Fatigue and Fracture Mechanics of Offshore Structures

Fatigue and Fracture Mechanics of Offshore Structures This page intentionally left blank UK . London and Bury St Edmunds.ENGINEERING RESEARCH SERIES Fatigue and Fracture Mechanics of Offshore Structures L S Etube Series Editor Duncan Dowson Professional Engineering Publishing Limited. All rights reserved. Data. stored in a retrieval system. Suffolk. or review. chemical. Professional Engineering Publishing Limited. Northgate Avenue. © Etube ISBN 1 86058 312 1 ISSN 1468-3938 ERS 4 A CIP catalogue record for this book is available from the British Library. Printed and bound in Great Britain by St. criticism. research. and conclusions developed by the Author are for information only and are not intended for use without independent substantiating investigation on the part of the potential users. photocopying.First published 2001 This publication is copyright under the Berne Convention and the International Copyright Convention. as permitted under the Copyright Designs and Patents Act 1988. Opinions expressed are those of the Author and are not necessarily those of the Institution of Mechanical Engineers or its publishers. IP32 6BW. or transmitted in any form or by any means. mechanical. Unlicensed multiple copying of this publication is illegal. electrical. Suffolk. electronic. without the prior permission of the copyright owners. Edmundsbury Press Limited. no part may be reproduced. . Inquiries should be addressed to: The Publishing Editor. UK. discussion. recording or otherwise. Apart from any fair dealing for the purpose of private study. Fax: +44 (1)284 705271. Bury St Edmunds. UK The publishers are not responsible for any statement made in this publication. CEng. His research interests include: • fatigue and the applications of fracture mechanics to engineering structures under realistic loading and environmental conditions. including regulatory bodies such as the UK Health and Safety Executive (HSE). • variable amplitude fatigue behaviour of offshore and related structures. structural integrity. in expanding the knowledge and understanding of structural steels used offshore and in related industry sectors. PhD. and reliability. He was appointed a lecturer in December 1997 and obtained his PhD in September 1998. • offshore safety. MIMechE) joined the Department of Mechanical Engineering at the University of London in October 1991 as an undergraduate.About the Author Dr Linus Etube (BEng. • risk analysis. • development of novel fracture mechanics models for engineering applications. Dr Etube has worked closely with a wide range of both UK-based and global organizations in the offshore oil and gas sector. • structural mechanics and failure analysis of offshore and related structures. After completing his BEng in 1994. he started his PhD research programme as a research student. . This page intentionally left blank . Related Titles IMechE Engineers' Data Book Second edition A Guide to Presenting Technical Information . and Related Industries Noise in Fluid Machinery Journal of Strain Analysis for Engineering Design C Matthews ISBN 186058 248 6 C Matthews ISBN 1 86058 249 4 IMechE Conference Transactions ISBN 1 86058 217 6 IMechE Seminar Publication Proceedings of IMechE ISBN 1 86058 246 X ISSN 0309-3247 Other titles in the Engineering Research Series Industrial Application of Environmentally Conscious Design (ERS1) Surface Inspection Techniques — Using the Integration of Innovative Machine Vision and Graphical Modelling Techniques (ERS2) Laser Modification of the Wettability Characteristics of Engineering Materials (ERS3) Adaptive Neural Control of Walking Robots (ERS5) Strategies for Collective Minimalist Mobile Robots (ERS6) T C McAloone ISBN 1 86058 239 7 ISSN 1468-3938 M L Smith ISBN 1 86058 292 3 ISSN 1468-3938 J Lawrence and L Li ISBN 1 86058 293 1 ISSN 1468-3938 ISBN 1 86058 294 X ISSN 1468-3938 ISBN 1 86058 318 0 ISSN 1468-3938 M J Randall C Melhuish For the full range of titles published by Professional Engineering Publishing contact: Sales Department Professional Engineering Publishing Limited Northgate Avenue Bury St Edmunds Suffolk IP32 6BW UK Tel:+44 (0)1284 724384 Fax:+44 (0)1284 718692 www.com .Effective Graphic Communication Fluid Machinery for the Oil. 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This page intentionally left blank . 6 Jack-up dynamic response 2.1 The pseudo random binary sequence technique 2.4 The JOSH model 2.3 Review of previous loading models 2.3.6.3 Hart/Wischung algorithm 2.2 Definition of hot spot stress 1.1 COLOS/C 12-20 series 2.6.3 Stress analysis of tubular joints 1.3.Contents Series Editor's Foreword Foreword Acknowledgements Notation Chapter 1 Literature Review 1.1 The transfer function approach 2.3.5 Generation of JOSH 2.5.4.2 Modelling of structural parameters 2.4 WASH sequence 2.1 S-N approach 1.3.2 Fatigue loading in Jack-up structures 2.5 Summary Chapter 2 Service Load Simulation 2.6.3.2 The Fracture Mechanics (FM) approach 1.2 The Morkov chain technique 2.3 Modelling of soil-structure interaction xiii xv xvii xxi 1 4 5 5 6 9 16 16 36 40 43 44 47 48 48 48 49 49 49 50 50 52 52 55 57 .4.1 Introduction 2.3 Methods of stress analysis 1.3.2 Review 1.2 UKOSRP II double-peaked spectrum 2.4 Fatigue design 1.5.1 Introduction and background 1.3.1 Definition of stresses in welded connections 1. 7 2.7.3 Fabrication of SE 702 specimens 3.2 The two-phase model (TPM) 4.1 4.2 Use of parametric equations 3.7 105 106 108 114 114 115 116 117 118 122 127 127 128 x .1 The average stress model 4.3.1 Test parameters and the JOSH sequence 3.3 Simulation of environmental conditions 3.4.7 Discussion 3.2 Crack growth curves 3.6 4.5.6 Fatigue test results 3.2 4.5 4.1 Details of test rig 3.1 Equivalent stress range approach 4.2 Equivalent crack growth concept 77 78 78 80 82 82 82 82 83 84 84 85 87 87 91 91 94 96 98 98 103 4.2 Consideration of test specimen geometry 3.3.4 S-N data 3.6.9 2.1 Newman-Raju SIF solution for surface cracks New semi-empirical Y factor solution Variable amplitude crack growth models 4.3.4.6.6.8 Summary Chapter 4 4.1 Experimental stress analysis procedure 3.2.3 Experimental set-up 3.4.8 2.3 Crack aspect ratio evolution 3.3 4.5.2 Test specimen consideration 3.4 Fracture Mechanics Analysis Introduction The stress intensity factor concept Experimental results Use of empirical SIF solutions 4.7.1 Fatigue crack initiation 3.6.4.4 Stress analysis of Y joints 3.Contents 2.3 The modified average stress model Adapted plate solutions 4.1 Properties of SE 702 3.5 Experimental fatigue testing 3.4.2 Test control and data acquisition 3.10 Modelling of wave loading Selection of sea states Discussion Summary 60 62 64 76 Chapter 3 Large-scale Fatigue Testing 3.2.2.1 Introduction 3. 10.Contents 4.12 Summary 130 132 134 136 138 139 140 147 149 149 153 161 Chapter 5 Conclusion 5.1 New normalized PSD equation 4.10.2 Conclusions and recommendations References Index xi .2 Formulation of the sea state equivalent stress concept 4.1 Summary 5.9 Consideration of sequence effects Fast assessment of offshore structures 4.8 4.11 Discussion 4.9.1 Use of sea state probability distribution model 4.10 Sea state probability model 4. This page intentionally left blank . Commissioning Editor in the Books Department. The volumes will supplement and not compete with the publication of peer-reviewed papers in journals. its comprehensive nature. but selective. a series of theses on a particular engineering topic. The development and operation of the North Sea oil and gas fields represents a truly remarkable technological achievement. or with the Series Editor. potential applications. account of the development of understanding and knowledge on the topic in a specially prepared single volume. Factors to be considered in the selection of items for the Series include the intrinsic quality of the thesis. reports to sponsors of research. and the relevance to the wider engineering community. University College.describing the research in much more complete form than is possible in journal papers. single higher degree theses. An important factor affecting the integrity of these huge offshore structures is the fatigue behaviour of welded tubular joints. In some disciplines this is accommodated when the thesis or engineering report is published in monograph form . and the present volume illustrates an engineering science approach to one of them. The fourth volume in the Series comes from London University and is entitled Fatigue and Fracture Mechanics of Offshore Structures by Linus Sone Etube Department of Mechanical Engineering. Professional Engineering Publishing Limited. submissions for higher doctorates. . Authors are invited to discuss ideas for new volumes with Sheril Leich. Selection of volumes for publication will be based mainly upon one of the following. the novelty of the subject.Series Editor's Foreword The nature of engineering research is such that many readers of papers in learned society journals wish to know more about the full story and background to the work reported. Many new engineering challenges have been encountered at various stages in the development and operation of the fields. The Engineering Research Series offers this opportunity to engineers in universities and industry and will thus disseminate wider accounts of engineering research progress than are currently available. or comprehensive industrial research reports. It is usual for university engineering research groups to undertake research on problems reflecting their expertise over several years. London. In such cases it may be appropriate to produce a comprehensive. The application of millions of cycles of variable amplitude loading is related to sea states and wave motion. The development of a standard loading history is described and realistic environmental conditions are considered.Fatigue and Fracture Mechanics of Offshore Structures The author has studied many aspects of the fatigue characteristics of such joints in Jackup offshore structures. This latest contribution to the Engineering Research Series enlarges the scope of topics covered by the early volumes. and wettability characteristics of engineering materials. surface inspection techniques. bringing together a balance of experimental and theoretical approaches to the problem. An account is given of large-scale fatigue testing and the detailed analysis of fatigue crack initiation and growth. Topics covered to date deal with aspects of design. Professor Duncan Dowson Series Editor Engineering Research Series xiv . Different fracture mechanics models for VACF crack growth prediction are compared. with respect to crack growth mechanisms in high-strength weldable Jack-up steels. of extensive cracking around the spud-can regions of several Jack-ups operating in the North Sea. fatigue is an important consideration in their design. It was thought that these steels might be more susceptible to hydrogen cracking and embrittlement. As a result. in the late 1980s and early 1990s. The factors that influence fatigue resistance of structural steels used in the construction of Jack-up structures are highlighted.Foreword The tubular welded joints used in the construction of offshore structures can experience millions of variable amplitude load cycles during their service life. The perceived difference in their behaviour was heightened by the discovery. These steels were thought to exhibit fatigue resistance properties which are different when compared with conventional fixed platform steels such as BS 4360 50D and BS 7191 355D. . Jack-up legs are made from a range of high-strength steels with yield strengths up to 700 MPa. This book contains results of an investigation undertaken to assess the performance of a typical high-strength weldable Jack-up steel under realistic loading and environmental conditions. Such fatigue loading represents a main cause of degradation of structural integrity in these structures. The methods used to model the relevant factors for inclusion in JOSH are presented with particular emphasis on loading and structural response interaction. and a novel improved generalized methodology for fast assessment of offshore structural welded joints is presented. Results and details of experimental Variable Amplitude Corrosion Fatigue (VACF) tests conducted using JOSH are reported and discussed. Details of the methodology employed to develop a typical Jack-up Offshore Standard load History (JOSH) are presented. This enhanced the need to study their behaviour under representative service loading conditions. This page intentionally left blank . Boswell and J. and Creusot Loire Industrie. which enabled me to acquire a solid grounding in the field of mechanical engineering. British Steel (now The Corus Group. I acknowledge financial support received from the Cameroon Government through the Ministry of Higher Education and Scientific Research in the form of an Overseas Scholarship. I would like to thank Dr F. Sharp for taking the time to review the manuscript and for their fine suggestions and recommendations. D. Statoil. Dr L S Etube Department of Mechanical Engineering University College London. P. Dover for the invaluable supervision and guidance given during the course of my PhD programme. I would also like to thank everyone in the Department of Mechanical Engineering. The financial support of a number of organizations made the successful completion of the work reported in this book possible. UK . subsequently developing a keen interest in structural integrity of engineering structures. F. especially my colleagues who all played an important role in providing the conducive and intellectually stimulating environment under which work presented in this book was conducted. Their stimulating discussions are invaluable. Brennan and Professor W. I would like to thank Professors L. I acknowledge the following organizations for their contribution (in-kind or financial): the UK Health and Safety Executive (HSE). from a merger between British Steel and Koninklijke Hoogovens). at University College London.Acknowledgements I wish to express my deep appreciation for the support offered by the following individuals and organizations. First. This page intentionally left blank . my sisters. . and guidance will always remain an inexhaustible source of inspiration for me. Daniel Etube. support.Delphine Ntube Etube. Their love.Christina Etube . and my wife .To my family This book is dedicated to my entire family.my brothers. To my mother . To my late father. who spent the greater part of his life educating and encouraging people to aspire for a deeper understanding of the things around them. This page intentionally left blank . half surface crack length Initial crack depth Final crack depth (except where otherwise defined) Scaling parameters (except where otherwise defined) Silver/silver chloride reference electrode Paris law material constants Drag coefficient. one-dimensional ACPD solution Life (number of cycles). i a af A. N1. p Crack depth (except where otherwise defined).Notation Roman a. Cp. p Ag/AgCl C. fl I Kmax. Tr. fB. fn. N3 Maximum and minimum stress intensity factors Critical mode I stress intensity factor Stress intensity factor for stress corrosion cracking Tubular joint chord length ith spectral moment ACPD crack depth modifier. Tz Hr. dominant period. Kmin KIC KISCC L Mi M x d1 N. shaping parameter Crack growth rate Tubular joint chord diameter Miner's cumulative damage ratio Error function of x Young's modulus Frequency. c ao. natural frequency. Cm C mj J. £2B G Hs ext. Period and frequency ratios Irregularity factor da/dN D Ds erf(x) E f. fp fnB. m CD. Tz ext Hs. initiation life. mean zero crossing period Non dimensional wave height. mass coefficient Paris law material constants for a multi-segment da/dN curve Empirical retardation parameter. through thickness life . peak frequency Frequency corrected non-dimensional parameters Shear modulus Extreme sea state parameters Significant wave height. TD. 0 Tubular joint dimensional parameters (except where otherwise defined) a Twice the ratio of chord length to chord diameter (2L/D) Ratio of brace diameter to chord diameter (d/D) P Ratio of chord diameter to twice chord thickness (D/2T) Y e Spectral bandwidth parameter e Angle around tubular joint chord/brace intersection v Poisson's ratio Damping ratio e Root mean square (RMS) value a Crack tip opening stress. AS.Notation P(x). T. Y Greek Symbols a. Vc. p(x) Exceedance of variable x. crack voltage. Kop Yield strength Oy Ratio of brace thickness to chord thickness (t/T) T Angular position or angle of inclination o Gamma function of x r(x) Stress intensity factor range AK Threshold stress intensity factor range AKth. reference voltage Stress spectrum given by Wirsching's equation D(f) Crack shape correction (CSC) factor ¥ Acronyms ACPD AVS CP Aalternating current potential difference Average stress Cathodic protection xxii . ACPD probe spacing. Effective stress intensity factor range AKeff A. Y. Shi S(f)N t T Y(a). stress intensity factor corresponding to aop Oop. p. Aa SB. Vr. probability of occurrence of variable x UEG diameter ratio modifying parameter UEG short chord modifying parameter Spud-can radius or chord radius (defined where applicable) Stress range Thickness effect parameters Equivalent stress. tB y Sh. equivalent stress for sea state i Normalized response spectrum Brace thickness or time or plate thickness (defined where applicable) Tubular joint chord thickness Stress intensity factor correction function (Y factor) VQB VQr R S. Notation CLI FEA IPB JOSH MAVS SCF TPM UKOSRP UEG UCL UKCS UTS OPB PSD SENB WASH Creusot Loire Industrie Finite element analysis In-plane bending Jack-up offshore standard load history Modified average stress Stress concentration factor Two-phase model United Kingdom Offshore Steels Research Project Underwater engineering group University College London United Kingdom Continental Shelf Ultimate tensile strength Out-of-plane bending Power spectral density (spectrum) Single edge notch bend Wave action standard history xxiii . This page intentionally left blank . It is important to note that most of the high-strength steels used in fixed structures are limited to topside applications and other less critical parts of the structure where fatigue damage is not a major concern. These structures are now being increasingly used as production platforms for marginal field development. because a reduction in weight can lead to the achievement of considerable saving in support substructure. can be minimized through the use of reduced plate thicknesses. and a fairly recent review [1. There are other potential benefits to be derived from the use of high-strength steels. different for Jack-up platforms that have traditionally been used for short-term drilling and maintenance operations. for example. It is designed to operate in a water depth of 100 m with an intended service life of thirty-five years. This is particularly relevant to offshore structures. extended periods at the same elevation in their fatigue design philosophy are included. 1 .Chapter 1 Literature Review 1. This is a five-fold increase when compared to 8 per cent in 1988.1 Introduction and background In recent years there has been considerable interest in the use of high-strength steels in the construction of offshore structures. Historically. however. there has been a great deal of interest in the use of high-strength steels for the fabrication of Jack-up structures when compared with fixed platforms. In recent designs. BP Harding is a typical example of this new generation of Jack-up platforms. However. the potential benefits of using high-strength steels have been recognized by the offshore oil and gas industry. Fabrication costs.1] showed that the proportion of higher strength steels used in fixed offshore structures had gone up to 40 per cent by 1995. This situation is. One main reason for this is to satisfy the desire for lightweight constructions. Fig. and Hitachi designs. Steels with nominal yield strength in the range of 450 to 700 MPa have commonly been used. 1. A review of different designs is presented in [1. Friede and Goldman. supplementary braces are frequently used between main brace midpoints to increase the buckling resistance of the structure and to provide adequate structural redundancy. each leg (Fig.1) is made of three or four longitudinal chord members that may contain a rack plate for elevating the hull and a series of interconnecting horizontal and diagonal tubular members (Fig. 1. The detailed leg structure will vary from one type of Jack-up to another. CFEM.Fatigue and Fracture Mechanics of Offshore Structures High-strength steels used in the construction of Jack-up structures are mainly limited to the fabrication of the legs. In this review the structures were classified according to the Jack-up design. MSC.2). 1.1 Typical lattice leg structure of a Jack-up platform Fig.2 Typical Jack-up leg chord with rack plate 2 . 1. some of which include Le Toumeau.2]. In some designs. In general. and worldwide. Fatigue performance of high-strength steels is subject to uncertainty and there is need to investigate their performance further.11]. As a result.Literature Review There has recently been a remarkable increase in the overall size of these structures.7]. but the basic design. very limited and this has been highlighted in reviews [1. Two principal sources of this uncertainty for high-strength steels lie in the effect of cathodic protection and variable amplitude corrosion fatigue. This has increased the risk of deterioration from long-term problems such as fatigue.9] only provides guidance for steels with yield strength less than 500 MPa.6] with typical yield strengths in the region of 350 MPa. Consequently the fatigue design guidance developed to date is not applicable to high-strength steels. The main reason for this is to satisfy the requirement to operate in deeper waters in predominantly harsher sectors of the North Sea.10]. 3 . it was accepted that high-strength steels are more susceptible to corrosion fatigue and hydrogen-induced stress corrosion cracking (HISCC) when compared with conventional fixed platform steels.12]. The absence of sufficient guidance on the use of high-strength steels and the lack of fatigue data is a matter for concern. This is all the more important due to the increasing proportion of higher strength steel grades used in offshore applications.2. This book is laid out in five chapters. carried out by the offshore oil and gas industry [1. SE 702 [1. 1. and this is reflected in the guidance published in 1995 [1. 1. Even the current draft ISO standard [1. Particular emphasis is given to design against fatigue failure under stochastic service loading and environmental conditions.5] and BS 7191 355D [1. Several Jack-ups are now used for production. This role requires long-term deployment and. The vast majority of research on the fatigue performance of tubular welded joints.e. curve is restricted to steels with guaranteed yield strengths of up to 400 MPa for nodal joints and 500 MPa for welded plate connections. therefore. An investigation of the effect of cathodic protection on the fatigue performance of a typical high-strength Jack-up steel under constant amplitude loading conditions is reported in [1.4] has focussed on conventional fixed offshore platform steels such as BS 4360 50D [1. Chapter 1 contains a review of the current state of knowledge in the fatigue design of offshore welded structures. This document has now been withdrawn. Fatigue data on higher strength tubular joints are. limits the opportunity for dry dock inspection and repair. The main conclusion drawn from the investigation was that the generation of hydrogen from the sacrificial anode systems protecting high-strength steel structures at levels that are excessively negative (i. This concern was strengthened by the discovery of extensive cracking in the spud-can region of Jack-ups operating in the United Kingdom Continental Shelf (UKCS) in the period of 1988-89 [1. with particular emphasis on the effects of stochastic service loading under cathodic protection conditions. This will allow designers of high-strength steel marine structures to use these materials with greater confidence. therefore. <-850mV Vs Ag/AgCl) can enhance fatigue crack growth and should be avoided.3.8]. This study was aimed at investigating the fatigue performance of the same steel. under realistic loading and environmental conditions. This chapter is concerned with a literature review of appropriate topics related to structural assessment. The distribution and level of stresses is important in both stress-life (S-N) and FM based methods used both at the design stage and during structural integrity assessment procedures. This chapter also contains new developments in this field. It is dedicated to the important subjects of stress analysis. are the two central ingredients for a fracture theory.2 Review Stress analysis of an engineering component containing a crack or crack-like defect and a failure model hypothesis. is also identified and highlighted in this final chapter. In this chapter. This emphasizes the importance of stress analysis in the process of implementing any fracture mechanics methodology for the assessment of structural integrity of cracked components. The results obtained are presented in the form of fatigue crack initiation and propagation behaviour and S-N data. as modelled and represented in JOSH. such as BS 4360 SOD.Fatigue and Fracture Mechanics of Offshore Structures A Jack-up Offshore Standard load History (JOSH) was developed as part of this investigation. The current practice on the design of offshore welded connections using both S-N analysis and FM is reviewed. Fracture Mechanics (FM) analyses of results are presented in Chapter 4. The book is concluded in Chapter 5 with a statement of the main findings and recommendations. Chapter 3 presents details of the large-scale fatigue testing programme conducted on tubular weld joints using the simulated service loading history. such as Jack-up platforms. existing FM models are compared with experimental data and the inherent limitations of the models. when applied under stochastic service loading conditions. and the role of variable amplitude corrosion fatigue in the failure of welded connections used in the fabrication of engineering structures. fatigue design. A novel generalized fracture mechanics approach for the assessment of fatigue crack growth in offshore installations is presented. 