or through-wall crack respectively, as shown in Fig. 4.9. There are cases where local failure is calculated in the ligament(s) ahead of the embedded or surface crack but, when the crack is re-characterised as a (larger) surface or through-wall crack, the component is predicted to be globally safe. If this condition is given, the failure analysis can be based on the re-characterised surface or through-wall crack. Allowance has, however, to be made for dynamic effects combined with a certain amount of additional crack growth at the surface for the break-through event. This is covered by adding a crack portion 2a + p in Fig. 4.9 (a) and t in Fig. 4.9 (b). If the ligament failure is predicted to be brittle,


41

(a)

2a

2a + p

2c

p

2c + 2a + p

(b) t

2c

2c + t

Figure 4.9: Crack re-characterisation in general application – (a) embedded crack; (b) semi-elliptical surface crack.

the fracture resistance used in the assessment of the re-characterised crack should be the dynamic or crack arrest toughness. Special care should be exercised for cases of large difference between static and dynamic toughness [4.2]. Note that, when it is used for assessing leakage rates, crack re-characterisation is also required in conjunction with a leak-before-break analysis. This information may be necessary to specify the time between the break-though of the crack and the detection of the leak. In this context, conservative assessment means an overestimation of this time span, which refers to an underestimation of the leakage area defined by the crack dimensions at break through. As a consequence, the crack size immediately after leakage should be modelled as realistically as possible and not potentially overestimated, as in Fig. 4.9. The SINTAP/FITNET recommendations for crack re-characterisation for leak-before-break are shown in Fig. 4.10.

4.2.6. Crack Orientation and Projected Crack Depth Frequently, cracks are oriented along a plane normal to the maximum principal stress direction – mode I crack opening. Even if they initially grow in another orientation, they will turn to mode I during further extension. Therefore, as a rule, a postulated crack will be aligned with the principal stress axes in cases where there is no clear indication of mixed mode loading, as described below. If the orientation of a real crack deviates from the mode I plane it can be projected onto the principal plane referring to the maximum principal stress.

42


after break-through c

at break-through (local instability) tensile loading t 2c

2c + t t

through-wall bending t 2c

2c + t

Figure 4.10: Crack re-characterisation in leak-before-break application. σ1

2c0 σ2

2c2

β

σ2

2c1

σ1

σ1

a

σ1

Figure 4.11: Simplified projection method for cracks not oriented on a principal plane (according to [4.1]).

A simple method for this is shown in Fig. 4.11. The projected crack depth, a, is given in the figure and the projected crack length, c, can be determined by √ √ c for 1 c1 ≥ 2 c2 √ √ c= 1 (4.13) c2 for 1 c1 < 2 c2 This simple solution can, however, yield non-conservative estimates in some cases. As an alternative, an approach based on energy release rate considerations is presented in [4.1] although it will not be described here in detail. The author gives an approximate solution for biaxial loading as c/co = cos2 + 05 1 − B sin cos + B2 sin2

(4.14)


for cracks projected to the maximum principal stress (1 plane, and

c/co = 1/B2 · cos2 + 05 1 − B sin cos + sin2

43

(4.15)

for cracks on the 2 principal stress plane, with B being the biaxiality ratio defined as B = 2 /1

for 2 > 1

(4.16)

In Eqns (4.14) and (4.15) the crack length c corresponds to half flaw length as shown in Fig. 4.11, or to the total length in the case of edge or corner cracks. Note that Eqns (4.14) and (4.15) are valid only if both principal stresses are positive. If 2 is negative (compressive), B should be set to zero and Eqn (4.14) should be applied [4.3, 4.4]. A conservative option is to set the equivalent crack size c equal to the measured crack size co irrespective of the crack orientation. The projection of a crack to the mode I plane is not admissible [4.5] when • the angle between the principal plane and the plane of the actual flaw exceeds a value of 20 , • there is only a small difference between the stress intensity factors on the planes of projection, • the maximum stress intensity factor and the maximum limit load belong to two different projection planes, • one of the principal stresses is significantly compressive, where significant means of an order similar to the maximum-principal stress. In such a case, a mixed-mode analysis should be performed taking into account the shear stresses as well. Guidance on this is given in Section 6.8.

4.3. Deformation Characteristics of the Material 4.3.1. General Remarks As with other material properties, tensile data should be obtained for the specific material and batch, in the correct product form and, if possible, at the relevant temperature and loading rate. If there is any indication of a possible change or degradation in properties as a result of ageing over the lifetime of the component, or as a consequence of a fabrication process, then this has to be taken into account. In some cases, such as rolled material, the specimen orientation can affect the tensile data. Usually, lower bound values of the yield strength and tensile strength

44


have to be used for an assessment. There are, however, exceptions that will be explained in the corresponding sections below. It has already been mentioned in Section 3.3 that the SINTAP/FITNET procedure is organised in different analysis options mainly with respect to the quality and completeness of the tensile data.

4.3.2. Engineering and True Stress-Strain Curve Both engineering and true stress-strain curves are used in a SINTAP/FITNET analysis. Based on the engineering curves, the yield strength Y and the ultimate tensile strength Rm are required for Option 1 and Option 2 analysis whereas the complete true stress–strain curve is used for Option 3 analysis. Finite element analyses in fracture mechanics contexts are usually based on true stress–strain curves. The true stress and strain data, t and t , can be determined from the engineering data, and , using: t = 1 +

(4.17)

t = ln1 +

(4.18)

and

Because Eqns (4.17) and (4.18) are based on the assumption of a homogeneous strain distribution along the gauge length of the tensile specimen, these equations are applicable only up to the onset of necking. Beyond this, the true stress can be determined from measurements of the actual cross section diameter in the necking region. In addition, since the neck – which by its nature is a notch – introduces a complex triaxial stress state, a further correction, such as the “Bridgman correction”, is needed to provide an estimate of the uniaxial stress that would exist if no necking took place. The relation between the engineering, the true, and the Bridgman corrected true stress–strain curves is schematically illustrated in Fig. 4.12.

4.3.3. Modulus of Elasticity (Young’s Modulus) and Poisson’s Ratio Young’s modulus and Poisson’s ratio values are also required for the temperature relevant to the component analysis to be carried out. Compendia can be used if no individual values are available; some approximate values are provided in Table 4.2 [4.6].


45

Stress

Ultimate tensile strength

Yield strength

True curve (correction for necking) True curve (no correction for necking) Engineering curve

Strain

Figure 4.12: Schematic comparison of engineering and true stress–strain curves. Table 4.2: Approximate values of Young’s modulus and Poisson’s ratio for various classes of materials (taken from [4.6]) Material Temperature Ferritic steels Steels with c. 12% Cr Austenitic steels Aluminium alloys Titanium alloys

Modulus of Elasticity, GPa

Poisson’s ratio

20 C

200 C

400 C

600 C

20 C

211 216 196 60−80 112−130

196 200 186 54−72 99−113

177 179 174 − 88−93

127 127 157 − 77−80

c. 0.30 c. 0.30 c. 0.30 c. 0.33 0.32−0.38

4.3.4. Yield Strength and Tensile Strength Note that, in SINTAP/FITNET, the yield strength of the material is designated by the general term Y . However, with respect to specific applications, it has different meanings varying from case to case. For materials with continuous yielding, that is, without yield strain (Lüders’ strain), Y refers to the proof strength of the material, Rp 02 , which is defined for a plastic strain of 0.2%. For materials showing a yield plateau, it refers to the lower yield strength ReL . For Option 0, 1 and 2 analyses, instead of the individually determined yield strength, specified minimum values given by manufacturer’s standards are acceptable. However, care should be taken as either the lower or upper yield plateau, ReL and ReH , can be quoted on test certificates, although it is usually the latter value. Therefore, in order to avoid non-conservatism, the value provided should

46


be factored by 0.95 when applied to the determination of the yield load FY (or ref or Lr respectively), unless it is certain that the data refer to the lower yield plateau. Note that, in the SINTAP/FITNET procedure, conservatism of the yield strength – and ultimate tensile strength – is defined quite differently depending on its use in the analysis. For determining FY , ref or Lr , conservatism is given by lower bound values. However, for estimating welding residual stresses (Section 6.6.4), conservatism refers to upper-bound values. Special care should be exercised for leak-before-break analyses where the conditions of conservatism can be very complex. Another case where upper-bound values are required is the estimation of a maximum critical crack size after an overload or proof test. In one special case – for estimating welding residual stress profiles – Y is defined as the room temperature proof strength for a strain of 1% for austenitic steels or, if this is not available, as 1.5 Rp02 . For the definition of mismatch ratio, M, the mean values of Y are used for both weld and base materials. In cases in which more than one measurement of Y is available, the lowest or highest value has to be chosen depending on what is conservative for that specific application.

4.3.5. Flow Stress The so-called flow stress, f , can be understood as an effective yield strength taking into account strain hardening. In the SINTAP/FITNET procedure it is defined as f = 05Y + Rm

(4.19)

Because the definition of f is somewhat arbitrary, variations of this definition are used in the literature and some other flaw assessment procedures. In the context of SINTAP/FITNET, only the specification according to Eqn (4.19) is permitted. For definition of the cut-off, Lr max , mean values of f and Y are used.

4.3.6. Strain Hardening Coefficient In general, the strain hardening coefficient N (0 > N > 1) is defined as the slope of the plastic branch of the stress–strain curve, when plotted in double-logarithmic co-ordinates. Based on this, the SINTAP procedure uses a conservative estimate, given by

N = 03 1 − Y (4.20) Rm


47

Strain hardening exponent N

0.4

Lower bound curve 0.3

0.2 0

0.1

0 0.6

0.7

0.8

0.9

1

σY/Rm

Figure 4.13: Derivation of the SINTAP/FITNET lower bound equation for the strain hardening coefficient N.

