Fracture and Fatigue of Welded Joints and Structures (Woodhead Publishing in Materials)

Fracture and fatigue of welded joints and structures © Woodhead Publishing Limited, 2011 Welded-Mcdonald-Pre.indd 1 3...

Author: Kenneth MacDonald

261 downloads 2154 Views 6MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Fracture and fatigue of welded joints and structures

© Woodhead Publishing Limited, 2011

Welded-Mcdonald-Pre.indd 1

3/23/11 1:52:28 PM

Related titles: Fatigue assessment of welded joints by local approaches: Second edition (ISBN 978-1-85573-948-2) Local approaches to fatigue assessment are used to predict the structural durability of welded joints, to optimise their design and to evaluate unforeseen joint failures. This completely reworked second edition of a standard work provides a systematic survey of the principles and practical applications of the various methods. It covers the hot spot structural stress approach to fatigue in general, the notch stress and notch strain approach to crack initiation and the fracture mechanics approach to crack propagation. Seam-welded and spot-welded joints in structural steels and aluminium alloys are also considered. Failure mechanisms of advanced welding processes (ISBN 978-1-84569-536-1) Many new, or relatively new, welding processes such as friction stir welding, resistance spot welding and laser welding are being increasingly adopted by companies to replace or improve on traditional welding techniques. Improvements in welding speed and ease of automation are often used as reasons for choosing advanced welding processes. Before advanced techniques are employed, their potential failure mechanisms should be well understood and their suitability for welding particular metals and alloys in different situations should be assessed. This important book will provide a critical analysis of advanced welding techniques and their potential failure mechanisms. Friction stir welding: from basics to applications (ISBN 978-1-84569-450-0) Friction stir welding (FSW) is a solid-state welding process that is gaining wide acceptance in industry, especially the shipbuilding, aerospace, mass transportation and automotive industries. FSW is particularly suited to those industries that use aluminium and its alloys. This authoritative book provides a comprehensive review of the subject of friction stir welding and covers topics such as process basics, equipment, modelling, inspection and quality control and applications. Details of these and other Woodhead Publishing materials books can be obtained by:  visiting our web site at www.woodheadpublishing.com  contacting Customer Services (e-mail: [email protected]; fax: +44 (0) 1223 832819; tel.: +44 (0) 1223 499140; address: Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge CB22 3HJ, UK) If you would like to receive information on forthcoming titles, please send your address details to: Francis Dodds (address, tel. and fax as above; e-mail: francis.dodds@ woodheadpublishing.com). Please confirm which subject areas you are interested in.



3/23/11 1:52:28 PM

Fracture and fatigue of welded joints and structures Edited by Kenneth A. Macdonald

Oxford

Cambridge

Philadelphia

New Delhi



3/23/11 1:52:28 PM

Published by Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge CB22 3HJ, UK www.woodheadpublishing.com Woodhead Publishing, 1518 Walnut Street, Suite 1100, Philadelphia, PA 19102-3406, USA Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com First published 2011, Woodhead Publishing Limited © Woodhead Publishing Limited, 2011 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials. Neither the authors nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 978-1-84569-513-2 (print) ISBN 978-0-85709-250-2 (online) The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acidfree and elemental chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by Replika Press Pvt Ltd, India Printed by TJI Digital, Padstow, Cornwall, UK



3/23/11 1:52:28 PM

Contents

Contributor contact details

Preface

ix xiii

Introduction

K. A. Macdonald, University of Stavanger, Norway

1

Part I Analysing fracture of welded joints and structures 1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Constraint-based fracture mechanics in predicting the failure of welded joints N. O’Dowd, University of Limerick, Ireland Introduction to constraint-based elastic-plastic fracture mechanics Constraint parameters Tabulation of Q-solutions Development of a failure assessment diagram (FAD) approach to incorporate constraint Effect of weld mismatch on crack tip constraint Full field (local approach) analysis for fracture assessment Conclusion References

17

17 18 22 25 27 28 28 28

2

Constraint fracture mechanics: test methods K. A. Macdonald, University of Stavanger, Norway, E. Østby and B. Nyhus, SINTEF Materials and Chemistry, Norway

31

2.1 2.2 2.3 2.4

Introduction High strains Two-parameter fracture mechanics Development of the single edge notch tension (SENT) test

31 32 35 36



3/23/11 1:52:28 PM

vi

Contents

2.5 2.6 2.7 2.8 2.9

Standardising the single edge notch tension (SENT) test Conclusions References Appendix: Codes and standards Nomenclature

51 54 55 57 58

3

Fracture assessment methods for welded structures I. Hadley, TWI, UK Introduction Development of engineering critical assessment (ECA) methods The failure assessment diagram (FAD) concept Specific engineering critical assessment (ECA) methods: R6 Specific engineering critical assessment (ECA) methods: BS 7910/PD6493 Specific engineering critical assessment (ECA) methods: structural integrity procedures for European industry (SINTAP)/European Fitness-for-Service Network (FITNET) Specific engineering critical assessment (ECA) methods: American Petroleum Institute (API)/American Society of Mechanical Engineers (ASME) Future trends References

60

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4

4.1 4.2 4.3 4.4 4.5 4.6

The use of fracture mechanics in the fatigue analysis of welded joints A. Hobbacher, University of Applied Sciences Wilhelmshaven, Germany Introduction to fracture mechanics Technical applications of fracture mechanics Fatigue assessment of welded joints using fracture mechanics Examples of practical application Conclusions References

60 63 64 67 72 81 85 87 88 91

91 93 97 107 110 111

Part II Analysing fatigue of welded joints and structures 5

115

Fatigue strength assessment of local stresses in welded joints W. Fricke, Hamburg University of Technology, Germany

5.1

Introduction

115



3/23/11 1:52:28 PM

Contents

vii

5.2 5.3 5.4 5.5 5.6

Types of stress Factors affecting the fatigue strength Fatigue strength assessment Conclusions References

117 124 129 137 137

6

139

Improving weld class systems in assessing the fatigue life of different welded joint designs B. Jonsson, Volvo Construction Equipment, Sweden

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10

Introduction Historic view Weld class system ISO 5817 Weld class systems at Volvo A consistent and objective weld class system Discussion Conclusions Future trends Source of further information and advice References

139 140 142 143 144 162 163 164 166 166

7

Fatigue design rules for welded structures S. J. Maddox, formerly at TWI, UK

168

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

Introduction Key features of welded joints influencing fatigue Fatigue crack propagation Design rules Future developments in the application of fatigue rules Conclusions References Appendix: fatigue design codes and standards

168 170 175 177 189 202 203 206

8

Fatigue assessment methods for variable amplitude loading of welded structures G. B. Marquis, Aalto University, Finland

208

8.1 8.2 8.3 8.4 8.5 8.6

Introduction Fatigue damage and assessment for variable amplitude loading Variable amplitude fatigue testing Future trends Sources of further information and advice References and further reading

208 214 226 233 234 235



3/23/11 1:52:29 PM

viii

Contents

9

Reliability apects in fatigue design of welded structures using selected local approaches: the example of k-nodes for offshore constructions C. M. Sonsino, Fraunhofer Institute for Structural Durability and System Reliability LBF, Germany

239

9.1 9.2 9.3 9.4 9.5

Introduction Selected decisive design parameters Selected design concepts by the example of K-nodes Conclusions References

239 239 261 273 274

10

Assessing residual stresses in predicting the service life of welded structures M. N. James, University of Plymouth, UK, D. G. Hattingh and W. H. Rall, Nelson Mandela Metropolitan University, South Africa and A. Steuwer, ESS Scandinavia, Sweden

10.1 10.2 10.3 10.4 10.5 10.6 10.7

Introduction Origins and types of stress Modification of stresses after welding Measurement Conclusions Acknowledgements References

276 278 283 285 292 293 293 297

276

11

Fatigue strength improvement methods

P. J. Haagensen, Norwegian University of Science and Technology (NTNU), Norway

11.1 11.2 11.3 11.4

297 298 301

11.5 11.6 11.7 11.8 11.9

Introduction Fatigue strength of welded joints Increasing the fatigue strength by improved design Improvements obtained by special plate, filler materials and welding methods Special welding methods Post-weld improvement methods Future trends Conclusions References and further reading

Index

331

305 307 307 324 327 327



3/23/11 1:52:29 PM


(* = main contact)

Editor

Chapter 2

K. A. Macdonald University of Stavanger Department of Mechanical and Structural Engineering and Materials Science N-4036 Stavanger Norway

K. A. Macdonald* University of Stavanger Department of Mechanical and Structural Engineering and Materials Science N-4036 Stavanger Norway

E-mail: [email protected]


Chapter 1 Professor Noel O’Dowd Department of Mechanical and Aeronautical Engineering Materials and Surface Science Institute University of Limerick Ireland E-mail: [email protected]

E. Østby and B. Nyhus SINTEF Materials and Chemistry Department of Applied Mechanics and Corrosion N-7465 Trondheim Norway

Chapter 3 I. Hadley TWI Abington Hall Granta Park Great Abington Cambridge CB21 6AL UK E-mail: [email protected]



3/23/11 1:52:29 PM

x


Chapter 4

Chapter 8

A. Hobbacher University of Applied Sciences Wilhelmshaven Germany

Professor G. B. Marquis Aalto University Department of Applied Mechanics P.O. Box 14300 FI-00076 Aalto Finland


Chapter 5


W. Fricke Ship Structural Design and Analysis Hamburg University of Technology (TUHH) Schwarzenbergstr. 95c 21073 Hamburg Germany

Chapter 9


C. M. Sonsino Fraunhofer Institute for Structural Durability and System Reliability LBF Bartningstr. 47 D-64289 Darmstadt Germany E-mail: [email protected]

Chapter 6 B. Jonsson Volvo Construction Equipment HL Division 360 42 Braås Sweden E-mail: [email protected]

Chapter 10 M. N. James* School of Engineering University of Plymouth Drake Circus Plymouth PL4 8AA UK

Chapter 7


S. J. Maddox TWI Granta Park Great Abington Cambridge CB21 6AL UK

D. G. Hattingh and W. H. Rall Mechanical Engineering Nelson Mandela Metropolitan University Gardham Avenue Box 77000 Port Elizabeth 6031 South Africa




3/23/11 1:52:29 PM


xi

A. Steuwer ESS Scandinavia Stora Algatan 4 22350 Lund Sweden

Chapter 11 P. J. Haagensen Norwegian University of Science and Technology (NTNU) 7491 Trondheim Norway E-mail: [email protected]



3/23/11 1:52:29 PM


3/23/11 1:52:29 PM

Preface

The motivation for writing this book is primarily to convey those aspects of current fracture and fatigue research that are important to general concepts of designing welded structures to avoid failure; and the ongoing assessment of the condition of structures and plant in service. Collectively termed structural integrity, these concepts often embrace the use of fracture mechanics – a branch of solid mechanics concerned with characterising the conditions surrounding stable or unstable growth of cracks. Although some academic circles are experiencing difficulty in attracting research interest and funding, especially from national sources who increasingly view fatigue and fracture as a mature subject area, societies around the world continue to experience failure of components and structures in this day and age. Quite an alarming state of affairs recalling that Wöhler’s experimental investigations of fatigue in train axles date from 1871 (in terms of eventual publication) and the birth of modern fracture mechanics can be traced back to the late 1940s following the Second World War’s Liberty ship failures that first arose in 1943. Our unfolding understanding of fracture mechanics and development of new characterising parameters to keep apace with greater levels of plastic strain capacity evident in modern steels continues to this day. The development of fatigue design guidance for welds was prompted by the rapid post-war adoption of welding as a dominant fabrication method for almost all types of metallic structure and process plant. The broader scope for encountering problems with fatigue and fracture problems in structures thus became truly immense. Countering this, design guidance has improved, becoming less uncertain, and fracture mechanics has blossomed to become a useful tool for examining influential factors – principally the deleterious effect of welding flaws related to both normal and poor quality fabrication. The net effect of all this is that there now appears to be evidence of a stabilised rate of in-service failures, at least in contrast to the galloping scale of the problems experienced in the second half of the 20th century. The content of this book naturally separates into the general subject areas of fracture and fatigue, natural, that is, in the context of welded joints. The



3/23/11 1:52:29 PM

xiv

Preface

nature and depth of the subject matter ranges from rigorous treatment of fundamental fracture mechanics parameters, to descriptive chapters covering topics of more general interest. While the fracture segment of the book is comprised of contributions from key researchers working on important developments in modern applied fracture mechanics, the remaining section of the book concerned with fatigue is largely drawn from a cohesive group of researchers and investigators from industry and academia who are all active members of Commission XIII of the International Institute of Welding. It is anticipated that this book will have relevance for researchers and post-graduate students of fatigue and fracture, as well as designers and materials specialists in an industrial setting responsible for issues of design and structural integrity of weldments. The intent of this book is that, by providing a collection of the important advances in fatigue design and fracture mechanics, it may encourage more robust design of new structures and improve the standard of care for structures in operation; and that it also initiates interest and further work on integrity of welded joints. In the preparation of this book, I am indebted to the contributing authors for their detailed and comprehensive treatment of their individual specialist subject areas and the resulting breadth of coverage achieved in the book. Kenneth A. Macdonald Hafrsfjord



3/23/11 1:52:29 PM

1

Constraint-based fracture mechanics in predicting the failure of welded joints

N. O ’ D o w d, University of Limerick, Ireland

Abstract: This chapter discusses constraint-based approaches, which have been introduced to reduce the level of conservatism inherent in a single parameter K- or J-based approach to fracture. The constraint-based approach incorporates additional information about the crack tip deformation to quantify the deviation from a high constraint stress field with the amplitude given by J. The theory behind constraint-based fracture is discussed and the different parameters used in the theory are outlined briefly. The incorporation of the constraint-based approach within the commonly used failure assessment diagram (FAD) approach is also described. Key words: fracture mechanics, constraint, failure assessment diagram, numerical models, finite element analysis, fracture parameters, non-linear fracture mechanics, Q-stress, T-stress.

1.1

Introduction to constraint-based elastic-plastic fracture mechanics

Non-linear fracture mechanics (NLFM) is applied to elastic-plastic materials when the extent of plastic deformation is such that the concept of smallscale yielding no longer holds. NLFM, using the J-integral, is based on the concept of J dominance, whereby the near tip stress and strain states are characterised by the J-integral (Rice, 1968) and for power law materials an associated Hutchinson, Rice, Rosengren (HRR) field (Rice and Rosengren, 1968; Hutchinson, 1968). The region where the crack tip fields are closely represented by the HRR field is known as the J dominance zone. For elastic-plastic materials, the applicability of the J approach is limited to so-called high constraint crack geometries. For example, when moderately sized laboratory crack geometries are loaded to general yield under tensile stress states, the J dominance zone is smaller than physically relevant length scales and the zone of finite strains (see e.g. Hancock et al., 1993; Shih et al.,1993). Under such conditions the near-tip stress distribution at physically significant distances from the crack tip can be significantly lower than the high constraint J dominant state. A typical result is shown in Fig. 1.1. Here the solid line shows the stress field ahead of a sharp crack (determined by finite-element (FE) analysis) and 17 © Woodhead Publishing Limited, 2011

Welded-Mcdonald-01.indd 17

3/23/11 1:42:37 PM

18

Fracture and fatigue of welded joints and structures 8.0 J/asy = 0.004 FE stress field

7.0

HRR

syy/sy

6.0 5.0 4.0 3.0 2.0 0.0

1.0

2.0

r/(J/sy)

3.0

4.0

5.0

1.1 Finite-element stress field for a sharp crack with an applied tensile stress field compared with the analytical HRR field. Here J is the J integral, r measures distance from the crack tip and sy is the material yield stress.

the symbols are the values for the HRR field at the corresponding J value. Distances are normalised by J/sy, where sy is the material yield strength, so the x-axis represents about 10 crack tip openings (assuming that the crack tip opening displacement, dt µ 0.5J/sy). It is clear that if the FE stress field is considered to represent the ‘actual’ stress field ahead of a sharp crack, then the HRR field significantly overestimates the crack tip stress field. While it is thus conservative to use the high constraint HRR field to represent the stress field ahead of a crack, in many cases it will be overly conservative. Indeed, fracture toughness values well above the critical mode I fracture (JIC) toughness have been measured in centre cracked tension specimens (e.g. Sumpter and Forbes, 1992). The concept of crack tip ‘constraint’ was thus developed to quantify this deviation from the stress state predicted by the use of the J integral and the HRR field alone. Under conditions of high crack tip constraint, such as those experienced in deeply cracked specimens under bend loading, the stress field will be close to the HRR distribution (considered to be the upper bound stress field for a power law hardening material) and under conditions of low crack tip constraint, such as those experienced in specimens under tension loading conditions the stress field will be below the HRR distribution (Fig. 1.1).

1.2

Constraint parameters

Two parameter approaches have been developed to analyse situations where J dominance does not hold, (see e.g. McMeeking and Parks, 1979; © Woodhead Publishing Limited, 2011


3/23/11 1:42:38 PM

Constraint-based fracture mechanics

19

Sumpter and Forbes, 1992; Hancock et al., 1993; Shih et al., 1993). The second parameter (the first being J) quantifies directly or indirectly the loss of constraint. This second parameter, will, in general, depend on geometry and material properties. The most common parameters used for this purpose are (i) the elastic T stress (williams, 1957), (ii) the Q stress (O’Dowd and Shih, 1991) and (iii) the A2 parameter (Yang et al., 1993a). The latter two parameters aim to quantify directly the stress field in the elastic-plastic material ahead of the crack tip, while the former aims to rank different geometries by their T values.

1.2.1

T stress

The T stress is the amplitude of the second term in the williams crack tip field for a linear elastic material. Using the convention of Fig. 1.2, the stress field for a linear elastic material may be represented as: Ê s 11 s 12 ˆ K Ê f11 f12 ˆ + Ê T 0 ˆ Á ˜ Á ˜= 2p r Ë f12 f22 ¯ ÁË 0 0 ˜¯ Ë s 12 s 22 ¯

1.1

In Equation 1.1 K is the linear elastic stress intensity factor and r measures distance from the crack tip (see Fig. 1.2). The stress s11 is the stress parallel to the crack face, s22 is normal to the crack faces and s12 is the shear stress. The quantities f11, f12, etc. are dimensionless functions which depend only on angle q and are tabulated in most textbooks on linear elastic fracture mechanics. The parameter T has dimensions of stress and as for K is obtained by consideration of the remote boundary conditions applied to a cracked specimen. It may be noted that T is a stress parallel to the crack faces and under linear elastic conditions is therefore not expected to have a strong effect on the driving force for crack growth. However, it has been shown that T can act as a characterising parameter for crack tip constraint. That is, for a given material, geometries which have the same or similar level of T stress have similar near-tip distributions when distance is normalised by J/s0. This approach may be considered to be an extension of the concept X2 s22 r q

s11 X1

s12

1.2 Convention for definition of crack tip fields.



3/23/11 1:42:39 PM

20


of small-scale yielding. Under small-scale yielding conditions K continues to describe the crack tip fields in an elastic-plastic material, although the deformation near the crack tip is represented by the HRR field and J. The T stress may be obtained from FE solutions using a line or contour integral similar to that used for J (see e.g. Sham, 1991) and tables of T stress solutions are available for a number of cracked geometries (e.g. Sherry et al., 1995).

1.2.2

A2 parameter

Using an asymptotic mathematical analysis, a three-term solution was developed to describe the stress fields for a crack in an elastic-plastic material. A Ramberg–Osgood (power law) description was used:

e = s +Êsˆ e 0 s 0 ÁË s 0 ˜¯

n

1.2

where n is the strain hardening exponent and s0, e0 are material parameters. (In Yang et al., 1993a, an additional parameter a was included, but it has been shown by Harkegard and Sorbo, 1998, and Kamel et al., 2009, that only three independent parameters, n, s0, e0 are required to represent uniquely a Ramberg–Osgood material response.) For such a material Chao and coworkers (Chao and Zhang, 1997; Yang et al., 1993b) showed that the stress field in the vicinity of the crack is given by 1

1

s s ij Ê J ˆ n+1 HRR J ˆ n+1 Ê r ˆ s (1) =Á s ij + A2 ÊÁ ˜ ˜ Á ˜ Ë e 0s 0 I n L¯ Ë L¯ ij s 0 Ë e 0s 0 I n r¯ t

Ê J ˆ 1 Ê r ˆ s (2) + A22 Á Ë e 0s 0 I n L˜¯ n + 1 ÁË L˜¯ ij

1.3

It may be noted that Equation 1.3 reduces to the HRR field when A2 = 0. Thus, J describes the amplitude of the HRR field and A2 characterises the ‘loss of constraint’, which results in a reduction in stress magnitude relative to the HRR field. The exponents s and t, the angular functions s˜ ij and the constant In in Equation 1.3 depend only on strain hardening exponent n. The parameter L is a characteristic, normalising length parameter which has generally been chosen as the crack length. For a given stress distribution, the value obtained for A2 will depend on the choice of characteristic length, L, but the overall amplitude of the stress field is unaffected. The functions s˜ ij and the exponents s and t have been tabulated in Chao and Zhang (1997) for a range of n values. The value of A2 may be obtained from FE analysis and will depend on specimen geometry, material properties and, to a lesser extent, the load magnitude.



3/23/11 1:42:40 PM


1.2.3

21

Q parameter

It was shown in O’Dowd and Shih (1991) that the near tip elastic-plastic stress fields may be represented in the following form which provides ‘an approximate, but robust, description of the near tip fields over physically significant distances’ (O’Dowd, 1992): sij = (sij)ref + Qs0dij

1.4

The first term in the above expression is a high constraint reference distribution and the second term is the difference field which quantifies the deviation from this high triaxiality field. The stress s0 is a normalising stress, typically representative of the material yield stress. The Kronecker delta term dij in the difference field indicates that the field represents a uniform hydrostatic stress ahead of the crack tip and the (dimensionless) parameter Q is the parameter which quantifies the magnitude of the difference term (typically Q < 0). The choice of reference field, sref, in Equation 1.4 will depend on the material. For a power law material a possible choice is the HRR distribution as in the J–A2 representation of Equation 1.3. However, numerical studies have shown that the uniformity of the hydrostatic stress is better satisfied when the difference was taken with respect to the stress field from an FE small-scale yielding solution with a remotely applied K-field (see Fig. 1.3). This stress distribution will show some deviation from the HRR field due to the contribution of the linear elastic deformation in the crack tip region. Note that, although not shown explicitly in Equation 1.4, the amplitude of the first term in the above expression will depend on the magnitude of the applied load and thus will depend on J. The second term in Equation 1.4 has no dependence on distance from s = K 2pr

r q Crack tip plastic zone

1.3 Determination of reference stress field from a ‘small-scale yielding’ analysis.



3/23/11 1:42:40 PM

22


the crack tip, r, but will depend on the magnitude of the applied load. In practice, the magnitude of Q is evaluated from FE solutions at a characteristic normalised distance ahead of the crack tip, typically at r/(J/s0) = 2 as proposed in O’Dowd and Shih (1991), which ensures that Q is evaluated at a physically significant distance (a multiple of the crack tip opening displacement). More recently, it has been proposed by Kamel et al. (2009) that Q be evaluated at a characteristic distance of r/(J/e0s0) = 0.004. This provides a value for Q which is less sensitive to the material description, but the characteristic distance is no longer a fixed multiple of crack tip opening displacement.

1.2.4

Modiﬁcations to the two parameter approach

Equations 1.3 and 1.4 have been found to provide a close representation of the stress field for tension geometries, shallow crack bend geometries and deep cracked bend geometries under low deformation. For deep cracked bend geometries under high levels of deformation the agreement between FE solutions and Equations 1.3 and 1.4 is less good. Therefore a three parameter approach has been proposed by Chao et al. (2004) to extend the application of constraint-based approaches to bend dominated geometries under extensive yielding. An additional parameter Dsb was defined to extend the applicability of the A2 approach (Equation 1.3) to account for the influence of the bending field: Ds = C M3 r b

1.5

where M is the global bending moment per unit length, b the ligament length, r distance from the crack tip and C a constant which may depend on applied load. A similar approach has also been suggested by Zhu and Leis (2006) to adjust Equation 1.4 to account for the bending term.

1.3

Tabulation of Q-solutions

As the J–Q description of the crack tip stress fields, described in Section 1.2.3, provides a relatively simple description of the crack tip fields, efforts have been made to tabulate Q solutions for a range of geometries from FE solutions. A typical result obtained from a 2D FE analysis is shown in Fig. 1.4. It may be seen that at low levels of deformation the value of Q is close to zero, indicating that high constraint conditions prevail while at larger levels of deformation when plasticity has spread throughout the specimen (large-scale yielding) the value of Q is significantly negative. A range of such solutions are provided in Sherry et al. (2005), for example. It may be noted that the Q value depends on material (in particular the value of the



3/23/11 1:42:40 PM

Constraint-based fracture mechanics 0.5

23

Centre-cracked tension, a/W = 0.1 Power law material, n = 10

0.0

Q –0.5

–1.0

–1.5 –2.0

–1.0

0.0 log [J/(ae0s0)]

1.0

2.0

1.4 Typical value of Q versus normalised J curve, for a shallow cracked centre cracked tension geometry and a power law material with n = 10.

hardening exponent n), specimen geometry and load level. Thus methods have been developed to simplify the representation of Q in cracked geometries and components as discussed in the next section.

1.3.1 Use of T stress to evaluate Q It was shown by Betegón and Hancock (1991) that although the T stress does not provide a direct description of the crack tip stresses for an elasticplastic material, T can be used as a characterising parameter to rank levels of constraint or to match the constraint in two geometries. In O’Dowd and Shih (1991) it was shown, furthermore, that, provided deformations are sufficiently low (outside the small-scale yielding regime but before conditions of large scale plasticity when the plastic zone has spread to the specimen boundary), there is a one-to-one relationship between T and Q (for a given material). Such a relation is shown in Fig. 1.5. The advantage of such an approach is that the T stress may be obtained from a linear elastic FE analysis (or from handbook solutions), avoiding the necessity for a non-linear (elastic-plastic) analysis which can be expensive in terms of computing resources. As discussed in Section 1.1, when constraint is considered, the crack tip stress fields no longer depend on a single parameter, J, but on J and Q. Thus, the fracture toughness is no longer expressed as a single number but as a toughness curve, Jc(Q), with the high constraint toughness JIC being a single point on this curve. By carrying out a range of tests on geometries of



3/23/11 1:42:41 PM

24

Fracture and fatigue of welded joints and structures 0.25 0.00 –0.25 –0.50 Q –0.75 –1.00 –1.25

n = 10 n=5

–1.50 –1.0

–0.5

0.0 T/sy

0.5

1.0

1.5 Relationship between T stress and Q for a power law hardening material. 800.0 700.0

Da = 1 mm

Kc(MPa m1/2)

600.0

Loading path for low constraint structure

Da = 0.5 mm

Loading path for high constraint structure

500.0 400.0 300.0 200.0 –2.0

–1.8

–1.6

–1.4

–1.2

–1.0 Q

–0.8

–0.6

–0.4

–0.2

0.0

1.6 Schematic of a toughness–constraint relation for a high strength, high toughness steel (adapted from O’Dowd and MacGillivray, 2004).

different constraint (ranging from deeply cracked bend geometries to shallow crack tension) the toughness curve may be constructed. A typical curve for a high strength, high toughness steel is illustrated in Fig. 1.6. The toughness curve is phrased here, with no loss of generality, in terms of KC rather than JC with KC obtained from the small-scale yielding relation, J = (1 – n2)K2/E.



3/23/11 1:42:41 PM


25

In order to carry out a fracture assessment therefore, the toughness– constraint curve must be known and in addition the crack driving force, in terms of J–Q (or K–Q) must be known. Two representative loading curves are illustrated in Fig. 1.6, representing a component under low and high constraint conditions, respectively. Fracture occurs when the loading path intersects the fracture curve, with the associated extent of crack growth Da determined by the relevant toughness curve. Examples of the application of constraint-based fracture mechanics to high pressure pipeline steels is provided in the studies of Ruggieri and coworkers, e.g. Ruggieri et al. (2006).

1.4

Development of a failure assessment diagram (FAD) approach to incorporate constraint

Structural integrity assessments are generally based on the lower bound fracture toughness, determined from a high constraint fracture toughness specimen, using e.g. deeply cracked single edge notch bend, SEN(B), or compact tension, C(T), specimens. This is the approach recommended in the British Standard BS 7910 (BS 7910:99, 1999) the UK Nuclear R6 (R6 Rev. 4, 2001) and the ASTM testing procedures (ASTM E 1820–01, 2001). In some cases, however, low constraint specimens, e.g. single edge notch tension SEN(T) can be used to obtain the fracture toughness value, provided it can be demonstrated that the constraint conditions of the component are matched by those of the test specimen. This approach is known as constraint matching and is adopted for example in Recommended Practice DNV RP–F108 (DNV-RP-F108, 2006) for the fracture assessment of offshore pipelines. A more general approach to incorporate the effect of constraint into structural integrity procedures is through modification of the failure assessment diagram (FAD). The discussion here is based on the British Standard, BS 7910, level 2B FAD, which relies on measured uniaxial material properties. The failure assessment curve (FAC) for a level 2B BS 7910 analysis is defined as follows: Ê ˆ K r = f (L (Lr ) = Á J ˜ Ë Je¯

–1/2

1.6

In Equation 1.6 Lr is the ratio between the applied load and the theoretical limit load and Kr is the ratio between the applied K and the fracture toughness Kmat. The ratio between the elastic-plastic J and the elastic J, J/Je in Equation 1.6 is given by J = Ee ref + 1 L3 Ê s y ˆ J e s y Lr 2 r ÁË Ee ref ˜¯

1.7



3/23/11 1:42:42 PM

26


In Equation 1.7, eref is the strain defined from the uniaxial stress–strain curve, using the corresponding reference stress, sref, obtained from Lr via, sref = syLr

1.8

where in Equations 1.7 and 1.8, sy is a measure of the material yield stress. A constraint-based FAD was developed in Ainsworth and O’Dowd (1995) and has been incorporated into the British Energy R6 failure assessment procedure. A constraint-dependent FAD is both geometry and material dependent. A number of simplifications are introduced in the R6 procedure to allow the constraint-dependent FAD to be constructed using only two additional parameters, a and b. A linear dependence of toughness, Kc, on constraint, Q, is assumed, such that Kc = Kc0 (1 – aQ)

1.9

where Kc0 is the toughness value corresponding to Q = 0. For the majority of materials 0 < a < 1. The dependence of the constraint parameter, Q, is also assumed to have a linear dependence on applied load, represented by: Q = bLr

1.10

The parameter b will depend on geometry and (more weakly) on the tensile response of the material. For most specimens, b < 0, so constraint decreases with increasing load. A modified FAD may then be constructed, with Ê ˆ Kr = Á J ˜ Ë Je¯

–1/2

[1 – ab Lr ]

1.11

where the term in square brackets accounts for the effect of constraint on the FAD. Note that the value of Kmat used in the definition of Kr is taken to be Kc0. The modified FAD thus depends on material through a and on geometry through b. A typical FAD for a high strength steel pipeline with a shallow crack loaded in tension is shown in Fig. 1.7. The value of a has been determined from fracture toughness testing and b from 3D FE analysis of a cracked pipe. It may be seen that if the effect of constraint is incorporated, the FAD in Figure 1.7 is expanded significantly, providing an increased safety margin for a given applied loading. Note also that at high values of Lr (near to plastic collapse) the constraint modified FAD and the original FAD are almost coincident. Thus there is little or no benefit from constraint in this region. The largest effect of constraint is seen in the region 0.4 < Lr < 1.0.



3/23/11 1:42:42 PM

Constraint-based fracture mechanics 1.2

27

Constraint modified level 2B FAD a = 0.6, b = –0.8

1.0

0.8

Kr

Level 2B FAD 0.6 0.4 0.2

0.0 0

0.2

0.4

0.6

0.8 Lr

1

1.2

1.4

1.6

1.7 FAD for a high strength steel pipeline with a shallow crack loaded in tension (adapted from O’Dowd and MacGillivray, 2004).

1.5

Effect of weld mismatch on crack tip constraint

If a crack lies within a weld or on the fusion line, the crack tip constraint will depend on the material mismatch. Typically, for a crack lying within an overmatched weld, the constraint will be reduced compared with that obtained for a homogeneous material at the same level of applied loading, as the plastic zone can easily extend into the parent material. For a crack lying within an under-matched weld, the reverse is the case – the deformation in the crack tip zone will be constrained by the higher strength weld material. Note that an increase or decrease in constraint due to over- or under-matching does not necessarily imply an increase or decrease in crack driving force as the crack driving force also depends on J, which is sensitive to weld over- or under-match. If a crack is located on the fusion line, the crack behaves as an interface crack and the HRR field distribution discussed in Section 1.1 no longer holds. This case was examined by Zhang et al. (1996) and the authors concluded that the effect of geometrical constraint was independent of mismatch and that the effect of mismatch could be incorporated through an additional parameter M, which depends on mismatch and material properties of the parent/weld material.



3/23/11 1:42:42 PM

28


1.6

Full field (local approach) analysis for fracture assessment

Constraint-based fracture mechanics approaches generally rely on numerical simulations to determine the crack tip constraint via the Q stress or T stress. An alternative approach to account for constraint effects in fracture mechanics is to undertake a full-field FE approach. This approach, often known as the local approach, requires a physical failure mechanism to be introduced within the FE analysis, e.g. the Gurson or Rouselier model (Gurson, 1977; Chaboche and Rousselier, 1983) to model ductile fracture via void growth. The crack tip damage mechanisms are then accounted for explicitly within the FE analysis and crack growth determined directly as an output from the analysis. However, among the drawbacks of these approaches are the complexity of the numerical modelling, the need for careful calibration and validation of the models and the fact that the models often provide results which are dependent on the FE mesh resolution. The constraint-based approach using parameters such as T, Q or A2 may thus be considered as a compromise between a conservative approach, based on a single parameter high constraint fracture toughness, and a more accurate complex approach, based on a full field FE solution. The local-based approach to fracture and consideration of constraint effects is discussed in detail by Dolby et al. (2005).

1.7

Conclusion

The accuracy of one parameter fracture mechanics approaches can be improved through the introduction of a constraint parameter or parameters. However, the improvement in accuracy needs to be balanced with the additional effort required to obtain the relevant information to carry out a constraint-based assessment. In general, a finite-element analysis will be required to obtain the constraint parameter, e.g. Q or A2, while additional fracture testing will be needed to obtain the dependence of fracture toughness on constraint for the material of interest.

1.8

References

Ainsworth R A and O’Dowd N P (1995), ‘Constraint in the failure assessment diagram approach for fracture assessment’, J Pressure Vessel Tech, 117, 260–267. ASTM E 1820–01 (2001), Standard test method for measurement of fracture toughness, ASTM E1820, Annual Book of ASTM Standards. Betegón C and Hancock J W (1991), ‘Two-parameter characterization of elastic-plastic crack-tip fields’, J Appl Mech, 58, 104–110. BS 7910:99 (1999), Guide on methods for assessing the acceptability of flaws in metallic structures, British Standards Institute, BS 7910:99.



3/23/11 1:42:42 PM


29

Chaboche J L and Rousselier G (1983), ‘On the plastic and viscoplastic constitutive equations. II. Application of internal variable concepts to the 316 stainless steel’, J Pressure Vessel Tech, 105, 159–164. Chao Y J and Zhang L (1997), Tables of plane strain crack tip fields: HRR and higher order terms, ME-Report 97-1, Department of Mechanical Engineering, University of South Carolina. Chao Y J, Zhu X K, Kim Y, Lar P S, Pechersky M J and Morgan MJ (2004), ‘Characterization of crack-tip field and constraint for bending specimens under large-scale yielding’, Int J Fracture, 127, 283–302. DNV-RP-F108 (2006), Recommended Practice DNV-RP-F108: Fracture Control for Pipeline Installation Methods Introducing Cyclic Plastic Strain, Det Norske Veritas. Dolby R E, Wiesner C S, Ainsworth R A, Burdekin F M, Hancock J, Milne I and O’Dowd N P (2005), ‘Review of a procedure for performing constraint and attenuation – corrected fracture mechanics safety case calculations for magnox reactor steel pressure vessels’, Int J Pressure Vessels Piping, 82, 496–508. Gurson, A L (1977), ‘Continuum theory of ductile rupture by void nucleation and growth. I. Yield criteria and flow rules for porous ductile media’, J Eng Matls Tech, 99, 2–15. Hancock J W, Reuter G and Parks D M (1993), ‘Constraint and toughness parameterized by T’ in Constraint Effects in Fracture, ASTM STP 1171, Hackett E M, Schwalbe K-H, and Dodds R H, Eds., American Society for Testing and Materials: Philadelphia, 21–40. Harkegard G and Sorbo S (1998), ‘Applicability of Neuber’s rule to the analysis of stress and strain concentration under creep conditions’, J Eng Mater Tech, 120, 224–229. Hutchinson J W (1968), ‘Singular behaviour at the end of a tensile crack in a hardening material’, J Mech Phys Solids, 16, 13–31. Kamel S, O’Dowd N P and Nikbin K M (2009), ‘Evaluation of two-parameter approaches to describe crack-tip fields in engineering structures’, J Press Vess Tech, 131, 031406 (8 pages). McMeeking R M and Parks D M (1979), ‘On criteria for J-dominance of crack tip fields in large scale yielding’ in Elastic-Plastic Fracture, ASTM STP 668, Landes J D, Begley J A and Clark G A, Eds., American Society for Testing and Materials, West Conshohocken, PA, 175–194. O’Dowd N P (1992), ‘Applications of two parameter approaches in elastic-plastic fracture mechanics’, Eng Fracture Mech, 52, 445–465. O’Dowd N P and MacGillivray H J (2004), Study of Girth Welds at High Strains, Imperial College Consultants report, ME025/3. O’Dowd N P and Shih C F (1991), ‘Family of crack-tip fields characterized by a triaxiality parameter – 1: Structure of fields’, J Mech Phys Solids, 39, 989–1015. R6, Rev. 4 (2001), Assessment of the Integrity of Structures Containing Defects, R6 Rev. 4, British Energy Generation Ltd, UK. Rice J R (1968), ‘A path independent integral and the approximate analysis of strain concentration by notches and cracks’, J Appl Mech, 35, 379–386. Rice J R and Rosengren G F (1968), ‘Plane-strain deformation near a crack tip in a power-law hardening material’, J Mech Phys Solids, 16, 1–12. Ruggieri C, Silva L A L and Cravero S (2006), ‘Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint’, Eng Fracture Mech, 73, 2123–2138.



3/23/11 1:42:42 PM

30


Sham, T L (1991), ‘Determination of the elastic T-term using higher order weight functions’, Int J Fracture, 48, 81–102. Sherry A H, France C C and Goldthorpe M R (1995), ‘Compendium of T-stress solutions for two and three dimensional cracked geometries’, Fatigue Fracture Eng Mats Struct, 18, 141–155. Sherry A H, Wilkes M A, Beardsmore D W and Lidbury D P G (2005), ‘Material constraint parameters for the assessment of shallow defects in structural components – Part I: parameter solutions’ Eng Fracture Mech, 72, 2373–2395. Shih C F, O’Dowd N P and Kirk M T (1993), ‘A framework for quantifying crack tip constraint’, in Constraint Effects in Fracture, ASTM STP 1171, Hackett E M, Schwalbe K-H and Dodds R H, Eds., American Society for Testing and Materials, Philadelphia, 134–159. Sumpter J D G and Forbes A T (1992), ‘Constraint based analysis of shallow cracks in mild steel’, in Proceedings of TWI/EWI/IS Int. Conf. Shallow Crack Fracture Mechanics Test and Applications, Dawes M G, Ed., Cambridge, UK. Williams M L (1957), ‘On the stress distribution at the base of a stationary crack’, J Appl Mech, 24, 109–114. Yang S, Chao Y J and Sutton M A (1993a), ‘Higher order asymptotic crack tip fields in a power-law hardening material’, Eng Fracture Mech, 45, 1–20. Yang S Chao Y and Sutton M (1993b), ‘Complete theoretical analysis for higher order asymptotic terms and the HRR zone at a crack tip for mode I and mode II loading of a hardening material’, Acta Mechanica, 98, 79–98. Zhang Z L, Hauge M and Thaulow C (1996), ‘Two-parameter characterization of the near tip stress fields for a bi-material elastic-plastic interface crack’, Int J Fracture, 79, 65–83. Zhu X-K and Leis B N (2006), ‘Bending modified J–Q theory and crack-tip constraint quantification’, Int J Fracture, 141, 115–134.



3/23/11 1:42:42 PM

2

Constraint fracture mechanics: test methods

K. A. M a c d o n a l d, University of Stavanger, Norway, E. Ø s t b y and B. N y h us, Sintef Materials and Chemistry, Norway

Abstract: Approaches to fracture assessment taking account of geometry constraint were first developed for offshore pipelines where predictions had typically been very conservative if conventional, deeply notched bend specimens were used. The single edge notch tension (SENT) specimen provides a lower level of crack-tip constraint that more closely matches that of the flaw in the pipe. This chapter outlines the basis of the current guidance for the use of SENT testing and how it is applied in practice, including consideration of the development of the SENT test for use in fracture control of pipelines. Areas requiring further research are highlighted, including limitations and aspects of specimen preparation, testing and analysis procedures that need to be addressed in order to standardise the test. Key words: fracture, welds, steel, constraint, testing, pipeline, girthweld, SENT.

2.1

Introduction

Engineering critical assessments (ECAs) are now commonly conducted during the design of structures to calculate tolerable sizes for flaws in welds. An ECA is a method for assessing the acceptability of a flaw in a structure, i.e. to demonstrate fitness-for-purpose. Pipeline welding codes and standards, e.g. BS 4515, API 1104 and DNVOS-F101, specify workmanship acceptance levels for welding defects in pipeline girth welds. These acceptance levels represent what a ‘good’ welder should be able to achieve. They are not fitness-for-purpose defect limits, nor do they always apply to all welded structures, or even all pipelines. Fortunately, fracture mechanics forms a rational basis for reaching informed decisions with regard to structural integrity. The benefits of ECA lie in avoiding unnecessary repairs and in determining if workmanship acceptance levels are themselves fit-for-purpose for the intended application. The latter point is particularly relevant to the design of pipelines subject to high static or cyclic strains because the partly historical safe limits for flaws promoted by the standards may have little bearing on the complex or severely loaded situations that are often prominent features of modern pipeline designs. An ECA is not required in all cases. The majority of existing onshore and 31 © Woodhead Publishing Limited, 2011


3/23/11 1:43:01 PM

32


offshore pipelines have been designed without ECAs, and have been installed and operated without incident. The reasons for the rise in popularity of the ECA can be partly attributed to the increased complexity of more recent pipeline designs, e.g. high temperatures and high pressures, deep water, aggressive internal conditions; installation methods involving plastic strain; and the use during construction of automatic ultrasonic testing (AUT) – rather than radiography – as the main inspection method. BS 7910 describes in detail how to conduct an engineering critical assessment. Codes and standards such as API 579 and R6 also give guidance, but are less commonly used in the pipeline industry. These methods are primarily stress-based and it is not straightforward to apply them to strainbased situations. It is interesting to note that PD 6493: 1980, the precursor to BS 7910, included the strain-based crack tip opening displacement (CTOD) design curve (Dawes, 1974). These generic codes and standards are supplemented by additional guidance in pipeline design codes and standards. DNV-RP-F108 was developed to provide additional guidance for ECAs of girth welds subject to cyclic plastic strains during installation. DNV-OS-F101 has since extended this guidance to consider both installation and operation. Both are intended to supplement the guidance given in BS 7910. In summary, ECAs often have a reputation of being over-conservative. Assessment of pipelines subject to high strains may indicate that only very small flaws would be acceptable, whereas practical experience has shown that the girth welds are highly tolerant of the presence of flaws. It was important to understand why ECA predictions could be overly conservative, or perhaps even non-conservative. Wide-ranging international research efforts examined a number of the issues surrounding pipeline ECAs including fracture toughness, tensile properties, misalignment (wall thickness tolerances and ovality); but it is the work on experimental measurement of fracture toughness and the importance of geometry constraint that is the focus of this chapter.

2.2

High strains

Axial plastic strain has an impact on girth weld flaw tolerance – particularly if cyclic in nature – which is in general lowered in comparison with elastic loading. The consequences of axial plastic strain during operation may be more severe than during installation because the pipeline is pressurised, further reducing flaw tolerance. Current procedures for assessing these conditions are either inadequate or inadequately validated (Cosham and Macdonald, 2008). A number of factors will affect flaw tolerance in addition to axial strain. For instance, the crack driving force is substantially greater when the pipeline is already at pressure when large axial strains are applied. On the other hand,



3/23/11 1:43:01 PM


33

material resistance is thought to be unchanged by the presence of biaxial strains from internal pressure. Early experimental work on wide plates for the UK nuclear power industry first revealed the deleterious effects on CTOD-based assessments of, in that case, equi-biaxial conditions (Garwood et al., 1989; Phaal et al., 1995). Recently published test results in pipes show that axial straining capacity is significantly reduced under biaxial load (Minaar et al., 2007; Østby and Hellesvik 2007). Current assessment procedures based on codified methods such BS 7910 experience difficulties in dealing with these conditions since they are essentially stress-based procedures and uncertainty surrounds their validity and safety. To illustrate this, comparison of the crack driving force (phrased in terms of J) for a simple surface cracked plate model computed directly from finite element analysis with that predicted using the reference stress formulation in BS 7910 (at level 2B) typically reveals a pronounced divergence at relatively low applied strains, in this case beyond approximately 1.7% (Fig. 2.1). The material’s stress–strain behaviour and geometry both have a significant bearing on this type of assessment. Similar comparisons in pipe geometries, but using the Kastner plastic collapse solution (Kastner et al., 1981) to define the reference stress, show a dependency of crack driving force slope on defect geometry, with both conservative and non-conservative results in different areas (Tkaczyk et al., 2007). Although embedded flaws are more likely to arise during fabrication than surface ones, easing the analysis by treating embedded flaws as surface flaws of equivalent dimensions (as in DNV-RP-F108) is simplistic, has not been fully validated and may not be conservative; especially if joint misalignment 5000

J (N mm–1)

4000

3000

2000

1000 BS 7910 Finite elements 0

0

2

4 6 Strain (%)

8

10

2.1 Crack driving force for a surface cracked plate.



3/23/11 1:43:01 PM

34


is present as this may cause increased plastic straining in the remaining ligament (Macdonald and Cheaitani, 2010). In more accurately replicating the levels of crack tip constraint of pipeline girth weld flaws, the single edge notch tension (SENT) specimen (Fig. 2.2) has still to be fully validated for fracture assessment of combined axial and pressure loading. However, there is growing experimental evidence that biaxial loading may not significantly influence ductile tearing resistance in plates (Garwood et al., 1989) and pipes (Minaar et al., 2007) loaded in tension; and that crack growth resistance measured in pipes under combined bending and internal pressure is similar to the R-curve obtained from SENT testing (Phaal et al., 1995; Østby and Hellesvik, 2007). The latter result is also supported by numerical simulation (Tkaczyk et al., 2007; Tyson et al., 2007), giving some cause for optimism that the SENT specimen geometry may also be applicable under such conditions. How residual stresses transverse to the girth weld relax with significant applied plastic axial strain is not well documented and the strain level at which they can safely be ignored remains to be defined. The failure assessment diagram (FAD) has proved to be a useful means P B Gripped area

W

H a

Gripped area

P

2.2 SENT specimen geometry.



3/23/11 1:43:01 PM


35

of evaluating the significance of flaws (witness the widespread use of BS 7910). A strain-based methodology would allow the assessment of elasticplastic fracture (by comparison of the crack driving force with fracture toughness) and failure by yielding or excessive straining (e.g. by comparison of a reference strain with a parameter based on material elongation). In a strain-based FAD the vertical axis would be based on J or CTOD and the horizontal axis would be phrased in terms of a reference strain rather than a reference stress. A general framework for such a procedure has been proposed where the form of the FAD is somewhat different compared with those for existing stress-based treatments (Budden, 2006) (Fig. 2.3). Research is ongoing to address the limitations of the current assessment methods, both in-house, e.g. ExxonMobil; and in joint industry projects, e.g. TWI, PRCI and SINTEF (Garwood et al., 1989; Wang et al., 2006; Østby, 2007).

2.3

Two-parameter fracture mechanics

The experimental approach of matching the constraint levels of test specimens to those of actual flaws in structures was facilitated by theoretical progress in two-parameter descriptions of crack-tip stress fields. A number of twoparameter approaches have been developed to analyse situations where the dominance of a single parameter breaks down, e.g. the J integral, and to quantify the deviation of the actual stress field (normally taken from numerical simulation) from the stress field predicted using J and the Hutchinson, Rice, Rosengren (HRR) field alone. This loss of constraint is readily quantified either directly or indirectly by a second single parameter (the first being J) which in general is dependent upon both geometry and material properties. The parameters that have so far found the most widespread acceptance are: 1.2

1.2

1.0 J r0.5

0.8

0.8 J r0.5

Stress-based FAD

1.0 0.6 0.4 0.2

0.6

0

0.4

0

0.25 0.50 0.75 1.00 1.25 1.50 Lr = sref/sY

0.2 0 0

10

20 Lr = eref/eY

30

40

2.3 Strain-based FAD (Budden, 2006).



3/23/11 1:43:01 PM

36


the elastic T stress (Williams, 1957; Betegón and Hancock, 1991); the elasticplastic Q stress (O’Dowd and Shih, 1991, 1992); and the A2 parameter (Yang et al., 1993). The first of these orders different geometries by ranking their T stress values, while the remaining two parameters aim to directly quantify the stress field in the elastic-plastic material ahead of the crack tip. The general problem of crack tip constraint and research aimed at understanding its effects are considered in more detail in Chapter 1. Dissatisfaction with the general state of over-conservatism in pipeline weld flaw assessment, and the growing awareness that geometry constraint was important (Fig. 2.4) (Pisarski and Wignal, 2002), drove efforts leading to the development of a methodology for design against fracture and plastic collapse of offshore pipelines (Bruschi et al., 2005; Østby, 2005; Sandvik et al., 2005; Thaulow et al., 2005). The need for guidance was great and development of the ECA methodology and improvements in fracture testing were consequently quickly introduced in DNV RP-F108 (Wästberg et al., 2004) for general use by industry.

2.4

Development of the single edge notch tension (SENT) test

2.4.1 Fracture control project Central to the development of the SENT specimen as a constraint-matched fracture mechanics test for pipeline girth welds was work performed at 0.05

0.04

SENB, a/W = 0.50 SENT, a/W = 0.50 Pipe 16 in OD, bending loading, a/t = 0.50 Pipe 16 in OD, tensile loading, a/t = 0.50

0.03 J/bsy

Increasing constraint 0.02

0.01

0 –0.2

SENB

0.0

SENT

0.2

0.4 –Q

Pipe

0.6

0.8

1.0

2.4 Effect of specimen geometry on crack tip constraint (Q) as a function of applied load expressed in terms of J (Pisarski and Wignal, 2002).



3/23/11 1:43:02 PM


37

NTNU1 and SINTEF2 in Norway, with the backdrop of the challenges facing conventional ECA in situations where over-conservatism was already a recognised problem. The academic and theoretical springboard for the work was the interest that advances elsewhere in two-parameter fracture mechanics were attracting. The objectives of the first fracture control project for offshore pipelines were to develop a methodology for design against fracture and plastic collapse of offshore pipelines (Bruschi et al., 2005; Østby, 2005; Sandvik et al., 2005; Thaulow et al., 2005), fracture control in this context being the design of pipelines to address the implications of high static and cyclic strains during installation/construction and operation. The methodology had to be suitable for including calibrated partial safety factors; and compatible with current design standards and other failure modes. A second project is underway aiming to address many of the obstacles to wider acceptance. It is important to complement analytical equations established for crack driving force based on strain (strain-based design) (Østby, 2005) with accurate measures of fracture resistance in order to develop a design guideline with calibrated safety factors. The majority of fracture toughness data in existence are derived from standardised deeply notched single edge notch bend (SENB) specimens (crack depth a/W = 0.5). Such specimens have a much higher geometry constraint ahead of the crack tip than circumferential cracks in tubes, inevitably leading to conservative results (Nyhus et al., 2002, 2003). Indeed, fracture toughness values well above the JIc toughness have been measured in low constraint centre cracked tension specimens (Sumpter and Forbes, 1992). These differences in crack tip constraint, combined with the differences in crack depth relative to the specimen width and in crack orientation with respect to the welding axis and pipe result in a significantly higher fracture toughness being obtained with SENT compared with SENB specimens. Furthermore, establishing the true level of conservatism is complicated by the high material dependence of increases in fracture toughness estimated from specimens with lower geometry constraint. Comparison of the fracture toughness and geometry constraint of equal crack depths in SENT specimens and pipes (Nyhus et al., 2003) concluded that shallow notched SENT specimens possess a level of geometry constraint similar to that of circumferential cracks in pipe (Fig. 2.5). This allows more accurate and relevant fracture toughness data to be established. This accounts in part for the rising level of interest shown in SENT specimens as the design has increased in popularity for estimating fracture toughness in pipes. The majority of fracture toughness data estimated from SENT specimens are used in accordance with guidelines established in the fracture control project 1

The Norwegian University of Science and Technology, Trondheim An independent research and technology organisation operating in partnership with NTNU

2



3/23/11 1:43:02 PM

38


Resistance (J, CTOD)

SENT (a/W = 0.2)

SENB (a/W = 0.2)

SENB (a/W = 0.5)

Constraint (Q, T, M)

2.5 Geometry constraint in SENB, SENT and circumferential flaws in pipes.

(Wästberg et al., 2004). This guideline, DNV RP-F108, requires the crack depth in the SENT specimen to be deeper than the crack in the pipe to ensure safe use of this design of specimen. Crack depths in the SENT specimens are commonly chosen somewhat deeper than the typical weld bead height. The size of the weld bead is often taken as a maximum limit on weld flaw height for embedded fabrication flaws (Macdonald and Hopkins, 1995a,b) – such as porosity, slag and lack of fusion – as they will be contained entirely within the weld run in which they were formed. The argument does not hold for cracks which may form quite independently of the weld beads. Flaws larger than the notch depth used in the SENT specimens would then be repaired independently of the ECA. Numerical simulations using FE show that SENT specimens have higher levels of geometry constraint than pipes containing equal crack depths. These findings are independent of: crack length; location on the internal or external pipe surface; and tension or bending loading (Nyhus et al., 2002; Wästberg et al., 2004). Assuming that geometry constraint increases with crack depth, it is therefore a requirement to introduce a crack depth in the SENT specimen that is deeper than the assessed crack in the pipe. The DNV guideline (Wästberg et al., 2004) is intended for pipeline installation and therefore the later interest in the effects of internal pressure and biaxial stress were not addressed in the original qualification program. Subsequent introduction



3/23/11 1:43:02 PM


39

of the SEnt specimen design into the main pipeline design standard, dnV oS-f101, had therefore to retain high constraint SEnb specimens in its requirements for EcA for operating pipelines (at pressure). Results from other projects indicate that the fracture toughness estimated from SEnt specimens is almost independent of the crack depth. in order to verify the wider dataset, and to confirm that fracture toughness estimated from SEnt specimens is also valid beyond the original limits of applicability (Wästberg et al., 2004), a programme of testing and finite element (FE) simulation examined the influence on fracture toughness of a wide range of crack sizes and internal pressure. the effects of misalignment and dissimilar thickness (on either side of the crack) were also assessed in order to determine if any correction to SEnt-based fracture toughness is needed for girth welds with these quite normal (intrinsic) geometric discontinuities.

2.4.2

J-integral in SENT specimens

the guidance recommends that fracture toughness (crack growth resistance) be characterised by J–R curves. the J-integral values from SEnt specimens are calculated for clamped conditions from equations 2.1–2.3 in Si units: J = Jel + Jpl

2.1

J el =

K 2 (1 – u 2 ) E

2.2

J pl =

hApl B(W – a0 )

2.3

where: a total crack length after test (mm) a0 original crack length (mm) Apl plastic area under the load – crack mouth opening displacement (cMod) curve at z = 0 (n mm2) B specimen width (mm) E elastic modulus (n/mm2) F load (n) J J integral (n/mm) Jel elastic J (n/mm) Jpl plastic J (n/mm) K stress intensity factor (n/mm1.5) W specimen height (mm) h eta factor v Poisson’s ratio and



3/23/11 1:43:03 PM

40


Ê pa ˆ 2 tanÁ Ë 2W ˜¯ K= F · Ê pa ˆ B W cosÁ Ë 2W ˜¯

3 ÏÔ È Ê aˆ Ê p a ˆ ˘ ¸Ô · Ì0.752 + 2..02 02 Á ˜ + 0.37 Í1 – sin Á ËW ¯ Ë 2W ˜¯ ˙˚ ˝Ô Î ÔÓ ˛

Ê Bˆ 5 Ï ¸ –Á ˜ Ô[196.719·e ËW ¯ – 64.642]· ÊÁ a0 ˆ˜ Ô ËW ¯ Ô Ô Ô Ê Bˆ 4Ô Ô+ [–493.511·e –ÁËW ˜¯ + 138.837]· Ê a0 ˆ Ô ÁË W ˜¯ Ô Ô Ô Ô Ê Bˆ 3 –Á ˜ Ô Ê a0 ˆ Ô ËW ¯ –106.207]· Á ˜ ÔÔ ÔÔ+ [463.503·e ËW ¯ h = 0.85 Ì ˝ B Ê ˆ 2 Ô Ô –Á ˜ Êa ˆ Ô+ [–201..862 862 ·e ËW ¯ + 34.532]· Á 0 ˜ Ô ËW ¯ Ô Ô Ô Ô Ê Bˆ Ô+ [39.413·e –ËÁW ¯˜ – 4.525]·· Ê a0 ˆ Ô ÁË W ˜¯ Ô Ô Ô Ô Ê Bˆ –Á ˜ Ô Ô ËW ¯ + 1.039] ÔÓ+ [–2.064 ·e Ô˛

2.4.3

Fracture mechanics testing

fracture mechanics testing was performed for SEnt specimens and SEnb specimens with a range of crack depths (fig. 2.6). the SEnt programme

2.3

11.5

2.3 (b)

(a) 4.0

11.5

11.5

4.0

11.5 (d)

(c) 5.7

5.7

11.5

11.5 (e)

(f)

2.6 Geometry of the standard (equal thickness and aligned) SENT and SENB specimens.



3/23/11 1:43:04 PM


41

also included misalignment and dissimilar wall thickness (Fig. 2.7), the aim being to study the effects of geometry constraint and asymmetric pipes/ specimens. The unstrained test material was 304 mm (12 inch) diameter grade X-65 linepipe with 14.9 mm wall thickness. The cross-section of the specimens was 2B ¥ B (23 ¥ 11.5 mm) (Fig. 2.8). Pipe curvature restricts the specimen thickness to some degree. Specimens were notched from the internal pipe surface to a range of depths. The clamping separation distance for the SENT specimens was 115 mm (based on 10W). All testing was performed at room temperature using a double clip gauge arrangement to calculate the CTOD values. CTOD–R curves were constructed using a multiple specimen technique whereby specimens were unloaded at different displacements (Fig. 2.9–2.11). The target crack depth was 2.3 mm. After testing, the actual initial crack depths were measured, which varied from 2.36 to 2.64 mm. It is clear from the driving force curves, Figs 2.12 and 2.13, that the strain capacity in the test was strongly dependent on this difference in the initial crack depth. Figures 2.12 and 2.13 show the crack driving force (CTOD) for SENT specimens under test. CTOD is plotted as a function of the strain in the specimen measured between the clamped region and the crack. The strain is in this area unaffected by both the crack and the clamps. The loading curve has several important features (Fig. 2.12, curve for a0 = 2.36 mm): 2.5

2.5 11.5

2.3 14.0

11.5 (a)

11.5 4.0 (b)

2.5

2.5

2.3 14.0

14.0

11.5

11.5 2.3

(c)

(d)

2.7 Geometry of the SENT specimens with dissimilar wall thickness and misalignment.

B

a 2B

2.8 Cross-section of SENT specimen and placement in the pipe wall.



3/23/11 1:43:04 PM

42

Fracture and fatigue of welded joints and structures 3.5 3.0

d (mm)

2.5 2.0 1.5 1.0

SENT SENT SENT SENB

0.5

(a/W (a/W (a/W (a/W

= = = =

0.2) 0.35) 0.5) 0.5)

0.0 0.0

0.5

1.0 1.5 Da (mm)

2.0

2.5

2.9. CTOD–R curves from SENT specimens with different crack depths compared with a conventional SENB specimen. 3.5 3.0

d (mm)

2.5 2.0 1.5 1.0

SENT SENT SENT SENT

0.5

(a/W = 0.2) (a/W = 0.35) (a/W = 0.2) fusion line (a/W = 0.35) fusion line

0.0 0.0

0.5

1.0 1.5 Da (mm)

2.0

2.5

2.10 Comparison of the CTOD–R curves for parent material and fusion line for SENT specimens with different crack depths.

∑ Initially the specimen and the ligament remain in the linear elastic region. ∑ The remaining ligament then begins to yield, and CTOD increases with almost no corresponding increase of global strain in the specimen. ∑ Once CTOD reaches approximately 0.5 mm, the ligament has passed the Lüders plateau and the material recommences strain hardening. Yield is eventually reached in the bulk of the specimen away from the crack.