4 . The results obtained from SE 702 are compared with those obtained from other high-strength steels and conventional fixed offshore platform steels. are identified. and the implications of some of the recommendations from the existing design codes are discussed. which will add to the existing body of knowledge in this field. which defines the events of crack extension. JOSH. The main sources of stresses in welded joints are given. The methodology adopted and how the different factors that affect the fatigue performance of Jack-up steels. Further work. is presented in Chapter 2. 1. as it provides vital information on the level and distribution of critical stresses in each component of the structure. as well as a review of the different stress analysis techniques available to the designer for their estimation. Stress analysis is also a very important step in the design process for engineering structures. Three main sources of stress have been identified in tubular welded joints: Nominal stresses. This section presents a definition of the stresses involved and the methodologies employed in determining the characteristic stress. These stresses can be calculated by considering the mechanism of load transfer through each tube and intersection using frame analysis and beam bending theory. Due to the complexity of joint geometry and shell behaviour of welded tubular joints that govern load response. These joints can be loaded in any combination of three modes. 5 . As an integral step in the design and assessment of engineering structural components. which is considered to control the fatigue life of tubular welded joints. OPB. Nominal stresses arise due to the tubes of the welded joint behaving as beams and columns. Non-uniform stress distribution leads to the existence of stress gradients and sites of stress concentrations. Great emphasis is placed on experimental techniques and the use of parametric equations. and axial loading The non-uniform distribution of stress has been demonstrated to occur both on the tubular joint surface and also through the joint thickness. out-of-plane (OPB). illustrated in Fig. These stress concentration sites represent regions where fatigue cracks can originate and propagate to cause structural failure. mostly along the chord and brace weld toes.3 Illustration of IPB. The nature of such stresses will depend entirely on the dimensions of the joint and the mode of loading. local stresses are non-uniformly distributed.3. 1.3 Stress analysis of tubular joints Offshore structures are made from welded tubular joints of varying complexity with respect to size. geometric stresses and notch stresses. These include axial loading. stress analysis is carried out to determine both the location and magnitude of these critical stresses. shape. and load carrying capacity. and inplane (IPB) bending. 1. 1.3.Literature Review 1. Fig.1 Definition of stresses in welded connections In both stress-life (S-N) and FM based methodologies for fatigue crack growth analysis critical stresses have to be determined for each component of the structure. can result in misinterpretation of this important parameter. These stresses are. The document states that stress concentration factors may be obtained from relevant tests or analyses. but fails to emphasize the need for it to be calculable and experimentally reproducible. 1. therefore. The hot spot stress excludes the contribution to the stress concentration caused by the notch effect of the weld geometry. therefore. This code also requires the SCF not to be less than 2.4.14] and. Due to the complexity and the variety of joint geometries used in the construction of offshore structures. 1. It also indicates that 'different stress components may be associated with different SCFs. therefore. Notch stresses arise from the notch effect or geometric discontinuity of the tube walls introduced by an abrupt change in section at the weld toe. These stresses are also commonly referred to as local stresses and are a function of weld size and geometry.e.Fatigue and Fracture Mechanics of Offshore Structures Geometric stresses. It has been noted [1. The definition of hot spot stress is not clear cut in the DnV rules for the design and construction of offshore structures [1. depending on the code used. the resulting threedimensional stress field is highly localized. the weld toe radius and angle) cannot be made identical for each joint configuration. 6 . This definition is not stated very clearly in many design codes [1. notch or local stresses are not propagated far through the wall thickness and.15]. the weld toe geometry (i. arise as a result of differences in the load response of braces and chords under the loading configuration. The definition is illustrated in Fig. The consequence of this has been the adoption of a characteristic stress range for the development of S-N curves. Different location of 'hot-spots' for the different stress components may be taken into account if relevant documentation on the locations is available'. Unlike nominal and geometric stresses.3.2 Definition of hot spot stress The hot spot stress is considered to control the complete fatigue life of a tubular welded joint. The greater the weld toe radius and the greater the overall angle of the weld toe. It is the stress at the weld toe calculated by manner of a linear extrapolation to the weld toe of the geometric stress. weld profiles in offshore structures cannot be controlled to such a degree that will lead to consistency in the distribution of notch stress concentrations in tubular welded joints. allows for the use of a single S-N curve in their design. As a result. This characteristic stress range is known as the hot spot stress range. the concept of the geometric stress range (GSR) has evolved as a practical basis for the fatigue design of tubular welded joints as it places many different structural geometries on a common basis and.13] that even with very tight quality control strategies in manufacturing yards. the more restraint there is on localized deformation and the higher the magnitude of local stresses. on the other hand. It is known that geometric stresses may cause the tube wall to bend in order to ensure compatibility in the deformation of the chord and brace around the intersection depending on the mode of loading.5. difficult to measure in a reproducible manner by any criteria. 5 recommended by DnV. due to the joint geometry or loading mode.42] The original document. X. while the Lloyd's Register equations [1. and overlapped K joints.18] are recommended for K and KT joint configurations. this document requires that the SCF values are limited to a minimum of 1. while the semi-empirical formulae due to Kuang are recommended for K and KT joints. however. These have now been revised [1.16]. It did not spell out the need for the hot spot stress to incorporate the effects of the overall chord and brace geometry.17] and LR recommends the use of Efthymiou equations for T. including the stiffening effects of the weld without the influence of the region of rapidly increasing and highly variable nonexperimentally determinable stress near the weld toe. Y. For particular cases where. 1. Compared to the minimum value of 2. had its limitations regarding the definition of hot spot stress. or a combination of both. a particular joint falls 7 .5.4 Schematic definition of hot spot stress in tubular joints [1. Fig.Literature Review Another document that attempts to impose a limiting value to the minimum SCF is that produced by Lloyd's Register (LR) of Shipping [1. It also recommends the use of empirical formulae proposed by Wordsworth and Smedley for calculating the brace and chord SCFs for T and X joints. the strain gauge should be sufficiently small to avoid averaging high and low strains in the regions of steep gradients'. The definition of hot spot stress in the United States is characterized by two main design codes. recommends the use of the finite element analysis (FEA) method to obtain hot spot stress and highlights the fact that 'When measuring hot-spot strain. These categories are covered very briefly in the following section. This requires that the higher SCF is used where this increases with the parameter of interest and where this reduces the limiting value at the parameter limit.20]. The API RP2A and AWS Dl. This definition of hot spot stress was a subject of discussion in the UK Offshore Steels Research Project (UKOSRP) and was drafted by the review panel set up by the Department of Energy to asses the results of the research programme. which defines the hot spot strain as The cyclic total range of strain which would be measured at the point of highest stress concentration in a welded connection . through experimental methods on steel and acrylic models. offer the necessary consistency required for determining SCFs in tubular welded joints.e.'. The American Petroleum Institute-RP2A [1. Using this definition the hot spot strain is taken as the absolute peak value obtained by a strain gauge placed near the weld toe. 8 . Though the guidance available on stress analysis of offshore welded tubular joints may seem limited as presented above. but draws attention to the fact that the concept of hot spot stress is applied differently in Europe and the US. In the US the emphasis is on the extrapolation of the maximum measured stress. This hot-spot stress incorporates the overall effects of joint geometry (i. the relative sizes of brace and chord) but omits the stress concentrating influence of the weld itself which results in a local stress distribution'..Fatigue and Fracture Mechanics of Offshore Structures outside the validity limits for the formulae indicated above. These approaches to stress analysis range from classical theoretical methods. depending on the mode of loading. This definition does not. It was used in the revised UK guidance notes. to numerical computer intensive methods such as finite element analysis and those based on parametric equations. like API-RP2A.. The greatest value around the brace/chord intersection of the extrapolation to the weld toe of the geometric stress distribution near the weld toe. This code. the approach in Europe relies on the extrapolation of the maximum principal stress. The UK Department of Energy Guidance notes give a clearer definition of hot spot stress as [1. This definition of hot spot stress is now accepted as an offshore standard for stress analysis of offshore tubular joints. The recommendations outlined in the codes above depend on the methodologies employed and the degree of accuracy required for any particular joint configuration and loading. there is a wide body of literature on stress analysis of tubular welded joints.19] defines hot spot stress as 'the stress in the immediate vicinity of a structural discontinuity'. This value is clearly a combination of geometric and notch stresses and is bound to vary from joint to joint. LR recommends the use of a conservative approach. This is the definition adopted in this book. therefore.21]. The current draft ISO standard maintains the concept of the geometric stress as the characterizing stress for fatigue analysis of welded connections.1-92 [1. 24] and Caulkins [1. These were in the form of empirical equations developed for stresses and deflections. Caulkins used a computer program FRAMETI. Due to the complexity of joint shapes and the shell behaviour governing load response of tubular joints. 9 . The stresses obtained by using this method were limited to axial loads applied through the chord and under IPB conditions. stress analysis of tubular welded joint intersections is difficult. Several methods have been used over the years for the analysis of stresses in welded joints.3 Methods of stress analysis Through careful examination and analysis of considerable experimental and theoretical data that were obtained after major research projects into the behaviour of offshore structures (such as the UKOSRP). This is particularly useful for the comparison of results presented in Chapter 3. However. Although Roark's work was not directly concerned with tubular joints. By the late 1960s. used Roark's results. his results were used by other researchers to make important contributions. to evaluate brace and chord stresses for T and Y joints under all three modes of loading and K joints under axial loading. This section presents a review of these analysis techniques used to evaluate stresses for fatigue assessment of offshore structures. the classical solution methods used by Kellogg [1. an important first step at the design stage and also during structural integrity assessment programmes. Its determination and evaluation is. a wide range of techniques have been developed and employed in assessing offshore structures. based on membrane cylindrical bending stress theory. after studying cylinders subjected to diametrically opposed concentrated loading. The stresses in the chord were then obtained by increasing the load intensity on the chord due to the axial forces in the brace by an appropriate factor and adding this to the load intensity on the chord due to bending stresses in the chord. Kellogg used an analogy of the behaviour of a circular cylinder. additional background and the basic principles behind the development of other methods are presented in this chapter. extensive experimental stress analysis was carried out on the tubular welded joints used in the course of the study presented in this book. For instance. Numerical methods were also used as early as 1955 through to the early 1960s. As a result. This was employed by computing the nominal stresses in the brace and treating this as a live load applied to the surface of the chord at the intersection.Literature Review 1. the hot spot stress at the intersection of welded tubular joints has been accepted to govern fatigue endurance of offshore structures. therefore. subjected to uniform circumferential loads and developed a method of obtaining stresses in the chord.3. as this knowledge provides a suitable platform from which any discrepancies between results obtained using different methods can be adequately explained. Nevertheless.23]. Stress analysis of tubular welded connections is not the main subject of this book. The methods vary in their degree of accuracy in modelling different geometries and loading cases. the results of which are presented in Chapter 3.22] and Toprac [1.25] were well established. the first attempts to analyse tubular joints using theoretical methods started in the early part of the 1950s and 1960s when Biljaard [1. As a result. a discussion on the use of strain gauges for experimental determination of stress concentration factors is presented. be taken in the scaling down of weld sizes for scaled down specimens.1 Experimental methods Most of the early information on the performance of tubular joints and tubular joint stress behaviour was obtained by experimental measurements on steel models. acrylic models.28] used the technique to study a range of tubular joint geometries and obtained detailed information on the distribution of stresses on the surface and also through the chord and brace walls near the intersection.Fatigue and Fracture Mechanics of Offshore Structures During stress analysis assessment of offshore structures for fatigue evaluation. This method was used in the course of the UKOSRP to study a wide range of T and K joints and the effect of varying their geometric parameters on their behaviour under different modes of loading. It is usually implemented by strain gauging scaled down models or full-scale replica of tubular welded joints.26] used it in the early 1970s to conduct three-dimensional stress analysis on T joints. is difficult through the use of theoretical methods. 1. these methods have been superseded by the use of FEA. However. In order to attain a high level of correlation with measurable stresses and strains encountered in a typical offshore structure. 10 . The use of steel models for stress analysis of offshore structural components is a wellestablished technique. It is also recommended that tolerances on dimensions be based on current offshore standards and the results interpreted in the light of actual specimen dimensions and geometry. Experimental methods can be categorized. 1. More recently. These techniques are not covered in detail in this book. Photoelasticity is particularly useful for joints with rather complicated geometries.27. therefore. and different approaches were being used to determine stresses in tubular welded joints using experimental methods. steel tubular joints used for stress analysis must be fabricated to standard offshore procedures to obtain satisfactory results. Fessler et al. depending on the modelling medium. [1. Experimental methods rely on the measurement of strain and hence stress concentration factors on scaled or full-scale models. experimental measurements. distribution of stress around the intersection and also through the joint thickness may be required. The results are compared with those predicted using parametric equations in Chapter 3. The stress concentration factors for the tubular joints presented in this book were based on experimental measurements. Bouwkamp carried out the first reported tests on tubular welded joints using this technique in 1966. The increased offshore activity in the North Sea in the 1970s lead to an increased need to predict stresses in tubular joints more accurately. It is known that unrealistically large welds can produce unrepresentative results. The determination of stresses in tubular welded joints. These include methods based on the use of steel models. and photoelastic models. used in the construction of today's increasingly complex structures. This book focusses on the latter two methods. Care must. and parametric equations.3.3. The method was developed in parallel with FEA. even though these have been improved tremendously over the years. Holliday and Graff [1. There are strict guidelines regarding the location of strain gauges for this purpose and Fig. 1. two-dimensional stresses on the surface of the specimen can be computed and transformed into principal stresses. This is achieved by multiplying the strains at the gauge locations with the Young's modulus of the material and appropriately taking into account any Poisson ratio effects. The relevant distances and tolerances on positioning the gauges are shown in Fig. This should be done with caution to avoid any unrepresentative results. The stresses at the weld toe are obtained experimentally by linear extrapolation to the weld toe of the experimentally measured principal stresses. may lead to underestimation of hot spot stress by up to 30 per cent.5 shows a schematic representation of the locations of the extrapolation gauges. The recommended practice in both AWS Dl.1-92 and API RP2A. This is mainly due to the fact that a direct multiplication approach like this does not take into account any deformation resulting from the Poisson ratio effect. Strain gauges should be positioned in accordance with recommendations of UKOSRP. Therefore. 1.5 Locations of strain gauges on tubular joints 11 . which considers the hot spot stress as the product of maximum measurable strain and Young's Modulus.6. 1. Fig.Literature Review The use of experimental stress analysis methods relies on the assumption that the twodimensional strains measured on the surface of the steel model remain linear. Wordsworth and Smedley [1.6 Recommended tolerances for locating strain gauges from the weld toe [1. high-capacity loading machines are required to provide measurable strains in full-scale and otherwise stiff specimens. There are other methods that have been successfully used in recent years. therefore. These include thermoelastic methods. It is also a very time consuming and expensive method.Fatigue and Fracture Mechanics of Offshore Structures Fig. This may pose a serious problem where changes in strain are very small and difficult to measure or. scaled-down acrylic models offered an alternative solution to full-scale tests carried out on steel models. only average strains over the region of interest can be measured. where a very steep strain gradient exists. if precautions are taken. on the other extreme. In addition. However due to the physical size of the gauges. 1. because extensive strain gauging is required to give detailed information on the stress distribution in the region of interest.29] used this method to investigate stresses in tubular welded joints.40] Experimental methods on steel models normally give representative and accurate results. and conducting measurements on acrylic models. as alternatives to strain gauging large-scale steel specimens where possible. when offshore activity in the North Sea increased tremendously and the more cost-effective methods of stress analysis of offshore tubular joints were being sought after. In the 1970s. Results obtained using this technique are. the use of brittle lacquers. 12 . commonly used as a benchmark for assessing the accuracy of other methods. A general review of some of these parametric equations is presented here. They can also be more prone to deformation due to creep. cheaper. Kuang studied forty-six T and Y joints under the three modes of loading. lower loads are required to produce measurable strains in acrylic models. strain gauges can be fitted before assembly. The equations proposed included design safety factors and influence factors for different loading configurations. A comparison between experimental measurements and SCFs obtained using parametric equations is presented in Chapter 3.35-1.33]. Smedley [1. equations of Kuang et al. However. thirty-seven K joints under in-plane bending. 