Equation (4.20) was obtained as a lower-bound curve (Fig. 4.13) to a large data set of individually determined N versus Y /Rm pairs. This set was based on a wide range of steels with yield strengths between 300 and 1,000 MPa and Y /Rm ratios between 0.65 and 0.95, although data from some aluminium alloys, brasses and nickel alloys were also included. Nevertheless, the general application to nonferrous materials should be treated with caution. Note, however, that if structures made of materials for which Eqn (4.20) is potentially not applicable have to be assessed, the general definition for determining N as the slope of the doublelogarithmic plotted plastic branch of the true stress–strain curve can still be used. The same type of approach is recommended by the authors of the present book for cases where an upper-bound N is needed for reasons of conservatism, as in the context of a proof test, although using a factor of 0.5 instead of 0.3 in Eqn (4.20) provides a mean fit to the data. Alternatively, Fig. 4.13 could be used to derive an upper-bound curve. Note that a number of further definitions of the strain hardening exponent are used in the literature. Although the parameter is commonly also designated as N or n, the values may strongly diverge so no use should be made of N values provided in external sources unless it can be demonstrated that the basic definition is compatible with SINTAP/FITNET or, at least, conservative with respect to this.

4.3.7. Yield Strain (Lüders’ Strain) In Option 2 and 3 analyses materials with and without yield strain must be identified. In many situations the data will be complete enough to establish the

48


yielding characteristics, but there are other cases where this may not be so. For structural steels, some indication can be obtained from the yield strength, the composition of the material and the process route. Guidance for the decision as to whether a yield plateau is expected or not is given in Table 4.3, in which the factors mentioned have been grouped according to standard specifications. It should, however, be recognised that the presence of a yield plateau is affected not only by the material and its test temperature, but also by the test method, the loading rate and the specimen design. Table 4.3 applies only to the steels listed. For other materials, the yielding behaviour should be individually established. If there is some doubt regarding whether a material shows a yield plateau or not, it is usually conservative to assume its presence. Again, exceptions are proof test and (partly) leak-beforebreak applications. If no individual measurements of the Lüders’ strain are available, a conservative estimate can be made using: 003751 − 0001 ReH for ReH ≤ 1000 MPa (4.21)

= 0 for ReH > 1000 MPa As in the case of the strain hardening coefficient in Eqn (4.20) the general solution for the Lüders’ strain was obtained empirically, but as a best fit to the data. Nevertheless, the solution is assumed to be conservative in many cases, since the Lüders’ strain is known to be smaller or even to disappear in large-scale tests, in particular in the presence of bending stress components.

4.3.8. Tensile Data Relevant to Welds In the case of weldments where the difference in yield strength between the base material (denoted B) and the weld metal (denoted W) is greater than 10%, strength mismatch effects have to be taken into account in the SINTAP/FITNET procedure. Guidance on how to do this is given in Section 6.11. Complete stress– strain curves for both materials have to be available for Option 3 analyses. For Option 2 analyses only the yield and ultimate tensile strength values of these materials are required. Local stress-strain curves can be obtained by mini-tensile tests [4.7, 4.8]. No detailed discussion on these types of test is provided here. Note, however, that care should be taken to avoid any affect of the machining procedure on the measured load-deformation curves. Care should also be exercised when mini specimens of rectangular cross sections are used, since the yielding pattern across the section differs from that of a circular cross section and this may affect


49

Table 4.3: Guidance for determining whether a yield plateau should be assumed Yield strength range (MPa) ≤350

Process route As–rolled

Normalised

>350 ≤500

NA

Yes

Mo, Cr, V, Nb, Al or Ti present

NA

No1

EN 10025 type compositions without microalloy additions

Conventional normalising

Yes

EN 10113 type compositions with microalloy additions

Conventional normalising

Yes

EN 10113 compositions

Controlled Rolled

EN 10113 compositions

Quenched & Tempered

As-Quenched

Assume yield plateau?

Heat treatment aspects

Conventional steels (e.g. EN 10025 grades) without microalloy additions

Controlled Rolled

Quenched & Tempered

>500 ≤1050

Composition aspects

—

Yes

Light TMCR schedules2 Heavy TMCR schedules3

Yes

Mo or B present with microalloy additions Cr, V, Nb or Ti

Heavy tempering favours plateau

Yes

Light tempering favours no plateau

Yes1

Mo or B not present but microalloying additions Cr, V, Nb or Ti are (V particularly strong effect)

Heavy tempering

Yes1 No1

Mo or B present with microalloy additions Cr, V, Nb or Ti

Tempering4

Light tempering

5

Tempering

Yes1

No1 No

Mo or B not present but microalloy additions Cr, V, Nb or Ti are

Tempering4 Tempering5

Yes No1

All compositions

NA

No

1) uncertain; 2) Y < 400 MPa; 3) Y > 400 MPa; 4) to Y < ∼690 MPa; 5) to Y ≥ ∼690 MPa.

50


the result at higher strains. A hybrid method consisting of measurements and finite element simulations is provided in [4.9]. Usually, lower-bound material tensile properties should be used for both base material and weld metal. It should, however, be kept in mind that the real strength of the material may deviate significantly from the specified minimum for the grade of material, so that the real yield strength of the material is frequently higher than required. Note that for the definition of mismatch ratio, M, the mean values of Y are used for both weld and base materials as stated before. It should also be kept in mind that weld tensile properties may vary through the thickness of a component and may be dependent on the specimen orientation. The tensile properties used should be the lowest (or highest) within the weld, irrespective of orientation and position, in order to provide conservative results.

4.3.9. Temperature and Strain Rate Dependency For situations in which the operating temperature is below room temperature but only the room temperature yield strength is available, the yield strength may be estimated by YT = YRT +

105 − 189 MPa 491 + 18 T

(4.22)

with Y given in MPa, T being the temperature of interest in C and RT being the room temperature. The strength parameters of ferritic or bainitic steels tend to increase with increasing loading rate and hence, in general, the use of quasi-static tensile properties will yield conservative results. Care should, however, be exercised for materials showing dynamic strain aging effects.

4.4. Toughness Characteristics of the Material 4.4.1. General Remarks Instructions on the determination of the fracture toughness are not part of the SINTAP/FITNET procedure. For these the user is referred to existing test procedures and standards, a list of which is given in the Appendix “Fracture Toughness Test Standards”. The information provided in this section is restricted to statistical and transferability aspects of fracture toughness, which, within SINTAP/FITNET, are generally designated by an index “mat”, although it refers to different meanings in


51

different applications, for example, resistance against cleavage, resistance against ductile crack initiation or resistance against ductile tearing (R-curve). The toughness data should, wherever possible, be obtained for the specific material and batch, in the correct product form, and at the relevant temperature and loading rate. Additionally, the orientation of the test specimens should correspond to the flaw orientation in the structure unless it can be shown that the specimen orientation does not affect the toughness. Particular attention should be paid to the size and number of specimens. In cases in which it is not possible to meet the component conditions, the data should be conservative with respect to the SINTAP/FITNET analysis. In most cases “conservative” means either lower-bound values, or a relatively small percentile value if a complete statistical analysis is performed. An upper-bound toughness value has to be used to specify the maximum crack size after a proof test. Note that, although in principle possible, the use of fracture toughness data from the open literature or from compendia should be exercised with care because toughness data may be much more sensitive than strength data to even minor changes in the manufacturing process, or to a particular fabrication route for a component.

4.4.2. The Fracture Toughness Transition Curve Materials with body-centred cubic and hexagonal lattices, such as ferritic and bainitic steels, show a transition behaviour from cleavage fracture at low temperatures to micro-ductile fracture at high temperatures. A schematic drawing is provided in Fig. 4.14. It is characterised by a very wide scatter band in the

Fracture Resistance

micro-ductile tearing + final cleavage

ductile-brittle transition

upper shelf

stable ductile crack initiation

cleavage

lower shelf Temperature

Figure 4.14: Ductile-to-brittle transition in ferritic or bainitic materials.

52


ductile-to-brittle transition range, as compared to rather moderate scatter bands in both the lower and the upper shelf. Most other materials, including austenitic steels, with face-centred cubic lattice will not fail by cleavage and, therefore, do not show such a transition behaviour. Note that the designation “cleavage” and “microductile” refers to microscopic fracture mechanisms and should not be mixed up with macroscopic features such as “brittle” and “ductile” or “flat” and “slant”. Although brittle fracture characterised by a flat fracture surface will frequently refer to cleavage, it can also occur in materials that do not fail by cleavage but are micro-ductile. When, following the common designation, the term “ductile-to-brittle transition” is used in this section, it should be kept in mind that “microductile-to-cleavage transition” is meant. In Fig. 4.15 the most frequently used fracture toughness parameters are summarised with respect to the toughness-temperature transition curve (of ferritic materials) and the force-displacement diagram of the test record. The parameters describe stable crack extension as well as unstable fracture. “Stable” means that the specimen fails only when the applied load is increased. In contrast, “unstable” means specimen failure will occur in any case, even if the load is kept constant or decreased. The failure of a specimen or component in a stable or unstable manner depends on a number of factors, including the material, the temperature and loading rate and whether loading is applied using a load controlled or displacement controlled regime. Information on whether a component will potentially fail in an unstable manner or not cannot, therefore, simply be taken from the record of a laboratory test.

lower shelf

ductile-brittle transition

upper shelf

δu Ju δ-Δa curve J-Δa curve δc KIc

Jc

δuc Juc

Temperature

δ0.2 /BL

δu Ju δuc Juc Force

Fracture Toughness

(a) Fracture parameters for unstable crack extension – As long as the forcedisplacement record is essentially linear up to unstable fracture, a plane strain fracture toughness KIc is determined. If it is non-linear prior to unstable fracture,

δc Jc

J0.2 /BL δ0.2 J0.2

KIc

δ0.2 /BL δ0.2 J0.2 /BL J0.2

Displacement

Figure 4.15: Fracture parameters relevant to temperature effects of ferritic and bainitic steels and to a force displacement diagram [4.10].