3/23/11 1:43:05 PM


43

3.5 3.0

d (mm)

2.5 2.0 1.5 SENT SENT SENT SENT SENT

1.0 0.5 0.0 0.0

0.5

(a/W = 0.35), Fig. 2.6(c) (dif. wall thickness), Fig. 2.7(c) (misal.), Fig. 2.7(a) (dif. wall thickness), Fig. 2.7(b) (dif. wall thickness), Fig. 2.7(d)

1.0 1.5 Da (mm)

2.0

2.5

2.11 CTOD–R curves for SENT specimens with different wall thickness and misalignment (refer to Figs 2.6 and 2.7). 3.0 a0 = 2.64 mm

CTOD (mm)

2.5 a0 = 2.36 mm

2.0 1.5

Necking

1.0

Yielding of the specimen

0.5 0.0 0.00

Yielding in the ligament Linear elastic loading 0.01

0.02 Strain (mm/mm)

0.03

0.04

2.12 CTOD as a function of strain for SENT specimens with crack depth a/W = 0.2 (refer to Fig. 2.6).

∑ The specimen continues deforming plastically where strain increases with increasing CTOD. ∑ Finally, the specimen reaches a maximum strain capacity dictated by necking and crack extension. Other fracture mechanics test results Fracture toughness data from other sources were used to widen the basis of qualification. CTOD–R curves for SENT specimens with crack depth



3/23/11 1:43:05 PM

44

Fracture and fatigue of welded joints and structures 3.0 2.5

CTOD (mm)

a0 = 2.63 mm 2.0 1.5 1.0 0.5 0.0 0.00

0.01

0.02 Strain (mm/mm)

0.03

0.04

2.13 CTOD as a function of strain for SENT specimens with dissimilar wall thickness (refer to Fig. 2.7). 1.6 SENB (a/W = 0.35) SENT (a/W = 0.55) SENT (a/W = 0.35)

1.4 1.2

d (mm)

1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.5

1.0 1.5 Da (mm)

2.0

2.5

2.14 CTOD–R curves for 13% Cr filler material (Nyhus et al., 2003).

a/W equal 0.35 and 0.55 and SENB specimens with a/W equal to 0.55 are compared in Fig. 2.14 (Nyhus et al., 2003). The specimens were taken from a pipe with outer diameter of 325 mm, and wall thickness of 12 mm. Base material was a high grade supermartensitic stainless steel, S13% Cr steel (2.5 Mo). The girth welds were made with a gas tungsten arc welding (GTAW) process and the filler material used was Thermanit 13/06 Mo. All specimens were notched in weld metal and testing was performed at room temperature. The cross-section of the SENT and SENB specimens was 20 ¥ 10 mm2 (Fig. 2.8).



3/23/11 1:43:06 PM


45

CTOD–R curves for SENT specimens with crack depth a/W equal to 0.20, 0.35 and 0.50 and SENB specimens with a/W equal to 0.50 are also compared in Fig. 2.15. The specimens were taken from a 13% Cr pipeline with outer diameter of 340 mm, and wall thickness equal to 15.3 mm. All specimens were notched in parent material and testing was performed at room temperature. The cross-section of the SENT and SENB specimens was 25.4 ¥ 12.7 mm2 (Fig. 2.8).

2.4.4 Numerical simulation Ductile tearing analyses formed the basis of numerical simulation using an implementation of the Gurson model (Zhang et al., 2000). This model takes into account the growth and coalescence of voids in the material. Axisymmetric conditions were assumed, modelling a pipe loaded in tension containing a fully circumferential crack. Biaxial loading was invoked by simultaneously applying internal pressure. Numerical simulations of ductile tearing are highly sensitive to mesh size and the assumed void volume fractions. As the main aim was to investigate the effect of biaxial loading on crack growth resistance, the local element size (0.1 mm) and the initial void volume fraction were chosen to give a crack growth resistance typical for pipeline steels. The dimensions of the modelled pipe were 400 mm outer diameter and 20 mm wall thickness. The pipe model was loaded in tension. Results from the finite element analysis (FEA) were presented in the form of CTOD-R curves plotted for crack depths of 20, 30 and 50% of the wall thickness (Fig. 2.16). A similar family of curves was derived for the case 3.5 BM BM BM BM

3.0

d (mm)

2.5

SENT SENT SENT SENB

(a/W (a/W (a/W (a/W

= = = =

0.2) 0.35) 0.5) 0.5)

2.0 1.5 1.0 0.5 0.0 0.0

0.5

Da (mm)

1.0

1.5

2.15 CTOD–R curves for 13% Cr parent material.



3/23/11 1:43:06 PM

46

Fracture and fatigue of welded joints and structures 1.8 1.6 1.4

d (mm)

1.2 1.0 0.8 0.6 0.4

a/T = 0.2

0.2

a/T = 0.3 a/T = 0.5

0.0 0.0

0.5

1.0

1.5 Da (mm)

2.0

2.5

3.0

2.16 CTOD–R curves for circumferential surface cracks with crack depths 20, 30 and 50% of the wall thickness.

1.8 1.6 1.4

d (mm)

1.2 1.0 0.8 0.6 0.4

no internal pressure

0.2

hoop stress = 0.4 ¥ SMYS hoop stress = 0.96 ¥ SMYS

0.0 0.0

0.5

1.0

1.5 Da (mm)

2.0

2.5

3.0

2.17 CTOD–R curves from FEA for a circumferential surface crack with crack depth 30% of the wall thickness. The pipes are loaded in tension without internal pressure; and with an internal pressure giving a hoop stress of 40% and 96% of the yield stress.

of 30% crack depth with simultaneously applied constant internal pressure, inducing levels of hoop stress equal to 40% and 96% of the yield stress (Fig. 2.17). The CTOD-R curves are plotted for increasing tension loads.



3/23/11 1:43:06 PM


47

2.4.5 Discussion Range of applicability of the SENT specimen The CTOD–R curves of SENT specimens tested, Figs 2.9, 2.14 and 2.15, have similar initial shapes and are independent of the initial crack length. The R-curve data extend far beyond what is normally assumed to be the valid limit – an extent of ductile tearing equal to 10% of the initial ligament is normally considered the upper limit of validity for CTOD–R curves. The present test data would thus have a validity limit lying between Δa = 0.58 and Δa = 1.0 mm given the initial crack depths. Within this limit on ductile crack growth almost all differences between the CTOD-R curves for the various crack depths vanish. The fracture toughness measured from SENT specimens was significantly higher than the fracture toughness from SENB specimens. The percentage increases in the SENT fracture toughness at Δa = 0.5 mm are: ∑ 54% for grade X-65 carbon steel, Fig. 2.9; ∑ 220% for the Thermanitt 13/06 filler material, Fig. 2.14; ∑ 83% for the13%Cr CRA material, Fig. 2.15. SENT specimens provide a significant reduction in conservatism compared with SENB specimens. The inherent conservatism of SENB specimens shows a strong material dependency, causing difficulty in performing probabilistic analysis of pipe failure based on testing of SENB specimens. SENT specimens are designed to give a more closely matched but still higher geometry constraint than pipes (Nyhus et al., 2003) (Fig. 2.18). The fracture toughness from SENT specimens is therefore expected to be much closer to the fracture toughness in the pipe and differences will be less material dependent than is the case for SENB specimens. Crack depth has no influence on the CTOD–R curves derived from the FE simulations of pipes (Fig. 2.16), and crack depth in SENT specimens has insignificant effect on the measured CTOD-R curves. These findings demonstrate that the fracture toughness from SENT specimens gives a measure for ductile materials suitable for application to a much wider range of crack depths in pipes than earlier assumed. Fracture toughness from SENT specimens is also insensitive to crack depth. Turning to the effect of internal pressure and biaxial stresses, the FE simulations of cracked pipes with the Gurson model showed no influence of biaxial stress on the CTOD–R curves. Measured experimentally, the effects of biaxial loading on fracture toughness are lost when substantial plastic strains are allowed to develop in the ligament (Garwood, 1991). Therefore, SENT specimens can safely be used in ECA of pipes in ductile materials subjected to axial or biaxial loading with no deleterious influence on the CTOD–R curve in either stress state.



3/23/11 1:43:06 PM

48

Fracture and fatigue of welded joints and structures 700

SENB, a/W = 0.2, 2B ¥ B SENTc, a/W = 0.2, 2B ¥ B Pipe, a = 4, 2c = 16, tension Pipe, a = 4, 2c = 16, bending Pipe, a = 4, 2c = 300, tension Pipe, a = 4, 2c = 300, bending

600

J (N/mm)

500 400 300 200 100 0 –1

–0.8

–0.6

Q

–0.4

–0.2

0

2.18 J versus Q for pipes (from FEA), SENT and SENB specimens with identical crack depths (Nyhus et al., 2003).

It is important to emphasise that even though crack depth and internal pressure have negligible influence on the fracture toughness, these parameters nonetheless have a strong influence on the failure probability because the crack driving force has marked sensitivity to both crack depth and internal pressure. All conclusions derive from testing and analysis performed on ductile materials – it is not presently known if similar conclusions can be drawn for brittle materials. Further experimental validation and numerical modelling is required. Effect of misalignment and dissimilar wall thickness Tolerances on linepipe geometry are controlled by standards but some variation within these limits is nonetheless to be expected and indeed is typical of produced linepipe. The resulting mismatch in ovality and dissimilar wall thickness may lead to misalignment of the girth welds, which in turn leads to asymmetric configurations of SENT specimens. These conditions might reduce the crack growth resistance (CTOD–R curve) (McClintock, 1990) making it necessary to investigate imperfect SENT specimen geometries to determine if any correction to fracture toughness was appropriate. Trends suggest that the fracture toughness is marginally reduced compared with the reference specimens (Fig. 2.11) for some geometries. Recall that the severe test geometries were chosen to provoke this effect and are not



3/23/11 1:43:07 PM


49

representative of realistic conditions for linepipe and girth welds produced in accordance with international standards. Therefore the reduction of fracture toughness is small and its influence is considered marginal in ECA analyses. However, the importance of crack driving force appears to be a relatively complex phenomenon from current studies. In any case, experimental fullscale validation of the effect of misalignment is still required. Driving force Load capacity is very sensitive to small differences in the initial crack depth (Fig. 2.12) because the load capacity of the specimen is similar to the load that gives global yielding in the specimen. The small differences in initial crack depth (2.36 and 2.64 mm) resulted in large differences in specimen strain capacity, 2.2% vs. only 0.3% respectively. In order to simplify defect assessments, the stress–strain curve is often represented by an established analytical equation such as the Ramber–Osgood power law fitted to the data, and the lüders plateau is often smoothed out as a result. The lüders plateau that appears in uniaxial stress–strain curves is not relevant under the high hydrostatic stress state in front of the crack tip and it has been argued on this basis that its removal is correct. However, the lüders plateau is extremely important for the development of crack driving force (Fig. 2.12). Considering the specimen with the shortest crack, 2.36 mm, as when the remaining ligament begins yielding, the CTOD increases with almost no corresponding increase in strain, but when the specimen later begins yielding, the strain increases with an almost constant value of CTOD. These sudden changes in slope are due to the lüders band. It is therefore important to include lüders plateaux in the stress–strain curves when these are used to establish crack driving force curves by FE simulations, or when using material-specific failure assessment diagrams. On the subject of SENT specimens with dissimilar wall thickness (Fig. 2.13) and with strain measured on the thinner side, in ECA analyses based on failure assessment diagrams, the smallest wall thickness would normally be used in the assessment, and the crack driving force would be increased due to misalignment. This means that the predicted strain capacity of dissimilar thickness specimens (Fig. 2.13) would be lower than the equal thickness specimens (Fig. 2.12). The test results show the opposite trend. The strain capacity is significantly higher for the specimens with dissimilar thickness, indeed for similar crack depths (2.63/2.64 mm) the strain capacity is almost 10 times higher for the specimens with dissimilar thickness. This is probably due to the fact that a bending moment is introduced in the dissimilar thickness specimens. This bending moment increases the axial yield load in the crack ligament, and thus a higher load is introduced over the full wall thickness. This causes the higher load capacity.



3/23/11 1:43:07 PM

50


The results show that an increase of the wall thickness on one side of a weld might be expected to increase the load capacity, despite the fact that the increase of the wall thickness will lead to some deleterious misalignment. This does not mean that dissimilar wall thicknesses are beneficial for the global strain capacity of a welded pipe. For a pipe globally in deformation control, e.g. in a reeling operation, there will be concentration of stress and strain close to the weld attracted to the pipe with the thinnest wall. This means that both the load capacity and the loading will be increased. Material strength mismatch inherent in welds affects not only crack driving force, but also in certain cases tearing resistance as well – so a constraint effect is also apparent. Numerical studies (Østby et al., 2010) and ongoing research suggest that the effect is typically greatest for narrow welds. Although in practical terms these effects may be considered to be fully incorporated when testing welds, the need for fundamental study of this phenomenon remains.

2.4.6 Development conclusions for the SENT test SENT specimens are designed to give similar strain fields ahead of the crack as pipes with equal crack depths and are therefore more suited for testing of fracture mechanics properties in pipes than conventional deeply notched SENB specimens. Fracture toughness in materials exhibiting ductile behaviour was studied for a range of important variables. Fracture toughness estimated from SENT specimens is significantly higher than for SENB specimens with negligible variation for crack depths, a/W, ranging from 0.2 to 0.55. Numerical simulation similarly indicated insignificant variation in fracture toughness for pipes with crack depths in the range 20 to 50% of the wall thickness and also showed no changes in fracture toughness (CTOD-R curve) arising from variation of internal pressure. Finally, SENT specimens with asymmetric geometries, misalignment and unequal wall thickness gave small reductions in the fracture toughness compared with symmetric specimens. ∑ Fracture toughness estimates from SENT specimens appear insensitive to crack depth, enhancing the prospect of eventual standardisation of crack depths in SENT specimens – a candidate figure of a/W = 0.3 is supported by the development work. ∑ SENT specimens give toughness values for ductile materials applicable across a much wider range of crack depths in pipes than earlier anticipated. The validity limit for use of SENT specimens can be extended to crack depths equal to 50% of the pipe wall thickness (the maximum extent of the current development work). ∑ Internal pressure has no influence on the fracture toughness for ductile materials, allowing SENT specimens to also be used for establishing fracture properties for use in assessment of biaxially loaded flaws. © Woodhead Publishing Limited, 2011


3/23/11 1:43:07 PM


51

∑ The small deleterious effect of asymmetry on fracture toughness is considered negligible in the context of ECA. ∑ Crack driving force appears sensitive to the presence of a Lüders band in the material’s tensile response. It is therefore important to include any Lüders plateaux in the stress–strain curves; and to avoid using analytical equations that remove or minimise these features when establishing the crack driving force curve by FE simulation or with material specific failure assessment diagrams.

2.5

Standardising the single edge notch tension (SENT) test

The wide interest in the constraint matched SENT test and its increasing use in pipelines makes it imperative that any necessary improvements to the testing and analysis methods are made to allow the method to be standardised. SENT test results invariably inform critical decisions about integrity of girth welds under high strain. The rise in popularity of the SENT specimen internationally has highlighted the need to minimise inter-laboratory variations, especially in relation to ensuring consistent results. This level of consistency can only be controlled by standardising the test method, recognising the effects that the variability inherent in the test can have on the outcome both of the test (fracture toughness) and of the ensuing assessment. It appears likely that BS 7448 will address SENT testing in a future revision as the committee has reportedly already begun work (Pisarski, 2010). The challenges and obstacles to standardisation of the SENT test, at least in the context of reserving it for application to pipes, primarily involve specimen preparation and testing; and matters relating to crack driving force and estimates of fracture toughness, including CTOD. A given issue may often be linked across both categories.

2.5.1 Specimen manufacture and testing Although the SENT methodology and development work were rapidly incorporated in detail into DNV RP-F108 and DNV OS-F101, the guidance in both documents refers to BS 7448 for the necessary detail surrounding specimen manufacture and preparation only found in testing standards. These established standards are mainly concerned with high constraint compact tension (CT) and SENB specimens designs and the various requirements placed on preparation and testing will differ significantly. Many points of detail remain to be considered in relation to bringing the validation of SENT testing up to identical levels of rigour as the standard test geometries and procedures. Aspects of testing that require particular attention include the following:



3/23/11 1:43:07 PM

52


∑

Fatigue precrack validity – straightness requirements. The existing shape requirements for fatigue precracking are intended for deeply notched SENB specimen designs in the range 0.45 < a/W < 0.7 while the typical SENT range is 0.2 < a/W < 0.5. Differences in initial depth will influence geometry constraint but did not influence fracture toughness over the relatively small range of conditions originally tested (Nyhus et al., 2002). On test validity requirements, it seems difficult to expect that long fronted precracks in SENT specimens can meet current test standard requirements (Pisarski, 2010) (Fig. 2.19). ∑ J determination. The fundamental formulation of the equations used for the J integral is challenged by issues of material inhomogeneity in weldments and the fact that cracks tearing under test are non-stationary. The guidance imposes a safety factor of 0.85 and places a limit on crack extension to capture these aspects. Alternative equations addressing these problems are available (Shen et al., 2004; Cravero and Ruggieri, 2007). ∑ Out of plane tearing. Tearing beyond the heat-affected zone (HAZ) into parent material is a recognised problem with conventional overmatched welds where the extending crack is attracted towards the region experiencing greatest strain, usually the HAZ and parent material (Macdonald and Lange, 2008). 45 Parent pipe Weld metal Heat-affected zone (HAZ)

40

(amax-amin)/a0 (%)

35 30 25

BS 7448 Part 2 limit

20 15 10

BS 7448 Part 1 limit

5 0 10

20

30

B (mm)

40

50

60

2.19 Variation of crack front straightness with specimen thickness in SENT specimens with 0.2 < a/W < 0.55, where a0 is the weighted average crack length determined according to BS 7448 Part 1 (Pisarski, 2010).



3/23/11 1:43:07 PM


∑

53

Residual stresses. Modest levels of side precompression (0.25% on each side of the SEnt specimen) appears to offset any disturbance of straight precrack development by residual stresses (Pisarski, 2010).

2.5.2

Fracture toughness and CTOD

fracture toughness estimates from SEnt specimens are insensitive to crack depth and a strong candidate figure of a/W = 0.3 has already emerged from development studies for the specimen (nyhus et al., 2005). Should cleavage behaviour be observed during testing with SEnt specimens then the resulting estimates of fracture toughness would likely be very sensitive to the level of geometry constraint present in the test, whereby small increases in constraint level could potentially reduce fracture toughness significantly. Although the guidance recommends caution in using such results, the factors influencing cleavage initiation under low geometry constraint need to be more fully investigated and understood. in such circumstances it would be safer to employ conventional high constraint SEnb specimens to provide lower bound estimates of fracture toughness. Fracture toughness is defined in terms of the J integral in the guidance and elsewhere in relation to SEnt testing. however, much of the development work and certainly the majority of the literature concerning EcA and circumferential flaws in pipeline girth welds at high strain phrase crack driving force in terms of ctod, rather than J. Given this considerable volume of relevant data, it is desirable to either transform the value of J estimated from SEnt specimens into an equivalent ctod, or estimate ctod directly from the SEnt test. dnV oS-f101 provides an equation for conducting such a transformation based on the general form:

d=

J s + s UtS ˆ Ê m Á yS ˜¯ 2 Ë

2.4

where m is a function of material strain hardening and crack depth, yS is yield strength and UtS is ultimate tensile strength. the a/W functions used in the formulation of J lead to underestimates of ctod on account of their original derivation for the SEnb geometry (Pisarski, 2010) where the level of underestimation can reach approximately 25% (fig. 2.20). less error prone is the simple estimation of ctod directly from the test based on measuring crack mouth displacements with a double clip gauge instrumentation: d = del + dpl

d=

2.5

(1 – u 2 )K I2 a + z1 + Vp1 – · (Vpp22 – Vp1) mEs yS z2 – z1

2.6



3/23/11 1:43:07 PM

54


4.00 CTOD from clip gauges CTOD from J (DNV OS F101)

CTOD (mm)

3.00

2.00

1.00

0.00 0.00

1.00

2.00 CTOD (mm) from FEA

3.00

4.00

2.20 Comparison of CTOD estimation derived from J in accordance with DNV OS-F101 and directly from clip gauge readings (35 mm ¥ 17.5 mm, a/W = 0.34) taken from grade X100 pipeline steel (Pisarski, 2010).

where: a original crack length (mm) K stress intensity factor (at unloading) (N/mm1.5) m constraint factor of unity or 2 Vpl plastic component of lower clip gauge reading (at unloading) (mm) Vp2 plastic component of upper clip gauge reading (at unloading) (mm) z1 lower knife edge height (mm) z2 upper knife edge height (mm) d CTOD (mm) del elastic portion of CTOD (mm) dpl plastic portion of CTOD (mm)

2.6

Conclusions

The constraint matched SENT test has removed much of the conservatism commonly held to be associated with structural integrity assessments of pipeline girth welds. The development of the specimen design was thorough and indeed paves the way for eventual standardisation of the specimen, both in terms of its design and preparation, and in the test procedure. The



3/23/11 1:43:08 PM


55

estimates of fracture toughness provided by SENT specimens and the extent of validity for transferring these estimates to assessments of flaw behaviour in pipelines are relatively well understood. The need for further work in support of standardisation efforts is recognised. Aspects of how the SENT specimen has been applied in practice, including the effect of crack depth; misalignment; dissimilar wall thicknesses; and the effects of biaxial loading have all been addressed in this chapter. Areas requiring further research are highlighted, including limitations and aspects of specimen preparation, testing and analysis procedures that need to be addressed in order to fully standardise the test.

2.7

References

Betegón, C. and Hancock, J. W., 1991, ‘Two parameter characterization of elastic-plastic crack-tip fields’, Journal of Applied Mechanics, 58, 104–110 Bruschi, R., Torselletti, E., Vitali, L., Hauge, M. and Levold, E., 2005, ‘Fracture control – offshore pipelines: current status of fracture assessment for pipeline limitations and the need for development’, Proceedings of OMAE2005, 24th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2005), 12–16, June, Halkidiki, Greece Budden, P. J., 2006, ‘Failure assessment diagram methods for strain-based fracture’, Engineering Fracture Mechanics, 73, 537–552 Cosham, A. and Macdonald, K. A., 2008, ‘Fracture control in pipelines under high plastic strains – a critique of DNV RP-F108’, paper IPC2008–64348, International Pipeline Conference, Calgary, Canada, 30 September–3 October Cravero, S. and Ruggieri, C., 2007, ‘Estimation procedure of J-resistance curves for SE(T) fracture toughness specimens using unloading compliance’, Engineering Fracture Mechanics, 74, 2735–2757 Dawes, M. G., 1974, ‘Brittle fracture in high strength weldments’, Welding Research International, 4, 41–73 Garwood, S.J., 1991, ‘The significance of biaxial loading on the fracture performance of a pressure vessel steel’, In: Pressure Vessel Integrity. ASME PVP-Vol. 213/MPC Vol. 32, 113–123 Garwood, S. J., Davey, T. G. and Creswell, S. L., 1989, ‘Behaviour of A533B under biaxial loading at +70°C’, International Journal of Pressure Vessels and Piping, 36, 199–224 Kastner, W., Rohrich, E., Schmitt, W. and Steinbuch, R., 1981, ‘Critical crack sizes in ductile piping’, International Journal of Pressure Vessels and Piping, 9, 197–219 Macdonald, K. A. and Cheaitani, M., 2010, ‘Engineering critical assessment in the complex girth welds of clad and lined linepipe materials’, paper IPC2010–31627, International Pipeline Conference, Calgary, Canada, 27 September – 1 October Macdonald, K. A. and Hopkins, P., 1995a, ‘The significance of non-planar defects in transmission pipeline girth welds: Part 1 – A literature review’, Pipes and Pipelines International, 40(2), 37–38 Macdonald, K. A. and Hopkins, P., 1995b, ‘The significance of non-planar defects in transmission pipeline girth welds: Part 2 – Description of the European Pipeline Research Group’s guidelines on acceptability and limits’, Pipes and Pipelines International, 40(3), 29–37 © Woodhead Publishing Limited, 2011


3/23/11 1:43:08 PM

56


Macdonald, K. A. and Lange, I., 2008, ‘Engineering critical assessment of thin-wall offshore pipelines’, Paper IPC2008–64188, International Pipeline Conference, Calgary, Canada, 30 September – 3 October McClintock, F. A., 1990, ‘Reduced crack growth ductility due to asymmetric configurations’, International Journal of Fracture, 42, 357–370 Minaar, K., Gioielli, P. C., Macia, M. L., Bardi, F., Biery, N. E. and Kan, W. C., 2007, ‘Predictive FEA modelling in pressurized full-scale tests’, Proceedings of ISOPE 2007, 17th International Offshore and Polar Engineering Conference, Lisbon, Portugal Nyhus, B., Østby, E., Thaulow, C., Zhang, Z. and Olden, V., 2002, “SENT testing and the effect of geometry constraint in high strength steel’, International Symposium High Strength Steel, 23–24 April, Verdal, Norway Nyhus, B., Loria, M. P. and Ørjasæter, O. L., 2003, ‘SENT specimens an alternative to SENB specimens for fracture mechanics testing of pipelines’, Proceedings of OMAE03, 22nd International Conference on Offshore Mechanics and Arctic Engineering, 8–13, June, Cancun, Mexico Nyhus, B., Østby, E., Knagenhjelm, H. O., Black, S. and Røstadsand, P. A., 2005, ‘Fracture control – offshore pipelines: experimental studies on the effect of crack depth and asymmetric geometries on the ductile tearing resistance’, Proceedings of OMAE2005, 24th International Conference on Offshore Mechanics and Arctic Engineering, 12–16, June, Halkidiki, Greece O’Dowd, N.P. and Shih, C.F., 1991, ‘Family of crack-tip fields characterised by a triaxiality parameter – I. Structure of the fields’, Journal of the Mechanics and Physics of Solids, 39, 989–1015 O’Dowd, N. P. and Shih, C. F., 1992, ‘Family of crack-tip fields characterized by a triaxiality parameter: Part 2 – Fracture applications’, Journal of the Mechanics and Physics of Solids, 40, 939–963 Østby, E., 2005, ‘Fracture control – offshore pipelines: new strain-based fracture mechanics equations including the effects of biaxial loading, mismatch and misalignment’, Proceedings of OMAE2005, 24th International Conference on Offshore Mechanics and Arctic Engineering, 12–16, June, Halkidiki, Greece Østby, E., 2007, ‘Fracture control offshore pipelines JIP – proposal for strain-based fracture assessment procedure’, Proceedings of ISOPE 2007, International Offshore and Polar Engineering Conference, Lisbon, Portugal Østby, E. and Hellesvik, A., 2007, ‘Fracture control offshore pipelines JIP – results from large-scale testing of the effect of biaxial loading on the strain capacity of pipes with defects’, Proceedings of ISOPE 2007, 17th International Offshore and Polar Engineering Conference, Lisbon, Portugal Østby, E., Nyhus, B., Kane, P.-A. and Thaulow, C., 2010, ‘The effect of weld metal mismatch level on failure mode in small-scale SENT testing of an X80 material’, Proceedings of ISOPE 2010, 20th International Offshore and Polar Engineering Conference, Beijing, China Phaal, R., Andrews, R. M. and Garwood, S. J., 1995, ‘TWI biaxial test program: 1984– 1994’, International Journal of Pressure Vessels and Piping, 64, 177–190 Pisarski, H. G., 2010, ‘Determination of pipe girth weld fracture toughness using SENT specimens’, paper IPC2010–31123, International Pipeline Conference, Calgary, Canada, 27 September – 1 October Pisarski, H. G. and Wignal, C., 2002, ‘Fracture toughness estimation for pipeline girth welds’, Proceedings of International Pipeline Conference, IPC 2002, Calgary, Alberta, Canada.



3/23/11 1:43:08 PM


57

Sandvik, A., Østby, E., Naess, A. and Sigurdsson, G., 2005, ‘Fracture control – offshore pipelines: probabilistic fracture assessment of circumferentially surface cracked ductile pipelines using simplified equations’, Proceedings of OMAE2005, 24th International Conference on Offshore Mechanics and Arctic Engineering, June 12–16, Halkidiki, Greece Shen, G., Tyson, W. R., Glover, A. and Horsley, D., 2004, ‘Constraint effects on linepipe toughness’, Pipeline Technology Conference, Ostend, Belgium, Vol.2, 703–720 Sumpter, J. D. G. and Forbes, A. T., 1992, ‘Constraint based analysis of shallow cracks in mild steel’, Proc. TWI/EWI/IS Proc. Int. Conf. Shallow Crack Fracture Mechanics Tests and Applications, Cambridge, UK Thaulow, C., Skallerud, B., Jayadevan, K. R. and Berg, E., 2005, ‘Fracture control – offshore pipelines: advantages of using direct calculations in fracture assessments of pipelines’, Proceedings of OMAE2005, 24th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2005), 12–16, June, Halkidiki, Greece Tkaczyk, T., O’Dowd, N. P. and Howard, B. P., 2007, ‘Comparison of crack driving force estimation schemes for weld defects in reeled pipelines’, Proceedings of ISOPE 2007, International Offshore and Polar Engineering Conference, Lisbon, Portugal Tyson, W. R, Shen, G. and Roy, G., 2007, ‘Effect of biaxial stress on ECA of pipelines under strain-based design’, Proceedings of ISOPE 2007, International Offshore and Polar Engineering Conference, Lisbon, Portugal Wang, Y.-Y., Liu, M., Horsley, D. and Zhou, J., 2006, ‘A quantitative approach to tensile strain capacity of pipelines’, Proceedings of IPC 2006, International Pipeline Conference, American Society of Mechanical Engineers, Calgary, Canada Wästberg, S. Pisarski, H. and Nyhus, B., 2004, ‘Guidelines for engineering critical assessments for pipeline installation methods introducing cyclic plastic strain’, Proceedings of OMAE04, 23rd International Conference on Offshore Mechanics and Arctic Engineering, 20–25, June, Vancouver, British Columbia, Canada Williams, M. L. 1957, ‘On the stress distribution at the base of a stationary crack’, Journal of Applied Mechanics, 24, 109–114 Yang, S., Chao, Y.J. and Sutton, M.A., 1993, ‘Higher order asymptotic crack tip fields in a power-law hardening material’, Engineering Fracture Mechanics, 45(1), 1–20 Zhang, Z. L., Thaulow. C. and Ødegaard, J., 2000, ‘A complete gurson model approach for ductile fracture’, Engineering Fracture Mechanics, 67, 155–168

2.8

Appendix: Codes and standards

API, 2005: API 1104, Welding of Pipelines and Related Facilities, API Standard 1104, Twentieth Edition, American Petroleum Institute, Washington, USA, November 2005 API, 2007: API 579-1:2007 ‘Fitness for service’, 2nd ed. ASTM E1290, Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement: ASTM E1290-08e1, American Society for Testing and Materials, Philadelphia, USA ASTM E1820, Standard Test Method for Measurement of Fracture Toughness: ASTM E1820-06e1, American Society for Testing and Materials, Philadelphia, USA. British Energy, 2005: Assessment of the Integrity of Structures containing Defects, R6-Revision 4, British Energy, June 2005 © Woodhead Publishing Limited, 2011


3/23/11 1:43:08 PM

58


BSI, 1991: BS 7448-1, Fracture mechanics toughness tests – Part 1; Method for determination of KIc, critical CTOD and critical J values of metallic materials, British Standards Institute, London, UK, 1991 BSI, 1997: BS 7448-2, Fracture mechanics toughness tests – Part 2; Method for determination of KIc, critical CTOD and critical J values of welds in metallic materials, British Standards Institute, London, UK, 1997 BSI, 1997: BS 7448 Part 4, Fracture mechanics toughness tests – Part 4; Method for determination of fracture resistance curves and initiation values for stable crack extension in metallic materials , British Standards Institute, London, UK, 1997 BSI, 2004: BS4515, Specification for welding of steel pipelines on land and offshore. carbon and carbon manganese steel pipelines, British Standards Institute, London, UK, November 2004 BSI, 2005: BS 7910 Guide on methods for assessing the acceptability of flaws in metallic structures, British Standards Institute, London, UK, 2005 DNV, 2006: DNV RP-F108, Fracture control for pipeline installation methods introducing cyclic plastic strain, recommended practice, Det Norske Veritas, January 2006 DNV, 2007: DNV OS-F101, Submarine pipeline systems, offshore standard, Det Norske Veritas, October 2007 ISO, 2010: ISO 15653, Metallic materials – Method of test for the determination of quasi-static fracture toughness of welds, 2010

2.9

Nomenclature

Abbreviations API American Petroleum Institute ASTM American Society for Testing and Materials BS British Standards CT compact tension CTOD crack tip opening displacement DNV Det Norske Veritas ECA engineering critical assessment FAD failure assessment diagram FE finite element FL fusion line GTAW gas tungsten arc welding HAZ heat affected zone HRR Hutchinson Rice Rosengren SENB single edge notched bending SENT single edge notched tensile WM weld metal



3/23/11 1:43:08 PM


59

Symbols – Latin characters a a0 Apl B B D e E F J Jel JIc Jpl K K Lr m t Vp1 Vp2 W z z1 z2

total crack length after test (mm) original crack length (mm) plastic area under the load-CMOD curve at z = 0 (N mm2) wall thickness (mm) specimen width (mm) diameter (mm) axial misalignment (mm) Young’s (elastic) modulus (N/mm2) load (N) J-integral (N/mm) elastic J (N/mm) mode-I critical J (N/mm) plastic J (N/mm) stress intensity factor (N/mm1.5) stress intensity factor (at unloading) (N/mm1.5) load ratio constraint factor, unity or 2 wall thickness (mm) plastic component of lower clip gauge reading (at unloading) (mm) plastic component of upper clip gauge reading (at unloading) (mm) specimen height (mm) knife edge height, (mm) lower knife edge height (mm) upper knife edge height (mm)

Symbols – Greek characters d el,nom ep sT, UTS sY, YS d Δa del dpl h n

crack tip opening displacement (mm) total nominal strain accumulated plastic strain tensile strength (N/mm2) yield strength (N/mm2) CTOD (mm) crack extension (stable tearing) (mm) elastic portion of CTOD (mm) plastic portion of CTOD (mm) eta factor Poisson’s ratio



3/23/11 1:43:08 PM

3

Fracture assessment methods for welded structures

I. H a d l e y, TWI, UK

Abstract: This chapter reviews the use of fracture assessment procedures such as BS 7910, R6, FITNET and API 579-1/ASME FFS-1 to analyse critical engineering structures that contain flaws, such as cracks or fabrication defects. Such procedures, also termed fitness-for-service (FFS) or engineering critical assessment (ECA) procedures, allow the user to demonstrate the safety of a metallic structure or component in which some aspect of design, manufacture or operation may not comply with a recognised engineering code. Each procedure is based on engineering fracture mechanics concepts and validated by testing, analysis and extensive experience. Whilst all of the major procedures have a common underlying technology, each one also has aspects that make it attractive to a particular user group. The background, current structure, status and main application of each procedure is summarised. Key words: fracture, fitness-for-service (FFS), fitness-for- purpose (FFP), engineering critical assessment (ECA), damage-tolerant/defect-tolerant design, failure assessment diagram (FAD), engineering fracture mechanics, flaw assessment.

3.1

Introduction

Fracture from defects in structurally critical welds is normally avoided by close adherence to a recognised construction code. This will typically cover the design, materials requirements, fabrication and inspection of the component, and possibly other aspects affecting integrity, such as pre-service testing (for example hydrotesting of pressure equipment), operational requirements and in-service inspection. This approach is based on many accumulated years of experience, and has been highly effective in avoidance of failure. Where some aspect of design, build quality or materials properties falls outside the experience embedded in the codes, however, an alternative approach may be required, based on engineering fracture mechanics. Here, the possibility of failure (by brittle or ductile fracture, or by plastic collapse of the component) associated with the presence of a real or postulated defect is explicitly modelled. The flawed component can then be conveniently classified as safe or unsafe, typically by using a failure assessment diagram or FAD. The technique is typically known as engineering critical assessment 60 © Woodhead Publishing Limited, 2011


3/23/11 1:43:33 PM


61

or ECA, and forms part of the category of methods known as fitness-forservice (FFS), fitness-for-purpose (FFP), or defect-tolerant design. This chapter reviews some of the most widely used methods of fracture assessment of welded structures, such as BS 7910, R6, Structural Integrity Procedures for European Industry (SINTAP), European Fitness-for-service Network (FITNET) and API 579-1/ASME FFS-1. The evolution of the methods and the relationship between rule-based construction codes and ECA methods is described, along with relationships between the different ECA methods, and special features of each. Attention is restricted to procedures that address fracture assessment, i.e. failure under static loading at low or ambient temperature due to the presence of flaws.

3.1.1 Development of design codes for fracture-critical components Pressure equipment, initially in the form of simple boilers, has been used since the early days of the industrial revolution. As reported by Woods and Baguley (1), the design and construction of boilers was left to the individual designer or manufacturer; failures and fatalities were common, peaking at the rate of around one per day in the late 1890s, as shown in Fig. 3.1. In the early years of the 20th century, the American Society of Mechanical Engineers (ASME) issued its first code for power boilers. The dramatic effects of the code can be inferred from Fig. 3.1; the annual number of explosions fell over the remainder of the century, in spite of a rise in mean steam pressure (and a rise in the total population of boilers, which is not considered in the figure). Figures from across the industrialised world (2–7) show the current 5000

300 St

ea

m

e pr

ss

ur

e

4000

Steam pressure (psi)

Boiler explosions in the United States

400

3000

200

2000 100

1000

0 0 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Year

3.1 Rates of boiler explosions in the USA.



3/23/11 1:43:34 PM

62


‘catastrophic’ failure rate of pressure vessels to be approximately 10 –5 to 10–6 per vessel year, although the precise figure varies somewhat among countries and depends on the type of equipment under consideration. The correct application of an appropriate code for design, construction, operation, inspection and maintenance of pressure equipment can therefore be expected to produce equipment with a very low failure rate. This is achieved through a combination of factors: ∑

Control of the operating stresses, and of the stress concentrations associated with changes of section, openings and other discontinuities. ∑ Control of the presence of flaws, especially at welds, by: qualification of both the weld procedure and the welders responsible for applying it, inspection (visual and non-destructive) of the finished product to ensure that it complies with the code (some ‘indications’ such as porosity or inclusions are inevitably associated with fusion welds, and the code will give guidance on what is considered acceptable). ∑ Control of the quality of materials, in terms of their chemical composition, tensile properties and (if the equipment will experience low-temperature operation) toughness. In practice this usually means the use of Charpy testing in order to demonstrate some degree of resistance to low temperature failure, especially if the vessel is constructed from a steel that undergoes a ductile–brittle transition as temperature is reduced. ∑ Application of a preservice pressure test in order to demonstrate the integrity of the equipment. This test, typically carried out using water as a test medium, is highly effective in weeding out potentially dangerous flaws or non-conforming material under conditions of relative safety, if the precautions mentioned earlier (inspection and control of materials qualities) have for some reason proved insufficient. An example of how these principles are implemented in a code is given by the European Pressure Vessel Code (8). Part 2 of the document (Materials) lists acceptable materials and includes an annex specifically addressing avoidance of brittle fracture. Part 3 (Design) gives methods for design by formulae (DBF), including determination of the required minimum thickness, weld joint efficiencies and the requirements for design of heads, stiffeners and openings. An alternative approach, design by analysis (DBA) is described in annexes to this part. Part 4 (Fabrication) covers such issues as welding qualification and manufacturing tolerances, while Part 5 (Inspection and Testing) covers the extent of inspection required and appropriate acceptance criteria. Of course, these principles also apply to other types of fracture-critical structures, including bridges, offshore structures, storage tanks, pipelines and shipping. The ECA techniques described in the remainder of this chapter can be applied to a wide range of welded and non-welded structures at all



3/23/11 1:43:34 PM


63

stages of the product life cycle, from design through fabrication, operation, life extension and decommissioning.

3.2

Development of engineering critical assessment (ECA) methods

Although rule-based standards such as the European Pressure Vessel Code have proved highly successful in terms of reducing the number of catastrophic failures in pressure equipment, there are inevitably situations that they do not address, for example cases where some aspect of materials properties, build quality or design fall outside the scope of the standard. Experience from failures shows that it is not the presence of flaws or brittle material per se that leads to failure, rather it is a combination of factors including the stresses on the flawed body and the service temperature, and that these factors can be quantified and related to each other via the discipline of engineering fracture mechanics. Consequently, a shortfall in, say, the toughness of a weldment normally used in the as-welded condition could be offset by the use of post-weld heat treatment to relieve welding residual stresses and reduce the driving force for failure. Fitness-for-service methods can be used in a variety of scenarios: ∑ ∑

∑ ∑ ∑ ∑

To make a decision as to whether a component containing a known fabrication flaw (or flaws) can be safely operated even though the flaws are not permitted by workmanship standards. To interpret the results of in-service inspection, e.g. to decide whether a component containing flaws propagating through fatigue crack growth or some other mechanism can be safely operated until the next shutdown/ inspection. To demonstrate that a particular inspection technique/procedure can safely detect and size flaws that could be critical to the integrity of a structure. To demonstrate whether or not post-weld heat treatment (PWHT) of thick-section components is necessary to ensure the integrity of a component. To support failure analysis by showing which scenarios could credibly lead to failure. To support life extension/change of use studies.

The development of structured procedures for carrying out ECA or FFS can be linked to a desire by industry and regulatory authorities to have a single, agreed and well-validated source of reference that could be used by all parties and would produce consistent results. Features of an ideal FFS document would include:



3/23/11 1:43:34 PM

64

∑ ∑ ∑ ∑ ∑ ∑ ∑


being logical, self-contained and user-friendly (especially where the most conservative options/levels are considered); different options depending on the information available to the user and the level of accuracy required; ability to be used at all stages of life, e.g. design, operation, life extension, failure analysis; fully validated; where possible, consist with historic methods, so that older analyses do not have to be repeated every time a new edition is produced; where possible, taking into account the reliability and accuracy of the result; using terminology and data that are readily available from design documents.

Five such procedures are summarised in Table 3.1 and described in more detail in section 3.4.

3.3

The failure assessment diagram (FAD) concept

The FAD concept is common to all of the fracture analysis methods described in Section 3.5, so is described in general terms here; a comprehensive review is given by Milne et al. (9). It has long been recognised that the static failure of a structure containing defects can fail either by fracture or by collapse. In the case of linear elastic fracture mechanics (LEFM), failure will occur Table 3.1 Comparison between major fracture assessment procedures Method

First published

Main user base

R6 1976 Nuclear power

Current status Continues to be maintained

BS 7910 1980 (as PD6493) General procedure, but Amendment particularly popular published in 2005, with upstream oil, gas revision due c 2012 and pipeline sector SINTAP 1999 General procedure

Now subsumed into FITNET procedure

API 579–1/ 2000 (as API 579) Downstream oil, gas ASME FFS-1 and chemical industry

Joint API/ASME procedure published in 2007

FITNET 2006 General procedure

Published document, will form the basis of future BS 7910 revisions. Publication of weldrelated fracture clauses by IIW also planned



3/23/11 1:43:34 PM


65

when the applied stress intensity, KI, attains a critical value known as the fracture toughness, Kmat: K I = s nom p a f (a /W )

3.1

Here, the nominal applied stress is snom, the flaw size is given by a, the structural width by W, and f (a/W) is a geometry function that is tabulated for common structures and specimen types (e.g. (10)). Consequently, the value of nominal stress at failure, sf, is given by:

sf =

K mat p a f (a (a /W )

3.2

at the same time, failure due to collapse is a function of the structural geometry and the ultimate tensile strength of the material, su, and the value of nominal stress at failure, sc, can be expressed as: sc = D(a/W) su

3.3

where D(a/W) is also available from handbooks (e.g. (11)). Both parameters can be normalised and the transition between leFM fracture and plastic collapse represented in the form of a single Fad, which is independent of component geometry and material. Various types of Fad have been adopted over the years, as described in Section 3.4; the version published in the first version of R6 is shown in Fig. 3.2. The proximity to plastic collapse is represented on the horizontal axis in the form of a parameter Sr, that of fracture on the vertical axis, Kr. 1.2 1.0

Potentially unsafe

Kr

0.8 0.6 0.4 0.2 0.0

Safe 0.0

0.2

0.4

0.6 Sr

0.8

1.0

1.2

3.2 Strip yield FAD, as given in the first edition of R6.



3/23/11 1:43:34 PM

66


The key benefit of the FAD is that it allows the user to apply LEFM concepts to the analysis of a structure in which the development of plasticity affects the failure load. As Sr, and hence plasticity, develops, so the permitted value of Kr reduces until Sr = 1, beyond which failure by plastic collapse is conceded. Consequently, a flaw can be analysed by calculating Kr and Sr independently and plotting the result on a FAD. If the point lies within the failure assessment line (FAL), it can be considered safe, if outside it is potentially unsafe. A point lying on the FAL represents a limiting condition, which could be expressed in terms of flaw size, applied stress, minimum required fracture toughness or some other parameter. In welded structures, the Kr axis needs to take account of all factors influencing crack driving force, namely primary stresses (from self-weight, pressure, live load), secondary stresses (typically welding residual stresses), thermal stresses and local stress concentrations. The horizontal axis of the FAD, which allows for plasticity, is in general affected only by primary stresses. Subsequent developments in EPFM (elastic-plastic fracture mechanics) led to the formulation of the FAD as it is now implemented in several ECA procedures (see Section 3.4). The ‘strip yield’ model shown in Fig. 3.2 has been supplanted by the so-called ‘Option 1’ FAD (in R6 terminology) or ‘Level 2/Level 3 FAD’ (BS 7910), which has the advantage of being independent of geometry and material (although the form of the FAD will depend on the yield behaviour of the material, as outlined later). The Sr axis has been replaced by a new plastic collapse parameter, Lr, but the principle underlying the method has remained the same since the first version of R6 was published. There are, of course, alternatives to the FAD approach, of which the most common are termed crack driving force (CDF) methods. Here, the crack driving force is calculated in terms of KI or equivalent (by means of parametric equations or finite element analysis (FEA), for example) and compared with the resistance of the structure, expressed in terms of fracture toughness. The CDF approach, however, requires a separate calculation of susceptibility to plastic collapse, hence the enduring popularity of FADbased methods. All of the procedures discussed in this chapter make a distinction between primary stresses (such as those due to pressure, self-weight and external loads) and secondary stresses (such as ‘local’ welding residual stress) which are self-balancing across the section thickness and may drive crack propagation, but not plastic collapse. Consequently, the Kr axis reflects the influence of both primary and secondary stresses, the Lr axis primary stresses only. The shape of the FAD, with Kr decreasing as a function of Lr takes account of interaction between crack driving force and plasticity for the case of the primary stresses. So far as secondary stresses are concerned, interaction



3/23/11 1:43:35 PM


67

can be accounted for by correcting the value of Kr using a factor designated either V or r. Some procedures allow the use of either parameter.

3.4

Specific engineering critical assessment (ECA) methods: R6

3.4.1 Background The UK nuclear industry’s flaw assessment technique, designated R6 (12), was first issued in 1976, with the aim of ensuring that safety cases concerning power plant (both nuclear and fossil fuel fired) should be carried out in a reproducible and consistent fashion. Although R6 was intended to be applicable in principle to all types of welded or fabricated structures, it gained its early reputation through its application to the analysis of thickwalled pressure vessels, often in the stress-relieved condition and made from ductile materials. The R6 method explicity considered the possibility of failure of structures from both brittle fracture and plastic collapse, and introduced the concept of an FAD to show the interaction between the two. This allowed the user to apply LEFM concepts to calculate KI, with the FAD showing how the permitted level of driving force (designated Kr, the ratio of the crack driving force to the characteristic fracture toughness) reduces as the net section stress or reference stress (normalised to the yield strength of the material), increases. An example of the approach is shown in Fig. 3.3, which shows the simplest 1.2 1.0

Potentially unsafe

Kr

0.8 Approx. Option 2; continuous yielding

0.6 Approx. Option 2; discontinuous yielding

0.4

Option 1 FAD; continuous yielding

0.2 0.0

Safe 0.0

0.2

0.4

0.6

Lr

0.8

1.0

1.2

1.4

3.3 R6 FADs for continuously and discontinuously yielding materials (sY = 400 N/mm2, sUTS = 500 N/mm2).



3/23/11 1:43:35 PM

68


(‘Option 1’ or ‘approximate Option 2’) R6 FADs for a continuously yielding material and a discontinuously yielding material, i.e. one showing Lüder’s plateau behaviour. R6 is now in its fourth major revision; selected milestones in the development of the procedure are shown in Table 3.2 (13).

3.4 2 Structure The current edition of R6 is arranged into basic chapters as follows: I Basic procedures II Inputs to basic procedures III Alternative approaches (including mixed-mode loading, constraint, allowance for strength mismatch, use of local approach, probabilistic techniques, leak-before-break, load history effects, calculation of residual stress, displacement-controlled loading) IV Compendia (K-solutions, limit load solutions for homogeneous and strength-mismatched structures, welding residual stress distributions, constraint parameters) V Validation and worked examples Emphasis is given here to the basic procedures of Chapters I and II, as these are widely used and have influenced several other procedures. As well as introducing the concept of the FAD, R6 introduced the notion of carrying out fracture assessment using different ‘options’ of analysis, depending on the nature of the data available to the analyst. The basic hierarchy of FADs in R6 Rev. 4 (discussed in more detail later) is as follows: Table 3.2 Selected milestones in the development of R6 (13) Revision Year of number publication

Features

1

1976

∑ Recognition of fast fracture and plastic collapse as limiting failure modes, use of ‘strip yield’ FAD

2

1980

∑ Methods for the treatment of secondary/residual stresses

3

1986

∑ Plastic collapse axis expressed in terms of Lr instead of Sr (strip yield FAD retained for C-Mn steels) ∑ New FADs ∑ Analysis may be based on tearing resistance curve, and not only on initiation toughness

4 2001

∑ ∑ ∑ ∑ ∑

Restructuring of document New FADs, compatible with SINTAP procedure Consideration of weld strength mismatch Consideration of crack tip constraint Many new appendices



3/23/11 1:43:35 PM


∑

∑ ∑

69

Option 1: does not require detailed stress–strain data; the FAD is defined as a single curve over the range for 0 < Lr < Lr,max, where Lr,max is the ratio of the uniaxial flow strength to the uniaxial yield strength or 0.2% proof strength. The curve is based on a lower bound fit to data for a range of materials and structures. Option 2: the FAD is defined on the basis of detailed stress–strain data for the material of interest, so that yielding in the ‘knee’ region of the FAD (around Lr = 1) can be more precisely defined. Option 3: the Fad is both material- and geometry-dependent, generated from FEA of the cracked structure

In practice, the idea of a single FAD (such as the strip yield FAD shown in Fig. 3.2) representing all possible materials has now been largely superseded, and materials (and thus FADs) are classified according to whether they show (or are likely to show) continuous or discontinuous yielding. Of course, this means that users who already know whether yielding is continuous or discontinuous are likely to have access to a stress–strain curve for the material in question, and could therefore go straight to an Option 2 rather than an Option 1 analysis. Table I.6.2 of R6 gives some advice on this matter; a range of steels are classified in terms of strength, processing route, composition and heat treatment, and information given as to whether or not discontinuous yielding is likely. On the basis of this information, users can adopt the so-called ‘approximate Option 2’ curve, as shown in Fig. 3.3. The simplest analysis available in R6 uses the so-called Option 1 Fad, a successor to the strip yield Fad shown in Fig. 3.2. Here, the relationship between Kr and Lr can be assumed to be independent of materials properties and structural geometry for 0 < Lr < 1, where: f(Lr) = (1 + 0.5L2r)–0.5 [0.3 + 0.7 exp (– 0.6L6r)]

3.4

This originates from the FAD given in R6 Rev.3 (which continues to be used by BS 7910 and API/ASME), but with some slight adjustments to harmonise with the FADs developed under the SINTAP project (see section 3.4.3) and to ensure that the Option 1 Fad lies within the Option 2. For Lr > 1, the form of the curve will depend on whether the yielding behaviour is continuous or discontinuous; for continuously yielding material, the Option 1 Fad follows equation 3.4 up to a ‘cut-off’ at a value Lr,max, which depends on the yield properties of the material. Lr,max =

sf sy

3.5

where sf is the flow strength and sy the yield or proof strength of the material. For Lr > Lr,max, Kr = 0. For materials known to show continuous yielding, but for which a full



3/23/11 1:43:35 PM

70


stress–strain curve is not available, the so-called ‘approximate Option 2’ curve is used for Lr values between 1 and Lr,max: f(Lr) = f(1)L(N–1)/2N r

3.6

where N is an estimate of the strain hardening exponent given by N = 0.3 [1 – (sy/sm)]

3.7

For discontinuously yielding materials, either the Option 1 curve (Equation 3.4) can be followed up to Lr = 1, or the ‘approximate Option 2’ Fad is used. This consists of three regions: f (Lr) = (1 + 0.5L2r )–0.5

3.8

up to Lr = 1. This is followed by a rapid drop in Kr at Lr = 1, reflecting the yield plateau: f (1) = Èl + 1 ˘ ÍÎ 2l ˙˚

–0.5

3.9

where

l = 1 + E De sy

3.10

s De = 0.0375 ÈÍ1 – y ˘˙ 1000 Î ˚

3.11

and

followed by the use of equation 3.6 in the range 1 < Lr < Lr,max. These ‘generic’ curves, for which detailed stress–strain data are not required, are illustrated in Fig. 3.3 for a steel with yield/proof strength of 400 N/mm2 and ultimate tensile strength (UTS) of 500 N/mm2. The Option 1 and approximate Option 2 curves are intended to represent a lower bound to fracture/plasticity interactions for a wide range of materials. Consequently, if the user has more detailed materials data available, a more accurate representation of the Fad can be achieved by using Option 2: È Ee L3s ˘ K r = Í ref + r y ˙ ÎLr s y 2Ee ref ˚

–0.5

3.12

Finally, in situations in which detailed elastic and elastic-plastic Fea of the cracked structure is available, it is possible to use the Option 3 curve, defined by the curve: f (Lr ) =

Je J ep

3.13



3/23/11 1:43:36 PM


71

for Lr < Lr,max. Here, Je and Jep are the values of J-integral derived from elastic and elastic-plastic analyses respectively at a load corresponding to the value Lr. The advantage of the Option 3 method is that it has the potential to produce a very accurate description of the system, the Fad being dependent on the loading system, flaw size and geometry and materials properties. Conversely, this means that the FAD has to be regenerated for every flaw size and loading condition, so considerable computational effort is required. The interaction between primary and secondary stresses is treated in R6 by the use of either the r or the V parameter, although these are consistent with each other. For example, if the parameter r is chosen, it is added to the Kr arising from both primary and secondary stresses as follows: Kr =

Kl +r K mat

3.14

where r is tabulated in section II.6 of R6 as function of an additional variable p c = KSI (Lr/KI ). Alternatively, the contribution to Kr that arises from secondary s stresses, KI, may be multiplied by a factor V, so that: p

Kr = Kl + VK ls

3.4.3

3.15

Special features

The previous section describes only the ‘basic’ R6 options described in Chapters I and II of R6. There are numerous other special features that make the procedure applicable to a wide range of structural integrity issues. For example, Chapter III includes guidance on mixed-mode loading, the effects of weld strength mis-match on integrity, constraint effects, leak-before-break (LBB) analysis, use of the local approach, calculation of residual stress in weldments, crack arrest, probabilistic fracture mechanics and treatment of displacement-controlled loading. The R6 procedures have been influenced by, and have influenced, several other nuclear standards and procedures such as aSMe XI and the Ge-ePRI procedure.

3.4.4

User group

The main user group for R6 continues to be the power industry, both nuclear and fossil fuel, although the style of the document means that it is not tied to a particular industry sector or type of component.

3.4.5

Status

R6 has continued to be maintained and developed, first by the UK central Electricity Generating Board (CEGB), later by the successor organisation © Woodhead Publishing Limited, 2011


3/23/11 1:43:36 PM

72


Nuclear Electric and now by an industrial collaboration managed by British Energy with contributions also from other UK organisations (Serco, RollsRoyce, TWI and Frazer-Nash Consultancy). It is underpinned by a number of UK research projects (e.g. 14–15), and maintains contact with BSI, TAGSI (Technical Advisory Group on Structural Integrity), and a number of European research initiatives and networks. It is now in its fourth major revision, supplied as a subscription document with amendments issued approximately once a year.

3.5

Specific engineering critical assessment (ECA) methods: BS 7910/PD6493

3.5.1 Background The British Standards Institution (BSI) has published a ‘generic’ UK flaw assessment procedure, BS 7910 (16), i.e. one that is not tied to a particular industry or type of structure. The history of the document is described in various publications (17) and (18), and is summarised in Fig. 3.4. The first flaw assessment procedure to be published by the BSI was PD6493:1980 (19), ‘Guidance on some methods for the derivation of acceptance levels for defects in fusion welded joints’. The ‘PD’ (for ‘published document’) designation reflected the fact that the document was not intended to be a standard, but a guidance document. Moreover, it did not lay claim to be the only, or definitive, approach. The intent behind the document was to bring fracture mechanics into more general industrial use and the procedures it contained reflected this (20). Statistical issues CTOD design curve

R6 FAD approach

PD6493: 1980 Paris fatigue law

Load history LBB

PD6539 (creep)

PD6493: 1991 Multilevel analysis

LTA BS 7910: 1999 (+ Amd 1)

Corrections and clarifications

FITNET

BS 7910: 2005 (+ Amd 1)

BS 7910: c2012

Kl/sref library

Mk (weld toe effects)

RS distributions library Mismatch

3.4 Development of BS 7910.



3/23/11 1:43:37 PM


73

PD6493:1980 was published at a time when the UK offshore oil and gas industry was enjoying a boom. The construction of offshore jackets, pressure vessels, process piping and pipelines had reached unprecedented levels, and the combination of new construction methods and materials with very short ‘windows’ of weather in which installation could be carried out provided a strong incentive to expedite construction and installation. At the same time, catastrophic failures of offshore structures such as the Sea Gem and the Alexander Kielland had underlined the importance of controlling the quality of materials and fabrication techniques. PD6493 proved invaluable in helping engineers to distinguish between ‘critical’ flaws that could lead to failure and ‘benign’ flaws that were, to a large extent, an inevitable product of welding (21). PD6493 addressed two modes of failure: brittle fracture and fatigue. For the case of components subjected to stresses below the materials yield strength, the fracture assessment method used LEFM to calculate the driving force, KI, for brittle fracture. Simple graphical methods were used to calculate KI as a function of flaw size and shape, component width and thickness, and applied and residual stresses. Through-thickness, surface-breaking and embedded flaws were addressed, but the only geometry explicitly considered was the flat plate. For components subjected to stresses above yield (i.e. when the sum of the ‘primary’ stresses from external loading and the ‘secondary’ stresses such as welding residual stress exceeded the yield strength of the material), the so-called crack tip opening displacement (CTOD) design curve was used (22). This was a relationship between applied strain ratio and critical flaw size, partly empirically based. Failure of the uncracked ligament by plastic collapse was considered separately. The emphasis in PD6493 reflects, of course, the materials and problems of concern at the time, especially in the UK offshore industry, namely fatigue crack growth and brittle fracture of carbon steels at ambient and low temperature. In contrast, R6 (see Section 3.4.1) was aimed at the power industry, where fatigue was less of an issue, but plastic collapse was a credible failure mode, especially at elevated temperatures. Fatigue assessment to PD6493:1980 used the Paris law. Fatigue crack growth constants for air and marine environments were given in the document, along with graphically-based solutions, essential in this era before the widespread use of personal computers. Although the PD6493 and R6 methods (described in more detail in Section 3.4.1) had been developed in parallel, and addressed the needs of different industry sectors, it soon became clear that the underlying technology was virtually identical (23) and the FAD approach to fracture assessment was adopted in the second (1991) edition of PD6493. Users were given the option of using one of three different FADs, depending largely on the materials data available to them. This hierarchical approach to fracture assessment has



3/23/11 1:43:37 PM

74


persisted ever since, although the ‘levels’ of analysis in PD6493/BS 7910 do not exactly coincide with the R6 ‘Options’. For simplified calculations, the FAD-based equivalent of PD6493:1980 was adopted. This so-called ‘level 1’ calculation included an inherent safety factor and assumed no interaction between plasticity and crack driving force. Level 2 calculations, used for more critical applications, employed a strip yield model of the relationship between plasticity and crack driving force, while Level 3 calculations, used for assessment of ductile tearing, used a FAD similar to the R6 Option 2 FAD. Although various commercial software programs were available about this time, they were considered insuitable because they either demanded a high level of fracture mechanics expertise or they did not use PD 6493 procedures. The step change in calculation complexity associated with the revised procedures encouraged the development of software tools to act as ‘text animators’ for the calculation procedure (24) and has since developed apace with the evolution of the procedures (25). In 1999, more radical changes took place, a few of which are noted below: ∑

The document was upgraded to become a British Standards Guide, BS 7910. ∑ Creep assessment methods, originally published in PD6539, were incorporated into the document. ∑ Corrosion assessment methods for locally thinned areas (LTAs) in pipelines were proposed, based on a major joint industry project carried out by British Gas. ∑ An expanded library of K-solutions and reference stress solutions was added, allowing analysis of plates, cylinders, round bars, spheres and complex welded joints. ∑ Residual stress (RS) distributions were presented for various common welding processes and geometries. ∑ Load history effects, in particular the role of warm prestressing and prior overload in integrity, were included in the document. ∑ Leak before break (LBB) methods were introduced. Since then, the technical content of BS 7910 has remained stable, although the second (2005) edition provided the committee with the opportunity to act on user feedback by correcting and clarifying selected parts of the procedure. The current version of the procedure includes Amendment 1, published in 2007 (16). A major revision of BS 7910 is currently under preparation (26), further details of which are given in Section 3.5.5.



3/23/11 1:43:37 PM


75

3.5.2 Structure The current version of BS 7910 includes methods for assessment of fracture, fatigue, creep and corrosion and is structured as follows: ∑

Sections 1–6 cover the philosophy of FFS and advice on the information required for assessment. ∑ Section 7 covers fracture resistance, the main theme of this chapter. ∑ Section 8 addresses fatigue crack growth. ∑ Section 9 covers creep crack growth. ∑ Section 10 addresses ‘other modes’ of failure, e.g. stress corrosion, buckling.