1.31] published in 1977.34]. Lloyd's Register equations Lloyd's Register proposed a set of parametric equations. and sixteen KT joints under balanced axial loading conditions in the inclined braces. [1. They can also be used to investigate the effects of ring stiffeners and welds on stress concentration factors.17].37] equations.3.29] based on a study of acrylic models.30] employed this approach to produce a weld fillet correction factor for T and 90 degree X joints based on the weld fillet leg length. First. the test rigs designed for applying these loads could be simpler. This makes it easier to use acrylic models to study stress distributions on very complex geometries.32] published in 1978 after the use of the finite element program NV332 to study stresses in T joints. and a lot lighter. For example. thirty-nine K joints under balanced axial loading. since their Young's modulus is usually a lot lower than the typical values for steel models. Some of the precautions include making estimates of Young's modulus at the same time at which the strain measurements are made. Second.3. There are other parametric equations such as those proposed by Efthymiou and Durkin [1. making it possible for strains and stresses to be obtained at those locations that are normally inaccessible in conventional welded steel models. Efthymiou [1. accurate and representative results can be obtained from acrylic models at a lower cost compared with steels models. Kuang et al.2 Parametric equations Based on several independent studies. with due precaution. a few sets of parametric equations have been published that have varying capabilities and degrees of accuracy in analysing various joint geometries. These were developed for simple tubular joints after completing a project sponsored by the UK Department of Energy to assess methods for deriving stress concentration factors (SCFs) in simple tubular joints. and a 13 . and the Hellier Connolly and Dover [1. Lloyd's Register [1. which were published in 1991. These equations include those of Wordsworth and Smedley [1. and taking due care when selecting the length of tubing and the required model scale. These equations were based on an existing database of SCFs previously derived from steel and acrylic models. The main disadvantage of using acrylic models is that the tubing may be susceptible to significant residual stresses that affect the surface of the specimen. and Gibstein's equations [1.Literature Review Acrylic models offer some advantages over steel models. As a result. there was a significant difference between the predictions from these two sets of equations for certain joints and loading configurations. Kuang assumed fixed chord end conditions to provide the necessary torsional restraint. were used and 150 joints under various loading configurations were studied. capable of explicitly modelling the tube thickness and weld profile. The SCFs for the brace were modified by a factor of 0. First. Gibstein After using the finite element program NV332 to study stresses in T joints. However. the modifying parameter VQB was assumed to be valid only for DT. it should be noted that the influence of a was deduced from Kuang's formulation and is included in the formulation for axial loading of tubular T joints. In obtaining these equations.0. The formulae are summarized in [1. Gibstein regarded the Gaussian points closest to the brace chord intersection to be representative of the locations for the 'hot spot' stresses and did not investigate the effect of the non-dimensional parameter. Y. However. Subsequently modified by Underwater Engineering Group (UEG) for joints with equal brace and chord diameters. It should be noted that the SCF obtained using this set of equations is that at the intersection line of the mid-surface between the brace and chord for the Y joints. described in detail in Chapter 3. Y. the equations were based on a three-dimensional finite element analysis using the program PMBSHELL. For these sets of equations the effect of the welds was not included and they were intended to yield the gross deformation SCF.31]. KT. and K joints [1.8 to ensure correlation between the predicted and experimental results.33]. Efthymiou and Durkin In Efthymiou and Durkin's paper which presented the set of equations for predicting SCFs for T. TKJOINT. The reason for the modification introduced by UEG was a recognition of the fact that the original equations underestimated the SCFs for joints with B = 1. They were based on a study conducted on seventeen T joints with both chord ends rigidly fixed. the effect of which was also investigated by varying the end conditions in a separate test that had simply supported chord ends. Three-dimensional curved shell elements.Fatigue and Fracture Mechanics of Offshore Structures single axial load in the 90 degree brace using a finite element program. Wordsworth and Smedley These parametric equations were developed for T. These equations are presented in reference [1. Y. and T joints for estimating the saddle point SCFs. a. Another geometric modifying parameter. and X joints.29]. Gibstein proposed a set of parametric equations to predict SCFs in T joints. X. was introduced to ensure better prediction for joints with y > 20 and it was assumed to be applicable to all joints. designers and classification authorities were still faced with a few problems. there was limited 14 . K. VQr. However. Second. they were based on results from acrylic models. 33] and were subsequently extended [1. The short chord correction factors were. the distribution of SCF was found to be symmetrical about the saddle position and the following expression that predicts the distribution of SCF was proposed where S(0) is the characteristic formula for the stress concentration factor around the chord brace intersection with a hot spot value of KHS. 15 . The set of equations proposed by Efthymiou and Durkin was developed to close up the gap that existed between predicted results from the equations of Kuang and Wordsworth and Smedley and to offer better prediction of SCFs for certain simple K and KT joints and for joints with overlapped braces. This involved nearly 900 thin shell FE models. developed to account for this. therefore. limited information was available for certain loading configurations in simple K and KT joints and also on joints with overlapped braces. Wide ranges of joint geometries under various modes of loading were studied. The formulae are summarized in reference [1. At the time of this publication.Literature Review information on SCFs in stiffened and multiplanar joints. For Y joints.36].The above equations were adopted for other parametric equations to facilitate the comparison of experimental results with those based on other parametric equations in Chapter 3. The results were compared with those obtained from a range of other techniques. This leads to a reduction in the deformation and stresses in the chord. for example under OPB. A fixity study was also carried out and the effects of chord end fixity were quantified where relevant.34] to cover X and KT joints. It was noted that using short chords interrupts the natural decay of chord deformation resulting from brace loading. These set of equations were modified to give the first set of parametric equations capable of predicting the stress distribution around the intersection of the brace and chord. Third. These equations are recommended by most design guidance notes and are highly consistent in the prediction of SCFs. This lead to the development of a comprehensive set of parametric equations for estimating SCFs in tubular welded Y and T joints. They were used in the development of generalized influence functions for the prediction of SCFs in planar and multi-planar joints subjected to arbitrary brace end loads and moments. A complete summary of these equations is given in reference [1. including the effect of chord length. Hellier Connolly and Dover Hellier Connolly and Dover carried out extensive and systematic FEA to study stresses in T and Y joints. the most comprehensive and widely used equations were those of Kuang and Wordsworth and Smedley. However. It has the advantage that it provides an assessment methodology that is based on a single 16 .Fatigue and Fracture Mechanics of Offshore Structures 1. This makes fatigue analysis of such structures very important. These include the SN approach and the fracture mechanics approach. Codification of the resulting data started around the 1850s when Wohler carried out his now classic experiments. As a result of the idealizations and approximations employed in the analysis process. is a very important tool for designers to use in the prediction of relative magnitudes of fatigue lives of structures at potentially critical points. 1.39] is The process of progressive localized permanent change occurring in a material subjected to conditions which produce fluctuating stresses and strains at some point or points and which may culminate in cracks or complete fracture after a sufficient number of fluctuations'. any fatigue analysis approach adopted will almost always be associated with some degree of identifiable uncertainty. Fatigue analysis.4. at the same time. reduce the level of confidence that may be associated with any exact calculations resulting from any particular fatigue life prediction methodology. Fatigue analysis methodologies have been shown to yield reliable estimates of fatigue life and two distinct approaches have evolved for use in fatigue life assessment of engineering structures. for example. however. This will include uncertainties resulting from inadequate understanding of the complete effect on the structure of the operational environment.38] is 'Failure of a metal under a repeated or otherwise varying load which never reaches a level sufficient to cause failure in a single application'. These welded intersections constitute regions of stress concentrations. Fatigue analysis can be rigourous. This was recognized well over a hundred years ago and research in this area started as far back as 1838. they give a clear indication that fatigue is a process of cumulative damage. and the relationship between this and the actual forces.4 Fatigue design One definition of fatigue given in reference [1. moments. Design for fatigue resistance and fatigue life prediction is an important aspect for consideration in a wide range of industries and engineering applications today. Another definition given in reference [1. steel offshore jackets and Jack-up legs consist mainly of tubular joints. Crack propagation may lead to eventual failure of the structure. and stresses experienced by the structure. In the offshore industry. which represent areas that are highly susceptible to crack initiation and subsequent propagation.1 The S-N approach The stress-life (S-N) approach is based on available fatigue test data. which are subjected to fatigue loading. The implication of this uncertainty is to introduce a potential for error and. These two definitions are not the only variants of the numerous definitions found in the vast literature available on fatigue and the behaviour of fatigue cracks. but it is by no means an exact science. which are formed by welding together intersecting brace and chord members. both at the design stage and also during structural integrity assessment programmes. which lead to the development of S-N curves. This is detected either visually or. Using data obtained from small-scale specimens tested in air. On the other hand.Literature Review parameter. N. S-N refers to the life or number of cycles to failure of the joint. by noting first loss of internally applied air pressure to the damaged member.. Such cracks are also deemed necessary to be '. S . more accurately. This definition. Like 'hot spot' stress. of the linear part of the stress distribution near the weld toe but removed from the region of rapidly rising stress immediately adjacent to it. under constant amplitude loading conditions.4. Even though the API RP2A was influenced to a large extent by the experience on the behaviour of platforms in the Gulf of Mexico.l provided the first guidance on the design of tubular joints against fatigue using S-N curves.42]. Projects like this lead to the generation of vast amounts of experimental data that were used to formulate the S-N curves for the Department of Energy Design Guidance notes and the Health and Safety Executive (HSE) design guidance. first published in 1984 [1. the 'hot spot' stress. was taken as that which denoted 'first through wall cracking. is based on a linear extrapolation to the weld toe. S. The curves recommended by the 1972 editions of API and AWS were developed on the basis of two concepts. The reason for adopting this definition is that it is appropriate to use a measure of life that will result in both detectable and reparable cracks in a structure that is capable of tolerating them without the intervention of catastrophic fracture.1. and the second was based on the 'hot spot' stress of the joint. In the early 1970s. used in S-N design curves has been a subject for consideration in the course of major research programmes such as the UKOSRP. (designated N2 in reference [1.3.41]) together with the 'hot spot' stress.1 Formulation of the basic S-N curves The S-N approach is well established for the design of offshore welded tubular joints and connections. the definition of fatigue life.41] and the subsequent revision [1. are the two parameters used to formulate S-N design curves and are given as 1.42]. This life. it has been used extensively to design structures for the harsher environments of the North Sea. The same definition of 'hot spot' stress used in the UKOSRP reports [1.. editions of both API RP2A and AWS Dl.40] was maintained in the Department of Energy's 'Background to new fatigue design guidance for steel welded joints in offshore structures'. designated N3. N. the definition of life. the S-N curve (called the 'X curve') was proposed with a note of caution from AWS. The first was an attempt to correlate failure to brace nominal stress. The implication was that calculated fatigue lives based on the proposed curves should be 17 . or by monitoring the output of strain gauges positioned adjacent to the crack at its deepest part'.2. discussed in Section 1. or the number of fatigue cycles to failure.small enough for the structure not to have to shed load and thereby (possibly) damage other joints' [1. The data were assessed by a review panel for fatigue guidance. thickness effect. design codes have been revised and the guidance on fatigue design has been modified. however. However.61 5. a major revision of the fatigue guidance notes was carried out. and K joint test results and recommended for joints having a chord wall thickness of 32 mm.43]. the design S-N curve given in Table 1. These revisions have not been given here in detail since they are available in respective codes and other relevant literature. based on available data. Under the section on 'Fatigue-allowable fatigue stresses'. The same data used in producing the API and AWS curves were also the basis of the curves in BS 6235 [1.164 3. After the completion of the first phase of the United Kingdom Offshore Steels Research Project (UKOSRP I) in 1984. appointed by the Department of Energy to ensure that relevant data were used in the revision of the UK Department of Energy Fatigue Design Guidance. Since 1984 when reference [1. an indication of how the fatigue guidance offered by the UK Department of Energy Guidance notes has evolved in more recent years is presented with consideration of other relevant factors that affect fatigue performance and how they have been incorporated into the S-N approach.44]. Following the increasing availability of experimental data. a substantial amount of data on the fatigue behaviour of offshore welded tubular joints was made available following the completion of other major research projects such as the UKOSRP II. To a large extent this constituted a driving force behind the initiation of extensive research programmes starting with UKOSRP I in 1973. Table 1. X. NPD [1.Fatigue and Fracture Mechanics of Offshore Structures viewed with a healthy amount of scepticism. The above statement of caution.2 was proposed.0 The document also addressed the modification to the basic curve for unprotected joints in seawater. and effects of weld improvement and treatment for low and high stress cycles.0 15. 18 .15].1. After excluding some categories of the available data to ensure that the selected data set covered the widest range of joint geometries and loading configurations. and DnV rules [1. more as design guidance than as an absolute requirement. is an indication that there were other factors at the time that were understood to govern fatigue but which had not yet been addressed. see Table 1. a basic T curve was proposed for fatigue design of tubular joints. This curve was based on sixty four T.1 The basic design T curve N < 107 Curve Log 10 (K1) m N<10 7 Log10 (K1) m T 12. including earlier editions of the UK Department of Energy guidance notes.21] was published. and W') similar to the classes for welded plates in the HSE guidance.3 The basic design P curve N <107 N <107 Curve Log10(K1) 12.0 5.76 16.3.47 TJ CJ OJ (Class B) OJ (Class C) OJ (Class D) OJ (Class E) OJ (Class F) OJ (Class F2) OJ (Class W) Log10 (K1) 12.0 This was based on 16 mm wall thickness (cf.0 5. The corresponding basic design S-N curves for flat or rolled plates is given in Table 1.0 5.01 13. Table 1. It recommends the TJ curve for welded tubular joints that are exposed to constant or variable amplitude loading.0 3. D.33 14.127 5.0 19 .4.0 Log 10 (K1) 15.637 m 5.0 3. mainly to retain consistency with previous guidance and other design codes.Literature Review Table 1.4 The basic design S-N curves from the ISO draft standard N <108 Curve N <108 Log 10 (K1) 15.33 5.0 16.97 m m 3. This basic design S-N curve for tubular joints was taken to correspond to two times the standard deviation of the Log 10 (N) below the mean S-N line for the 16 mm data.02 11. depending on the classification for the connection.0 4.63 12.182 m P 3.0 3.0 3.0 16.0 5. This could be (B.06 13.0 5.0 5.63 10.0 3. These equations are given in Table 1.17 15. The slope of -1/3 was adopted for the T' curve. the CJ curve for cast nodes. and the OJ curve for other welded connections.80 11.69 14.0 5.0 4.18 12. F. F2.0 5. 32 mm for earlier revision) and allowances were made for other relevant factors. Table 1.476 3.2 The basic design T' curve N < 107 N < 107 Curve Log10 (K1) m Log10(K1) m T' 12.04 14.48 15. The existence of an endurance limit was accounted for by a change in slope of the basic curve from -1/3 to -1/5 at 107 cycles.97 14. E. C.5 3.0 The current draft ISO standard recommends a new set of basic design S-N curves based on the joint type. a reduction may result for greater wall thickness.45] and different researchers have since put forward different arguments to explain this phenomenon. Marshall [1. These important considerations and the associated 'penalties' applied to the basic design S-N curves are covered below. these need to be taken into consideration when using these curves for the design of welded connections. This book addresses part of this problem.4. that the average growth rate of these cracks is higher in specimens with wall thickness in excess of 32 mm. It was demonstrated by Wylde and Mcdonald in 1979 [1. some of the data that were available were excluded from the statistical analysis carried out by the review panel for fatigue guidance after the screening process. There are other important factors that should be taken into consideration when using S-N curves. The book also presents new methods for assessing fatigue damage under variable amplitude loading conditions and identifies the likely differences in S-N behaviour of highstrength steels when compared with conventional fixed-platform steels. Some of the categories that were excluded include the database on variable amplitude loading and data obtained from tests carried out on specimens with wall thickness less than 16 mm. with adequate cathodic protection. The implication of this is that. 1. Even though a wide range of these factors had been studied. Despite the exclusion of some of the data sets on the grounds that they were not adequate.1. were not considered adequate to be incorporated in the proposed design curves. It has also been demonstrated that this effect could be operative for chord wall thickness as high as 75 mm and the trend has equally been observed to occur in simpler welded connections such as T butt welded plates. Thickness effects on fatigue resistance Considerable research work into the effect of wall thickness on fatigue resistance of a component or structure has been carried out and documented. As a result. The implication of this is that the design guidance is very limited for real engineering structures subjected to variable amplitude loading. instead of an increase in fatigue resistance as wall thickness is increased. allowances were made for these relevant factors to be considered when using the design S-N curves. It presents new data on high-strength steels and identifies the key issues to be considered when dealing with variable amplitude fatigue.Fatigue and Fracture Mechanics of Offshore Structures The draft ISO standard also recommends that the above curves should be used for both air and seawater applications. This effect has been widely referred to as the 'thickness effect'. It has been demonstrated for a given 'hotspot' stress.2 The implication of other factors' fatigue performance Other relevant factors effect the fatigue behaviour of welded connections. Some of these factors are discussed below. A great proportion of the fatigue life of tubular joints is spent in the propagation of fatigue cracks.46] studied size effect on tubular welded joints in the early 1980s and suggested that the phenomenon is not only related to plate thickness and that other 20 . the data available when the T' and P curves were proposed. This adds significantly to current knowledge on variable amplitude corrosion fatigue performance of high-strength steels. It is.7. Other researchers [1. This view followed Haibach's findings [1. 21 . After reviewing further fatigue test data. and y is the thickness correction exponent. Based on this observation. the effect of a lower throughthickness stress gradient. They also observed increases in the weld toe stress concentration factors for thicker joints. In the earlier edition of the UK Department of Energy Fatigue Guidance notes [1.Literature Review parameters. it was demonstrated that the thickness effect also occurs in joints with chord wall thickness below the previous limiting thickness of 32 mm.K region. A value of 0.51] argue that size effect is due to a combination of increased weld toe stresses and. the stress range that results in the same fatigue endurance at a thickness t. which controls a high proportion of the fatigue life and more significantly so in smaller welded joints. such as the weld toe and the associated size of the local notch zone could be more important. A new reference thickness of 16 mm was proposed for tubular joints and plates with a conservative thickness correction exponent of 0. This is by no means an exhaustive review of studies conducted to quantify thickness effects on the fatigue strength of tubular joints. [1. however. Webster et al.21]. to some degree.25 was recommended for the thickness correction exponent. widely accepted that the effect can be detrimental to fatigue performance. This argument focussed the size effect on crack growth in the low A. tB and 5.48] noted a decrease in fatigue strength by about a third by increasing the plate from 38 mm to 100 mm. This correction factor is applied as a penalty factor to thicknesses greater than the reference thickness. 1. This is expressed as SB is the stress range at the reference thickness. After a review of experimental data.3. the reference thickness was taken as 32 mm for tubular joints and 22 mm for plates. The effect of thickness on the design S-N curve is demonstrated in Fig. a correction factor was proposed.49-1. He noted that there was a fall in fatigue strength as a result of an increase in the weld size alone.47] when he investigated the effect of fillet weld throat size on 50 mm thick plates in the late 1970s. y. another explanation based on higher local stresses was proposed. 8 Schematic illustration of thickness effects [1.Fatigue and Fracture Mechanics of Offshore Structures Fig. 1. this does not explain the fact that this phenomenon is less pronounced for axial loading than has been observed under situations where bending loads are involved. cannot be dismissed. A: Illustration of stress gradient for pure bending B: Effect of thickness on AK and mode of fracture Fig. 1.52] 22 . However.7 Illustration of thickness effect on S-N curve The argument that thickness effect is not just related to plate thickness and that other parameters. such as the weld toe and the associated size of the local notch zone could be more important. The main reason for this decision was that free corrosion may lead to pitting. The consequence of these two aspects is that. The following curves (Table 1. Environmental effects on fatigue resistance The environmental conditions experienced for welded connections in service can vary. 1. fully immersed and also on the level of any cathodic protection (CP) applied. This effectively removes the fatigue limit. A penalty factor of two on design fatigue life was recommended for unprotected joints. and also due to the lack of sufficient experimental data. Corrosion pits act as stress concentration sites where crack initiation and subsequent propagation can take place. depending on the location of the connection in the structure. In particular. three recommendations were made in earlier codes regarding the use of design S-N curves and the environment. This section presents important discussion on some of the key issues relating to corrosion fatigue and the likely impact of CP.assuming that their distribution per unit volume is uniform. The change in slope at 107 cycles was not to be applicable to joints under free corrosion.8. the way this is incorporated in the use of design S-N. there is a greater probability of initiating a fatigue crack in the thicker specimen. due to the presence of a more severe stress field.5) were proposed for use in the design of protected joints and for those under free corrosion conditions and are the latest proposed revisions to fatigue guidance [1. even though a fatigue crack has a longer propagation path in a thicker specimen. This will depend on factors such as whether the joint is in the splash zone. for a given crack size. It was also recommended that the air curve be used for adequately protected joints. 