53

but the stable crack extension including blunting is less than 0.2 mm, the parameters c and Jc are determined at the point of instability. This type of test record is usually obtained in the ductile-to-brittle transition range. If stable crack extension exceeds 0.2 mm prior to unstable fracture the parameters will be designated as u and Ju . This is usually associated with a material condition close to the upper shelf. If the amount of stable crack extension prior to unstable fracture is unknown the fracture parameters are designated as uc and Juc . (b) Fracture parameters for stable crack extension – The parameters 02/BL and J02/BL characterise the resistance against stable crack initiation. They are, however, based on the pragmatic definition of the material resistance at a value of 0.2 mm stable crack extension, excluding the crack extension due to blunting. This definition, on the one hand, allows easy and accurate measurements of crack extension and, on the other hand, is still close enough to the “real” crack initiation. In contrast to this, the parameters 02 and J02 represent the material resistance at a value of 0.2 mm of total crack extension including the blunting component. Further alternative parameters such as i and Ji , which are based on stretch zone measurements in a scanning electron microscope, are not shown in the figure. If the resistance against unstable ductile crack extension has to be determined, crack resistance (R) curves based on or J, - a or J- a are used.

4.4.3. Lower Shelf Fracture Toughness Lower shelf fracture toughness is usually characterised by the plane strain fracture toughness KIc . Note that the use of KQ values, which refer to a geometrydependent fracture toughness in cases where the size criterion of linear elastic fracture mechanics is not fulfilled, is not recommended here. Instead it is recommended that the tests are repeated with larger specimens or, better still, that the evaluation of the tests is based on the concepts of elastic-plastic fracture mechanics such as the crack tip opening displacement or the J-integral. If no more than three replicate tests are available for a material condition, which commonly refers to the minimum requirement of the test standards, a simplified statistical analysis based on the lowest value should be performed. According to BS 7910 [4.5], an equivalent of the minimum of three is recommended if more than three tests are available. This equivalent refers to • the lowest value for 3 to 5 test data, • the second lowest for 6 to 10 test data, and • the third lowest for 11 to 15 test data.

54


Caution should, however, be exercised when the minimum toughness in terms of CTOD, mat , is less than half the average of three specimens, or the maximum toughness is more than twice this average, and the same should be assumed for the J-integral. In terms of Kmat this refers to a minimum toughness less than 70% or a maximum toughness more than 140% compared to the average of three specimens. Such pronounced variations point to more excessive scatter with the consequence that more test data are needed. If enough data are available, the Master Curve approach, as described in detail in Sections 4.4.5.2 and 4.4.5.3, should be applied as a maximum likelihood method.

4.4.4. Upper Shelf Fracture Toughness At the upper shelf the fracture behaviour is characterised by the so-called R or fracture resistance curve. The increase in fracture toughness in terms of the J-integral, J, or the crack tip opening displacement, , is determined as a function of stable crack extension a. Based on this curve an initiation fracture toughness is defined for the onset of stable ductile-crack extension (ductile tearing) where different definitions (02/BL , J02/BL , 02 , J02 , i , Ji ) are used in the common test procedures and standards as described in Section 4.4.2 (b). Although the slope of the R-curve is, in principle, a geometry dependent measure, the resistance against stable crack extension can be regarded as geometry independent. Usually, R-curves obtained from centre-cracked tension-loaded panels show a significantly higher slope than R-curves obtained from bend specimens. Other parameters affecting the slope of the R-curve are the crack length, the ligament length-to-thickness ratio and the strain hardening of the material. A more detailed discussion of the problem is provided in Section 4.4.6. As the scatter in data representing the onset of ductile tearing is rather small, it is usually sufficient to base the characteristic initiation toughness on the minimum value of three valid test results. However, if the lowest value in the data set is more than 10% below the highest value in terms of Kmat or more than 20% in terms of mat or Jmat , this indicates inhomogeneous behaviour. In this case, metallographic sectioning should be undertaken to ensure that the pre-fatigued crack tip is located in the microstructure of interest, and consideration should be given to performing more tests. If more than three specimens have been tested, a complete statistical analysis can be performed. The characteristic value should then be taken as a mean-minusone standard deviation or a 20% percentile of the fitted R-curve. According to [4.11] the relative scatter band in upper-shelf toughness has been found to be broadly independent of crack extension and to be typically less than 10% of the mean value corresponding to a crack extension of 1 mm. Although this


55

practical approach is not recommended in the final documents of SINTAP and FITNET (however, see R6 [4.3]) it is used in the following example to determine a lower-bound R-curve from an experimental data set. Example 4.4: The J- a curve is given by the data points of Table 4.4. The regression analysis according to ESIS P3 [4.12] J = A + C · aD

(4.23)

provides the coefficients A = 0, C = 800 and D = 069 (J in N/mm, a in mm). Based on these coefficients a lower bound curve reduced by 10% is obtained as J = 720 · a069 (Fig. 4.16). With the blunting line determined by JBL = 375 · Rm · aBL

(4.24)

and a tensile strength of Rm = 640 MPa, a J02/BL lower-bound design value is obtained as 283 N/mm. Note that for ferritic or bainitic steels, it is important to ensure that the temperature of interest is high enough to avoid any risk of brittle fracture occurring from proximity to the ductile-to-brittle transition. This is, however, not a trivial task because it refers to component conditions rather than test specimen conditions. Nevertheless, in order to avoid the risk of cleavage, it is recommended that the specimens are tested at just below the temperature of interest and that they are investigated for cleavage events, using fracture surface and metallographic sectioning as appropriate, following the test. Useful information can also be obtained from Charpy data. If there is some indication that the component could fail in the ductile-to-brittle transition regime, a Master Curve analysis according to Section 4.4.5.2 should be carried out. Table 4.4: Example 4.4: Experimental R curve data J-integral in N/mm 160 195 215 250 280

a in mm

J-integral in N/mm

a in mm

J-integral in N/mm

a in mm

0.09 0.13 0.15 0.16 0.25

345 395 425 455 545

035 035 040 045 055

660 675 680 725 1095

080 065 095 080 160

56


1200

Blunting line: J = 3.75 Rm Δa

J-integral in N/mm

1000

Fit + 10%

800

Fit – 10% (Lower bound)

0.2 mm 600

400

J0.2,BL

Fit: J (N/mm) = 800 ⋅ Δa (mm)0.69

200

Rm = 640 MPa 0

0

0.4

0.8

1.2

1.6

Stable crack extension Δa in mm

Figure 4.16: Example 4.4: Lower bound R-curve pragmatically derived by lowering the mean curve according to Eqn (4.23) by 10%.

In R6 [4.3] it is recommended that potential ductile-to-brittle transition data should only be assessed if the stable crack extension prior to fracture is shown experimentally not to exceed 0.2 mm. This means that the data analysed should be restricted to c or Jc rather than u or Ju as described in Section 4.4.2.

4.4.5. Ductile to Brittle Transition 4.4.5.1. The Weakest Link Model As a consequence of the usual large scatter band of fracture toughness data in the ductile-to-brittle transition range of ferritic or bainitic materials, which is explained by the so-called weakest link model, statistical treatment is indispensable. The scientific basis of the weakest link model, first proposed in [4.13], is the assumption of randomly distributed small regions of very low toughness, called “weak links”. When a critical stress is reached at the location of one of these “weak links” the whole specimen (or component) breaks, in a similar manner to a chain failing when one of its links breaks. The stresses ahead of a crack show a distinct peak which broadens and shifts into the ligament with increasing crack driving force in terms of or J. The distance of the first “weak link” from the


57

crack tip varies from specimen to specimen due to the irregular distribution of the “weak links” in the ligament. As a consequence, the shift of the stress peak necessary to trigger the “weak link” and the resulting crack driving force is also quite different and this explains the observed scatter of fracture toughness in the ductile-to-brittle transition. A further consequence of the weakest link mechanism is a statistically based “specimen thickness effect”. This has to be distinguished from the constraintbased geometry dependency which will be the subject of Section 4.4.6. Strictly speaking, the statistical “thickness effect” is not an effect of the specimen (or component) dimensions, but of the crack front length. The longer the crack front, the greater is the probability that find a “weak link” will be found near the crack tip. Therefore, from a statistical point of view, a larger crack front length must correspond with a smaller scatter band, but the lower bounds of the scatter bands of specimens with smaller and larger crack front lengths should be identical. 4.4.5.2. The Master Curve Approach (Stage 1) 4.4.5.2.1. Introduction In SINTAP/FITNET the scatter in fracture toughness is modelled by the so-called Master Curve concept of VTT (e.g., [4.14]), which also forms the basis of ASTM (American Society for Testing and Materials) test standard E 1921 [4.15] (latest version [4.16]). It is based on a three-parameter Weibull distribution of a number of replicate test results: m Kmat − Kmin (4.25) P = 1 − exp − Ko − Kmin with P being the failure probability (of the test specimens), Kmat the fracture toughness in terms of the K-factor, Ko the scale parameter, Kmin the shift parameter and m the shape parameter of the distribution. In general application, Ko , Kmin and m are fit parameters. However, in the Master Curve concept, two of these are fixed. For ferritic steels with yield strengths between Y = 275 and 825 Mpa, the shape parameter is given by m = 4 and the shift parameter by Kmin = 20 MPa ·m1/2 . In this section the Master Curve basic or “stage 1” approach is presented. The SINTAP/FITNET variation for inhomogeneous material states (stages 2 and 3) will be introduced in Section 4.4.5.2. The steps in the Master Curve approach are set out in detail for both homogeneous and inhomogeneous materials. This makes the presentation quite long compared to the presentations for fracture toughness determination in other regimes or for other materials, where there is less scatter and where fracture toughness determination is more straightforward.