A series of annexes (A–U) provide essential (‘normative’) information such as K-solutions, residual stress distributions and reference stress solutions, or constitute ‘informative’ annexes with advice on subjects such as fracture toughness testing of welds, effects of weld strength mismatch, mixed mode loading, leak before break, Charpy-fracture toughness correlations and reliability. The structure of the fracture assessment procedures in BS 7910 is described in more detail below. The concept is that three ‘levels’ of analysis are available, the choice of level depending on the information available to the user in terms of stress input and materials properties. The Level 1 procedure has its roots in the CTOD design curve, and treats brittle fracture and plastic collapse as independent, non-interacting events. Consequently, the user does not need to consider primary/secondary stress interaction factors (V or r), and the FAD is a simple rectangle. In order to compensate for these simplifications, the Level 1 procedures include a number of built-in safety factors. When a more precise description of failure conditions is required, the Level 2 or Level 3 procedures can be used. If the ‘generalised FAD’ is chosen, the user has a choice between continuous yielding and discontinuous, i.e. it is discontinuous if the material shows a Lüder’s plateau or a load drop. So far as the FAD for Lr values up to 1 are concerned, BS 7910 treats the two cases (continuous and discontinuous yielding) as identical, using equation (10) of BS 7910, which originates from Revision 3 of R6:

f(Lr) = (1 – 0.14L2r)[0.3 + 0.7 exp (– 0.65L6r)]

3.16

The sharp fall-off in permitted Kr at Lr > 1 for discontinuously yielding materials originates from the SINTAP project (see section 3.4.3), so the BS 7910 curve as a whole is a hybrid of the R6 Rev. 3 and SINTAP FADs. Where detailed stress–strain data are available, a more accurate FAD can be constructed directly from the stress–strain curve:



3/23/11 1:43:37 PM

76


È Ee L3s ˘ K r = Í ref + r y ˙ ÎLr s y 2Ee ref ˚

–0.5

3.17

In BS 7910, this is termed the level 2B FAD (if fracture toughness is given in terms of a single value of toughness, such as J0.2Bl, dc, KIc) or the level 3B FAD (if fracture toughness is given in terms of a tearing resistance curve). a comparison of Fads used in Pd6493 and BS 7910 is shown in Fig. 3.5. The x-axis is expressed in terms of the plastic collapse parameter Lr (rather than Sr, the term used in earlier versions of the procedure) in all cases, to facilitate comparison.

3.5.3

Special features

The title of the original PD6493 document (‘Guidance on some methods for the derivation of acceptance levels for defects in fusion welded joints’) indicates that the main emphasis of the document was on welded joints (later, the change from PD6493 to BS 7910 included a change of title to reflect the fact that the methods are applicable to metallic joints in general). Several aspects of BS 7910 (some of which do not appear in other procedures) make it particularly applicable to welded joints, and these are summarised below: ∑

Welded joints inevitably introduce some form of discontinuity in a structure, as a result of misalignment. This can be caused by eccentricity (e.g. offset between the two sides of a butt weld), by joining components of different thickness, by angular misalignment, or by some combination PD6493 Level 2 (superseded)

1.0

0.8

Level 1

Kr

0.6

0.4

Level 2a/3a (discontinuous yielding)

Level 2a/3a (continuous yielding)

0.2 Lr,max 0.0 0.00

0.25

0.50

0.75 Lr

1.00

1.25

1.50

3.5 Comparison of FADs used in PD6493 and BS 7910.



3/23/11 1:43:38 PM


∑

of these factors. The result is that there will be local bending stresses that will affect both the stress intensity factor and the susceptibility to plastic collapse. annex d of BS 7910 includes a table of formulae showing how these secondary bending stresses can be calculated as a function of the misalignment, and incorporated into an ECA. Consequently, there is a direct link between the permitted levels of misalignment (which are typically stipulated by construction codes) and the implications of this on structural integrity. In practice, the effects of misalignment can be very significant, both for fracture and fatigue assessment. The weld toe represents a region of local stress concentration, and this should be taken into account in the calculation of stress intensity factor for cracks located at the weld toe. BS 7910 includes parametric formulae for the calculation of a factor Mk, which represents the ratio: Mk =

∑

77

K l for for crack in str structure containing weld eld toe K l for for crack in same st structur cture without weld toe

Solutions for Mk are given in annex M of BS 7910, as a function of the ‘leg length’ of the weld (the distance between the weld toes), the section thickness, loading mode and the position for calculation of Mk (i.e. the distance from the weld toe). In practice, the Mk correction is significant only for crack tips lying relatively close to the weld toe (a < 0.3B, where ‘a’ is crack depth and ‘B’ is section thickness), and is therefore relevant mainly for the analysis of relatively shallow cracks, including fatigue cracks initiating at the weld toe. Some of the solutions given in BS 7910 are based on 2D finite element modelling and therefore strictly applicable only to straight-fronted cracks, while others are based on 3D modelling and can be applied to semi-elliptical surface-breaking cracks at a weld toe. In the fracture assessment clause (clause 7) BS 7910 gives advice on the likely magnitude of residual stress in weldments in the as-welded condition, after post-weld heat-treatment and after application of a high primary stress. The residual stress is usually assumed to act as a uniform tensile membrane stress across the section thickness; the so-called ‘Level 1’ approach to residual stress estimation. although this assumption is not realistic (‘local’ secondary stresses are in general balanced across the section thickness), it is conservative for the purposes of defect assessment and is often the only safe assumption that can be made in many cases, given the likely variations in the residual stress profile from weld to weld, and the uncertainties in locating the exact position of a defect by non-destructive testing (NDT). an alternative to the ‘level 1’ assumptions is given in annex Q, which includes a compendium of residual stress distributions for welds in the as-welded condition, including butt welds in plates, circumferential and



3/23/11 1:43:38 PM

78

∑


axial welds in pipes and repair welds. The current Annex M (compendium of K-solutions) does not explicitly support variable stress distributions of the kind shown in Annex Q, the assumption being that they can be handled by stress linearisation, either across the flaw or across the full section thickness. However, Annex Q could be implemented by use of ‘… handbook solutions, numerical modelling or weight function methods…’ provided that the procedure is fully documented. BS 7910 explicitly addresses fabrication flaws, recognising the need to aim for high quality welding. While flaw assessment procedures have sometimes been criticised on the grounds that they condone poor welding, it should be noted that the Introduction to BS 7910 states the opposite:

. . . a proliferation of flaws, even if shown to be acceptable by an ECA, is regarded as indicating that quality is in need of improvement. The use of an ECA can in no circumstances be viewed as an alternative to good workmanship. The response to flaws not conforming to workmanship criteria needs to be the correction of the fault in the process causing the non-conformance. The philosophy that the methods covered by this standard are complementary to, and not a replacement for, good quality workmanship is inherently assumed in this standard.

Of course, this does not preclude the use of BS 7910 for analysis of inservice flaws such as fatigue cracks, or for applications such as failure analysis.

3.5.4 User group Historically, the main user group for BS 7910 and its predecessor PD6493 has been the offshore oil and gas industry. The procedure allows for rapid, robust calculation of defect tolerance, albeit at the expense of excessive conservatism in some cases. The emphasis tends to be on avoidance of failure, rather than prediction of failure conditions. It should be borne in mind that the procedure was developed primarily in order to make rapid decisions about whether or not to repair fabrication flaws, rather than in order to predict precise failure conditions, probability of failure or safety factor against failure. Consequently, a flaw that lies outside the FAL and is originally judged to be ‘unsafe’ may well prove to be safe when re-analysed using more sophisticated methods. BS 7910 is recognised and cited by a number of national and international codes and standards, including codes for pipelines, pressure vessels, gas cylinders and offshore equipment/structures.



3/23/11 1:43:38 PM


79

3.5.5 Maintenance BS 7910 is owned and distributed by the BSI, with technical input provided by a permanent committee. This comprises volunteers from groups representing manufacturers, certification bodies, health and safety organisations, academia and end users. The detailed technical content is developed by a series of ‘panels’ (sub committees), covering particular topics such as fracture, fatigue, creep, corrosion, residual stress and materials properties. The committee maintains informal contact with the developers of other procedures, e.g. R6, FITNET and American Petroleum Institute/American Society for Mechanical Engineers (API/ASME). At the time of writing, BS 7910 is being extensively revised. The main source documents for this new edition will be the current edition of BS 7910, plus the R6 and FITNET documents (see Sections 3.4.1 and 3.4.3). The principles behind the new edition, also described in (26) are: ∑

to preserve compatibility with previous editions of BS 7910 (unless the methods are obsolete or there is evidence that they are unsafe); this avoids the need to re-visit analyses carried out with an earlier edition of the procedure, and makes the document more amenable to returning and occasional users; ∑ to harmonise with other procedures (especially R6 and FITNET) wherever possible; ∑ to support the use of the more advanced analysis techniques now available (for example, analyses utilising weld strength mismatch and constraint), while still allowing analyses based on simple, conservative inputs (e.g. for life extension of structures built long ago, for which data may be very sketchy). Some of the main proposed new features can be summarised as: ∑

removal of the current Level 1 procedures and the related ‘manual’ procedure of Annex N; ∑ replacement of the fracture assessment levels with options, designated 1–3 and structured in a similar manner to FITNET and R6; ∑ inclusion of weld metal strength mismatch concepts in the calculation of Lr; ∑ inclusion of a procedure for constraint-based analysis; ∑ expansion and revision of the residual stress annex; ∑ inclusion of an appendix giving advice on NDE (non-destructive examination). The revised edition, which draws extensively on FITNET and R6, is due to be published around 2012. The major changes will be in the area of fracture analysis (clause 7 of the current Bs 7910); Table 3.3 summarises the hierarchy



3/23/11 1:43:38 PM

80


Table 3.3 Levels of analysis in the proposed BS 7910:2012 procedures Description BS 7910 2005 FITNET R6

Proposed BS 7910: 2012

Charpy/fracture Annex J Option 0 – toughness correlations

Annex J (use Option 1 FAD)

Simple screening Level 1 – – method

No longer required

Generic FAD, Level 2a Option 1, single-point value of single-point fracture toughness, analysis continuous yielding

Option 1 or ‘approximate Option 2 curve, continuous yielding’

Option 1 (continuous or discontinuous sub-options)

Generic FAD, single- Level 2a Option 1, point value of single-point fracture toughness, analysis discontinuous yielding

Option 1 (up to Lr = 1 only) or ‘approximate Option 2 curve, discontinuous yielding’

Option 1 (continuous or discontinuous sub-options)

Material-specific Level 2b Option 3, Option 2 FAD, single-point single-point value of fracture analysis toughness

Option 2

Generic FAD, Level 3a Option 1, Option 1 fracture toughness tearing expressed as tearing analysis resistance curve

Option 1 (can be continuous or discontinuous)

Material-specific FAD, Level 3b Option 3, fracture toughness tearing expressed as analysis tearing resistance curve

Option 2

Option 2

FEA-based analysis Level 3c Option 4 Option 3 (can include mismatch effects)

Option 3 or 3m

Mismatch analysis, based on tensile properties only

Not Option 2 – considered

Option 1m (Annex I)

Mismatch analysis, Not Option 3m – based on full considered stress-strain curves

Option 2m (Annex I)

Constraint-based analysis

Annex

Not Option 5 considered

–



3/23/11 1:43:38 PM


81

of fracture assessments in the new procedure, and how it compares with existing procedures.

3.6

Specific engineering critical assessment (ECA) methods: structural integrity procedures for European industry (SINTAP)/European Fitnessfor-service Network (FITNET)

3.6.1 Background The SINTAP project was a collaborative European R&D project running between 1996 and 1999. The output of the project was a fracture assessment procedure (27), in which the same flawed structure could be analysed using several different options, the choice between them depending on the quality of the data available. The intention was to develop a procedure suitable for a range of different industries and types of analysis. Consequently, a bridge operator faced with a defect in an 80-year-old bridge for which little or no materials data were available might nevertheless be able to assess and ‘pass’ the defect based on a very simple and conservative SINTAP analysis. A more advanced SINTAP option might be used to assess the reasons for failure of a newly constructed welded pressure vessel, taking into account the detailed microstructure (and thus the fracture toughness) of the failed region, the strength mismatch between weld metal and parent metal, the effect of the pre-service hydrotest on failure conditions and the detailed geometry of the vessel. SINTAP was influenced by the R6 and BS 7910 procedures and by the research and development programmes of its participants, who represented a range of European industries, Research and Technology Organisations (RTOs) and universities. It has, in turn, influenced both R6 and BS 7910, in particular in its formulation of the FAD and the distinction between FADs for continuously and discontinuously yielding materials. Subsequently, the main principles of the SINTAP procedure were absorbed into the FITNET procedure, a more broadly based European defect assessment procedure produced as the output of a European thematic network, running between 2002 and 2006.

3.6.2 Structure Like BS 7910, the FITNET procedure (28–29) addresses fatigue, corrosion damage and creep as well as fracture. It is currently available in a two-volume set, the first of which sets out the basic procedures, the second of which is a series of annexes containing essential information such as K-solutions and limit load solutions, plus ‘informative’ annexes on a variety of subjects,



3/23/11 1:43:38 PM

82


including advice on NDT and on sources of materials data. A third volume, containing information on the validation of the procedure, case studies and worked examples, is due for publication shortly. A workbook based on the procedure is also available (30), and further background information is given in (31–34). The fracture section of FITNET was built largely on the concepts developed in the SINTAP project, so can be considered to have superseded SINTAP, although the latter is still available, along with the supporting research reports (35). So far as the hierarchy of the FITNET fracture assessment procedure is concerned, there are numerous methods available, as shown in Table 3.4. At one extreme (Option 0), the user is assumed to have only Charpy Table 3.4 Fracture analysis options in FITNET Option no. Type of tensile data required

Type of fracture toughness data required

Other information

0 (basic) YS or SMYS None; Charpy only energy only

Relies on correlations; applicable to ferritic steels only

1 (standard) YS and UTS Single-point fracture toughness data or tearing resistance curves

Based on tensile properties of the weaker material (typically the PM) and the fracture toughness of the material in which the flaw is located

2 (mismatch) YS and UTS of PM and WM

Single-point fracture toughness data or tearing resistance curves

Takes account of strength mismatch; typically worth applying only if M ≥ 1.1 or M < 0.9

3 (stress– Full stress–strain strain) curves for PM and WM


Takes account of material stress–strain behaviour; can also incorporate strength mismatch

4 (J integral) Full stress–strain curves for PM and WM


CDF approach only; elasticplastic FEA is used to calculate the driving force for the cracked body

5 (constraint) Full stress–strain curves for PM and WM

Relationship between fracture toughness and crack-tip constraint, e.g. J as a function of T stress

Can take into account constraint effects, by matching crack tip constraint in the test specimen and the cracked structure

YS, yield (or proof) strength; SMYS, specified minimum yield strength; PM, parent metal; WM, weld metal; M, mismatch ratio (ratio of WM yield strength to PM yield strength).



3/23/11 1:43:38 PM


83

energy and yield strength data (or specified minimum values of the same) available. The yield strength is used to estimate UTS, the Charpy energy to estimate Kmat and a simplified analysis can be carried out. The intention is, however, that assessments should be based wherever possible on fracture mechanics data, using one or more of Options 1–5, depending on the nature of the information available. The Option 1 curves in FITNeT are identical to the so-called ‘approximate Option 2’ curves of R6; detailed stress–strain data are assumed not to be available, but the user has some concept of likely yielding behaviour. For materials which show continuous yielding: f(Lr) = (1 + 0.5L2r)–0.5[0.3 + 0.7 exp (– mL6r)]

3.18

for Lr up to 1.0. Unlike the R6 Option 1 curve, this includes a materialdependent term, m, where: Ê ˆ m = min Á 0.001 E ; 0.6˜ Rp Ë ¯

3.19

where E is the elastic modulus of the material and Rp is the proof strength. For discontinuously yielding materials, a discontinuity occurs at Lr = 1, and the Fad is similar to that seen in Fig. 3.3. Option 1 of FITNeT is therefore broadly similar to ‘approximate Option 2’ of R6. a distinction is made between continuously and discontinuously yielding materials, but detailed stress–strain data are not required and the work-hardening behaviour is estimated from the yield and tensile properties. Where users have detailed stress–strain data, Option 3 can be used. The FAD is identical to the R6 Option 2 or BS 7910 level 2b/3b Fads. Of course, one of the features of welded joints is that there are differences in strength, composition and microstructure between the weld metal and the parent metal. There will also be differences in microstructure and strength between the heat affected zone (HAZ) and parent metal. Most structural joints require the weld metal to ‘overmatch’ the parent metal. loading of the joint is then based on the properties of the parent metal, with the result that any flaws in the weld metal are to some extent shielded from the effects of the loading by virtue of the weld metal strength. For situations in which there is significant strength difference (typically more than about 10% difference in yield strength) between the weld metal and parent metal, FITNET includes the option to account for this mismatch, using Option 2. While it is recognised that Lr can be conservatively calculated by assuming the tensile properties of the lower strength material (weld metal or parent metal) in an Option 1 or Option 3 calculation, Option 2 allows the user to benefit from the strength mismatch. The maximum benefit arises for collapse-dominated cases in which there is high strength mismatch, with collapse load potentially increasing by



3/23/11 1:43:38 PM

84


the ratio sfs/sfw, where sfs is the flow strength of the stronger component and sfw that of the weaker. Where a full stress–strain curve is available for both the parent and weld metals, mismatch can be incorporated into an Option 3 analysis (by defining a single ‘equivalent’ stress–strain curve), allowing in principle a more accurate assessment than would be possible with Option 2. A demonstration of the potential of Options 2 and 3 is given in Koçak et al. (36), Seib et al. (37) and Hadley and Moore (38), which describe analyses and tests on a range of overmatched and undermatched welded wide plate specimens. The Option 4 procedures of FITNET are broadly similar to those of Option 3 in R6 or Option 3c in BS 7910; elastic-plastic FEA is used to model the cracked structure and the driving force is determined directly from FEA. However, unlike R6 and BS 7910, FITNET Option 4 uses a CDF approach, and has no explicit FAD-based equivalent. Finally, Option 5 gives the user the chance to combine detailed modelling of the driving force with constraintdependent fracture toughness.

3.6.3 Special features FITNET was conceived as a pan-European document for use by a range of industry, and not allied to any particular construction code or component type. Particular features of the fracture clauses include: ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

a hierarchy of fracture assessment methods from Option 0 to Option 5; clear distinction between FADs on the basis of the yielding behaviour of the material; treatment of weld strength mismatch (under- or over-matching); treatment of crack tip constraint; a choice of driving force parameters; either CTOD (d) or K can be used; a choice between CDF or FAD-based methods; a range of ‘alternative’ fracture assessment techniques, including LBB, crack arrest, fracture under mixed mode loading; a section outlining ‘additional’ fracture assessment techniques (on the whole, these are less well-developed than those classified as ‘alternative’). These include the use of the local approach, treatment of ‘non-sharp’ flaws and advice on dynamic effects on tensile and fracture toughness determination.

3.6.4 User group FITNET is a new document, which will be used as a source document for the forthcoming BS 7910 and IIW procedures (see section 3.5). Examples of



3/23/11 1:43:39 PM


85

its potential application to pressure vessels, aerospace components and even medical devices are given in the final conference proceedings (39).

3.6.5 Status FITNET version MK8 is currently available as a stand-alone procedure, but some errors and omissions have inevitably been identified subsequent to publication, and are recorded on the network website (40). Elements of FITNET will be included in future versions of BS 7910 and the IIW procedure, as outlined in Section 3.5.

3.7

Specific engineering critical assessment (ECA) methods: American Petroleum Institute (API)/ American Society for Mechanical Enginners (ASME)

3.7.1 Background In the USA, the development of the API 579 procedure, first published in 2000 (41), was driven principally by the need to address flaws and damage found during the operation of refinery and petrochemical plant, in particular pressure vessels, piping and tanks designed, fabricated, operated and inspected in accordance with ASME and API standards. Of particular concern was the need to maintain the safety of older equipment in which in-service damage could have accumulated. There was also a drive to produce a method that would be compatible with US Occupational Safety and Health (OHSA) legislation and would ensure consistency between different analysts addressing a similar problem. A joint industry project, the Materials Properties Council (MPC), concluded in 1991 that the FFS standards in existence at that time did not adequately cover the many types of flaw and damage found in the refining and petrochemical industries. The response to this was a document organised by damage type (for example, general and local metal loss, pitting corrosion, hydrogen-induced cracking, laminations) and covering the inspection, analysis and future avoidance of such damage in a systematic fashion. The document is also organised by ‘levels’ of analysis, but in contrast with the other FFS methods described in this chapter, the ‘level’ of analysis envisaged by the API procedure is explicitly linked to the skills and qualifications of the analyst, as shown in Table 3.5. Following the publication of the original API 579 procedure in 2000, the work of a joint API/ASME committee led to the revision and expansion of the document in its current form, namely API 579-1/ASME FFS-1 (42).



3/23/11 1:43:39 PM

86


Table 3.5 Levels of analysis in the API-579 and API/ASME procedures Level Application

Skills, qualification and experience of analyst

1

Plant inspector or plant engineer

Conservative screening method requiring minimal information from inspection; little computation required (results often tabulated for easy interpretation during plant inspection)

2 Less conservative method than Level 1, but requiring more detailed calculation 3

Plant engineer or specialist engineer (experienced and knowledgeable in FFS methods)

Detailed inspection information required, Specialist engineer (experienced plus details of component geometry, and knowledgeable in stresses and materials properties. FFS methods)

3.7.2 Structure The API/ASME procedure is intimately connected to the ASME codes for boilers, pressure vessels, tanks and piping and to ASTM material grades although it does not preclude the use of other design codes or materials. The document starts with two introductory chapters introducing terms, responsibilities and the principles of FFS procedures. Thereafter, the document is laid out in a consistent manner, with each chapter addressing a particular type of damage, e.g. general metal loss, local metal loss, pitting corrosion, hydrogen blistering, assessment of crack-like flaws. For each type of damage, sub-sections of the chapter address the data requirements, applicability and limitations of the procedure, assessment method (at three different levels), remediation of damage, remaining life analysis and inservice monitoring. The emphasis is on user-friendliness, with flow charts, tables and graphs used wherever possible, with data given in both SI and US customary units.

3.7.3 Special features Two chapters of the API/ASME are of particular interest for fracture assessment: Chapter 3 (Assessment of existing equipment for brittle fracture) and Chapter 9 (Assessment of crack-like flaws). Chapter 3 is essentially a screening technique, and is not intended for use where crack-like flaws are encountered or expected; for this situation, the user needs to consult Chapter 9. The analysis of crack-like flaws at Level 3 (described in Chapter 9 of the procedure) is broadly similar to the approach adopted by BS 7910 and R6, and these methods are in fact explicitly referenced as alternatives. There are,



3/23/11 1:43:39 PM


87

however, certain features unique to API 579 and its successor, API 579-1/ ASME FFS-1: ∑

K-solutions for internal and external axial and circumferential flaws in cylinders, and for internal and external surface flaws in spheres, were derived directly from FEA for a wide range of geometries and loading conditions. ∑ Stress intensity can be derived for arbitrary through-wall stress distributions – this represents an advantage compared with the current edition of BS 7910, in which K-solutions are given in terms of membrane and bending stresses only. ∑ Appendix F of the procedure gives advice on sourcing materials data such as fracture toughness and includes Charpy/fracture toughness correlations from Sections III and XI of the ASME Boiler and Pressure Vessel Code. ∑ Appendix B allows the user to define reference stress from the elasticplastic J solution rather than from a limit load solution. This removes the substantial geometry-dependence of FAD and takes weld metal strength mismatch into account. ∑ Appendix E contains a range of residual stress distributions, based mainly on FEA modelling. ∑ The background to the procedure is published in a series of reports by the Welding Research Council (WRC).

3.7.4 User group The procedure is maintained and developed by a joint API/ASME committee, with representatives from a range of industries, both within and outside the USA.

3.7.5 Status The committee is working towards a new edition of the API/ASME flaw assessment procedure (43–44), with a publication date of around 2012.

3.8

Future trends

There is a continuing drive to improve the precision of fracture assessment methods, with the ultimate aim of predicting failure conditions or assigning a probability of failure rather than simply making a run/repair decision. Constraint-based fracture mechanics methods, described in Chapter 1 (O’Dowd) of this volume, have an important role to play here, combined with the constraint matched fracture mechanics testing described in Chapter



3/23/11 1:43:39 PM

88


2 (Macdonald, Østby and Nyhus). The use of probabilistic methods, and analysis methods that take weld strength mismatch into account, are also likely to increase. There is also increasing interest in strain-based assessment, as described below.

3.8.1 Strain-based assessment There is increasing interest in situations in which flawed (or potentially flawed) structures are subjected to known displacements or strains, rather than to load-controlled forces. Examples include offshore pipelines installed by reeling, or structure subjected to thermal/seismic loads that induce yielding during operation. BS 7910 does not currently address the analysis of flawed structures subjected to plastic straining in detail, although DNV RP F108 (45) and Appendix A of DNV OS F101 (46) include effectively modified versions of BS 7910 fracture assessment procedures specific to the analysis of pipelines installed using methods involving cyclic plastic straining. Extensive research in this area of strain-based analysis is continuing on a number of fronts, and a new section III.16 of the R6 procedure has been prepared, proposing the use of a strain-based FAD (SB-FAD), analogous to the stress-based FAD currently used by BS 7910 and R6. This concept has been scrutinised by the UK TAGSI committee. There is clearly scope for the development of either an additional annex to BS 7910 or a stand-alone strain-based analysis procedure document. In view of the extensive revisions required for the main stress-based procedure and the fact that strain-based methods are still under active development, there are, however, no plans to include strain-based methods in the immediate next edition of BS 7910.

3.9

References

1. Woods, G.E. and Baguley, R.B., Practical guide to ASME B31.3, Casti Publishing Inc., 1996. 2. Smith, T.A. and Warwick, R.G., ‘A survey of defects in pressure vessels in the UK for the period 1962–1978 and its relevance to nuclear primary circuits’. International Journal of Pressure Vessels and Piping, 1983, 11, 127–166. 3. Davenport, T.J., ‘A further study of pressure vessel failures in the UK’, International Conference on Reliability Techniques and their application, Reliability ’91, London, UK, 10–12 June 1991. 4. Harrop, L.P., ‘The integrity of pressure vessels’, Science Progress, 1983, 68, 423–457. 5. Bush, S.H., ‘Statistics of pressure vessel and piping failures’, in Pressure Vessel and Piping Technology 1985; a decade of progress, 1985, ed Sundarajan, C.R., ASME, New York. Also published in ASME Journal of Pressure Vessel Technology, 1988, 110, 225–233. 6. Engel, J.R., (ed) ‘Pressure vessel failure statistics and probabilities’, Nuclear Safety, 1974, 15(4), 387–399.



3/23/11 1:43:39 PM


89

7. Hadley, I., Phaal, R. and Hurworth, S., ‘Reliability of LPG bullets’, presented at International Conference on Pressure systems: operation and risk management, IMechE, London, 24–25 October 1995. 8. BS EN 13445:2002: ‘Unfired pressure vessels’. 9. Milne, I., Ritchie, R.O. and Karihaloo, B. (eds), ‘Failure analysis diagram methods’ Section 7.03 of Comprehensive Structural Integrity, Volumes 1-10, 2003, Elsevier; http://www.knovel.com/web/portal/browse/display?_EXT_KNOVEL_DISPLAY_ bookid=1872. 10. Murakami, Y., Stress Intensity Factors Handbook, 2006, Elsevier Science. 11. Miller, A.G., Review of Limit Loads of Structures Containing Defects, 1985, 2nd edition, CEGB Report TPRD/B/0093/N82 Rev 1, Berkeley, Glos.: BNL-Central Electricity Generating Board. 12. R6: Assessment of the Integrity of Structures containing Defects, Revision 4, 2001, including updates to Amendment 8, 2010, British Energy Generation Ltd, Gloucester. 13. Dowling, A.R., Sharples, J.K. and Budden, P.J., ‘An Overview of R6 Revision 4’, ASME PVP 2001, 423, pp. 33–39. 14. Sharples, J.K. and Watson, C.T., ‘UK research programme on fracture mechanics: latest review of progress’, Proceedings of PVP 2008, 2008 ASME Pressure Vessels and Piping Division Conference, 27–31 July 2008, Chicago, IL. 15. Bate, S.K., et al., ‘UK research programme on residual stresses – a review of progress, Proceedings of PVP 2008, 2008 ASME Pressure Vessels and Piping Division Conference, 27–31 July 2008, Chicago, IL. 16. BS 7910:2005 (incorporating Amendment 1); ‘Guide to methods for assessing the acceptability of flaws in metallic structures’. 17. Hadley, I., Maddox, S.J. and Wiesner, C.S., ‘PD6493 becomes BS 7910: what’s new in fracture and fatigue assessment’, I. Mech E. seminar on Flaw Assessment in Pressure Equipment and Welded Structures, 8 June 1999, London, UK. 18. Hadley, I., ‘BS 7910: History and future developments’, Paper PVP2009-78057, ASME 2009 Pressure Vessels and Piping Conference, 26–30 July 2009, Prague, Czech Republic. 19. PD6493, ‘Guidance on some methods for the derivation of acceptance levels for defects in fusion welded joints’. 20. Burdekin, F.M., ‘The PD6493 approach to significance of defects’, paper 37, Proc. Conf. Fitness for Purpose Validation of Welded Structures, 17–19 November 1981, London, UK. 21. Burdekin, F.M., ‘Some defects do – some defects don’t’, Metal Construction, 1982, February, 91–94. 22. Dawes, M.G., ‘Brittle fracture in high strength weldments,’ Welding Research International, 1974, 4, 41–73. 23. Burdekin, F.M., Garwood, S.J. and Milne, I., ‘The basis for the technical revisions to the Fracture Clauses of PD 6493’, paper 37, Int. Conf. Weld Failures, 21–24 November, 1988, TWI, London, UK. 24. Laures, J.-P., Garwood, S.J., Willoughby, A.A. and Maddox, S.J., ‘Assessment methods and software for the tolerance of defects’, Proc. Conf. Welded Structures ’90, TWI, 26–28 November 1990, London, UK. 25. Booth, G.S., Garwood, S.J., Phaal, R., Hurworth, S.J. and Brown, P.A., ‘Fitness for purpose assessment of flaws using microcomputer software’, paper 30, 5th Int. Conf. Computer Technology in Welding, 3–4 June 1992, Cambridge, UK.



3/23/11 1:43:39 PM

90


26. Hadley, I., Budden, P.J., Ainsworth, R.A. and Sharples, J., ‘The future of the BS 7910 flaw assessment procedures’, Paper PVP2010-25582, ASME 2010 Pressure Vessels and Piping Conference, 18–22 July 2010, Washington, USA. 27. SINTAP, ‘Structural integrity procedures for European Industry’, 1999, BRITEEURAM contract No. BRPR-CT95-0024 (see http://www.eurofitnet.org/sintap_index. html). 28. Koçak, M., Webster, S., Janosch, J.J., Ainsworth, R.A. and Koers, R., FITNET Fitnessfor-Service (FFS) – Procedure (Volume 1), GKSS Research Center, Geesthacht, 2008; http://www.eurofitnet.org/. 29. Koçak, M., Hadley, I., Szavai, S., Tkach, Y., Taylor, N., FITNET Fitness-for-Service (FFS) – Annex (Volume 2), GKSS Research Center, Geesthacht, 2008; http://www. eurofitnet.org/. 30. Zerbst, U., Schödel, M., Webster, S. and Ainsworth, R., ‘Fitness-for-service fracture assessment of structures containing cracks’, A workbook based on the European SINTAP/FITNET procedure, Elsevier, 2007. 31. Koçak, M., ‘FITNET fitness-for-service procedure: an overview’, FITNET 06-04, see (36). 32. Koçak, M., ‘FITNET fitness-for-service procedure: an overview’, International Institute of Welding, Welding in the World, 2007, 1, (5-6), 94–105. 33. Koçak, M., ‘Fitness for service analysis of structures using the FITNET procedure: an overview’, in: Offshore Mechanics and Arctic Engineering (OMAE 2005). Proceedings, 24th International Conference, Halkidiki, Greece, 12–17, June 2005. American Society of Mechanical Engineers, New York, 2005. 34. Koçak, M., ‘FITNET fitness-for-service procedure: an overview’, European Seminar on Pressure Equipment (ESOPE), Paris, 9–11 October 2007. 35. http://www.eurofitnet.org/sintap_docs.html 36. Koçak, M., Seib, E. and Motarjemi, A., 2006, ‘Treatments of structural welds using FITNET fitness-for-service procedure: FITNET 06-013’, see (32). 37. Seib, E., Volkan Uz, M. and Koçak, M., ‘Fracture analysis of thin-walled laser beam and friction stir welded Al-alloys using the FITNET procedure’, FITNET 06-019, see (32). 38. Hadley, I. and Moore, P., ‘Validation of fracture assessment procedures through full-scale testing: FITNET 06-018’, see (32). 39. Proceedings of the International Conference on Fitness-for-service (FITNET 2006), 17-19 May, Shell Global Solutions, Amsterdam, The Netherlands. 40. http://www.eurofitnet.org 41. API 579 2000, ‘Recommended Practice for Fitness-for-service’, American Petroleum Institute, Washington, DC, 2000. 42. API 579-1/ASME FFS-1 2007, ‘Fitness-for-service’, American Petroleum Institute, Washington, DC, 2007. 43. Osage, D.A. and Janelle, J.L. ‘API579-1/SME FFS-1 2007 – A joint API/ASME fitness for service standard for pressurized equipment’, ASME Pressure Vessels and Piping Conference, 27–31 July 2008, Chicago, Illinois, USA (PVP2008-61796). 44. API 579-2/ASME FFS-2 2009: FFS Example problem manual, August 2009, API. 45. DNV RP F108, ‘Fracture Control for Pipeline Installation Methods Introducing Cyclic Plastic Strain’, Det Norske Veritas, 2006. 46. DNV OS F101, ‘Submarine Pipeline Systems’, Det Norske Veritas, 2007.



3/23/11 1:43:39 PM

4

The use of fracture mechanics in the fatigue analysis of welded joints

A. H o b b a c h e r, University of Applied Sciences Wilhelmshaven, Germany

Abstract: Classical analyses of the load carrying capacity of structures considered idealized components which reflected the underlying theories, e.g. ideal geometries, material properties and surfaces. The gap to the behaviour of a real component with all possible types of imperfections was bridged by a more or less adequate engineering assessment and safety factor, or by monitoring in service. Fracture mechanics can solve the problem in an analytical way by connecting material properties, geometry, imperfections and loading of a component. Nowadays fracture mechanics has become a fundamental tool for structural integrity engineering. The chapter gives a short introduction into the basics and the technical application of fracture mechanics in terms of fatigue. Some examples outline possible applications. The chapter concludes with a reference list of important literature for a deeper study. Key words: materials, welding, welded joint, fracture mechanics, fatigue.

4.1

Introduction to fracture mechanics

Conventional analyses of strength and especially of fatigue are based on the assumption of flawless materials. Classical assessment methods were developed for these conditions using the principles of technical continuum mechanics. However real materials and components are not flawless, they may contain inner imperfections, such as inclusions, cavities, pores or surface flaws, in the form of cracks, indents, grooves from machining, and corrosion, in contrast to the assumption of the flawless material state. Thus, there was a gap between theoretical calculations and practical experience, which the application of appropriate experimental application factors attempted to reduce. This approach was futile in most cases. Fracture mechanics was developed to close this gap. It is the theory of strength of flawed components. The first theory was developed by Griffith in 1920 [1]. He investigated the strength of glass containing small cracks. He developed the basic equations by energy considerations comparing elastic energy set free and surface energy consumed by opening a crack. Later Irwin [2] and Sneddon [3] investigated the stress field in the vicinity of a crack tip (eq. 4.1) by integration of the basic differential equations of elasticity. This was performed first on an infinite plate containing a crack (Fig. 4.1). 91 © Woodhead Publishing Limited, 2011


3/23/11 1:45:59 PM

92


s = remote stress

y sy

Infinite plate

txy

Stress field near crack tip

sx

sx txy sy r

2a

Polar coordinates to material element

Crack ϕ

x s

4.1 Infinite plate with centre crack.

È jÊ j 3j ˆ Í cos Á1 – sin sin ˜ 2 2 2¯ Ë È sx ˘ Í Í ˙ Í KI jÊ j 3j ˆ Í sy ˙ = Í cos Á1 + sin sin ˜ 2 2 2¯ Ë 2p r Í Ít ˙ xy ÍÎ ˙˚ Í j j 3j Í cos sin cos 2 2 2 Î

˘ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˚

4.1

This two-dimensional solution for the stress field of a centre-cracked infinite plate shows that the constant KI = s · √(pa) is the significant term. Since all stress fields in the vicinity of a crack are similar, KI is the significant parameter for the description of the elastic field. It is the so-called stress intensity factor (SIF). Other crack configurations differ by a factor Y(a), and so the universal formulation is derived as (eq. 4.2) K I = s p a · Y (a )

4.2

Other methods for description of the stress-strain field at a crack tip have been developed. The crack opening displacement (COD) and the J integral are mentioned here. A crack can be opened in different modes (Fig. 4.2). Most important is the crack opening mode I. The other modes and their combinations, the mixed mode loadings, are of minor significance. There is only a two-dimensional stress state at the surface of the plate, the so-called plane stress condition. Deeper inside a thick plate, a threedimensional stress state develops because of the restrained contraction in the thickness direction. This state is called plane strain. Under this condition, the critical resistance of a material to fracture KIc is lowest. It is a material



3/23/11 1:45:59 PM

The use of fracture mechanics in fatigue analysis F

Crack opening by force F

F

F

F

F

F

93

Mode I

Mode II

Mode III

4.2 Different crack opening modes.

property called fracture toughness Kmat, which depends on the material, temperature and, to some extent, the rate of loading. In materials testing for fracture toughness, a minimum wall thickness of the specimens must be present in order to ensure the plane strain state. The basic equation for the assessment of a fracture, i.e. unstable crack propagation of a component, is K ≥ Kmat, in other terms, the loading of a crack tip in terms of SIF must exceed the material resistance against fracture, i.e. fracture toughness. This is strictly true for brittle materials. In ductile materials, a plastic zone around the crack tip develops. If this plastic zone is small in comparison to the dimensions of the crack, the assessment can be done in the same way without a major error. Crack propagation under cyclic load can be divided into the short crack propagation, long crack propagation and final onset of fracture. The short crack behaviour is observed at crack dimensions which are about equal to the micro-structural dimensions of the material or to the plastic zone. It is described by the Kitagawa diagram. Cracks with larger dimensions are considered as long cracks. The cyclic crack propagation of long cracks is described by fatigue crack growth curves or in a special case by the Paris power law [4]. A further crack propagation under constant load can occur under corrosive conditions. If there is a susceptible combination of a metal and a chemical agent and a certain level of stress, then stress corrosion cracking will set in. The threshold level for crack propagation in terms of the stress intensity factor is known as KIscc.

4.2

Technical application of fracture mechanics

4.2.1 Critical crack size The failure due to a rapid crack extension may occur for two reasons. The first is that the section under consideration may be statically overloaded, i.e.



3/23/11 1:45:59 PM

94


the applied stress from load exceeds the tensile strength of the material. The other possibility for failure is the rapid onset of propagation of an existing crack, when the applied stress intensity factor exceeds the fracture toughness of the material. The interaction of both failure modes can be assessed by the so-called R6 method (Fig. 4.3). The abscissa of the diagram is the ratio of applied stress to the critical tensile stress, e.g. yield stress, Sr = s/ fy , the ordinate is the ratio of the applied stress intensity factor to fracture toughness Kr = K/Kmat, where Kmat is the characteristic fracture toughness of the material. Then the fracture assessment curve separates the areas of safety and of a possible failure [5].

4.2.2 Crack propagation Crack propagation data are usually plotted as stress intensity factor range log ΔK vs. crack propagation rate log da/dN (Fig. 4.4). The central portion (II) of the plot can be represented as straight line or the classical Paris power law. In the region of larger SIF ranges (III), there is an acceleration of crack propagation until the final rupture occurs, which can be assessed with the fracture assessment diagram (FAD) in Fig. 4.3. The situation for smaller cracks in the region (I) is more complex (Fig. 4.5). A threshold level of the SIF range exists for long cracks, but this threshold level does not apply to describe the behaviour of short cracks. The separation of long cracks from short ones is not always clear, but a few statements can be made. A crack that is completely within the plastic zone is likely to behave as a short crack. Often cracks which are smaller than 1.0 to 0.5 mm in the direction of propagation are considered to be short. If cracks that are smaller than 0.5 mm are assessed in terms of fatigue, procedures which use the cyclic J integral are preferred. The problem of short crack

Normalised SIF Kr

Area of possible failure Fracture assessment diagram Point to be assessed

Kr = f (Sr)

Area of safety Degree of plastification of ligament, Sr = s/sc

4.3 Fracture assessment diagram of the R6 method.



3/23/11 1:45:59 PM

The use of fracture mechanics in fatigue analysis

95

10–3 mm/cycle II

III Kc

Klc

Plane strain

Plane stress )m

10–4

/d

N

=

C(

DK

Ds

da

Crack propagation rate, da/dN

I

10–5

2a

DKth

DK = Ds paY Ds

10–6 102

t

R=0

103 N/mm3/2 Stress intensity factor range, DK

104

4.4 Fatigue crack growth diagram.

10–3

m

10–4

= a

=

0.

10–5

0.

01

1 m

m

m

m

a

=

1 m

Short cracks

a

Crack propagation rate da/dN

Steel SM58Q UTS = 666 N/mm2

10

–6

Dsn = 800 700 600 N/mm2

Long crack

R=–1

10–7 50

N/mm3/2 100

200 500 1000 2000 Cyclic stress intensity factor DK

5000

4.5 Short crack behaviour [6] with region of the Paris power law [4].



3/23/11 1:45:59 PM

96


propagation is in development, but it has only a limited significance for the technical application. A more accurate separation uses an estimation of the radius of the cyclic plastic zone which can be derived from the formula (eq. 4.3) 2 plane lane str stress Ê ˆ ÏÔ 1 D rpl = 1 Á DK ˜ · Ì 2 4p Ë fy ¯ (1 – 2n ) pllane ane strain ÓÔ

4.3

where Drpl is the radius of the cyclic plastic zone, fy is the cyclic yield strength and v is Poisson’s ratio. The formula is an estimation at R = 0 without any consideration of a possible crack closure. Linear-elastic fracture mechanics can be applied if the radius is smaller than 1/5 to 1/10 in comparison with the actual crack. The regions (I) and (II) in Fig. 4.4 can be described by a mathematical representation which is the Paris power law: da = c · DK m 0 ddN N

for for

DK tthh £ DK £ K mat

4.4

where C0 and exponent m are material parameters, DKth is the threshold level range, which depend on the stress ratio R, DK is the applied stress intensity factor range and Kmat is the fracture toughness in plane strain or plane stress. During cyclic loading, a crack can be closed in the lower stress part of a cycle. This crack closure is considered by the introduction of an effective stress intensity factor range, which is smaller than that calculated from the exterior loads, DKeff < DK. Different approaches have been developed for the calculation of DKeff but this effect is considered in most applications by modifying the Paris power law in respect to the stress ratio R = mins/maxs or minK/maxK. Forman formula [7]

C1 · DK m1 da = dN (1 – R) · K c – DK dN

BS 7910 [5]

da = C · DK m 2 2 ef eff dN dN

Hobbacher [8]

C0 · DK m da = dN (1 – R) – DK /K c dN

4.5 DK eff ef

DK – DK th 1–R

4.6

for DKth ≤ DK ≤ Kc 4.7

Equations 4.5 and 4.6 require a recalculation of the material parameters in comparison with the original power law (eq. 4.4). Equation 4.6 can be used directly with the material data found in literature. The cyclic crack propagation in a centre-cracked infinite plate as shown in Fig. 4.1 can be calculated directly from the integration of eq. 4.4, since the



3/23/11 1:45:59 PM


97

correction function Y(a) is unity. The number of cycles N starting from an initial crack ai propagating to a final crack af under the constant amplitude cyclic stress Ds becomes N=

=

af

Úa

i

da = C0 · DK m

af

Úa

i

da C0 · (Ds · p · aa)m

È 1 ˘ 2 · – (m1– 2)/2 ˙ m m /2 Í (m – 2) 2)/2 (m – 2) · C0 · Ds · p af ÎÍai ˚˙

4.8

In the general case at a correction function Y(a) and at a variable amplitude stress history, the integration can only be performed by numerical methods. Two methods are available, based on incremental crack growth Da = ai – ai–1: n

N= S

i =1

ai – ai –1 (da /dN )i

4.9

or on incremental cycles DN = Ni – Ni–1: n

aend = astart (N i – N i –1 ) tart + S (da /dN )i · (N i =1

4.10

If eq. 4.9 is used, subdivision into n logarithmic increments according to eq. 4.11 is recommended: art +ix ar x = (log aendd – log astatartrt )/n then ai = 10 log astarart

4.11

The use of eq. 4.8 is only possible at a constant amplitude loading. The methods of eq. 4.9 and 4.10 require a higher numerical effort, but can handle variable amplitude loading and are very appropriate for computing.

4.3

Fatigue assessment of welded joints using fracture mechanics

4.3.1

Categorisation of detected cracks or imperfections

The main application of fracture mechanics is the assessments of components containing defects. These flaws or imperfections may originate from the production of the material, from production processes of the component or by a crack initiation under service loads. Here, only welded joints are considered, but the assessment procedure is not confined to that. Weld imperfections are detected by the use of non-destructive testing (NDT) methods. In cases of special safety requirements, cracks are assumed in dimensions which are just under the detectable level by the NDT methods



3/23/11 1:46:00 PM

98


applied. The detected imperfections or cracks may have different shapes, e.g. voluminous inclusions with sharp edges or planar lack of fusion. Fracture mechanics as an assessment tool of these imperfections is mostly based on elliptical cracks by mathematical reasons. In consequence, the real NDT indication must be transformed into an elliptical crack which can be processed later by the methods of fracture mechanics. The categorisation of the detected imperfections into the applicable type of crack must be done (Figs 4.6–4.8) and the dimensions of the circumscribing ellipse must be defined. In most cases multiple imperfections are present, which may interact and become effective as a combined larger one. These possible interactions must be considered. Recommendations and codes [5, 8–10] provide tools for this consideration (Figs 4.7 and 4.8). The procedure has three steps: 1. Performing NDT inspection and documentation of the indications. 2. Definition of the type of crack as either through-wall, surface, embedded or edge crack. 3. Creation of circumscribing ellipses and checking for possible interactions. Several codes and recommendations [5, 8–10] give a clear guidance for the categorisation of cracks and checking of possible interactions. Figure 4.8 shows an example of a practical application. Besides the weld imperfections there are additional possible sites of cracks initiation in welded joints. These are the weld toe transition in fillet and butt welds, the root gap of fillet welds and the weld bead itself.

4.3.2 Stress analysis for fracture mechanics Each assessment method is based on a specific definition of stress. The total stress in a plate can be separated into membrane stress sm, shell bending stress sb and a remaining non-linear peak stress snl, which is self-equilibrating (Fig. 4.9). Through-wall crack Embedded cracks

Surface cracks

4.6 Types of crack.



3/23/11 1:46:00 PM


2c1

2c2

2c1

2c

s

2c2

2a1 s 2a2

a2

2a1

2c1

s1

2c2

2c2

2c1

a1

4.7 Examples of possible interactions of imperfections [9].

s

a2

2a2 s2 2a1

2a1 2a2 s2 a1


3/23/11 1:46:00 PM

2c1

2c1 s

s1

2c

2c2

2c2

2a2

2a

100

Fracture and fatigue of welded joints and structures 2c

Cladding

2c

a a

Laminar indication

1 = 2c 1> 2a 2a

t 2a

2a

2c

4.8 Transfer of NDT into elliptical cracks [10]. Notch stress = sm + sb + snl

t

x

4.9 Stress parts in a welded plate.

Different fatigue assessment methods are based on different stress definitions: ∑ ∑ ∑

Nominal stress method requires only the average stress in section. Structural hot spot stress method uses membrane and shell bending stress disregarding the non-linear peak. Fracture mechanics considers all the stresses and their distribution through the wall.

In general cases where no parametric formulae or solutions are available, a finite element analysis (FEA) is mandatory. From the stress distribution through the wall, the stress parts can be separated. Membrane stress

s m = 1t ·

Úx =0 s (x ) · dx

Shell bending stress

s b = 62 · t

Úx =0

x =t

x =t

Êt ˆ (s ((xx ) – s m ) · Á – x˜ · dx Ë2 ¯ 4.12



3/23/11 1:46:00 PM


Non-linear peak stress

101

2x ˆ 2x Ê s nl (x ) = s (x ) – s m – Á1 – ˜ · s b t¯ Ë

where t is the wall thickness and x is the coordinate from the surface through the wall. For fracture mechanics crack propagation calculations, maximum principal stress is governing. This is due to the fact that the maximum elastic energy release occurs at a crack growth perpendicular to the direction of the maximum principal stress. In the case of plates, the stress state on the surface is always two dimensional. Since most of the fatigue life is spent at small dimensions of the propagating crack, the stress perpendicular to the surface, which may occur deeper inside the cracked body, does not need to be considered in fatigue assessment. A further simplification is the consideration of a twodimensional slice from a three-dimensional body. comparative calculations show that there could be an error up to 9% in terms of stress intensity factors, but on the conservative side [11]. residual stresses from welding, assembling or from other sources must be considered. In most cases there is no or only incomplete knowledge. Here, the residual stresses must be estimated or considered by assuming a high stress ratio of e.g. R = 0.5.

4.3.3

Determination of SIF

General determination The general equation (4.1) for the determination of the stress intensity factor indicates that the difference from a centre crack in an infinite plate to an arbitrary geometric crack configuration is considered by the correction function Y(a). In existing compilations of stress intensity factor solutions, parametric formulae or diagrams are given for the direct determination of the SIF or for the correction function [12–17]. For surface and embedded cracks in plates under tension and bending solutions have been developed which serve as a reference standard (Newman–Raju: [14–16]). An example is presented in Table 4.1. Corrections for the weld toe The additional stress magnification due to the weld toe at welded joints can be considered by an additional factor or function Mk(a) [18]. The formulation of the SIF thus becomes K = s m · p · a · Ym (a ) · M k,m (a ) + s b · p · a · Yb (a ) · M k,b k,b (a ) 4.13



3/23/11 1:46:00 PM

102


Table 4.1 Example of a parametric formula for the stress intensity factor [15] Surface cracks in a plate under membrane and shell bending stress c

c a

t

b

b = distance to nearest edge The formulae for the stress intensity factor KI are valid for a/c 1

4.15

In practical application, the establishing of a formula like eq. 4.15 is not necessary. The calculation of Mk can be directly included into the stepwise integration process as described in Section 4.2.2. These Mk formulae refer to a two-dimensional solution (see Table 4.2). The crack propagation on the surface, i.e. the evolution of the aspect ratio a:c in three-dimensional bodies has to be considered by an adequate assumption. A conservative approach is to take the stress at the surface or also at 0.1 mm under the surface for the crack propagation calculation of the parameter c. A further approach is to take the aspect ratio as given in equation 4.17. The recent development of three-dimensional weight functions may be a solution to this problem [22].

4.3.4

Material parameters

The material parameters for the Paris power law are derived from crack propagation experiments. The data are scattered as shown in Figs 4.11 Table 4.2 Example of a parametric formula for the Mk function [21] t

V

q

H

a

T

A

Validity range of the parametric formula: Dimensions min max H/T 0.2 1 W/T 0.2 1 q 15 60 A/T 0.175 1.3 t/T 0.5 20

W Êa ˆ Mk = C · Á ˜ ËT ¯

k

but Mk ≤ 1 2

ÊH ˆ ÊH ˆ ÊW ˆ ÊW ˆ C = 0.7061 – 0.4091 Á ˜ + 0.1596 Á ˜ + 0.3739 Á ˜ – 0 0.1329 1329 Á ˜ ËT ¯ ËT ¯ ËT ¯ ËT ¯ 2

2

ÊH ˆ ÊH ˆ ÊW ˆ ÊW ˆ k = – 0.2434 – 0.3939 Á ˜ + 0.1536 Á ˜ + 0.3004 Á ˜ – 0 0.0995 0995 Á ˜ ËT ¯ ËT ¯ ËT ¯ ËT ¯

2



3/23/11 1:46:01 PM

104


2 1.5

10–3

Rate of crack propagation d(2a)/dN (mm/cycle)

Ds

5 4 2a

3

2

Ds

1.5

10–4

Weld metal A Weld metal B Weld metal C Weld metal D Weld metal E

5

Weld metal F Simulated heat-affected zone (HAZ) in mild steel

4 3

Simulated HAZ in BS 968 (950 °C heat treatment) Simulated HAZ in BS 968 (1100 °C heat treatment)

2

Tempered HAZ in BS 968 (1100 °C heat treatment, tempered at 650°C)

1.5

10–5 300

Steel to BS 968 400

500 1000 2000 Range of stress intensity factor DK [N mm–3/2]

3000

4.11 Crack propagation data in steel [23].

and 4.12. An upper bound line has to be defined for a further practical application. In most cases a straight line was chosen as is usually done for the representation of S–N curves. Table 4.3 shows the parameters of the da/ dN curve which is specified in several codes or recommendations (BS 7919,



3/23/11 1:46:01 PM


105

Crack growth rate da/dN (m/cycle)

10–4 R = 0.1

6005A-T6 6082-T6 5454-H24 7020-T6

10–5 10–6 10–7 10–8

6005A-T6

10–9 10–10 10–11 10

2

5 102 2 5 103 2 5 Stress intensity factor range DK (N/mm3/2)

104

4.12 Crack propagation data in aluminium [24]. Table 4.3 Material parameters for the Paris power law (dimensions in mm and N) [5, 8] Material

Constant C0 Exponent Threshold values DKth ([N mm–3/2]) m R ≥ 0.5 0 ≤ R ≤ 0.5 R < 0 Surface crack depth < 1 mm

Steel

5.21 ¥ 10–13 3.00

63

170–214 · R

170

≤ 63

Aluminium 1.41 ¥ 10–11 3.00

21

56.7–72.3 · R

56.7

≤ 21

IIW). These data are valid only for non-corrosive environments and absence of elevated temperatures or creep. In most cases, data of residual stress are not readily available. In this case for reasons of conservative design, it is recommended to assume a high level of residual stress and to use the parameters for R = + 0.5 as described earlier. These crack propagation data do not apply for time-dependent effects, such as creep and corrosion. In applications at elevated temperatures where creep is not significant or for other metals than steel, the constant C0 and the values of DKth can be estimated by equation 4.16: C0 = C0,steel,20 °c

Ê Esteel,20 °c ˆ ·Á ˜¯ E Ë

3



3/23/11 1:46:01 PM

106

and


Ê ˆ E DK th = DK th,steel,20 °c · Á Ë Esteel,20 °c ˜¯

4.16

where Esteel,20 °C is the elasticity modulus, C0,steel,20 °C is the constant of the Paris power law and ΔKth,steel,20 °C is the threshold value of the stress intensity factor, all for steel at a temperature of 20 °C.

4.3.5

Initial crack size

The initial crack size must be determined by the available techniques of non-destructive inspection. This must be done as accurately as possible. The calculated number of cycles is very sensitive to the dimensional parameters of the initial crack. This is especially true for the crack depth ai. The aspect ratio a:c is of secondary importance. In most cases it can be estimated. An aspect ratio of a:c = 1:10 is adequate for butt welds in most cases. For fillet welds in cruciform joints, the following aspects (eq. 4.17) are recommended [25]. Since the stress magnification due to the weld toe is maintained at the surface while the crack tip is growing into the depth and into lower stressed areas of the plate, the crack will grow faster in the direction of the surface than in that of the depth. This applies especially for weld toes in fillet weld. Equation (4.17) describes a typical development of the aspect ratio. Ï 0.5 forr x < 0.062 mm a = ÔÔ 1/(6.34 – 0.27/a ) ffor 0.0622 ≤ a ≤ 3mm 2c Ì Ô0 forr x > 3mm ÔÓ

4.17

In practical applications, an adequate safety margin for the crack depth ai should be assumed. In critical cases at high safety requirements, crack dimensions in order of magnitude of the detection level of the applied NDT technique are taken in order to make life estimations or to define inspection intervals by fracture mechanics. In welded joints there are the irregularities of the weld bead surface and the weld transition at the toe. These irregularities can act as small flaws, which shorten the portion of live cycles spent in crack initiation. As a consequence, the biggest portion of live cycles is spent in crack propagation. It was often looked for these small initial cracks, but the results are not completely definite. Nevertheless, the fact that most of the live cycles are spent in crack propagation justifies the application of fracture mechanics to welded joints. on the basis of experimental fatigue test data and the materials parameters of the Paris power law, theoretical initial crack sizes ai can be determined by fitting. The results give values of ai = 0.15 … 0.05 mm [5, 8, 25]. Effects



3/23/11 1:46:01 PM


107

of short crack behaviour are ignored in this method. They are inherently covered by the fitting of the data.

4.3.6 Final crack size The final crack dimensions for a rapid onset of fracture can be determined by the conventional methods of fracture mechanics. Very often this is not necessary. The biggest portion of the number of life cycles is spent at small cracks. For a plate of 25 mm thickness for example it is insignificant if a final crack was chosen of 10 mm, 12 mm or 18 mm. There is only a difference of a few cycles, which is usually negligible. The same applies for the materials parameter for the Paris power law. Most of the life cycles fall into the stage II part of the da/dN curve in which the classical formulation of the law can be applied (eq. 4.4). In stage III at the acceleration of the crack growth, there are only a few cycles which can be neglected in most practical applications.

4.4

Examples of practical application

4.4.1 Assessment of imperfections found by NDT in a welded joint (1) In a cruciform welded joint with K-butt and fillet welds (Fig. 4.13) of steel, both inclusions in a line and spots of lack of fusion have been found by NDT. For this reason it was decided to make a fracture mechanics assessment. These inclusions are located from 2 to 5 mm under the surface. A re-categorisation using the recommendations in codes [5] and [9] indicates that the ligament between the inclusions and the surface is too small to become effective. The imperfections must be categorised as surface cracks. The imperfections extend over nearly the whole width of the component. A final assessment made clear that the imperfections should be regarded as a through-going crack from edge to edge. The dimensional parameters of the weld have been measured and compared with the drawings. The additional fillet had a weld toe angle of 45°, the leg lengths on the plates were 12 mm. Sub-surface inclusion line

30 mm

2 mm 25 mm 3 mm

Sub-surface inclusion line

4.13 Cruciform joint with K-butt welds and slag line under surface.



3/23/11 1:46:01 PM

108


With an initial crack ai = 5 mm and a final crack depth of half the wall thickness af = 15 mm, the calculations have been performed. The loading in service was Ds = 100 MPa. The material parameters for crack propagation have been taken from Table 4.3, while the formulae for Mk(a) and Y(a) have been taken from [9]. After setting the initial values, the algorithm can be easily run: 1 2 3 4 5 6 7

Set initial parameters DO WHILE crack a < af Calculate SIF DK using Mk(a) and Y(a) Calculate increment in cycles DN = Da/(C0 · DKm) Add cycles N = N + DN Add crack depth a = a + Da LOOP

The result of the computation gave 30 300 cycles. This corresponds to a fatigue class FAT of the flawed component according to IIW recommendations [8] of FAT 25 MPa.

4.4.2 Assessment of imperfections found by NDT in a welded joint (2) The tensile plate of steel in a welded component was 30 mm thick and 400 mm wide. A transverse stiffener of the same thickness was welded on with two-sided fillet welds. The leg lengths of the welds were 12 mm. In NDT two surface cracks or defects have been found (Fig. 4.14). There have been multiple cracks close together. Applying the recategorisation procedure according to [5], it was found that there is a coalescence between the cracks. They had to be treated as one single defect. The dimensions of the circumscribing ellipse was a = 1 mm and 2c = 20 mm. It was estimated by a critical engineering assessment that cracks up to one half of wall thickness could be tolerated including a reasonable safety margin. This leads to an assumed final crack depth of 15 mm.

Surface cracks

Circumscribing ellipse

2c

a a = 1 mm 2c = 20 mm

30 mm

Surface cracks

400 mm

4.14 Tensile plate with welded-on transverse stiffener containing surface flaws.



3/23/11 1:46:02 PM


109

The computation was done with the material parameters as given in Section 4.3. The aspect ratio of a:c = 1:10 was kept constant. The formulae for surface crack and for the influence of stress magnification have been taken from [5] and [8]. The result was 158 000 cycles or a fatigue class [8] of FAT = 43 MPa. These data gave a rational basis for further decisions, which might have been: Reject the component, use until a replacement is available or repair it.

4.4.3 Assessment of a finite element output of a welded joint for fatigue A fillet weld on a thick-walled steel plate in a special geometrical configuration had to be assessed. No corresponding structural details could be found in the detailed catalogues of codes, so a finite element analysis was performed. The weld toe transition was modelled assuming a toe radius of 1 mm. The stresses have been read from the anticipated crack path; see Fig. 4.15. The stress parts have been separated according to Fig. 4.7 and formulae 4.12. After that, the non-linear stress magnification factors kt,nl(x) have been determined. With that function, the function Mk(a) could be determined and the stress intensity factors have been calculated, from which the number of live cycles eventually could be derived. The nodal stresses of the elements have been used as supporting points for the interpolation of the stresses. The computation starts with the separation of stress parts resulting in sm = 82.55 MPa and sb,max = 22.5 MPa. The Stress components through thickness 300 Membrane stress 250

Bending stress Non-linear stress

Stress (MPa)

200

Total stress

150 100 50 0 –50

0

10

20

30 40 50 60 70 Distance from surface (t = 100 mm)

80

90

100

4.15 Stress separation of finite element results.



3/23/11 1:46:02 PM

110


remaining stress part is the non-linear peak stress. The integration was done numerically by a stepwise integration of crack and cycle increments and by a parallel computing of the stress intensity factors DK and of the function Mk. The step at the beginning was Da = 0.1 mm; 250 steps have been used. The aspect ratio was kept constant to a:c = 1:10 for conservative estimations. Table 4.4 shows the evolution of the crack depth a. The results can be converted in a fatigue class FAT according to the IIW recommendations [8], which is the stress range at 2 million cycles and R = + 0.5. This class is FAT 53 MPa, but it must be considered that this fatigue class was derived for a wall thickness of 100 mm. A recalculation to 25 mm, on which the fatigue data of IIW recommendations are based, using a wall thickness correction exponent of n = 0.3 results in a fatigue class of FAT 80 MPa. In very thick-walled or voluminous components, the consideration of the stress distribution through the whole section is not necessary. The linearisation and separation of stress needs only to be done in a reasonable surrounding of the estimated final crack. A possible error can be estimated by the function fw in Table 4.1.