23 . which also has a higher probability of containing inherent manufacturing flaws .Literature Review As illustrated in Fig. It was recognized that the environment could have detrimental effects on fatigue performance of tubular joints relative to air. As a result. there are two likely causes for thickness effect under bending conditions. This implies that a fatigue crack of a given size will be subjected to a higher stress in a thicker specimen. Based on this.42]. which may exist at low stress levels in a non-corrosive environment. the probability of initiation is higher in thicker specimens where they can also propagate faster. The first of these is the existence of a lower through-thickness stress gradient in a thicker plate. which may also exhibit a low critical stress intensity factor range. a larger surface area or volume of material is subjected to a higher stress level in the thicker specimen. The second reason for this behaviour is that. This higher stress level will lead to a higher crack growth rate in the thicker specimen. 0 16.637 These curves effectively represent a factor of two on design fatigue life.705 12. The degree of susceptibility of a particular material will largely depend on the complex interaction between the hydrogen equilibrium in the vicinity of the crack tip and the stress intensity factor. Corrosion fatigue crack growth rates under cathodic protection conditions also depend on the level of cathodic protection. and the interaction between these two damage processes.5 The basic design S-N curves for protected and freely corroding joints N<10 7 Curve Tubulars Plates Tubulars Plates Log10(K1) 12. the rate of material deterioration due to corrosion. The main reason for this change in approach to the design of protected joints was that further fatigue tests carried out before the 1990 revision to the design guidance notes [1. it is possible that the current reduction factor of two on fatigue life may not be directly relevant in the design of structures made from higher strength steels. recommends the use of the same basic S-N curves for both air and seawater with adequate protection for steels with a yield strength of less than 500MPa. however. show that an environmental factor may still be applicable even for adequately protected joints. which never reaches a level sufficient to cause failure in a single application'. among other variables.0 5.0 3. on the other hand. Since the effect of hydrogen produced under cathodic protection conditions varies for different grades of steel.0 Protected joints 3. The occurrence of corrosion under fatigue loading conditions leads to a situation where the damage process depends on the severity of the fatigue loading.00 11. This implication is discussed in greater detail in Chapter 3 where results of the fatigue tests carried out in this study are compared with those from previous tests on conventional fixed platform steels such as BS 4360 50D. This phenomenon is known as corrosion fatigue.42] under adequate cathodic protection levels did not show trends in fatigue lives comparable to air tests. could be defined simply as a process by which a metal's chemical structure is changed resulting in gradual deterioration by being slowly 'eaten' away in a chemical oxidation-reduction reaction.Fatigue and Fracture Mechanics of Offshore Structures Table 1. Fatigue under CP conditions is influenced by many factors.5 3.0 N<107 Log10 (K1) m 5. Results from tests conducted as part of the study presented in this book for higher strength steels and newly generated data on high-strength steels. even for adequately protected joints.784 m Free corrosion 3.127 15. The current draft ISO standard [1. 24 .9].175 11. Corrosion fatigue One definition of fatigue quoted earlier is 'Failure of a metal under a repeated or otherwise varying load. Corrosion. some of which have been demonstrated to be different from material to material. therefore. For tests in aqueous environments the presence of oxygen was demonstrated to be necessary to induce corrosion fatigue. if this simulation is carried out in an unrepresentative environment. Environment assisted fatigue is a major cause for concern and contributes significantly towards the failure of structures. which is precipitated as a reddish brown substance. very important. Iron(II) hydroxide is not a very stable compound due to the presence of iron(II) ions (Fe2+). quickly oxidized to produce the more stable iron(III) hydroxide Fe(OH)3. This form of the hydroxide is. then misleading results can be obtained. Different ideas have been proposed to explain the basic mechanism of corrosion fatigue during the initiation stage.9. 1. Obtaining representative loading conditions for such structures is. They demonstrated that the combined presence of water vapour and oxygen was the cause of atmospheric effects. This can be adequately modelled by use of wave power spectra. However.Literature Review Corrosion fatigue involves unique failure mechanisms that are very complex and depend on the stage of the fatigue process. The early work of Gough and Sopwith [1. therefore. Predicting the behaviour of a structural crack entails estimating the load states that the structure will have to withstand. the mechanism that operates during the crack propagation stage is very complicated and not well understood for high-strength steels. the main constituent of rust. together with the transfer function approach in the frequency domain as discussed in Chapter 2. The dissolution of iron in an aqueous solution can be represented as follows The resulting free electrons from the above process reacted with water and dissolved oxygen to give hydroxide ions as shown in the following equation The corrosion process is effected when the iron ions react with the hydroxide ions resulting in the formation of iron(II) hydroxide as follows The above reaction is shown schematically in Fig. 25 . However.53] has shown that air does decrease fatigue life relative to tests in vacua. that are very complex and depend on the stage of the corrosion fatigue process. The processes of corrosion fatigue and hydrogen embrittlement of high-strength steels are a complex combination of chemical reactions. Subsequent combination of atomic hydrogen at these voids forms hydrogen gas. In a fairly recent review [1.54].Fatigue and Fracture Mechanics of Offshore Structures Fig. Three of the more plausible theories include the pressure. decohesion. and surface energy.55] has led to the view that other mechanisms may be involved in the process of hydrogen embrittlement. five main theories that have been proposed to explain this phenomenon were highlighted. the mechanism that operates during the crack propagation stage is very complicated and not well understood for high-strength steels. But the overall process can be represented by the following simple reduction-oxidation reaction. then leads to the formation of 'pockets' of high pressure within the metal. Various models have been proposed to explain the basic mechanism of corrosion fatigue during the initiation stage. The pressure theory is based on the assumption that atomic hydrogen generated during cathodic protection is absorbed into the microstructure of the steel.9 Illustration of the corrosion process Oxygen is not an absolute requirement for the inducement of corrosion fatigue. However. 26 . but the occurrence of hydrogen embrittlement in high-strength steels in a relatively low-pressure environment [1. Corrosion fatigue involves unique failure mechanisms. 1. and diffuses through the metal lattice structure collecting into voids and/or defects within the metal. but increased crack growth rates under CP conditions help to provide an explanation that hydrogen embrittlement is a possible mechanism. and the possible role of hydrogen is now thought to play a more significant part in the embrittlement of high-strength steels. There is evidence to support this theory. Literature Review The surface energy and decohesion theories are similar. For this reason initiation mechanisms for these structures are considered not to be as important as in the case of smooth polished specimens. This means that the energy required to produce a new surface. The decohesion theory suggests that the presence of hydrogen will tend to lower the inter-atomic energy and. There is little evidence to support the hydride formation theory. Some of these aspects and their effects on the fatigue resistance of offshore structures are covered in greater detail in the following sections. salt content. The surface energy theory. This contradicts the surface energy and decohesion. However. to produce a fatigue crack. This is very significant for offshore structures in that most of the fatigue life of the structural components is characterized by crack propagation.56]. For this type of specimen. This suggests that the presence of hydrogen will favour the formation of brittle hydrides in the vicinity of the crack tip leading to the embrittlement of the steel. degree of aeration.e. Easy movement of dislocations in the presence of hydrogen implies that high-strength steels will show a greater tendency to ductile behaviour. make it easier for the inter-atomic bonds to be broken. therefore. Typically 90 per cent of the air fatigue life of smooth polished specimens may be associated with the initiation of fatigue cracks and only 10 per cent with their growth [1. This is possible due to a combination of sequence effects and crack tip blunting that may arise from the electrochemical action of the environment. resulting in higherthan-expected crack growth rates. therefore. One of the difficulties in quantifying corrosion fatigue and hydrogen embrittlement in high-strength steels is the large number of variables involved. and chemical composition of the corrosive environment. Other theories that have been proposed to explain hydrogen embrittlement in highstrength steels include the hydride formation and the local plasticity theories. crack initiation and associated mechanisms are very important. However. and the loading frequency. higher-than-expected crack growth rates will prevail in the presence of hydrogen. The way they can be controlled during fatigue testing is presented in Chapter 3. the presence of a corrosive environment can drastically reduce fatigue life by reducing the fatigue crack initiation life to about 10 per cent of the total life. under variable amplitude loading conditions. local flow velocity. thereby reducing the possibility of cleavage fracture. pH. on the other hand. temperature. This suggests that the presence of hydrogen tends to reduce the total stress required for dislocation movement. is less than expected and. Under these circumstances. it is important to distinguish between crack arrest and the absence of initiation. suggests that the presence of hydrogen will decrease the surface energy of newly formed surfaces. 27 . crack arrest is possible. There is even less evidence to support the local plasticity theory. Initiation of corrosion fatigue cracks The fatigue life of smooth polished specimens is dominated by fatigue crack initiation. theories and there is little evidence to indicate this kind of behaviour in high-strength steels. These variables include alloying elements in the structural member. i. it is possible that high-strength steels would exhibit an entirely different behaviour under realistic loading and environmental conditions. and that the mechanism with the fastest kinematics will dominate the fatigue crack initiation process. Even under circumstances where this is not the case. The effect of pitting on the initiation of corrosion fatigue cracks is dependent upon details of pit formation. Localized cracking of the oxide layer under cyclic loading exposes fresh metal surfaces that subsequently undergo the same process. as it is justifiable in some cases and unjustifiable in others. BS 7191 (355D). Propagation of corrosion fatigue cracks The fatigue life of offshore welded tubular joints is dominated by fatigue crack propagation. and how these affect the fatigue life of offshore welded tubular joints. The most relevant aspects of specimen characteristics. are discussed in Chapter 3. and API X85 are now available. and structural response for any particular structure. The effects of stress states and stress-time interactions are determined by the loading mode and a combination of wave loading. This comparison is covered in greater detail in Chapter 3. Laird and Duquette [1. grain boundary attack. 450F. defects are developed in these structures relatively quickly and their service life is determined by how fast they propagate through individual components under the relatively low frequency loading that characterizes corrosion fatigue in offshore structures. For offshore welded tubular joints. component stress state. The following two sections review the effects of cathodic protection and variable amplitude loading on the fatigue performance characteristics of welded tubular joints. Four factors have been highlighted to be the most significant influences on the fatigue life of welded tubular joints. hydrogen-assisted cracking. It is also important to recognize the fact that different mechanisms of initiation are possible. environmental effects. and some of the corrosion fatigue crack initiation data for steels such as BS 4360 (50D). These aspects are covered in Chapter 2. Considerable research has been carried out on structural steels used for jacket structures. 'perhaps pits observed at failure were not the cause of corrosion fatigue but rather the result of it'. which often represents well over 80 per cent of total life. wave excitation frequency. Depending on the operative initiation mechanism. This conclusion is not applicable to all cases of corrosion fatigue. This can cause localized pitting of the metal surface resulting in the production of stress concentration sites. These include specimen characteristics.57] concluded that for steels. Corrosion fatigue crack initiation and the role of pitting has been the subject of much discussion. and localized attack at protruding slip steps are all possible mechanisms for corrosion fatigue crack initiation. The way these conditions are modelled for tests conducted as part of the study presented in this book are discussed further in Chapters 2 and 3. therefore. For example.Fatigue and Fracture Mechanics of Offshore Structures One of the basic mechanisms of corrosion fatigue during the initiation stage can be explained thus: a corrosive environment attacks the surface of a metal producing an oxide film. and stress-time interaction effects. 28 . crack growth data are of practical significance for corrosion fatigue since these joints are assumed to have fabrication defects when they are commissioned. In general. Fatigue crack propagation rates in vacua have been observed [1. and over-protection. 29 . It is a remedial measure that was originally thought to improve corrosion fatigue life to a level comparable to that in air. air fatigue data are used as a basis for comparing the performance of steels in different environments.Literature Review Effects of cathodic protection on fatigue crack growth A great deal of effort has been concentrated over a period of several years on studying the effect of the environment on fatigue resistance of engineering materials. The equilibrium potential for free corrosion of bare steel in seawater is approximately -650mV with respect to Ag/AgCl reference electrode.57] to be lower than those in air at lower stress levels. the difficulty in maintaining a uniform CP over the entire structure. This dependence of fatigue behaviour on electrode potential is shown schematically in Fig.10. and the actual levels of these potentials. CP is achievable in two ways. 1. Cathodic protection (CP) is the most widely used method for preventing corrosion. One of the methods involves attaching a sacrificial anode to the structure to be protected. The other requires the application of a cathodic potential or current to the structure to be protected by use of an external current generator. This behaviour is important for highstrength steels and is discussed further in Chapter 3. Depending on the method adopted. This impressed current method was used for the corrosion fatigue tests carried out as part of this study and it is described in greater detail in Chapter 3. The levels of CP used can be classed into three categories: under-protection or free corrosion. although it is known that air is not inert with respect to fatigue crack growth. are known to have considerable effect on the fatigue crack propagation rates of materials exposed to corrosive environments under CP conditions. These categories are a function of the relative magnitudes of the protection potential and the equilibrium potential for the free corrosion of bare steel in seawater. adequate protection. and it is now well established that a corrosive environment could have serious detrimental effects on the performance of steel components subjected to fatigue. This section presents a general review of corrosion fatigue and examines some of the mechanisms that have been identified in the more recent years. 57] Adequate CP is said to be achieved when the protection potential reaches a level that is just sufficient to prevent dissolution of iron ions in the aqueous solution. Fatigue tests carried out under free corrosion potentials (-600 mV to -700 mV) have been shown to produce shorter fatigue lives when compared to air tests [1. however. Tests on API-X65 steel also show that cathodic overprotection can result in accelerated crack growth rates when compared to free corrosion and air fatigue crack growth data [1. 1. These tests show similar environmental reduction factors between two and three with the larger reduction factors occurring at lower stresses. However. 1. However.64]. Previous research. as the data for tests conducted using cathodic potentials in excess of -1000 mV are limited.58-1. as data for tubular joints seem to exhibit inconsistency.62]. There seems to be general agreement that the use of adequate cathodic protection can produce corrosion fatigue performance of initially smooth specimens of the lower strength structural steels comparable to that in air. individual welded tubular joint test programmes show a trend towards longer lives at low stresses with a CP level of -850 mV.Fatigue and Fracture Mechanics of Offshore Structures Fig. there was some discrepancy between the seawater tests carried out as part of the UKOSRP II programme when compared in terms of environmental reductions factors with results obtained from the UKOSRP I plate joint tests. This adequate CP level has been identified to be around -850 mV and has been used in a wide range of fatigue tests as part of the UKOSRP programmes. For example.63. the effect of moderate CP potentials on welded tubular joints is far less conclusive. The fatigue test results in this book have assessed the effect of CP on high-strength steels. especially on high-strength steels and primarily on mediumstrength steel plate specimen tests. and are presented in Chapter 3. suggests that very negative cathodic potentials may have a detrimental effect on the fatigue performance of BS 4360 50D in seawater. The influence of cathodic over-protection on fatigue crack growth rates is even less conclusive. 30 .10 Effect of electrode potential on fatigue [1. suggesting a possible effect from a greater exposure time characteristic of tests carried out at lower stress ranges. However. This may be condensed into representative sea states characterized by wave energy spectra. depending on the loading. SE 702. A number of tests have been conducted [1. A review of UK and other design guidance suggests that CP potentials more negative than -850 mV may be detrimental to steels with strength levels above 700 MPa and that in some instances even -800 mV may be detrimental to steels with yield strengths higher than 800 MPa [1. For instance. especially for high-strength steels. for example.Literature Review The effects of both under-protection and over-protection are of considerable importance for crack growth in a corrosive environment under CP conditions. 1. This effect may be worse for higher strength steels. a brief review of current guidance on the design of offshore structures subjected to variable amplitude fatigue using S-N curves is given here. The stress response calculated for each location is combined into the long-term stress distribution used in calculating the cumulative damage ratio. under the section on fatigue analysis. while in-service loading experienced by most engineering structures has both variable amplitude and frequency content. especially due to the fact that different materials may show different responses to these two extreme conditions. 1. recommends that the wave climate should be derived as the aggregate of all sea states to be expected over the long period. where the effects of CP on both fatigue crack initiation and propagation are examined for a typical high-strength steel. it is known that some steels are susceptible to hydrogen embrittlement cracking depending on the level of protection potential used. The approach outlined does not make any allowances for any sequence or sea state interaction effects that may be present under service loading conditions where several sea states of different significant wave heights may characterize the long-term distribution of stresses in a structure. the following section presents a discussion on the likely impact of service loading conditions on fatigue performance. The effect of environmental loading (variable amplitude loading) on fatigue performance and crack propagation in high-strength steels is an important aspect of the material presented in this book. This aspect of variable amplitude corrosion fatigue in offshore structures is reported in greater detail in Chapters 3 and 4 where the results of fatigue tests are presented in terms of a sea state sequence and the variations in crack growth rates accounted for. which are thought to be more susceptible to hydrogen embrittlement cracking. and it is covered in greater detail in Chapters 2 and 3. However. There is evidence that cathodic polarization may be of little benefit in reducing corrosion fatigue crack growth rates and that cathodic over-protection may be detrimental.66.65]. Tests on API X65 pipeline steel have shown that high CP potentials can increase crack growth rates by as much as fifty times over those observed in air. the data were not incorporated in design S-N curves proposed by HSE.4. The current edition of API RP2A. 31 . This dependence of crack growth rates is discussed further in Chapters 3 and 4. Variable amplitude fatigue The current guidance on fatigue assessment and design of welded connections is still rather limited with respect to the variable amplitude loading. Although data on the effects of variable amplitude loading are limited for this class of steels. The available design S-N curves are largely based on constant amplitude tests.67] under variable amplitude loading conditions. Constant amplitude loading is generally assumed when analysing the behaviour of tubular joints. The document recommends a similar damage summation model to that in API RP2A.e. This is a very conservative level and is relevant to practical situations were inspection and maintenance operations are limited. i. 1.11 Effect of Miner's damage rule on S-N curves 32 . Similarly. in establishing the long-term distribution of stress range. Fig.0'. The DnV rules also require that. The damage summation level Ds recommended by this code is however. current. The recommendations proposed by UK Department of Energy guidance notes were based on variable amplitude tests carried out on welded plates with respect to a best-fit constant amplitude curve from tests on similar joints. At present. The document recommends the use of a damage summation level of unity for both tubulars and plates. and so on should be accounted for.Fatigue and Fracture Mechanics of Offshore Structures The earlier editions of the Norwegian Petroleum Directorate Design Rules do not provide any specific guidance on the effect of variable amplitude loading.11. wind. 