58


4.4.5.2.2. Determination of the Scale Parameter Ko The steps for determining the scale parameter Ko are summarised in Fig. 4.17. Step 1 – The fracture toughness data in terms of Jmat or mat are transferred into Kmat values by Kmat = m · mat · Y · E 1 − 2 (4.26) or Kmat =

Jmat · E 1 − 2

(4.27)

Input toughness data set [N data Jmat or δmat]

Step 1

Transfer toughness data to Kmat in MPa · m1/2

Step 2

Sort toughness data

Step 3

Determine the according failure probability

Step 4

Apply the census criterion

Step 5

If necessary: adjust to 25 mm specimen thickness

Step 6

Determine the scale parameter Ko for the test specimens

Step 7

Transfer Ko to component conditions

Step 8

Determine fractile values for the fracture toughness

Figure 4.17: Master Curve (Stage 1) approach: The determination of the scale parameter Ko and its transfer to component conditions.


59

respectively. In terms of the fracture parameters, according to Section 4.4.2 the Jmat or mat data can be c , Jc , u , Ju , uc or Juc values. They are determined at the point of instability and no validity criterion is applied prior to the Master Curve analysis. Note that the Kmat values in Eqns (4.26) and (4.27) have to be expressed in MPa · m1/2 . The parameter m in Eqn (4.26) is a constraint parameter which in SINTAP/FITNET is conservatively chosen as m = 15 for steels with a strain hardening coefficient N ≥ 005. Note that for conditions different from small-scale yielding, Kmat is a formally deduced parameter representing mat or Jmat in terms of K instead of being a critical stress intensity factor which is not defined for contained or net-section yielding conditions. If a CDF approach which is based on the CTOD or J-integral is applied, the Kmat data have to be re-converted to mat or Jmat using Eqn (4.26) or (4.27) after completing the Master Curve analysis. If an FAD approach is carried out, Kmat is directly used as the input parameter (with respect to FAD and CDF see Sections 6.2 and 6.3). Step 2 – The adjusted Kmat data have to be sorted beginning with the smallest value so that Kmat i < Kmat i + 1 < · · · < Kmat N

(4.28)

In Eqn (4.28) N designates the number of specimens tested and i is a counter variable (i = 1 to N). Step 3 – For each data point (i) a failure probability Pi (of the test specimen) is determined as Pi = i − 03/N + 04

(4.29)

Step 4 – All Kmat i ≥ Kcen have to be excluded (censored) from the subsequent analysis. The censoring criterion Kcen is introduced in order to avoid significant influence of geometry from low- constraint conditions on the toughness values. 1 Kcen = E · bo · Y (4.30) 30 In Eqn (4.30) the yield strength Y refers to test temperature conditions. The quantity bo is the initial length (W-ao ) of the uncracked ligament at the beginning of the test. Specimens that did not fail by cleavage are also censored. All other

60


data are treated as uncensored. In addition, a censoring parameter i is introduced; for censored data i = 0 and for uncensored data i = 1. Note that in the 2005 update of ASTM E 1921-05 [4.16] a further censoring criterion is introduced for tests with more than 0.05 (W-ao ) or 1 mm (whichever is smaller) stable crack extension prior to fracture. Step 5 – In cases in which the toughness has been determined by specimens with a thickness B other than 25 mm (the latter referring to so-called 1T bend specimens with “1” standing for B = 1 inch, approximately 25 mm, according to ASTM nomenclature) Kmat has to be adjusted to B = 25 mm. This is done by Kmat 25 = 20 + Kmat − 20 · B/251/ 4

(4.31)

with Kmat and Kmat 25 in MPa · m1/2 and the specimen thickness B used in the test in mm. In the following, the Kmat term is generally assumed as adjusted values. Step 6 – Using the information available so far, the scale parameter Ko is determined as

Ko = 20 +

⎧ ⎪ ⎪ ⎨

⎫1 / 4 ⎪ ⎪ ⎬

N 1 Kmat i − 204 N ⎪ ⎪ ⎪ ⎪ ⎩ i i=1 ⎭

(4.32)

i=1

This refers to a failure probability P of the specimen of 63.2%. If the number of uncensored values is designated by r, Eqn (4.32) can be re-written as

N 1 K i − 204 Ko = 20 + r i=1 mat

1/ 4

(4.33)

Step 7 – So far the scale parameter Ko is defined for bend specimens with a thickness B of 25 mm. In order to apply it to real structures with crack lengths deviating from 25 mm, Ko has to be adapted to the real crack front lengths . This is done by

1 4 = 25 mm / Ko = 20 + Ko = 25 mm − Kmin · with Ko in MPa · m1/2 and in mm.

(4.34)


61

Step 8 – With m = 4, Kmin = 20 MPa · m1/2 and the component corrected Ko value of Eqn (4.34), Eqn (4.35) can be used to obtain fracture toughness values for arbitrary percentile values of P, 5% or 20%, for example: Kmat P = 20 + Ko − 20 · − ln 1 − P 1/ 4

(4.35)

again with Kmat P in MPa · m1/2 and in mm. Example 4.5: A data set of 10 Jmat experiments comprises the following data (all in N/mm): 22.5 / 31.5 / 15.0 / 46.5 / 24.5 / 58.5 / 41.5 / 30.5 / 46.0 / 48.5 for a steel with E = 210 GPa and = 03. These refer to the following Kmat values (in MPa · m1/2 : 72.1 / 85.3 / 58.8 / 103.6 / 75.2 / 116.2 / 97.9 / 83.9 / 103.0 / 105.8 (Step 1). Sorting the data (Step 2) and determining the according failure probabilities P (Step 3) gives the pairs of values summarised in Table 4.5. With a specimen width of 50 mm and an initial crack size of ao = 2815 mm, which gives a ligament length bo = 50–2815 mm = 2185 mm, the censoring criterion is obtained as Kcen = 287 MPa · m1/2 from Eqn (4.30) (Step 4). This means that none of the Kmat values above has to be censored in this special case. The values have been obtained by C(T) specimens with a thickness B of 25 mm and so no thickness adjustment (Step 5) had to be carried out. Using Eqn (4.32), the scale parameter Ko is obtained as Ko = 956 MPa · m1/2 (Step 6). Assuming a crack front length in the component of = 25 mm, no transfer of Ko (Step 7) is necessary in the present example. Finally, the analysis provides percentile toughness values of Table 4.5: Example 4.5: Sorted toughness values in terms of Kmat (i) (in MPa · m1/2 ) and the corresponding specimen failure probabilities Pi after Step 3 i 1 2 3 4 5 6 7 8 9 10

Kmat (i) in MPa · m1/2

Pi

588 721 752 839 853 979 1030 1036 1058 1162

0.067 0.163 0.260 0.356 0.452 0.548 0.644 0.740 0.837 0.933

62


100

P = 1 – exp –

Failure probability P in %

80

(Kmat – Kmin)

m

(Ko – Kmin)

Kmin = 20 MPa ⋅ m1/2 m=4

60

Ko = 95 . 6 MPa ⋅ m1/2 (P = 63.2%) Kmat (P = 20%) = 72 MPa ⋅ m1/2 Kmat (P = 5%) = 56 MPa ⋅ m1/2

40

P = 20% 20 P = 5% 0

0

60 80 100 20 40 Fracture toughness Kmat in MPa ⋅ m1/2

120

Figure 4.18: Example 4.5: Resulting toughness distribution and percentile values for P = 5% and 20%.

Kmat P = 5% = 56 MPa · m1/2 and Kmat P = 20% = 72 MPa · m1/2 by applying Eqn (4.35) (Step 8). The result is shown in Fig. 4.18. The user should decide on which percentile value to finally base the SINTAP/ FITNET analysis. It should be noted that the failure probability of the test specimens is not identical with the failure probability of the component under consideration. SINTAP/FITNET offers a complete reliability analysis (Section 6.13) as an alternative to choosing a lower percentile value of the fracture toughness. In addition to the SINTAP/FITNET variant of the Master Curve approach, ASTM E 1921-05 [4.16] adds a criterion for identifying “outliers” which deviate greatly from the rest of the data set. First, the percentile values of Kmat for 2% and 98% are determined by Kmat 2% = 0415 · Kmed + 1170 MPa · m1/ 2

(4.36)

Kmat 98% = 1547 · Kmed − 1094 MPa · m1/ 2

(4.37)

with Kmat and Kmed being provided in MPa · m1/2 . Mean value Kmed and scale parameter Ko are correlated by Kmed = Kmin + Ko − Kmin · ln 2 1/ 4

(4.38)


63

If a value is outside this limit it is regarded as an “outlier”, the influence of which can be reduced by testing additional specimens. The “outlier” should, however not be discarded from the data used for determining Ko and Kmed , since further “outliers” can indicate inhomogeneous material. Within SINTAP/FITNET an inhomogeneity analysis (stages 2 and/or 3; see Section 4.4.5.3) is recommended in any case. In [4.17, 4.18] the authors propose an alternative lower-bound method based on a modified two-parameter Weibull distribution of the type √ ln 2/Jo · Jmat − JLB for P ≤ 05 (4.39) P= 1 − exp −Jmat /Jo m

for P > 05 with the shape parameter being m = 2 and Jo being the scale parameter in terms of the J integral (or the crack tip opening respectively). Unlike the Master Curve approach, Eqn (4.39) is not part of SINTAP/FITNET. For probabilities P > 05 Eqn (4.39) follows the Weibull distribution. Below this value the P-Jmat function is modelled by a straight line with the slope at P = 05. The toughness data in terms of Jmat are censored by a criterion Jcen =

1 b · 30 o Y

(4.40)

Values of Jmat i ≥ Jcen have to be excluded from the subsequent analysis. If no Jmat value is censored, an engineering lower-bound value, JLB , referring to P = 0 in the model or to a probability lower than P = 25% in the Master Curve approach, can be determined by JLB = 023Jo = 026Jmed