4.5

Conclusions

The application of fracture mechanics needs more knowledge and expertise than some other methods. The basic introduction in fracture mechanics and the short outline of fatigue problems, which can be assessed by fracture mechanics, give only a first insight into the wide area. More general knowledge should be acquired by the thorough study of a textbook. Fatigue assessments in practical applications should be made under the guidance of Table 4.4 Stepwise integration of crack growth (table shows only selected crack lengths) x (mm)

Ds (MPa)

a (mm)

Y (a)

Mk (a)

DK DN (N mm–3/2) (cycles)

N (cycles)

0 0.1 0.2 0.5 1.0 2.0 5.0 10 25 50 75 100

300 249.96 219.92 189.8 154.6 129.2 113 104 94 80 64 60

–

– – 1.104 1.106 1.109 1.117 1.144 1.202 1.490 2.574 – –

– – 2.477 2.093 1.805 1.518 1.268 1.145 1.057 1.024 – –

– – 161 273 354 435 598 810 1466 3471 – –

– –

0.1 0.2 0.5 1.0 2.0 5.0 10 25 50 – –

– – 47834 44856 29488 31383 43699 29933 24865 5652 – –

47834 92690 122178 153561 197260 227193 252058 257710 – –



3/23/11 1:46:02 PM


111

accepted codes or recommendations [5, 8–10]. It is also recommended to monitor the relevant literature. Besides the assessment of weld imperfections in respect to fatigue, the fracture mechanics method will gain more significance for fatigue design in the future. New types of welded joints, variations of dimensional parameters and weld shape can be evaluated. The only drawback is the numerical effort, but this will diminish with the further development of electronic computation. Weld imperfections are usually assessed by introduced quality systems such as ISO 5817 [26]. The problem is that this standard was developed as a tool for understanding between welders and inspectors. Later it was used as a quality system and in consequence, the different levels of quality for different types of imperfections are not consistent in terms of fatigue. It will be one task of the future to bring both in line. Another task is the standardisation of the application fracture mechanics for fatigue estimations of welded joints in the design stage. This potential has not yet been exploited.

4.6

References

[1] Griffith A.A.: The phenomenon of rupture and flow in solids. Tran. Roy. Soc. 1920, A221, 163–198. [2] Irwin C.R.: Analysis of stresses and strains near the end of a crack transversing a plate. J. Appl. Mech. 1957, 24, 361–364. [3] Sneddon N.: The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. Roy. Soc. Ser. A 1946, 187, 229–250. [4] Paris P.C. and Erdogan F.: A critical analysis of crack propagation laws. J. Basic Engng. (ASME) 1963, 85, 528–539. [5] BS 7910:2005: Guidance on methods for assessing the acceptability of flaws in metallic structures. British Standard Institution, London. [6] Radaj D., Sonsino C.M. and Fricke W.: Fatigue Assessment of Welded Joints by Local Concepts, 2nd edition. Woodhead Publishing Cambridge, UK, 2006. [7] Forman, R.G., Kearny V.E. and Engle R.M.: Numerical analysis of crack propagation in cyclic loaded structures. J. Basic Engng. (ASME) 1967, 89, 459–464. [8] Hobbacher A.: Fatigue Design of Welded Joints and Components. Abington Publishing, Cambridge, UK, 1996 (IIW Doc. XIII-1539/XV-845-96) and update 2008 (IIW Doc. XIII-2151-07/XV-1254-07), Welding Research Council, New York, Bulletin 520, 2009. [9] Fracture mechanics proof of strength for engineering components (Bruchmechanischer Festigkeitsnachweis für Maschinenbauteile), VDMA Frankfurt Germany, 2006. [10] ASME 1998. Boiler and Pressure Vessel Code, Section III, Rules for construction of nuclear power plant components. The American Society of Mechanical Eng., New York. [11] Pang H.L.J.: A review of stress intensity factors for a semi-elliptical surface crack in a plate and fillet welded joint. IIW Document XIII-1433-91. [12] Murakami Y.: Stress Intensity Factors Handbook. Pergamon Press, Oxford, UK 1987. [13] Rooke D.P. and Cartwright D.J.: Compendium of Stress Intensity Factors. Her Majesty’s Stationary Office, London, 1976.



3/23/11 1:46:02 PM

112


[14] Newman J.C. and Raju I.S.: Stress intensity factor equations for cracks in threedimensional finite bodies. ASTM STP 1983, 791, I-238 – I-265. [15] Newman J.C. and Raju I.S.: Stress intensity factors for internal surface cracks in cylindrical pressure vessels. J. Pressure Vessel Technol., 1980, 102, 342–346. [16] Newman J.C. and Raju I.S.: An empirical stress intensity factor equation for the surface crack. Engineering Fracture Mechanics, 1981, 15, No 1–2, 185–192. [17] Frank K.H. and Fisher J.W.: Fatigue strength of fillet welded cruciform joints. J. Structural Div., Proc. ASCE, 1979, 105, 1727–1740. [18] Maddox S.J. and Andrews R.M.: Stress intensity factors for weld toe cracks, in Localized Damage Computer Aided Assessment and Control. Aliabadi M.H., Brebbia C.A. and Cartwright D.J. (Editors). Computational Mechanics Publications, Southampton, co-published with Springer-Verlag, Heidelberg, 1990. [19] Bueckner H.F.: Ein neues Verfahren zur Berechnung von Spannungsintensitätsfaktoren (A new method for calculation of stress intensity factors). Z. Angewandte Mathematik und Mechanik, 1970, 50, 529–546. [20] Albrecht P. and Yamada K.: Rapid calculation of stress intensity factors. J. Struct. Div. ASCE, 1977, 103(ST2), 377–389. [21] Hobbacher A.: Stress intensity factors of welded joints. Engineering Fracture Mechanics, 1993, 46, no 2, pp. 173–182, and 1994, 49, no 2, 323. [22] Shen G., Plumtree A. and Glinka G.: Weight function for the surface point of semi-elliptical surface crack in a finite thickness plate. Engineering Fracture Mechanics, 1991, 40, no. 1, 167–176. [23] Maddox S.J.: Fatigue crack propagation in weld metal and HAZ. Metal Constr. 1970, 2(7), 285–289. [24] Jaccard R.: Fatigue crack propagation in aluminium. IIW Doc. XIII-1377-90. [25] Nykänen T., Marquis G. and Björk T.: Simplified assessment of weld quality for fatigue loaded cruciform joints. IIW Document XIII-2177-07. [26] ISO 5817:2003 (EN 25817:2003), Quality levels for imperfections.



3/23/11 1:46:02 PM

5

Fatigue strength assessment of local stresses in welded joints W. F r i c k e, Hamburg University of Technology, Germany

Abstract: This chapter discusses common approaches for fatigue strength assessment of welded joints. These are based on different types of stresses, which are described in detail at the beginning. Subsequently, several factors affecting the fatigue strength are discussed with a special focus on welded joints, which are considered in the approaches in different ways. Then the chapter outlines S–N approaches using different types of stress for the S–N curves together with a damage accumulation law. The alternative crack propagation approach is only briefly addressed, being the subject of other chapters. Key words: fatigue strength assessment, nominal stress approach, structural stress approach, notch stress approach, notch strain approach.

5.1

Introduction

Metal structures may fail either from extreme loads occurring during their service life, resulting in failure modes such as yielding, buckling or rupture of structural components, followed probably by the collapse of the whole structure, or from variable or repeated loads in service, resulting in the formation of one or several cracks, which is called fatigue. Welded structures are particularly prone to fatigue due to adverse geometric and metallurgical effects induced by welding. Fatigue is a very complex phenomenon; however, many observations have been made and knowledge has been gained about the fatigue behaviour of structures and the governing parameters that influence fatigue. Approaches have been developed to assess the fatigue strength of welded structures during the design stage and afterwards in the event of a fabrication defect or a crack occurring in service. There is a great demand from the industry and generally from society to consider the state-of-the-art when designing structures and assessing the probability of fatigue failures. The formation of fatigue cracks starts with microstructural processes damaging the material and initiating microcracks which join and grow in the presence of cyclic stresses. This process results in a ‘technical crack’ usually at the surface which has a length in the order of 1 mm and thus can be detected by common technical means. The stable propagation of the 115 © Woodhead Publishing Limited, 2011


3/23/11 1:46:25 PM

116


microcracks and afterwards the macrocracks occurs normally with a rate of 10–8 to 10–3 mm/cycle. Figure 5.1 shows a typical fatigue crack and its surface at a welded joint due to stable crack propagation. It can be stated that in small-scale test specimens, the number of cycles during crack initiation and early propagation is quite large compared with the total number, while the opposite can be true in larger structures due to the long crack propagation phase and effects of load-shedding and redistribution.

(a)

(b)

5.1 Fatigue crack at an attachment end (a) and fracture surface of a bulb plate stiffener at an attachment end (b).



3/23/11 1:46:25 PM

Fatigue strength assessment of local stresses in welded joints

117

Dominating parameters governing the crack initiation and propagation are first of all the number and the amplitude or range of occurring stress cycles. Other parameters will be dealt with in Section 5.3. The stresses at welds are particularly influenced by notch effects due to the weld shape. Stress concentrations occur mainly at the weld toes, but also at weld roots as illustrated by the force flow in Fig. 5.2. The latter are highly stressed in case of non- or partial penetration welds with non-welded root faces. The approaches for fatigue strength assessment are based on different types of stress or stress intensity which take the local stress concentrations more or less into account. The different types of stress are described in Section 5.2, while Section 5.4 gives an overview of the approaches which will be dealt with in more detail in subsequent chapters. Further information about fatigue of welded structures and approaches for fatigue assessment can be found in several textbooks, among then Gurney (1979), Maddox (1991), Radaj (1990) and Radaj et al. (2006).

5.2

Types of stress

5.2.1 Overview Structural discontinuities, including welded joints, cause irregular stress distributions and concentrations. It has been found that different types of stress can be used as an appropriate parameter to assess the fatigue strength. The situation is illustrated in Fig. 5.3 by the example of a longitudinal stiffener welded to an axially loaded plate. Cracks usually initiate at the toe of the fillet weld around the stiffener termination. The nominal stress sn can be regarded here as the undisturbed, far-field stress. The longitudinal stress s at the plate surface increases due to the structural discontinuity when approaching the stiffener, called structural hot-spot stress shs at the weld toe for this reason. An additional rise to the so-called notch stress sk can be observed close to the weld, caused by the notch effect at the weld toe.

5.2 Examples of welded joints with force flow illustrating stress concentrations at weld toes and roots.



3/23/11 1:46:25 PM

118

Fracture and fatigue of welded joints and structures sk

shs

Stress s on plate surface

sn

t

5.3 Distribution of longitudinal stress in front of a longitudinal stiffener on an axially loaded plate.

A corresponding stress gradient occurs at the weld toe also in the thickness direction. A suitable parameter for the fatigue strength can be the endurable nominal stress range Dsn, together with a parameter describing the notch effect of the longitudinal stiffener (the so-called fatigue class), but also the structural stress range Dshs or the notch stress range Dsk at the weld toe. The latter may include elastic-plastic effects; thus the elastic-plastic strain can be a more suitable parameter in this case. Alternatively to the elastic notch stress, a stress intensity factor can be used for very sharp notches and crack tips. All stress types will be described further in the following sections, while the stress intensity factor for crack tips, which allows also the analysis of the stable crack propagation, is mainly dealt with in chapters 3 and 4.

5.2.2

Nominal stress

The nominal stress has been described in connection with the example in Fig. 5.3 as the undisturbed far-field stress. In a more general sense, it can be defined by integral load parameters and sectional properties which allow its determination also in a section at the fatigue-critical point. This might be necessary when the nominal stress is varying along the structure. in the example (Fig. 5.3), the nominal stress would normally be defined as

sn = F A

5.1

where F is the force acting in the plate and A the cross-sectional area. in a bending case, the acting bending moment would be divided by the section modulus of the component in question. Figure 5.4 shows a cruciform joint with load-carrying fillet welds. Here, a nominal stress can be defined in the plate in front of the weld toe where an



3/23/11 1:46:26 PM


t^ s^

119

s^ sn,w

= nominal weld stress

t^

sn

sn

a

5.4 Cruciform joint with potential crack locations at the weld toe and root and nominal stresses in the plate and weld throat.

initiated crack would propagate through the plate (plate failure). However, also the weld root can be prone to fatigue, where a crack would propagate from the end of the non-welded root face to the weld surface (weld failure). As this failure mode depends on the stress in the weld rather than in the plate, a special nominal stress sn,w is defined for weld failure, which is usually determined by distributing the plate force over both weld throat thicknesses a:

s n,w =

sn · t 2a

5.2

in principle, the nominal weld stress is the vector sum of the averaged shear and normal stresses in the weld throat area as indicated in Fig. 5.4. It should be noted that a clear definition of the nominal stress is necessary for a fatigue assessment using fatigue classes. The stress-raising effects of the structural detail and the welded joint are generally excluded. However, macro-geometrical stress raisers which are not typical for the welded detail have to be considered in a modified nominal stress. Examples for such stress raisers are larger cut-outs close to the welded detail and reduced effective widths of wide and/or curved flanges.

5.2.3

Structural stress

contrary to the nominal stress, the structural stress contains effects of the structural configuration, such as the stress increase due to the longitudinal



3/23/11 1:46:26 PM

120


stiffener shown in Fig. 5.3. However, the local stress increase due to the weld toe notch is excluded as indicated by the dotted line in the figure. Sometimes, also the terms hot-spot stress and geometrical stress are used, the latter because the structural geometry is considered. Different proposals exist for the determination of the structural stress at the weld toe, which is actually a fictive, non-measurable stress. The most common way is the extrapolation of the measured or computed surface stress to the weld toe, resulting in the so-called structural hot-spot stress. As it is generally assumed that the influence of the weld toe notch vanishes in a distance of 0.3t–0.4t from the weld toe (Niemi et al., 2006), where t is the adjoining plate thickness, the stress distribution outside this area is used for stress extrapolation. Figure 5.5a shows the stress extrapolation recommended by the International Institute of Welding (IIW). In the case of a steep nonlinear stress increase, a quadratic extrapolation might be more suitable. This is also recommended for edge attachments where the plate thickness is no more appropriate for the determination of the extrapolation points. Instead, fixed points, 4 mm, 8 mm and 12 mm away from the weld toe, are recommended (Fig. 5.5b). The surface stress extrapolation can be performed numerically and experimentally (Fricke, 2002; Niemi et al., 2006). The structural stress can also be regarded as the sum of the axial and bending stress in a plate or shell, i.e. the stress at the surface after a stress linearization in the thickness direction. This clearly defined structural stress for plate-type structures can only be determined numerically. It coincides with the stress obtained by surface extrapolation as shown in Fig. 5.3; however slight deviations are possible depending on the extrapolation procedure. The stress linearised in the plate thickness direction allows not only the maximum stress at the surface, but also the stress gradient to be considered

shs

s0.4t

s4 mm

shs

s1.0t

s8 mm

s12 mm

4 mm t

8 mm 12 mm

0.4 t 1.0 t (a)

(b)

5.5 Determination of the structural hot-spot stress by surface stress extrapolation for attachments (a) on a plate surface and (b) at a plate edge.



3/23/11 1:46:27 PM


121

in the fatigue strength assessment. This is the case in the approach by Dong (2001), who also proposed a special procedure using the stresses in a certain distance away from the weld toe as finite element results are more reliable there because of the stress singularity at the weld toe. In the case of edge attachments, the stress gradient is obtained by linearisation over the anticipated crack length determining the fatigue life. A special case are attachments on both sides, where the linearisation is performed only to the symmetry line. A drawback of the structural stress approach is that the structural stress in front of fillet welds does not account for the load carried by the welds, i.e. it remains the same for full-load as well as for non-load carrying welds. This is illustrated by Fig. 5.4, where the structural stress – determined by through-thickness linearisation, for example – corresponds generally to the nominal stress. An alternative offers the structural stress approach by Xiao and Yamada (2004), who proposed to take the stress at a location 1 mm below the weld toe on the anticipated crack path as structural stress parameter (Fig. 5.6b). They show that the local stress increase of the weld toe already disappears at this depth for a reference detail, i.e. a cruciform joint with non-load carrying fillet welds and 10 mm plate thickness. Crack propagation analyses have shown that the stress at this location is correlated well with the short-crack propagation phase determining mainly the fatigue life. The 1 mm stress is affected by the force flow of full-load and non-load carrying fillet welds. As another alternative, Poutiainen (2006) proposes a multi-linear stress distribution in the thickness direction considering the stress carried by the fillet welds. The structural stresses described concern only weld toes. However, it is also possible to define a structural stress in a weld, e.g. by stress linearisation over the weld throat or weld leg. This is particularly meaningful for fillet welds subjected to local bending such as one-sided welds or welds around cover plates subjected to lateral loads (Fricke et al., 2006).

ss

ss 1 mm t

t

(a)

(b)

5.6 Through-thickness stress linearisation and structural stress 1 mm below the weld toe.



3/23/11 1:46:27 PM

122


5.2.4 Elastic notch stress and stress intensity The notch stress for example in the weld toe, which is in general numerically determined assuming linear elastic material behaviour, takes the local weld geometry into account. However, very large stress values can occur, depending on the notch radius. For a radius approaching zero, i.e. a sharp notch, the theoretical elastic stress even becomes infinite, i.e. singular. The fatigue behaviour of sharp notches is, however, less determined by the high, localised stress peak, but more by effects of the material structure preventing excessive local yielding and supporting the notch root. These socalled microstructural support effects can be taken into account by evaluating the local stress gradient, by averaging the stress over a certain distance or volume or by taking the stress at a critical distance away from the notch root, using in all cases material-dependent data. The result is the fatigueeffective notch stress. More details of the approaches have been described among others by Radaj et al. (2006). The stress-averaging approach originally proposed by Neuber has gained practical significance in the approach by Radaj (1990), who introduced a correspondingly increased fictitious notch radius of rref = 1 mm for sharp weld toes and weld roots for an actual radius of zero as the worst case. Figure 5.7 shows the fictitious notch rounding of weld toes and roots for a cruciform joint and a butt joint. At non-fused root faces, a so-called keyhole notch is arranged, placing the vertex point of the circle at the end of the slit, i.e. the location of the weld root. The weld shape is usually idealised; however, the actual shape having, for example, a certain flank angle can also be modelled. The approach is included in the fatigue design recommendations of the IIW (Hobbacher, 2009) as the effective notch stress approach. rref

5.7 Fictitious notch rounding of weld toes and weld roots (Hobbacher, 2009).



3/23/11 1:46:27 PM


123

As the keyhole notch weakens the structure, a modified notch rounding with a reference radius rref = 0.05 mm has been proposed particularly for root failures at structures made of thin sheets, i.e. plates with thickness below 5 mm. The computed elastic notch stress is of course much higher than for the notch rounding mentioned before, but also the endurable stress ranges; see Section 5.4.4. Alternatively, the stress intensity factor can be used for the fatigue strength assessment at points with a stress singularity. The use of the stress intensity factor according to Irwin (Tada et al., 2000) at crack tips or crack-like slits is well known, such as the non-fused root faces of nonpenetrating welds. For the numerical analysis of the latter, the length of the slit can be assumed as initial crack length, while an initial crack length has to be assumed at weld toes. Frequently, a length between 0.05 and 0.2 mm is assumed for design purposes representing a small defect or flaw. It should be noted that the stress intensity factor is influenced by the local weld geometry; however, the influence diminishes with increasing crack length. A stress intensity factor can be determined also for sharp V-shaped notches occurring at weld toes, called the notch stress intensity factor (N-SIF). The numerical determination of these factors and their applicability to the fatigue strength assessment of welded joints have been shown by Lazzarin et al. (2009). Using the strain energy density over a control volume around the notch, the N-SIF can be determined with a relatively coarse finite element model.

5.2.5 Elastic-plastic stress and strain As the elastic limit of the material is frequently exceeded during cyclic loading, the elastic-plastic stress and strain considering these effects can be regarded as another parameter for the fatigue strength assessment. They are suitable particularly for the assessment of large load cycles in connection with low-cycle fatigue. Figure 5.8 illustrates the over-proportional increase of the local strain e and the under-proportional increase of the local stress s during first loading (curve 1–2) and the formation of hysteresis loops in the s–e diagram in the subsequent load cycles in the elastic-plastic domain. The vertex points of the hysteresis loops can be determined with a nonlinear finite element analysis using the cyclic material law, which may differ from the monotonic material law obtained from the tensile test. Alternatively, approximation formulae exist for the calculation of the elastic-plastic stress and strain. Neuber’s rule assumes that the product of the over-proportionally increasing local strain e and the under-proportionally increasing local stress s depends on the elastic notch stress se and Young’s modulus E as follows:



3/23/11 1:46:27 PM

124

Fracture and fatigue of welded joints and structures Load

s

2

4

1

1

Time 3

2,4,6

6

5

e

3,5

5.8 Elastic-plastic notch stress and strain during cyclic loading.

s ·e =

s e2 E

5.3

The second equation necessary for the determination of s and e is the cyclic material law. it should be noted that the local straining in relatively sharp notches is limited due to the surrounding elastic material. Nonlinear finite element analyses as well as Neuber’s rule consider this so-called macrostructural support effect. The elastic-plastic notch stress and strain are used more frequently in the fatigue strength assessment of rounded notches in the parent material instead of welded joints for the following two reasons: 1. The weld shape is irregular and often characterised by small defects. 2. The material properties of the parent and weld material and the heataffected zone differ from each other; the changes occur in or close to the weld toe with the highest notch stress. Furthermore, the aforementioned material-related microsupport effects are relevant.

5.3

Factors affecting the fatigue strength

5.3.1

Overview

As mentioned at the beginning of the chapter, the fatigue strength of a structure is mainly influenced by the number and the amplitude or range of stress cycles. The stress range is at this moment understood to include notch effects. The relationship between endurable stress ranges and number of stress cycles is given by the well-known S–N (or Woehler) curve, see Fig. 5.13 below. Other factors affect the fatigue strength to a lesser degree. The following factors will briefly be discussed in this section with special focus on welded joints:



3/23/11 1:46:28 PM


∑ ∑ ∑ ∑ ∑

125

material; mean stress and stress ratio; residual stress; weld quality and imperfections; size effect.

Also the effect of fatigue strength improvement methods should be mentioned here. These are a subject of the last chapter. As it is not intended to include all details and references dealing with these factors, reference is made to the basic literature mentioned in Section 5.1.

5.3.2

Material

The material type has a large influence on the fatigue behaviour. For instance, the fatigue strength of structures made of aluminium alloy is roughly smaller than that of steel structures by a factor of 2.5. The type of material affects also the notch and mean stress sensitivity. Within one material type the fatigue strength depends on the material strength only for relatively mild notches, whereas it has been found to be almost the same for structures with relatively strong notch effects including welds. This has led to codes and recommendations where the fatigue strength of welded joints is independent of the material strength within one material type. A direct consequence is that special care is needed when designing welded structures of high strength materials and that the higher strength cannot be utilised in case of high cyclic stresses, unless the notch effects are reduced, e.g. by fatigue strength improvement methods.

5.3.3

Mean stress and stress ratio

Mean stress affects the fatigue strength in a way that it is reduced with increasing mean stress. For loading with constant stress ranges, the mean stress is expressed by the well-known stress ratio R: R=

sl su

5.4

where s l is the lower and s u is the upper stress of the stress cycle considered. A mean stress sensitivity can be defined, describing the difference between the fatigue strength in the high cycle domain for R = –1 (alternating stress) and that for R = 0 (tensile pulsating stress), divided by the second one. Different materials show different mean stress sensitivities (e.g. aluminium alloy more than steel). Also high strength materials reveal a higher mean stress sensitivity than low strength materials of the same type. Mean stress



3/23/11 1:46:28 PM

126


affects not only the crack initiation, but also strongly the crack propagation in the form of crack closure during the compressive part of the load cycle. Because high residual stresses are present, the mean stress effect can be very small in welded joints as explained in the following section.

5.3.4 Residual stress Owing to the welding process and the high heat input, residual stresses and distortions are induced in welded structures. These residual stresses are superimposed on the stresses caused by the external loading. In this way they act in a similar way to mean stresses as illustrated in Fig. 5.9 for a pure alternating stress (R = –1) and a positive residual stress sr acting at a critical location. Frequently high tensile residual stresses are present at weld toes which are generated during the cooling-down process after welding. These may even be close to the yield stress sy. In this case, the yield stress is exceeded in the first load cycle, causing partial relaxation of the residual stress such that the superimposed stress just reaches the yield stress again, see Fig. 5.9c, if a perfectly plastic material law is assumed beyond the yield limit. This means that in welded joints the stress cycles generally reach the yield stress if notable tensile residual stresses are present. That is why the mean stress has no remarkable effect on the fatigue strength in structures with high residual stresses. At notches like welds, however, the influence of residual stresses is much more complex. The reason is that the welding-induced residual stresses are not only relaxed, but load-induced stresses are built-up. This means a redistribution of residual stresses, which depend also on the notch effect. Furthermore, under variable amplitude loading the redistribution depends on the preceding load cycles resulting in a pronounced load sequence effect on the fatigue strength. s

s

Stress due to external load

s sy

sr

sr

sr

Time

(a)

Time

(b)

Time

(c)

5.9 History of cyclic stress due to external load (a), superimposed with tensile residual stress sr (b) and limited by the yield stress sy (c).



3/23/11 1:46:28 PM


127

5.3.5 Weld quality and imperfections A weld is never perfect and contains deviations from a perfect shape such as increased flank angle, excess weld metal, misalignment, etc. and irregularities such as pores, undercuts, slag inclusions, lack of fusion, etc. These are called imperfections as long as they are within the permissible limits given by relevant Standards, otherwise they are called defects requiring correcting measures. The fatigue strength of welds, where cracks initiate at the weld toe, is mainly influenced by the weld toe radius and the flank angle; see Fig. 5.10. Of course, undercuts play a significant role too here. Misalignments also impair the fatigue strength of axially loaded structures due to the formation of secondary bending stresses, as exemplified in Fig. 5.11. The superimposed nominal and secondary bending stress can be regarded as structural stress ss. For an unrestrained joint with axial misalignment e, this can be calculated directly: r

r = weld toe radius

q

q = weld flank angle

5.10 Main geometry parameters at the weld toe affecting the fatigue strength. ss

sn

(a) Angular distortion

sn

e

t

ss

(b) Misalignment

5.11 Increased structural stresses at axially loaded joints with misalignment.



3/23/11 1:46:29 PM

128


eˆ Ê s s = s n Á1 + 3 ˜ t¯ Ë

5.5

where t is the plate thickness. The resulting stress can be rather high. A common misalignment of 10–15% of the plate thickness results in a stress increase by 30–45%.

5.3.6

Size effect

The last parameter to be mentioned particularly for welded structures is the so-called size effect which means that the fatigue strength becomes smaller when the size of the structural component increases. in addition to the statistical effect, meaning that the probability of weak points increases with the size of the structure, the so-called plate thickness effect plays an important role in the design of fatigue-resistant welded structures. The decrease of the fatigue strength of welds for increased plate thickness is explained by two effects: 1. As the weld toe radius remains more or less constant, the ratio between toe radius and plate thickness becomes smaller for thicker plates so that the notch stress is increased. 2. The residual stress field is often characterised by a high tensile stress at the weld toes and compressive stress in between for equilibrium reasons. Figure 5.12 shows an example, where it becomes apparent that the tensile part is spread over a larger depth in the thicker plate. This means that the propagation of a crack initiating at the weld toe will be much faster because it stays longer in the field of tensile residual stresses. The plate thickness effect is usually considered only above a reference thickness t0 with the following reduction factor ft on fatigue strength proposed by Gurney (1979): Zone with tensile residual stress

Zone with tensile residual stress

(+)

(+) (–)

(–) sr

sr

5.12 Residual stress distribution assumed in a thin and a thick structure.



3/23/11 1:46:29 PM


Êt ˆ ft = Á 0 ˜ Ët¯

129

n

5.6

The exponent n varies between n = 0.1 for longitudinal attachments welded to plate edges, 0.2 for butt-welded joints and 0.3 for fillet-welded joints (Niemi et al., 2006). The reference thickness t0 defined in codes and recommendations ranges from 22 to 25 mm for plate-type structures. Below this, no thickness effect is assumed which can be justified by the counteracting effect of misalignments becoming more severe in thinner structures.

5.4

Fatigue strength assessment

5.4.1

Overview

The fatigue strength of welded structures is usually assessed by the following: ∑

∑

The so-called S–N approach, using appropriate S–N curves either directly in the case of constant amplitude loading or indirectly in conjunction with a damage accumulation law in the case of variable amplitude loading; the failure criterion is normally specimen fracture which is assumed to correspond to a through-thickness crack in a larger structure. The crack propagation approach, normally using the well-known Paris–Erdogan Law for the crack propagation phase up to a specified failure criterion. The crack initiation phase is either neglected, if an initial crack is assumed or an existing crack is present, or estimated on the basis of an S–N curve for crack initiation.

While the crack propagation approach is dealt with in chapter 4, the S–N approach is described in more detail in the following because several variants exist in connection with the types of stresses described in Section 5.2. Basic elements of the S–N approach are illustrated in Fig. 5.13, showing the stress spectrum, which is stepped for numerical analyses, the S–N curve for constant amplitude loading with the well-known correction in the high cycle domain after Haibach (1969) to account for variable amplitudes and the life curve resulting from similar stress spectra. in a fatigue assessment, the life curve for variable amplitude loading is usually based on the Palmgren– Miner Rule, describing the damage sum D from partial damages occurring at different stress levels i: Ê ni ˆ D = S Á ˜ £ DL i Ë Ni ¯

5.7

where ni is the number of stress cycles occurring at level i and Ni is the number of endured stress cycles at level i according to the S–N curve; see



3/23/11 1:46:30 PM

130

Fracture and fatigue of welded joints and structures Dsmax Stress spectrum Dsi (cumulative distribution (log) of stress range) S–N curve (Woehler curve) for constant amplitude loading

Dsmax

Life curve (Gassner curve) for spectrum with varying Dsmax

Dsi ni

Correction for variable amplitude loading Ni

N (log)

5.13 Basic elements of the S–N approach.

Fig. 5.13. Failure occurs when the limit damage sum DL is reached, being frequently set to 0.5 (Hobbacher, 2009). Usually, a conservative design S–N curve is used for design purposes. A typical failure probability corresponds to 97.7%, which means a curve lying two standard deviations below the mean curve assuming Gaussian distribution of lives in a logarithmic scale. An unfavourable mean stress and residual stress state are usually assumed. As mentioned before, the approach varies according to the type of stress applied.

5.4.2 Nominal stress approach In the nominal stress approach, S–N curves based on a well-defined nominal stress are used, giving the fatigue strength of the same or a similar welded detail. For this purpose, results of existing fatigue tests were gathered and re-evaluated with regard to the fatigue strength of comparable details (Gurney and Maddox, 1972; Olivier and Ritter, 1979–1985). From this, design S–N curves were derived for various typical structural details, as exemplified in Fig. 5.14. The S–N curves according to the recommendations of the IIW are characterised by their fatigue strength at two million cycles, the socalled FAT class in N/mm2, and a slope exponent k = 3 above and k = 5 below the knee point at 10 million cycles for variable amplitude loading. The curves for welded joints are limited by the FAT 160 curve for parent material (steel) with k = 5. It should be noted that typical misalignment effects are already included in the fatigue classes as these were present in the underlying fatigue tests. Similar design S–N curves and detail catalogues can be found in various codes and guidelines. Usually a relatively high quality level is required. Further details are given in Chapter 7.



3/23/11 1:46:30 PM

Permissible nominal stress range, Dsn (N/mm2)

Fatigue strength assessment of local stresses in welded joints 300

k= 5

200 k=

3

Endurance limit

160 125 100 80

60

63 50 40

40

Structural steels IIW

FAT class

100 80

131

2k

–1

20

10 105

106 107 Number of cycles, N (a) Structural detail

108

FAT class 100 90–125 80–90 80 71 63 50–80 40–50 (b)

5.14 Selection of design S–N curves for the nominal stress approach and associated structural details according to IIW recommendation (Hobbacher, 2009).

5.4.3 Structural stress approaches As the effects of the structural geometry, which are contained in the different fatigue classes of the nominal stress approach, are already considered in the structural stress, a single design S–N curve may be expected for each weld type in the structural stress approach. Different evaluations of fatigue tests have been performed for the different structural stress approaches.



3/23/11 1:46:30 PM

132


Hot spot stress range, Dshs (N/mm2)

400

Structural steels

300

200 FA T

90

100 Specimens Components

80 60

(II

W

)

105 106 Number of cycles to failure, Nf (a)

400

Pf = 2.3%

Hot spot stress range, Dshs (N/mm2)

Figure 5.15 shows an evaluation for transverse fillet welds and attachment ends based on the measured structural hot-spot stress extrapolated over the reference points 0.4t and 1.0t away from the weld toe; see also Fig. 5.5a. Generally, the classification into FAT 90 would be appropriate; however, it is interesting to note that the fatigue lives of non-load carrying welds (full symbols in Fig. 5.15a) are somewhat higher than those of load-carrying welds (open symbols). Therefore FAT 100 would be justified for non-load carrying fillet welds (Niemi et al., 2006). The reason for having two classes is that the more severe stress concentration in load-carrying fillet welds is not considered in the structural stress. In case of multiaxial loading, the principal stress acting approximately perpendicular to the weld toe within a deviation of ±60° is normally considered,

107

Structural steels

300

200 FA T

100

(II

W

)

Specimens Components

80 60

90

105

106 107 Number of cycles to failure, Nf (b)

5.15 Evaluation of fatigue tests for transverse fillet welds and for fillet-welded ends of longitudinal attachments based on the structural hot-spot stress, after Maddox (2002).



3/23/11 1:46:31 PM


133

as long as the stress components act proportionally. Alternatively, interaction formulae between the single stress components can be used, which are also applicable to non-proportional loading. For further details see Chapter 9. As measured structural stresses are the basis of the design S–N curves, they already include the effect of specimen misalignment. The stress analysis during design normally considers a perfect structure without misalignment. In plate-type structures, pronounced effects of misalignment on the structural stresses must therefore be considered, which is first of all necessary for butt joints and fillet-welded cruciform joints (because of a possible axial misalignment) as well as for fillet-welded one-sided transverse attachments (because of a possible angular misalignment). If no detailed data are available, the IIW recommendations (Hobbacher, 2009) suggest the multiplication of the axial stress at the weld toe with given factors which consider the effect of misalignment in the range up to 15% of the plate thickness. Dong (2001 and 2004) re-analysed a large number of fatigue tests using the structural stress acting perpendicular to the weld line and a special stress parameter containing the effect of the structural stress gradient in the plate thickness direction and also the plate thickness effect, based on fracture mechanics considerations. These effects are therefore explicitly accounted for in the approach, while misalignment effects are included as far as they were present in the fatigue test specimens. The plate thickness effect is also included in the structural stress proposed by Xiao and Yamada (2004) at the location 1 mm below the weld toe. The authors found that the design S–N curve according to FAT 100 for steel is appropriate also for their approach, being demonstrated for various attachments and plate thicknesses. The principal stress should be used particularly for load-carrying fillet welds (Feltz and Fricke, 2009). Pronounced misalignment effects should be separately considered. Radaj et al. (2006) show a comparison of the three approaches applied to three different structural details, an edge attachment, a cover plate and a load carrying flange attachment. The structural stresses, computed in a round-robin, varied to some extent, but the fatigue lives resulting from the approaches differed not very much and showed reasonable agreement with the tests except for the flange attachment, where compressive residual stresses were present in the critical weld toe resulting in a very long fatigue life. Finally, the assessment of root failure of fillet welds subjected mainly to throat bending is dealt with. The evaluation of different types of test specimens based on the structural weld stress leads to a design S–N curve according to FAT 71–80, if mainly a normal stress is acting perpendicular to the weld leg extending from the non-fused root faces, being linearised over the leg length (Fricke et al., 2006). Other load conditions, e.g. predominant shear parallel to the non-fused root faces, should better be assessed with the notch stress or the crack propagation approach.



3/23/11 1:46:31 PM

134


5.4.4 Notch stress and stress intensity factor approaches The notch stress approach allows the fatigue strength of both weld toes and weld roots to be assessed. For the effective notch stress approach (Hobbacher, 2009), using a reference notch radius rref = 1 mm for structures with a plate thickness of 5 mm and more, various fatigue tests have been re-analysed with corresponding finite element models, yielding a design S–N curve according to FAT 225 at steel if the maximum principal stress range in the notch is used. Figure 5.16 shows an example for such an evaluation performed by Feltz and Fricke (2009). The results for root failure are very conservative because of the over-estimated notch stress at keyhole notches with loading parallel to the slit. It should be noted that the approach includes the plate thickness effect for the whole range of plate thicknesses, while pronounced misalignment effects need to be considered separately. A problem can occur with mild notches as the approach presupposes naturally formed, as-welded toes and roots. Therefore, an effective notch stress of at least 1.6 times the structural stress should be assumed. Furthermore, the design S–N curve is limited in the upper part by the curve for parent material in a similar way as the nominal stress S–N curves; see Fig. 5.14. This is considered by performing an additional fatigue strength check for the parent material just in front of the weld toe using the structural stress acting there. Without these measures, the approach might be non-conservative. A re-evaluation of fatigue tests has been performed for different materials

Notch stress range, Dsk (N/mm2)

10000

Lap joint:

t

a

Doubler plate: 1000

100

10 105

Lap joint, t = 12 mm: a = 3 mm a = 7 mm Doubler plate, t = 12 mm: a = 3 mm a = 7 mm

FAT 225 Rª0 m=3

106 No. of load cycles, N

Toe crack Root crack 107

5.16 Assessment of fatigue tests on 12 mm thick lap joints and doubler plates with different weld throat thicknesses a based on the effective notch stress (Feltz and Fricke, 2009).



3/23/11 1:46:31 PM


135

and also for the small-size notch approach which applies to thin-sheet structures using a reference radius rref = 0.05 mm. Table 5.1 shows the resulting FAT classes for welds at steel, aluminium alloys and magnesium for both reference radii, based on the maximum principal stress in the notch. It should be noted that welds subjected predominantly to shear parallel to the weld line have shown fatigue lives being on the non-conservative side (Sonsino, 2009). This subject is currently under investigation. An assessment based on the equivalent von Mises stress with FAT classes reduced by one step is recommended here for the present. Stress intensity factors have alternatively been used for the fatigue strength assessment of critical locations such as spot welds. The notch stress intensity factor approach by Lazzarin et al. (2009) mentioned in Section 5.2.4, yields design S–N curves with reasonable scatter for welded joints at steel and aluminium depending on the notch stress intensity factor range. For practical purposes, the use of the notch strain energy density may be advantageous. Figure 5.17 shows an evaluation of fatigue test data of steel joints, yielding a relationship between the strain energy range DW1 under mode I loading and fatigue lives with a slope exponent k = 1.5. Table 5.1 Characteristic fatigue strength (N/mm2) for welds of different materials based on maximum principal notch stress determined with rref = 1 mm and rref = 0.05 mm (Fricke, 2008; Sonsino, 2009) Reference notch radius

Steel

Aluminium alloys

Magnesium

1 mm 0.05 mm

225 630

71 180

28 71

Averaged strain energy density, DW1 (N mm/mm3)

5

50% 2.3%

1 0.5

Pf = 97.7%

Fillet-welded joints (transverse attachments) Steels R = 0–0.3

k= 1.5

Previous tests New tests

0.1 104

105 106 Cycles to failure, Nf

107

5.17 Fatigue test data (toe failures) for fillet-welded transverse attachment joints in steel in relation to the averaged total strain energy density in mode I loading (after Lazzarin et al., 2003).



3/23/11 1:46:32 PM

136


As in the notch stress approach, the plate thickness effect is included and pronounced misalignment effects have to be considered separately.

5.4.5

Notch strain approach

contrary to all aforementioned approaches, the notch strain approach uses the elastic-plastic strain in the notch root as relevant parameter and considers crack initiation as failure criterion (and not specimen fracture). This means that a crack propagation analysis up to a definite crack length should follow when the whole fatigue life is assessed. The notch strain approach is particularly useful for the assessment of the low cycle fatigue with very large stress amplitudes. The crack initiation life is usually described by a strain S–N curve. Figure 5.18 shows typical strain S–N curves derived from small-scale tests for the parent material and heat-affected zone of a structural steel. The strain S–N curve is usually expressed by the Manson–Coffin equation:

e a = e a el + e a pl =

s f¢ (2 N )b + e f ¢ ((22N )c E

5.8

where ea is the total strain amplitude, consisting of the elastic portion ea el and the plastic portion ea pl, N is the number of cycles until crack initiation and sf ¢, ef ¢, b and c are the fatigue strength coefficient, fatigue ductility coefficient, fatigue strength exponent and fatigue ductility exponent, respectively. The strain S–N curves for the parent material, the heat-affected zone and also the weld material might be quite different as shown in the figure. Alternatively, the crack initiation life can be assessed on the basis of a

CMn steel StE290.7 (sY0.01 = 338, sU = 469 N/mm2)

1 Strain amplitude, ea%

ea

0.1

eael eapl

ai ª 1 mm

Parent material HAZ (small scale) 0.01 103

104

105 Strain reversals, 2N

106

107

5.18 Strain S–N curve of a structural steel for parent material and heat-affected zone (HAZ), after Bohlmann (1995).



3/23/11 1:46:32 PM


137

special damage parameter, taking into account the mean stress effect. Details can be found in the relevant literature (summarised, for example, by Radaj et al., 2006).

5.5

Conclusions

Various approaches exist for the fatigue strength assessment of welded joints. These can generally be classified into S–N approaches, using S–N curves for constant amplitude loading and a suitable damage accumulation law to account for variable amplitudes, and crack propagation approaches, assuming an initial crack and using the stress intensity factor and a crack propagation law to assess the life up to a final crack length. The chapter focuses on S–N approaches based on different types of stresses, such as the nominal stress, the structural stress, the notch stress and stress intensity, and the elastic-plastic notch strain. These consider the structural and local stress increase in different ways. Further factors affecting the fatigue strength have briefly been described with particular view on welded joints, such as the material type, stress ratio and residual stresses, weld quality and imperfections and size effects. These are considered in the approaches in different ways as well. Modern numerical methods and electronic data processing allow local stresses to be analysed to an increasing extent. The S–N approaches are very practical as they require only one stress parameter at the critical location for the fatigue strength assessment. It can be expected that crack propagation approaches and the numerical simulation of the local stress and strain in connection with variable amplitude loading will gain significance in the future. Generally it has to be emphasised that the experimental validation remains important in view of the number and randomness of influence parameters on the fatigue behaviour of welded joints.

5.6

References

Bohlmann B (1995), ‘Applications of local approaches to the fatigue assessment of welded tubular joints’, IIW-Doc XIII-1591-95, Int Inst of Welding Dong P (2001), ‘A structural stress definition and numerical implementation for fatigue analysis of welded joints’, Int J Fatigue, 23, 865–876 Dong P (2004), ‘The mesh-insensitive structural stress and master S–N curve method for ship structures’, Proc OMAE Specialty Conf on FPSO Systems, OMAE-FPSO’040021, Houston Tx, ASME Int. Petroleum Techn. Inst Feltz O and Fricke W (2009), ‘Experimental and numerical fatigue analysis of partial-load and full-load carrying fillet welds at doubler and lap joints’, In: Analysis and Design of Marine Structures (Ed. C. Guedes Soares & P.K. Das), Taylor & Francis, London Fricke W (2002), ‘Recommended hot spot analysis procedure for structural details of ships and FPSOs based on round-robin FE analyses’, Int J of Offshore and Polar Engng, 12 (1), 40–47



3/23/11 1:46:32 PM

138


Fricke W (2008), ‘Guideline for the fatigue assessment by notch stress analysis for welded structures’, IIW-Doc XIII-2240r1-08/XV-1289r1-08, Int Inst of Welding Fricke W, Kahl A and Paetzold H (2006), ‘Fatigue assessment of root cracking of fillet welds subject to throat bending using the structural stress approach’, Welding in the World, 50, No. 7/8 Gurney T R (1979), Fatigue of Welded Structures, Cambridge, University Press (2nd edn). Gurney T R and Maddox S J (1972), ‘Determination of fatigue design stresses for welded structures from an analysis of data’, Metal Construction and British Welding J, Nov, 418–422 Haibach, E (1969), Modified linear damage accumulation hypothesis accounting for the decay in endurance limit with increasing damage (in German). Technische Mitteilung TM 50/70, Fraunhofer-Institut für Betriebsfestigkeit (LBF), Darmstadt. Hobbacher A (2009), Recommendations for Fatigue Design of Welded Joints and Components. IIW doc.1823-07, Welding Research Council Bulletin 520, New York. Lazzarin P, Lassen T and Livieri P (2003), A notch stress intensity approach applied to fatigue life predictions of welded joints with different weld toe geometry’, Fatigue Fract Engng Mater Struct, 26, 49–58. Lazzarin P, Meneghetti G, Berto F and Zappalorto M (2009), ‘Practical application of the N-SIF approach in fatigue strength assessment of welded joints’, Welding in the World, 53, No. 3/4 Maddox S J (1991), Fatigue Strength of Welded Structures, Cambridge, Abington Publ (2nd edn) Maddox SJ (2002), ‘Hot-spot stress design curves for fatigue assessment of welded structures’, Int J Offshore & Polar Engng 12, 134–141 Niemi E, Fricke W and Maddox S J (2006), Fatigue Analysis of Welded Components – Designer’s Guide to the Structural Hot Spot Stress Approach, Cambridge, Woodhead Publishing Olivier R and Ritter W (1979–1985), Catalogue of S–N curves of welded joints in structural steels, DVS-Bericht 56, Düsseldorf, DVS Poutiainen, I (2006), A modified structural stress method for fatigue assessment of welded structures, Doct Thesis 251, Lappeenranta University of Technology Radaj D (1990), Design and Analysis of Fatigue-resistant Welded Structures, Cambridge, Abington Publ Radaj D, Sonsino CM and Fricke W (2006), Fatigue Assessment of Welded Joints by Local Approaches, Woodhead Publ (2nd edn) Sonsino CM (2009), ‘A consideration of allowable equivalent stresses for fatigue design of welded joints according to the notch stress concept with reference radii rref = 1.00 and 0.05 mm’, Welding in the World, 53, No. 3/4 Tada H, Paris P C and Irwin G R (2000), The Stress Analysis of Cracks Handbook, American Soc of Mech Engnrs Xiao Z G and Yamada K (2004), ‘A method of determining geometric stress for fatigue strength evaluation of steel welded joints’, Int J Fatigue, 26, 1277–1293, and IIW Doc XIII-2022-04/XV-1175-04



3/23/11 1:46:32 PM

6

Improving weld class systems in assessing the fatigue life of different welded joint designs

B. J o n s s o n, Volvo Construction Equipment, Sweden

Abstract: A welded structure is built by researchers with experience from design, analysis, production and control. Historically, these different researchers have had only limited dialogue and each group has focused on their own narrow field of interest. This has led to inconsistencies in the definition of so-called ‘weld class systems’ which have been primarily developed based on concepts related to good workmanship but have little or no relation to the actual performance of the welded structure. A new weld class system with an objective to focus on design for purpose has been developed as a Volvo standard. This system is described in this chapter. The new standard has three quality levels for fatigue: as-welded normal quality, as-welded high quality and post-weld treated quality. It contains acceptance limits which are consistent with the expected fatigue strength and which can more objectively handle revisions. Further, a fourth weld class level is defined for static loaded welds since the demands for these are quite different than those for fatigue loaded joints. This new system will help in the development of new structures with lower weight and increased reliability. Key words: weld classes, weld quality, weld imperfections, fatigue strength, fracture mechanics, effective notch method.

6.1

Introduction

Welded structures subjected to variable amplitude loads such as those in the automative industry are very common in engineering. The design of these welds has traditionally used simplified methods such as the nominal stress approach, although the physical fatigue problem may be very complex involving many different types of defects, residual stresses, relaxation, multi-axial loads and more. One reason for using simple methods is that the current regulations, via the nominal stress levels, try to cover for all things using a statistical view. Sometime during the 1990s new methods began to be developed partly due to increased computer power, but also to a deeper understanding between the design offices and the production quality level. These new methods are commonly known as ‘local’-based methods, where the designer tries to study 139 © Woodhead Publishing Limited, 2011


3/23/11 1:46:49 PM

140


the stress levels (or stress intensity levels) in the actual point of interest. This is in contrast to the ‘nominal’ approach, where the stress far from the weld is used. One obvious disadvantage with the nominal approach is that the inside (root side) of the weld may be disregarded. This would be quite all right if the weld is fully penetrated, leaving no non-fused parts behind. However, for most fillet welds this is not the case. Another disadvantage is that it is often difficult or even impossible to define the nominal stress level, especially in complex structures. It is thus important that the design process uses methods where these uncertainties are removed. This chapter describes the result where local-based methods have been used and also the importance of a close teamwork between the design engineers and the production people. This not only leads to an improved quality level and thereby an increased fatigue life, but also and at the same time, it is quite possible to optimise the design and make use of such things as high strength steel and post-treatment of welds. Lightweight structures will in the future play an important role due to environmental care, which can be expressed as improved productivity and lower specific fuel consumption. In this context one should realise that it will also become necessary to balance the cost of the product with the quality level, in order to make the best choice. The communication tool between design and production is the drawing of the structure. This document contains not only the dimensions of plates and other components, but also information of the quality level(s) and preferably figures stating the consequence of a failure. For welds, the quality rules are regulated in so-called weld classes, where the different imperfections in welds are given levels, acceptance limits, stating the demands. Current weld class systems, however, have some problems inherited from the past and these can be expressed as being subjective in revisions and having a weak relation to fatigue. A new defined weld class system, where these problems are removed or improved, is presented along with new acceptance limits.

6.2

Historic view

The story of strength started several hundred years ago and was at that time probably based only on practical methods. One wonderful description about the use of metal can be found in my first student book on strength [1], where the Swedish project leader, Cristopher Polhem (1661–1751), described his problems. In a free translation from (old) Swedish he concluded that: ‘iron may be stronger than a tree, but this impression of strength may be misleading since the products of the art of forging are not as safe as the trees produced by mother nature’. Perhaps Polhem had stumbled across some defect problem. Since then a lot has happened and one major step was taken when August Wohler (1819–1914) around 1850 first discovered the problem of fatigue.



3/23/11 1:46:49 PM

Improving weld class systems in assessing fatigue life

141

His method is still used today over all the world in the design of fatigueloaded structures. He was appointed to solve the failure of railway axles which were designed to withstand yield. However, no one had expected that failures could arise due to cyclic loading below the yield. The design and dimensions of welds have for a long time been made using so-called ‘nominal’ methods. One reason is that this employs a simple method to solve a very complex problem. The welding process produces heat which alters the material’s properties and will most likely give rise to defects and geometrical discontinuities, create residual stresses and introduce distortions during cooling to room temperature. All of these things are difficult to quantify. As a result, baseline data (the Wohler curve) for welded joints are usually obtained from many but small sample tests of various weld joint details including most of the effects mentioned above. The analysis then becomes easy: all that is needed is to choose a weld joint and determine the nominal stress level (hence the name ‘nominal’). In real cases, however, this method requires quite a lot of experience and engineering judgement. It is often found that the actual joint is not present in the regulation and also that the nominal stress level is difficult or even impossible to define in a complex structure. On top of this the root side of the weld may include a design crack due to lack of penetration; this is especially so for fillet welds without preparation of the plate edges and becomes a problem when the tested Wohler data are valid only for the toe side of the weld. The use of fracture mechanics saw daylight between the two world wars, when the first welded ships at sea were built, and increased the understanding of fatigue. A lot of mysterious failures occurred, when Liberty ships going far out on the oceans suddenly sank, the cause of failure was lost on the bottom of the sea. During the 1930s one ship was broken in two pieces in a harbour. That was the first time the failures could be studied closely and could be said to be the beginning of fracture mechanics. One well-known name in this area is Alan Arnold Griffith (1893–1963), who tried to explain the phenomenon of cracks and what governs them. This was actually an example where fatigue was studied using ‘local’ methods since the stress state was studied at the very point of the crack tip. This method (fracture mechanics) is still today the best way to study fatigue problems; all knowledge needed is the defect size or crack size. The law used here is generally referred to as the Paris law which governs how fast a crack grows under cyclic loading. Paris developed these formulas during the 1960s together with Erdogan. Somewhere during the 1990s, new development was seen using the concept of ‘local’ methods. One of the reasons was faster and bigger computers, but another important realisation was the connection to production. People began to understand that fatigue in welds is closely related to the production process and the defects and discontinuities that arise. Since fatigue primarily is (local) geometrical based (and not material based), the only way to study



3/23/11 1:46:50 PM

142


it is to make use of local-based methods. One of the most attractive is the effective notch method, which can take both the toe side and the root side of the weld into account and replace the real world geometry with a fictitious radius. Here it measures the stress concentration at the actual point of interest and the result can be related to one Wohler curve. The original S–N curve (S = stress, N = number of cycles) that Wohler derived was taken from tests using rotating bending, a method that is still commonly used! This gives a curve which is based on constant amplitude loads, and for components having such loads, all is fine. Here a possibility to design against a so-called fatigue limit, below which no failures occur, is at hand (this was the clue of Wohler’s research back in the 1850s). However, within many industries the loading conditions are of variable amplitude and in such cases the fatigue limit, more or less, ceases to exist. Another effect is that the residual stresses, which right after production can be of the order of yield, may relax when the biggest load amplitude is added on top of the residual stress field. When facing a situation of variable amplitude loads, the calculation of the loads often needs to be simplified. One way is to compress the different load levels into one level, having the same effect regarding fatigue, by performing a so-called rain flow counting. This was first done by Tatsuo Endo (1925–1989). So in summary, the history of fatigue started with the Wohler curve, which connects the stress range (or amplitude) to the number of cycles, and this is still in use. The way the stress is measured has, however, changed from nominal to local-based and this has proven to work well for the complex world of welds.

6.3

Weld class system ISO 5817

The quality rules for welds as a standard (ISO) were released in 2003. They described acceptance limits for most imperfections expected in normal fabrication. There are three classes (quality levels) designated by letters B, C and D, where B has the highest quality. The rules are applicable for plate thicknesses above 0.5 mm and cover all types of welds. Many material types are also included as well as many types of welding processes, although arc welding is the main focus. Imperfections such as cracks and lack of fusion are not allowed in any class for obvious reasons, but incomplete or lack of root penetration is tolerated in ISO 5817 to some degree in class D. In a situation of varying loads leading to a potential of fatigue, the root side is very important, implying that class D can only be used for static load cases. However, this is not stated anywhere, so obvious care must be taken for users. Common imperfections such as undercuts, convexity, angle, leg length, throat, misalignments and pores are given acceptance limits in most classes with harder tolerances with increasing



3/23/11 1:46:50 PM


143

designation. Investigations made have, however, shown that the connection between the limits and fatigue is weak; see ref. [2]. One important feature used in many weld classes is the term ‘even transition’. This means that the area where the weld ends and the plate starts (the toe) should have a geometry described as even. In a fatigue situation where the local geometry plays a key role, this is very important. For static load cases, however, this ‘even transition’ is not important at all, but the requirement is given even for class D, contradicting the statement about the root above. A major problem with the term ‘even’ is that it cannot be measured, which leads to subjective results in the revision of welds. Investigations made reveal that there is no clear opinion over the concept of ‘even’: in many ordinary cases the judgement among a group of people is divided, one half says a transition is even and the other half says it is not.

6.4

Weld class systems at Volvo

During the 1970 and 1980 decades a new Swedish regulation for steel structures saw daylight. Work based on this regulation started in Volvo and the result was Volvo STD 5606,51 (and later STD 181-0001), which was written in 1989. Since then this has been the weld class system in use. The acceptance limits in these weld classes, having the main designations A, B, C and D, are to a great extent built on workmanship in the production; ‘this is what you get’ so to say. No scientific analysis was made to balance the different defects or discontinuities. Comparing with ISO 5817 the acceptance limits are very alike and one could suspect that the background for them is the same. In Volvo’s STD a connection to strength was stated via a so-called Kx-factor, a feature which is not present in ISO 5817. The Kx-factor is a kind of a stress concentration factor containing joint type and load direction and with different values between the different weld classes. The Kx-factor is used together with the nominal stress level and has one ground level of 315 MPa at 2E6 cycles for median strength. The two lowest classes, C and D, cover static loads, and if fatigue loads are at hand, an additional designation U should be added (as an example DU instead of D). In such cases, when U is added, the weld should have at least an ‘even transition’. The two highest classes, A and B, are both aimed at fatigue loaded welds, without having to state U. Comparing the classes for typical welds, the fatigue life of CU is twice the one in DU according to the Kx-values. Comparing with ISO 5817, the situation is very similar regarding the problem with even transition: it is a very important feature in fatigue cases, but it cannot be measured. During the years around 2000 it became clear that the current weld classes had some problems. One was the above-mentioned even transition requirement and another was the focus on the toe side of the weld. The Kx-



3/23/11 1:46:50 PM

144


values all aim at the toe side, neglecting the root side. Often welds have lack of penetration on the root side, which can best be characterised as a defect similar to a crack. Even in cases with prepared plates one cannot guarantee that a full penetration is at hand unless the plate has welds on both sides. Another common problem in conjunction with the Kx-factor is that it assumes the use of nominal stresses. These are possible to define in a simple structure, but in complex ones the situation is quite different. Here the stresses vary in both direction and position in such a way that it is more or less impossible to define the nominal stress level. When all these drawbacks became evident, the use of new methods, so-called local-based methods, came into use. After some years of work, the understanding of the situation led to the development of a new weld class system, STD 181-0004. Here, the new acceptance limits were set so that different discontinuities had the same impact on fatigue. The old requirement ‘even’ transition was replaced by a toe radius requirement, which may inherit measuring difficulties, but is a much better tool in the revision of welds. At the same time the root side is given measures directly stated on the drawing, so that both the toe side and the root side get the appropriate attention.

6.5

A consistent and objective weld class system

The basic information in a weld class system, such as ISO 5817 [3] or Volvo’s STD 5605 [4], is to define rules for the quality of welds. The current rules in these systems, however, do not reflect the fatigue life of the weld geometry well. Investigations [2] indicate that the type of defect plays a bigger role than the quality level itself and also that some defects or error types are very important, while others are not. This implies that for a certain quality level the fatigue life can vary one or two magnitudes depending on what kind of error is present. Also, if the quality level is raised, say from D to C in a weld, one cannot be certain that the fatigue life will be increased. Another example is the so-called ‘even transition’ condition, an important demand often used in weld class systems. This term expresses a requirement of the transition area between the weld toe and the plate surface. The problem is that the control is made visually by the eye and is thus a very subjective method. Here a clear need of a more objective measure is obvious. Another closely related problem is the design of the weld root. The weld classes are within the old Volvo’s system related to the stress levels through the Kx-factor (equivalent to FAT values) and this relation concerns only the toe side of the weld since nominal stresses are being used. This view has the drawback that the root side is neglected and not taken into account. Most of the failures in the supporting structures during the last decades concern the root side of welds and one reason is this described problem. One has to bear in mind that the only important measure for the root side is the size of the



3/23/11 1:46:50 PM


145

root defect that may be present if full penetration is not at hand. This could be seen as a negligence, but could most probably be explained by the view that there should not be any root defects after welding. This is unfortunately not the case especially for fillet welds and care of this point is thus needed. Adding together all the above leads to the conclusion that there is a great need for a new system, one where these problems are removed. The new weld class system is divided into three different quality levels (VD, VC, VB) for fatigue loaded structures and one for static loaded structures (VS). The first two classes stand for the ‘as-welded condition’, normal quality (VD) and high quality (VC). The last and highest class (VB) stands for ‘post-treated welds’ regardless of the kind of treatment. The different types of occurring errors and defects can be divided into three categories: outer defects (toe side), inner defects (root side) and invisible defects (like inner pores); see Fig. 6.1. These are treated differently, so that the weld class system defines rules for the toe side and for the invisible types, since defects occurring here are statistically distributed. The root side, however, has a fatigue life governed mainly or only by the size of the root defect, which is normally the same along the weld. This means that a demand as a measure on the drawing works best, implying that the root side should not be a part of the weld class system at all. The acceptance

(Toe) Outer quality e.g. undercut cold laps

(Root) Inner quality e.g. poor penetration

Non-visible errors e.g. lack of fusion pores

6.1 Three different categories of errors. Outer quality and non-visible errors are treated in the new weld class system, inner quality is given as measure(s) on the drawing.



3/23/11 1:46:50 PM

146


limits for occurring errors (on the toe side and for invisible types) should be describing only those having an impact on the fatigue life. One important target in the new weld classes regarding these errors is that the acceptance limits should reflect a fatigue life which is the same for different types of errors in one weld class (quality level). Also, if the quality level is increased one step, the fatigue life should be expected to increase a factor of 2 or alternatively the stress could be raised by 25%. In general, the acceptance limits are positioned two standard deviations (2S) away from the median FAT level. Using an ordinary assumption on S this gives a factor of 1.3 in stress range (if S is measured on log N). The design of a weld can thus connect the analysis to the weld classes on the drawing. Other error types, which have little impact on the fatigue life, are left out of the weld classes unless other reasons require their presence. Most important for the fatigue life among the outside (toe) features is the transition area, where current systems have the requirement ‘even’. In the new system, the term ‘even’ is replaced by a requirement on the radius, which is more objective and more important: it can be measured.

6.5.1 Penetration of welds In many welds, especially in fillet welds without weld preparation, the fusion does not penetrate the plate completely, leaving a gap of non-melted material behind. This works as a crack-like defect and will lead to failures at least in situations of load-carrying joints. If such a failure has occurred, the crack has started at the root, often kinked off a bit and has finally become visible in the middle of the throat. This is actually an easy and quick way to judge whether the failure has started from the toe or root since toe failures obviously will be spotted at the toe region. In the analysis phase of a project it is of course important to know where the weakest points are and for the root side of the weld, the size of the penetration is the most important measure. Since sizes, due to life requirements, can be calculated using local-based methods, it is more natural to have this measure stated on the drawing instead of a general acceptance limit in the weld class system. So in accordance with the throat size, which is often given on the drawing as an a-size, the needed penetration is given as an s-size for butt welds and i-size for fillet welds. This has the advantage that the root side is given more attention than before since both analysis and production need to consider these values in each case.