'taken equal to 1.1 to 1. The effect of Miner's rule on an S-N curve is shown in Fig. unlike API. 1.0.0 for any part of the structure unless otherwise specified by the NPD'. variable loads arising from influences such as waves. The same damage summation rule was recommended by AWS with a damage summation level of one third for critical joints. Miner's rule is generally accepted. DnV recommends the use of Miner's rule for the determination of cumulative damage. Lloyd's Register of Shipping also recommends the use of Miner's rule with a summation level 'normally taken as 1. It indicates that the calculated damage summation failure limit should range from 0. Any other fatigue damage prediction method requires an assumption on the accumulation of damage resulting from variable amplitude stress cycles of any stress sequence. Cycle counting methods can be broadly classified into two categories conventional and theoretical methods. however. that are directly relevant to fatigue damage. Conventional methods of cycle counting Cycle counting is the process of reducing a complex variable amplitude load history into a number of constant amplitude stress excursions. A number of possible models have been proposed to explain the variability in crack growth rates observed under variable amplitude loading and to predict fatigue crack growth under these conditions. discussed in Chapter 4. and crack tip profile. For sinusoidal loading. crack closure. and falls to zero again at the maximum stress. using the crack opening displacement for each cycle. that can be related to available constant amplitude test data. by calculating the relevant strain rate for the crack tip. Triangular wave forms also give an initially high strain rate that decreases as the maximum load is approached. Unloading is. a region of rapidly deforming material where new surfaces are being created at a rate that is not easily definable. The relationship between crack tip strain rate and variable amplitude loading fatigue cycles is not as clear as the case for constant amplitude waveforms due to possible sequence effects. reaches a maximum during the loading cycle. which could be quite significant. or load interaction effects. the strain rate will be zero at the minimum stress. it has been shown that the strain rate will initially be very high but decreases with increasing load for monotonic loading. The implications of this assumption are discussed further in Chapter 4. The effect of loading conditions on corrosion fatigue crack growth can be understood only by studying the effect this has on the crack tip. The more commonly used 33 . as a number of them may be operating simultaneously. For example. This approach is very difficult and not well understood for conditions where the stress time behaviour and the crack tip stress intensity factor range both determine crack growth rate. In each of these models. The method of cycle counting used often depends on the occurrences in the particular sequence that are considered to be significant in terms of fatigue damage. This is very important as it is used in identifying significant events in the sequence.Literature Review Variable amplitude used within the context of existing methods and codes based on SN curves makes a fundamental assumption that individual fatigue cycles from a variable amplitude loading process cause the same damage as if each cycle were part of a constant amplitude series. This is a necessary step. that needs to be carried out in order to predict fatigue crack growth in components subjected to variable amplitude loading. One thing that is commonly encountered when dealing with variable amplitude fatigue analysis for both S-N and fracture mechanics approaches is the requirement for cycle counting. Hence in a cyclic loading situation the region at the crack tip will experience high strain rates with the continual generation of new surface if the crack is growing. affected by factors such as reversed plastic flow. Several cycle counting methods have been developed. separate mechanisms involved are not necessarily exclusive. crack extension. The following section presents details of established methods used in analysing variable amplitude load sequences. 69-1. A number of different rainflow counting techniques can be identified that vary in principle from the original rainflow method [1. is made between two successive zero crossings. In determining the number of cycles in a sequence.71]. In this way positive and 34 . It has since become a generic term that describes any cycle counting method that identifies closed hysteresis loops in the stress-strain response of a material subjected to cyclic loading and represents the most accurate method for local strain type analysis. range. This method will amplify small variations in stress and increase overall excursions of stresses in the sequence. Some of these methods are discussed below. When the stress-strain response of the material is considered.Fatigue and Fracture Mechanics of Offshore Structures include rainflow. hysteresis loop counting and ordered overall range counting. This method can be used to record information on the actual stress ranges that have occurred. In an alternative peak counting method. Peak counting Peak counting can be implemented in a number of ways. each range is assumed to form one half cycle. and peak counting. This method is known as positive peak counting. The distortion introduced by using positive peak counting can be avoided by using net peak counting. Peak counting can also be implemented by setting a datum at the lowest stress in the sequence and counting only the positive peaks present. the mean stress of the hysteresis loops can also be determined. These depend on how the significant events (load peaks) are counted. Positive and negative peak counting is implemented. it does not give any information on the actual peaks unless the stress returns to zero between cycles. To implement net peak counting. only one count of the highest peak. positive or negative.68] on cycle counting. by counting positive peaks above and negative troughs below zero which fall into prescribed increments. Rainflow counting The rainflow counting method derived its name from an analogy used by Matsuishi and Endo in their early work [1. When used in conjunction with the predicted stress-strain response of a material. This approach assumes that all minima occur at the datum level. the zero stress line is taken as the datum when it is reached. which is taken as the datum. However. These include methods such as range-pair counting. Using this technique implies that troughs which are negative peaks above or positive peaks below zero are not taken into account directly. This means that using this method will lead to considerable distortion of the original sequence as significant load excursions may be ignore. One of the most important considerations in cycle counting is that the basis of the counting method needs to be compatible with the understanding of the relevance of stress fluctuations to the fatigue process. This is known as the zerocrossing peak counting and ignores all peaks smaller than the highest between zerocrossings. peaks are measured from the preceding trough root. if both positive and negative ranges are included. Range counting Simple range counting requires that only the stress or strain ranges between successive reversals are counted. When the positive and negative peak counting method is used in conjunction with this method. this method of cycle counting provides insight into the effect of a given strain history on the material's response. for example. The method is based on the identification of local maximum and minimum stresses or strains in the sequence. Since fatigue damage is largely influenced by larger fluctuations in stress. Range counting is quite popular because it can easily be implemented to extract the required load ranges from any known sequence. range-pair counting is independent of the smallest variations neglected. This is particularly relevant for the counting methods like rainflow that aim to be more conservative by combining the most damaging fatigue cycles first. It may also be difficult to pair negative and positive ranges. In this way. Level crossing counting This is a cycle counting method where a count is made when the load. The stress axis of the sequence is divided into a number of increments as required. The implication of this is that the effect of a particular cycle. However. It is also more conservative in terms of fatigue damage as it leads to the identification of large cycles. The difficulty of assuming a mean level in the simple range counting method can be overcome by also counting the mean value associated with each range. This means that the overall sequence may be heavily distorted by using this method. However. Like other cycle counting methods. Like the previous methods. although a great part of the sequence can also be retained due to the pairing conditions. it can also lead to loss of a considerable part of the overall sequence. for example. the inability to pair all ranges is removed as a count is not made unless the ranges pair. a count is made each time a negatively sloped portion of the sequence crosses an increment located below the reference stress level. the most damaging combination in terms of fatigue are obtained by first forming the largest cycles. or half-cycle. The main disadvantage of this counting method is that it can produce a large number of small cycles for wide band sequences. but when zero is used as the reference level it is known as zero crossing counting. This method of cycle counting will not retain the sequence of stress variations. 35 . or strain in the sequence crosses a specified level. Unlike simple range counting and range-mean counting methods. A count is made each time a positively sloped portion of the stress history crosses an increment located above the reference level. An alternative implementation of range counting is range-pair counting.Literature Review negative ranges are paired to form complete cycles that are assumed to have the same mean. Where sequence effects are insignificant. the individual crossings have to be combined to form complete cycles. any analysis based on range counting may be unconservative for long-term fatigue damage assessment. although range pair counting. Similarly. When range counting is implemented in this way it is referred to as range mean counting. Zero crossing counting is significant for offshore structures as it is used to establish sea state statistics. is capable of showing good agreement with total excursion of the original sequence by retaining a great part of the sequence as a result of the pairing conditions. stress. Also. may be incorporated into a fatigue damage analysis before it actually occurs. The reference level can be arbitrarily selected. this is not always the case. level crossing counting does not lead to a complete reproduction of the original sequence and will lead to a misplacement of load excursions in the sequence. this will have very few implications on the accuracy of fatigue crack growth prediction. without a pre-knowledge of the loading sequence. Figure 1. Unlike corrosion fatigue crack growth where the environment influences crack propagation mechanisms. such as design life prediction and failure analysis.2. 1. but it is not a problem when dealing with sequences used in variable amplitude fatigue testing programmes.12 shows the characteristic sigmoid shape of the do/dN versus AK curve [1. Some of the existing FM models are discussed in Chapter 4 and compared with experimental results. Application areas in the offshore industry have also been identified and reported in the literature [1. Often this relies on the use of FM fatigue tests to determine the values of certain material constants.4. Theoretical methods of cycle counting Conventional cycle counting methods described above require the generation of the variable amplitude sequence of interest. in the offshore oil and gas industry and other sectors. This approach. difficult to implement when dealing with service loading experienced by offshore structures in the North Sea.75] in logarithmic scale. This section of the book presents basic concepts of FM analysis of cracked bodies. This is the typical shape of this curve exhibited by crack growth in air. for example.72-1. the most powerful and useful technological tool available for describing and solving fatigue crack problems. This trend will continue with increasing interest and advances in structural integrity monitoring technology. however. Fracture mechanics analysis is.4. This approach is. One of the most significant shortcomings of the method is that it cannot be used in assessing the structural integrity of cracked tubular joints in service. 36 . and the aircraft industry. This is usually a lengthy process. 1. The need to calculate equivalent stresses under conditions like this.1 Fatigue crack growth modelling In the various practical uses of fracture mechanics. The use of FM in the analysis of structural components subjected to fatigue loading is increasing.2 The fracture mechanics (FM) approach The S-N approach has been used extensively to design welded connections for offshore applications. but the way they can be incorporated into a more robust methodology for fatigue crack growth assessment in offshore structures is presented and discussed in Chapter 4 both for S-N and fracture analysis. as these are readily available for cycle counting.74]. atomic power generation. at present. however. leads to the development of fast assessment methods for use during structural integrity assessment procedures. has its limitations. fatigue crack propagation rates or curves in a particular environment and operating conditions have to be determined. These methods are not covered in detail in this book. The practical use of FM has been established for use on large turbine and electric generator rotor components.Fatigue and Fracture Mechanics of Offshore Structures especially for offshore structures where sea state interaction effects are most likely to be too significant to be ignored in any crack growth prediction model. It is a simulation with crack growth models for mechanical evaluation of the strengths of cracked bodies or the behaviour of fatigue cracks. crack growth in air is mainly governed by deformation-controlled mechanisms. AK. The behaviour of crack growth in this region is attributed to two forms of resistance to crack growth. The rate of crack propagation in region 3 increases rapidly until fracture. 1. Behaviour in this region is dependent on microstructural features and it is of considerable importance in service components.12 Characteristic da/dN Vs AK curve [1. This region corresponds to the onset of unstable and rapid crack growth and is characterized by either the material's fracture toughness or. by plastic instability. in the case of ductile materials.76] The curve is characterized by three distinctive regions within which the fatigue crack growth rate exhibits distinctively different dependencies on the stress intensity factor (SIF) range. extrinsic and intrinsic resistance.Literature Review Fig. Region 2 is characterized by stable crack growth and can be described by the Paris equation 37 . has been described as a continuum process not strongly dependent on the microstructure. Environment has little effect in this region and deformation mechanisms are similar to that characteristic of monotonic loading. Region 1 is characterized by a rapid decrease in crack growth rate with decreasing cyclic plastic zone size. Crack growth in region 2. on the other hand. Fatigue life assessment based on FM involves calculating the number of fatigue cycles required for a given increase in crack size. This is implemented by assuming a suitable crack growth law such as the Paris equation. In practice. There is abundant literature on crack advance and crack propagation mechanisms in the literature on fatigue.Fatigue and Fracture Mechanics of Offshore Structures is the crack growth rate. This review on fatigue crack growth only cites early views that were proposed to explain crack growth and the observed striations.05 to 2. The majority of crack growth in engineering structures can be considered to lie in this region and may represent more than 80 per cent of the fatigue life of tubular joints and welded connections. but the general FM approach to fatigue life prediction will require: the selection of a suitable crack growth law. while other researchers suggested that the striations are formed as a result of alternate blunting and sharpening of the crack tip during cyclic loading. 1. but it is important to note that fatigue crack growth in region 2 forms the basis for linear elastic FM analysis. is a parameter that expresses the effect of load range on the crack. 38 . and C and m are material constants. Using this technique the number of fatigue cycles required to extend a fatigue crack from an initial depth ai to any depth af is given as The stress intensity factor range. Secondary mechanisms such as brittle intergranular or transgranular microfractures that result in discrete growth increments.77].78]. the use of suitable crack growth material constants (C and m). It describes the stress field associated with the cracked body at the crack tip. AM is the SIF range. 1. AK.4.76. have also been observed [1.2.78] suggested that striation formation was the result of a cleavage fracture ahead of the crack tip. calculations depicted in the above equations may be more complex. Cracks in region 2 have been observed to grow by the formation of striations that range in size from 0.2 Fatigue life assessment based on FM The fatigue life of a welded tubular joint is characterized by the propagation of fatigue cracks.5 micrometers [1. The use of the damage tolerant design philosophy for welded connections is. Y is the modifying shape parameter that depends on the crack geometry and the geometry of the specimen. This has lead to what has now become common thinking that defects are always inherently present in welded structures and that crack propagation represents a substantial per centage of total fatigue life of welded joints. Forsyth [1. This cannot be presented here exhaustively. therefore. well accepted. In 1962. various correction factors have to be used to account for boundary effects. the size and shape of the crack.2. Fig. considerations for environmental effects. For mode I. In this section the main stages involved in any FM approach to fatigue crack growth prediction are reviewed. determination of stress intensity factors. fracture mechanics relies on analysing the stress field in the vicinity of the crack tip. and loading geometry. These modes are shown schematically in Fig. Modes II and III tend to be less significant with negligible contributions to crack growth. and III (tearing mode). 7. The SEF is the parameter adopted to describe the elastic stress field in a cracked body around the crack tip for any given mode of crack extension. These include modes I (opening mode). rather than the infinite stress due to the stress singularity at the crack tip. or displacement of crack faces. it is given as For surface cracks in engineering structures. 1. for example. finite 39 . The overall correction function. To overcome this problem. deformation.Literature Review determination of the appropriate stress ranges.4. 1. Mode I is characterized by tension normal to the crack faces. The nature of this stress field depends on the mode of crack extension. and the geometry of the cracked component. may account for aspects such as a free front surface. This is discussed in greater detail in Chapters 4 where the equivalent stress concept is linked to sea state spectra and used to model interaction effects on fatigue crack growth in offshore structures. It is a function of applied stress. This is due to the existence of a stress singularity. II (sliding mode).3 Determination of SIFs The concept of SCF becomes inapplicable in the analysis of stresses near the crack tip. Y(a).13. This methodology can be heavily dependent on the nature of the load sequence used in the analysis and whether a cycle-by-cycle approach is preferred in order to account for any sequence effects that may be present. crack shape. loading. and subsequent integration of the selected crack growth law for the applied loads. It is the predominant mode for most practical applications.13 Modes of crack deformation or extension Cracks are extended or deformed in one or a combination of modes. The use of parametric equations. presence of geometrical discontinuity. based on either acrylic models or FEA validated by experimental results. However. However. and effects arising from changes in structural restraint in the component. and the accuracy required.5 Summary Stress analysis and fatigue design of tubular welded connections have been reviewed in this chapter. A summary of the recommended parametric equations for the sample joint geometry used in this book is shown Table 1.6. A variety of solutions have been proposed to model this parameter but these are not discussed in detail in this book. depending on the element formulation used in the analysis and the computational time required for the accuracy needed. Despite the availability of all the methods discussed for determining the stresses and SCFs in tubular welded joints. 1. an illustration is given in Chapter 4 on how it can be derived for tubular welded joints using flat plate solutions.note equation is generally conservative There is no parametric equation for this load case Not recommend the parametric equation. The use of strain gauge measurements on steel models is known to be the most reliable way of determining SCFs. cost. this method can be time consuming where detail is important for large number of specimens and it can also represent an expensive way of calculating SCFs. since it fails to meet the acceptance criteria The equation cannot be recommended since there are less than 15 steel and acrylic joints in the SCF database Words Efthy 40 . Table 1. crack shape. This is a potentially expensive technique. a non-uniform stress field.Fatigue and Fracture Mechanics of Offshore Structures plate width. Photoelastic methods have largely been superseded by finite element analysis (FEA). the method adopted for any particular design will depend on the constraints of time.6 Recommended parametric equations for Y joints under OPB Location Chord side Brace side Words Efthy Kuang UEG LR UCL V Vc N/A X X* Kuang UEG LR UCL X V V V V V X* V V V V V Key Wordsworth and Smedley equations Efthymiou and Durkin equations Kuang equations UEG equations Lloyd's Register equations UCL Equations (HCD) Recommend the parametric equation Recommend the parametric equation . can represent a very quick way of checking SCFs before any detailed analysis is carried out. and FEA may be required for more complicated three-dimensional geometries commonly found in engineering structures. 1. These are often used due to lack of adequate understanding of the fatigue performance characteristics of a particular material [1.81].80] concluded that when compared with other parametric equations. The S-N method relies on the use of available experimental data. At the same time. and restrictions on the loading configuration covered by any particular set of parametric equations. This is demonstrated by the modification of the reduction factors on fatigue life as more data have become available to give less conservative estimates and narrow down the largely unnecessary safety margins. These restrictions constitute a limitation in the use of parametric equations to determine SCF in tubular welded joints. or a very good. 41 . However. consistency in the predicted results is also important. The Efthymiou equations are recommended by the current draft ISO standard partly for this reason and also because they offer the best. Each set of parametric equations is limited in application in one of three ways. the two approaches available are the S-N and the FM approach. even for use in the design of high-strength steel installations. Efthymiou equations and the Lloyd's design equations have considerable advantages in consistency and coverage. fracture mechanics remains the most powerful and useful scientific tool for describing and solving fatigue crack problems. As a result. the Lloyd's equations were found to be more conservative (41 per cent) than Efthymiou equations (19 per cent). However. the potential for using FM analysis for both design and also for structural integrity analysis and inspection scheduling for offshore structures will gain more ground. but as more reliable experimental data become available. At present. since currently available parametric equations are limited in applicability. large factors of safety or reduction factors on fatigue life are still applied to give conservative results and also to account for different factors that are known to control the fatigue performance of welded joints. There are restrictions in the types of joint geometry that can be analysed using these equations. On the subject of fatigue design. In addition they are applicable to overlapped K and KT joints.Literature Review Parametric equations provide an expedient analysis route for obtaining SCFs. Based on the SCF database. restrictions on parametric validity range. as more material data become available. Currently there is no guidance available on the use of high-strength steels (ay >500 MPa). Different parametric equations will yield results that vary in accuracy. This is an important aspect for this book. due to the inherent scatter associated with the limited experimental data available. available recommended equations are only suitable for simple planar joints. the design of more complex joint geometries still requires the use of some form of FEA. depending on the joint geometry and the validity range. The use of fracture mechanics and the different models available for the analysis of engineering structures subjected to variable amplitude fatigue will be discussed in greater detail in Chapter 4. this method of fatigue design will also become increasingly more reliable and cost effective. However. Efthymiou equations also provided a better fit to the SCF database examined when compared to the Lloyd's equations. Recent studies [1. option for the prediction of SCFs for all joint types.79. Fatigue and Fracture Mechanics of Offshore Structures Through this review it is apparent that one of the difficulties in trying to quantify variable amplitude corrosion fatigue is the large number of variables involved that operate together to influence fatigue crack growth at any one time. These variables include: material properties determined by the alloying elements present; the nature of the corrosive environment determined by its chemical composition; and, additional factors such as flow velocity, temperature, pH, and degree of aeration, the magnitude of cyclic loads applied, and also the loading frequency. These factors can, however, be adequately controlled in a laboratory to carry out tests under realistic loading and environmental conditions as described in Chapter 3. A considerable amount of data is now available for fixed platform structural steels such as 50D. There are significantly less fatigue data available on high-strength steels. 