(4.41)

In Eqn (4.41), Jmed is simply the average value of the data set Jmed =

N 1 J N i=1 mat

(4.42)

If a number of p values are censored, JLB is obtained as JLB = 026 · · Jmed

(4.43)

with Jmed =

N−p 1 J N − p i=1 mat

(4.44)

64


and = 1 + 1286 · p

(4.45)

The standard deviation of JLB is estimated by JLB ≈ 013 · Jmed /r

(4.46)

where r designates the number of uncensored data, that is, r + p = N. When the toughness distributions described so far have to be used in the context of a reliability analysis (Section 6.13), they usually have to be rewritten in terms of coefficients of variation, for example as quotients of the standard deviations (Kmat or Jmat and the mean values (Kmed or Jmed . The transfer is realised by Eqns (4.47) to (4.50). 1 (4.47) Kmed = Kmin + Ko − Kmin · 1 + m 2 1 2 − 1+ (4.48) Kmat = Ko − Kmin · 1 + m m With Kmin = 20 MPa · m1/2 , m = 4 and the Gamma functions 125 = 09064 and 15 = 088623, Kmed and Kmat are obtained as Kmed = 09064 · Ko + 1872

(4.49)

Kmat = 02543 · Ko − 5086

(4.50)

and

Example 4.6: The results of Example 4.5 (Ko = 956MPa · m1/2 , Kmin = 20 MPa · m1/2 and m = 4) are rewritten in terms of mean value and standard deviation of the Weibull distribution. Using Eqns (4.49) and (4.50) the mean value is obtained as Kmed = 885 MPa · m1/2 and the standard deviation Kmat = 192 MPa · m1/2 . Based on these data the coefficient of variation is COV = 022. 4.4.5.2.3. Determination of the transition temperature To The Master Curve reference temperature, To , is defined as the temperature T at which the mean value Kmed of a set of 1T size specimens (B ≈ 25 mm) is 100 MPa · m1/2 . Once this measure is known the complete Kmed -temperature curve Kmed = 30 + 70 exp 0019 T − To in MPa · m1/ 2

(4.51)


65

for this specimen size can be reconstructed with T and To being in C. In conjunction with Ko = 11033 · Kmed − 20653

(4.52)

and Eqn (4.35) Kmat P = 20 + Ko − 20 · − ln 1 − P 1/ 4

(4.53)

(Kmat and Ko in MPa · m1/2 , the toughness values for a specific probability P, can be determined for any temperature. The Master Curve according to Eqn (4.51) is defined for a temperature range To ± 50 C [4.16]. While To could be determined from a test set of data points at one test temperature by solving Eqn (4.51) for To , the method recommended in SINTAP/FITNET uses data points Kmat (i) at different temperatures Ti in conjunction with an iterative approach: N i exp 0019 Ti − To

11 + 77 exp 0019 Ti − To

i=1 N Kmat i − 20 4 exp 0019 Ti − To

− = 0 (4.54) 11 + 77 exp 0019 Ti − To 5 i=1 The censoring parameter i is i = 0 for censored data that either did not fail by cleavage or showed a toughness equal or larger than Kcen in Eqn (4.31). The yield strength Y refers for each data point to the corresponding test temperature Ti . For uncensored data, the parameter i is chosen as i = 1. The toughness values Kmat (i) are adjusted to a specimen thickness B = 25 mm. Example 4.7: Toughness data sets of a pressure vessel steel have been determined by 1T size specimens at −154 C, −91 C, −60 C, −40 C, −20 C, and 0 C (Table 4.6), the data being taken from [4.19]. In addition to the toughness values Kmat and the yield strength Y at test temperature, the censoring criterion according to Eqn (4.31) are provided in Table 4.6 for an initial ligament size of bo = 22 mm and a Young’s modulus of 210 GPa. At T = −40 C one out of ten specimens fails the censoring criterion, at T = −20 C seven specimens fail and at 0 C all of the specimens fail. The Master Curve analysis provided the Kmed and Ko values as well as percentile values of the toughness as a function of temperature and these are summarised in Table 4.7 and Fig. 4.19.

66


Table 4.6: Example 4.7: Kmat data set at test temperatures between −154 and 0 C. The original data are taken from [4.19] T C

Y MPa

T C

Y MPa

−154 −154 −154 −154 −154 −154 −154 −154 −154 −154 −154

677 677 677 677 677 677 677 677 677 677 677

435 443 524 356 438 483 463 384 304 556 413

322 9 322 9 322 9 322 9 322 9 322 9 322 9 322 9 322 9 322 9 322 9

1 1 1 1 1 1 1 1 1 1 1

−40 −40 −40 −40 −40 −40 −40 −40 −40 −40

504 504 504 504 504 504 504 504 504 504

207 7 157 5 237 8 165 7 268 8 217 7 223 8 266 9 251 5 324 1

278 6 278 6 278 6 278 6 278 6 278 6 278 6 278 6 278 6 278 6

1 1 1 1 1 1 1 1 1 0

−91 −91 −91 −91 −91 −91 −91 −91 −91 −91

538 538 538 538 538 538 538 538 538 538

719 855 586 1036 753 1164 980 838 1031 1060

287 8 287 8 287 8 287 8 287 8 287 8 287 8 287 8 287 8 287 8

1 1 1 1 1 1 1 1 1 1

−20 −20 −20 −20 −20 −20 −20 −20 −20 −20

475 475 475 475 475 475 475 475 475 475

212 2 204 1 275 5 197 0 289 1 274 5 389 0 386 9 484 5 335 2

270 5 270 5 270 5 270 5 270 5 270 5 270 5 270 5 270 5 270 5

1 1 0 1 0 0 0 0 0 0

−60 −60 −60 −60 −60 −60 −60 −60 −60 −60

506 506 506 506 506 506 506 506 506 506

1950 1591 1171 1508 1105 1614 1847 1383 2138 1496

279 1 279 1 279 1 279 1 279 1 279 1 279 1 279 1 279 1 279 1

1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0

470 470 470 470 470 470 470 470 470 470

343 5 714 3 731 9 734 7 735 3 739 8 742 6 743 8 752 0 759 9

269 0 269 0 269 0 269 0 269 0 269 0 269 0 269 0 269 0 269 0

0 0 0 0 0 0 0 0 0 0

Kmat Kcen i MPa · m1/2 MPa · m1/2

Kmat Kcen i MPa · m1/2 MPa · m1/2

4.4.5.2.4. Minimum Numbers of Specimens to be Tested No statement can be made about the overall number of specimens to be tested in the ductile-to-brittle transition range. There exist, however, clues to the minimum


67

Table 4.7: Example 4.7: Results of the Master Curve analysis T C

Kmed MPa · m1/2 (P = 50%)

Ko MPa · m1/2 (P = 632%)

Kmat MPa · m1/2 (P = 5%)

Kmat MPa · m1/2 (P = 20%)

−154 −91 −60 −40 −20 0

489 925 1426 1946 2707 3820

51 8 997 1548 2121 2958 4181

351 579 842 1114 1512 2095

435 748 1127 1520 2095 2936

Validity range?

outside inside inside inside outside outside

9 Specimens 500

Fracture toughness Kmat in MPa ⋅ m1/2

To = – 85°C Ko (P = 63.2%)

400 Validity range for To

Kmed (P = 50%)

300 Kmat (P = 20%) 200 Kmat (P = 5%) 100 ?? ? ? ? ? ? ?? ?

0 – 80 – 60 – 40 – 20 0 20 40 60 80 Temperature difference T-To in °C

100

Figure 4.19: Example 4.7: Results of the Master Curve analysis.

number of “valid” tests needed to fulfil the requirement in Eqn (4.30). When the mean value of Kmed for 1T size specimens is greater than 83 MPa·m1/2 , the required minimum number of valid tests is six. For smaller Kmed values the required number goes up to ten (Table 4.8) [4.16]. The definition for valid tests of weldments is extended by a further criterion – metallographic consistency – with the consequence that the number of tests is increased. According to [4.5] a minimum of 12 valid tests is necessary for HAZ

68


Table 4.8: Number of valid Kmat values required for Master Curve analysis according to [4.16] Kmed range 1T equivalent in MPa·m1/2 100 to 84 83 to 66 65 to 58 57 to 53 52 to 50

Number of valid Kmat values required 6 7 8 9 10

cracks and ductile-to-brittle transition range, otherwise excessive scatter has to be expected. Small test pieces such as pre-cracked Charpy specimens can lead to a very large number of “invalid” tests with respect of Eqn (4.31) when tested close to the T0 temperature. In such cases the testing should be performed at temperatures below T0 where more data can be expected to fulfil the censoring criterion. In addition, it is required that the fatigue crack has to sample the type and portion of the specified microstructure to characterise the HAZ toughness. If the HAZ exhibits upper-shelf behaviour the scatter is limited and in that case three “valid” data points are regarded as sufficient. However, when the HAZ operates in the ductile-to-brittle transition range, or excessive scatter is expected, a minimum of 12 valid tests, more in some cases, is indicated [4.5]. 4.4.5.3. Statistical Aspects of Fracture Toughness in Inhomogeneous Materials 4.4.5.3.1. The Inhomogeneity Problem The Master Curve introduced in Section 4.4.5.2 –stage 1 analysis – is intended for homogeneous materials showing ductile-to-brittle transition behaviour. Note, however, that fully homogeneous materials are exceptional rather than usual. Forgings, for example, will frequently have a different toughness at the plate centre and the surface. The effect is even more pronounced in weldments, which can include ductile as well as brittle zones across the weld and the adjacent material. This means in statistical terminology that different samples – according to the different material states – are mixed together. The result is schematically illustrated in Fig. 4.20. Assume two materials of quite different toughness characteristics, with the first material being the more brittle. Even though five data points of the second material are censored its distribution still tends towards much


(a)

69

(b) 100 Material 1

Failure probability P

Material 2

Material 1

Toughness

80

Mixed

60

40

Material 2

20

0

Census criterion

Toughness

Figure 4.20: Schematic illustration of the effect of inhomogeneous materials such as forgings or weldments on the toughness distribution.

higher toughness values. When the distributions from both materials are randomly mixed together and censored, the resulting distribution will be in between the two original distributions. It will show higher toughness values than the distribution from the first material, even at its lower tail. What is needed, therefore, is a procedure for “demixing” the various subsets of potentially inhomogeneous materials. Two methods are provided in SINTAP/FITNET in order to solve this problem. The first comprises the so-called stage 2 and stage 3 Master Curve analyses that were developed by VTT in the SINTAP project. These are lower bound analyses, that is, they describe the statistics of the more brittle material but neglect the fracture behaviour of the more ductile zones. The second method is designated the bi-modal Master Curve analysis and is incorporated in the FITNET procedure as additional information. For detailed information on the derivation and verification of both methods see [4.20]. The bi-modal Master Curve differs from the basic (stage 1) and the stage 2/ stage 3 methods in that it describes the toughness distribution of inhomogeneous materials as a combination of two separate distributions. This makes it particularly efficient for extreme inhomogeneity, for example, in describing heat affected zone data. In the following sections, both methods will be introduced.