6.5.2 Transition radius One of the most important measures of the weld regarding fatigue is the transition area between the weld toe and the plate. In the current weld



3/23/11 1:46:50 PM


147

class system there is a requirement stating that ‘even’ transition should be met. This is, however, not a technically quantified term, since it cannot be measured and since revision is made visually, it also leads to a subjective result. A better approach, which is used in the new weld class system, is to base the result on stress concentration factors. This could then be translated into geometric measures, leading to a more objective method in the revisions. In the new weld classes the radius alone is used (see Fig. 6.2), where Kt = 2.5 equivalent to R = 1 mm is shown. The approach does not involve the angle and the thickness due to simplicity. The Kt factor is defined for a non-load-carrying cruciform joint, where the penetration plays no role. For load-carrying joints the penetration has an impact on the Kt factor, but this case can be excluded since the root side of the weld in this load direction is the weakest point. As seen from Fig. 6.3 [5], the radius should be > 1 mm for a high quality weld. The normal quality level of welds does not require the same size of the radius. One way to study the requirements for this case is to set the radius when the stress concentration (Kt) shifts from blunt to sharp. An elliptical notch has a stress concentration Kt = 1 + 2√(D/R) with blunt to sharp transition for Kt = √(D/a0), where D = depth, R = radius and a0 = (∆Kth/2Dsu)2 [6]. Using an analogy with the toe transition having Kt = 1 + √(t/R)/2, where t = thickness, this results in t = 16D. Inserting this in the blunt to sharp transition one gets Dsu = 2Kt*DKth/√t. For typical values of the threshold Even transition (Kt = 2.5, t = 12 mm)

2.00 1.75

Toe radius (mm)

1.50 1.25 1.00 0.75 0.50 With angle Without angle

0.25 0.00 0

10

20

30

40 50 60 Angle (degrees)

70

80

90

6.2 Stress concentration in the toe transition in a fillet weld using the toe radius and with or without the angle.



3/23/11 1:46:50 PM

148

Fracture and fatigue of welded joints and structures Life as a function of radius (nominal stress = 100 MPa) (cold lap size < 0.10 mm)

Life (cycles)

1.0E+07

1.0E+06

Cold lap (0,1) Goal 2E6 1.0E+05 0

0.2

0.4

0.6 Radius (mm)

0.8

1.0

1.2

6.3 Calculated fatigue life in a cruciform joint. Life of 2E6 cycles is reached when radius ª 1 mm. Transition from sharp to blunt notch

1000

Kt = 5, t10

Fatigue limit range (MPa)

900

Kt = 5, t20

800

Kt = 3, t10

700

Kt = 3, t20

600

Typical

500 400 300 200 100 0 0

2

4 6 Threshold (MPa m2)

8

10

6.4 Transition from a blunt to a sharp stress concentration in a weld toe can be determined to at least Kt > 5.

(DKth = 2–5 MPa√m) and the fatigue limit range (Dsu = 300–600 MPa) one reaches a value Kt > 5. This implies that the toe radius shifts to a sharp transition for R ≈ 0.1–0.3 mm; see Fig. 6.4.



3/23/11 1:46:51 PM


149

The same size can be found by studying the formulas for Kt = 1 + 0.5√(t/R) together with Kf = 1 + q(Kt – 1), where q = the notch sensitivity = 1/(1 + A/R) and A is a material parameter of the ultimate strength [7,8]. This leads to the expression Kf = 1 + [0.5√(t/R)]/(1 + A/R); see Fig. 6.5. As shown, this expression has a maximum at R = A and if this is interpreted as a transition from blunt to sharp Kt it results in a radius R ≈ 0.25 mm for typical materials. The steps in quality with a radius of 0.25 mm (for VD, normal quality) to 1 mm (VC, high quality) and to 4 mm for a post-treated weld (VB) could be compared with the results in ref. [9]. Here the mean characteristic stress range was expressed as a measured formula: Ds ≈ 156 * (R/t)0.12 or a calculated formula: Ds ≈ 160 * (R/t)0.125, where the starting defects were supposed to be < 0.05 mm. Using t = 10 mm as a typical thickness, one arrives at an increase of approximately 20% higher strength between radii, which is somewhat lower than the principle of 25% difference used in the new weld classes system.

6.5.3 Cold laps Cold laps are a type of error occurring when melted material has not been merged with the cold plate surface. This produces a crack-like defect, often Stress concentration Kf regarding fatigue life (t = 10 mm) [Kf = 1 + (Kt – 1)/(1 + A/R)]

Kf

3

2

Rm = 500 MPa Max 1 0

0.2

0.4 0.6 Radius (mm)

0.8

1

6.5 Stress concentration Kf as a function of weld toe radius.



3/23/11 1:46:51 PM

150


very small, which is parallel to the plate; see Fig. 6.6. It can be produced from spatter, forming local rounded laps (a/c = 1), or from too high welding speed, when line cold laps (a/c = 0) are formed. The latter case can be studied in a 2D model (see Fig. 6.7) using fracture mechanics [10]. It can be seen

6.6 A cold lap with a size of 0.1–0.2 mm.

Cold lap a/c = 0

Root defect Crack growth to t/2

6.7 Non-load-carrying cruciform joint with a cold lap.



3/23/11 1:46:52 PM


151

Stress intensities range (MPa, sq. root (m))

that the cold lap has a mixed mode at start, with a big influence from mode KII. This gives arise to a kink angle of around 50 degrees at the first step and, very quickly, the cold lap is transformed to a sharp vertical crack, now in mode KI. In fact, after the first steps of crack growth, the stress intensity tends to be somewhat higher for smaller initial cold laps; see Fig. 6.8. The overall result is that the fatigue life for different cold lap sizes tends to be more or less constant for cold lap sizes over a certain value; see Fig. 6.9, Stress intensity for different cold lap sizes at start and after two steps of crack growth Kt = 2.4 (R = 1), nominal stress 100 MPa

7 6 5 4 3 2 1 0 0.00

0.05

0.10 At start

0.15

0.20 0.25 Cold lap (mm) After 0.2 mm

0.30

0.35

0.40

0.45

After 0.5 mm

6.8 Stress intensities for different starting cold lap sizes. Note that the stress intensities after the first steps of growth tend to be somewhat lower for bigger cold laps.

Life (cycles)

1.E+07

1.E+06

Kt = 2.5, 100 MPa Kt = 4.0, 80 MPa 1.E+05 0.01

0.1 Cold lap size (mm)

1

6.9 Life in a cruciform joint with different toe geometries and having different starting cold lap sizes, 2D analysis.



3/23/11 1:46:52 PM

152


depending on the geometry of the toe transition area. For a weld in ‘high quality’ one can see that the cold lap size needs to be very small (< 0.1 mm) in order to reach 2 million cycles, but for ‘normal quality’, the requirement is easier, cold laps < approximately 1 mm. After discussions with revision people among others, the acceptance limit was set to half this value (0.5 mm) since 1 mm was regarded to be too big from the production point of view. These results are valid for line cold laps, but if spatter produced cold laps are at hand, then one could expect to have a/c = 1, requiring a 3D analysis; see Fig. 6.10. The result shows that the cold lap behaves differently along the crack front. At the top, the mixed mode is very similar to the 2D case with a great kink angle influenced by KII. At the edge, however, the mixed mode is KIII, resulting in a small kink angle. The cold lap having a/c = 1 at the beginning, now grows towards a line cold lap (a/c = 0) and all together this results in a fatigue life that is two-to three times longer; see also ref. [11]. However, the acceptance limits are set according to line cold laps. The fact that an existing cold lap over, say, 0.3 mm leads to a crack growth and shortened life implies that a lot of failures could be expected since cold laps are believed to be common. These failures are, however, not the case and the most probable explanation is that in the plants there is normally a blasting operation after welding, preceding the painting. The blasting operation will induce residual stresses in compression and close most of any small existing cold laps. This means that the need of a blast operation before painting also hinders a lot of possible crack growth positions.

6.5.4 Lack of fusion When the weld process for some reason is not right, the result is often lack of fusion. The position could be anywhere from the root to the surface or even between layers. Lack of fusion is a kind of defect that should not be present at all. The analysis of these defects is rather straightforward using fracture mechanics and if the positions are favourable (say, for instance, in the middle the weld, as in Fig. 6.11), it is quite possible to reach an adequate fatigue life. However, if they are close to the root side or close to the surface or toe area, then the size of the defect becomes very important. This means that in the weld class system one cannot generally allow these defects in any class. On the other hand, if lack of fusion is found in production it is possible to perform a fracture mechanics analysis and often find that the component can be used without any repairs.

6.5.5 Undercuts If the welding parameters are not optimal (one example is too low welding speed), it can lead to undercuts along the weld. This type of error can be



3/23/11 1:46:52 PM



3/23/11 1:46:52 PM

0.15 mm

Depth 0.02 mm

16

Step 2 KI 0 mm

2

Step 1 KI+KIII

=2

=3

Approx N a = 0.6 mm a/c = 0.2

Depth (^ to paper) approx. 2 mm approx. 0.3 mm 0 mm

Appr N/2 a = 0.3 mm a/c = 0.4

Kink angle approx. 80 approx. 70 approx. 50

Start a = 0.2 mm a/c = 1

Step = 1

Mode Step 3 : KI Step 2 : KI Step 1 : KI+KII

cdirection

adirection

6.10 3D crack growth for a spatter induced cold lap. The view is seen from above showing the crack front and its shape. As seen the result at 12 o’clock has a great kink angle (mixed mode KII, compare with 2D) and at 3 and 9 o’clock the kink angle is small (mixed mode KIII at step 1).

3 and 9 o’clock

30

Kink angle

(^ to paper)

Step 3 KI

Mode

Toe line

1 mm

12 o’clock

154


Crack growth

Weld surface of the fillet weld

Initial length of lack of fusion

Crack growth Root crack

6.11 Lack of fusion positioned in the middle of the side of a fillet weld. In this case, if non-load-carrying situation is assumed, a rather long fatigue life could be expected.

analysed using the effective notch method, where the real radius is replaced by an effective R = 1 mm. Studying a fillet weld (see Fig. 6.12), the result shows an influence from the size of the undercut. When setting the acceptance limits, the idea is that the normal weld is free from undercuts and the worst acceptable undercut is positioned two standard deviations from this level. This gives a limit in the studied case equal to 0.6 mm or in relation to the thickness t = 10 mm expressed as 0.06t. If, on the other hand, a butt weld is studied in the same way, a lower limit is reached; see Fig. 6.13. Here the acceptance limits point at 0.35 mm or, in relation to the thickness, 0.035t. It might be possible to have different values for fillet welds and butt welds, but since many welds are a mix of these two it can lead to difficulties in the revision. To avoid these problems and have a simple tool, the average of these two results is used. This leads to an acceptance limit of 0.05t for normal quality as-welded condition and this is well in line with IIW’s recommendations [12].

6.5.6 Throat size The throat size (a) concerns only fillet welds. There are different methods to define the throat size and the one used here is: a = the height of the greatest inscribed triangle having equal leg length. A too small throat can



3/23/11 1:46:53 PM


155

Non-load-carrying cruciform joint with undercut (using the effective notch method)

400 350

Stress S1 (MPa)

300 250 200 150 VD, 80 MPa (R = 1)

100

FAT 225 1.3*stress (d = 0)

50

Acceptance limit

0 0

0.5

1.0 1.5 Depth (d ) of undercut (mm)

2.0

6.12 Stress levels in a fillet weld having an undercut. Acceptance limit is taken as the stress level 2 standard deviations above a fillet weld without undercut.

450

Butt weld having an undercut (using the effective notch method)

400 350

Stress S1 (MPa)

300 250 200 150 VD (100 MPa)

100

FAT 225 1.3*stress (d = 0) Acceptance limit

50 0 0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 Depth (d) in the undercut (mm)

0.8

0.9

1

6.13 Stress levels in a butt weld having an undercut. Acceptance limit is taken as the stress level 2 standard deviations above a butt weld without undercut.



3/23/11 1:46:53 PM

156


be assumed to have an impact on both the toe side and the root side. The toe side can easily be analysed using the effective notch method and for a fillet in an as-welded condition, normal quality, the result is given in Fig. 6.14. As shown, the stress level is more or less independent of the throat size and this implies that the throat size does not play a role at the toe for fatigue loaded welds. However, a fatigue loaded weld also needs to withstand static loads and from this point of view, an acceptance limit is needed. The only influence seen in Fig. 6.14 comes from the thickness, where t = 15 mm seems to fit the FAT 225 value and the curves also seem to fit the standard stress thickness correction

S = S0 * (t/t0)n

with an exponent n ≈ 0.2–0.3. The root side of the weld is influenced by the throat size for load-carrying welds. Studying this case there are two methods: fracture mechanics and notch method. A comparison between these two methods has been made (see Figs 6.15–6.17). As seen in Fig. 6.17, the calculated life coincides well for the two methods even for high Kt (large root defects). This is used when the acceptance limits have been set for the root side. If no penetration is assumed, the worst and designing case is at hand. Assuming a typical throat size as the median level and positioning the acceptance limits two standard deviations away, see Fig. 6.18, one gets a result of 0.7a. The acceptance limit of the throat size should thus be – 0.3a.

Maximum stresses at the toe using the notch method in a non-load-carrying cruciform joint with or without penetration R = 1 mm in model, stress level = 80 MPa

Principal stress S1 (MPa)

300 250 200 150 100

t = 20 t = 15 t = 10 FAT 225

50 0 0

2

4 6 Throat size = a (mm)

8

10

6.14 Stresses in the weld toe as function of the throat size a for different thicknesses.



3/23/11 1:46:53 PM


157

Case B1 R1 a5 O45 i0, t = 15, a = 5, i= 2, radie = 1, theta = 45

6.15 Influence from throat size on the root side, model built using the effective notch method (Ansys).

6.5.7 Misalignments If two plates are welded together either in a fillet or in a butt weld and these are not met in the right position or in the right angle, then misalignments are at hand. These can thus be of two kinds: axial or angular; see Fig. 6.19. When tension loads are applied to the joint, secondary bending moments occur and this can have a great influence on the fatigue life. The stress raising effect can be expressed as a factor Km and in IIW’s recommendations [12] formulas are given for different cases. One of the parameters in these formulas (l) reflects the restraint of the joint, which is illustrated in Fig. 6.20. Assuming unrestrained case, symmetrical lengths of the plates and neglecting the influence of straightening from the loads one can deduce all cases into one simple formula: Km = 1 + 3e/t, where e = misalignment and t = thickness. Identifying the median level as no misalignment and the acceptance limits as two standard deviations away (1.3 in stresses) this leads to 1 + 3e/t = 1.3 or e/t = 0.1. So for both butt welds and fillet welds and also for both axial and angular misalignment the acceptance limit is e/t < 0.1. © Woodhead Publishing Limited, 2011


3/23/11 1:46:54 PM

158


Symmetry

Deformed structure shown

Crack growth

Symmetry Start defect = root defect for a penetration of 4 mm

6.16 Influence from throat size on the root side, model built using fracture mechanics (Franc2D).

1.E+07

Life in root of a weld in a load-carrying cruciform joint (t = 10,15, 20 with a = 5, 7, 9 having nominal stress = 100 MPa) Notch method LEFM No penetration

Life (cycles)

1.E+06

1.E+05

1.E+04 0

1

2

3

Kt

4

5

6

7

6.17 Comparison between the effective notch method and linear fracture mechanics as a function of Kt in the root of a weld. LEFM = linear elastic fracture mechanisms.



3/23/11 1:46:54 PM

Improving weld class systems in assessing fatigue life Maximum principal sttress in the root of a load-carrying cruciform joint (notch method, penetration = 0 mm, nominal stress = 100 MPa)

1600

t = 10 mm

1400

t = 15 mm

1200

Stress = S1 (MPa)

159

t = 20 mm

1000

Median a5

800

Median a7

600

Median a9 1.3*median

400

1.3*median

200 0

1.3*median 0

2

4 6 Throat size = a (mm)

8

10

6.18 Influence from throat size on the stresses in the root. Horizontal lines indicate which throat size is equivalent to 1.3*median stress level.

e Butt weld e

Fillet weld

e

e

Axial misalignment

Angular misalignment

6.19 Misalignments (e) in fillet and butt welds.

The case when two different thicknesses meet, having one of the plate surfaces in plane, automatically leads to something which could be called misalignment, since the middle lines are not coincident. However, if this case is treated under misalignment then thickness changes above 10% would be prohibited. This implies that thickness changes should not be treated as misalignment in the weld class system; on the contrary, a thickness change should be analysed and designed to withstand the loads.



3/23/11 1:46:55 PM

160


Unrestrained case, deformation is S-shaped

Restrained case, deformation is bending

6.20 Axial misalignment in a butt weld with different types of boundary conditions. Analysis made in Ansys (2D). Restrained case gives higher stresses. Deformation is highly exaggerated.

6.5.8 Pores Welding often produces different kinds of pores. Most of them are spherical but other forms can exist. The current weld class systems have many different cases and the impression is that they should be simplified. There are two kinds of acceptance limits: single pores and clustered pores with acceptance limits either expressed as a relation to thickness or throat size or as a percentage of a measured area. For a single inner pore of size D one could assume an equivalent semielliptical crack (a/c = 1) positioned in a typical weld area of 10*10 mm2. The stress level depends on the position of the pore, but a reasonable assumption is to use nominal values. Using fracture mechanics in Afgrow to calculate the crack growth [13] (see Fig. 6.21), one can define acceptance limits at 2 million cycles as 2, 3 and 4 mm for the three different classes (see Fig. 6.22). If a pore is positioned at the surface one can assume a surface-breaking semi-elliptical crack having a/c = 2. Analysis in the same way then results in somewhat lower acceptance limits 1, 2 and 3 mm respectively, implying that surface pores are more damaging than inner ones. The analysis above does not take into account pores having a/c > 1 or pores close to each other. So rules for these cases must be formulated. If a is assumed constant and a/c > 1, then a longer life than a/c = 1 is reached. This implies that the size of a pore should be taken as its greatest extension. If two pores (of perhaps different sizes) are close to each other, a stressraising factor is at hand. Studying the stress concentration (Kt) and plotting the results with different relative distances one can see that it is the biggest pore size that governs Kt (see Figs 6.23 and 6.24). If Kt is plotted as function of distance related to the biggest pore size, then the curves coincide and this



3/23/11 1:46:55 PM

Improving weld class systems in assessing fatigue life Centre full-elliptic embedded flaw – standard solution

161 Y

10 mm

Pore starting size = 2 mm

10 mm

6.21 Semi-elliptical crack in a square section equivalent to a pore in a weld (Afgrow model). Stresses are perpendicular to the paper.

Life of a circular defect (‘flat’ inner pore) In a weld area : t*w = 10*10 mm

5.E+06

VD (edge, 80 MPa) VC (edge, 100 MPa) VB (edge, 125 MPa)

Life (cycles)

4.E+06 3.E+06 2.E+06 1.E+06 0.E+06 0

1

2 3 4 Diameter of pore (mm)

5

6

6.22 Life of an inner pore calculated with fracture mechanics.



3/23/11 1:46:55 PM

162


Kt for two holes (pores), D1 = 5 mm (in plane stresses) D1/D2 = 1 D1/D2 = 2 D1/D2 = 5 Standard solution

6 5

Kt

4 3 2 1 0 0

0.5

1 Distance/D1

1.5

2

6.23 Stress concentration Kt plotted against relative distance to D1. Note that the curves coincide.

7

Kt for two holes (pores), D1 = 5 mm (in plane stresses)

Kt

6 5

D1/D2 = 1

4

D1/D2 = 2

3

D1/D2 = 5 Standard solution

2 1 0 0

1

Distance/D2

2

3

6.24 Stress concentration Kt plotted against relative distance to D2. Note that the curves do not coincide.

leads to the following rule: if the distance between two pores is less than the biggest pore size, then they should be regarded as one single pore. In ISO 5817, the opposite is stated and this seems not right.

6.6

Discussion

The current weld classes, as stated in the international ISO 5817 or in Volvo’s STD 5605, have been shown to have a weak relation to fatigue. This is unsatisfactory and leads to a difficult situation especially when the design processes of today drive towards higher performance and optimised



3/23/11 1:46:56 PM


163

geometries. If the process from drawing, analysis, production and control of the welds lack a stable platform (the weld classes) then there is a risk of failures. Especially the use of high strength steel in welded structures, that require high quality welds, will be suffering from weaknesses in the current weld classification systems. The new weld classes define three levels of quality, two as-welded and one post-treated. Apart from these three there is also one class for static cases, since the demands on these differ considerably. Some principles have been set before the definition of the acceptance limits were made. First of all, error types in one weld class level should have the same life and, second, a shift from one weld class level to a higher, should reflect either twice the fatigue life or an increase of 25% in allowed stress level. Apart from these principles, only error types important for fatigue life are defined in the different classes; other types of errors have the same limits for all classes. Most important points regarding the fatigue in welds are the toe area and the root area. The new weld class system, as described above, has divided these two points and they are thus treated quite separately. The root side, if not fully penetrated, may serve as starting defect, the greater the defect the shorter the life. Designing against fatigue is thus dependent on the needed penetration. This means that the root side should not be a part of the weld class system at all. Instead, the best way is to define the root side as a measure on the drawing and support the value through analysis. The toe side on the other hand has most of the fatigue failures from the transition area between the weld and the plate. Here the local geometry is the most important factor, especially in the form of a too small radius or other defects. This is therefore the main purpose of the new weld class system: define acceptance limits for radius, cold laps and undercuts in order to get a fatigue life well related to the expected life. Error types inside the material such as pores, etc. are also treated in the weld class system since they may serve as starting point for fatigue failures.

6.7

Conclusions

In conclusion the following can be stated about current weld class systems: ∑ ∑

the relation between acceptance limits and fatigue life is weak; within one class (quality level) some error types have a short life and some a long life; ∑ some error types show no influence on the fatigue life; ∑ the ‘even transition’ condition is subjective and cannot be measured. A new weld class system has been outlined in this chapter, since the current ones do not reflect fatigue life phenomena well. The new system has three



3/23/11 1:46:56 PM

164


quality levels, VD and VC for ‘as-welded’ condition and VB for ‘post-treated’ welds and is built according to the following principles: ∑ ∑ ∑ ∑ ∑ ∑ ∑

weld classes governs the toe side and invisible defects (like inner pores); the root side is governed by measures on the drawing and is not a part of the weld classes; only error types important for fatigue loads are described; different error types within one class (one quality level) have the same fatigue life; if the weld class is increased one step, twice the fatigue life can be expected or 25% higher stress can be used; the old ‘even transition’ is replaced by demands on the toe radius; static loaded welds have one class itself (VS).

6.8

Future trends

Engineers today working with fatigue in welds face many opportunities. Much work is being done in the area, many conferences over the world address this field and hundreds of papers are being published every year. The most common design today is the use of nominal methods; one reason for this is the regulations, which provide tables of S–N curves over ordinary welded joints. It has been known for many decades that the crack growth part of a fatigue life to a great extent is governed by local geometry discontinuities or defects. This is certainly true for welds, which contain a variety of defects, implying that the initiation part of the fatigue life can be neglected. Lately it has become clear that the traditional nominal methods have drawbacks closely related to the local effect of fatigue. Consequently, a local phenomenon must be solved by a local method and one clear trend today is that such methods are more and more in use for fatigue loaded welds. The most convenient one is the so-called ‘effective notch’ method, where the real world geometry is replaced by a fictitious radius in which the stress is measured. This method works well on both toe side and root side of the weld and is mainly verified for load directions perpendicular to the weld. A lot of work is ongoing to solve general load cases such as multi-axial stress cases. Other methods such as the ‘hot spot’ method, the ‘mesh insensitive structural’ method and the ‘critical distance’ method are all focusing on the toe side, but lack the ability to solve the root side of the weld. Another local method is linear fracture mechanics, where the real world crack is modelled in the computer and the stress intensities are determined. This is, however, seldom in use and one reason is the amount of work needed. Most finite element (FE) programs today can easily calculate any stress field



3/23/11 1:46:56 PM


165

but the stress intensity at the crack tip requires more attention. In some of them this is possible without too much work, but when it comes to calculation of automatic crack growth, there are only a very few software programs. In 3D this is a tough task to solve, since the mesh around the moving crack needs to be not only remeshed for every step, but also moved in the right direction, the latter being a difficult task for example mixed mode cases. In order to give designers a tool to build optimised lightweight structures, a future trend would thus be to build software able to automatically calculate the crack path in a general 3D structure without having to put a lot of work into the task, personal or computational. In the simulation area many studies have been made around the welding process itself. The cooling of the melted material builds up high residual stresses, often with levels around the yield. The stress field from the loads will then be added on top, giving a complicated situation to handle in design since the residual stress is generally unknown. Another complication in situations where variable amplitude loads are present is that the total stress will most likely exceed the yield, leading to a relaxation of the residual stresses. Not knowing the resulting values of these stresses and in order to take all this into account, designers today have to take a (sometimes very) conservative approach and assume that all loads are damaging and that any influence of the mean stress effect is neglected at least for complex structures. In the future this means that there is a possibility to simulate not only the stresses from the loads, but also to calculate the relaxed residual stress field and take this into account in the design. One has to bear in mind, though, that this task is demanding for two reasons: both the calculation of the weld process residual stresses and the relaxation later are highly nonlinear problems. In order to succeed, a lot of knowledge has to be gained about processes and material and also, but not least, the computer power needs to be substantial. The quality of the welds can be described as the local geometry around the weld itself. This implies that the design should use local-based methods and also that the production and the control of the real world weld are essential. The connection between design and production is supposed to be mirrored by the so-called weld classes. However, the regulations of today do not fulfil this task. In this chapter a new weld class system is described, where the connection between acceptance limits and fatigue life is based on scientific data. This means that we can establish a revision system, where the aim of the design fits into the accomplished weld. Revision of welds should be made accordingly and here different kinds of vision system may serve as the best tool for the visible side of the weld. A vision system uses a light source and captures the geometry with one or two cameras and feeds the result into a computer, where the analysis of the weld geometry is made. This geometry could also be transferred into a finite element method (FEM) analysis program for calculation of, for instance, the stress concentration,



3/23/11 1:46:56 PM

166


which could serve as a ‘go’ or ‘no go’ answer. Taking this trend into the future, with very fast computers, it would be possible to transfer the actual weld geometry via a vision system into a computer and analyse the weld bead directly for approval. Today the environmental care and need for decreased fuel consumption leads designers into the area of lightweight structures. This means that the stress levels are increased and to achieve the same or better fatigue life, an increase of strength and weld quality is needed. To solve this, the trend today is to use high strength steel and post-treated welds. At the same time, when the outside of the weld is improved, the inside of the weld may be critical if no actions are taken here. This leads to another tough demand: improved penetration. Much effort is being expended today in order to achieve this improved penetration.

6.9

Sources of further information and advice

A designer of welded structures has today a lot of facts at hand. Several regulations exist and a lot of research is being made all over the world, which are presented on conferences and in papers. However, consideration of all parts of the weld including both toe side and root side of the weld is fundamental. There are only two methods that are able to accomplish this: linear fracture mechanics and the effective notch method. Both are so-called local-based methods and are described in ref. [12] along with some other methods; see also http://www.iiw-iis.org/TheIIW/pages/default.aspx The cooperation between a design office and a production department is another important concern. Today (within the EU) the international standard uses quality rules according to STD 5817 to make revisions of the local geometry of a weld. A problem here is that the connection to fatigue is weak, leading to problems when a designer must state the weld class on the drawing. A new weld class system has been built up within Volvo, STD 181-0004, where the connection between quality rules and fatigue is clearer. This new system is public, since suppliers are obliged to use it; see also http://violin. volvo.net/volvogroup/corporate/en/volvo_group_homepage.htm.

6.10

References

[1] ‘Hållfasthetslära’ by Jan Hult. Almqvist&Wiksell Stockholm/Gebers förlag, 1966. [2] ‘Analysis of fatigue life in two weld class systems, LITH-IKP-EX–05/2302–SE. Master thesis work by N. Karlsson, P-H. Lenander, November 2005. [3] ‘Welding-fusion-welded joints in steel, quality levels for imperfections, ISO 5817’. Swedish standard, SS-EN ISO 5817:2004. [4] ‘Welding manual, design and analysis, 5.501E’. Volvo group standard, 1989. [5] Fatigue assessment of complex welded steel structures. Doctoral thesis by J. Martinsson, 2005. © Woodhead Publishing Limited, 2011


3/23/11 1:46:56 PM


167

[6] ‘Use of simplified models in fatigue prediction of real components’. Proceedings from FATIGUE 2002 by V. Chaves, D. Taylor. [7] ‘Stress concentration factors’, R.E. Peterson. [8] ‘Fatigue design of vehicle components: methodology and applications’, Report 88–23. Doctoral thesis by J. Samuelsson. [9] ‘Integrated fatigue design and manufacturing for welded structures’. Paper from Fatigue Design conf. 2007 in Senlis by G. Marquis. [10] ‘Franc2D, a two dimensional crack propagation simulator, Users guide, ver 3.1’ by P. Wawrzynek, A. Ingraffea. [11] ‘Residual stress analysis and fatigue assessment of welded steel structures’. Doctoral thesis by Z. Barsoum, 2008. [12] ‘Recommendations for fatigue design of welded joints and components, XIII2151r1-07/XV-1254r1-07’. IIW document by A. Hobbacher. [13] ‘Afgrow AFRL-VA-WP-TR-2000-XXXX’. Users guide and technical manual by J. A. Harter.



3/23/11 1:46:56 PM

7

Fatigue design rules for welded structures

S. J. M a d d o x, formerly at TWI, UK

Abstract: The use of fatigue design rules offers the most effective means of avoiding fatigue failures in welded structures. This chapter outlines the basis of current rules and how they are applied in different specifications, including consideration of residual stresses, size effect, material, welding process and environment. Areas needing further research are highlighted, including adaptation of current rules for use with finite element stress analysis, development of local stress approaches, the treatment of complex loading and cumulative damage calculations. Key words: fatigue, design, welds, steel, aluminium, FEA, corrosion.

7.1

Introduction

Fatigue is the process by which a crack can form and then grow under repeated or fluctuating loading. Welded joints can exhibit particularly poor fatigue properties (Gurney, 1979, 2006; Fisher, 1984; Maddox, 1991), as illustrated in Fig. 7.1. This shows S–N curves, the most common way to

400

Stress range (N/mm2)

300 200 100

50

R=0 Grade 50 structural steel 10

105

106

Cycles

107

108

7.1 Effect of welding on fatigue strength.

168 © Woodhead Publishing Limited, 2011


3/23/11 1:47:29 PM


169

present fatigue test data and design curves. They relate applied stress range, Ds (maximum – minimum stress in a cycle), and the resulting fatigue life in cycles, N, obtained in fatigue tests performed under constant amplitude loading. Over a wide range these are linear on log–log scales, so that they have the form:

Dsm · N = A

7.1

where m and A are material constants. In view of the low fatigue performance of widely used welded joints, design stresses in welded structures are frequently governed by fatigue considerations. Even so, the majority of service failures are attributable to fatigue. This emphasises the need for careful consideration of potential fatigue failure at the design stage, and for clear design guidance. In fact, considerable effort has gone into the production or revision of fatigue design rules in recent years, particularly in the European Union in view of the adoption of common Standards. Some of these refer to specific structures while others refer to welded joints in general (see Appendix). The main features of the majority of the modern national and international rules are in good agreement, reflecting the general acceptance of certain basic principles upon which fatigue design rules for welded joints should be based. Even so, there are important areas, both in fundamental assumptions and the practical application of the rules, where improvements are needed, as reviewed periodically (Maddox, 1992, 1997, 2003a). Perhaps the most significant relates to the increasing use by designers of finite element stress analysis (FEA). There are practical difficulties of relating FEA outputs to current fatigue design data but also current rules offer little scope for utilising the very detailed information about stresses and stress distributions provided by FEA. It is envisaged that this situation will lead to quite radical changes to current design rules in the near future. The aim of this chapter is to provide an overview of the basis and current status of the most widely used fatigue design rules for welded structures and the ways in which they are likely to develop in future. In this respect, apart from the need for improvements in the scope of current rules attention will be drawn to important deficiencies in the rules that are still the subject of research. Introductions to such topics are provided but some receive more detailed discussion in other chapters in the book. As an aid to understanding the basis of current rules, the chapter starts with a description of the key features of welded joints that influence their fatigue properties and the use of fracture mechanics for modelling the fatigue process. In this respect it will be evident that most attention has been focused on welded steels and that the most comprehensive design rules refer to welded steel components and structures.



3/23/11 1:47:29 PM

170


7.2

Key features of welded joints influencing fatigue

7.2.1 Geometric stress concentration The geometries of most welded joints introduce rough surfaces and changes of section, features that cause local stress concentration when the joint is loaded. Thus, they offer sites for fatigue crack initiation. Some, notably weld surface ripples, are relatively mild and indeed continuous welds in which the fatigue loading acts parallel to the weld (generally referred to as longitudinal welds in the fatigue context), as shown in Fig. 7.2, are among the highest fatigue performance welded joints. In contrast, the sharp section change at the ends of discontinuous longitudinal welds and the toes of any transverse welds (i.e. loaded at right angles to the weld) introduce severe stress concentrations under loading normal to the weld (referred to as transverse welds in the fatigue context). Examples are shown in Fig. 7.3; some of the weld details included are among the lowest fatigue performance welded joints.

7.2.2 Flaws Recalling Fig. 7.1, stress analysis of the basic profile of the transverse fillet weld would reveal a stress concentration factor at the toe of similar magnitude to that at the edge of the hole. However, as seen its fatigue performance is considerably lower. This is a reflection of the fact that the stress concentration at the toe or end of a weld is actually even more severe than indicated by the profile alone. A further illustration of this is found in the cruciform fillet welded joint shown in Fig. 7.4, which also highlights another important source of stress concentration in joints with partial penetration welds. Transversely loaded cruciform joints made with fillet welds contain what amount to embedded cracks in the form of the unfused region due to incomplete weld penetration. Consequently, fatigue cracks can propagate from the ends of

7.2 Examples of continuous longitudinal butt and fillet welds in which fatigue failure initiates at mild stress concentrations (weld ripples, stop/starts or the weld root).



3/23/11 1:47:30 PM


171

7.3 Examples of weld details in which the fatigue failure initiates at the stress concentration due to a weld toe or end.

a

b

7.4 Fatigue cracking in fillet-welded cruciform joint: (a) crack growth from weld roots; (b) crack growth to failure from weld toe.

this zone, the weld roots, through the weld throat (arrowed ‘a’ in Fig. 7.4). However, unless the incomplete penetration region is quite large, the weld toe tends to be the more severe of the two potential crack initiation sites and fatigue failure is from the weld toe, as in the case shown (arrowed ‘b’



3/23/11 1:47:30 PM

172


in Fig. 7.4). In order to understand the reason for this it is necessary to look in more detail at the weld toe. A key feature of weld toes in steel is the inevitable presence of sharp discontinuities. Undercut and cold laps are examples, but more important, on a much smaller scale, are small (typically 0.1 to 0.4 mm in depth) nonmetallic intrusions (Signes et al., 1967). The weld toe fatigue crack in Fig. 7.4 has initiated at such a flaw. Unlike undercut and cold laps, which can usually be avoided by control of the welding, these intrusions are an inherent feature of welds made in steel by production arc welding processes. A significant consequence of the combined effect of a severe geometric stress concentration due to the sharp section change and inherent cracklike flaws is that fatigue cracks readily initiate at weld toes or ends and the majority of the resulting fatigue life of the welded joint may be spent simply propagating a crack. In contrast, fatigue crack initiation can occupy the majority of the lives of unwelded components, even those containing notches like the drilled hole in Fig. 7 1. This is why the fatigue performance of welded joints tends to be much poorer than that of unwelded material. Weld toe intrusions similar to those described above have not been found in aluminium alloys and they may not occur in steels welded by processes such as tungsten inert gas (TIG), laser, electron beam and friction. However, the severe geometric stress concentrations due to sharp section changes are still produced and other features such as undercut, cold laps and liquation cracks do occur. As a result, fatigue cracks readily initiate and usually the fatigue life is still dominated by fatigue crack propagation. This has important implications with regard to fatigue design S–N curves and the factors which influence the fatigue lives of welded joints, because those that influence crack initiation can be quite different from those that affect crack growth. Apart from the flaws considered above, which are either inherent in welding or deliberately introduced as in the case of cruciform or T-joints made with partial-penetration fillet welds, welding can introduce flaws such as gas pores, non-metallic inclusions and even cracks. These are generally limited, or avoided in the case of cracking, by proper choice of welding conditions and appropriate inspection. If they are present in a fatigue-loaded weld they may provide sites for fatigue crack initiation. However, their assessment usually falls outside the scope of fatigue design rules, as will be discussed later.

7.2.3 Residual stress Welding residual stresses are caused by differential thermal expansion and contraction of the weld metal and parent material. This is illustrated in Fig. 7.5 for longitudinal residual stresses (transverse residual stresses are also



3/23/11 1:47:30 PM


173

Hot Immediately after welding

Cold

Cold Cold

After cooling if contraction allowed

Cold

Cold Cold

After cooling with contraction resisted

Cold

Cold

Tension Compression

Residual stress

7.5 Formation of residual stresses due to welding.

induced, although these generally have compressive and tensile zones within the weld). Residual stress levels in and near to the weld can be very high, up to material yield strength magnitude in highly constrained situations, which is the case in most real structures. Apart from welding, similar high tensile residual stresses (referred to as long range or restraint stresses) are likely to be introduced during the assembly of a structure from components, due to imperfect fit-up. Unlike welding residual stresses, it is not generally possible to relax these by stress relief heat treatment. High tensile residual stresses have a very significant effect on fatigue. Any applied fluctuating stresses are superimposed onto the residual stress, as illustrated in Fig. 7.6. If this is as high as tensile yield, the resulting effective stress cycles down from yield, the range being unchanged (Gurney, 1979). Thus, the welded joint experiences the most severe effect of tensile mean stress. This is true even for applied compressive stresses. If these conclusions are correct, the fatigue lives of welded joints containing high tensile residual stresses should be independent of applied mean stress for either tensile or compressive applied stresses. This has, in fact, been confirmed experimentally many times, notably by Fisher and co-workers (Fisher, 1997). In the example shown in Fig. 7.7, the results were obtained from steel plate specimens with longitudinal fillet welded attachments. Very high tensile residual stresses acting along the weld, that is the direction of fatigue loading, are produced in such specimens. Similar results for other weld details have been obtained from large-scale welded beams. Perhaps the most striking results are those obtained under purely compressive stresses. Such loading would not be expected to cause any fatigue cracking at all in a residual stress-free un-



3/23/11 1:47:30 PM

174

Fracture and fatigue of welded joints and structures Stress Residual stress (tensile yield) Ds R=0 Ds

Effective stress range for all R values

R = –1

Time

Ds

0

Ds

R = 0 (compression)

7.6 Effect of superimposing cyclic stress onto existing yield magnitude tensile residual stress. 250 Structural steel


200 150

100

50

Symbol Loading Zero compression R = –1 R=0 R = 0.5 R = 0.67

105

106 Endurance (cycles)

107

2 ¥ 107

7.7 Test results illustrating that the fatigue lives of welded joints containing high tensile residual stress are independent of applied stress ratio.

welded component. As a result of the influence of tensile residual stresses, the fatigue lives of welded joints are related to the full stress range in the S–N curve, regardless of whether it is tensile or compressive. One issue that should be mentioned is the fact that residual stresses can change as a result of shakedown from subsequent applied loading (McClung, 2007). Indeed, relaxation of tensile welding-induced residual



3/23/11 1:47:31 PM


175

stress in direct proportion to the magnitude of the applied stress has been observed following the application of a single tensile stress cycle (Iida and Takanashi, 1997). Such residual stress relaxation should have occurred in the specimens used to generate the test results in Fig. 7.7, but still they behaved in the manner expected if they did contain high tensile residual stresses throughout their lives. It seems that the relaxed residual stress was still sufficiently high compared with the magnitude of the applied cyclic stresses to produce effective stresses that were fully tensile, even when the applied stress was partly or fully compressive. The situation may not be so simple in the case of variable amplitude loading, a topic that is discussed later.

7.3

Fatigue crack propagation

In the case of those situations in which the fatigue life of a welded joint is expected to consist almost entirely of the propagation of a pre-existing flaw, notably fatigue failure from the weld toe, weld end or weld root, fracture mechanics offers a technique for describing the progress of fatigue cracking mathematically and hence of calculating the fatigue life of the welded joint (Maddox, 1974; BSI, 2005). The basis of the application of fracture mechanics to fatigue is the relationship between the rate of crack propagation da/dN and the stress intensity factor range DK, based on the applied cyclic nominal stress range Ds and the current crack size a: DK = YDs p a

7.2

where Y is a function of the welded joint geometry and the crack size and shape. For many practical cases the crack propagation relationship has the simple form: da = C (DK )n ddN N

7.3

where C and n are material constants which are determined experimentally. Thus, if the fatigue crack growth rate is plotted as a function of the applied stress intensity factor range, on log–log axes, for most of the fatigue crack growth there is a linear relationship between the crack growth rate and DK range, often termed the Paris law after Paul Paris who first observed it, as shown in Fig. 7.8. This linear relationship is truncated at low values of applied DK by the threshold value of DK, below which no fatigue crack growth occurs, and at high values of applied K by the approach to failure (e.g. yielding, fracture). Increasing the applied stress ratio usually increases da/dN for a given DK in the Paris law regime but reduces the values of



3/23/11 1:47:31 PM

176

Fracture and fatigue of welded joints and structures 10–3

Rate of crack growth, da/dN (mm/cycle)

Kmax Kc (K at fracture) 10–4

da/dN = C(DK)n (paris law)

10–5

10–6

Ds

2a

10–7 DK = YDs pa DK DKo (threshold DK) 10–8 50

100 200 300 500 1000 2000 3000 Stress intensity factor range, DK) (N/mm3/2)

7.8 Fatigue crack growth data presented in fracture mechanics terms.

DK at which the transitions occur in the threshold and near failure regions, depending on the material. The value of the relationship between da/dN and DK is that it can be integrated to calculate the fatigue life N of an initial crack ai propagating to some final size amax under applied stress range Ds, as follows: amax

Úa

i

da = C Ds n N (Y p a )n

7.4

or Ds n N = 1 C

amax

Úa

i

da (Y p a )n

7.5

Indeed, the flexibility of this approach is such that any of the four main variables, ai, amax, Ds and N can be calculated if the other three are known. In the context of the fatigue behaviour of new welded joints failing from inherent crack-like features, such as from the weld toe, all the terms on the right-hand side of Eq. [7.5] are essentially constant, resulting in the equation:



3/23/11 1:47:32 PM


177

Dsn N = constant

7.6

Recalling Eq. [7.1], this is the equation of the S–N curve for the weld detail concerned and it will be seen that it has the same slope n as the crack propagation law.

7.4

Design rules

7.4.1 S–N curves Most fatigue design rules present a series of S–N curves (Eq. 7.1) for particular weld details (Fig. 7.9), relating the nominal stress range, Ds, adjacent to the weld detail and the corresponding fatigue life, N. These are derived from fatigue test data, obtained under constant amplitude loading from welded specimens, by statistical analysis (Gurney and Maddox, 1973). In most instances, linear regression analysis of log Ds versus log N is used, regarding log N as the dependent variable, to establish the mean S–N curve. Design is then based on a lower curve, typically two standard deviations of log N below the mean (mean – 2SD), representing approximately 97.7% probability of survival. For greater safety, some pressure vessel rules use mean – 3SD of log N curves, corresponding to approximately 99.9% survival probability. The definition of fatigue failure in the tests performed to generate the Ds–N data varies, examples being the achievement of a detectable fatigue 400

Curves stop at static design limit

300


200 FAT 125 100

100

70 50

50

20

Constant amplitude fatigue limits (CAFLs)

Curves extrapolated beyond CAFL at shallower slope for use in cumulative damage calculations

105

106 107 Endurance (cycles)

108

7.9 Typical fatigue design S–N curves, of the form Sm N = constant and corresponding weld details showing IIW classification, site for fatigue cracking and direction of loading considered.



3/23/11 1:47:33 PM

178


crack, fatigue cracking through at least half of the loaded member thickness and, in the case of axially loaded test specimens, complete rupture of the specimen, which usually effectively coincides with the production of a through-thickness crack. Most design rules equate the fatigue life to the last example, the number of cycles required to produce through-thickness fatigue cracking. An implicit assumption is that the material’s tensile strength and fracture toughness are sufficient to tolerate such cracking. If in doubt, the designer should take steps to check these properties. The linear S–N is assumed to extend up to nominal stress levels corresponding to static design limits for the material. If the weld detail experiences local strains up to and beyond yield, such that the deformation of the material concerned is controlled by surrounding elastic material (i.e. ‘shake-down’ under strain control), the S–N curve can be extrapolated back to the low-cycle regime with the same slope. In this region, it is based on the pseudo-elastic stress range (strain range, x; elastic modulus, E ). This approach is commonly relevant to pressure vessel design (Maddox, 1994, 2003b). In the high-cycle regime, a constant amplitude fatigue limit (CAFL), below which fatigue failure will not occur, may be introduced, usually when the S–N curve reaches a particular endurance. Stress ranges corresponding to N = 2 ¥ 106, 5 ¥ 106 or 107 cycles are typically chosen, depending on the design rules. In fact, some rules adopt different endurance limits depending on the severity of the stress concentration associated with the welded joint. For example, flush ground butt welds could be expected to behave like plain unwelded material and reach their fatigue limit at around 2 ¥ 106 cycles, whereas in weld details containing crack-like features, such as fillet welds, the fatigue limit corresponds to the fatigue crack growth threshold and this might not be reached before 107. Indeed, there is increasing evidence that even this endurance may be too short and an endurance limit closer to 108 cycles is actually appropriate for some weld details (Maddox, 2003a). To compensate for this uncertainty the IIW (Hobbacher, 2009) has avoided the use of what amounts to a cut-off at the selected endurance limit and instead assumes that the S–N curve is extrapolated beyond 107 cycles at the very shallow slope of m = 22. Specific values of the slopes of the S–N curves are sometimes imposed. In particular, the lower curves may be assumed to be parallel, in recognition of the fact that they represent mainly crack growth. Furthermore, as noted earlier, their slopes are similar to the slope of the Paris fatigue crack growth law, which for most weldable structural materials results in n = m ª 3. Shallower S–N curves (i.e. m > 3) may be adopted if the detail is one in which fatigue crack initiation occupies a significant proportion of the total fatigue life. The S–N curves refer to fatigue failure under applied normal or direct stresses. To cover cases in which fatigue failure may occur under applied shear stresses some fatigue design rules include curves of the same form



3/23/11 1:47:33 PM


179

relating fatigue life N and applied nominal shear stress range Dt. These are typically shallower than S–N curves, with m = 5 (Hobbacher, 2009; EN, 2005) or even up to 8 (BSI, 1993).

7.4.2 Classification systems A classification system links descriptions of weld details with the appropriate design S–N curves. The class or category usually depends on the joint type, geometry and direction of loading, and it relates to a particular location and mode of fatigue cracking (Fig. 7.9). Such information, which is usually presented in tables that include sketches of examples of relevant weld details, can help in deducing the appropriate classification for a detail not specifically described. The design S–N curves are usually produced using one of two approaches: 1. An arbitrary grid of S–N curves, usually equally spaced, is defined and the curve closest to the selected lower bound to experimental data is allocated. 2. The design curves are derived directly from experimental data. Such curves are not usually equally spaced or parallel. These are then referred to in terms of arbitrary letters (e.g. AASHTO, 2008; BSI, 1993) or, increasingly, by the stress range at 2 ¥ 106 cycles (e.g. EN, 2005; Hobbacher, 2009), maybe together with the slope m of the S–N curve. A clear advantage of the latter is that it quantifies fatigue strength. As an example, the influential IIW scheme (Hobbacher, 2009) uses equally spaced Ds–N curves, all with a slope of m = 3, designated FAT Ds2¥106 cycles, where Ds2¥106 cycles is the fatigue strength in N/mm2 or MPa at 2 ¥ 106 cycles. In addition, two Dt–N curves, each with a slope of m = 5, are provided, their designations being of the form Dt 2¥106 cycles/5. The IIW design classifications are used in this chapter for comparison with fatigue test data.

7.4.3 Stresses used with S–N curves Fatigue design rules are based mainly upon data generated from tests on either beams or small-scale plate specimens incorporating the weld detail of interest, subjected to unidirectional loading. Thus, the fatigue test results can be expressed in terms of the nominal applied stress in the region of the test detail and the same stress is usually specified for use with design S–N curves. When appropriate, for example under combined or multi-axial loading, the relevant principal stress range is used, although for failure from the toe of a biaxial-loaded joint the stress component parallel to the weld can be ignored as long as it is less than 75% of the stress acting normal to the weld (Brozzetti et al., 1992). As an alternative to the principal stress,



3/23/11 1:47:33 PM

180


some industries favour the use of the von Mises or Tresca equivalent stress for combining stresses. A significant contrast between these stresses and the principal stress is that they are scalar quantities of unknown direction. Thus, in general they must be assumed to be acting in the least favourable direction and therefore used in conjunction with the lowest possible design curve for the detail concerned. This eliminates one of the key features of fatigue design rules that recognise that both the weld detail type and the direction it is loaded can have a very significant effect on the choice of design curve and hence fatigue performance. In the case of weld details that fail by fatigue crack growth from the weld root through the throat, the nominal stress range on the weld throat is used. If this is composed of both normal and shear stresses they are usually combined using their vector sum (Ds2 + Dt2)0.5 to give the resultant stress range. If the weld detail under consideration is itself within the field of influence of a further source of stress concentration, the nominal stress must be increased accordingly when calculating the stress experienced by the joint. The resulting stress is sometimes called the ‘modified nominal stress range’. An important development that will be discussed in more detail later is the use of the hot-spot structural stress, which includes more formally the stress concentration effects of both the weld detail and the surrounding structure. One feature of welded joints that can be the cause of an additional stress concentration is misalignment (Maddox, 1985a). Indeed, in contrast to many other features of welding that are regarded as imperfections, it is one that proves to be more harmful than is generally acknowledged by the workmanshipbased weld quality standards. It is particularly common in butt welded and cruciform joints in which, under loading transverse to the welded joint, it leads to secondary bending. Unfortunately, the extent of misalignment in the specimens that provided the database used to establish the design S–N curves is not generally known. Without such data, it is not possible to state precisely what allowance for misalignment is already included in the design curves, contributing to inaccuracies in design. Whatever the situation, it is important that the designer should always consider the effect of misalignment and adjust his stress calculations accordingly, for example by assuming that the extent of misalignment allowed by the fabrication standard will be present. Alternatively, of course, control of misalignment can be seen as one way to gain advantage in fatigue design by achieving better fabrication quality. In this case, the designer would specify the allowable misalignment to match his design stresses. Formulae are available for estimating the secondary bending stress due to various forms of misalignment (e.g. BSI, 2005), or they could be calculated by finite element stress analysis (FEA) of the actual structural part concerned.



3/23/11 1:47:33 PM


181

In general, the data used to determine a design S–N curve come from tests of a particular weld detail, subjected to loading in a particular direction, which results in a particular mode of fatigue failure (see Figs 7.2, 7.3 and 7.9). Sometimes different details gave similar fatigue performance, in which case their data may have been combined. Even so, an important feature of each design curve is that it is used in conjunction with the stress acting in the appropriate direction with respect to the potential fatigue failure mode being considered. In general, this will be the principal stress acting closest to the relevant direction, typically within 45° but sometimes up to 60°, or the stress component acting in the actual direction of interest. A further feature of the database that should be noted is that it relates to loading conditions that were either fully or predominantly axial, the latter arising in structural specimens such as beams tested in bending where the stress gradient through the section would have been low. It is generally found that there is an increase in fatigue performance with increase in applied stress gradient such that the fatigue life of a given welded joint under shell bending conditions could be more than double that obtained under axial loading (Maddox and Gurney, 1987; Gurney, 1992). The effect is particularly pronounced in thin plates loaded in bending. At present little or no account is taken of this in fatigue design rules, probably because of the practical difficulty of separating the axial and bending stress components in most actual structures. The most notable exception is the rules for tubular joints, where the most likely form of fatigue failure occurs as a result of local shell bending in one of the tube walls. However, if it proved to be useful, fracture mechanics calculations could be used to establish design factors based on the degree of bending and plate thickness for increasing allowable fatigue design stresses for welded joints subjected to bending. Finally, as noted earlier, all the design curves are expressed in terms of the full stress range, Ds or Dt, regardless of applied mean stress, to allow for the presence of high tensile residual stresses.

7.4.4 Residual stress relief All the widely used fatigue design codes accept the principle that tensile residual stresses up to yield strength magnitude are present in a welded structure, with the result that its fatigue life will be independent of mean stress and depend only on the applied stress range, even if this is compressive. However, it is frequently questioned as being too conservative, chiefly on the basis that residual stresses will actually be relaxed or redistributed as a result of post-weld stress relief treatment or indeed, as noted earlier, simply the application of fatigue loading. Furthermore, welding also introduces compressive residual stresses and sometimes these coincide with the region where fatigue cracking is most likely to occur. In the case of stress relief,



3/23/11 1:47:33 PM

182


fatigue data obtained from small-scale steel specimens confirm the potential benefit, but only if the loading is predominantly compressive (Maddox, 1991). This is consistent with the fact that rate of fatigue crack propagation in structural steels is largely independent of applied mean stress for fully tensile loading and only influenced by mean stress for predominantly compressive loading. Thus, the design rules could be modified to take account of stress relief, either by providing different (shallower) S–N curves or by ignoring part of the applied compressive stress. An example of the latter in some codes (e.g. BSI, 1993) is to assume that only 60% of the compressive part of the applied stress range is damaging. However, against this there is the practical problem that effective stress relief of real structures, which can seldom be checked, is not easy and parts may contain high tensile residual stresses even after post-weld heat treatment. In addition, assembly of welded parts introduces new long-range residual stresses due to imperfect fit-up and these can be just as harmful as those due to welding. Thus, there is limited scope for neglecting tensile residual stresses. The situation is similar in those cases where compressive residual stresses are expected, in that subsequent manufacturing operations might induce tensile residual stress. In addition, in both cases, the fatigue loading might produce high tensile mean stress conditions comparable with those resulting from the presence of high tensile residual stress. Thus, overall it is prudent to base design on the fatigue behaviour of welded joints containing high tensile residual stress or tested under conditions of high tensile mean stress.

7.4.5 Cumulative damage under variable amplitude spectrum loading The design S–N curves refer to constant amplitude loading. In order to use them to assess components subjected to variable amplitude loading in service, all the main fatigue rules specify the use of Miner’s rule: n1 n2 n n + + 3 + … = S i ≤ 1 at failure N1 N 2 N 3 Ni

7.7 where ni are the numbers of applied stress cycles at stress ranges Dsi and Ni are the endurances obtained from the design curve at Dsi. In addition, allowance is usually made for the fact that once fatigue cracks have started to propagate under stress levels above the CAFL, stresses below that limit, for which N = •, will gradually become damaging and hence cannot be neglected. The common method is to extrapolate the S–N curve beyond the CAFL at a shallower slope, typically m = 5 instead of 3. This shallower curve is usually terminated with an absolute fatigue limit, typically at N = 108 cycles. As will be seen later, there are now serious doubts about the



3/23/11 1:47:33 PM


183

validity of both Miner’s rule and the method of treating stress ranges below the CAFL.

7.4.6 Scale effect One of the limitations of the data used to establish current design S–N curves is that they were obtained from a small plate thickness range. Most came from specimens 10–15 mm thick, with some up to around 25 mm thick. However, it is now generally accepted that there is a geometric scale effect, such that fatigue performance tends to decrease with increase in the dimensions of a welded joint (Maddox, 1987; Gurney, 1991). A size effect can be expected from statistical considerations, the chance of introducing a particularly severe stress concentration or flaw increasing with size, and the presence or not of residual stress. However, the one referred to here concerns the effect of the stress concentration due to the weld detail on fatigue crack growth from the weld toe. This effect, which decreases as the crack grows away from the toe through the thickness, depends on the crack depth to plate thickness ratio. Thus, a crack in a thick section is influenced to a greater crack depth than in a thin one. This has been confirmed experimentally many times. As a consequence, stress ranges obtained from the design curve may need to be reduced when designing thick sections. Attention has focused mainly on the effect of the main plate thickness in welded joints failing from the toe. The resulting well-known ‘thickness effect’ is now a feature of most fatigue design rules. It has the form (tref/t)k where t = plate thickness, tref = reference plate thickness up to which the design S–N curves are directly applicable (typically 13–25 mm) and k is usually 0.25. Meanwhile, research has highlighted a more general scale effect, such that the exponent k depends on the severity of the welded joint stress concentration and the scale effect itself is due to more than just plate thickness (Maddox, 1987; Gurney, 1991; Orjasaeter, 1995). As a result, some design rules incorporate the following: ∑

k varying from 0.1 for mild stress concentrations to 0.3 for severe ones; ∑ use of an effective thickness teff that depends on the actual plate thickness and the proportions of the welded joint (see Fig. 7.10).

A third effect, usually neglected in fatigue design rules, is the potential benefit of smaller dimensions than those associated with the design S–N database, that is, generally below 10 mm. This is not surprising in view of the structural engineering background to most rules. In fact, the same rules could be applied to standard arc welded details in thin sections, down to around 4 mm, but they may be too conservative. There is some support for a



3/23/11 1:47:33 PM

184


Relative fatigue strength

2.0

Typical current design penalty (assuming proposed scale factors for tref = 12 mm tref = 12 mm and exponent = 0.25) L

1.5

t > 12 mm:

t

ÏÔ ¸Ô Scale factor = Ì12˝ Ô ef ˛ ÓÔt eff L/t 0.83

1.0 0.9

Experimental L/t = 0.83 L/t = 1.67 L/t > 2

0.8 0.7

1.67

0.6 1

5 10 20 30 plate thickness, t (mm)

where teff = 0.5L for L/t < 2 = t for L/t > 2 t < 12 mm: Ï ¸ Scale factor = Ì 2 ˝ ÓL/ t ˛

0.25

Ï1 12¸ Ì ˝ Ót ˛

0.13

>2

Fracture mechanics 0.5

0.25

50

100

7.10 Fatigue data for welded aluminium alloy that illustrate thickness effect based on effective thickness as function of L and t and provide support for potential ‘thinness’ benefit (Maddox, 1995, 2003a).

corresponding ‘thinness effect’ bonus for thin plates, especially those loaded in bending (Maddox, 1995).

7.4.7

Effect of type and strength of material

one of the most important consequences of the dominance of fatigue crack growth in the lives of welded joints is the fact that fatigue strength does not increase with increase in material strength, rate of crack growth being largely insensitive to material tensile strength. This contrasts with unwelded material. Consequently, design curves for welded joints are independent of material tensile strength. The principle was established over 40 years ago (Gurney, 1979) and yet the quest for methods of utilising high strength steels to advantage in fatigue loaded welded structures still receives considerable attention. one of the more promising findings is that post-weld improvement techniques which introduce a significant fatigue crack initiation period, such as weld toe dressing, provide greater benefit for high strength than low strength steels. However, the dependence on steel strength is still rather weak (Fig. 7.11), reflecting the severe stress concentration represented by the welded joint. Similarly, the benefit of improvement techniques that rely on the introduction of compressive residual stress, such as peening, appears to increase with material tensile strength (Maddox, 1985b). However, as yet no account is taken of such findings in design rules. There is also scope for using high strength materials under some spectrum



3/23/11 1:47:34 PM

Fatigue strength at 2 ¥ 106 cycles (N/mm2)


185

600 500

400



300 200 100 0 300

}

TIG dressed weld from Maddox (2003a) Toe ground weld Martinez et al. (1997) 500 700 900 Ultimate tensile strength of steel (N/mm2)

1100

7.11 Effect of steel tensile strength on fatigue strength and potential for using weld toe improvement techniques to enable high strength materials to be used to advantage.

loading conditions, because of their ability to carry a small number of very high stress cycles. There is no doubt that most fatigue design information relates to welded structural steels, although there has been a significant increase in research concerned with welded aluminium alloys in recent years, much of it related to the drafting of new European design rules. However, the same principles as those described for steels are applicable to welded joints in other metals, with fatigue strengths varying from those for steel roughly in proportion to the elastic modulus of the material (excluding any environmental effects). This has been confirmed for stainless steels (Razmjoo, 1995; Branco et al., 2001) and for the lower class details in aluminium alloys, where fatigue crack growth dominates (Maddox, 1982). However, comprehensive fatigue rules now available for aluminium structures offer a better choice than adapting the rules for steels (EN, 2007).

7.4.8 Effect of welding defects Reference has been made to the highly significant crack-like flaws that provide fatigue crack initiation sites at weld toes. These, or similarly severe local weld toe discontinuities, are unavoidable in production welding and therefore their effect is included in the design S–N curves that refer to fatigue failure from a weld toe. However, other flaws can be introduced by welding and they might also act as fatigue crack initiation sites. The standard design S–N curves discussed earlier do not cover fatigue failure from such flaws.



3/23/11 1:47:34 PM

186


Of particular significance are crack-like flaws such as those due to lack of fusion, incomplete weld penetration or an actual cracking mechanism such as hydrogen cracking. In general such flaws are considered to be unacceptable and if detected need to be repaired. However, fatigue cracking can also originate at flaws that are not crack-like, notably embedded inclusions and gas pores, and in such cases they may be acceptable as long as the resulting fatigue life is no less than that required. In this respect it is important to note that the stress concentration effect of an embedded volumetric flaw is rarely as severe as that of a weld toe. Consequently, a measure of its acceptance is that it does not reduce the fatigue life below that expected for weld toe failure. The assessment of volumetric flaws on this basis would be greatly facilitated if their fatigue performance could be expressed using S–N curves, a tall order in view of the wide variation in size, shape and location of such flaws. However, accepting a level of approximation, it has proved possible do this using fatigue data generated in tests on butt welded joints (Harrison, 1972). The butt welds concerned were made with either slag inclusions or porosity deliberately introduced. It is a measure of the tolerance of welds to such flaws that it was necessary to flush grind most of them to ensure that fatigue failure initiated at the flaw and not the weld toe. It was found that in each case the severity of the flaw could be characterised using a single parameter, the length of a slag inclusion or the volume of gas pores, expressed as a percentage of the projected area of the weld on a radiograph. This allowed the test results to be broken down into groups which exhibited similar fatigue strengths and establish lower bound S–N curves for design purposes. For ease of comparison with the fatigue strength of the welded joint without the embedded flaw, the approach was to compare the data with the grid of standard S–N curves and establish acceptance limits corresponding to those standard curves. An example of data from butt welds containing porosity compared with some of the IIW design S–N curves is shown in Fig. 7.12. Data for welds with slag inclusions were assessed in the same way and used to establish the acceptance levels for steel butt welds corresponding to the design curves shown in Table 7.1. The separate limits for slag inclusions reflect the finding that stress-relief by post-weld heat treatment (pwht) was beneficial as a result of the removal of hydrogen from around the flaw. It may also be noted that the upper limit on porosity is related purely to its effect in masking other more important flaws during inspection. In practice, as seen in Fig. 7.12, much higher levels are still associated with very high fatigue performance. In contrast, surface-breaking porosity can be very harmful and should normally be repaired. A striking illustration of its effect is that the fatigue strength of a flush ground butt weld can be lower than the original weld if sub-surface porosity is exposed by the grinding. Further guidance on



3/23/11 1:47:34 PM



500

187

IIW FAT class

400

100

300

90 80 71 63

200

Data from steel butt welds containing porosity Up to 3% porosity 3 to 6% porosity 100 6 to 8% porosity 80 104


107

7.12 Fatigue data for butt welds in steel failing from porosity. Table 7.1 Acceptance limits for embedded volumetric defects related to IIW design S–N curves IIW design S–N curve

FAT FAT FAT FAT FAT FAT

100 90 80 71 63 56 and lower

Maximum allowable length of slag inclusion, mm As-welded

Stress-relieved (pwht)

1.5 2.5 4 10 35 No limit

7.5 19 58 No limit No limit No limit

Limits for porosity expressed as percentage of area on radiograph 3 3 3 5 5 5

the application of the fitness-for-purpose approach for assessing weld flaws can be found in BS 7910 (BSI, 2005).