42 Chapter 2 Service Load Simulation 2.1 Introduction Jack-up platforms are self-elevating platforms that have conventionally been used extensively in the North Sea to drill exploratory and production wells and for other short-term offshore operations. As highlighted in Chapter 1, many of these platforms are now designed to operate in deeper waters as production platforms. The TPG 500 production Jack-up design [2.1] and the production platform used for the marginal Siri field [2.2] are examples. Their use as production platforms for marginal field development means long-term deployment. This change of use increases the potential risk of eventual fatigue failure. Typical examples of fatigue failures are represented by incidents such as Ranger 1 (1979) where the mat/column connection failed due to fatigue and the Pool 145 (1982) where fatigue was also the cause of failure. The introduction of the Safety Case Regulations [2.3] for structures on the UK Continental Shelf (UKCS) is designed, in part, to minimize such risk of structural failure. It requires the owner or operator of an offshore installation to demonstrate that all hazards, with the potential to cause an accident, have been identified and sufficient measures taken to reduce the risk to a level that is reasonably practicable. This risk may be associated with potential material failure due to fatigue. As a result, both material selection for critical parts and in-service inspection are integral parts of the risk reduction process. This can only be satisfactorily achieved through adequate guidance. As highlighted in Chapter 1, however, fatigue design guidance for highstrength steels under sustained North Sea conditions is limited. There is, therefore, a need for adequate understanding of their fatigue behaviour under realistic variable amplitude loading and environmental conditions. In-service loading of offshore structures, such as Jack-up platforms, is mainly due to wave and/or wind action with variable amplitude and frequency content. As Jack-ups 43 Fatigue and Fracture Mechanics of Offshore Structures move into deeper waters fatigue loading becomes more sensitive to the dynamic response of the structure. This means that the effects of dynamics and structural response become more important and must be modelled if realistic results are to be obtained. It has since been recognized that predicted fatigue lives for offshore structures should be confirmed by large-scale tests under simulated service loading. This provides important information on the crack growth mechanisms under realistic loading and environmental conditions. Such knowledge contributes significantly towards the development of appropriate design codes for use by offshore designers. It also enables designers to assess the validity of the adaptation of the damage calculation procedure and for in-service integrity assessment. This chapter covers the relevant methodology used [2.4] in the assessment of highstrength steels used in offshore structures. It looks at the influences on fatigue resistance of structural steels used in the construction of offshore structures such as a Jack-up platform. The environmental loading and structural response interaction are discussed and emphasis is placed on how the relevant factors were modelled to produce the Jack-up Offshore Standard load History (JOSH). These factors especially include wave loading, Jack-up structural dynamic response, and the effect of a corrosive environment. As a benchmark for validating the analytical results presented, model results are compared with service measurements made on a typical Jack-up platform operating at two different locations in the North Sea. This chapter also presents and discusses the advantages and disadvantages of previous simulated load histories and further emphasizes the significance of JOSH in the fatigue analysis of high-strength steel Jack-up structures. 2.2 Fatigue loading in Jack-up structures Fatigue is the main source of structural degradation of offshore structures and this has been the focus of many major research programmes. Fatigue is sensitive to many factors that may be different in each application area. As a result, previous research experience and understanding of the fatigue performance of conventional fixed platform steels such BS 4360 50D and BS 7191 355D, which have been heavily researched, cannot be easily extrapolated to predict the behaviour of high-strength steels. In order to increase the understanding of the fatigue performance of these steels under realistic service loading conditions, it is important that the relevant factors that influence their performance in service are identified and included in the analysis. Jack-up platforms exhibit non-linear dynamic response in different sea states and can be exposed to different wave loading conditions at different locations in the North Sea. For a typical Jack-up structure used as a mobile drilling unit, transportation loading for moving from one location to another can be very important. This led to the proposal [2.5] that transit loads should be included in any simulated service load history. Four simulation options were envisaged, as shown in Fig. 2.1. The most suitable simulation option for production Jack-up platforms contains transportation loading at the beginning of the loading sequence. This is relevant to 44 Service Load Simulation Jack-ups used for production since it is representative of a situation where the transportation loads are experienced by the structure while it is towed to the installation site. Fig. 2.1 Options for simulating transit loading in Jack-ups Fig. 2.2 Wet transport of a self-propelling Jack-up 45 This type of loading is.2.2 and 2. For production Jack-ups. except under circumstances where transportation loads are severe enough to cause leg failure or plastic deformation.Fatigue and Fracture Mechanics of Offshore Structures Fig. however.3 Dry transport of a Jack-up using a low loader Data on typical transit loads experienced by Jack-up platforms are very limited as this depends on the method of transportation to the installation site. are dependent on three broad categories of influences: the wave loading regime. In both cases the Jack-up rig legs may be fully elevated. 2. 2. Self-propelling Jack-ups are transported as shown in Fig.3 show typical Jack-up transportation modes. this would represent only a small per centage of total fatigue damage experienced by the structure during its design life. whereas dry toe is implemented by transporting the Jack-up on a carrier. as shown in Figs 2. The characteristics of fatigue loading under service conditions that apply to offshore structures such as Jack-up platforms. structural features. and environmental conditions. Depending on the weather conditions and the turbulence of the sea. difficult to quantify for inclusion in a typical load history for a production Jack-up. large bending moments can be induced on the legs during transportation.2 and 2. Figures 2. 2.3. 46 .3. as shown in Fig. These features are covered in detail in this chapter with an illustration of the analysis procedure using a Jack-up platform. 7] and the associated C-12-20 series.Service Load Simulation 2. On the other hand. The objective then.3 Review of previous loading models Fatigue testing of specimens and structures started in the mid-19th century. By the mid-1950s. which is considered by most as the beginning of the era of modern fatigue testing. Research work on fatigue behaviour of different structures continued. This contributes tremendously to increasing the general understanding of variable amplitude fatigue testing and the development of prediction methods for fatigue crack growth analysis. as it is today.38]. including their advantages and disadvantages.10]. The development of standardized load histories for fatigue testing of offshore structural components had progressed rather slowly and had not received great attention until fairly recently. Conducting tests under simulated service conditions allows for comparison of results obtained from different laboratories across the world. are covered in greater detail in this section. With the development of servo-hydraulic actuators and microprocessors. the Hart/Wirsching algorithm [2.6]. This period saw the development of the COLOS (Common Load Sequence) for the European Coal and Steel Community Research Programme II [2.11]. This also supports the provision of guidance for laboratories undertaking the tests. The Comet jet airliner accidents of 1954 had a very significant effect. Since then. 47 . Codification of the resulting data can be said to have started around the 1850s. Some of these models. was to produce standardized load histories intended for use in fatigue testing.8]. Repeated loading tests were carried out and laboratory testing of specimens continued since then through the 1920s and 1940s. the double peaked spectrum. the whole art of fatigue testing entered a new phase. highlighting the main differences between these models and the JOSH model. standardized load spectra were developed for the aircraft and automotive industries in the late 1960s. fatigue crack growth testing. A well known example is FALSTAFF (Fighter Aircraft Loading Standard For Fatigue) [2. By the early 1970s aircraft components were being tested using standardized load sequences. These included structural fatigue testing. 2. since they stimulated extensive fatigue testing of aircraft structures. as demonstrated in a comprehensive review on fatigue [1. resulting in the accumulation of a considerable amount of empirical data. and the WASH (Wave Action Standard History) sequence [2. the ultimate aim has been to simulate service loading conditions and to conduct fatigue tests under realistic service loading conditions. This saw an era with the potential for testing structural components by applying increasingly complex loads. three main trends had emerged. Attention was turned to the development of standardized load histories for testing welded offshore tubular structures in the early 1980s and through into the 1990s. when Wohler carried out his now classic experiments that lead to the determination of S-N curves. developed for UKOSRP [2. and the development of design codes from the data available.9. not be appropriate for use in the variable amplitude corrosion fatigue testing of Jack-up steel tubular joints since the frequency content under realistic conditions is very important. The overall spectrum was built up using seven stationary Gaussian spectra of different RMS values. proposed by Wirsching. and the associated C-12-20 series. this sequence did not model the long-term variation in sea state RMS and. However.Fatigue and Fracture Mechanics of Offshore Structures 2. It was based on data obtained from the Forties Bravo platform and other relevant data. This type of spectrum would. The UCL double-peak spectrum and the frequency content of the resulting load history was represented by the double-peak power spectrum. For structures operating under conditions with significant resonance effects. This was based upon the original relationship proposed by Wirsching and given as 48 . was not representative of reallife wave-induced stress history. and the frequency control was far from accurate. and some features that could be represented by other sea states were missing. All stationary spectra were stepped by about 5 per cent of the peak load in order to produce a random distribution of peaks.2 UKOSRPII double-peaked spectrum This double-peaked spectrum was developed for random load fatigue testing in the UKOSRP II.3 Hart/Wirsching algorithm This was the most sophisticated simulation of North Sea stress histories available in early 1986 that modelled the long-term variation in sea state RMS. since a suitable pseudo-random generator was developed at UCL using a binary shift register.1COLOS/C-12-20 series COLOS was developed for the European Coal and Steel Community Research Programme III. Like the COLOS/C-12-20.3. It was a modification of the fatigue loading spectrum. The resulting time history from this spectrum could be pseudo-random. 2. since it was based on a single stormy sea state. 2. This type of load history has peaks that can be defined by a Rayleigh distribution.3. it could not be used directly for the fatigue testing of Jack-up steels without introducing the necessary modifications that would allow for Jack-up specific response characteristics to be accounted for. therefore. As a result. to produce a spectrum similar in appearance to the long-term stress history of deep-water structures. this sequence did not completely model the realistic load history. represent a single narrow band stress spectrum with constant RMS. while dynamic effects are ignored. therefore. This sequence. COLOS was not representative of real-life loading.3. The main drawback with COLOS is the fact that only the forcing loads are taken into account. and the pseudo random binary sequence technique (PRBS)for simulating the stationary random load history for each sea state. The randomness in the generated load history was produced using the pseudo-random binary sequence technique (PRBS). 49 . Hs is the significant wave height of a wave with dominant period TD. used in the generation of JOSH. the most realistic simulation for the fatigue testing of offshore structures.11-2.4 WASH sequence The Hart proposal was.13] is the same as the Hart proposal but there are three main features that are unique to the WASH model.4 The JOSH model The WASH model is the state of the art in the simulation of realistic service loading for fatigue testing of fixed offshore structural materials. However.3. Both these techniques and their implementation are discussed below. by the end of 1986. The Jack-up structural response data. 2. These include the Markov chain technique for simulating the random sea state sequence. This makes the modelled sea state sequence a more realistic and consistent simulation of the monitored service behaviour.14]. like the WASH model. research work undertaken to develop WASH was in progress. The basic philosophy of the WASH model [2. For this spectrum the three lowest sea states for the original spectrum were omitted and the highest three were combined.Service Load Simulation where o(f) is the stress spectral density function expressed as a function of wave frequency. f. 2. were also modelled and validated with data obtained from service measurements. The signal generation mechanism in WASH was designed as a 'standard'. The long-term random history was simulated by use of a discrete Markov chain model that allowed the sequence of sea states to be adequately modelled.5 Generation of Josh The JOSH model. relies on the use of advanced simulation techniques to generate the realistic loading history. The duration of each sea state was also taken into account. Around this same period. The main differences between these two models is that the JOSH takes into account the dynamic response characteristics of the more dynamically sensitive Jack-up platforms. it cannot be applied directly to Jack-ups. since resonance effects tend to dominate the power spectral density (PSD) functions for typical Jack-up platforms [2. A realistic sequencing of sea states represented the major difference between this model and previous models that relied on using power spectra based on the extreme stormy sea conditions. 2. or to remain at the current state. The natural frequency of the structure is given by fn and £ is the damping factor while A and (p are scaling factors. This was achieved by defining a state transition matrix containing the probabilities for each sea state to move up or down one state. It also relies on the use of a representative combination of sea state data observed in service from a typical Jack-up site in the North Sea. 5. SE(f). relevant to the PSD. 2. is generated from the corresponding power spectral density function for that sea state. This is expressed as The second step involves the generation of the filter function that is given in the angular frequency domain as The white noise signal generated by the shift register is then finally filtered to give the required loading history. Sx(f). These include: the random range generator. Although only discrete frequencies occur in the pseudo random binary signal generated in this way.15]. Fourier summation random walk technique.1 PRBS The random load history. Previous studies have also shown that the feedback loop size does not show any significant effect on either the sequence root mean square value or the weighted average stress range ratio. obtained from the white noise spectrum. hx(T). This has the advantage over other methods in that it makes use of a shift register of a certain length.5. and PRBS. can be preserved. In order to reproduce any relevant loading characteristics from any particular PSD function. It. This contains weights that are used to amplify the desired frequency content for any given sea state PSD function. not only in reproducing the frequency content of the power spectrum. The detailed procedure used in implementing this technique is not given in this book. The last method was used in the WASH framework and the same procedure was adapted for the development of JOSH. Further details can be found in [2. they are so closely spaced that the characteristics of broad band random loading.2The Markov chain technique The Markov chain is used in reproducing the long-term sequencing of a combination of naturally occurring sea states. within the duration of any particular sea state. Hx(f). For offshore applications. nx(t). such that This method gives very good simulation for any given power spectrum. but also in maintaining the long-term statistics so that they are representative of the PSD. Four different methods can be used in this process. the Markovian load range generator.Fatigue and Fracture Mechanics of Offshore Structures 2. This superior frequency control is the major advantage of this technique since this is very important for corrosion fatigue. offers a considerable advantage over other simulation techniques. In its mathematical form it relies on using output points from a shift register that is filtered through a filter function. the filter function is taken as the inverse discrete Fourier transform of the transfer function. the long-term distribution 50 . therefore. typical for offshore structures. This type of stochastic process is known as a Markov chain. a state transition matrix can be defined that contains the probabilities for each state to either move up (j=i+1) or down (j=i-1) one state. i. in. as long as the individual states are defined. For example. to represent the long-term probability distribution of sea states.. it can be stated mathematically that Where H(n) is a matrix containing the probability of occurrence of each sea state after n transitions. suppose this process {Sn. the occurrence of individual sea states does not affect the long-term probability distribution of all the sea states. .3. For offshore applications these defined states may consist of a range of typically occurring sea states characterized by their probability of occurrence and mean zero crossing period. Such data are commonly available for typical sites and are often presented as scatter diagrams. Sn=i.2. such as the significant wave height and their average duration. As a result.. i2. i1. 51 . after a large number of transitions. If at time n. However. or to remain (j=i) in its original state. Ti is the transpose of the Markov chain matrix that allows the state transition matrix. the following conditions will always be applicable Based on this representation. j and for all n>0. represented by discrete approximations of their exponential conditional distribution. The value Pij represents the probability that the process will make a transition from state i to state j. there is always a chance or probability Pij that it will move to state j such that for all states i0. . . then each value can be considered to be a defined state.} takes on a finite or countable number of possible values. such that The state transition matrix is obtained from the individual sea state characteristics. whenever the process is in state i.n = 1. the characteristics of which are determined by the long-term probability distribution of sea states. then the process is said to be in state i. Considering that probabilities are non negative and that the process must make a transition from one state into another.Service Load Simulation of naturally occurring sea states can be analysed as a stochastic process. It can be used in the implementation of service load simulation for any engineering structure. For offshore applications. Fatigue and Fracture Mechanics of Offshore Structures 2. As a benchmark for comparison of results.4 Typical Jack-up platform 52 . modelled results have been compared with service measurements carried out on a typical Jack-up platform operating at typical North Sea sites [2.1 The transfer function approach Figure 2. Fig. The methodology used to determine model response is presented here. 2. 2. The methodology used to ensure that the above factors. structural features. 2.6. or influences. Figure 2. The way these features can be modelled to produce realistic results is presented in this section.4 shows a typical Jack-up platform.6 Jack-up dynamic response Categories of influences for the fatigue performance of structural steels used in the construction of offshore structures have been identified.5 shows a simplified Jack-up model.16].14. These include wave loading regime. Detailed mathematical modelling was carried out to investigate the behaviour of this theoretical model under wave excitation. and environmental conditions. are accounted for is discussed. mass. Each element H(ij) relates the deflection in freedom i on the structure due to an excitation force in freedom j when all others are unrestrained and unforced For random loading such as that experienced by offshore structures. depends on the stiffness. which results from this. It is important to consider the physical interpretation of the transfer function matrix. the response in each of the n degrees of freedom may be calculated as 53 . Dynamic response. Both of these affect the transfer function given as where H ( j w ) i s the complex transfer (or receptance) matrix. 