70


4.4.5.3.2. Master Curve approach Stages 2 and 3: Correction of the scale parameter Ko (a) Stage 2 analysis – lower tail estimation The stage 2 analysis is an iterative procedure performing a lower tail estimation, checking and correcting any undue influence of toughness values in the upper tail of the distribution by stepwise reduction of the censoring criterion Step 1 – K0 and Kmed are determined following the basic concept (Eqns 4.32 and 4.47/4.49). Kmed is designated as Kmed (step 1). Step 2 – The censoring criterion of Eqn (4.30) is replaced by Kcen = Kmed (step 1), which reduces the number of “valid” data and increases the number of censored data. With this new information the analysis is repeated, again based on Eqns (4.32 and 4.47/4.49) but resulting in new values of K0 and Kmed , the new Kmed being designated as Kmed (step 2). If Kmed (step 2) ≥ Kmed (step 1) no inhomogeneity is detected, otherwise the analysis has to be continued with step 3. Step 3 – The censoring criterion of Eqn (4.30) is replaced by Kcen = Kmed (step 2) which again reduces the number of “valid” data and increases the number of censored data. The analysis is repeated as before and the new Kmed is designated as Kmed (step 3). If Kmed (step 3) ≥ Kmed (step 2) no inhomogeneity is stated. Otherwise the analysis has to be repeated again, and so on. Final Step – If the overall number of data in the data set, N, is 10 or more the analysis is terminated when Kmed (step n + 1) ≥ Kmed (step n). If the number of data in the data set is less than 10, a stage 3 (or minimum value) estimation has to be performed as described below. (b) Stage 3 analysis – minimum value estimation At stage 3, a minimum value estimation is performed to check, and make allowance for, extreme inhomogeneity in the material. An additional safety factor is incorporated for cases in which the number of tests is small. As in stage 2, a stage 3 analysis consists of different steps Step 1 – The smallest value Kmat of the test set has to be identified and designated as Kmatmin . For this, K0 has to be determined as K0min by √ K0min = N/ln 21/ 4 Kmin − 20 + 20 in MPa m (4.55)


71

Step 2 – K0min is compared with the last K0 , that is, K0 (step n), of the stage 2 analysis, K0min > 09 K0 (step n) indicating that the data set is homogeneous. The values K0 (Step n) and Kmed (Step n) obtained in “Stage 2” can therefore be taken as representative and used for determining the final value for K0 in step 3 below. However, K0min ≤ 09 K0 (step n) indicates significant inhomogeneity. In this case K0 (step n) has to be replaced by K0min before it is used for determining the final value for K0 in step 3 below. Step 3 – The final values of K0 and Kmed which will be used in the subsequent failure assessment include a small data set safety correction K0 =

1 −1/ 2

1 + 025 r

K0 Step n − 20 + 20 in MPa

√

m

(4.56)

or K0 =

1 −1/ 2

1 + 025 r

K0min − 20 + 20 in MPa

√ m

(4.57)

respectively where r is the number of uncensored data points. The mean value Kmed is obtained from K0 by Eqn (4.49). It is recommended that all three analysis stages are employed when the number of tests is between three and nine. With an increasing number of tests, the influence of the penalty for small data sets is gradually reduced. For ten and more tests, only stages 1 and 2 need to be used. However, stage 3 may still be employed for indicative purposes, especially where there is evidence of gross inhomogeneity in the material, as occurs in welds or heat affected zone material. In such cases, it may be concluded that the characteristic value is based upon the stage 3 result, or alternatively, such a result may be used as guidance in a sensitivity analysis. 4.4.5.3.3. Master Curve approach Stages 2 and 3: Correction of the transition temperature To (a) Stage 2 analysis – lower tail estimation Step 1 – The temperature T0 is determined by Eqn (4.54) as described above and designated as T0 – step 1. Step 2 – Subsequently all data Kmati > 30 + 70 exp 0019 T − T0 step 1 in MPa

√ m

(4.58)

72


have to be censored and replaced by Kmati = 30 + 70 exp 0019 T − T0 step1 in MPa

√ m

(4.59)

Based on this modified input information. T0 is determined using Eqn (4.54) with i = 0 for the censored data. The newly obtained value of T0 is then designated as T0 (step 2). If T0 step 2 ≤ T0 step 1 no inhomogeneity is present. Otherwise the analysis has to be continued with step 3. Step 3 – The censoring criterion is replaced by Kmati > 30 + 70 exp 0019 T − T0 step 2 in MPa

√ m

(4.60)

√ m

(4.61)

the censored data are replaced by Kmati = 30 + 70 exp 0019 T − T0 step 2 in MPa

and the analysis is repeated. If T0 step 3 ≤ T0 step 2 no inhomogeneity is stated. Otherwise the analysis has to be repeated again, and so on. Final Step – If the overall number of data in the data set, N, is 10 or more, the analysis is terminated when T0 step n + 1 ≤ T0 step n. If the number of data in the data set is less than 10, a stage 3 estimation has to be performed as described below. (b) Stage 3 analysis – minimum value estimation Step 1 – For each “valid” Kmati with respect to Eqn (4.30), a T0 value is determined by 1 1 1/ 4 T0 = Ti − ln Kmati − 20 × n/ln 2 − 11 (4.62) 0019 77 Step 2 – The largest of these values, T0max , is then compared to T0 step n of the stage 2 analysis. If T0max −8 C < T0 step n, the data may be considered to be homogenous and T0 step n is taken as representative. If, however, T0max −8 C ≥ T0 step n, this indicates inhomogeneous data. In this case T0max is assumed to be representative. Step 3 – In all cases, a small data set safety correction has to be performed using √ (4.63) T0 = T0 step n + 14 r


73

or T0 = T0max + 14

√ r

(4.64)

respectively, with r being the number of uncensored data. From T0 , the Kmed temperature curve is determined by Eqn (4.51) and the K0 -temperature curve by K0 = 31 + 77 exp 0019 T − T0 in MPa

√ m

(4.65)

4.4.5.3.4. The Bi-modal Master Curve Approach The total cumulative probability is expressed as a bimodal distribution 4 4 Kmat − Kmin Kmat − Kmin P = 1 − Pa · exp − − 1 − Pa · exp − K01 − Kmin K02 − Kmin (4.66) with the toughness, Kmat , and the scale parameters, K01 and K02 , of the two constituents in MPa · m1/2 , and Pa being the probability that the toughness belongs to distribution 1. Note that in the case of multi temperature data the scale parameters K01 and K02 are expressed in terms of the corresponding transition temperatures, T01 and T02 . In contrast to the one parameter of the basic Master Curve analysis three parameters have to be determined. The analysis is based on a maximum likelihood procedure where the likelihood, L, is expressed as L=

n 1− 1 · f 2 · S1−2 · · f n · S1−n (4.67) fcii · Sci i = fc11 · S1− c1 c2 cn c2 cn i=1

In Eqn (4.67) fc is the probability density function 4 Kmat − Kmin 3 Kmat − Kmin fc = 4 · Pa · 4 · exp − K01 − Kmin K01 − Kmin 4 Kmat − Kmin 3 Kmat − Kmin − 4 · 1 − Pa · 4 · exp − K02 − Kmin K02 − Kmin

(4.68)

and Sc is the survival function 4 4 Kmat − Kmin Kmat − Kmin + 1 − Pa · exp − (4.69) Sc = Pa · exp − K01 − Kmin K02 − Kmin

74


The parameter is the censoring parameter as in the basic approach. Equation (4.67) is solved so as to maximise L. The numerical procedure can be simplified by taking the logarithm of L so that a summation equation is obtained: ln L =

n

i · ln fci + 1 − i · ln Sci

i=1

= 1 · ln fc1 + 1 − 1 · ln Sc1 + 2 · ln fc2 + 1 − 2 · ln Sc2

+ · · · + n · ln fcn + 1 − n · ln Scn (4.70) In this case ln(L) has to be maximised. 4.4.5.3.5. Application Ranges of the Different Approaches The stage 2/stage 3 Master Curve analyses have been developed for the analysis of small data sets in order to provide representative lower-bound toughness values as input data to structural assessment. However, they should not be used for the determination of transition temperature shifts or for the determination of the average fracture toughness. In contrast, the bi-modal Master Curve approach needs data sets of sufficient size since the accuracy of its fit parameters depends on the number of data belonging to the material areas of interest.