7.4.9 Effect of environment The environment, including temperatures other than ambient, can influence fatigue performance, often reducing fatigue lives. Few fatigue design rules provide anything other than vague reference to environmental effects. Design penalties for corrosion arise mainly because crack growth rates are increased. The introduction of more severe notches (e.g. corrosion pitting) is largely ignored. However, a long-term study directed mainly at weathering steels (for use without any surface protection), exposed outdoors for up to 6 years,



3/23/11 1:47:35 PM

188


highlighted this aspect (Müller, 1996). Corrosion pitting did not intensify the notch effect of butt and fillet welds and their fatigue performance was not affected. However, it did degrade the surface of unwelded steel, reducing its fatigue strength to that of the butt welds. The same result was found for normal structural steel, showing that unless unwelded plate surfaces are protected against corrosion, fatigue strength could decrease with time to that of a weld. Since such parts are likely to be designed to much higher stresses than welds, the consequences of premature failure could be more serious. In the context of welded structures, the corrosive environment that has received most attention, and for which design guidance exists, is seawater. This was prompted by the need for safe offshore structures for oil and gas recovery. Most experiments related to structural C–Mn steels under North Sea conditions, that is seawater temperatures of 6–10 °C and the wave loading frequency of 0.17–1 Hz. However, they still offer useful guidance that could be relevant in other circumstances. Current rules (HSE, 1995; ISO, 2007; DNV, 2010) suggest that the effect of free corrosion is to reduce fatigue life by a factor of 3 and to eliminate the fatigue limit. Cathodic protection can inhibit corrosion, but it can also be detrimental to fatigue performance as a result of hydrogen embrittlement. Consequently, there is still a design penalty of 2.5 on life at relatively high applied stresses and in-air performance is only achieved near the fatigue limit. Stainless steels are, of course, usually selected because of their corrosion resistance. However, fatigue tests on austenitic stainless steels freely corroding in seawater indicate a rather similar effect to that seen in C–Mn steels, around a 3-fold increase in fatigue crack growth rate or reduction in fatigue life (Branco et al., 2001). The same has been observed in duplex stainless steels, although in this case the effect is confined to relatively high DK, or more specifically high Kmax values. In particular, there does not appear to be any detrimental effect of the environment on the fatigue crack growth threshold or da/dN if Kmax is below around 1000 N/mm3/2. However, above this da/dN is typically two to three times higher than in air, or up to seven times higher if the crack is propagating in a coarse-grained-heat-affected zone microstructure (Branco et al., 2001). The situation is worse with cathodic protection such that, again only for high Kmax, da/dN may be 20 times higher than in air. In general, these characteristics of the corrosion-fatigue behaviour of duplex are consistent with a hydrogen embrittlement mechanism. The same mechanism results in even poorer fatigue performance in the presence of hydrogen sulphide (Baxter et al., 2007), increasing da/dN by two orders of magnitude, depending on the hydrogen sulphide concentration. Thus, special care is needed in the application of these stainless steels offshore when fatigue is possible. In general, corrosion fatigue damage tends to increase with increase in temperature. However, temperature can affect fatigue even in the absence of a



3/23/11 1:47:35 PM


189

corrosive environment. Some design codes provide guidance on the influence of elevated temperature, which generally reduces fatigue strength. Up to the creep regime, the effect is usually accommodated simply by allowing for the reduction in the elastic modulus of the material at the temperature of interest. Fatigue crack growth rates generally decrease at sub-zero temperatures and, unless a corresponding reduction in fracture toughness reduces the crack size at failure significantly, the fatigue lives of welded joints are usually higher than those at room temperature.

7.5

Future developments in the application of fatigue rules

7.5.1

Variable amplitude fatigue loading

Miner’s rule is universally adopted as the method for estimating fatigue lives under variable amplitude loading. In some cases it is assumed that ∑ ni/Ni = 1 at failure, where the stress history consists of ni cycles of stresses Dsi and Ni is the life at Dsi from the design curve. In others, for conservatism, ∑ ni/Ni < 1 is required. The method became accepted for application to welded joints as a result of fatigue tests in the 1960s and early 1970s, mainly conducted under block programme loading. However, more recent fatigue tests performed under realistic random loading conditions have tended to throw doubt on the validity of Miner’s rule and there are now many reported cases where ∑ n/N was < 1 at failure, down to below 0.5 (Berger et al., 2002; Gurney, 2006). This apparent contradiction with the early work is probably due to the fact that block programme loading tends to encourage crack growth retardation, which extends fatigue life. apart from doubts about Miner’s rule, there is also mounting evidence that the current method does not take due account of the damaging effect of stresses below the fatigue limit (Marquis, 1996; Zhang and Maddox, 2009). Both deficiencies are evident from the fatigue test results shown in Fig. 7.13. In this, use is made of the equivalent constant amplitude stress range, Dseq, for presenting the results obtained under the variable amplitude spectrum loading. assuming that Miner’s rule is correct, this is given by: Ds eq

Ê S D s im ni ˆ =Á Ë S ni ˜¯

1/m

7.8

where m is the slope of the constant amplitude S–N curve and the variable amplitude loading spectrum is expressed in terms of the number of cycles ni applied at stress range Dsi. If Miner’s rule is correct then constant and variable amplitude test results obtained from the same welded joint should agree. as seen in Fig. 7.13, this was certainly not the case and all lives



3/23/11 1:47:35 PM

190


Stress of equivalent stress range (N/mm2)

300 Mean constant amplitude S–N curve

200 150 100

R = 0.1

Steel plates with edge gussets Constant amplitude Spectrum loading 50 Curves expected from spectrum tests using Miner’s rule and constant amplitude S–N curve with: Slope change at N = 107 cycles No slope change Lowest stress range in spectrum = 10 N/mm2, Sn/N = 0.51 assuming single slope S–N curve

20 15 104

105


107

5 ¥ 107

7.13 Fatigue test results for steel plates with welded edge gussets that illustrate the damaging effect of stresses below the fatigue limit and over-estimation of fatigue lives by Miner’s rule (Maddox, 2003a).

obtained under spectrum loading were less, around half, than expected from the constant amplitude S–N curve. Furthermore, the difference between the expected and actual lives increases (i.e. Miner’s rule is even less safe) in the very long-life regime if it is assumed that stress ranges below the CAFL, assumed to coincide with N = 107 cycles, as in most design rules can be accounted for using the S–N curve extrapolated beyond the CAFL with a shallower slope. In this particular case, stress ranges down to 10 N/mm2, 26% of the assumed CAFL, proved to be at least as damaging as implied by the S–N curve extrapolated without changing the slope. The above problems seem to be associated with wide-band spectrum loading conditions, the damaging effect of small stress fluctuations being greater in a variable amplitude sequence than under constant amplitude loading. It is thought that this situation arises because, for a given stress fluctuation, crack closure may occur under constant but not under variable amplitude loading. Thus, it has been suggested that Miner’s rule should be adequate provided the constant amplitude data are obtained under conditions where the crack tip will always be open, that is at high tensile mean stresses, and the slope change in the S–N curve is assumed to occur at a lower effective fatigue limit (Niemi, 1997). However, the test results shown in Fig. 7.14 (Tilly, 1985; Maddox, 2003a) indicate that this may not be the case. It seems inconceivable that crack closure occurred under either the constant or variable amplitude loading conditions used, suggesting that there must be an explanation for the lower than expected fatigue lives obtained under spectrum loading that



3/23/11 1:47:35 PM


191

Stress

200

Constant amplitude

100

50 Stress

Equivalent constant amplitude stress range (N/mm2)

250 R=0 Time

Smax Time Smax constant

20 105


108

7.14 Fatigue test results for steel plates with fillet welded attachments that illustrate the influence of applied mean stress on fatigue lives obtained under spectrum loading (Maddox, 2003a; Tilly, 1985).

is not related only to crack closure. At the moment, that explanation is not known and the issue is a topic for continuing research. Meanwhile, an interim solution is to adopt a lower Miner’s rule summation than ∑ n/N = 1, perhaps 0.5, and to extrapolate the constant amplitude S–N curve without a slope change down to an effective fatigue limit corresponding to N > 107 cycles, possibly as low as the stress range corresponding to a constant amplitude life as high as 108 cycles for the lower fatigue strength weld details. The deficiencies in current cumulative damage design rules and research aimed at solving them are considered in more detail in Chapter 8 by Marquis.

7.5.2 Complex loading It is now realised that the methods recommended in some current fatigue design rules for assessing weld details subjected to complex, combined or multi-axial loading can be unsafe (Sonsino, 1997). Of particular significance are situations in which the principal stress directions change during the fatigue loading cycle (i.e. non‑proportional loading). The most common approach is to base design on the maximum principal or equivalent stress range used in conjunction with the design S–N curve for unidirectional loading conditions. Experimental data support such an approach for proportional loading, but much lower lives than expected have been obtained under non‑proportional loading (Sonsino, 1995; Sonsino et al., 2001). In fact, an alternative method is given in the Eurocode 3 (EN, 2005) and previous IIW (Hobbacher, 1996)



3/23/11 1:47:36 PM

192


rules, which provide different S–N curves for assessing normal and shear stresses, with slopes m = 3 or 5 respectively. This is: Ê nˆ Ê nˆ + ÁS ˜ ÁË S N ˜¯ Ë N ¯ sshear stress nor l stres norma tr s tres £ 1 in Eurocode 3, or £ 0.5 in IIW

7.9

at the end of the fatigue life, where n is the number of applied stress cycles and N is the endurance from the appropriate design curve at that stress. The lower IIW summation value reflects the preliminary indications that nonproportional loading was more damaging than proportional. However, as seen in Fig. 7.15, even this approach can be unsafe when applied to actual data. This approach has been revised in the latest IIW rules (Hobbacher, 2009). These problems and research aimed at solving them are considered in more detail in Chapter 9 by Sonsino.

7.5.3

Use of FEA in fatigue design

General

Maximum nominal principal stress range (N/mm2)

a shortcoming of current fatigue design rules is that they have not kept pace with computing developments in design, notably the use of FEa. The basic design method embodied in the rules was actually developed over 30 years 600

predicted curves for non-proportional torsion/bending = 0 – 1.0 (Hobbacher, 1996)

300

t/s = 1.0

200 150 t/s = 0 – 0.14 100

80/5

Fillet welded steel pipe-flange joints 50 40

FAT 100/5

Bending and torsion, proportional [Refs 89,92,93 of Maddox (2003a)] Bending and torsion, non-proportional [Refs 89,93 of Maddox (2003a)] Tension and torsion, non-proportional [Ref. 91 of Maddox (2003a)] Unbroken

30 104

105

Endurance (cycles)

106

107

7.15 Evaluation of fatigue data for steel flange-pipe fillet welds failing from the toe, tested under combined bending or tension and torsion (Maddox, 2003a).



3/23/11 1:47:36 PM


193

ago, when computers were something of a novelty and structural analysis relied mainly on the use of standard formulae and experience. Thus, it was entirely reasonable that fatigue design should be based on the use of nominal stresses, as is currently the case. However, computer-based analyses like FEA are now used routinely in structural design and, with increased computing power, their capabilities are increasing. Some preliminary guidance is available on the determination of the stresses to be used in conjunction with the current nominal stress-based design rules (Niemi et al., 2006). However, this is regarded as an interim solution in that new design methods that take more advantage of the potential output from FEA may be required. Such methods based on consideration of stresses close to the region of potential fatigue crack formation are referred to as ‘local approaches’, the two main ones being the hot-spot stress and notch stress methods, as discussed in more detail in Chapter 5 by Fricke. Hot-spot stress approach A method for designing weld details from the viewpoint of potential failure from the weld toe is the hot-spot stress approach. Although this has been applied to tubular structures for many years, guidance is now available on its application to plate structures (Niemi, 1995; Niemi et al., 2006). In this approach, the stress adjacent to the weld is estimated, usually by extrapolation from the stress distribution approaching the weld, as obtained by FEA or perhaps from strain measurements on the surface (Fig. 7.16). The resulting local stress is intended to include the stress concentration effect of the welded joint, but to exclude the notch effect of the weld toe itself. This stress is generally referred to as the structural, or geometric, stress and its value at the weld toe is termed the structural hot-spot stress. It should be possible to express the fatigue strength of a whole range of welded joints in terms of the hot spot stress using fewer curves than at present. The structural hot-spot stress is then used in conjunction with S–N curves that do not incorporate the stress concentration effect of the weld detail. However, the fatigue design S–N curves in current rules, for use in conjunction with nominal stresses, do include allowance for the influence of the welded joint. Therefore, the base data need to be re-evaluated in terms of the structural hot-spot stress. The hot-spot stress approach should lead to increased accuracy in fatigue design. The current nominal stress-based design curves include some allowance for the stress concentration effect of the weld detail, but in a rather crude way. That stress concentration effect is known to depend on the dimensions and proportions of the weld detail but the fatigue data used to establish the design curve will have been obtained from a variety of test specimens with varying geometry. FEA enables the actual geometry and dimensions to be



3/23/11 1:47:36 PM

194


Stress

Hot-spot stress by linear extrapolation

Surface stress distribution approaching weld toe

Distance from weld toe Using surface stresses (e.g. measured): – Surface stress extrapolation (SSE) Structural stress

Actual stress

shot-spot

t

t(y)

sx(y)

tm

sm sb ∑ Using through-thickness stress distribution (e.g. from numerical analysis) to determine equivalent membrane (sm) and bending (sb) stresses by: – Through-thickness iontegratoin (TTI) – Nodal forces (NF) method

7.16 Calculation of structural hot-spot stress.

modelled leading to a more precise estimate of the stress concentration due to the weld detail. In order to be in a position to provide more definitive guidance on the use of the hot-spot stress approach, two key issues need to be addressed: ∑ ∑

The definition of the hot-spot stress and how it is obtained from stress analysis. The choice of hot-spot stress design S–N curves.

In relation to the first, there have been significant developments following the earlier IIW methods based on extrapolation to the weld toe from the



3/23/11 1:47:36 PM


195

surface stresses approaching the weld, for use with either measured or calculated stresses (Fig. 7.16). However, in the context of FEA, another development has been methods in which the structural stress is calculated from the distributions of forces and moments underneath the weld toe. Extrapolation from surface stresses is particularly suitable for estimating the hot-spot stress from strain measurements. However, using the same technique with stresses obtained by FEA can involve complex post-processing. Alternatives make use of the through-thickness stress distribution (see Fig. 7.16) to calculate the equivalent membrane and bending stress components (Dong et al., 2002; Wei and Maddox, 2007). One technique uses nodal stresses to calculate the membrane and bending stresses by through-thickness integration (TTI). Another uses equilibrium arguments to replace the actual stress distribution with the equivalent membrane and bending stress components using nodal forces (NF). This is claimed to be less sensitive to the choice of finite element mesh type and size than the other methods. The TTI and NF methods estimate the structural stress from the distributions of forces and moments underneath the weld toe. A practical problem with both the TTI and NF methods is that some judgement may be needed to decide the extent of the section thickness over which the calculation of forces and moments should be made. Clearly, the stress concentration effect of a weld detail on the flange of an I-section beam will depend not on the full depth of the beam but only on the stress distribution through the flange thickness. Similarly, the stress distribution across the full thickness of a very thick member may not be relevant and some effective section may need to be established. It is anticipated that further experience in the development of these methods will lead to clearer guidance on their practical application. With regard to hot-spot stress design S–N curves current evidence (Maddox, 2002) suggests that nominal stress-based curves for transverse butt welds will be suitable, either FAT90 or FAT100 in the IIW scheme, a possible distinction being between fully load-carrying and nominally non-load-carrying welds as indicated in Fig. 7.17 (Maddox, 2001). Effective notch stress approach An important feature of the hot-spot stress is that it excludes the local notch effect of the weld toe. A further development, which actually requires detailed stress analysis such as is possible with FEA, is an approach that aims to include part of the local notch effect. This is the effective notch stress approach, developed mainly by Radaj (1990). It involves determination of the local stress at the point of fatigue crack initiation (weld toe or root). Since the actual weld toe or root is likely to be very sharp, theoretically this stress could be infinite. To avoid this problem, and indeed to avoid the



3/23/11 1:47:37 PM

196


Structural hot-spot stress range (IIW) (N/mm2)

500

Load-carrying

400 350 300 250

Non-load-carrying

200

Mean-2SD, loadcarrying (just below FAT 90)

150

Plate specimens

Mean-2SD, non-loadcarrying (coincides with FAT 100)

Non-load-carrying weld Load-carrying weld 100 Structural components 90 Non-load-carrying weld 80 Load-carrying weld 70 Unbroken 60 104 105 106 Endurance (cycles)

107 2 ¥ 107

7.17 Fatigue test results for welded steel specimens and components expressed in terms of the hot-spot stress range determined using SSE (Maddox, 2001).

Notch stress range (N/mm2)

1000 Fatigue data for butt and fillet welded joints (Olivier et al., 1989 Köttgen; et al., 1991)

500

300 200

100 104

IIW FAT 225 design curve

105


107

108

7.18 Fatigue data obtained from butt and fillet welded steel specimens expressed in terms of the effective notch stress range (from Fricke, 2008).

problem that the local geometry will vary and in any case be unknown to the designer, it has been found that representing it with a 1 mm radius leads to local stresses that allow reasonably consistent correlation of fatigue test results obtained from different welded joints and justification for a single design S–N curve for fatigue failure from the weld toe or root. An example of such data obtained from a range of fillet and butt welded steel specimens is shown together with the proposed IIW FAT 225 design curve in Fig.



3/23/11 1:47:37 PM


197

7.18 (Olivier et al., 1989; Köttgen et al., 1991). This design curve may be compared with the highest IIW nominal stress-based curve for transverse butt welds, FAT 100. The IIW has been active in developing the notch stress approach and guidance on FEA based largely on experience gained from round-robin stress analysis exercises involving many stress analysts is available (Fricke, 2008). The notch stress approach is included in some fatigue design rules (e.g. DNV, 2010) but further work is still needed for its wider acceptance, in particular to clarify the range of welded joint types and dimensions to which it applies, to develop possible alternative models (e.g. the use of a 0.05 mm radius for very thin components (Sonsino, 2008) and to define aspects of welded joint geometry (Pedersen et al., 2010) and quality, such as weld toe profile (Barsoum and Jonsson, 2008), that may need to be controlled or covered by a lower design curve.

7.5.4 Welding process General Most of the data used to derive design S–N curves were obtained from arc welded specimens. Thus, there is the need to meet the growing demand for fatigue design data for other welding processes, such as electron beam, friction, laser and, for very thin sections, resistance welding. Some data are available for all these processes, chiefly for butt joints in the first three examples and lap joints in the last, and there is some justification for applying existing design data (Maddox, 1997). However, this might overlook extra benefit which could arise in some cases, notably friction stir welding and indeed TIG and plasma arc welds. TIG and plasma welding It is known that the toes of TIG and plasma welds do not contain the sharp crack-like flaws that provide the sites for fatigue crack initiation in other arc welds (Watkinson et al., 1971). Thus, they would be expected to display superior fatigue properties. However, investigation of this was not conclusive in that use of these processes did not necessarily produce better fatigue properties than similar details with manual weld arc (MMA) welds (Branco et al., 1997). The project focused on relatively thin sections for which, even with MMA welding, relatively high fatigue strengths were obtained. This might have clouded the issue. More recent studies of the fatigue performance of pipes girth welded from one side provide further evidence. In this case, the relevant part of the weld is the root on the inside of the pipe since this tends to be the critical location for fatigue crack initiation. Similar fatigue strengths have been obtained from welds with TIG, metal inert gas (MIG) © Woodhead Publishing Limited, 2011


3/23/11 1:47:37 PM

198


and MMA root passes (Maddox, 2008). Thus, in spite of the lack of nonmetallic crack-like flaws and relatively favourable profiles, it seems that TIG and plasma weld toes can still represent severe stress concentrations from which fatigue cracks readily initiate. A similar situation has been observed in butt welded aluminium alloys (Maddox, 2003c). Although TIG welding can produce superior fatigue properties, the lower bound fatigue behaviour is exactly the same as for MIG welds. Non-arc welding There is growing interest in the use of non-arc welding to fabricate components and structures that will experience fatigue loading and the inclusion of appropriate fatigue design data in codes and standards is long overdue. As in the case of TIG and plasma welds, there is no direct evidence that nonarc welds, such as power beam or friction welds, contain crack-like flaws at the weld toe or edge (although to the author’s knowledge this has not been investigated in any depth). Therefore, again there is reason to suppose that they might display superior fatigue properties to arc welds. Power beam welding (electron beam or laser) in particular offers great potential for increased productivity, being capable of rapidly welding thick sections from one side in a single pass. In the case of butt welds under transverse loading, available data (Elliott and Wylde, 1984; Wylde and Elliott, 1984; Iida et al., 1986; Manteghi and Punshon, 1998), Fig. 7.19(a), provide good support for IIW FAT 100, comparable with the best two-sided arc butt welds. Full penetration welding must be achieved, with identifiable cap and root beads. Their profiles are less critical and the following ranges are all consistent with the data in Fig. 7.19(a): weld toe angle from 10° to 50°; weld toe radius from 0.4 to 4 mm; weld bead height from 1 to 2.5 mm; weld bead width from 5 to 25 mm. However, an important limitation is that all the data were obtained at R = 0.1 from relatively small-scale specimens that may not have incorporated high tensile residual stresses. Therefore, it may be prudent to adopt lower FAT 90 for the design of real structures. In such rapid ‘one-shot’ welds there is clearly the danger that it may be difficult to ensure full penetration and incomplete penetration, underfill and undercut are potential flaws. The data in Fig. 7.19(b) show that flaws up to 1.4 mm deep can reduce the classification to FAT 71 (Elliott and Wylde, 1984; Wylde and Elliott, 1984; Manteghi and Punshon, 1998). However, FAT 80 satisfies all the results for flaws less than 1 mm in depth. Clearly, partial penetration welds would not be used deliberately, but such data help in setting acceptance levels for flaws. The increased use of laser welding in shipbuilding has prompted the need for fatigue data. There is less published information than in the case



3/23/11 1:47:37 PM

Fatigue design rules for welded structures 400

R = 0.1

300 Stress range (N/mm2)

199

FAT 100 FAT 80 13 mm thick, as-welded Wylde & Elliott (1984) Elliott & Wylde (1984) Manteghi & Punshon (1998): Unbacked Permanent steel backing 20 mm thick, as-welded and stress relieved Iida et al. (1986) Unbroken

200 150

100

50 104

Mean ± 2SD enclosing data (m = 3) 105

106 Endurance (cycles) (a)

107

400 R = 0.1 300 Stress range (N/mm2)

13 mm 200

100

Root or cap toe flaws

Wylde & Elliott (1984) Undercut (1–1.2 mm) Elliott & Wylde (1984) Slight back groove (0.5 mm max.) Severe back groove (1 mm max.) Incomplete penetration (2 mm max.)

FAT 100

Manteghi & Punshon (1998) Undercut (0.25 mm max.) Undercut (1.4 mm max.) Unbroken

50 104

Mean ± 2 SD (m = 3) 105

FAT 71 106 Endurance (cycles) (b)

107

2 ¥ 107

7.19 Fatigue test results for transverse electron beam butt welds: (a) full penetration welds; (b) welds with surface imperfections.

of electron beam welds but available data for transverse butt welds show that they behave in a similar way to electron beam welds. Published data for plates with laser-welded attachments and for cruciform joints (Maddox, 1997) are also consistent with the arc weld design curves. However, the absence of any significant fillet emphasises the need to ensure full-penetration welding, especially in load‑carrying joints.



3/23/11 1:47:38 PM

200


Friction welding can also be used to make butt joints, usually between rods or tubes. An interesting feature of such joints is that they may not contain high tensile residual stresses due to welding in the region of highest stress concentration; they may indeed be compressive. In spite of this available data again support a design classification between FAT 90 and 100. When non-arc welded joints are incorporated in the design rules, it will be necessary to draw attention to potential problems peculiar to those processes. For example, some caution may be needed in the case of laser welding to avoid the production of hard brittle martensite in steel; care will also be needed to ensure full penetration or at least a reasonable weld root profile in single‑sided welds. A relatively recent process that deserves mention is friction-stir welding (FSW). This was invented by TWI and is now being developed for a wide range of industrial applications. Most attention has focused on aluminium alloys (Maddox, 2003d), but the joining of steel and other metals is under development. In the context of aluminium alloys, a particular advantage of this friction process is that the material is not melted. As a result, high strength 2000 and 7000 series alloys, which are difficult to weld by fusion processes due to solidification problems, are readily welded. Friction stir butt welds, which are made from one side without the need for joint preparation, are virtually flush with the parent material and it is not surprising to find that, under similar conditions, their fatigue properties compare very favourably with those for fusion welds. A typical example for 5 mm thick 6000 series alloys (Ranes et al., 1995), tested under the relatively severe loading condition of R = 0.5, is shown in Fig. 7.20. The results are widely scattered, presumably reflecting variations in the joint quality. Indeed, even lower results have been recorded from joints containing identifiable flaws. Research is needed to determine the nature and significance of flaws and weld quality in general with the aim of establishing the condition that will ensure upper bound fatigue performance. In addition the scope for using FSW for other joint configurations needs investigation; currently, the process is confined to only butt and lap joints. It is probably premature to provide fatigue design data for friction-stir welds, except to note that they perform at least as well as similar joints made by other welding processes. A final category not covered by current fatigue design rules is resistance welding. This is particularly widely used for joining thin sheet material but, as discussed later, current fatigue design guidance tends to be directed specifically at joints in thick sections, generally greater than 10 mm. Apart from this difference, the type of joint produced by a resistance welding process, usually spot or resistance seam welding for sheet material, may not be suitable for treatment using the nominal stress-based approach in the rules. The most common option is some form of lap joint, and the inherent misalignment in such joints means that their fatigue performance tends to be



3/23/11 1:47:38 PM


201

200 150


Unwelded 100 FSW from one side (two test series)

50 R = 0.5

20

10 104

MIG welded

6000 series aluminium alloy Eurocode 9 design curves for transverse butt welds in aluminium alloy 1 Cat. 28-4, welded from both sides 2 Cat. 18-3.2, welded from one side 105

1 2


107

7.20 Fatigue test results for plain and butt-welded 6000 series aluminium alloy illustrating the potentially high performance of friction stir welds (Maddox, 2003a).

dominated by the bending moment induced. Consequently, measures such as the combination of spot welding and adhesive bonding, which reduce this bending, are beneficial to fatigue performance. In the past, fatigue test data from spot welds were presented in terms of the applied force per spot rather than a stress. This made it difficult to compare the fatigue performance of joints made with different thicknesses of material or using different spotweld sizes, as well as complicating the design process. However, in recent years several attempts have been made to remedy this situation by defining the structural stress controlling fatigue and capable of correlating test data. Good correlation of fatigue data obtained from a variety of spot-welded joints and structural components was achieved (Maddox, 1997) using the author’s local structural stress (Maddox, 1992), a combination of the local membrane and out-of-plane bending stresses at the edge of the spot weld (where fatigue cracking initiates) and given by: Local str structural stress = 2P + 3P ct wt

7.10

where P = applied force range, c = spot weld circumference, w = sheet width and t = sheet thickness. The data indicated that FaT 125 would be a suitable design curve for use with this local structural stress. However, from the practical viewpoint, it may not be so easy to estimate it in a real structure. The important out-of-plane bending component 3P/wt will depend on any eccentricity in the joint and the extent to which it is resisted, for example by design or the use of adhesive. The most suitable way to estimate



3/23/11 1:47:38 PM

202


the actual stress in the vicinity of a spot weld is probably by finite element stress analysis. Good progress has been made in applying such an approach in the automotive industry (Radaj et al., 2006).

7.5.5 Weld quality One possible interpretation of the use of lower bound fatigue data for design is that account is taken of the very worst weld quality (as it affects the particular failure mode being assessed). For general design rules, which will be used by a wide range of industries of varying ability, this is a reasonable state of affairs, especially as even the worst quality laboratory welded specimen is likely to be of reasonably good quality. However, the increasing need for economy and competitiveness in fabrications highlights the need for more flexibility and, in particular, the ability for manufacturers to gain credit, in terms of increased fatigue design stresses, for improving weld quality. Guidance is available (BSI, 2005) to enable allowable imperfections to be specified, or unexpected flaws to be assessed, on a fitness-for-purpose basis. However, the concentration is on imperfections which might reduce fatigue life. What is required now is similar guidance for features which have the potential to guarantee fatigue lives above the design curves. Preliminary steps have been taken to link fatigue design but further work is needed to rationalise them further. A price to pay may be more extensive inspection, probably of both butt and fillet welds. Further discussion of the good progress being made in this area is contained in Chapter 6 by Jonsson.

7.6

Conclusions

The most recent fatigue design rules for welded structures have a common basis and offer comprehensive coverage of key factors affecting fatigue life. Improvements would include wider coverage of different welding processes and corrosive environments; specific design guidance directed at welded joints in very thin sections, including allowance for bending; development of local approaches to keep pace with the increasing use of FEA; a design method based on the good progress made in research into fatigue under non-proportional loading; safer cumulative damage methods. The adoption of a single classification scheme, preferably using the fatigue strength at 2 ¥ 106 cycles, would also reduce confusion between design rules. A serious source of error in the application of fatigue rules is estimation of the service stress history. Any progress that can be made in improving the designer’s ability to specify fatigue loading, or the monitoring of structures to detect evidence of premature fatigue, may well be just as important as improvements to design rules.



3/23/11 1:47:38 PM


7.7

203

References

Publications of special interest have been marked *. These all refer generally to fatigue or fatigue design of welded structures. AASHTO, 2008: ‘Bridge welding code’ (fatigue rules as in AWS D1.5.2008). Barsoum Z and Jonsson B, 2008: ‘Fatigue assessment and LEFM [linear elastic fracture mechanics] analysis of cruciform joints fabricated with different welding processes’, Welding in the World, vol. 52, no. 7–8, pp 93–105. Baxter D P, Maddox S J and Pargeter R J, 2007: ‘Corrosion fatigue behaviour of welded risers and pipelines’, Proceedings 26th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2007, San Diego, California, 10–15 June 2007. Paper no. 29360. *Berger C, Eulitz K-G, Heuler P, Kotte K-L, Naundorf H, Schuetz W, Sonsino C M, Wimmer A and Zenner H, 2002: ‘Betriebsfestigkeit in Germany – an overview’, Int. J. Fatigue, vol. 24, no. 6, pp 603–625. Branco C M, Gomes E C and Maddox S J, 1997: ‘Fatigue performance of tungsten inert gas (TIG) and plasma welds’, Proc. IIW Conference Performance of Dynamically Loaded Welded Structures, WRC, New York, pp 157–177. Branco C M, Maddox S J and Sonsino C M, 2001: ‘Fatigue design of welded stainless steels’, ECSC Report EUR 19972, Official Publications of the European Community, Luxembourg. BSI, 1993: BS7608: ‘Code of Practice: Fatigue design and assessment of steel structures’, British Standard, BSI, London. BSI, 2005: BS 7910 ‘Guide on methods for assessing the acceptability of flaws in metallic structures’, BSI, London. Brozzetti J, Chabroline B and Raoul J, 1992: ‘Background document on fatigue design rules in Eurocode 3, Part 2: Bridges’, CTICM report no. 10.003-7. *Dong P, Hong J K, Osage D and Prager M, 2002 ‘Master curve method for fatigue evaluation of welded components’, Welding Research Council Bulletin 474. DNV, 2010: ‘Fatigue design of offshore steel structures’, Recommended Practice DNVRP-C203, DNV, Oslo, Norway. Elliott S and Wylde J G, 1984: ‘The fatigue strength of electron beam transverse butt joints in carbon manganese steels’, Welding Institute Research Report 232/1984. EN, 2005: Eurocode 3: ‘Design of steel structures – Part 1–9: Fatigue’, EN 1993-1-9, European Committee for Standardisation, Brussels. EN, 2007: ‘Eurocode 9: ‘Design of aluminium structures – Part 1–3: Structures susceptible to fatigue’, EN 1999-1-3, European Committee for Standardisation, Brussels. *Fisher J W, 1984: Fatigue and Fracture in Steel Bridges, Wiley Interscience New York, ISBN 0-471-80469-X. *Fisher J W, 1997: ‘Improved performance through large scale dynamic testing of structures’, IIW Intl. Conf. on Performance of Dynamically Loaded Welded Structures, Welding Research Council, New York. *Fricke W, 2008: ‘Guideline for fatigue assessment by notch stress analysis for welded structures’, IIW document XIII-2240-08/XV-1289-08, International Institute of Welding. *Gurney T R, 1979: Fatigue of Welded Structures, 2nd Edition, Cambridge University Press, Cambridge. Gurney T R, 1991: The Fatigue Strength of Transverse Fillet Welded Joints – A study of the influence of joint geometry, Abington Publishing, Abington, Cambridge.



3/23/11 1:47:38 PM

204


Gurney T R, 1992: Fatigue of Steel Bridge Decks, HMSO, London. *Gurney T R, 2006: Cumulative Damage of Welded Joints, Woodhead Publishing Ltd., Cambridge. Gurney T R and Maddox S J, 1973: ‘A re-analysis of fatigue data for welded joints in steel’, Welding Res. Intl., vol. 3, no 4, pp 1–54. Harrison J D, 1972: ‘The basis for a proposed acceptance standard for weld defects, Metal Construction and British Welding J., Part 1: Porosity, vol. 4, no. 3, pp 99–107 and Part 2: Slag inclusions, vol. 4, no. 7, pp 262–268. *Hobbacher A, 1996: Fatigue Design of Welded Joints and Components, International Institute of Welding, Abington Publishing, Abington, Cambridge. *Hobbacher A, 2009: Recommendations for Fatigue Design of Welded Joints and Components, International Institute of Welding, WRC Bulletin 520, Welding Research Council, New York. HSE, 1995: Offshore Installations: ‘Guidance on design, construction and certification’, UK Health and Safety Executive, 4th Edition, 1990, Amendment No. 3, London (no longer supported by HSE). Iida K and Takanashi M, 1997: ‘Relaxation of welding residual stresses by cyclic zero-totension loading’, IIW document XIII-1685-97, International Institute of Welding. Iida K, Yamauchi T, Satoh M and Takano G, 1986: ‘Fatigue strength of electron beam welded joint of carbon steel’, IIW document XIII-1201-86, International Institute of Welding. ISO, 2007: ‘Petroleum and natural gas industries – Fixed steel offshore structures’, BS EN ISO 19902:2007. Köttgen V B, Olivier R and Seeger T, 1991: ‘Fatigue analysis of welded connections based on local stresses’, IIW document XIII-1408-91, International Institute of Welding. McClung R C, 2007: ‘A literature survey on the stability and significance of residual stresses during fatigue’, Fatigue Fracture Engi. Materi. Structures, vol. 30, no. 3. pp 173–205. Maddox S J, 1974: ‘Assessing the significance of flaws in welds subjected to fatigue’, Welding J., Sept., pp 401s–410s. Maddox S J, 1982: ‘Fatigue design of welded aluminium alloys structures’, Proc. 2nd Intl. Conf. on Aluminium Weldments, Aluminium-Verlag, Dusseldorf. Maddox S J, 1985a: ‘Fitness for purpose assessment of misalignment in transverse butt welds subject to fatigue loading’, IIW Document XIII-1180-85, International Institute of Welding. Maddox S J, 1985b: ‘Improving the fatigue strength of welded joints by peening’, Metal Construction, vol. 17, no. 4, pp 220–224. Maddox S J, 1987: The Effect of Plate Thickness on the Fatigue Strength of Fillet Welds, Abington Publishing, Abington, Cambridge. *Maddox S J, 1991: Fatigue Strength of Welded Structures, Abington Publishing, Abington, Cambridge. *Maddox S J, 1992: ‘Fatigue design of welded structures’, Proc. Intl. Conf. Engineering Design in Welded Constructions, Pergamon Press for the International Institute of Welding, Oxford, ISBN: 0-08-041910-0, p 31. Maddox S J, 1994: ‘Fatigue aspects of pressure vessel design’, Chapter 9, in Pressure Vessel Design, Concepts and Principles, E & F N Spon, London. Maddox S J, 1995: ‘Scale effect in fatigue of fillet welded aluminium alloys’, Proc. 6th Intl, Conf. on Aluminium Weldments, American Welding Society, Miami, FL, pp 77–94. *Maddox S J, 1997: ‘Developments in fatigue design codes and fitness‑for‑service



3/23/11 1:47:38 PM


205

assessment methods’, IIW Intl. Conf. on Performance of Dynamically Loaded Welded Structures, Welding Research Council, New York, pp 22–42. Maddox S J, 2001: ‘Hot-spot fatigue data for welded steel and aluminium as a basis for design’, IIW Document XIII-1900a-01, International Institute of Welding. Maddox S J, 2002: ‘Recommended hot-spot stress design S–N curves for fatigue assessment of FPSOs’, Int. J Offshore Polar Eng., vol. 12, no. 2, pp 134–141. *Maddox S J, 2003a: ‘Key developments in the fatigue design of welded constructions’, 2003 IIW Portevin Lecture, Proc. IIW Int. Conf. ‘Welded Construction for Urban Infrastructure’, ISIM Timisoara. *Maddox S J, 2003b: ‘Assessment of pressure vessel design rules on the basis of fatigue test data’, in Pressure Equipment Technology: Theory and Practice, Professional Engineering Publishing Ltd, London, pp 401–412. Maddox S J, 2003c: ‘Review of fatigue assessment procedures for welded aluminium structures’, Int. J. Fatigue, vol. 25, no. 12, pp 1359–1378. Maddox S J (Editor), 2003d: ‘Special section: friction stir welding’ Int. J. Fatigue, vol. 25, no. 12, pp 1357–1409. Maddox S J, 2008: ‘Fatigue of transverse butt welds made from one side’, Welding and Cutting, vol. 7, no. 1, pp 44–52. Maddox S J and Gurney T R, 1987: ‘Fatigue tests on joints in orthotropic decks’, Proc. Int. Conf. on Fatigue of Welded Constructions, The Welding Institute, 1987. Manteghi S and Punshon C S, 1998: ‘Fatigue tests on electron beam welded C-Mn steel butt joints’, TWI J., vol. 7, no. 3, pp. 573–616. Marquis G, 1996: ‘Long life spectrum fatigue of carbon and stainless steel welds’, Fatigue Fracture Eng. Mater. Structures, vol. 19, no. 6, p 739. Martinez L L, Blom A F, Trogen H and Dahle T, 1997: ‘Fatigue behaviour of steels with strength levels between 350 and 900 MPa – influence of post-weld treatment under spectrum loading’, Proc. Conf. Welded High-strength Steel Structures’, EMAS, West Midlands, pp 361–376. Müller F, 1996: ‘Fatigue of weathering steels in as-received and welded material states within a weathering period of six years’, IIW document XIII-1616-96, International Institute of Welding. *Niemi E, 1995: Stress Determination for Fatigue Analysis of Welded Components, International Institute of Welding, Abington Publishing, Abington, Cambridge. Niemi E, 1997: ‘Random loading behaviour of welded components’, Proc. IIW Conf. on Performance of Dynamically Loaded Welded Structures, Welding Research Council, New York. *Niemi E, Fricke W and Maddox S J, 2006: ‘Fatigue Analysis of Welded Components – Designer’s guide to the structural hot-spot stress approach’, International Institute of Welding, Woodhead Publishing Ltd, Cambridge. Orjasaeter O, 1995: ‘Effect of plate thickness on fatigue of welded components’, IIW Document XIII‑1582-95, International Institute of Welding. Olivier R, Köttgen V B and Seeger T, 1989: ‘Welded connections I: Fatigue assessment of welded connections based on local stresses’ (transl.), Forschungskuratorium Maschinenbau, Bericht No. 143, Frankfurt. Pedersen M M, Mouritsen O O, Hansen M R, Andersen J G and Wenderby J, 2010: ‘Re-analysis of fatigue data for welded joints using notch stress approach’, Int. J. Fatigue, vol. 32, no. 10, pp 1620–1626. *Radaj D, 1990: Design and Analysis of Fatigue Resistant Welded Structures, Abington Publishing Ltd, Abington, Cambridge.



3/23/11 1:47:38 PM

206


*Radaj D, Sonsino C M and Fricke W, 2006: Fatigue Assessment of Welded Joints by Local Approaches, Woodhead Publishing Ltd, Cambridge. Ranes M, Kluken A O and Midling O T, 1995: ‘Fatigue properties of as-welded AA6005 and AA6082 aluminium alloys in T1 and T5 temper condition’, Proc 4th Int. Conf. on Trends in Welding Research, Gatlinburg TN, pp 639–644. Razmjoo G R, 1995: ‘Design guidance on fatigue of welded stainless steel joints’, Proc. of Offshore Mechanics and Arctic Engineering Conference (OMAE’95), vol. 3, Materials Engineering, ASME, 163–171. Signes F S, Baker R G, Harrison J D and Burdekin F M, 1967: ‘Factors affecting the fatigue strength of welded high strength steels’, British Welding J., vol. 14, no. 3, p 108. Sonsino C M, 1995: ‘Multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses’, Int. J. Fatigue, vol. 17, no. 1, pp 55–70. Sonsino C M, 1997: ‘Multiaxial and random loading of welded structures’, IIW Intl. Conf. on Performance of Dynamically Loaded Welded Structures, Welding Research Council, New York, pp 317–331. Sonsino C M, 2008: Suggested allowable equivalent stresses for fatigue design of welded joints according to the notch stress approach with reference radii rref = 1.00 and 0.05 mm, IIW Doc. XIII-2216-08/XV-1285-08, International Institute of Welding Sonsino C M, Kuppers M, Gäth N, Maddox S J and Razmjoo G R, 2001: ‘Fatigue behaviour of welded high strength components under combined multiaxial variable amplitude loading’, ECSC Report No EUR 20050, Office of the Official Publications of the European Communities, Luxembourg. Tilly G, 1985: ‘Fatigue of land-based structures’, Int. J. Fatigue, vol. 7, no. 2, pp 67–78. Watkinson F, Bodger P H and Harrison J D, 1971: ‘The fatigue strength of welded joints in high-strength steels and methods for its improvement’, Proc. Conf. on Fatigue of Welded Structures’. TWI, Abington, Cambridge. Wei L W and Maddox S J, 2007: ‘Structural hot spot stress based fatigue design of welded structures using finite element analysis’, In: Fatigue 2007. Durability and Fatigue. Proceedings, 6th International Conference, Cambridge, Ed: M.R. Bache, P.A. Blackmore, E.R. Cawte, P. Roberts and J.R. Yates. Publ: Sheffield, S11 9QX, UK; Engineering Integrity Society. Wylde J G and Elliott S, 1984: ‘The fatigue strength of transverse butt welded joints made by electron beam welding process in a C-Mn steel’, IIW Document XIII-114284, International Institute of Welding. Zhang Y-H and Maddox S J, 2009: ‘Investigation of fatigue damage to welded joints under variable amplitude loading spectra’, Int. J Fatigue, vol 31, no. 1, pp 138–152.

7.8

Appendix: fatigue design codes and standards

7.8.1 Fatigue design of specific structures AASHTO, 2008: ‘Bridge welding code’ (fatigue rules as in AWS D1.5:2008). API, 1993: American Petroleum Institute: ‘Recommended practice for planning, designing and constructing fixed offshore platforms’, RP2A, 20th Edition, API, Washington.



3/23/11 1:47:39 PM


207

BSI, 1980: British Standards Institute: ‘Steel, concrete and composite bridges: Part 10 – Code of Practice for Fatigue’, BSI, London (to be superseded by BS EN 1993-1-9:2005 ‘Design of steel structures – Part 1–9 Fatigue strength’). HSE, 1995: Offshore Installations: ‘Guidance on design, construction and certification’, UK Health and Safety Executive, 4th Edition, 1990, Amendment No. 3, London (no longer supported by HSE). ISO, 2007: ‘Petroleum and natural gas industries – Fixed steel offshore structures’, BS EN ISO 19902:2007. DNV, 2010: ‘Fatigue design of offshore steel structures’, Recommended Practice DNV-RP-C203, DNV, Oslo, Norway. EN, 2009: Unfired Pressure Vessel Standard, EN13445:3 ‘Design’, European Committee for Standardisation, Brussels.

7.8.2 Fatigue design of welded joints AWS, 1996: American Welding Society: ‘Structural Welding Code – Steel’, ANSI/AWS D.1., AWS, Miami BSI, 1992: BS 8118, Part 1: ‘Structural use of aluminium: Code of practice for design’, British Standards Institution, BSI, London (to be replaced by BS EN 1999-1-3:2007 Part 1–3 ‘Fatigue’ for use in conjunction with BS PD 6702, which recommends use of the alternative fatigue rules in prENV 1999-2:1998). BSI, 1993: BS7608: ‘Code of Practice: Fatigue design and assessment of steel structures’, British Standard, BSI, London. EN, 2005: Eurocode 3: ‘Design of steel structures – Part 1–9: Fatigue’, EN 1993-1-9, European Committee for Standardisation, Brussels. EN, 2007: ‘Eurocode 9: ‘Design of aluminium structures – Part 1–3: Structures susceptible to fatigue’, EN 1999-1-3, European Committee for Standardisation, Brussels.

7.8.3 Fatigue assessment procedures API, 2007: API 579-1:2007 ‘Fitness for service’, 2nd ed. BSI, 2005: BS 7910 ‘Guide on methods for assessing the acceptability of flaws in metallic structures’, BSI, London.



3/23/11 1:47:39 PM

8

Fatigue assessment methods for variable amplitude loading of welded structures

G. B. M a r q u i s, Aalto University, Finland

Abstract: Fatigue loading of most engineering structures involves variable amplitude stress cycles. This chapter starts by introducing alternate types of variable amplitude loading and methods for describing and simplifying load–time histories. Fatigue assessment methods for variable amplitude loading of welded structures based on S–N or crack propagation analysis are explained including the important features of load sequence effects and the influence of variable amplitude loading on small crack growth. Important issues to consider when planning, executing and reporting variable amplitude fatigue test results as well as hints on future trends and additional reading are also given. Key words: variable amplitude loading, load spectrum, load–time history, rainflow cycle counting, damage accumulation, load sequence effects.

8.1

Introduction

Because of its significance in the ground vehicle, offshore, transportation and aircraft industries, variable amplitude fatigue has been extensively studied for several decades. Entire industries have emerged for collecting and evaluating variable amplitude load histories for structures. In some cases these histories are reproduced in the laboratory for evaluating materials, components and complex structures. Design guidance documents for welded structures are, to a large degree, based on results from constant amplitude testing because it is a relatively fast and inexpensive method of classifying different weld geometries and quantifying a number of other important features that influence weld fatigue strength. Ongoing research has led to numerous assessment methods for extending this data to variable amplitude loading based on traditional S–N curves or on crack propagation analysis. These topics approximate the sections in this chapter. The first section introduces alternate types of variable amplitude loading and methods for describing and simplifying load–time histories. Each simplification step also results in the loss of some information which, depending on the application, may or may not be significant. Some important terms are also defined. Section 8.2 presents fatigue assessment methods for variable amplitude loading of welded structures. Fatigue assessment can be accomplished based on S–N curves either by damage summation or using the equivalent stress principle. 208 © Woodhead Publishing Limited, 2011


3/23/11 1:47:56 PM

Fatigue assessment methods for variable amplitude loading

209

More advanced analyses, which consider load sequence effects and initial defect sizes, are possible using crack propagation analysis. Section 8.3 addresses some issues to consider when planning, executing and reporting variable amplitude fatigue test results. The final sections give hints on future trends and additional reading.

8.1.1 Variable and constant amplitude fatigue loading Under constant amplitude loading a knee point stress range is observed below which fatigue lives become very long for only small changes in stress range. Experimentally, the fatigue life which corresponds to the knee point is usually observed between one and ten million cycles. For example, the most recent IIW recommendations for fatigue design of welded joints and components (Hobbacher, 2009) conservatively suggest that the knee point for design purposes occurs at 1 ¥ 107 cycles. These recommendations further suggest that for constant amplitude loading, every 10% reduction in stress range below the knee point results in a one decade increase in fatigue life. Most textbooks include the concept of a fatigue limit which implies that below the knee point, fatigue life becomes infinite. During variable amplitude loading, the problem is more complex and guidelines for identifying individual cycles in a complex load history and computing the fatigue damage contribution of these cycles must be defined. During variable amplitude loading there are a number of special phenomena that are not observed for constant amplitude loading. Tensile overloads may interact with other mechanisms such as creep, yielding or fracture while compressive overloads may influence local buckling or produce secondary bending stresses. Welding-induced residual stresses, which are known to play an important factor in the fatigue of welded structures (Maddox, 1991), can be significantly altered by variable amplitude loading with either beneficial or detrimental consequences. Even more important are the local stresses that occur in the crack tip region which often accelerate fatigue crack growth rate, but, under some circumstances, decelerate the growth of a fatigue crack. In spite of the important differences between constant and variable amplitude fatigue loading, the majority of design data is still based on constant amplitude testing. Large databases for many joint types are available. The local and structural geometric stress concentrations that greatly influence the fatigue strength of welded structures will have similar influence for both constant and variable amplitude loading. The standard deviation in fatigue strength will be similar, but not identical, in both load cases.

8.1.2 Forms of variable amplitude loading In its most simple form, variable amplitude loading indicates single over- or underload cycles in an otherwise constant amplitude history. With increasing © Woodhead Publishing Limited, 2011


3/23/11 1:47:56 PM

210


complexity load amplitudes may change at regular intervals or, in the most complicated case, both load amplitude and mean stress may change with each loading cycle. Figure 8.1 shows several commonly encountered types s

(a)

0

Time s

(b)

0

Time s

(c)

0 s

(d)

Time

0

Time s

(e)

0

Time

8.1 Examples of several variable amplitude load histories.



3/23/11 1:47:56 PM


211

of variable amplitude loading. Rotating, reciprocating or process machinery is often considered to experience constant amplitude loading as shown in Fig. 8.1(a); however, even this equipment may be subjected to periods of overload or time varying changes in mean stress as shown in Fig. 8.1(b). Fatigue loading is predominantly constant amplitude, but the existence of overload events or mean stress changes means that fatigue should be assessed as variable amplitude loading. In some cases, mean stress changes are not due to changes in the operation of a piece of equipment, but may be due to external factors. For example, temperature changes may cause large thermal mean stress shifts which are superimposed on the normal operating stresses. Figure 8.1(c) shows loading that may occur, for example, in pressure equipment, lifting devices or bridges. The load changes at intervals between a constant minimum (or maximum) stress and a maximum (minimum) stress. The large block-wise mean stress shift in Fig. 8.1(d) may be present for aircraft components which show a ground-to-air shift or bulk transport vehicles which show large empty-to-full mean stress changes superimposed with random operation loads. Figure 8.1(e) shows a load history where both stress range and mean stress change with each cycle. This type of loading may exist for work vehicles or structures exited by random events such as wind or waves. In some literature, the loading represented by Figs 8.1(c–e) is termed spectrum loading because it is either an exact replica or approximation of a loading history or loading spectra that occurs during service. Spectrum loading is an important subset of variable amplitude fatigue.

8.1.3 Cycle counting and presentation of load histories In Figs 8.1 (a–c) individual fatigue cycles are easy to identify. For the more random load histories shown in Figs 8.1 (d, e) the individual cycles are not obvious. Load histories consist of a series of load turning points and also the time information between turning points. During fatigue analysis or testing, it is rarely practical to work with entire load histories and various levels of simplification have been adopted. It is important to recognise, however, that some information is lost during each simplification step and engineering judgement must be used to justify each step. The first task is to identify individual load cycles from a complex variable amplitude load history. The most common method for identifying individual cycles is the so-called rainflow count method (Endo et al., 1967; Dowling and Socie, 1982). The procedure is well documented in many engineering textbooks (Stephens et al., 2001; Gurney, 2006; Dowling, 2007) and will not be duplicated here. For long variable histories, the results are conveniently presented in the form of a matrix or histogram in which cycles of similar magnitude and mean stress are grouped together into classes and cycles smaller than a



3/23/11 1:47:56 PM

212


defined lower limit are ignored. Figure 8.2 presents an example of a 32 ¥ 32 rainflow matrix presented as a histogram. In this figure it is easy to see that the majority of the load cycles have mean stresses near zero, but that a number of small cycles may have large compressive or tensile mean stresses. During cycle counting, the time information of the history and order of cycles is lost. in the absence of a corrosive environment, this information has a negligible effect. Owing to the high residual stresses that often exist in welded structures in the as-welded condition, mean stress information is normally not included in the fatigue analysis procedure. From this observation it follows that mean stress information can be ignored and that the rainflow histogram can be presented as a two-dimensional cycle count and/or exceedance diagram. Figure 8.3 shows the data from Fig. 8.2 presented in this form. The cycle count histogram presents the number of cycles of a specified size while the exceedance diagram presents cycles equal to or greater than a specified size. Exceedance diagrams provide a convenient means for defining some of the statistical information found in variable amplitude load spectra. stress range exceedance can be written as a Weibull-type distribution: È Ê Ds ˆ k ˘ ln [[N N (Ds )] = ln (N tot ) Í1 – Á ˜ ˙ ÍÎ Ë Ds max ¯ ˙˚

8.1

Cycles 100 000 10 000 1000 100

0

10

20 40 Stress range (% of max.)

20 60 80

–10 100

1

10 0 Mean stress

–20

8.2 Example of a 32 ¥ 32 rainflow cycle count histogram.



3/23/11 1:47:57 PM


213

100 Cycles Exceedance cycles

Ds (%)

80 60 40 20 0 1

10

100

1000 Cycles

10 000

100 000

1 000 000

8.3 Cycle distribution diagram and cycle exceedance diagram for the rainflow histogram of Fig. 8.2.

where N(Ds) is number of cycles with ranges exceeding Ds, Dsmax is the largest stress range in the load history, Ntot is the number of cycles in the load history and k is the Weibull shape parameter. Figure 8.4 shows the influence of the Weibull shape parameter on the resulting cycle distribution and exceedance distribution. In both figures the total number of cycles is 100 000, but the lower k value greatly increases the number, and expected fatigue damage, of small cycles in the load history. It can be noted that Eq. 8.1 defines a continuous distribution but Fig. 8.4 presents results discretised into 32 range classes as would be the case following rainflow counting. For many realistic load histories, the number of small cycles may be extremely large and, for practical reasons, may be excluded both during fatigue assessment and during laboratory testing. Often an omission level, DsL, defined as a fraction of the maximum stress range in the spectrum, is used to define the size of smallest stress cycles to be considered. Figure 8.5 shows exceedance diagrams for three spectra with the same k and Ntot but with alternate DsL. By varying these three variables, k, Ntot and DsL, a wide variety of variable amplitude load histories can be characterised for analysis or testing. It was natural that many early studies of variable amplitude fatigue with random load histories borrowed concepts and nomenclature from signal processing and vibration analysis. For this reason some nomenclature found in literature is slightly different from that presented here. The reader should be aware that the term clipping ratio is 1/DsL and the shape parameter is sometimes defined as 1/k rather than k.