2. and overall damping of the structure.Service Load Simulation Fig. Dynamic loading varies with time and/or direction.5 Simplified model of Jack-up platform It is important at this stage to distinguish between dynamic loading and dynamic response. The following sections present the way the important parameters that affect the dynamic response of Jack-ups were accounted for in the analysis.6. which is a summation of the overall nodal effect for the n degrees of freedom. This implies that the cross-correlation functions will not be zero. The time domain is the more useful form for fatigue testing of offshore structures. However.Fatigue and Fracture Mechanics of Offshore Structures where Sxixi the spectral density of the response xi(t) in freedom i of the structure and SF F is the cross spectral density between the force in freedom r and the force in freedom s. 54 . To ensure this. based on a direct integrationtype analysis to obtaining a generalized representative spectrum. together with a relevant forcing spectrum Syy(f). of the structure can be obtained thus This approach. 2. analysis that superimposes responses in such a way that the cross correlation functions and hence the cross spectral densities are assumed negligible leads to satisfactory and conservative estimates. When applied directly to an offshore structure. was also considered. Using this approach gives the following simplified equation This is a realistic approach and represents the effect due to each individual random force. it was important that a representative Jack-up transfer function was obtained. a representative response spectrum. Fatigue loading in offshore structures is such that many forces on the structure are caused by the same basic wave and wind action. yields a frequency domain solution that can be transformed into a time sequence using the approach [2.17] presented in Section 2.5. An alternative approach. This method was not studied further because it was thought that the approximation errors were significant and did not reproduce service conditions adequately. depicted in Fig. The model transfer function agreed very closely with the service data obtained for the same Jack-up operating at two different sites in the North Sea. results obtained by analysing the model were compared with data obtained from in-service field measurements. with a well-defined transfer function H(f). For the work presented in this book. Sxx(f). 2. Consideration of a typical in-service Jackup platform. used as a benchmark to validate model results. The importance of the wave-loading regime used in the analysis is discussed in greater detail in Chapter 4. This Jack-up was built in 1986 and is owned by Maersk Drilling. 2. such as Jack-up platforms.18]. In order to obtain realistic results it is important that these effects are adequately modelled.2. cantilever Jack-up with a leg length of 156.6.2Modelling of structural parameters The characteristics and influences of fatigue loading that apply to offshore structures. This section of the book covers the effects of structural features and how these can be modelled to generate representative results.Service Load Simulation Fig. The Maersk Guardian has an electric rack and pinion jacking system. is a necessary starting point for the analysis and this is introduced in this section. Its legs are triangular and it can operate in a maximum water depth of about 106 m. It is an independent three-legged.6. It has an helideck just over 25 m in diameter with a refuelling system of 14440 gallons and provides accommodation for ninety-four persons [2. have already been highlighted.1 Study of an in-service Jack-up platform The in-service Jack-up considered for comparison and validation of results is the Maersk Guardian.77 m.6 Schematic illustration of the transfer function approach 2. 55 . self-elevating. This included the topside mass (or deck mass) and the distribution of mass per unit length of legs. therefore. the Maersk Guardian Jack-up platform was selected as a benchmark for comparing modelled structural response characteristics with service measurements made on a typical Jack-up under wave excitation in the North Sea. and variability. The second parameter is a function of the third and fourth. The first parameter depends on the nature of the excitation spectrum and is discussed in Chapter 4. Because of the uncertainty. of the increase in mass resulting from marine growth. Mem. This relies on using an equivalent cylindrical leg section.Fatigue and Fracture Mechanics of Offshore Structures The Maersk Guardian Jack-up platform has features that are representative of a wide range of Jack-up platforms deployed in the North Sea and worldwide. (2) natural frequency. which has the same structural and hydrodynamic properties as the actual Jack-up legs. These components were determined using the method of equivalent Jack-up leg sections.2. (4) effective stiffness of structure. Due to the availability of these service data. These details were obtained from the Maersk company and represented typical structural data on the Maersk Guardian Jack-up platform. A comprehensive structural measurement programme was carried out on this platform during the winter of 1988-89 in the southern North Sea (Silver Pit) [2. The last three are of particular interest as they represent physical properties of the structure. the effect of increase in mass due to marine growth was not modelled. The added mass was. the added mass. The most important parameters determining dynamic effects of a structure are: (1) excitation frequency. The nature of a structure's complex transfer function depends on all these parameters. (3) effective mass of structure. and (5) the overall damping of the structure. This is assumed to be negligible compared to the overall mass of a typical Jack-up platform.16]. The actual values are not given in this book because of confidentiality. An important addition to the normal structural mass.6. Mam and (2) mass of externally entrained water. taken to consist of two components: (1) mass of water contained within the submerged part of the structure. 2. the two components of added mass were obtained as follows 56 . These are covered in greater detail in the following sections. Using this approach.2 Effective mass of structure and mass matrix The mass matrix was modelled by considering the details of structural mass and its distribution.14] and during the winter of 1990-91 in the central North Sea (Ekofisk complex) [2. was also considered. However. This was taken as 2 for this analysis. rather than drag dominated loading. Even after a site assessment the values obtained are subject to variability. and it is common practice to consider a parametric study to ensure that the worst combination of values are chosen to produce conservative solutions. Hydrodynamic damping is non-linear and complete modelling requires non-linear analysis. Nonlinear effects are more severe in the latter. This method is more expensive but has the advantage in that. 2. 2.3 Stiffness of structure and stiffness matrix This was derived from the generalized stiffness matrix. One of these relies on the use of a finite element approach. For this method. for example. is the mass coefficient of the structure.3.19.21. the foundation is assumed to be rigid.3 Modelling of soil-structure interaction Soil structure interaction is a very important aspect in Jack-up dynamic response and this area has and continues to attract a lot of research interest [2. 2. Previous research [2. 2. There are two established methods for modelling the soil to study the problem of soilstructure interaction. The details of the approach adopted in selecting the stiffness of the linear springs used in the model are presented in Section 2. A site assessment is recommended in order to determine the soil properties. However there are documented values and typical values for spring steel. and the springs representing the soil are assumed to perform as uncoupled elements. 2. based on the equivalent leg structure. 2. the first two natural modes of vibration and a damping ratio of 4 per cent (Silver Pit location).24]. 2.6. 2. 2.6.19] has shown that estimates of damping calculated using the spectral peaks and the half power bandwidth method range from 2 per cent to 5 per cent over a wide range of representative sea states.17]. Structural damping is difficult to determine and cannot be determined analytically.2. with coupled springs at the relevant nodes to model the effect of leg structure-soil interaction.4 per cent to 0. 2.20.8 per cent [2.6. was obtained using Rayleigh damping coefficients. variation of soil properties with depth can be analysed. namely structural damping and hydrodynamic damping.14.Service Load Simulation Cm.22. This method is satisfactory and is the more popular 57 .4 Damping of structure and damping matrix The overall damping of the structure was considered to have two contributing components. The damping matrix. Hydrodynamic damping is also important and the methodology used is based on obtaining damping due to motion in-line with the flow.6. used in this analysis. range from 0.2.23. linearization yields satisfactory results for large structures under the action of small waves. The second approach relies on the use of a lumped mass model. This value was based on information supplied by the Maersk Company on the Maersk Guardian Jack-up.16. This is more applicable to inertia. The density of seawater is p and a is the equivalent radius. 5 is minimal. This is because there is very little variation as the Poisson's ratio changes from 0. formulae have been derived using elastic theory.5 for all calculations is small compared to other uncertainties. E of the soil.17]. the radius of circular base.8. rotational. In both cases the sensitivity of stiffness to changes in Poisson's ratio between 0. and K0 are the vertical.5. which relate spring constants to the shear modulus. and Young's Modulus. Poisson's ratio is known to vary between 0. G.5 for soft saturated clays [2. The variation of vertical and horizontal stiffness with Poisson's ratio is shown in Fig.7 and 2. This trend is shown in Figs 2. The derived formulae are based on the spring constant of a rigid circular base on an elastic half space and given by Kv. K0.7. The second approach was adopted for this analysis.3 for dry granular soils to 0. and torsional stiffnesses respectively.1 to 0. while the effect of Poisson's ratio on the rotational stiffness is shown in Fig. 2. Kh.Fatigue and Fracture Mechanics of Offshore Structures approach used in modelling soil structure interaction.1 and 0. It is also known that any errors caused by using a value of Poisson's ratio equal to 0. 2. 58 . Based on this approach. This can be taken as the spud-can radius.8. horizontal. v is Poisson's ratio and R. The horizontal and rotational springs were considered sufficient to model the soil structure interaction. Quoted values of Young's moduli for different soil types are given in reference [2.7 Variation of vertical and horizontal stiffness with Poisson's ratio Fig. 2.4 was considered representative of the soil type. 2.17] and the value assumed for this analysis is typical of loose sandy soil that lies in the range of 40 MPa to 80 MPa. 59 . This site has a sandy soil structure. A Poisson's ratio of 0.Service Load Simulation Fig.8 Variation of rotational stiffness with Poisson's ratio Some of the in-service results used in the validation of the model were measured on the Maersk Guardian Jack-up while at the Silver Pit location. these are dynamic in nature. such that 60 . The design wave approach is based on this methodology and is applied by defining a wave. In this approach. as a function of significant wave height Hs. mean zero crossing period Tz. it is adequate to consider variable loads in terms of an equivalent static load. The design wave approach is not satisfactory for smaller waves with excitation frequencies that can lead to structural resonance.25]. using spectral density functions and the transfer function approach. Due to a combination of the form of the Jack-up structure and the nature of the loads it experiences in service. It relies. Another approach is based on a design to a statistical wave description. any analysis using an equivalent static load. The PM spectrum was adopted by several design codes and it has been successfully used to analyse threaded tension leg platform tethers in the North Sea [2.7 Modelling of wave loading In-service loading of Jack-ups is mainly due to wave and/or wind action. It expresses the wave PSD.26]. however. The validity of such an approach depends on two main factors. For many design purposes. without taking into account the variability in the service loads. and directions.Fatigue and Fracture Mechanics of Offshore Structures 2. This method allows for adequate characterization of fatigue-inducing loads. during which wave statistics of the random sea may be stationary (sea states). (3) the ease of handling non-linear effects. JONSWAP spectrum. Some of the better-known. The first factor is the form of the structure and the second is the nature of the load. whose probability of occurrence is such that it represents the maximum wave that the structure will encounter within the return period. The modified PM spectrum was chosen for the study presented in this book and a newly modified version of the spectrum is given in Chapter 4. (2) the existence of short periods. on the linearity of superposition of wave components. More generally. and (4) the resulting physically interpretable solution. Considerable research work has been done on modelling ocean waves. periods. and wave frequency f. The main reasons for using this approach are: (1) the successful use of wave power spectra to describe water surface elevation. the occurrence of waves incident on the structure is expressed in terms of a probability of occurrence of waves with specific wave heights. of large height and period range. dynamic loading is all loading that has an appreciable variation with time. and the modified version of the PM spectrum. The methodology used here is a frequency domain analysis. Syy(f). This approach is only realistic from the viewpoint of designing against static structural failure due to a large wave. and does not permit fatigue damage to be considered within the design. PiersonMoskowitz (PM) spectrum [2. would be unrepresentative. one-dimensional wave spectra that have been developed to describe ocean waves include the Bretchneider spectrum. based on the linear wave theory. Fig. This method of analysis relies on the use of the transfer function approach. which can be transformed into a load history in the time domain. The main advantage of this approach is that it allows for a site-independent transfer function to be determined. The transfer function can then be subsequently used to obtain the response spectrum.9 Comparison of measured wave spectrum at Silver Pit with modified PM spectrum 61 . and has been adopted as the most appropriate expression of water surface behaviour for a fully developed open sea. It may be used to generate a force spectrum. and hence the stress spectrum directly. 2.Service Load Simulation This spectrum is based on extensive oceanographic data. and a direct integration-type analysis. This method was preferred over the alternative method. respectively. 2. The values of B for the Ekofisk and Silver Pit locations were found. giving an alternative form of equation (2. This peak frequency effect is shown clearly in Figs 2. It is a site-dependent parameter and its magnitude depends on sea state parameters. incorporated into the PM spectrum to account for this effect.044 respectively. A peak frequency correction parameter.Fatigue and Fracture Mechanics of Offshore Structures Fig. therefore. using this approach directly with the PM spectrum. using a curve fitting method.21) as Equation (2.9 and 2. 62 . was. This is due to the fact that most of the wave energy in wave spectra measured at typical Jack-up sites is concentrated at frequencies slightly higher than that predicted by equation (2. B.8 Selection of sea states This section introduces a study of the environmental influences on the stress PSD and highlights the importance of using representative sea states. to study the variable amplitude corrosion fatigue behaviour of high-strength Jack-up steels. such as the significant wave height and the mean zero crossing period. and modelling the effects of the corrosive environment. The relationship between B and the peak frequency of the wave energy spectrum is a linear one.10 for data obtained from the Silver Pit and Ekofisk locations.10 Comparison of measured wave spectrum at Ekofisk with modified PM spectrum However.21). can lead to an inaccurate representation of the frequency content of the generated time history. to be 0. as given above.016 and 0.22) is more accurate and yields a wave energy spectrum closer to the measured spectra for both locations used in this study. 2. The sea states used for the JOSH model are presented in Table 2.25 7.2 6. has shown that the distribution of significant wave height.25 2.25 4.75 4.25 8.7 7.1.9 9.75 5.11] to be well fitted by the following expression The associated mean zero crossing period Tz for a wave of significant height Hs is given as This modelled distribution agrees very closely with sea state data.8 7.5 5. observed at typical Jack-up locations in the North Sea. The Gumbel distribution is given as where P(x) is the exceedance of the variable x.00 Mean zero crossing period (s) 5.4 8.75 2. Hs.2 1 2 3 4 5 6 7 8 9 10 11 12 63 .75 3.1 Summary of sea states used for JOSH Sea state number Significant wave height (m) 1.25 3.9 6.25 6.5 6. is more accurately described by the Gumbel distribution.Service Load Simulation A detailed examination of oceanographic data for the North Sea. observed over a period of five years. Table 2. Observed sea state data was found [2.9 8.1 7.25 1.4 7. as seen in Figs 2.6. using data obtained from the Silver Pit and the Ekofisk complex in the North Sea. used to generate the response spectrum. Sxx(f).11-2. The sensitivity of the normalized transfer function to changes in damping is not very high. respectively.14-2.Fatigue and Fracture Mechanics of Offshore Structures 2.1. 2. As shown in Figs 2.16. Fig. The corresponding results for the Ekofisk complex are shown in Figs 2.11 Model and measured service NTF for the Silver Pit location with 2 per cent damping 64 .13 for the data obtained from the Silver Pit location.9 Discussion The Jack-up transfer function H(f). was obtained using the procedure outlined in Section 2.5 per cent damping.16 there is a very close match in the model and service transfer functions for 4 per cent and 5.13 and 2. 13 Model and measured service NTF for the Silver Pit location with 4 per cent damping 65 . 2. 2.Service Load Simulation Fig.12 Model and measured service NTF for the Ekofisk complex with 2 per cent damping Fig. Fatigue and Fracture Mechanics of Offshore Structures Fig. 2. 2.15 Model and measured service NTF for the Silver Pit location with 6 per cent damping 66 .14 Model and measured service NTF for the Ekofisk complex with 4 per cent damping Fig. 10 and 2.9 and 2.576xl010Nm/rad was seen to give the best agreement between the service and peak frequency of about 0. based on a rotational and translational spring system. These are shown in Figs 2.2 per cent. This value was obtained with a standard deviation confidence range of 1.9 and 2.10 show the measured wave elevation spectra for the respective locations compared with those predicted by the PM and modified PM spectra. respectively.24 Hz for the data obtained from the Silver Pit location. and model. from the measured wave elevation and response spectra for each site considered.5 per cent. a rotational spring stiffness of 2.Service Load Simulation Fig. A rotational spring stiffness of 5.16] a similar approach was used with values of 2. This is confirmed by the model results obtained for this study for both cases with 4. 2.7 per cent. pinned. Figures 2. respectively. implying that the most likely damping estimates were between 4.16 Model and measured service NTF for the Ekofisk complex with 5. For the data obtained at the Ekofisk complex. The 67 . Both these values compare very well with those presented in references [2. as shown in Fig. For this investigation three cases were studied: fixed.18 for the Ekofisk complex.365xl010 Nm/rad was used. In reference [2.0 per cent and 5. in each case.14] and [2.5 per cent damping for the Silver Pit location and Ekofisk complex.17 for the Silver Pit location and in Figs 2. together with a damping ratio of 5.3 and 6. 2. The service transfer functions were obtained.5 per cent.7xl010Nm/rad for rotational stiffness and a mean damping ratio of 5.13.16].5 per cent damping Peak frequency matching of the transfer functions was carried out by varying the stiffness of the rotational and translational springs used to model the effect of legfoundation interaction. 2.18 Measured service response spectrum at the Ekofisk complex 68 .17 and 2.Fatigue and Fracture Mechanics of Offshore Structures measured service response spectra for the Silver Pit and Ekofisk locations are shown in Figs 2. 2. Fig.17 Measured service response spectrum at the Silver Pit location Fig.18. respectively. 2. These were compared with service transfer functions predicted by using the PM spectrum with a peak frequency correction.19 and 2.20 NTF for measured and modified PM spectra for Ekofisk complex 69 . respectively.19 NTF for measured and modified PM spectra for Silver Pit Fig. This comparison is shown in Figs 2. Fig.20 for the Silver Pit and Ekofisk locations. 2.Service Load Simulation Using these spectra it was possible to obtain the corresponding service transfer functions for the two sites. 1 Hz.21. and/or as a result of non-linear effects. This effect is either due to inaccuracies in measuring the energy of the ocean waves at very low frequencies. 2.Fatigue and Fracture Mechanics of Offshore Structures The agreement in the NTFs is especially good for frequencies higher than 0. It was observed that the effect of the translational spring constant on the transfer function is negligible. Fig. 2. as the spring constant is increased. Below 0. This figure also shows that. 2. This is illustrated in Fig.21 Effect of rotational and translational stiffness on the transfer function 70 . which shows that the model transfer function is identical for cases 2 and 3 using identical rotational springs. The overall effect of varying the rotational spring stiffness on the NTF is shown in Fig. the normalized transfer function for case 2 approaches that for case 1 as expected.1 Hz the discrepancy in the transfer functions was greater.22. Overall.24. the magnitude of the rotational transfer function was found to increase exponentially with water depth. 71 . 2. Results obtained from this study show that the nature of the transfer function is very sensitive to the operating water depth. the results obtained from the sensitivity study on the rotational transfer function (RTF) are shown in Fig.23.Service Load Simulation Fig. For the Silver Pit location.22 Convergence of transfer function to fixed case A sensitivity analysis was carried out to quantify the effect of water depth on the model transfer function. 2. as shown in Fig. 2. 23 Effect of water depth on rotational TF Fig.Fatigue and Fracture Mechanics of Offshore Structures Fig. 2.24 Sensitivity of rotational TF to water depth 72 . 2. respectively. Fig.26. on the other hand. respectively.25. It can be seen from this figure that the TTF exhibits an approximately linear dependence on water depth. a 5 per cent and 30 per cent increase in water depth lead to about 25 per cent and 250 per cent increase in the magnitude of RTF. 2.Service Load Simulation The results obtained on the sensitivity of the translational transfer to changes in water depth are shown in Fig. This is shown in Fig.25 Effect of water depth on TTF 73 . An equivalent increase in water depth of 5 per cent and 30 per cent only leads to an increase in magnitude of about 9 per cent and 45 per cent. 2. 2. The effect of increasing water depth on the TTF. Figure 2. For the rotational transfer function (RTF).25 also shows that the effect on the magnitude of the translational transfer function is less severe as the water depth is increased. is not as significant as the effect on the rotational transfer function. 74 . In a similar manner. normalizing the PSD preserves the frequency content of any resulting time history. by applying a suitable scaling factor to meet the needs of any testing conditions. This is the best way of varying the testing time for a particular joint. although the magnitudes of the rotational and translational transfer functions increase with depth at different rates. 