4.4.6. Constraint Dependency of Fracture Toughness 4.4.6.1. Constraint and Stress Triaxiality The fracture toughness, Kmat , is commonly derived from deeply cracked bend specimens with almost square ligaments, using recommended testing standards and validity criteria. These are designed to ensure high constraint conditions near the crack tip that correspond to lower-bound toughness values independent of specimen size and geometry. However, there is evidence that the material resistance to fracture is increased for specimens – or components – with shallow flaws, or panels loaded in tension since these conditions lead to lower constraint around the crack. In general, the fracture resistance is dependent on the component size and geometry as well as on the loading type – bending versus tension. The geometry dependency of R-curves is schematically illustrated in Fig. 4.21. Usually, constraint is modelled by parameters describing the triaxiality of the stress state at the crack tip. An overview on the various parameters that affect this triaxiality and, as a consequence, the fracture resistance of the material, is


75

(a)

Blunti ng line

J-integral or CTOD-δ

Middle crack tension

Bending

ng line

Increasing B

Blunti


(b)

B

ng line

Increasing b/B

Blunti


(c)

B

b

Stable crack extension Δa

Figure 4.21: The geometry dependency of R-curves – (a) Effect of loading geometry; (b) Effect of specimen thickness (out-of-plane constraint); (c) Effect of ligament slimness (in-plane constraint).

provided in Fig. 4.22. In addition, strength mismatch, for example, in weldments, can also have an effect on the constraint – see Section 6.11.5.3. A consequence of the constraint, or traxiality, effect is that a single parameter such as K, or J is insufficient to describe accurately the stress and strain fields near the crack tip. A unique crack tip field such as the K field, see the Glossary “stress intensity factor”, or the HRR field, see the Glossary “crack tip

log stress


Triaxiallity

76

N

1

f(Lr) Lr

log strain a W

Relative crack depth a / W

Strain hardening exponent N

Ligament yielding Lr

Triaxiallity

Fy Fx

Fx

φ

Fy

Biaxial loading Fx /Fy

Tension

σ b /σ t

Bending

Crack front position φ

Figure 4.22: Parameters which affect the triaxiality of the stress state ahead of a crack.

opening displacement” and “J-integral”, exists only under idealised conditions. As a consequence, the complete characterisation of the stress-strain field by means of fracture mechanics requires a second parameter or further parameters in addition to K, or J. Note that the proposals on how to include constraint in the SINTAP/FITNET analysis set out in this section are not intended to be mandatory. Instead, they can be used in conjunction with the general approach to estimate an additional reserve factor in cases of low constraint geometries. As a rule, the application of standard fracture toughness values will lead to conservative SINTAP/FITNET results. Again, an exception is the determination of the crack size after a proof test. Caution should also be exercised in the case of semi-elliptical surface cracks, as within the framework of a leak-before-break analysis. A special approach to the constraint issue is provided for thin-walled structures in Section 6.10. 4.4.6.2. Constraint Parameters Various parameters for quantifying the local stress triaxiality as a measure of constraint have been proposed, three of which will be briefly introduced in the following section. (a) Triaxiality parameter h The local stress triaxiality can be described by h r z = h r z e r z

(4.71)


77

with h being the hydrostatic stress h =

3 1 1 · kk = · xx + yy + zz 3 k=1 3

(4.72)

and e being the equivalent stress, for example, according to von Mises 1 e = √ · xx − yy 2 + yy − zz 2 + zz − xx 2 + 6 · xy 2 + yz 2 + zx 2 2 (4.73) The corresponding coordinate system is shown in Fig. 4.23. (a) y

σyy τyx

x

τyz τxy

τzy

τxz

τzx

σxx

σzz

Crack front z

σyy

(b) y τxy τxy

Crack

σxx

σxx τxy

τxy

r σyy

θ x

Figure 4.23: Coordinate system at the crack – (a) Three-dimensional stress field at an arbitrary point in the uncracked ligament ahead of the crack; (b) Two-dimensional presentation including the coordinates and r.

78


Although the h parameter can characterise the actual three-dimensional stress state without any limiting assumption, it is not recommended within SINTAP/FITNET because it is not a constant but is dependent on the distance, r, to the crack tip for strain hardening materials. Additionally, it requires a full three dimensional finite element calculation for its determination. (b) T-stress The non-singular constant stress, T, derived from the linear elastic asymptotic solution K ij = √ fij + T1i 1j 2r

(4.74)

(ij – Kronecker symbol; ij = 1 for i = j and ij = 0 for i = j) represents a crack-parallel stress component that contributes to the stress field but is not included in the K-factor solution. The value of T may be calculated from elastic finite element analysis. Analytical solutions for T are available in compendia, for example, [4.21, 4.22]. An example is given in Fig. 4.24. For a given geometry but with varying stress distributions across the section, T can be obtained by the weight function method. In the literature, T values are sometimes presented as normalised by the stress intensity factor and flaw size √ B = T a K (4.75)

a

θ

0.4

σb

a /c = 0.3 λ=1

2c 0.2 λ ⋅ σb

2H

T/σ

a /t: 0.4 0 0.3 – 0.2

λ ⋅ σb σ b

t 2W

0.2 0.1

– 0.4 – 0.6

0

20

40 60 θ in degree

80

Figure 4.24: Example of a T-stress solution for a plate with a surface crack subjected to combined in- and out-of-plane bending [4.21].


79

or in terms of some nominal applied stress. In the example of Fig. 4.24, T is given as normalised by with being the nominal stress in the general K-factor expression √ KI = · a · Y

(4.76)

The most important shortcoming of the T-stress concept is that its definition is restricted to elastic material behaviour, but it has been found still to describe crack tip constraint for some degree of yielding (see (c) below). (c) Q-stress The elastic-plastic Q-stress is defined by ij r = ij ref r + Q · o ij

(4.77)

with o usually taken as, for example, the yield strength of the material, and ij ref r being a reference stress field which can be defined in different ways but usually represents the HRR field, see the Glossary “crack tip opening displacement” and “J-integral”. A shortcoming of Q is that it not only depends on the location ahead of the crack tip, and r, but also takes different values for the various stress components, for an in-depth discussion see [4.23]. In order to make the concept practicable, the Q-stress is commonly referred to only one point in the ligament, at = 0 and r = 2J/o . Q values may be calculated from elastic-plastic finite element analyses. Q is a function of the geometry, the flaw size, the type of loading, the material stress-strain curve and the magnitude of the loading. A limited number of graphical and analytical solutions are available in the literature, for example, [4.24, 4.25]. An example is given in Fig. 4.25. For linear elastic conditions Lr ≤ 05 T and Q are related by (see [4.27]) Q=

T/Y 05 · T/Y

for − 05 < T/Y ≤ 0 for 0 < T/Y ≤ 05

(4.78)

4.4.6.3. The Structural Constraint Factor ß and its Effect on Fracture Toughness A special structural constraint parameter, [4.27], is used within SINTAP/FITNET that can be obtained from both the elastic T-stress and the hydrostatic Q-stress [4.28, 4.29]. As the T-stress requires only elastic calculations, it is recommended for initial evaluations. The Q-stress is expected to provide more accurate assessments, particularly when plasticity becomes widespread, and

80


0.5 2c 0

t

a/t = 0.25 2c/a = 6

a

θ

2W/t = 4 n = 10 (n according to Ramberg-Osgood)

– 0.5 Q

45°

–1

θ = 90° 30°

– 1.5

16.6° 2.4°

–2

0

0.02

0.04 0.06 Jlocal /(a ⋅ σo)

0.08

0.1

Figure 4.25: Q-stress solution for a tension loaded plate with a semi-elliptical surface crack (data according to [4.26]).

should be used when more refined estimates of load margins are required, or as part of sensitivity studies. Based on T, the factor is defined by T =

T Lr Y

(4.79)

or based on Q, by Q = Q Lr

(4.80)

The factor is then used to determine a constraint dependent fracture toughc c ness designated as Kmat . At high values of constraint (Lr > 0, Kmat may be simply taken as equal to Kmat as obtained from conventional deeply cracked bend specimens. For negative levels of constraint (Lr < 0), the influence of constraint may be broadly summarised as follows c • in the lower shelf, Kmat increases as Lr becomes more negative, • in the upper shelf, there is little influence of constraint on the fracture toughness at stable crack initiation but considerable influence on ductile tearing resistance, that is, the slope of the R-curve increases as Lr becomes more negative. • the ductile-to-brittle transition region of ferritic or bainitic steels is shifted to a lower temperature as Lr becomes increasingly negative.


81

In [4.28] the authors have shown that the increase in fracture toughness in both the brittle and ductile regimes may be represented by an expression of the form for Lr > 0 Kmat c Kmat = (4.81) k Kmat 1 + · −Lr for Lr ≤ 0 with and k being material and temperature dependent constants. An application of the -concept is provided in Fig. 4.26. Example 4.8: An example of a T-stress based solution, taken from the SINTAP/ FITNET compendium [4.29], is provided in Fig. 4.27 and Tables 4.9 and 4.10. It refers to a hollow cylinder with a closed inner circumferential surface crack under tension loading. The inner radius is Ri = 100 mm, the wall thickness is t = 10 mm. The crack size varies from 1 mm to 3 mm, 5 mm and 7 mm. The factor is obtained from a a 2 a 3 a 4 a 5 + X2 + X3 + X4 + X5 = X0 + X1 t t t t t a 6 + X6 for 0 ≤ a/t ≤ 08 and H/t = 10 (4.82) t for the present geometry. The coefficients Xi are given in Table 4.9. The and k values are assumed as = 215 and k = 2 as in Fig. 4.26. Using these data, the results in Table 4.10 and Fig. 4.27 are obtained. An alternative method for the generation of and k values was recently developed in the context of the revised R6 routine and adopted by SINTAP/FITNET.