3/23/11 1:47:57 PM

214

Fracture and fatigue of welded joints and structures 100 Cycles Exceedance cycles

Ds (%)

80 60

k = 1.0 40 20 0 1

10

100

1000 Cycles

10 000

100 000

100 Cycles Exceedance cycles

80

Ds (%)

60 k = 2.0 40 20 0 1

10

100

1000 Cycles

10 000

100 000

8.4 Examples of cycle distribution and cycle exceedance diagrams using the Weibull shape parameter.

8.2

Fatigue damage and assessment for variable amplitude loading

8.2.1

Assessment based on S–N curves

Cycle counting provides the first important tool for assessing fatigue during variable amplitude loading; the second important tool is a method for assessing cumulative damage. The earliest work on cumulative damage assessment has been attributed to Palmgren (1924) and later independently developed by Miner (1945). The Palmgren–Miner rule simply states that an individual stress cycle, which is part of a variable amplitude load history, will contribute the same fatigue damage as that same cycle when it is part of a constant amplitude load history. Mathematically this is expressed as 8.2 S ni = D N f,i



3/23/11 1:47:57 PM


215

100 DsL = 0 DsL = 0.15

80

DsL = 0.30

Ds (%)

60 40

k = 1.0 Ntot = 100 000

20 0 1

10

100

1000 Cycles

10 000

100 000

8.5 Three sample spectra with identical Ntot and shape parameters (k = 1) but different DsL.

where D = 1.0 at failure, ni is the number of cycles of size Dsi and Nf,i is the number of constant amplitude cycles to failure for the structure subjected to Dsi. The great advantage of Eq. 8.2 is its simplicity. However, this simple rule attributes very little or zero fatigue damage to cycles with stress ranges below the constant amplitude knee point. In many variable amplitude load situations a significant portion of the fatigue cycles are below the constant amplitude knee point and Eq. 8.2 becomes non-conservative. Haibach (1970) was among the first researchers to address the question of the damage contribution of small cycles as part of a loading spectrum. To account for the influence of small cycles, he postulated a continuously decreasing fatigue limit for components as damage is accumulated. His expression for a decreasing fatigue limit results in the extension of the S–N curve below the constant amplitude knee point using a reduced slope damage line of m2 = (2m1 – 1) where m1 is the slope of the S–N slope above the knee point. This reduced damage slope for small cycles within a spectrum is now a common feature in many design codes including the most recent IIW recommendations (Hobbacher, 2009). The Haibach principle was a step forward compared with the original Palmgren–Miner but was based on very little experimental data. A significant amount of variable amplitude testing became possible only later with the introduction of computer-controlled closed loop testing systems. A number of studies have revealed the difficulties with both the original Palmgren–Miner rule and the Haibach modification. Several extensive studies in Germany (Schütz and Heuler, 1993; Berger et al., 2002) have shown that fatigue life was consistently overpredicted when estimations were based on linear damage accumulation rules and constant amplitude testing. Many researchers have



3/23/11 1:47:58 PM

216


proposed modifications of Eq. (8.2) or entirely new concepts to damage accumulation during variable amplitude loading. Fatemi and Yang (1998) surveyed and categorised many cumulative damage rules and report more than 50 alternate hypotheses. Many of these were developed specifically to account for the effect of cycles below the constant amplitude knee point. None of these hypotheses has shown to be both easy to use and generally applicable and Eq. (8.2) is used with the simple modification that, at failure, D ≤ 1.0. The damage assessment principles recommended by the IIW are summarised with the help of Fig. 8.6. For stress cycles with ranges greater than the stress corresponding to the knee point, the variable and constant amplitude curves have identical slopes m1 = 3. For cycles below this stress range an assumed slope m2 = (2m1 – 1) = 5 is used. Equation (8.2), using Nf,i from Fig. 8.6, is employed with D = 0.5. Some experimental studies on very long-life variable amplitude fatigue loading of welded structures where the majority of fatigue cycles were below the constant amplitude knee point have suggested that the knee point should not be used and that an S–N line with constant slope should be used for all stress cycles m2 = m1 = 3 (Fisher et al., 1993; Dahle, 1994; Marquis, 1995). The influence of small amplitude stress cycles in a variable amplitude spectrum is a greater problem in cases where the shape parameter, k < 1; see Fig. 8.5. In such cases the proportion of fatigue damage contributed by the small cycles is greater. The knee point recommended by the IIW was increased from 5 ¥ 106 to 1 ¥ 107 cycles in its most recent revision. This provides a conservative fatigue assessment in most cases. Ds 1

200

100

m1 = 3

Above the knee point the same curve is used Knee point

Constant amplitude loading 10% reduction per decade, m3 = 22

Variable amplitude loading

20

1 m2 = 5 (2m1 – 1)

10 104

105

106 107 Nf, cycles to failure

108

109

8.6 The bi-linear S–N design curve according to the IIW. (FAT 80)



3/23/11 1:47:58 PM


217

another parameter that is frequently used to characterise a variable amplitude load history is the irregularity factor: I=

Nm N tot

8.3

where Ntot is the total number of cycles in a load history and Nm is the number of positive up-crossings through stress level m. in most cases m will be chosen as either zero or the mean stress of the largest cycle in the variable amplitude history. For example, with m = 0, the load histories in Figs 8.1(a, b) will have I = 1.0, the load history in Fig. 8.1(d) will have I ª 0.6 and the load history in Fig. 8.1(e) will have I < 0.1. it is generally observed that as the variable amplitude loading becomes more irregular, i.e., as I decreases, the computed damage, D, at failure also decreases. ibsø and agerskov (1993), for example, have proposed that D = 2I – 1 can be used in design. This was shown to fit data variable amplitude histories 0.745 < I < 1.0. For I = 0.745 this relation gives D = 0.49 which is nearly identical to the iiW recommendation D = 0.5. Very little test data are available for welded structures with load histories representing I < 0.5 and the iiW recommendations contain a warning that D may be as low as 0.2. After individual cycles have been identified and the concept of fatigue damage is defined, a further simplification that is often performed is to present the load spectrum as a single ‘equivalent’ value (Dover, 1979). The concept is that the information from a stress histogram can be simplified into a single constant amplitude equivalent stress range value given by: 1

Ds eq

m1 Êq m1 ˆ S D s n i i Á i =1 ˜ =Á ˜ N tot Á ˜ Ë ¯

8.4

where Ntot is the total number of cycles in a load history, q is the total number of stress classes in the histogram, Dsi is the stress range for stress class i, ni is the number of cycles of size Dsi and m1 is the slope of the S–N line used to assess fatigue life. The equivalent stress range, Dseq, therefore represents a constant amplitude stress range that would give the same number of cycles to failure as the complex load history. as with the simple Palmgren–Miner rule, Dseq does not consider the complex interaction between cycles with different amplitudes and mean stresses. However, Dseq can be used as a method for reducing



3/23/11 1:47:58 PM

218


a complex stress history into a single number that is easily compared. For example, samuelsson (1988) developed the twin concepts duty, which is a function of service life and Dseq, and capacity which depends on the global and local geometry of the weld. These are random variables that can be used to assess failure probabilities for complex welded structures. The equivalent stress range concept in Eq. 8.4 is easily derived assuming a constant S–N slope and D = 1. Niemi (1997) has presented a modified form of Eq. 8.3 which allows the equivalent stress range to be computed for bi-linear s-N lines and for various values of D: 1

Ds eq

Ê S D s im1 ni + D s k(m1 –m2 ) · S D s (jm2 )n j ˆ m1 =Á1 · ˜ S ni + S n j ËD ¯

8.5

where Dsk is the stress range associated with the knee observed during constant amplitude loading, ni is the number of cycles of stress Dsi where Dsi > Dsk, nj is the number of cycles of stress Dsj where Dsj < Dsk, m1 is the slope of S–N line above the knee point, m2 = 2m1 –1 is the slope of S–N line below the knee point and D is the damage sum, e.g. D = 0.5. The value Dseq computed from either Eqs. 8.4 and 8.5 can be used to compute life directly from an S–N line with constant slope m2 = m1 = 3. The equivalent stress concept is the final simplification step for a variable amplitude time history. in each step some information is lost at the expense of convenience. Table 8.1 summarises the simplifying assumptions and the information lost. The first level of simplification, i.e. rainflow cycle counting, is nearly always performed. However, even this common step loses information on load frequency content which may be significant for corrosion fatigue studies or structures with potential vibration problems. Table 8.1 Steps applied for simplifying a stress vs. time history and the results of the simplification Level of Information lost simplification

Result

0

None

Stress (or strain) vs. time history

1

Cycle sequence, frequency content

Rainflow count

2

Mean stress data

Exceedance diagram or cycle stress range diagram

3

Cycle distribution, number of cycles Equivalent stress and omission level



3/23/11 1:47:59 PM


219

Cycle sequence information is also lost, which may be important if mean stress changes occur at regular intervals or if cycle ranges vary according to a regular pattern. The loss of mean stress data associated with the second level of simplification is not usually too important for welded structures, but may significantly influence fatigue life in the cases of highly irregular load histories. If level 2 simplification is justified, then level 3 simplification is also normally a good assumption. However, the lost information may be important when deciding on a suitable omission level or when assessing potentially harmful effects caused by large tensile or compressive stresses. Example 8.1. Figure 8.7 shows three alternate spectra with identical block lengths, Ntot = 250 000 cycles, and DsL = 15% but with different shape parameters. Table 8.2 summarises the stress range and number of cycles of different sizes for the three load spectra assuming that the largest cycle in the spectrum corresponds to Dsmax = 150 MPa. It is assumed that the fatigue damage can be assessed with the variable amplitude S–N curve shown in Fig. 8.6 which corresponds to FAT 80. This curve intersects Nf = 2 ¥ 106 cycles at Ds = 80 MPa and Dsk = 46.7 MPa at 1 ¥ 107 cycles. The second assumption is that the S–N slope does change at the knee point but continues at a constant slope m2 = m1 = 3. Table 8.2 also shows the computed damage per cycle based on these two alternate assumptions. The influence of spectrum shape on the computed fatigue life and Dseq are summarised in Table 8.3. As is seen in the table, the single slope and bi-linear S–N lines have only a minor influence for the k = 2.0 spectrum, i.e. computed fatigue life is reduced by less than 6%. By contrast, for the k = 0.5 spectrum the single slope S–N assumption results in a predicted 45% reduction in fatigue life as compared with the bi-linear curve. Thus, the S–N slope below the knee point is much 150 k = 0.5 k = 1.0 k = 2.0

125

Ds (MPa)

100 75 Ntot = 250 000 50 DsL = 0.15Dsmax 25 0 1

10

100

1000 Cycles

10 000

100 000 1 000 000

8.7 Three sample spectra with identical Ntot and DsL but different shape parameters.



3/23/11 1:47:59 PM

220


Table 8.2 Summary of the stress range and number of cycles of different sizes for the three load spectra assuming that the largest cycle in the spectrum corresponds to Dsmax = 150 MPa. The computed damage per cycle based on these two alternate assumptions is also shown i

Dsi

k = 0.5 ni

k = 1.0 ni

k = 2.0 ni

Damage per cycle

32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11

150.0 145.3 140.6 135.8 131.1 126.4 121.7 116.9 112.2 107.5 102.8 98.0 93.3 88.6 83.9 79.2 74.4 69.7 65.0 60.3 55.5 50.8

1 1 0 1 1 2 3 3 5 8 12 17 26 40 63 97 155 251 411 691 1 182 2 073

1 1 1 2 3 4 7 11 17 26 42 66 103 163 255 401 630 990 1 556 2 445 3 842 6 038

1 2 4 7 13 26 47 85 150 256 427 692 1 095 1 684 2 522 3 674 5 209 7 176 9 608 12 494 15 763 19 282

3.3 3.0 2.7 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.1 9.2 7.9 6.8 5.8 4.8 4.0 3.3 2.7 2.1 1.7 1.3

j

Dsj

Knee point

10 9 8 7 6 5 1–4

46.1 41.4 36.6 31.9 27.2 22.5 –

3 740 6 968 13 485 27 317 58 555 134 892 0

9 487 14 909 23 428 36 814 57 851 90 907 0

22 836 26 143 28 867 30 651 31 161 30 125 0

Ntot

–

250 000

250 000

250 000

¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥

10–6 10–6 10–6 10–6 10–6 10–6 10–6 10–6 10–6 10–6 10–6 10–7 10–7 10–7 10–7 10–7 10–7 10–7 10–7 10–7 10–7 10–7

D/cy, m2 = 5 9.4 5.5 3.0 1.5 6.7 2.6 –

¥ ¥ ¥ ¥ ¥ ¥

10–8 10–8 10–8 10–8 10–8 10–9

D/cy, m2 = 3 9.6 6.9 4.8 3.2 2.0 1.1 –

–

¥ ¥ ¥ ¥ ¥ ¥

10–8 10–8 10–8 10–8 10–8 10–8

–

Table 8.3 Influence of spectrum shape and equation for Dseq on the computed fatigue life Equation 8.4

Equation 8.5

Spectrum

Dseq

Computed spectrum repetition to failure

Dseq

Computed spectrum repetition to failure

k = 0.5 k = 1.0 k = 2.0

29.2 34.5 49.3

165 99 34

23.9 31.0 48.1

298 137 36



3/23/11 1:48:00 PM


221

more important for spectra with exceedance diagrams with k < 1 where the proportion of fatigue damage contributed by the small cycles is greater.

8.2.2

Assessment based on crack propagation

airframe structures are frequently designed using a damage-tolerant approach which means that crack-like defects of a specific size are assumed to exist. Fatigue assessment then becomes a task of evaluating the expected growth rate of these defects. it is not surprising, therefore, that much of the important research on crack growth during constant and variable amplitude loading has been developed in this industry. in order to predict fatigue crack propagation, numerous empirical or semi-empirical equations have been proposed to relate fatigue crack growth rate data to the parameter DK. among the proposed equations, the Paris–Erdogan relationship (Paris and Erdogan, 1963) is commonly accepted and used in practice for a wide range of mode i cracks. This relationship is given as da = CDK m ddN N

8.6

where da/dN is the crack extension per cycle, DK is the stress intensity factor range and C and m are material constants. This equation is recommended by the iiW for calculating the fatigue crack propagation rate of welded joints made of steel or aluminium (Hobbacher, 2009). Procedures for integrating Eq. 8.6 are found in many basic fatigue textbooks. For design, the crack growth coefficient, C, is replaced by the characteristic value, C0, corresponding to the 95% survival probability value. if, however, crack propagation assessment is being made of specific components, it may be more appropriate to use the 50% survival probability value, Cm. in most cases Cm ª C0/3. in variable amplitude loading, there will invariably be a number of cycles with very small DK. in such cases it is necessary to introduce the threshold stress intensity range, DKth. Equation 8.6 then becomes m forr DK > DK tthh da = C0 DK fo dN dN 0 ffor DK £ DK th

8.7

da = C (DK m – DK m ) 0 th ddN N

8.8

or

Values of C0, m and DKth for weldable C–Mn steel and aluminium are summarised in Tables 8.4 and 8.5. From these tables it is noted that both crack depth and stress ratio, R, influence DKth. More details of fracture mechanics-based fatigue assessment are given in Hobbacher 2009.



3/23/11 1:48:00 PM

222


Table 8.4 IIW recommended parameters for crack propagation analysis of welded steel structures (Hobbacher, 2009) Units

Coefficient and exponent

DKth R ≥ 0.5

0.5 > R ≥ 0 R < 0

Surface crack depth < 1 mm

DK (N mm–2/3) da/dN (mm/cycle)

C0 = 5.21 x 10–13 m = 3.0

63

170–214R

170

£ 63

DK (MPa ÷m) da/dN (m/cycle)

C0 = 1.65 ¥ 10–11 m = 3.0

20

5.4–6.8 R

5.4

£ 2.0

Table 8.5 IIW recommended parameters for crack propagation analysis of welded aluminium structures (Hobbacher, 2009) Units

Coefficient and exponent

DKth R ≥ 0.5

C0 = 1.41 ¥ 10–11 21 DK (N mm–2/3) da/dN (mm/cycle) m = 3.0 DK (MPa ÷m) da/dN (m/cycle)

C0 = 4.46 ¥ 10–10 0.7 m = 3.0

0.5 > R ≥ 0

R2 for this factor. ∑ Clamping of the plates during fabrication that may prevent distortion. In other words, restraining distortion during welding may lead to higher levels of residual stress. Standard welding texts provide guidance on ways on minimising distortion [e.g. 28] through weld design and sequencing, as severe distortion in thinner structures can lead to unwanted changes in natural frequency of the structure (with possible consequences for vibration-induced fatigue crack growth) and occasionally to buckling. In practice, the level of tensile residual stress at a weld depends on weld process (solid state or fusion) and the ratio of thermal strain during cooling to the yield strain in the material [27]. Thus for C–Mn steels the thermal © Woodhead Publishing Limited, 2011


3/23/11 1:49:16 PM

280


s–

s+

x Diffracted beam

y z

Incident beam

Strain sT s+

s– Welding direction

sL

Friction stir welding (FSW) line

10.1 (a) Definition of a typical weld geometry (in this case a friction stir weld) and coordinate system. (b) The associated typical residual stress profiles in the longitudinal sL and transverse sT direction at mid-distance respectively. Also shown is the gauge volume defined by the incident and diffracted beam, and the associated direction of measured strain (ST in this case).

contraction strain is around five times greater than the yield strain [27] and yield magnitude residual strains are likely at fusion welds. In titanium and aluminium welds residual stress magnitudes may be less than half of the yield strength, while in friction stir welding peak tensile residual stresses may be less than a quarter of the yield strength. Stresses parallel with the weld run generally have higher magnitudes than transverse or short transverse stresses. These points are amplified in Figs 10.2–10.5 below. Figure 10.2 gives three-dimensional residual stress profiles as a function of transverse position for a seven-pass metal inert gas (MIG) fusion weld made with overmatched filler metal in a 12 mm plate of high strength roller quenched and tempered steel [29]. In this diagram sL is the longitudinal stress parallel to the weld run (x), sT is the stress transverse to the weld (y) and sST is the stress in the short transverse or through-thickness direction (z) and the profiles correspond to z = 5 mm. The inset in Fig. 10.2 shows a cross-section of the weld macrostructure. The measured parent plate (PP)



3/23/11 1:49:17 PM

Assessing residual stresses

281

800

sl

600

st sst

Stress (MPa)

400

z = 5 mm

200

0

–200

–50

–40

–30

–20 –10 0 10 20 Distance from weld centreline (mm)

30

40

50

10.2 Three-dimensional stress profiles in a 12 mm plate of 800 MPa yield strength RQT701 steel at 5 mm depth. Error bars vary from about 100 MPa in the weld metal to 20 MPa in the parent material. The inset shows a macrograph of the weld cross-section.

yield strength was 801 MPa and the tensile strength 846 MPa, while the weld metal yield strength was 880 MPa. Peak tensile residual stress magnitudes in the weld are some 600 MPa in the longitudinal direction and around 400 MPa in the transverse direction. Peak tensile values of the longitudinal residual stress are around 600 MPa, or some 75% of PP yield strength, while peak tensile values of the transverse residual stress are around 50% of the PP yield strength. Figure 10.3 presents residual stress data from the same 12 mm welded plate as a function of depth (z) in the plate, which is a standard way of presenting such data. Curves for longitudinal (sL), transverse (sT) and short transverse (sST) stresses are given in the diagram at three transverse positions in the plate, relative to the weld centreline (y = 0 mm). While the diagrams shown in Figs 10.2 and 10.3 are both useful, the most widely quoted characteristics of residual stress distributions tend to be peak tensile values. In terms of assessing fatigue and fracture behaviour of welds, however, it is more appropriate to consider the actual residual stresses near potential crack initiation sites, which are often the weld toe positions which may not coincide with peak tensile residual stresses.



3/23/11 1:49:17 PM

282


700 Toe is z = 0 mm Root is z = 12 mm

600

y = 0.5 mm sL

500

y = 0.5 mm st y = 0.5 mm sst

Stress (MPa)

400

y = 5.5 mm sL

300

y = 5.5 mm sT y = 5.5 mm sST

200

y = 11.5 mm sL

100

y = 11.5 mm sT y = 11.5 mm sST

0 –100 –200 –300 0

2

4

6 8 Plate depth z (mm)

10

12

10.3 Residual stress data as a function of measurement depth in the 12 mm plate. Curves are presented for transverse (y) positions of 0.5 mm, 5.5 mm and 11.5 mm, where 0 mm is the weld centreline.

Similar values of peak tensile residual stress to those observed in the 12 mm plate were measured in thicker 50 mm plate of S460ML thermomechanically rolled steel [15]. Data were obtained at selected positions through the thickness in a 14-pass submerged arc weld. The yield strength in this steel was 488 MPa and the tensile strength was 572 MPa. Weld metal tensile strength was some 560 MPa. Figure 10.4 shows residual stress data in the three coordinate directions measured some 22 mm below the weld crown. Peak values of tensile residual stress are elevated by triaxal constraint and are similar in value to those measured in the thinner plate, at least in the longitudinal and transverse directions at this mid-depth in the plate, but are much lower near the crown or the root of the weld. Thus fairly constant peak values of tensile stress may occur in steel welds across a wide range of plate thickness. Figure 10.5 gives typical longitudinal and transverse stresses for a friction stir weld made in 6 mm plate of 5083-H321 aluminium alloy [17] and peak tensile values of longitudinal residual stress (100 MPa) are about 40% of the yield strength of the alloy. Peak tensile values of the transverse stress are around 40 MPa, i.e. some 16% of yield strength. Measured residual stresses in fusion welded 8 mm plate of 5083-H321 are very similar in magnitude to those shown in Fig. 10.5 [24].



3/23/11 1:49:17 PM


283

800 Longitudinal stress Transverse stress Normal stress

Residual stress (MPa)

600

400

200

0

–200

–400 –100

–80

–60

–40 –20 0 20 40 Transverse distance from weld (mm)

60

80

100

10.4 Residual stresses in a 50 mm plate of S460ML steel measured some 22 mm below the weld crown using neutron diffraction. The inset shows a macrograph of the weld cross-section.

10.3

Modification of stresses after welding

A wide range of factors may modify residual stresses at a particular welded joint and a number of these have been summarised by Leggatt [27]. Major contributors to stress redistribution include post-weld machining operations, thermal treatments and mechanical treatments such as vibration stress relief or autofrettage. Post-weld heat treatment (PWHT) may cause a 50–75% reduction in peak residual stress values [e.g. 27] with the overall shape of stress distributions remaining similar. The influence of service loading is highly variable, depending on the cyclic stress–strain curve of the material, the magnitude of applied loads and the number of load cycles experienced, and it is hard to draw any definitive general conclusions. Work by Lachmann et al. [30] on butt welds in 10 mm thick plates of S355 structural steel (minimum yield strength = 355 MPa) demonstrated a considerable reduction in peak residual stresses after a single cycle of applied load with magnitudes between 350 and 550 MPa. The reduction ranged from some 25% at 350 MPa load to around 90% at 550 MPa. Residual stresses continued to decrease slightly for around 10 load cycles then stabilised over the next several thousand cycles before starting to decrease again. Iida and Takanashi [22] considered the relaxation of residual stresses around a hole drilled in bead-on-plate welds made in 11 mm plates of 316



3/23/11 1:49:18 PM

284


Longitudinal stress transverse section (MPa)

150

Retreating side

Advancing side 348 436 617 870

100

50

0

–50

–100

–150 –80

–60

–40 –20 0 20 40 Transverse distance from weld centreline (mm) (a)

Retreating side Transverse stress transverse section (MPa)

rpm rpm rpm rpm

60

80

Advancing side 348 436 617 870

60

rpm rpm rpm rpm

40

20

0

–20 –80

–60

–40 –20 0 20 40 Transverse distance from weld centreline (mm) (b)

60

80

10.5 (a) Longitudinal residual stresses in friction stir welds made in 6 mm plate of a 254 MPa proof strength 5083-H321 aluminium alloy. Tool travel speed was 185 mm/min and data for four different rotational speeds are shown, (b) Transverse residual stresses in friction stir welds made in 6 mm plate of a 254 MPa proof strength 5083-H321 aluminium alloy. Tool travel speed was 185 mm/min and data for four different rotational speeds are shown.



3/23/11 1:49:18 PM


285

stainless steel and 9 mm plates of SM490A structural steel (yield strength 415 MPa). They found that cyclic loading of the welds (in the range of 50–90% of yield strength) gave broadly similar results to those found in Lachmann et al. [30], i.e. a significant reduction in residual stresses in the first load cycle and a further steady decay up to >106 load cycles. The initial reduction in peak residual stress magnitude depended on the applied load and cycling with an applied stress ratio R = 0 producing a larger amount of stress relaxation than using R = –1. This sequence of relaxation of residual stresses, i.e. a substantial decrease in the first load cycle, followed by a further much slower decrease in residual stresses has also been reported for cyclic loading of shot peened specimens [23]. In their work, Zhuang and Halford [23] developed a predictive residual stress relaxation model which should be applicable to welded structures, based upon the Bauschinger effect and a back-stress based plasticity stressstrain relationship. Work by James et al. [24, 25] has considered the influence of 1 and 100 cycles at various applied loads using stress ratios R = 0.1 and –1, on the residual stresses in FS and MIG welds in 8 mm 5083-H321 aluminium plates. In this strain hardening alloy they found that fatigue loading accentuated the compressive and tensile peak stresses, while retaining the overall form of the residual stress field. There was an associated translation of the stress distribution to be more tensile and increasing the number of applied fatigue cycles from 1 to 100 tended to increase this translation effect. Hence fatigue cycling did not relax the residual stresses in these plates, but rather led to a two-fold increase in peak tensile residual stresses for an applied bending stress of 150 MPa (R = 0.1), and a four-fold increase for an applied bending stress of 250 MPa. These bending stresses correspond to observed fatigue lives of around 107 cycles and 105 cycles respectively in 40 mm wide specimens.

10.4

Measurement

Several excellent reviews and books dealing with residual stress measurements have recently been published [26, 31–35]. They cover the nature and origins of residual stresses [31], their measurement [26, 32] and the selection of an appropriate technique [33]. They are not focused on welds and therefore consider the full range of techniques available to measure residual stresses, including mechanical techniques such as surface contour or curvature [14] and hole drilling [36, 37], diffraction techniques [38], and other methods (e.g. ultrasonic and magnetic techniques). The most advanced and precise techniques for mapping residual stresses non-destructively in welds involve synchrotron X-ray and neutron diffraction strain scanning, which are particularly useful when the data are used to



3/23/11 1:49:18 PM

286


validate finite element (FE) models. The use of neutron diffraction techniques to measure residual stresses in thick multipass welds dates back more than 20 years [39], while high spatial resolution synchrotron X-ray radiation has been applied to welds for perhaps a decade [40]. Access to these instruments is open to all sectors of engineering but may require some introduction to the use of these non-routine instruments, with both commercial proprietary and publicly funded access modes being available. Applications of these techniques encompass basic welding research through to the high technology, safety-critical industrial sectors, e.g. aircraft engines and components. The use of neutron diffraction techniques for residual stress measurement has been codified in an ISO VAMAS document [41]. A very significant amount of residual stress measurement on welded structures in heavy engineering (e.g. offshore platforms) and ground vehicles (cars and railway carriages) still relies on strain rosettes and hole drilling techniques [e.g. 42, 43]. Although the equipment used in these techniques is portable, and relatively straightforward in application, they provide a limited number of near-surface data points confined to locations >0.5 mm from stress concentrators such as weld toes. This rest of this chapter will outline the application of these three techniques to residual stress measurement.

10.4.1 Neutron and synchrotron X-ray stress measurements Similar to conventional laboratory X-ray stress measurements, neutron and synchrotron X-ray measurements of stress are based on the principles of diffraction, i.e. Bragg’s law. To this end, diffraction uses the underlying crystal structure as an internal strain gauge which deforms (elastically) under residual or applied stresses. Radiation sources exist only at national or international large-scale facilities such as those mentioned in Section 10.1. Virtually every large scale facility now supports at least one dedicated instrument (a so-called ‘beam line’) for materials engineering research. The key difference between neutron and synchrotron X-ray radiation, and conventional X-rays is that in the latter case the measurement region and gauge volume are confined to the very near surface area, whilst the penetration capabilities of neutron and brilliant (highly intense) ‘hard’ (highly energetic) X-rays allow the gathering of residual stress measurement several millimetres or centimetres into the material. The concept of a gauge volume is therefore a cornerstone of the techniques, and it generally defines the spatial resolution. It is the volume element defined by the intersection of the incident beam and the section of the material which is visible to the detector through secondary slits (conventionally called the diffracted beam) (see Fig. 10.1). Generally speaking, only diffraction events from the material contained with this volume element contribute to the residual stress measurement. In



3/23/11 1:49:18 PM


287

practice, apart from the inelastic scattering, a certain amount of multiple (elastic) scattering can occur, which increases with increasing path length in the sample, both of which add to the background noise in the measure diffraction peaks. While it is straightforward to choose a cuboidal or rectangularly shaped gauge volume with the neutron method, the coupling of penetration capability to wavelength (energy) of X-rays causes the gauge volume to become more elongated the further one penetrates into the sample. this coupling is due to the fact that harder X-rays (with shorter wavelength) have greater penetration capabilities but significantly reduce the diffraction angle. The elongation of the diamond-shaped gauge volume can be estimated by 1/tan q where tan q = a/b = r, the ratio between the short and long axis of the gauge volume. Hence for a diffraction angle of 9.8° such as occurs for the aluminium 311 reflection at 60 keV beam energy, the elongation of the gauge volume amounts to 1/r = 0.085 or nearly 1:12. By moving the sample around this fixed measurement volume, diffraction peaks and hence strain in different areas of the sample can be measured and stresses are inferred from the measured strain using elasticity theory. Owing to the high intensity and the ability to focus X-rays, spatial resolutions of micron size can in principle be achieved, while the practical limit in terms of spatial resolution for neutron techniques tends to be on the millimetre scale. When comparing residual stresses obtained from numerical analyses with those measured using diffraction techniques the differences between the ‘calculation volume’ (related to mesh element size) and the gauge volume have to taken into account [44]. Diffraction peaks contain a wealth of information about the material. The exact peak profiles are the result of material properties such as texture, grain size, microstrain, dislocations, temperature, as well as instrumental contributions such as energy band width of the incident beam and slit size. Nonetheless, the measured peak position (lattice spacing) is principally a function of the unstrained crystal lattice parameter of the material and the applied or residual macrostresses. Bragg’s law (l = 2d sin q) determines the position of a diffraction peak and the strain e = Dd/d can be obtained by either angular dispersive (varying q) or energy dispersive (varying l) methods for both neutrons and synchrotron X-rays. thus for a given orientation and position in the sample, the calculated tensor strain component

efy =

d – d0 d0

depends on the unstrained lattice parameter and is measured in a particular direction fy at a particular point in the sample. in order to determine the stresses at this position it is, in principle, necessary to resolve the strains in many directions, in order to solve the fundamental equation of diffraction stress analysis: © Woodhead Publishing Limited, 2011


3/23/11 1:49:19 PM

288


efy = e11 cos2 f sin2 y + e12 sin 2f sin2 y + e22 sin2 f sin2 y

+ e13 cos f sin 2y + e23 sin f sin 2y + e33 cos2 y

Knowing the elastic strain tensor and basic (isotropic) material properties such as Young’s modulus E and Poisson’s ratio v, one can calculate the stresses using elasticity theory. It is clear that diffraction-based stress measurement techniques rely critically on the unstrained lattice parameter d0 against which measured lattice spacings are compared to estimate the strain. In homogeneous materials, many techniques exist which can provide reliable estimates of the unstrained lattice parameter through, for example, far-field measurements in areas where very low residual stresses exist or via stress and moment balancing techniques. In inhomogeneous samples, such as welds made with filler metal of a different composition from the parent alloy, or welds in materials which undergo substantial microstructural changes during welding, such as age-hardening alloys, the local variation of the unstrained lattice spacing (or parameter) has to be measured directly [45]. Typical measurement times to determine one strain component in a particular direction lie in a range from the order of seconds (synchrotron) to the order of minutes (neutron). The increasing brilliance of synchrotron X-rays has rapidly reduced counting times to acquire a single diffraction peak, opening up the opportunity to undertaken in situ and parametric studies, such as the one shown in Fig. 10.6 [46]. Residual stress measurement using neutron or synchrotron X-ray diffraction techniques arguably provides the most accurate stress data (typical uncertainties of tens of MPa), and therefore merits special recognition. Additionally, neutron and synchrotron X-ray facilities are adjusting to the increasing demand from the materials engineering community by providing easier access to these techniques, and improving the support facilities for applied materials and engineering research. Because of their particular nature, these techniques are best employed via key experiments in strategic research and development, rather than used in routine inspection.

10.4.2 Strain rosettes and hole drilling The hole drilling technique is a semi-destructive and cost-effective method used to determine residual stress and its use dates back as far as 1934, but there has only been widespread use since the 1950s and the advent of bondable strain gauges. Grant et al. [47] give a useful overview of incremental hole drilling techniques [36, 37] which are used to determine the stress variation with depth in components with steep near-surface stress gradients. A number of papers have also dealt with the difficulties attendant on hole drilling techniques (e.g. hole ovality and inclined holes), while the uncertainties



3/23/11 1:49:19 PM


6

0

1

Sample x dimension (mm) 0 1 2

289

2 (ii)

(i) 5

a-lattice

4 3 2 1 0

8 (iii)

(iv) 6

4

4 c-lattice

5

3

2

¥ 10–3

Sample y dimension (mm)

6

2

0

1

–2

0

–4

6

(v)

(vi)

4 3 2

(311) d–hydride

5

1 0

(a)

10.6 This figure shows the stresses around the crack tip in a singleedge notched tension (SENT) specimen of hydrided Zircalloy [44]. These images highlight the capabilities of the synchrotron X-ray diffraction techniques in terms of spatial resolution, phase sensitivity and speed of measurement. (a) applied stresses in the loaded condition; (b) residual stresses in the unloaded condition. (Colour images are available on request from the authors.)



3/23/11 1:49:19 PM

290


6

0

1

Sample x dimension (mm) 2 0 1

2 (ii)

(i) 5

a-lattice

4 3 2 1 0

3 (iv)

(iii)

2

5 1 c-lattice

4 3

0

2

¥ 10–3

Sample y dimension (mm)

6

–1

1 –2 0 –3

6

(v)

(vi)

(311) d–hydride

5 4 3 2 1 0

(b)

10.6 Continued

in the technique have been summarised in a recent code of practice [48]. Various methods can be used to produce the stress relieving hole, including high speed drilling, abrasive hole drilling and electrodischarge machining (EDM).



3/23/11 1:49:19 PM


291

Standard equipment for high speed hole drilling utilises a specialised turbine and drill bit mounted on a platform that has a controllable vertical displacement. Voltage output from the strain rosette is passed through a strain amplifier and data logging equipment. Modern equipment allows drilling in steps of 0.01 mm or less thus providing accurate assessment of near-surface relieved strains in the component. The technique involves gluing a multiple element strain gauge rosette (normally three gauges) to a component at the position where the stresses are to be measured. Various types of specialised strain gauge rosette have been developed for residual stress assessment using hole drilling. The advantage of using these rosettes is that the calibration constants and subsequent data reduction methods are readily available. The choice of strain gauge configuration would generally depend on the depth to which the stress needs to be determined, the required accuracy of the measurement and the type (or geometry) of the component to be investigated. If a blind hole is to be drilled into the component, it is done in incremental steps to a depth of the same order of size as of the hole diameter, and the readings are recorded of the relaxed strains arising from the drilling process [47]. A number of calculation methods have been developed and are currently in use to transform the measured strains into residual stress magnitudes and some of these analytical techniques are compared by Lord et al. [49]. All of these were developed in an attempt to solve specific problems in stress analysis and it therefore means that each of the methods has limitations. One of the main considerations is whether or not there is a uniform stress in the component, i.e. where there is little or no change in stress magnitude throughout the depth of the drilled hole. Using uniform calculation methods when the stresses are non-uniform, even in blind-hole drilling can lead to significant errors where the maximum value calculated will be less than the actual value [50]. For uniform stresses and incremental hole drilling ASTM Standard E837-08 [50] describes a method which is easy to use and accurate. The depth below the surface over which the relieved strains can be detected and stresses calculated is approximately equal to the diameter of the drilled hole. This arises because the gauges simply are not sensitive enough to measure the relieved strains any deeper into the component. The purpose of drilling the hole incrementally is to determine whether the relieved stress is indeed uniform over the drilling depth and Hausler et al. [51] consider the accuracy of determining the uniformity of stress with hole depth. More often than not the stress distribution within a component will be non-uniform with depth and Grant et al. [47] give details of the techniques used to calculate stresses in such cases. They also discuss a number of issues that can influence the accuracy of measurements, which include: ∑

operator skill and expertise which affect all processes from gauge application to measurement and strain conversion; © Woodhead Publishing Limited, 2011


3/23/11 1:49:19 PM

292

∑ ∑ ∑

∑ ∑ ∑


surface preparation which influences the stress distribution, especially near the surface, and if not carefully done may induce additional surface stresses; the type of drilling technique as stresses may be induced due to the cutting process; gauge size – smaller gauges are better for near surface stress, but more sensitive to errors such as misalignment and hole size measurement errors; larger gauges allow stress detection to greater depths, but are less localised than the smaller gauges; spacing of holes – errors of up to 7% have been recorded when holes were drilled within 4.5¥ the hole diameter from each other; alignment of the drill bit with the centre of the strain gauge – the calibration factors are determined by assuming the hole is perfectly concentric with the strain gauge; alloy properties can influence the cutting process and therefore the measurements.

Despite these potential difficulties, automated incremental hole drilling systems provide high levels of reliability and repeatability and are widely used in industrial practice to obtain ‘representative’ residual stress data at welds (and in many other components). The work by Iida and Takanashi [22] has already been mentioned above and other studies have used hole drilling experiments to examine the effect on residual stresses of PWHT [52].

10.5

Conclusions

It is hoped that the rather brief overview given above of diffraction and hole drilling techniques used to measure residual stresses at welds will allow a reader to assess which method may be most useful in any particular application. This chapter has therefore sought to provide a number of key references where further information can be obtained and, in particular, to outline the capability of synchrotron and neutron diffraction techniques in providing detailed information on residual stresses at welds. Representative data have been presented for solid state welds in aluminium plates 6–8 mm thick and fusion welds in steel plates up to 50 mm thick. Some of the difficulties associated with the gauge volume concept in diffraction measurements have been discussed. A considerable amount of further research is necessary to expand the knowledge base of residual stresses at welds, in both the aswelded and post-weld heat-treated conditions, and to explore the effect of weld improvement techniques alongside the stabilisation and shake-down of stresses that occurs under cyclic loading. Nonetheless, it is clear that the amount of data that can be relatively easily obtained and its high level of reliability and repeatability open the door to improvements in the handling of residual stresses by structural integrity codes. Detailed examination of © Woodhead Publishing Limited, 2011


3/23/11 1:49:19 PM


293

residual stresses in specific large components of complex geometry is now also routinely possible.

10.6

Acknowledgements

The authors gratefully acknowledge the allocation of neutron diffraction beam time on the SALSA instrument at the ILL (experiments 7-01-167 and 7-01-196), and synchrotron diffraction beam time at the ESRF on the ID31 instrument (experiment ME-992).

10.7

References

1. BS 7910: 1997, Guide on Methods of Assessing the Acceptability of Flaws in Structures, British Standards Institution, London. 2. BS EN 1993-1-9:2005, Eurocode 3. Design of steel structures: Fatigue, British Standards Institution, London. 3. BS EN 1999-1-3:2007, Eurocode 9. Design of aluminium structures: Structures susceptible to fatigue, British Standards Institution, London. 4. R6 – Revision 4 (2004), Assessment of The Integrity of Structures Containing Defects, British Energy, Gloucester. 5. W S Pellini (1983), Guidelines for fracture-safe and fatigue-reliable design of steel structures, The Welding Institute, Abington. 6. P J Bouchard (2008), Code characterisation of weld residual stress levels and the problem of innate scatter, International Journal of Pressure Vessels and Piping 85 pp.152–165. 7. R C Wimpory, C Ohms, M Hofmann, R Schneider and A G Youtsos (2009), Statistical analysis of residual stress determinations using neutron diffraction, International Journal of Pressure Vessels and Piping 86 pp.48–62. 8. R P Skelton, I W Goodall, G A Webster and M W Spindler (2003), Factors affecting reheat cracking in the HAZ of austenitic steel weldments, International Journal of Pressure Vessels and Piping 80 pp.441–445. 9. H E Hånninen (2007), Stress corrosion cracking, Comprehensive Structural Integrity, Elsevier, Chapter 6.01, pp.1–29. 10. S A Shipilov (2008), Stress corrosion cracking and corrosion fatigue: a record of progress, 1873–1973, Environment-induced Cracking of Materials, Elsevier, pp.507–557. 11. M N James (2009), Designing against LMAC in galvanised steel structures, Engineering Failure Analysis 16 pp.1051–1061. 12. C M Sonsino (2009), Effect of residual stresses on the fatigue behaviour of welded joints depending on loading conditions and weld geometry, International Journal of Fatigue 31 pp.88–101. 13. R H Leggatt, D J Smith, S D Smith and F Faure (1996), Development and experimental validation of the deep hole method for residual stress measurement, Journal of Strain Analysis for Engineering Design, 31 3, pp.177–186. 14. M B Prime (2001), Cross-sectional mapping of residual stresses by measuring the surface contour after a cut, Journal of Engineering Materials and Technology 123 pp.162–168.



3/23/11 1:49:19 PM

294


15. M N James, S-P Ting, D G Hattingh and H Lombard (2005), Residual Strains in Thick Higher Strength Steel Weld Using SALSA, Experiment Report 7-01-167, Institut Laue-Langevin, Grenoble, France. 16. M N James, S-P Ting, M Bosi, H Lombard and D G Hattingh (2009), Residual strain and hardness as predictors of the fatigue ranking of steel welds, accepted by International Journal of Fatigue 31, pp.1366–1377. 17. H Lombard, D G Hattingh, A Steuwer, M N James (2009), Effect of process parameters on the residual stresses in AA5083-H321 friction stir welds, materials science and engineering A 501 pp.119–124. 18. M Peel, A Steuwer, M Preuss and P J Withers (2003), Microstructure, mechanical properties and residual stresses as a function of welding speed in aluminium AA5083 friction stir welds, Acta Materialia 51 pp.4791–4801. 19. G A Webster and A N Ezeilo (2001), Residual stress distributions and their influence on fatigue lifetimes, International Journal of Fatigue 23 pp.S375–S383. 20. P J Bouchard (2008), Residual stresses in lifetime and structural integrity assessment, Encyclopedia of Materials: Science and Technology, Elsevier, pp.8134–8142. 21. M N James, D J Hughes, Z Chen, H Lombard, D G Hattingh, D Asquith, J R Yates and P J Webster (2007), Residual stresses and fatigue performance, Engineering Failure Analysis 14 pp.384–395. 22. K Iida and M Takanashi (1998), Relaxation of welding residual stresses by reversed and repeated loadings, Welding in the World 41 4 pp.27–40. 23. W Z Zhuang and G R Halford (2001), Investigation of residual stress relaxation under cyclic load, International Journal of Fatigue 23 pp.S31–S37. 24. M N James, D J Hughes, D G Hattingh, G Mills and P J Webster (2009), Residual stress and strain in MIG butt welds in 5083-H321 aluminium: as-welded and fatigue cycled, International Journal of Fatigue 31 pp.28–40. 25. M N James, D J Hughes, D G Hattingh, G R Bradley, G Mills and P J Webster (2004), Synchrotron diffraction measurement of residual stresses in friction stir welded 5383-H321 aluminium butt joints and their modification by fatigue cycling, Fatigue and Fracture of Engineering Materials and Structures 27 pp.187–202. 26. P J Withers and H K D H Bhadeshia (2001), Residual stress Part 1 – measurement techniques, Materials Science and Technology 17 pp.355–365. 27. R H Leggatt (2008), Residual stresses in welded structures, International Journal of Pressure Vessels and Piping 85 pp.144–151. 28. ASM Handbook, Volume 6, Welding, Brazing and Soldering (2003), ASM International, Materials Park, OH. 29. M N James, P J Webster, D J Hughes, Z Chen, N Ratel, S-P Ting, G Bruno and A Steuwer (2006), Correlating weld process conditions, residual strain and stress and mechanical properties for high strength steel – the role of neutron diffraction, Materials Science and Engineering A427 pp.16–26. 30. C Lachmann, T Nitschke-Pagel and H Wohlfahrt (2000), Characterisation of residual stress relaxation in fatigue loaded welded joints by X-ray diffraction and Barkhausen noise method, Materials Science Forum 347–349 pp.374–381. 31. P J Withers and H K D H Bhadeshia (2001), Residual stress Part 2 – nature and origins, Materials Science and Technology 17 pp.366–375. 32. P J Withers, M Turskia, L Edwards, P J Bouchard and D J Buttle (2008), Recent advances in residual stress measurement, International Journal of Pressure Vessels and Piping 85 pp.118–127. 33. F A Kandil, J D Lord, A T Fry and P V Grant (2001), A Review of Residual Stress



3/23/11 1:49:19 PM


34. 35.

36.

37.

38. 39.

40.

41. 42.

43.

44.

45.

46.

47.

48.

49.

295

Measurement Techniques – A guide to technique selection, NPL Report MATC(A)04, National Physical Laboratory, Teddington. M E Fitzpatrick and A Lodini (2003), Analysis of Residual Stresses Using Neutron and Synchrotron Radiation, Taylor & Francis, London. M Hutchings, P J Withers, T M Holden and T Lorentzen (2005), Introduction to the Characterisation of Residual Stress by Neutron Diffraction, CRC Press, Taylor & Francis, London, New York. G S Schajer (1988), Measurement of non-uniform residual stress using the hole drilling method. Part 1 – stress calculation procedures, Transactions of the ASME, 110 October 1988 pp.338–343. G S Schajer (1988), Measurement of non-uniform residual stress using the hole drilling method. Part 2 – practical application of the integral method, Transactions of the ASME, 110 October 1988 pp.344–349. P J Withers (2008), Residual stresses: measurement by diffraction, Encyclopedia of Materials: Science and Technology, Elsevier, pp.8158–8169. D J Smith, R H Leggatt, G A Webster, HJ McGillivray, P J Webster and G Mills (1988), Neutron diffraction measurements of residual stress and plastic deformation in an aluminium alloy weld, Journal of Strain Analysis, 23 4 pp.201–211. R A Owen, R V Preston, P J Withers, H R Shercliff and P J Webster (2003), Neutron and synchrotron measurements of residual strain in TIG welded aluminium alloy 2024, Materials Science and Engineering A346 pp.159–167. ISO/TTA 3:2001(E), Polycrystalline materials – determination of residual stresses by neutron diffraction, 2001, International Organisation for Standardisation, Geneva. D Kosteas (1988), Estimating residual stresses and their effect in welded aluminium components in fatigue, Analytical and Experimental Methods for Residual Stress Effects in Fatigue, ASTM STP 1004, R L Champoux, J H Underwood and J A Kapp (eds), American Society for Testing and Materials, Philadelphia, PA, pp.122–130. J R Cho, B Y Lee, Y H Moon and C J Van Tyne (2004), Investigation of residual stress and post weld heat treatment of multi-pass welds by finite element method and experiments, Journal of Materials Processing Technology 155–156 pp.1690– 1695. J W H Price, A Ziara-Paradowska, S Joshi, T Finlayson, C Semetay and H Nied (2008), Comparison of experimental and theoretical residual stresses in welds: the issue of gauge volume, International Journal of Mechanical Sciences 50 3 pp.513–521. D J Hughes, M N James, D G Hattingh and P J Webster (2003), The use of combs for evaluation of strain-free references for residual strain measurements by neutron and synchrotron X-ray diffraction, Journal of Neutron Research 11 pp.289–293. A Steuwer, J E Daniels and M J Peel (2009), In situ crack growth studies of hydrided Zircaloy-4 on a single-edge notched tensile specimen, Scripta Materialia, 61, 4, pp. 431–433. P V Grant, J D Lord and P S Whitehead (2006), The Measurement of Residual Stresses by the Incremental Hole Drilling Technique, NPL Good Practice Guide No. 53, National Physical Laboratory, Teddington. R Oettel (2000), The determination of uncertainties in residual stress measurement (Using the hole drilling technique), Manual of Codes of Practice for the Determination of Uncertainties in Mechanical Tests on Metallic Materials: Code of Practice No. 15, Standards Measurement & Testing Project No. SMT4-CT97-2165.42. J D Lord, A T Fry and P V Grant (2002), A UK Residual Stress Intercomparison



3/23/11 1:49:20 PM

296


exercise – An Examination of the XRD and Hole Drilling Techniques, NPL Report MATC (A)98, May 2002. 50. ASTM Standard E837-08 (2008), Standard Test Method for Determining Residual Stresses by the Hole Drilling Strain Gage Method, American Society for testing and Materials, Philadelphia, PA. 51. H Hausler, G Konig and H Kockelmann (1987), On the accuracy of determining the variation with depth of residual stresses by means of the hole drilling method, Residual Stresses in Science and Technology, pp.257–264. 52. H T Kanga, Y-L Leeb, and X J Sun (2008), Effects of residual stress and heat treatment on fatigue strength of weldments, Materials Science and Engineering, A497 1–2 pp.37–43.



3/23/11 1:49:20 PM

11


P. J. H a a g e n s e n, Norwegian University of Science and Technology (NTNU), Norway

Abstract: Methods for improving the fatigue performance of welded structures are reviewed, and the suitability of individual methods for industrial applications are evaluated. Methods involving geometry modification and residual stress obtained by peening are dealt with in some detail. Methods involving weld shape modification are introduced during the initial welding process. The influence of various factors such as base material strength, residual stress, variable amplitude service loading and specimen size are examined. In this chapter recommendations are given for a unified approach for the derivation of S–N curves for use in design with regard to the influence of main influencing parameters such as base material strength, size, weld and joint geometry, and stress concentration factor of the joint. Key words: improvement methods, good design practice, grinding, TIG dressing, peening methods, repair, life extension.

11.1

Introduction

Fatigue failures in welded structures generally initiate at locations of high structural stress where crack-like defects as well as high tensile welding stresses are present. The major part of the fatigue life is therefore spent in the growth stage with a very short crack initiation stage. Employing good design practice can reduce local stress peaks and extend the fatigue life in many cases. Additionally, the use of welding processes and fabrication methods that improve the local geometry at the weld and result in small defects may also improve fatigue performance. However, these improvements may be insufficient or impracticable to execute in a fabrication environment and the use of more extensive weld modification techniques are then necessary in order to obtain large increases in fatigue life. This paper provides a review of commonly used weld improvement techniques such as grinding, tungsten inert gas (TIG) remelting and peening techniques, including recently developed high frequency peening devices, e.g. ultrasonic impact treatment (UIT). Developments in welding technology such as the low transformation temperature (LTT) weld metals are also reviewed. Additionally, recently developed grades of steels with microstructural barriers to crack growth that provide greater resistance to fatigue are discussed. 297 © Woodhead Publishing Limited, 2011


3/23/11 1:50:33 PM

298


The performance of improvement techniques under various conditions such as variable amplitude loading, high peak stresses and corrosive conditions is discussed. The question of larger increases in fatigue performance improved welds in high strength steels is also discussed. While improvement techniques such as cold rolling and shot peening are used routinely in the fabrication of mechanical components in e.g. automotive and aerospace industries, applications of similar techniques in welded structures are still limited. In fact, the main use of improvement techniques has been in repair and upgrading of ageing structures such as bridges and offshore structures. However, with the introduction of the International Institute of Welding (IIW) guidance on improvement techniques there is now scope for more widespread use of such techniques. Recent examples of successful applications to marine structures are described and commented on. Future areas of research and development to obtain improved fatigue performance of welded structures are identified.

11.2

Fatigue strength of welded joints

From a fatigue strength consideration a welded joint represents a weak link in a structure. While the fatigue limit in terms of stress range for a polished specimen is approximately equal to the ultimate tensile strength (UTS) of the material, the fatigue strength of unnotched plates with as-rolled surface is of the order of one-third of this (Gurney, 1979). As indicated in Fig. 11.1, which shows typical S–N curves for steels used in welded structures, this is reduced further if a stress concentration, e.g. a hole, is introduced. However, if the cross-section is increased by a welded attachment the fatigue strength drops significantly, as illustrated in Fig. 11.1, and there is no longer a clear relationship between the fatigue strength and the ultimate tensile strength. It is evident from the S–N diagram in Fig. 11.1 that the welded joint is substantially weaker in fatigue than the notched specimen even though the stress concentration factors at the welded joint and the machined notch are of similar magnitude. In addition to the effect of the weld as a stress raiser caused by the change of section, two other important factors contribute to the poor fatigue performance. Firstly, the welding process always results in weld defects, e.g. lack of fusion, and pores. Defects at or near the weld toe such as slag inclusions or lack of penetration are particularly harmful, because they effectively act as small cracks in an area of high local stress and therefore nearly eliminate the crack initiation phase of the fatigue life. Since crack propagation rates in steel alloys are virtually independent of static strength a fatigue crack grows at the same speed in a welded high strength steel as in a lower grade steel. For this reason the allowable fatigue strength is the same for all grades of steel in current design rules for welded structures (Maddox, 1991). Secondly, welding residual stresses are built up



3/23/11 1:50:33 PM


1 1 Stress range (MPa)

100

1

~8

299

Fatigue limit ª 0.3UTS

~5 Fatigue limit ª 0.3UTS/Kt

3

50

Fatigue limit = 40 to 80 MPa independent of UTS

UTS = ultimate tensile strength Kt = stress concentration factor of notch 10 104

105

106 Cycles

107

108

11.1 Typical fatigue strength of unwelded plate, notched plate and welded plate material, schematic.

during contraction of the weld metal. Tensile residual stresses of at least yield stress magnitude are formed at the weld, with the result that the local stress at the weld fluctuates down from the yield stress when external loading is superimposed. The fatigue performance of as-welded joints is therefore significantly reduced by the welding residual stresses. Short range stresses are formed when the weld metal cools and shrinks. Shrinking is resisted by the cool metal plates and tensile and compressive stresses are introduced; see Fig. 11.2. In addition to the local welding stresses long range or global stresses are set up due to constraint from adjacent structural members by the use of force during fit-up; see Fig. 11.3. Global residual stresses act over the entire structure and cannot be relaxed by heat treatment unless the entire structure is stress relieved. From the above discussion it can be concluded that the low fatigue strength of welded joint is associated with a very short crack initiation period which is generally found to be in the range of about 10–20% of the total life, depending on the method of observation and definition of the crack length at the end of the initiation period. Comparing this with a crack initiation period of more than 90% typically observed for smooth unwelded specimens there is obviously scope for a substantial increase in life by



3/23/11 1:50:34 PM

300


delaying crack initiation. Additionally, tensile residual stresses are always present and contribute significantly to the low fatigue strength of welded joints. This description of the problems related to the fatigue performance of welded joints also points towards possible solutions, which could involve the following strategies for delaying crack initiation: ∑ Remove crack-like defects at the weld toe. ∑ Reduce the stress concentration at the weld. ∑ Remove harmful tensile welding residual stresses or better, introduce compressive stresses. However, post-weld improvement techniques may not only be complicated to perform but they are also likely to increase fabrication costs significantly; therefore efforts should be made to increase the fatigue strength in the design stage and during fabrication. Possible means for increasing the fatigue strength are illustrated in Fig. 11.4. Some of the more obvious means for improving the fatigue strength by design and fabrication are briefly described in the following sections but the Peak stress at weld toe

Nominal stress

Cold lap

Undercut Crack-like defect

Hydrogen crack

Heat-affected zone (HAZ) Fusion line

Lack of penetration Lack of fusion (a)

11.2 Main conditions that determine the fatigue strength of welded joints: (a) defects; (b) residual stresses (after Haagensen, 1985).



3/23/11 1:50:34 PM


301

Tension

Compression

Tension

Transversal residual stress

Compression

Longitudinal residual stress

(b)

11.2 Continued

emphasis is on improvement methods, either applied during fabrication or as post-weld treatments.

11.3

Increasing the fatigue strength by improved design

As indicated in Fig. 11.4 the first step to obtain a long fatigue life is to avoid unwanted loads induced by resonance and vibration. Resonance is often a problem for structures that experience wind loading, e.g. highway structures for signs and lightning poles, or heavy tower structures, e.g. for wind turbines.



3/23/11 1:50:34 PM

302


11.3 Global residual stresses introduced by the use of force during fit-up. Good design practice • Minimise fatigue loads, e.g. by avoiding resonance and vibration • Use connections with low stress concentration factor • Place welds in areas of low stress • Protect against corrosion

High quality fabrication • Materials suitable for welding • Welding process giving sound welds • Optimise groove and weld geometry • Highly qualified welders

Weld improvement • Apply during fabrication, including the use of special materials for plates and filler material • Use post-weld improvement techniques

High fatigue strength

11.4 Factors that contribute to higher fatigue strength in welded structures.

Seawater currents may induce resonance in pipes, e.g. in risers or free spanning pipelines. While the prediction of vibration conditions is possible for single elements, the problem is much more complex for multi-member systems such as piping in energy-producing plants which may be excited by a wide frequency spectrum. The problems involved in mitigating unwanted fatigue loads are outside the scope of this survey, as are the problems associated with fatigue strength reduction by corrosion. In Fig. 11.4 the next step is to optimise the structure with respect to stress concentrations. Increased fatigue strength can be obtained by paying attention



3/23/11 1:50:35 PM


303

to good detail design, particularly by lowering the stress at the weld or by moving the weld outside stress concentrations. Good detail design involves minimising local stresses, e.g. by avoiding eccentricities and secondary bending moments. Welds should be placed in areas of low stress, i.e. outside stress concentrations. In members subjected to bending, fatigue critical details such as attachments, cover plates or cut-outs should be placed at or near the neutral axis. Placing such details in areas of compressive stress will not necessarily mitigate the problem, since it is the applied stress range, not the mean stress that has the strongest influence on fatigue life of welded details. Examples of good detail design are shown in Figs 11.5 and 11.6. Guidelines for good design practice have recently been published by the European Convention of Constructional Steelwork (ECCS, 2000). Some design guidance is included in fatigue design recommendations, i.e. details with low stress concentrations are given higher design classes than similar details with more abrupt transitions; examples are shown in Fig. 11.5.

1

4

1:4

1:4

Improved design

11.5 Improved structural details (adapted from ECCS, 2000). Non-uniform flow of stress. Only suitable for static load

Welds moved to areas of low stress. Smooth transition

Welds reduced and moved. The material must have good formability

Increasing fatigue strength

11.6 Improved structural details, with permission (Sperle et al., 1996).



3/23/11 1:50:35 PM

304


11.3.1 Improved fabrication methods As noted before the fatigue performance depends on the stress concentration created by the weld, and therefore various techniques have been tried to reduce the local stress at the weld toe. One such technique is weld profiling which is included by the American Welding Society (AWS, 1996). Weld profiling is a method that is an integral part of the welding process itself. This is obviously attractive from a production point of view since there is no need to perform an additional treatment of the weld with a different type of equipment, which would increase costs and complicate inspection. The use of special electrodes with improved wetting and flow characteristics is another possibility for improving the weld geometry, and the improvements obtained are of the same order of magnitude as for controlled profile welds; see earlier reviews (Haagensen, 1985, 1996; Manteghi and Maddox, 2004). However, the use of such electrodes is difficult in positional welding so the practical application is limited. Improved weld profiles In the AWS Structural Welding Code (AWS, 1996) a low stress concentration factor is aimed for by controlling the overall shape of the weld to obtain a concave profile and by requiring a gradual transition at the weld toe. The ‘disc test’ or ‘dime test’ was originally specified by AWS to ensure an acceptable weld. Although modified later (AWS, 1994, D1.1) the basic requirements are to a radiused shape of the weld and a requirement to the notch at the weld toe. If the weld does not pass the so-called disc test at the weld toe or at the interbead notches (crevices), remedial grinding has to be carried out. The baseline data for the AWS improved profile X1 curve were obtained from tests on tubular joints in the early 1970s; apparently no tests were made on flat plate joints. According to the AWS the designer can use a higher curve if profile control is applied, if not he has to use the lower X2 curve. Tests were made in France (Bignonnet, 1987) and Norway (Haagensen, 1985) on planar joints (transverse fillet welds) with controlled profiles. The test results show very similar improvements in fatigue strength, generally between 25% and 30% at long lives. European tests on tubular joints with improved welds have given mixed results, and in the early United kingdom offshore steel Research Project (UKOSRP) and European Coal and Steel Company (ECSC) programmes no effect of weld profile control was found, while later Dutch tests gave three times longer fatigue lives for tubular joints with improved profile and ground weld toe. Tests on tubular joints with welds according to AWS and special controlled weld profiles (CWP) with longer leg lengths gave lives that were four times longer for the CWP joint than the AWS profile joints, for the same hot spot range (Dijkstra and Noordhoek, 1985) Similar



3/23/11 1:50:35 PM


305

results have been obtained in British tests on tubular joints (Maddox et al., 1995), i.e. the AWS improved profile alone gives little or no improvement. However, significant improvements are obtained in tubular joints if profile control involves a longer leg length that moves the weld toe into a region of lower stress, or when the weld toe is ground. In the latter case the interbead crevices may require grinding as well (Maddox et al., 1995; Karé, 1989). Lawrence and co-workers have experimented with a similar concept of moving the weld into an area of lower stress (Dimitrakis and Lawrence, 2001). This concept involves the extension of wrap-around welds at the ends of fillet-welded longitudinal attachments, called stress diffusers. The principle is shown in Fig. 11.7. The shape of weld terminations was optimised by finite element (FE) analyses. Fatigue testing of the improved welds were reported to give 32% higher fatigue strength at 2 million cycles than the standard configuration in Fig 11.7a. However, the extra production time may limit the use of this method. Another factor which has been shown to extend the fatigue life of butt welds is the waviness of the weld toe line (Chapetti and Otegui, 1995). In welds with high waviness cracks are initiated only at the crests of the waves and this means a large degree of mismatch between the cracks, which delays crack coalescence and gives longer fatigue lives (Chapetti and Otegui, 1995). This effect could possibly explain the fact that the service lives of welds made by automatic welding processes are usually considerably shorter than the lives of manual welds (Gurney, 1979). The effect is illustrated in Fig. 11.8. Up to 50% longer fatigue lives were reported for optimised wave shapes (Chapetti and Otegui, 1995, 1997).

11.4

Improvements obtained by special plate material, filler materials or welding methods

11.4.1 Special plate materials Increased fatigue strength can be obtained by steel materials that offer higher resistance to crack propagation. One example is the so-called Fatigue Crack

Weld (a)

(b)

11.7 Fillet weld terminations: (a) standard condition; (b) with stress diffusers (adapted from Dimitrakis and Lawrence, 2001).



3/23/11 1:50:35 PM

306

Fracture and fatigue of welded joints and structures (a)

(b)

Stress

Stress

Weld toe irregularity

11.8 Butt welds with different waviness; initiation and crack growth occurs earlier in the straight weld toe line in (a) than in case (b) where many cracks initiate separately at each peak along the weld toe line (after Chapetti and Otegui, 1995, 1997).

Arrester (FCA) steel (Konda et al., 2003). These steels typically consist of a mixed ferrite and bainite microstructure. The phase boundaries between bainite and ferrite give higher resistance to crack growth by crack branching, resulting in higher fatigue strength both for unwelded plate and weldments (Konda et al., 2003). FCA steels are typically produced with specified minimum yield strength of 355 MPa, and have been applied in the repair of cracked ship structures. FCA steels have not yet reached a stage of development for general use; the fatigue properties of these steels are therefore discussed in more detail in Section 11.7 on future developments.

11.4.2 Special weld metals Electrodes with favourable flow chararacteristics Special filler materials were developed in Japan in the 1970s for improved fatigue strengths due to good wetting and flow properties (Kado et al., 1975; Kobyashi et al., 1977). The electrodes are manual metal arc electrodes with flux that give favourable weld to plate transition and large toe radii and therefore an overall improved weld shape. The large toe radii obtained with these electrodes give a substantial reduction in the stress concentration factor, typically from around 3 to 1.2–1.5 for fillet welds. Using these electrodes in test programmes aimed at improving the fatigue performance of high strength steels with 400 to 800 MPa yield strength, improvements from 50% to 85% were obtained, the largest increases in fatigue strength being



3/23/11 1:50:35 PM


307

reported for the higher strength steels. Tests on plate T-joints in Norway gave improvements of approximately 25% (Haagensen, 1985). The main concern about the special electrodes is their use in positional welding where the easy flow of the filler material may be a disadvantage. This type of electrode has therefore not attained widespread use. Electrodes that give compressive residual stresses Some filler materials undergo a martensitic transformation at relatively low temperatures and result in a stress field with compressive stress transverse to the weld. These favourable stresses give higher fatigue strength. The early versions of these LTT electrodes (Ohta et al., 1994) had poor welding properties and resulted in unfavourable weld geometries. However, later versions with different chemical composition have shown greater promise for use, especially under loading conditions without high peak loads, or conditions that do not give stress corrosion cracking. Further discussion of LTT electrodes is given in Section 11.6.3. Nickel-based electrode Recent tests on carbon steel pipes and carbon steel pipes with stainless steel cladding have shown some promise of achieving higher than usual fatigue strength for pipes in risers and pipelines (Kristoffersen et al., 2008). Further discussion on fatigue strength of pipes with nickel-based filler material is found in the section on future developments in improvement methods.

11.5

Special welding methods

Friction stir welding (FSW) is a recently developed joining method in which no filler material is added, and the base material is not melted. Instead, heat developed from a rotating pin softens the plate edges to the point where material from the two plates are mixed or stirred together at the weld line. FSW joints exhibit excellent fatigue properties compared with conventional welds as illustrated in Fig. 11.9 which shows a fatigue strength close to that of the base material (Haagensen et al., 2001).

11.6

Post-weld improvement methods

As noted before the three most important factors reducing the fatigue strength of welded joint are: ∑

weld geometry – the transition of the cross-section gives a local stress peak;



3/23/11 1:50:36 PM



3/23/11 1:50:36 PM

20 103

50

100

Friction stir welding

300

400

104

MIG on extruded backing

Plasma arc welding

FSW

Base metal

105 106 Number of cycles (N)

Base material

MIG on extruded backing

107

108

TMIG on ceramic backing

11.9 Fatigue strength of friction stir weld compared with data for unwelded plates and conventional welds in 6068 aluminium plates (Haagensen et al., 2001).

Stress range DS (MPa)


∑ ∑

309

weld defects – undercuts and slag intrusions at the weld toe provide early crack initiation; residual stresses – high tensile stresses arising from weld metal shrinkage and from fit up loads reduce fatigue life.

The aim of post-weld improvement methods is to mitigate one or more of these factors. Most weld shape modification methods such as grinding and TIG dressing also remove or reduce weld defects. Mechanical deformation of the weld toe also modifies the shape of the weld, but may also introduce new types of defect. Depending on the main contribution to higher fatigue strength, post-weld improvement techniques can be placed in two main groups: 1. Weld geometry techniques 2. Residual stress techniques Improvement techniques within the two groups are shown in Figs 11.9 and 11.10. Methods that are included in the IIW recommendations on improvement techniques (Haagensen and Maddox, 2007) are indicated in Figs 11.10 and 11.11. Weld improvement techniques have been successfully applied to bridges, offshore structures, ships and land-based structures such as railway cars and earth moving equipment. Wider use has been restricted by the lack of industry guidance. To meet this challenge a working group was formed within IIW Commission XIII – Fatigue in 1990 to provide recommendations for

Burr grinding Machining methods

Disc grinding Water jet gouging TIG dressing

Weld geometry improvement methods

Remelting methods

Plasma dressing Laser dressing

Special welding techniques

Weld profile control (AWS) Special electrodes

11.10 Weld geometry improvement techniques (after Haagensen, 1985).



3/23/11 1:50:36 PM

310

Fracture and fatigue of welded joints and structures Hammer peening

Peening methods

Shot peening Ultrasonic peening

Mechanical methods

Overloading methods

Residual stress Methods

Needle peening

Initial overloading Local compression Thermal stress relief

Thermal methods

Spot heating Gunnert’s method Low temperature transformation electrodes

11.11 Residual stress modification improvement techniques.

the application of improvement techniques to welded steel and aluminium structures. In most other design recommendations, weld improvement techniques are intended to be applied only in connection with repair of structures that have experienced fatigue cracking during service, or new structures that need upgrading during a late stage during construction. In contrast, the IIW design recommendations are intended to provide higher design stresses also for improved new welded structures. In this section the four types of improvement techniques specified in the IIW recommendations are described in some detail, and allowable stresses in terms of S–N curves are shown. Examples of application to real-life structures are described, and new methods showing promise for industrial use are described. The following description of post-weld improvement methods is based on the IIW recommendations.