SEN(B) specimen M(T) specimen (a /W = 0.6) M(T) specimen (a /W = 0.8)

c

Kmat in MPa · m1/2

300

200

100

k=2 α = 2.15 Kmat = 77 MPa · m1/2 c Kmat = Kmat [1 + α (–β · Lr)k]

0 –1.4 –1.2

–1.0

–0.8

–0.6

–0.4

–0.2

0

0.2

0.4

T/σY = βT · Lr

Figure 4.26: Experimental determination of the parameters and k of Eqn (4.81) (lower bound) of a mild steel at −50 C (according to [4.30]).

82


140

130 a

Ri Ro

110 t 2H

100

a = 1 mm 3 mm 5 mm 7 mm

c

Kmat in MPa · m1/2

120

90

80

Kmat (standard test) = 77 MPa · m1/2 70

0.2

0.4

0.6

0.8

1.0

Lr c Figure 4.27: Example 4.8: Constraint corrected toughness values as Kmat a function of crack depth, a, and ligament yielding, Lr .

Table 4.9: Hollow cylinder with a closed inner circumferential surface crack under tension loading : Polynomial coefficients for determining . The solution is restricted to H/t = 10 Ri /t

X0

X1

X2

X3

X4

X5

X6

2.5 5.0 10 20

−051 −051 −051 −051

−05247 −04074 −03490 −03175

52871 40608 33111 27925

−19103 −13768 −11111 −93521

36294 27014 24588 23048

−35242 −28024 −27936 −26860

13536 11330 11687 10808

Based on extensive finite element analyses [4.30] and empirical correlations of the coefficients and k with the E/Y ratio, the strain hardening exponent n, given by /0 = /0 n 0

for ≤ 0 for > 0

(4.83)


83

c Table 4.10: Example 4.8: Constraint corrected toughness values Kmat as a function of crack depth, a, and ligament yielding, Lr

Crack depth a (mm)

(based on Tstress) Eqn (4.82)

Ligament yielding factor Lr

Constraint corrected c toughness Kmat in 1/2 MPa·m

1 1 1 1 1

−05211 −05211 −05211 −05211 −05211

02 04 06 08 10

788 842 932 1058 1220

3 3 3 3 3

−04771 −04771 −04771 −04771 −04771

02 04 06 08 10

785 830 906 1011 1147

5 5 5 5 5

−03696 −03696 −03696 −03696 −03696

02 04 06 08 10

779 806 851 915 996

7 7 7 7 7

−02806 −02806 −02806 −02806 −02806

02 04 06 08 10

775 791 817 853 900

(with o being the limit of proportionality which is related to o by Young’s modulus, o = o /E) and the exponent m in the Weibull distribution of the Beremin model [4.31], given by m P = 1 − exp − w u

(4.84)

(with u and m being fit parameters of the model and w being the Weibull stress) have been generated and summarised in tables. The Weibull exponent m is obtained by matching experimental cleavage fracture toughness data to values obtained from the Beremin model. In order to obtain reliable estimates of m, experimental data that cover two significantly different constraint levels are necessary.

84


Table 4.11: Look-up table for and k defined with respect to T/Y (according to [4.30]) E/Y

n Eqn (4.83)

m Eqn (4.84) 5

10

15

20

k

k

k

k

500 600 700

5 5 5

0797 0894 0962

214 200 180

1097 1125 1156

141 141 141

0873 0870 0877

128 129 131

0786 0780 0785

130 133 136

400 500 600

10 10 10

0768 0914 1049

232 236 230

2591 2680 2781

203 203 205

3689 3847 4084

190 192 196

4147 4387 4804

176 179 186

200 300 400

20 20 20

0539 0712 0929

169 208 256

3941 3993 4042

260 260 260

8815 9353 9575

295 303 307

1163 1350 1525

260 280 303

A selection of and k values obtained by this method are provided in Table 4.11, which is part of the tables in the R6 and SINTAP/FITNET compendia. 4.4.6.4. T-Stress Corrected Toughness Values in the Context of the Master Curve Approach T-stress based corrections have been proposed for use in the Master Curve approach, as described in Section 4.4.5.2, in [4.32] and as adopted in the FITNET document. In order to avoid confusion with the temperature T, the authors use the term Tstress for designating the T-stress. For Tstress < 0 the toughness Kmat can be corrected by

√ √ −Tstress c Kmat ≈ 20 MPa m + Kmat − 20 MPa m · exp 0019 · (4.85) 10 MPa with Kmat denoting the standard, plane strain, toughness determined by deeplyc the constraint corrected toughness. The transicracked bend specimens, and Kmat tion temperature To can be corrected by

Tstress Tstress T0c ≈ T0 + or T0c ≈ T0 + (4.86) 10 MPa/K 10 MPa/o C


85

In Eqn (4.86) To is the transition temperature determined from standard bend specimens and T0c is its constraint corrected counterpart.

4.4.7. Reference Toughness Based on Charpy Data 4.4.7.1. General Aspects In practical applications there are cases in which no fracture toughness data are available, as in the assessment of a component that was constructed decades ago and for which no data can be generated retrospectively due to lack of material. For such situations SINTAP/FITNET contains a number of empirical correlations for estimating the fracture toughness from Charpy data. Note, however, that the price to be paid for this kind of analysis can be over-conservative results. Numerous correlations between Charpy and fracture toughness data, usually for a limited class of materials, are available in the scientific literature and in compendia, for a limited overview see, for example, [4.33]. Because they are purely empirical, the equations should only be applied to those materials for which they were obtained. SINTAP/FITNET contains lower-bound correlations for a wide range of steels, primarily with yield strengths between 250 and 600 MPa, for the lower and upper shelf and for the ductile transition range. These are given below for CV in Joule, B in mm, Y and E in MPa, toughness in MPa · m1/2 and temperature in C. 4.4.7.2. Lower Shelf and Lower Transition The proposed correlation for steel ! Kmat = 12 CV − 20 · 25/B025

(4.87)

is based on the Master Curve approach for a 5% percentile of fracture toughness at a Charpy energy of CV = 27 J. Its application is restricted to 3J ≤ CV < 27J. The Kmat estimate should be based on a minimum of three Charpy tests. Note that Eqn (4.87) is more conservative than most other empirical correlations for steel, which are usually mean curves, but is in line with empirical lower bound correlations [4.34]. If neither fracture toughness data nor Charpy test data are available, a conservative lower bound toughness of Kmat = 20 MPa · m1/2 can be used for ferritic steels.

86


4.4.7.3. Upper Shelf Correlations are provided for KJ02 values corresponding to 0.2 mm stable crack extension and for R curves [4.33]. KJ02 can be estimated as a lower bound Kmat = KJ02 =

0133·C0256 1 128 Vus · E · 053 C · 02 Vus 1000 · 1 − 2

(4.88)

In Eqn (4.88), CVus designates upper-shelf Charpy energy in J. Alternatively, KJ02 can be determined by Kmat = KJ02 ≈ 119 · C0545 Vus

(4.89)

for steels. The application range of Eqns (4.88) and (4.89) is restricted to 170 MPa ≤ Y ≤ 1000 MPa and 20 J ≤ CVus ≤ 300 J and to cases for which brittle material behaviour can be excluded. Note, however, that even fully ductile Charpy specimen behaviour, that is, 100% shear fracture appearance, cannot automatically guarantee that the structure will also behave in a ductile manner at the same temperature. In particular, caution should be exercised for thick-walled components and for some low carbon and low sulphur steels. A lower bound R-curve (5% percentile) can be estimated by J = J a = 1 mm · am

(4.90)

with J a = 1 mm being the J-integral corresponding to a stable crack extension

a of 1 mm approximated by J a = 1 mm =

053 · C128 Vus · exp

T − 20 − 400 C

(4.91)

(for T in C) and the empirical exponent m being determined by m=

0133 · C0256 Vus · exp

T − 20 C Y − − + 003 2000 C 4664 MPa

(4.92)

The correlation was developed from 112 multi-specimen test data sets covering material properties 171 MPa ≤ Y ≤ 985 MPa and 20 J ≤ CVus ≤ 300 J and test temperatures −100 C ≤ T ≤ 300 C.


87

4.4.7.4. Ductile-to-Brittle Transition The estimates in the ductile-to-brittle transition range are based on empirical correlations between the transition temperature T0 and the Charpy transition temperature T27J (or T28J . Based on the general relationship T0 = T27J − 18 C standard deviation ± 15 C

(4.93)

a lower bound estimate is given by T0 = T27J − 3 C

(4.94)

The fracture toughness Kmat for an arbitrary specimen thickness B (or crack front length ) can then be determined by Kmat in MPam1/2 = 20 + 77 · exp 0019 · T − T27J − 3 C

025 025 B 1 × · ln 25 1−P

(4.95)

For cases in which no transition temperature T27J (or T28J is available, T27J can conservatively be determined by

C CV · CVus − 27J T27J = TCV − · ln (4.96) 4 A · CVus − CV with C being the slope of the CV -T transition curve in C, conservatively corrected, however, by a factor of 2, and where A = 27J. C can be estimated by C ≈ 34 C +

Y C − Vus 351 143

(4.97)

where T27J and TCV in C; Y in MPa; CV and CVus in J. TCV is the temperature at which Charpy data are available and CVus is the upper-shelf Charpy energy as above. If the upper-shelf energy is unknown, it can be assumed to be twice the highest measured impact energy value. If only the upper-shelf energy is known, Eqn (4.96) is replaced by

C 19 · CVus − 27J (4.98) T27J = Tus − · ln 4 27J with Tus being the lowest test temperature.

88


4.4.7.5. Sub-Sized Charpy Specimens When the component thickness is less than 10 mm, sub-sized Charpy specimens may be used. Note that the use of smaller specimens yields a shift Tss in the transition temperature that can be estimated using

Tss = −514 · ln 2B/10025 − 1

(4.99)

with B being the thickness (

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