11.6.1 Weld toe grinding Grinding can be carried out with a rotary burr grinder or disc grinder, the former requiring more time and therefore incurring somewhat higher costs.



3/23/11 1:50:36 PM


311

However, disc grinding removes material at a high rate and welds in thin plates may be damaged. Moreover, the grinding marks are perpendicular to the stress direction and this and the effect on fatigue life is generally somewhat less than for burr grinding. To ensure the removal of slag intrusions grinding has to be extended to a depth of minimum 0.5 mm below the bottom of any visible undercut, as specified in the British design rules for offshore structures (Department of Energy, 1993); see Fig. 11.12. The slight reduction in plate thickness and corresponding increase in nominal stress is insignificant for plates of 10 mm or larger thickness. Thin plates require special attention, and a maximum depth of 2 mm or 7% is imposed, as indicated in Fig. 11.12. Corrosion pitting of the ground metal surface virtually eliminates the benefit of burr grinding. The ground surface must therefore be adequately protected. The protection may be of a temporary nature, as would be the case for a part of an offshore structure which would eventually be submerged and protected by a cathodic protection system. In other cases permanent protection must be provided by other means, e.g. a paint system. Fatigue strength of joints improved by grinding The benefit of weld toe grinding for steel can be claimed only for details in FAT 90 class or lower in the IIW notation for S–N curves. This limitation is due to the fact that the higher classes include non-welded details, the lives of which are not governed by weld toe failure or the welds that have been already been improved, e.g. by grinding the weld flush with the surface. For IIW FAT 90 class or lower details the benefit of burr grinding corresponds to an increase in allowable stress range by a factor of 1.5, corresponding to a factor of 3.4 on life. In addition, it can be assumed that the constant amplitude fatigue limit corresponds to an endurance of 2 ¥ 106. The maximum class is FAT 100, as shown in Fig. 11.13. In cases where the structural stress (hot-spot stress) approach is used, the improvement factor needs to be derived for an equivalent detail using its fatigue class based on nominal stress in conjunction with the limits specified above.

11.6.2 Weld toe re-melting techniques Remelting of the weld toe using either TIG (gas tungsten are welding, GTAW) or plasma welding equipment generally produces large increases in fatigue strength, for several reasons. Firstly, the smoother weld toe transition reduces the stress concentration factor; secondly, slag inclusions and undercuts are almost completely removed; and thirdly, the increased



3/23/11 1:50:36 PM


Grinding depth

r

Original toe

Original profile

Ground profile

r/d > 4

r/t > 0.25

Root

Plate

Depth measurement

Depth gauge

11.12 Burr grinding techniques (Haagensen and Maddox, 2007, with permission from IIW).

t

d

d = min. 0.5 mm below undercut, max. 2 mm or 7% of thickness t

o tt oa d r th ine a um int im ma n i M be


3/23/11 1:50:37 PM

Weld


313

Stress range Ds (MPa)

1000

FAT 160 112 (90) 100 (80) 90 (71) 80 (63) 71 (56) 63 (50) 56 (45) 45 (40) 45 (40)

100

10 1.E+04

1.E+05

1.E+06 Number of cycles, N

1.E+07

1.E+0.8

11.13 Design S–N curves for details improved by weld toe burr grinding in steel structures, variable amplitude loading (Haagensen and Maddox, 2007, with permission from IIW).

surface hardness in the remelted zone has been found to contribute to the higher fatigue strength. The original residual stress field is also changed; however, both tensile as well as compressive residual stresses have been found following TIG dressing. Plasma dressing generally tends to give better results than TIG dressing, which is attributed to the higher heat input and the larger pool of melted metal obtained with plasma dressing (Kado et al., 1975; Shimada et al., 1977). TIG and plasma dressing Standard TIG (GTAW) welding equipment is widely available in welding shops and welders are normally familiar with this method, making it a convenient improvement method, usually performed without any filler material. Guidance for the optimum conditions for TIG dressing in the form of tolerance boxes were developed in the UK (Millington, 1973). Later work



3/23/11 1:50:37 PM

314


in Japan (Kado et al., 1975) confirmed the optimum conditions defined by Millington and the same guidance is used in the IIW recommendations on improvement techniques (Haagensen and Maddox, 2007). Typical heat inputs are relatively low at 1.0 to 1.2 kJ/mm. For the older type C–Mn steels with a relatively high carbon content (Ceq > ~0.40), the low heat input would result in the formation of martensite and excessive hardness levels in the heat-affected zone. A technique involving a second TIG run was developed to temper the first run at the toe, to obtain acceptable hardness levels of less than 300 HV10 (Haagensen, 1978). The second run also contributes to a better weld toe geometry. However, the hardness problem associated with TIG dressing is largely eliminated with the use of modern low carbon steels, but the problem remains in repair of older structures. TIG remelting also introduces a residual stress field, which, like the welding process used for depositing the weld metal, usually gives tensile stresses at the surface; however compressive stresses at the weld toe following TIG dressing have also been reported. The TIG dressing method is illustrated in Figs 11.14 and 11.15. Plasma dressing is similar to TIG dressing. The main difference is a higher heat input which is beneficial because it gives a larger weld pool and therefore a wider and deeper re-melted zone which is more tolerant to variations at the weld toe (Booth and Baxter, 1979). TIG and plasma dressing are sensitive to operator skill, and it is important to clean the weld and plate to avoid pores. In addition to carefully chosen operating conditions such as welding current, welding speed and shield gas flow rate, the chemistry of the weld metal and plate material influence the result. Owing to the complexity of optimising TIG and plasma dressing it is essential that the procedure is validated through a ‘TIG dressing procedure qualification test’, similar to the welding procedure qualification tests that are arranged for welding new combinations of materials and joints. Figure 11.15 shows the appearance of a TIG dressed weld. TIG and plasma dressing are suitable for automated treatment. Figure 11.16 shows equipment for robotic plasma dressing (Alnes, 2004). The magnitude of the improvement for the TIG and plasma improvement techniques depend primarily on the joint severity and also to some extent on base material strength (Haagensen, 1996). Improvements range from about 10% for butt welds in mild steel plates to about 140% for fillet welded high strength steels have been reported in the literature. Typical improvements for medium strength steels are in the range 50 to 70% over the as-welded strength. The increases in fatigue strength for toe grinding and TIG or plasma dressed joints are reported to be of similar magnitude in investigations where the treatments have been compared (Manteghi and Maddox, 2004). TIG dressing is similar to burr grinding in the sense that the increase in fatigue strength is obtained primarily by reducing the stress concentration and



3/23/11 1:50:37 PM


315

11.14 TIG dressing (Haagensen, 1991).

by removing defects at the weld toe, without changing the residual stresses significantly. Therefore the improvements are similar for the two methods and the same benefits in design stresses are given, i.e. the S–N curves in Fig. 11.13 are valid also for TIG dressed welds. As for burr ground joints the benefit of TIG dressing for steel can be claimed only for details in FAT 90 class or lower in the IIW notation for S–N curves; see Fig. 11.13.

11.6.3 Residual stress methods Some improvement in fatigue behaviour is obtained by removing welding residual stresses by post-weld heat treatment, especially if the applied load



3/23/11 1:50:37 PM

316


11.15 Fillet weld before and after TIG dressing (Haagensen, 1991).

cycle is wholly or partly in compression. However, the largest benefits are obtained if compressive residual stresses are introduced. Commonly used residual stress methods are hammer peening, wire bundle (or needle peening) and shot peening. A relatively new method, ultrasonic impact treatment, which has been developed at the Paton Welding Institute has attracted considerable attention in recent years because it is less noisy and less cumbersome to use than hammer and wire peening (Trufiakov et al., 1995; Statnikov, 1997). A similar method, ultrasonic peening (UP), is described in a later section. Hammer peening Hammer peening is usually performed with a pneumatic hammer fitted solid tool with a rounded tip of 3–7 mm radius. Optimum results for hammer peening are obtained after four passes , giving a severely deformed weld toe, with an indentation depth of about 0.2–0.5 mm, providing a simple inspection criterion. Hammer peening is a noisy and tedious operation; however, the increase in fatigue strength is generally higher than for grinding and TIG dressing and the treatment has been widely used in repair and life extension projects (Haagensen et al., 2000). Using a lightweight riveting gun with vibration damping (Fig. 11.17) gives a better working environment. Hammer peening causes deformation to a depth of 3–5 mm and introduces a residual stress that has a maximum about 2 mm below the surface. The groove produced by hammer peening is similar in shape to that resulting from grinding, While the groove may look smooth and shiny, lap-type defects of the order of 0.1 mm deep may be present and cracks initiate at about the same time as in as-welded joints. The main increase in life is



3/23/11 1:50:37 PM


317

11.16 Automated TIG dressing (Alnes, 2004).

therefore due to a longer crack growth stage, not due to a longer crack initiation period. Needle peening In the needle peening treatment compressive residual stresses are induced by repeatedly striking the weld toe region with a bundle of round-tipped rods or needles. Compared with hammer peening, it is generally more suitable when large areas need to be treated, e.g. welds in tubular joints. As in



3/23/11 1:50:38 PM

318


11.17 Examples of pneumatic riveting guns used for hammer peening (Haagensen and Maddox, 2007, with permission from IIW).

the case of hammer peening, the IIW specifications are restricted to plate thickness of 4 mm for steel and 8 mm for aluminium. Figure 11.18 shows typical equipment used for needle peening. UIT and UP These methods are similar to needle peening; the main difference in the equipment is that the rods are excited by an ultrasonic generator which operate at frequencies in the 20–40 kHz range. The rods, however, move at



3/23/11 1:50:38 PM


319

11.18 Typical needle peening equipment (Haagensen and Maddox, 2007 with permission from IIW).

their resonance frequency, which is typically about 200 Hz. Compared with hammer peening the noise is much lower and movement of tool is less, making the equipment more comfortable in use than the other peening techniques. UIT and UP methods have been applied to several bridge retrofitting projects in the United States and Canada. Historical developments and applications of these methods have been described by Statnikov (1997) and Kudryatvsev et al. (2004). High frequency impact treatment (HiFIT) The equipment used is similar to that used in needle peening, the main difference being in a somewhat higher peening frequency (Weich, 2009a). When fitted with a single tool head rather than multiple rods or needles, the HiFIT equipment is very similar to standard pneumatic hammer peening tools used in the past. Fatigue strength of joints improved by peening The improvements for hammer peening are among the highest reported for any improvement methods, with failures sometimes occurring outside the weld. The magnitude of the improvement depends as for most improvement techniques primarily on the joint severity, but also on base material strength. Residual stresses induced by peening are sensitive to high stress peaks which cause stress relaxation and loss of improvement. For this reason the improvements in fatigue strength reported in the literature vary from about 50% to more than 200% (Weich, 2009b). The dependency of peak stress



3/23/11 1:50:38 PM

320


magnitude can be described in terms of R-ratio dependency (Huo et al., 2005; Weich, 2009b). In the IIW Recommendations a factor of 1.5 is allowed for peened steel components. This can only be claimed for details in design Class FAT 90 or lower in the IIW notation for S–N curves. This limitation is due to the fact that the higher classes include non-welded details, the lives of which are not governed by weld toe failure or the welds that have been already been improved, e.g. by grinding the weld flush with the surface. For IIW FAT 90 or lower classes for steel the benefit consists of an upgrading to Category 125 with a constant amplitude fatigue limit at 2 ¥ 106 cycles, as shown in Fig. 11.19. Effect of variable amplitude loading The potential for loss of improvement under variable amplitude loading for components improved by residual stress techniques has been extensively studied

Stress range Ds (MPa)

1000

FAT 160 112 (90) 100 (80) 90 (71) 80 (63) 71 (56) 63 (50) 56 (45) 45 (40) 45 (40)

100

10 1.E+04

1.E+05

1.E+06 Number of cycles, N

1.E+07

1.E+0.8

11.19 Design S–N curves for details improved by hammer peening or needle peening in steel structures, variable amplitude loading (Haagensen and Maddox, 2007, with permission from IIW).



3/23/11 1:50:38 PM


321

(Manteghi and Maddox, 2004; Huo et al., 2005; Wang et al., 2009; Barsoum and Gustafsson, 2009). The loss of effectiveness of the treatment depends on the combination of high stress peaks and the R-ratio that give the largest relaxation of the residual stresses. In the tests conducted by Manteghi and Maddox the increase in fatigue life for hammer peened joints under variable amplitude loading was only higher by a factor of 2, compared with a factor of 8 for constant amplitude loading, whereas Huo et al., found a much lower reduction in fatigue strength caused by variable amplitude loading. Since the fatigue strength improvement benefit of hammer peening is sensitive to the applied stress ratio the benefit in the IIW Recommendation is valid for R ≤ 0.15. For high R-ratio fatigue cycles, R > 0.4, no fatigue strength improvement can be claimed without fatigue testing. For 0.15 < R ≤ 0.28 the benefit for hammer peening is assumed to be the same as for grinding or TIG dressing. i.e. a fatigue class increase of two limited to a maximum design class of FAT 112 for steel and FAT 45 for aluminium. For 0.28 < R ≤ 0.4 the benefit for hammer peening is one fatigue class increase for details with design Class 90 or less for steel or Class 40 or less for aluminium. This is summarised in Table 11.1. Tests on specimens welded with LTT electrodes, e.g. Barsoum and Gustafsson (2009), generally show lower improvement than other residual stress methods in which mechanical deformation is involved. This is likely due to the fact that the weld toe is severely deformed in, for example, hammer peened specimens, giving an improved geometry while there is no geometry improvement in LTT specimens. Other residual stress methods LTT welding electrodes As noted before this type of filler material has recently been developed in Japan to produce high compressive stresses at the weld, and several reports indicate increases in fatigue strength of the same magnitude as for peening methods (Ohta et al., 1999; Miki and Anami, 2001). Miki and Anami Table 11.1 Summary of stress ratio effects on fatigue improvement by hammer peening (Haagensen and Maddox, 2007) Stress ratio

Improvement

R < 0.15

Up three fatigue classes as outlined in the section above

0.15 < R < 0.28

Up two fatigue classes: the same as for burr grinding or TIG dressing

0.28 < R < 0.4

Up one fatigue class for details with design Class 90 or less for steel or Class 40 or less for aluminium

R > 0.4

No improvement or fatigue; testing required if improvement is claimed



3/23/11 1:50:38 PM

322


reported that the effectiveness of the LTT method was slightly lower than for hammer peening, but considerably larger than TIG dressing (Miki and Anami, 2001). Figure 11.20 shows the effect of the martensitic (Ms) transformation on the elongation of the weld metal (ef represents transition strain); in Fig. 11.21 the effect of the residual stresses on the fatigue strength is shown for specimens that had been stress relieved after welding. Combinations of improvement methods The combination of two improvement methods, particularly a weld geometry method and a residual stress method, are likely to give large improvements. One example is TIG dressing and UIT which resulted in the fatigue strength of fillet welds in high strength steel being restored to that of the base material (Haagensen et al., 1998); see Fig. 11.22. Other examples are toe grinding plus hammer peening showing similar improvements. More common combinations are grinding plus shot peening TIG dressing, plus shot peening and AWS weld profile control (Bignonnet, 1987). In such cases the resulting improvement may be double that of a single method. Especially in the low cycle region, where a residual stress method applied alone gives only a small improvement, the combination is effective, probably due to the improved geometry.

Elongation

Developed welding wire

Ms

Conventional welding wire

Ms

ef Shrinkage ef Expansion 0

500

1000 Temperature (°C)

1500

11.20 Relationship between strain and temperature during cooling of LLT filler material (Ohta et al., 1999, with permission from IIW).



3/23/11 1:50:38 PM

Fatigue strength improvement methods Steel HT780 HT580 HT780

Stress range, D/s (MPa)

500

Welding wire 10Cr–10Ni KC60 KM80

No. of passes 3 1 3

323

Condition PWHT As-welded As-welded

Developed welded joints

Conventional welded joints

100

50 104

105 106 Number of cycles to failure, Nf (cycles)

107

11.21 S–N data for HT80 steel specimens with longitudinal attachments (Ohta et al., 1999, with permission from IIW).

Influence of steel strength In the past, results from test various test programmes have indicated that weld improvement methods could give an increase in fatigue strength that was higher for higher strength steels. Examples are shown in Figs 11.23 and 11.24. The increase is assumed to be caused by a longer crack initiation period for ground and TIG dressed welds while higher residual would contribute to the effect for peened joints. However, the variation in the results are large and, as noted before, especially for residual stress methods the improvements are lower under variable amplitude loading. Therefore the observed higher improvements for higher grades of steel have as yet not been introduced in fatigue design rules. If high strength steels are to be used it is recommended to establish a project-specific testing programme that includes test specimens that are similar to the actual structural component with regard to material, fabrication and loading conditions. An example of selecting and optimising an improvement process for specific structural components in mobile cranes has recently been published. Grinding and peening methods have been used extensively to repair or upgrade offshore structures (Haagensen et al., 2000; Haagensen, 2003a). These two applications have been proved by annual inspections to be successful for long periods of time as no cracking has been found in improved welds;



3/23/11 1:50:39 PM

324


(a)

Stress range DS (MPa)

600

TIG+UIT UIT

400

TIG As-welded (NTNU)

200

100

50 104

105 106 Number of cycles (N) (b)

107

11.22 Effect of TIG dressing combined with ultrasonic impact treatment. NTNU = Norwegian University of Science and Technology (Haagensen et al., 1998).

however, cracking has been observed in welds that were considered to have so low levels of stress that improvement was assumed to be unnecessary.

11.7

Future trends

It is expected that the use of welding electrodes that give higher fatigue strength, LTT filler material, and nickel-based electrodes will increase due to the fact that these methods are applied during the fabrication process, thus avoiding extra equipment and special procedures. Also further development of high frequency peening devices is expected to result in lighter and less expensive equipment that is less noisy and more user friendly than traditional hammer peening tools.

11.8

Conclusions

Improvement methods have been examined in many investigations over the last 15–20 years and the following main conclusions may be drawn from a survey of this work: © Woodhead Publishing Limited, 2011


3/23/11 1:50:39 PM


% improvement, stress range at 2 million cycles

250

TIG dressing

200

150

100

50

0 0

Mean line

100 200

250

% improvement, stress range at 2 million cycles

325

300 400 500 600 700 800 900 1000 Ultimate tensile strength (MPa)

Hammer peening

200

150

100 Mean line, TIG dressing

50

0 0

100 200

300 400 500 600 700 800 900 1000 Ultimate tensile strength (MPa)

11.23 Influence of steel strength on improvement in fatigue strength for TIG dressed and hammer peened welds (Bignonnet et al., 1987).



3/23/11 1:50:39 PM

326


250

TIG dressing

Stress range at 2 million cycles

200

150

100

As-welded

50

0

0

200

250

400 600 800 Ultimate tensile strength (MPa)

1000

1200

1000

1200

Ultrasonic impact treatment

Stress range at 2 million cycles

200

150

100

As-welded

50

0

0

200

400 600 800 Ultimate tensile strength (MPa)

11.24 Increase in fatigue strength for higher strength steels (after Haagensen, 1985; data from Lopez Martinez and Blom, 1997).



3/23/11 1:50:40 PM


327

∑ Experimental evidence and fatigue life predictions indicate that substantial increases in fatigue strength can be obtained consistently when improvement methods are used. However, the full potential of weld improvement method can only be obtained if premature failures from other locations, e.g. the weld root, can be avoided. ∑ Residual stress techniques are generally highly effective but introduce challenges with regard to the possibilities of introducing defects that can reduce the effectiveness of the treatment. Residual stress techniques are also susceptible to reduction in effectiveness under variable amplitude loading conditions. ∑ The degree of improvement is generally larger for higher strength steels than for mild steels, but this is not always the case and fatigue testing on actual production components is recommended. ∑ The problems of quality control are similar to those involved in the welding process itself. The question of employing an improvement method is therefore related to costs and the benefit allowed in design rules. ∑ The IIW Recommendations on improvement are based on a large number of investigations in many countries and are therefore suggested as a conservative basis for increasing the design stresses for new structures or for repair and life extension of structures that have suffered fatigue damage.

11.9

References and further reading

AWS, 1994: Structural Welding Code–Steel, ANSI/AWS D1.1-94, 15th Edition. AWS, 1996: Structural Welding Code–Steel, ANSI/AWS D1.1-9, 15th Edition. Alnes Ø, 2004: ‘Fatigue of Welded High Strength Steels’, Master Thesis, NTNU. Barsoum Z and Gustafsson M, 2009: ‘Fatigue of high strength steel joints welded with low temperature transformation consumables’, Engineering Failure Analysis, 16, p. 2186. Bignonnet A, 1987: ‘Improving the fatigue strength of welded structures’, Steel in Marine Structures, Elsevier, Amsterdam. Bignonnet A et al., 1987: ‘The application of shot peening to improve the fatigue life of welded steel structures’, Steel in Marine Structures, Elsevier, 1987. Booth G S, 1983 (Ed.): Improving the Fatigue Performance of Welded Joints, The Welding Institute, Abington. Booth G S and Baxter C F G, 1979: ‘Fatigue tests on plasma dressed fillet welded joints’, Welding Institute Report 87/1979. Chapetti M D and Otegui J L, 1995: ‘Importance of toe irregularity for fatigue resistance of automatic welds’, International Journal of Fatigue 17, pp. 531–538. Chapetti M D and Otegui J L, 1997: ‘Controlled toe waviness as a means to increase fatigue resistance of automatic welds in transverse’, International Journal of Fatigue, 19, pp. 667–675. Department of Energy, 1993: Offshore Installations: Guidance on Design and Construction, UK. Dijkstra O D and Noordhoek C, 1985: ‘The effect of grinding and special welding profile



3/23/11 1:50:40 PM

328


on the fatigue behaviour of large scale tubular joints’, OTC Paper 4866, Offshore Technology Conf., Houston, Texas. Dimitrakis S D and Lawrence F V, 2001: ‘Improving the fatigue performance of fillet weld terminations’, Fatigue & Fracture of Engineering Materials & Structures, 24, Issue 6, p. 429. ECCS, 2000: ‘Good Design Practice. A guideline for fatigue design’, European Convention of Constructional Steelwork Publication No. 105. Fisher J W, 1997: ‘Improved performance through large scale dynamic testing of structures’, IIW Intl. Conf. on Performance of Dynamically Loaded Welded Structures, Welding Research Council, New York. Gurney T R, 1979: Fatigue of welded structures, 2nd Edition, Cambridge University Press, Cambridge. Haagensen P J, 1978: ‘Effect of TIG dressing on fatigue performance and hardness of steel weldments’, ASTM STP 648. Haagensen P J, 1985: ‘Improving the fatigue strength of welded joints’, Chapter 4, Fatigue Handbook. Offshore Steel Structures, Ed. A. Almar Næss, Tapir, Trondheim. Haagensen P J, 1991: ‘Fatigue strength of TIG dressed welded steel joints’, ECSC Conf. Steel in marine structures’, Paris, France, 12–14 June. Haagensen P J, 1996: ‘Weld improvement methods – applications and implementation in design codes’ Int. Conf. on Fatigue of Welded Structures, Senlis, France, 12–14 June. Haagensen P J, 2003a: ‘Improvement techniques for higher weld quality in new design and life extension of aging structures’, IIW Fatigue Seminar, Lappeenranta University of Technology, March. Haagensen, P J, 2003b: ‘Fatigue life extension of structural details of a floating production unit by weld improvement methods’, Proc. of OMAE 2003, 22nd International Conference on Offshore Mechanics and Arctic Engineering, 8–13 June, Cancun, Mexico. Haagensen P J and Maddox S J, 2007: ‘IIW Recommendations on post-weld improvement of steel and aluminium structures’, IIW Doc. XIII-2200r7-07, revised 6 July 2010. Haagensen P J et al., 1998: Introductory fatigue tests on welded joints in high strength steel and aluminium improved by various methods including ultrasonic impact treatment (UIT). IIW Doc. XIII-1748-98. Haagensen P J et al., 2000: ‘Repair and strengthening of the Veslefrikk B floating production platform’, Proc. OMAE 2000, 19th International Conference on Offshore Mechanics and Arctic Engineering, 14–17, February New Orleans. Haagensen P J et al., 2001: ‘Fatigue of light metals’, technical report, SINTEF Materials Technology, Sept. 2001. Hobbacher A, 2008 (Ed): Fatigue design of welded joints and components, IIW Doc. 1965-03/Xv-1127-03. Huo L, Wang D and Zhang Y, 2005: ‘Investigation of the fatigue behaviour of the welded joints treated by TIG dressing and ultrasonic peening under variable-amplitude load’, Int. J Fatigue, 27, pp. 95–101. Kado S et al., 1975: ‘The improvement of fatigue strength in welded high tensile strength steels by additional weld run with coated electrodes’, IIW Doc. XIII-772-75. Kado S et al., 1988: ‘The improvement of fatigue strength in welded high tensile strength steels by additional weld run with coated electrodes’, IIW Doc. XIII-1289-88. Karé R F, 1989: ‘Influence of weld profile on fatigue crack growth in tubular welded joints’, Ph.D thesis, Univeristy College London, Department of Mechanical Engineering. Knight J W, 1978: Improving the Fatigue Strength of Fillet Welded Joints by Grinding and Peening, Welding Research International. Vol.8 (6), 1978. © Woodhead Publishing Limited, 2011


3/23/11 1:50:40 PM


329

Kobyashi K et al., 1977: ‘Improvements in the fatigue strength of fillet welded joint by use of the new welding electrode’, IIW doc. XIII-828-77. Konda N et al., 2003: ‘Development of structural steel with superior resistance against fatigue crack growth’, Proceedings of OMAE’03, 22nd International Conference on Offshore Mechanics and Arctic Engineering, June 8-13, Cancun, Mexico. Kristoffersen S, Haagensen P J and Rørvik G, 2008: Full scale fatigue testing of fatigue enhanced girth welds in clad pipe for SCRs installed by reeling, OMAE, 2007. Kudryavtsev Y et al., 2004: ‘Fatigue life improvement of welded elements by ultrasonic peening’, IIW Doc. XIII-2010-04. Lieurade H P et al., 1992: ‘Efficiency of improvement techniques on the fatigue strength as a function of the type of welded joint’, IIW Doc. XIII-1467-92. Lopez Martinez L, 1997: ‘Fatigue behaviour of steels with strength levels between 350 and 900MPa – influence of post weld treatment under spectrum loading’, Proc. Welded High Strength Steel Structures under Spectrum loading, Ed. A.F. Blom, EMAS, North European Engineering & Science Conference, NESCO, Stockholm. Maddox S J, 1991: Fatigue Strength of Welded Structures, Abington Publishing, Abington, Cambridge. Maddox S J, 1992: ‘Fatigue design of welded structures’, Engineering Design in Welded Constructions, Pergamon, Oxford. Maddox S J, Wylde J G and Yamamoto N, 1995: ‘Significance of weld profile on the fatigue lives of tubular joints’, Proc. 14th Offshore Mechanics on Arctic Engineering Conference, Vol.III, Materials Engineering, ASME, OMAE, 1995. Manteghi S and Maddox S J, 2004: ‘Methods for fatigue life improvement of welded joints in medium and high strength steels’, IIW Doc. XIII-2006-2004. Miki C and Anami K, 2001: Fatigue Strength Improvement of Welded Joints Using Low Temperature Transformation Welding Materials, Institute of Welding Technique, Technical University of Braunschweig, Germany. Millington D, 1973: ‘TIG dressing for the improvement of fatigue properties in welded high strength steels’, Welding Institute Report C215/22/. Ohta S et al., 1994: ‘Methods of improving the fatigue strength of welded joints by various toe treatments’, IIW Doc. XIII-1289-88. Ohta S et al., 1999: ‘Fatigue strength improvement of box welds by low transformation temperature welding wire and PWHT’, IIW Doc. XIII-1758-99. Shimada W et al., 1977: Improvement of fatigue strength in fillet welded joint by CO2 soft plasma arc dressing on weld toe, IIW Doc. XIII-830-77. Sperle, J O et al., 1996: Sheet Steel Handbook – design and fabrication in high strength sheet steel, SSAB Tunnplåt, p. 3:10. Statnikov E S, 1997: Applications of Operational Ultrasonic Impact Treatment (UIT), Technologies in Production of Welded Joints, IIW Doc. XIII-1667-97. Trufiakov V I et al., 1995: Ultrasonic impact treatment of welded joints, IIW Doc. XIII-1609-95. Wang, T et al., 2009: ‘Discussion on fatigue design of welded joints enhanced by ultrasonic peening treatment (UPT)’, International Journal of Fatigue 31, pp. 644–650. Watkinson F, Bodger P H and Harrison J D, 1971: ‘The fatigue strength of welded joints in high-strength steels and methods for its improvement’, Proc. Conf. on Fatigue of Welded Structures’, TWI, Abington, Cambridge. Weich, I, 2009a: ‘Edge layer condition and fatigue strength of welds improved by mechanical post weld treatment’, IIW Doc. XIII-2265-09. Weich I, 2009b, PhD Thesis, Technical University of Braunschweig.



3/23/11 1:50:40 PM

Index

A2 parameter, 19, 20 abrasive hole drilling, 290 American Petroleum Institute/American Society of Mechanical Engineers, 85–7 levels of analysis in proposed BS 7910:2012 procedures, 80 special features, 86–7 status, 87 structure, 86 user group, 87 American Society of Mechanical Engineers, 61, 85–7 API 579, 32, 85, 86 API 1104, 31 API 579-1/ASME FFS-1, 85 applied stress range, 176 ‘as-welded condition,’ 145 ASME see American Society of Mechanical Engineers ASME XI, 71 ASTM E 837–08, 291 ASTM E 1820–01, 25 AUT see automatic ultrasonic testing automated incremental hole drilling systems, 292 automatic ultrasonic testing, 32 AWS Structural Welding Codes, 304 beam line, 286 Bragg’s law, 286, 287 BS 7448, 51 BS 7910, 32, 33, 35, 187 BS 7910:99, 25 BS 4515-1, 31 BS 7910/PD 6493, 72–81 analysis levels in API-579 and API/ASME procedures, 86 BS 7910 development, 72 FADs used in PD 6493 and BS 7910, 76 maintenance, 79–81 special features, 76–8 structure, 75–6 user group, 78 burr grinding, 314–15 technique, 312

CDF see crack driving force Charpy testing, 62 clipping ratio, 213 cold laps, 149–52 complex loading, 191–2 constant amplitude fatigue loading, 209 constant amplitude loading, 182 constraint fracture mechanics, 31–55, 57–9 constraint parameters, 18–22 A2 parameter, 20 convention for crack tip fields definition, 19 modifications to the two parameter approach, 22 Q parameter, 21–2 reference stress field determination from small-scale yielding analysis, 21 T stress, 19–20 CTOD for SENT specimens crack depth, 43 dissimilar wall thickness, 44 CTOD–R curves circumferential surface cracks with wall thickness crack depths, 46 Cr filler material, 44 Cr parent material, 45 FEA for circumferential surface crack, 46 parent material vs fusion line for SENT specimens with different crack depths, 42 SENT specimens vs conventional SENB specimen, 42 SENT specimens with different wall thickness and misalignment, 43 elastic-plastic fracture mechanics, 17–18 finite-element stress field for sharp crack, 18 failure assessment diagram development approach to incorporate constraint, 25–7 high strength steel pipeline with shallow crack loaded in tension, 27 full field (local approach) analysis for fracture assessment, 28

330 © Woodhead Publishing Limited, 2011

Welded-Mcdonald-Index.indd 330

3/23/11 1:51:18 PM

Index high strains, 32–5 crack driving force for surface cracked plate, 33 strain-based FAD, 35 predicting welded joints failure, 17–28 Q-solutions tabulation, 22–5 Q value vs J curve, 23 T stress and Q for power law hardening material, 24 T stress to evaluate Q, 23–5 toughness–constraint relation for steel, 24 SENT specimen crack front straightness variation with specimen thickness, 52 cross-section and placement in pipe wall, 41 geometry, 34 geometry with dissimilar wall thickness and misalignment, 41 single edge notch tension test, 36, 37–54 development, 36 geometry constraint in SENB, SENT and circumferential flaws, 38 geometry of standard SENT and SENB specimens, 40 J vs Q for pipes, SENT and SENB specimens, 48 other fracture mechanics test results, 43, 44–5 standardising, 51–4 test methods, 31–55, 57–9 two-parameter fracture mechanics, 35, 36 specimen geometry effect on crack tip constraint, 36 weld mismatch effect on crack tip constraint, 27 constraint matching, 25 corrosion-fatigue damage, 188–9 corrosion pitting, 187–8 crack categorisation, 97–8 interactions of imperfection, 99 transfer of NDT into elliptical cracks, 100 types of crack, 98 crack driving force, 66 crack growth, 4, 9–10 crack opening displacement, 92 crack propagation, 94–7, 129 fatigue assessment, 221–6 load sequence effects, 222–4, 227 small cycle effects, 224, 225–6 fatigue crack growth diagram, 95 fracture assessment diagram of R6 method, 94 short crack behaviour with Paris power law region, 95 crack retardation, 224 crack tip opening displacement, 7, 32, 73 estimation, 54 fracture toughness, 53–4 critical crack size, 93–4 CTOD see crack tip opening displacement

331

cumulative damage, 182–3 cycle counting, 211–14 cyclic loading, 1 cyclic nominal stress, 175 DBA see design by analysis DBF see design by formulae defect-tolerant design, 61 defects, 127 design by analysis, 62 design by formulae, 62 dime test, 304 disc test, 304 DNV-OS-F101, 31, 32, 39, 51, 53 DNV-RP-F108, 32, 33, 36, 38, 51 DNV-RP-F108:2006, 25 ECA see engineering critical assessment EDM see electrodischarge machining effective notch stress approach, 122, 142, 157, 158, 164, 195–7 effective stress intensity factor, 223 elastic energy balance theory of fracture see Griffith’s theory elastic notch stress, 122–3 fictitious notch rounding, 122 elastic-plastic fracture mechanics, 66 elastic-plastic strain, 118 elastic plastic stress, 123–4 stress and strain during cyclic loading, 124 elastic stresses, 3 electrodischarge machining, 290 engineering critical assessment, 31, 60–1 development, 63–4 specific assessment methods, 67–87 see also fracture assessment methods EPFM see elastic-plastic fracture mechanics equivalent stress range, 217–18 European Pressure Vessel Code, 62, 63 ‘even transition,’ 143, 144 FAD see failure assessment diagram failure assessment curve, 25 failure assessment diagram, 25–7, 34–5, 64, 65–7 high strength steel pipeline with shallow crack loaded in tension, 27 failure assessment line, 66 fatigue, 1–2, 8–10, 115, 168 crack propagation, 175–7 fatigue crack growth data, 176 design codes and standards, 206–7 assessment procedures, 207 specific structures, 206–7 welded joints, 207 design rules, 177–89 acceptance limits for embedded volumetric defects, 187 classification systems, 179 cumulative damage under variable amplitude spectrum loading, 182–3



3/23/11 1:51:18 PM

332

Index

effect of welding on fatigue strength, 168 environment, 187–9 fatigue data for butt welds in steel, 187 fatigue data for welded aluminium alloy, 184 residual stress relief, 181–2 scale effect, 183–4 S–N curves, 177–9 S–N curves and corresponding weld details, 177 steel tensile strength on fatigue strength, 185 stresses used with S–N curves, 179–81 type and strength of material, 184–5 welded structures, 168–202 welding defects, 185–7 future developments in fatigue rules application, 189–202 complex loading, 191–2 fatigue data evaluation for steel flangepipe fillet welds, 192 fatigue data from butt and fillet welded steel, 196 FEA in fatigue design, 192–7 structural hot-spot stress calculation, 194 variable amplitude fatigue loading, 189–91 weld quality, 202 welding process, 197–202 test results plain and butt-welded 6000 series aluminium alloy, 201 steel plates with fillet welded attachments, 191 steel plates with welded edge gussets, 190 transverse electron beam butt welds, 199 welded steel specimens and components, 196 welded joints influencing fatigue, 170–5 continuous longitudinal butt and fillet welds, 170 cyclic stress onto existing yield magnitude tensile residual stress, 174 fatigue cracking in fillet-welded cruciform joint, 171 fatigue lives, 174 flaws, 170–2 geometric stress concentration, 170 residual stress, 172–5 residual stresses formation, 173 weld details, 171 fatigue analysis fracture mechanics of welded joints, 91–111 different crack opening modes, 93 fatigue assessment, 97–107 infinite plate with centre crack, 92 overview, 91–3 practical application, 107–10 technical application, 93–7 fatigue assessment

variable amplitude loading of welded structures, 208–34 cycle counting and presentation of load histories, 211–14, 215 fatigue damage, 214–26 future trends, 233–4 variable amplitude fatigue testing, 227–33 variable amplitude loading forms, 209–11 variable and constant amplitude fatigue loading, 209 fatigue class, 118 fatigue crack, 3, 9, 116 Fatigue Crack Arrester steel, 305–6 fatigue damage, 217 fatigue design improvement concepts for welded joints, 261 cumulative damage, 243, 245, 246 S–N curve modification and fatigue life calculation, 245 welded joints real damage sum distribution, 246 fatigue life testing results as-welded steel specimens, 250 as-welded thick and semi-ductile aluminium joints, 251 geometry, modelling and fatigue life, 239, 242–3, 244–5 notch stresses for reference radius, 244 root side notch position on stress concentration under axial loading, 243 stress deviations on fatigue life, 245 weld geometry on fatigue behaviour of butt welds, 242 multiaxial spectrum loading evaluation as-welded aluminium joints, 257 as-welded steel and stress-relieved joints, 255, 256 multiaxial stress states, 245–54, 255–7 errors by formal (scalar) application of von Mises hypothesis, 249 fertiliser plant stirrers, 248 laser beam-welded overlapped thin and ductile aluminium tube–tube specimens, 253 recommended assessment procedure, 252 wind power plant loading components, 247 safety factors, 254, 258–61 allowable stresses determination, 258 durability life determination for safety components, 259 loading, strength and probability of failure, 258 partition of components according to aspects of safety and functionability, 260 theoretical probabilities of failure according to IIW recommendations, 261 selected design concepts by the example of K-nodes, 261–73



3/23/11 1:51:18 PM

Index comparison of calculations with experiments, 267–8 design concepts and prerequisites, 261–7, 268, 269 welded structures improvement using local approaches, 239–74 influencing parameters of durability, 240 knowledge interaction for reliable design, 274 offshore oil platform, 242 offshore wind power plant, 241 reliability and safety aspects for fatigue loaded components, 240 reliability and safety aspects in fatigue design, 241 selected decisive design parameters, 239, 242–61 fatigue effective notch stress, 122 fatigue endurance, 9 fatigue failure, 178–9 fatigue fracture, 9 fatigue life, 177 assessment in differing welded joint designs, 139–66 consistent and objective weld class system, 144–62 future trends, 164–6 historic view, 140–2 weld class system ISO 5817, 142–3 weld class systems at Volvo, 143–4 fatigue limit, 178 fatigue loading, 285 fatigue strength assessment, 129–37 local stresses in welded joints, 115–37 factors, 124–9 types of stress, 117–24 nominal stress approach, 130–1 notch strain approach, 136–7 notch stress and SIF approaches, 134–6 structural stress approach, 131–3 fatigue strength improvement, 297–327 factors reducing the fatigue strength of welded joint, 307, 309 residual stresses, 309 weld defects, 309 weld geometry, 307 future trends, 324, 327 improved design, 301–5, 306 butt welds with different waviness, 306 fabrication methods, 304–5 factors that contribute to higher fatigue strength, 302 fillet weld terminations, 305 structural details with abrupt transitions, 303 structural details with permission, 303 weld profiles, 304–5 post-weld improvement methods, 307, 309–24, 325–6 burr grinding technique, 312

333

effect of TIG dressing combined with UIT, 324 increase in fatigue strength for higher strength steels, 326 residual stress methods, 315–24 residual stress modification improvement techniques, 310 weld geometry improvement techniques, 309 weld toe grinding, 310–11 weld toe re-melting techniques, 311, 313–15, 316, 317 special plate material, filler materials or welding methods, 305–7 special plate materials, 305–6 special weld metals, 306–7 electrodes that give compressive residual stresses, 307 electrodes with favourable flow characteristics, 306–7 nickel-based electrode, 307 special welding methods, 307, 308 friction stir weld compared with data for unwelded plates and conventional welds, 308 welded joints, 298–301, 302 conditions that determine the fatigue strength of welded joints, 300–1 global residual stresses, 302 unwelded plate, notched plate and welded plate material, 299 FCA steel see Fatigue Crack Arrester steel FEA see finite element analysis FFP see fitness-for-purpose FFS see fitness-for-service final crack size, 107 finite element analysis, 17, 18, 45, 100, 169 fatigue design, 192–7 effective notch stress approach, 195–7 hot-spot stress approach, 193–5 welded joint assessment, 109–10 crack growth stepwise integration, 110 stress separation, 109 finite element method, 8 finite element modelling, 77 finite element simulation, 39 First Law of Thermodynamics, 4 fitness-for-purpose, 61 fitness-for-service, 61 FITNET, 81–5 flaws, 170–2 fracture analysis, 2 fracture assessment diagram, 94 fracture assessment methods API/ASME, 85–7 levels of analysis in proposed BS 7910:2012 procedures, 80 special features, 86–7 status, 87 structure, 86



3/23/11 1:51:18 PM

334

Index

user group, 87 BS 7910/PD 6493, 72–81 analysis levels in API-579 and API/ ASME procedures, 86 BS 7910 development, 72 FADs used in PD 6493 and BS 7910, 76 maintenance, 79–81 special features, 76–8 structure, 75–6 user group, 78 design codes development for fracture-critical components, 61–3 rates of boiler explosions in USA, 61 engineering critical assessment methods development, 63–4 comparison between major fracture assessment procedures, 64 failure assessment diagram concept, 64, 65–7 strip yield, 65 full field (local approach) analysis, 28 future trends, 87–8 strain-based assessment, 88 R6, 67–72 development milestones, 68 FADs for continuously and discontinuously yielding materials, 67 special features, 71 status, 71–2 structure, 68, 69–71 user group, 71 SINTAP/FITNET, 81–5 fracture analysis options in FITNET, 82 special features, 84 status, 85 structure, 81–4 user group, 84–5 specific engineering critical assessment methods, 67–87 welded structures, 60–88 fracture mechanics, 2–3, 141, 152, 156, 158, 160, 161, 164–5 fatigue analysis of welded joints, 91–111 cracks/imperfection categorisation, 97–8 final crack size, 107 initial crack size, 106–7 material parameters, 103–6 overview, 91–3 practical application, 107–10 SIF determination, 101–3 stress analysis, 98–101 technical application, 93–7 see also linear elastic fracture mechanics fracture toughness, 65, 92–3 friction stir welding, 200, 307 friction welding, 200 FSW see friction stir welding gas tungsten arc welding, 44 Gassner curve, 226

gauge volume, 286 Gaussian amplitude distribution, 248 GE-EPRI procedure, 71 geometric stress concentration, 170 geometrical stress, 120 geometry correction factor, 6 Gough–Pollard algorithm, 248 Griffith energy balance, 4 Griffith’s equation, 4 modification, 5 Griffith’s theory, 2, 4 GTAW see gas tungsten arc welding Haibach principle, 215 hammer peening, 316–17 influence of steel strength on improvement in fatigue strength, 325 pneumatic riveting guns, 318 S–N curves for details improved by hammer or needle peening, 320 stress ratio effects on fatigue improvement, 321 heat-affected zone, 52, 83, 279 HiFIT see high frequency impact treatment high constraint crack geometries, 17 high frequency impact treatment, 319 high speed drilling, 290 hole drilling technique, 288, 290–2 hot-spot stress approach, 180, 193–5, 264, 311 HRR field see Hutchinson, Rice, Rosengren field Hutchinson, Rice, Rosengren field, 35 imperfections, 127 Inglis’ infinite stress paradox, 4 initial crack size, 106–7 inner defects, 145 International Institute of Welding, 120 invisible defects, 145 ISO 5817, 111, 142–3, 144, 162 ISO VAMAS document, 286 J dominance zone, 17 J integral, 17, 92, 94 joint restraint, 279 K-nodes comparison of calculations with experiments, 267–8 accuracy of fatigue life estimations, 273 experimental vs calculated crack propagation lives, 272 hot-spot concept application for the welded K-nodes evaluation, 270 notch stress concept application for the welded K-nodes evaluation, 271 design concepts and prerequisites, 261–7, 268, 269 COLOS spectrum, 264 crack propagation in the chord of a K-node, 267



3/23/11 1:51:18 PM

Index crack propagation law for steel in air and seawater, 266 FAT values according to notch stress concept, 266 fatigue design concepts for welded joints, 261 geometry of welded K-nodes, 263 hot-spot and weld local notch stresses in critical area of weld seam, 268 results presented by load ranges vs fatigue life, 265 test and calculation results obtained with welded K-nodes, 269 selected design concepts, 261–73 Kastner plastic collapse solution, 33 keyhole notch, 122 Kitagawa diagram, 93 Kronecker delta, 21 Kt factor, 147 Kx-factor, 143, 144 lack of fusion, 152 laser welding, 198–9 LEFM see linear elastic fracture mechanics level 1 calculations, 74, 77 linear elastic fracture mechanics, 2–8, 64 Griffith energy balance, 4 Inglis solution for elastic stresses at crack tip, 3 Irwin’s and Orowan’s modification to Griffith equation, 4–5 limitations, 7–8 methods of determining stress intensity factors, 8 stress intensity fracture, 5–7 local structural stress, 201 long range stresses, 173 longitudinal welds, 170 low transformation temperature electrodes, 307

335

S–N curves for details improved by hammer or needle peening, 320 net residual stress, 279 Neuber’s rule, 123–4 neutron diffraction strain scanning, 286–8 nickel-based electrode, 307 NLFM see non-linear fracture mechanics nodal forces, 195 nominal stress, 117, 118–19, 130–1 cruciform joint with potential crack locations at weld toe and root, 119 structural details according to IIW recommendation, 131 non-arc welding, 198–202 non-destructive testing, 77, 97–8 imperfections in a cruciform welded joint, 107–8 cruciform joint with K-butt welds and slag line under surface, 107 imperfections in welded joint, 108–9 tensile plate with welded-on transverse stiffener with surface flaws, 108 non-linear fracture mechanics, 17 notch strain approach, 136–7 strain S–N curve, 136 notch stress, 117–18, 134–6, 264 fatigue strength characteristic, 135 fatigue test data, 135 fatigue tests assessment, 134 notch stress intensity factor, 123 outer defects, 145

macrostructural support effect, 124 Manson–Coffin equation, 136 manual weld arc welds, 197 MARC, 264 material parameters, 103–6 aluminium crack propagation data, 105 Paris power law, 105 steel crack propagation data, 104 Materials Properties Council, 85 maximum principal stress, 252, 254 mean stress, 125–6 mean stress sensitivity, 125 microstructural support effects, 122 Miner’s rule, 182, 189–91 misalignments, 157, 159–60 MMA welds see manual weld arc welds MPC see Materials Properties Council

Palmgren–Miner damage sum, 254 Palmgren–Miner rule, 129, 214–15, 217, 243, 248, 262 Palmgren–Miner summation, 254 Paris Law, 73, 93, 96, 175–6 see also Paris–Erdogan Law Paris–Erdogan curve, 264, 268 Paris–Erdogan Law, 129, 221 PD 6493:1980, 32, 72–81 plane strain, 92 plane stress, 92 plasma dressing, 314–15 plasma welding, 197–8 plastic zone, 7 plate thickness effect, 128–9 residual stress distribution, 128 pores, 160–2 ‘post-treated welds,’ 145 post-weld heat treatment, 63, 186, 283 power beam welding, 198 power law, 20 Principal Stress Hypothesis, 247, 254, 262 PWHT see post-weld heat treatment

NDT see non-destructive testing needle peening, 317–18 equipment, 319

Q parameter, 21–2 reference stress field determination from small-scale yielding analysis, 21



3/23/11 1:51:18 PM

336

Index

Q stress, 19 R6 procedure, 25, 26, 67–72, 94 development milestones, 68 FADs for continuously and discontinuously yielding materials, 67 special features, 71 status, 71–2 structure, 68–71 user group, 71 residual stress, 74, 126, 172–5, 209 assessing and modelling in welded structures, 276–93 cyclic stress from external load, 126 measurement, 285–92 neutron and synchrotron X-ray stress measurements, 286–8 strain rosettes and hole drilling, 288, 290–2 stresses around the crack tip in singleedge notched tension specimen, 289–90 origins and types of stress, 278–83, 284 data as function of measurement depth in 12 mm plate, 282 longitudinal and transverse stresses for a friction stir weld, 284 residual stresses in 50 mm plate, 283 three-dimensional stress profiles, 281 weld geometry and associated residual stress profiles, 280 stresses modification after welding, 283, 285 residual stress methods, 315–24 effect of variable amplitude loading, 320–1 fatigue strength of joints improved by peening, 319–20 hammer peening, 316–17 high frequency impact treatment, 319 needle peening, 317–18 other methods, 321–4 combinations of improvement methods, 322–3 influence of steel strength, 323–4 LTT welding electrodes, 321–2 S–N data for HT80 steel specimens, 323 strain and temperature during cooling of LLT filler material, 322 UIT and UP, 318–19 residual stress relief, 181–2 resistance welding, 200–1 restraint stresses, 173 scale effect, 183–4 SENB see single edge notch bend SENT see single edge notch tension service loading, 283 SIF see stress intensity factor single edge notch bend, 37 single edge notch tension test, 25, 34, 57–9 development, 36, 37–50

fracture control project, 36, 37–9 fracture mechanics testing, 40–5 J-integral in SENT specimens, 39–40 numerical simulation, 45, 46 specimen applicability, 47–8 driving force, 49–50 effect of misalignment and dissimilar wall thickness, 48–9 other fracture mechanics test results, 43, 44–5 specimen geometry, 10 standardising, 51–4 CTOD estimation, 54 fracture toughness and CTOD, 53–4 specimen manufacture and testing, 51–3 SINTAP see Structural Integrity Procedures for European Industry S–N approach, 129 basic elements, 130 S–N curves, 142, 168–9, 177–9, 182, 214–21, 226 stresses used, 179–81 special plate materials, 305–6 special weld metals, 306–7 spectrum loading, 211 stainless steels, 188 STD 5605, 162–3 STD 5606,51, 143 STD 181-0001, 143 STD 181-0004, 144 STD 565 [3], 144 strain-based methodology, 35 strain energy release rate, 2 strain rosettes technique, 288, 290–2 stress, 117–24 longitudinal stress distribution, 118 stress analysis, 98, 100–1 stress parts in welded plate, 100 stress-averaging approach, 122 stress diffusers, 305 stress intensity factor, 2, 5–7, 101–3, 118, 175 correction function variation in cruciform joint with K-butt welds, 102 determination methods, 8 general determination, 101 Mk function in parametric formula, 103 parametric formula, 102 weld toe corrections, 101–3 see also notch stress intensity factor structural hot-spot stress, 117, 120 Structural Integrity Procedures for European Industry, 81–5 fracture analysis options in FITNET, 82 special features, 84 status, 85 structure, 81–4 user group, 84–5 structural stress, 119–21, 131–3 fatigue tests evaluation, 132 surface stress extrapolation, 120 through-thickness stress linearisation, 121 synchrotron X-ray, 286–8



3/23/11 1:51:18 PM

Index T stress, 19–20 convention for crack tip fields definition, 19 technical crack, 115–16 theory of strength of flawed components see fracture mechanics Thermanit 13/06 Mo., 44 ‘thickness effect,’ 183 ‘thinness effect,’ 184 threshold stress intensity range, 221 throat size, 154 through-thickness integration, 195 toe transition, 147 transition radius, 146–9 transverse welds, 170 Tresca hypothesis, 246, 247 TTI see through-thickness integration tungsten inert gas dressing, 313–15 combined with ultrasonic impact treatment, 324 fillet weld before and after TIG dressing, 316 influence of steel strength on improvement in fatigue strength, 325 tungsten inert gas welding, 197–8 UIT see ultrasonic impact treatment ultimate tensile strength, 298 ultrasonic impact treatment, 318–19 ultrasonic peening, 318–19 undercuts, 152, 154, 155 UTS see ultimate tensile strength variable amplitude fatigue testing, 227–33 variable amplitude loading cycle counting and presentation of load histories, 211–14, 215 rainflow cycle count histogram, 212 three sample spectra, 215 cycle distribution and cycle exceedance diagrams rainflow histogram, 213 Weibull shape parameter, 214 fatigue assessment methods in welded structures, 208–34 future trends, 233–4 variable amplitude fatigue testing, 227–33 variable and constant amplitude fatigue loading, 209 fatigue damage and assessment, 214–26 alternate spectra with identical block lengths, 219 assessment based on crack propagation, 221–6 assessment based on S–N curves, 214–21 bilinear S–N design curve, 216 historical eight-block programme test of Gassner, 227 simplifying stress vs. time history, 218 spectrum shape and equation on computed fatigue life, 220 stress range and number of cycles for

337

three load spectra, 220 variable amplitude crack growth life prediction models, 223 forms, 209–11 load histories, 210 future developments, 189–91 IIW recommended parameters for crack propagation analysis welded aluminium structures, 222 welded steel structures, 222 variable amplitude fatigue testing, 227–33 omission level on computed small cycle damage, 230 reporting data, 231–3 sample spectra with identical shape parameters, 230 short load spectrum segment, 232 S–N presentation of spectrum load data, 233 spectrum shape on computed small cycle damage, 229 standard loading histories, 228 test load spectra, 228–31 variable amplitude spectrum loading, 182–3 Volvo, 143–4 Volvo STD 5606,51, 143 von Mises hypothesis, 245, 247 errors by formal (scalar) application, 249 von Mises stress, 252, 254 Weibull distribution, 212–13, 231 weld class systems cold laps, 149–52 0.1–0.2 mm, 150 3D crack growth, 153 life in cruciform joint, 151 non-load-carrying cruciform joint, 150 stress intensities, 151 fatigue life assessment of differing welded joint designs, 139–66 consistent and objective weld class system, 144–62 future trends, 164–6 historic view, 140–2 ISO 5817, 142–3 Volvo, 143–4 lack of fusion, 152, 154 middle of the side of a fillet weld, 154 misalignments, 157, 159–60 axial misalignment in a butt weld, 160 fillet and butt welds, 159 pores, 160–2 life calculated with fracture mechanics, 161 semi-elliptical crack, 161 stress concentration plotted against relative distance D1, 162 stress concentration plotted against relative distance D2, 162 quality, 144–62



3/23/11 1:51:18 PM

338

Index

categories of errors, 145 weld penetration, 146 throat size, 154, 156–7, 158, 159 effective notch method, 157 effective notch method vs linear fracture mechanics, 158 fracture mechanics, 158 stresses in the root, 159 stresses in the weld toe, 156 transition radius, 146–9 blunt to a sharp stress concentration, 148 calculated fatigue life in a cruciform joint, 148 stress concentration as a function of weld toe radius, 149 stress concentration in the toe transition, 147 undercuts, 152, 154, 155 stress levels in a butt weld, 155 stress levels in a fillet weld, 155 weld penetration, 146 weld profiling, 304 weld quality, 127–8, 202 geometry parameters, 127 structural stresses at axially loaded joints, 127 weld toe grinding, 310–11, 311 burr grinding technique, 312 design S–N curves for details improved by weld toe burr grinding, 313 fatigue strength of joints improved by grinding, 311 weld toe re-melting techniques, 311, 313–15, 316, 317 automated TIG dressing, 317 fillet weld before and after TIG dressing, 316 TIG and plasma redressing, 313–15 TIG dressing, 315 weld toes, 172 weld zone, 279 welded joints constraint-based fracture mechanics in predicting failure, 17–28 constraint-based elastic-plastic fracture mechanics, 17–18 constraint parameters, 18–22 failure assessment diagram development approach to incorporate constraint, 25–7 full field (local approach) analysis for fracture assessment, 28 Q-solutions tabulation, 22–5 weld mismatch effect on crack tip constraint, 27 fatigue strength assessment of local stresses, 115–37 factors, 124–9 fatigue crack at an attachment end, 116 force flow illustrating stress concentrations, 117 types of stresses, 117–24

fracture mechanics in fatigue analysis, 91–111 different crack opening modes, 93 fatigue assessment, 97–107 infinite plate with centre crack, 92 overview, 91–3 practical application, 107–10 technical application, 93–7 improving weld class systems in fatigue life assessment, 139–66 consistent and objective weld class system, 144–62 future trends, 164–6 historic view, 140–2 weld class system ISO 5817, 142–3 weld class systems at Volvo, 143–4 welded structures assessing and modelling residual stresses, 276–93 measurement, 285–92 origins and types of stress, 278–83, 284 stresses modification after welding, 283, 285 fatigue assessment methods variable amplitude loading, 208–34 cycle counting and presentation of load histories, 211–14, 215 fatigue damage, 214–26 future trends, 233–4 variable amplitude fatigue testing, 227–33 variable amplitude loading forms, 209–11 variable and constant amplitude fatigue loading, 209 fatigue design improvement using local approaches, 239–74 decisive design parameters, 239, 242–61 design concepts by the example of K-nodes, 261–73 fatigue design rules, 168–202 crack propagation, 175–7 design rules, 177–89 future developments, 189–202 welded joints influencing fatigue, 170–5 fracture assessment methods, 60–88 API/ASME, 85–7 BS 7910/PD 6493 method, 72–81 ECA methods development, 63–4 failure assessment diagram concept, 64, 65–7 future trends, 87–8 R6 method, 67–72 SINTAP/FITNET, 81–5 welding, 141 welding defects, 185–7 welding process, 197–202 non-arc welding, 198–202 TIG and plasma welding, 197–8 Westergaard’s method, 5 Wheeler model, 224 Woehler curves, 141, 142, 226, 254



3/23/11 1:51:19 PM

Fracture and Fatigue of Welded Joints and Structures (Woodhead Publishing in Materials)

Fatigue of Structures and Materials

Fatigue of Structures and Materials

Fatigue of Structures and Materials

fatigue and fracture mechanics of offshore structures

Fatigue Life Prediction of Composites and Composite Structures (Woodhead Publishing in Materials)

Fatigue Life Analyses of Welded Structures: Flaws

Building Decorative Materials (Woodhead Publishing in Materials)

Design and Analysis of Fatigue Resistant Welded Structures

Fatigue Assessment of Welded Joints by Local Approaches

Lifetime Estimation of Welded Joints

Teaching and Education in Fracture and Fatigue

Bioactive Glasses: Materials, Properties and Applications (Woodhead Publishing in Materials)

Cumulative damage of welded joints

Welding and Joining of Magnesium Alloys (Woodhead Publishing in Materials)

Fatigue and Fracture Reliability Engineering

Lifetime Estimation of Welded Joints

Thermal Barrier Coatings (Woodhead Publishing in Materials)

Multiscale Deformation and Fracture in Materials and Structures

Damage and Fracture of Composite Materials and Structures

Biomedical Composites (Woodhead Publishing in Materials)

MIG Welding Guide (Woodhead Publishing in Materials)

High Temperature Superconductors (Woodhead Publishing in Materials)

Creep and Fracture of Engineering Materials and Structures (matsci)

Creep and Fatigue in Polymer Matrix Composites (Woodhead Publishing in Materials)

Nanolithography and Patterning Techniques in Microelectronics (Woodhead Publishing in Materials)

Sustainability of Construction Materials (Woodhead Publishing in Materials)

Sintering of Advanced Materials (Woodhead Publishing in Materials)

Fatigue Failure of Textile Fibres (Woodhead Publishing Series in Textiles)

Materials in Sports Equipment, Volume 2 (Woodhead Publishing in Materials)

Hydrometallurgy: Principles and Applications (Woodhead Publishing in Materials)

Fracture and Fatigue of Welded Joints and Structures (Woodhead Publishing in Materials)

Fatigue of Structures and Materials

Fatigue of Structures and Materials

Fatigue of Structures and Materials

fatigue and fracture mechanics of offshore structures

Fatigue Life Prediction of Composites and Composite Structures (Woodhead Publishing in Materials)

Fatigue Life Analyses of Welded Structures: Flaws

Building Decorative Materials (Woodhead Publishing in Materials)

Design and Analysis of Fatigue Resistant Welded Structures

Fatigue Assessment of Welded Joints by Local Approaches

Lifetime Estimation of Welded Joints

Teaching and Education in Fracture and Fatigue

Bioactive Glasses: Materials, Properties and Applications (Woodhead Publishing in Materials)

Cumulative damage of welded joints

Welding and Joining of Magnesium Alloys (Woodhead Publishing in Materials)

Fatigue and Fracture Reliability Engineering

Lifetime Estimation of Welded Joints

Thermal Barrier Coatings (Woodhead Publishing in Materials)

Multiscale Deformation and Fracture in Materials and Structures

Damage and Fracture of Composite Materials and Structures

Biomedical Composites (Woodhead Publishing in Materials)

MIG Welding Guide (Woodhead Publishing in Materials)

High Temperature Superconductors (Woodhead Publishing in Materials)

Creep and Fracture of Engineering Materials and Structures (matsci)

Creep and Fatigue in Polymer Matrix Composites (Woodhead Publishing in Materials)

Nanolithography and Patterning Techniques in Microelectronics (Woodhead Publishing in Materials)

Sustainability of Construction Materials (Woodhead Publishing in Materials)

Sintering of Advanced Materials (Woodhead Publishing in Materials)

Fatigue Failure of Textile Fibres (Woodhead Publishing Series in Textiles)

Materials in Sports Equipment, Volume 2 (Woodhead Publishing in Materials)

Hydrometallurgy: Principles and Applications (Woodhead Publishing in Materials)

Recommend Documents