2. but allows for the magnitude of the peaks to be varied. as required.26 Sensitivity of TTF to water depth It was observed that. instead of altering the frequency content of the load history. which is important for corrosion fatigue behaviour of offshore structures. they are equivalent when normalized for any particular water depth.Fatigue and Fracture Mechanics of Offshore Structures Fig. 2.28 Measured and model PSD for the Ekofisk complex The response spectra. used to generate JOSH.Service Load Simulation Fig. 2. In a similar manner the predicted response spectra for the Maersk Guardian Jack-up platform at the Silver Pit and Ekofisk locations were compared with those measured at the 75 .27 Measured and model PSD for the Silver Pit Location Fig. were based on the model transfer function and the modified PM spectra for the different sea states used. However. The overall prediction of the distribution of energy across the frequency range of interest in both cases is good. Further details of JOSH are presented in Chapter 3. and noise in the measured data. has also been presented. The influences on fatigue resistance of structural steels used in the construction of a typical Jack-up leg structure have been presented. Figures 2. 76 . that are not accounted for in the model.10 Summary This chapter has introduced.27 and 2. The methodology used for the work presented in this book to model these relevant influences. the relevant analytical work that was carried out to ensure that realistic results are obtained for this study. together with the large-scale fatigue testing programme undertaken in this study using the simulated sequence. 2. there are slight discrepancies in both cases. This chapter has introduced and discussed the results of a comparative study between model and service data and demonstrated the level of agreement between the two sets of data.28 show this comparison. possibly due to a combination non-linear effects.Fatigue and Fracture Mechanics of Offshore Structures respective locations. and discussed. The objective of this study was to assess the effect of realistic variable amplitude loading and cathodic protection (CP) on the fatigue crack growth behaviour. Secondly the simulated history was used to carry out variable amplitude fatigue tests using large-scale welded tubular Y joints made from a typical high-strength steel. and this acted as an incentive for carrying out this investigation. of SE 702 . SE 702.1 Introduction Fatigue tests on large-scale tubular welded joints have been performed.Chapter 3 Large-scale Fatigue Testing 3. This aspect of the study was covered in Chapter 2. in recent years. and subsequent fatigue life.a typical high-strength steel used in the construction of Jack-up rig legs. A large number of these tests have been conducted on conventional fixed platform steels such as BS 4360 50D and BS 7191 355D. The lack of fatigue data on high-strength steels under these applications was highlighted in Chapter 1. The main objective of the study was to investigate the fatigue performance of high-strength steels used in the construction of offshore structures under realistic loading and environmental conditions. there has been a steady increase in the use of high-strength steels in the construction of offshore structures. This was done firstly by developing a simulated service loading history for a typical Jack-up platform operating in the North Sea environment. to characterize the fatigue behaviour of steels used offshore. for many years. Conducting these tests can be very expensive. 77 . The expense is justified on the grounds that crack growth behaviour in tubular welded joints is complex and cannot be reproduced by conducting tests on simple welded specimens. One air and three seawater fatigue tests under CP were carried out under simulated environmental loading conditions. However. 02 0. and other high-strength steels.1 0.069 0. and 3.05 0.474 0.3 < 0. 1.01 In Table 3. The parallel study investigated the effect of CP on the same steel under constant amplitude loading conditions on large-scale welded T joints. fatigue crack growth rates.007 0. 3.404 0.125 1.55 < 0. It is Creusot Loire Industrie's (CLI) equivalent of the A517GrQ standard. 3.19 0.0005 0. The results are presented in the form of initiation behaviour.003 0. The chemical properties of the material are given in Table 3.3. The mechanical and chemical properties of SE 702 are also presented.01 <0.1] on lower strength steels.Fatigue and Fracture Mechanics of Offshore Structures This chapter presents details of the testing programme and the results obtained from the study.001 0.1.185 0.011 0. SE 702. These results are compared with results from previous studies [1. is a member of the Super Elso (SE) family of steels. 1. This section describes the geometry in detail.4.0012 0.008 0.007 1.08 <0.467 0.51 0.1 the specified chemical composition is compared with independent chemical analysis results [3.003 <0.25 <0. those obtained from a parallel study [1.01 0.7 <0.12 1.34 0. the chemical properties of the batch of steel from which the joints were made meets the specified standard for 78 .11] on SE 702.004 <0.009 1.004 0.256 <0.05 - CLI analysis 0.1 Properties of SE 702 The steel.003 0.48 0.14 <0.1 Chemical composition of SE 702 Element Specified C Mn Si S P Ni Cr Mo B V Cu Sn Al Ti Co Nb As Pb <0.2.9 <0.1. 1.64.65.2] carried out on a piece of the material cut from one of the Y joints used during the tests.01 <1.2 Test specimen consideration Large-scale welded Y joints made from SE 702 were used for this study. As shown from Table 3.5 <0.003 UCL analysis 0. and stress life (S-N) data. Table 3. It is of high strength.Large-scale Fatigue Testing each of the alloying elements. The specified mechanical properties for SE 702 are given in Table 3. Vickers hardness values for the parent plate were approximately 250 HV. was that SE 702 has a uniform fine-grained microstructure. should have an ultimate tensile strength in the region of 800 MPa.3]. The results from Cranfield are given in Table 3. carried out at Cranfield University [3.2 Quoted mechanical properties of SE 702 Material SE 702 ay (MPa) UTS (MPa) 790 / 940 700 (minimum) Elongation (per cent) 16 These results compare well with the specified mechanical properties. These included hardness measurements.12] that carbon steel with Vickers hardness values in this range. These were also compared with results from tensile tests. except for manganese which is higher than the guaranteed maximum.2.92 0. weld metal. but they generally show that the actual mechanical properties of the steel are better than those specified in Table 3.3.91 0. This agrees with the values shown in Table 3. oy (MPa) UTS (MPa) 1 2 3 4 5 Average 755 744 744 750 750 748 823 813 807 816 815 815 Reduction in area (per cent) 66 61 65 64 64 63 Elongation (per cent) Yield ratio (oy/UTS) 21 20 20 20 20 20 0. and the heat affect zone (HAZ) are compared with specified values in Table 3. Table 3. weld metal. with a good combination of mechanical properties.92 One of the conclusions made from the results obtained from Cranfield University. Table 3. and the heat affected zone obtained from the qualification weld sample. and it has been suggested [1.3. This value was considered acceptable for SE 702. 79 .92 0.3 Measured mechanical properties of SE 702 Specimen No.2. using specimens made from the same batch of steel used in the fabrication of largescale Y joint specimens.4. This difference in the percentage of manganese present in the steel was not thought to be particularly relevant to its fatigue performance since manganese acts as a de-oxidizing agent.92 0.92 0. The results obtained for parent. Other measurements were made on the parent metal. and it was noted that it has good ductility and excellent low-temperature toughness. The tubes are.1. Fig. a complex combination of joint geometries may result.2.2 Consideration of test specimen geometry A typical Jack-up leg structure is made from steel tubes formed into a threedimensional space frame. therefore. 80 . Each lattice leg may be composed of longitudinal chord members that may contain a rack plate for elevating the hull with interconnecting horizontal and diagonal tubular members. and the degree of structural redundancy. These geometries will usually be a combination of planar and multiplanar joints. 3.1 Typical planar and multi-planar joints used offshore However. planar joints are more commonly used. These tubular welded joints are usually made from materials of generally high strength. it has been established that the magnitude and the distribution of hot spot stresses around the intersection governs the fatigue performance of these joints. Depending on the overall structural requirements. welded together at the intersections or joints. as shown in Fig. have a good understanding of the performance of more complex joint geometries. 3.4 Hardness data for SE 702 Specimen 1 2 1 2 1 2 Average Range Sample Size Weld metal ROOT CAP 305 249 305 253 276-336 245-251 260-336 247-258 4 10 10 4 CGHAZ ROOT 311 300 373-409 262-363 363^01 272-345 8 10 CAP 392 389 Parent plate 253 260 242-268 243-274 11 11 9 10 3. This invariably implies that once the fatigue behaviour of simple planar joints under known hot spot stresses is understood and the stress distribution in the more complex joints known. it is possible to relate them and.Fatigue and Fracture Mechanics of Offshore Structures Table 3. normally. Due to the practical difficulties involved in testing full-scale multiplanar joints in the laboratory. 5.3 shows the welded intersection for one of the joints. A summary of the detailed dimensions of the joint is given in Table 3.Large-scale Fatigue Testing Fig. 3.5 The Y joint dimensional parameters are also given in Table 3. 81 .3 Illustration of brace seam weld and intersection weld on Y joint The joint geometry used for this study is of the Y configuration shown in Fig 3 2 figure 3. 3. The specimen dimensions were chosen to allow direct comparison with earlier tubular joint test programmes performed at University College London using lower strength steels.2 Detailed geometry of Y joint used for large-scale fatigue testing Fig. 1 Details of test rig A purpose-built reaction frame was available and this was used for the entire test programme. 3. This was designed to allow for out-of-plane bending (OPB) tests on Y joints.2. in accordance with the French standard NFP22-471 [3. As shown in Fig.3 Fabrication ofSE 702 specimens It is important that the welded joints are representative of those used in the construction of offshore structures. Information on the instrumentation used for the control of load and environmental conditions is also presented. The chord and brace tubes were made by seam welding two halves of rolled 16 mm thick plate. Post weld heat treatment (PWHT) was applied to the seam welds with preheating temperature of 125°C.0 and 0 = 35o 3. France) with experience in the fabrication of offshore structures.4]. as this is known to have an effect on the resulting fatigue life of the joints.3 Experimental set-up This section describes the experimental facilities used in this study.5 Detailed dimensions of Y joint Length Diameter (mm) (mm) 2480 457 324 1390 Brace angle = 35 degrees a (2L/D) = 10. as contained in the relevant sequence file. B (d/D) = 0. 82 .71. The joints were fabricated by a welding contractor (PAUMECA S.3 shows the seam weld on the brace and the brace/chord intersection string weld.3. the weld quality was good and no weld toe grinding was employed. This includes details of test rigs used. t(t/T) = 1.2 Test control and data acquisition The actuator was controlled with an INSTRON mini-controller via an advanced fatigue testing software.28. In this mode the specimen is subjected to load cycles of a pre-defined amplitude. A. The load was applied using a 250 KN hydraulic actuator. Figure 3. of Le Breuil. All tests conducted were performed under load control.Fatigue and Fracture Mechanics of Offshore Structures Table 3.3. Chord Brace Thickness (mm) 16 16 y(D/2T) = 14.5 kJ/mm.85. The FLAPS system is able to generate different types of wave forms and also has the necessary capability to play back any developed realistic load sequence. 3. The dime test was performed on all welds and no weld failed the test.5]. and data acquisition system.3. fatigue testing software. All welds successfully passed a full ultrasonic inspection. FLAPS [3. The welding was carried out using a gas metal arc welding (GMAW) process with a heat input of less than 2. 3. 3. therefore. The fully aerated seawater was maintained between temperature limits of 8°C and 10°C using an external refrigeration system. The welded intersection.6] crack depth measurements at fixed points around the chord brace intersection where the fatigue crack was expected to occur. 3. to through-wall penetration. However. and the influences of any cathodic protection system have to be modelled in the laboratory to obtain representative results.8] was circulated from a reservoir through a closed loop passing through the environment chamber. It was. N1. by use of wave power spectra. The effects of these chemical reactions. ACPD measurements were performed using a U10 crack microguage [3.3. possible to monitor crack growth at seventy-two sites around the chord brace intersection.Large-scale Fatigue Testing FLAPS also has the facility for obtaining crack growth data in the course of a fatigue test. As a result. then misleading results can be obtained.2. This section reiterates the importance of modelling both the loading and environmental conditions. where the fatigue crack was expected to grow.7]. if the simulated loading is applied to test specimens in an unrepresentative environment. By choosing suitable inspection intervals it was possible to use this technique to follow crack growth from initiation. it is important that tests are conducted under conditions that are representative of the environment loading system for relevant applications. together with a 144-channel ACM3 switching unit.8-8.3 Simulation of environmental conditions Previous research and understanding of the effect of a corrosive environment on the fatigue performance of structural steels was introduced and reviewed in Chapter 1.3. The processes of corrosion fatigue and hydrogen embrittlement of Jack-up steels are a complex combination of chemical reactions. one channel for measuring the crack voltage and the other for measuring the reference voltage. Fatigue crack development was monitored by taking alternating current potential difference (ACPD) [3. The pH of the seawater was also monitored in the course of each test and maintained between 7. The loading is modelled. This technique is an established non-destructive inspection technique. Two channels were used for each measurement site.1 Seawater environment All the corrosion fatigue tests were carried out under simulated environmental conditions. was immersed in seawater.6].2 Cathodic protection system Cathodic protection is normally used in service to reduce the rate of corrosion to a level that will allow the structure to attain its design life. together with the transfer function approach described in Chapter 2. This was achieved by the use of an environment chamber around the chord/brace intersection. Fatigue performance is a function of the severity of the corrosive environment and the interaction of cyclic loading. including other components [3. It has been successfully applied to the non-destructive inspection of welded joints of varying geometry.3. N3. service loading. 83 . Artificial seawater made to ASTM D1141 [3.3. 3. This was applied and maintained at a steady level (-800 mV and -1000 mV) with respect to Ag/AgCl reference electrode for all the corrosion fatigue tests.3. 3. away from the region of rapidly increasing stress influenced by a combination of loading and chord/brace deformation. A soak time of two weeks was implemented to achieve polarization of the specimen and allow hydrogen to diffuse through the steel. the study concluded that varying the soak time from two to eight weeks had very little effect on the results obtained for SE 702. These two gauges were used to 84 .4. A fatigue test on a simple specimen may only last a day or two. The overall longer exposure period for largescale tests. For largescale tests. At each measurement site the gauges were placed 10 and 20 mm from the chord weld toe and the measurements from these two positions at each site were linearly extrapolated to the weld toe to obtain the appropriate hot spot stresses. each joint was subjected to a 'soak time' where the joint was immersed in seawater with the CP applied and maintained at the appropriate level. The effect of soak time on the fatigue performance of SE 702 was investigated at Cranfield University [3. on the other hand. The gauges were placed around the brace/chord intersection. Three rosette gauges were also placed on the brace. The length of time required to achieve a uniform through-thickness hydrogen concentration is dependent on the diffusion coefficient for the material and the thickness of the specimens used. Two methods were used in this process. The two-week soak time was used to allow results to be compared with those from previous studies that employed a similar soak time.Fatigue and Fracture Mechanics of Offshore Structures Prior to the application of fatigue loading. An important consideration when conducting tests on tubular welded joints is the likely duration of the test. to obtain strains and stresses on the surface of the joint near the intersection. makes the through-thickness hydrogen concentration gradient at the commencement of loading less critical. Although other researchers have noted that there can be significant differences. 3.4 Stress analysis of Y joints Extensive stress analysis of the joints used for this study was carried out before each test. in accordance with recommendations of UKOSRP II. 2 mm rosette gauges were used for all the tubular joints tested. Experimental stress analysis using strain gauges and parametric equations. One close enough to the brace toe to measure the effect of the stress field determined by the combined deformation of the chord/brace intersection. which may last several weeks.1 Experimental stress analysis procedure The hot spot stress concentration factor for each joint was measured experimentally using strain gauges. and the soak time for such a test will have a significant impact on its resulting life. since the surface of the specimen is still charged with hydrogen for a further period before crack initiation after the soak time. the soak time is less critical when compared with that for a test on a simple specimen. The other two gauges were placed 500 mm and 800 mm from the brace toe. This section presents the procedure employed and compares the results obtained 3.3] by carrying out tests employing a soak time of two and eight weeks. In order to obtain accurate results for the stress concentration factors. The parametric equations of Efthymiou and Durkin.25 3. and this was compared with results from simple beam bending type analysis. This was carried out by increasing the applied load from 0 per cent to 10 per cent.Large-scale Fatigue Testing measure the experimental nominal stresses and the extrapolated value to the brace weld toe.2 Use of parametric equations Figure 3.86 5. The stresses measured by these gauges were used to obtain the appropriate stress concentration factors. The experimental results were very consistent and an average SCF of 4.68 5. This value is typical for Y joints under out-of-plane bending with the dimensions shown in Fig.04 8.45 -28.07 4. Kuang.43 -23.4 shows how the SCFs predicted by the various parametric equations compare with the experimental values obtained for all the Y joints tested.6 Summary of measured Y joint SCFs Method HCD W&S E&D Kuang Measured Predicted Test ID/Percentage difference in measured and predicted SCF SCF LEYOPB1A LEYOPB2C LEYOPB3C LEYOPB4C (Y4) (Y3) (Y2) (Yl) -1. Three different sets of measurements were taken for each site and average values of stress concentration factors were determined.73 5. These equations only give the hot spot SCF. This was also used as a measure of the chord end fixity.3 3. Using these three gauges. and the UEG modified versions of Wordsworth and Smedley do not predict the variation of stress concentration factors around the intersection.57 -29.6 where they are compared with values predicted using parametric equations. SCF is used in all cases to produce the trends shown in Fig.4.53 -2.69 -20. The Hellier Connolly Dover (HCD) equation for the variation of SCF around the intersection for a given chord saddle hot spot.4 4.63 4. For all three stages of loading the measured stresses were checked to ensure repeatability and consistency in all cases. For the first two stages of loading intermediate measurements were made at 6 per cent load.6 4. The effect of load path on the measured stress concentration factors was also investigated. This was considered very important since it was the only way of checking for any stress hysteresis effects. 3. Table 3. Wordsworth. and Smedley. it was possible to measure the variation of stress along the brace with applied load.47 was obtained.13 18.2.20 12.70 8.29 20. from 10 per cent back to 0 per cent and up again to 10 per cent. 3.73 14.97 15.4.85 4.54 2. 85 .81 14. A summary of SCFs obtained for the joints is given in Table 3. and to ensure that there was no rotation of the chord within the fixed end castilations. The values obtained were 4. and 4.4 per cent less than the measured average value of 4.57. The Efthymiou and Durkin equation and the equations of Wordsworth and Smedley overpredict by 18 per cent and 9.3. the HCD equation gives the best agreement with the experimental results (for Y joints) after considering the scatter shown in Fig. 3. which gives a value of 3.54 compared with the measured value of 4. These results are consistent with a very small scatter.34 per cent. 86 . The only equation which underpredicts the chord saddle hot spot SCF is Kuang's equation. 4. respectively. 22. respectively. 0 per cent. and LEYOPB4C respectively.5.4 for LEYOPB2C.6 for the first joint LEYOPB1A. and 4.6.4 Comparison of measured and predicted SCFs for Y joints For all the parametric equations used. LEYOPB3C.Fatigue and Fracture Mechanics of Offshore Structures Fig. The HCD equation predicts a hot spot SCF of 4. 3.6. The SCFs measured on the other three Y joints varied very slightly from the first.5 per cent.52 per cent. The percentage differences of these values from the first are 6. 7.9].1 Test parameters and the JOSH sequence A summary of the test parameters for the entire test programme undertaken is given in Table 3.11] are compared with those obtained from variable amplitude tests [3. It is thought that CP could have a greater effect on the corrosion fatigue behaviour of SE 702 steel than on lower-strength steels such as BS 4360 50D and BS 7191 355D.Large-scale Fatigue Testing Fig. even -800 mV may be harmful to steels with strength levels above 800 MPa [1. Later in this chapter. and their distribution in JOSH is shown in Figs 3. The effect of CP on hydrogen embrittlement is particularly relevant to high-strength steels.1.7. All tests were conducted under variable amplitude loading conditions. to assess the effect of environmental loading under CP conditions. The output turning points for the whole sequence were scaled to ±100 per cent. A study on the effect of CP on the fatigue performance of SE 702 has been carried out [1.5.5 Deviation of predicted SCFs from experimental values 3.5 Experimental fatigue testing Three major variables in the test programme were the hot spot stress and the CP level applied. results from reference [1. A review of UK and other design guidance suggests that negative potentials in excess of -850 mV (Ag/AgCl) may be detrimental to steels with strength levels above 700 MPa. 3.66].6 and 3. The sea states used are summarized in Table 2. 3. Each transition was taken to last for a period of ten minutes. In each case the sequence was simulated from 4000 transitions of twelve sea states.11] using constant amplitude loading. in some instances. In a recent study it was highlighted that. 87 . The equivalent stresses indicated were obtained after rainflow cycle counting of the sequence used in each case. 62 8.76 200.12 111.48 21. stress (MPa) RMS (MPa) Clipping ratio Equiv.29 280744 Air LEYOP2C 1-12 975.23 81. stress (MPa) Min.53 89. stress (MPa) Total number of cycles CP (mV) Environment LEYOP1A 3-12 701.42 20.0 532025 LEYOP3C 1-12 783.Fatigue and Fracture Mechanics of Offshore Structures Table 3.42 20.7 Summary of parameters of JOSH Sea states used Max. 3.6 Distribution of sea states in JOSH2C 88 .34 8.75 8.34 8.38 21.73 250.0 532025 LEYOP4C 1-12 783.76 200.53 89.59 180.0 532025 -800 Seawater -800 Seawater -1000 Seawater Fig. The normalized PSD functions. £ is the damping ratio.4] to be given as (see Chapter 4 for derivation) Where fn is the natural frequency of the structure. S(f)N for the JOSH sea states have been demonstrated [2. is different from that in the sequence (JOSH2C) used for the corrosion tests.Large-scale Fatigue Testing Fig. Tr. 3. 89 . and Q. used for the air test CLEYOPB1A). Hr. are non dimensional parameters given as The distribution of sea states in the sequence (JOSH1A).7 Distribution of sea states in JOSH1A All variants of JOSH are based on the same sea state PSDs. The reason for this difference is that the first two sea states (sea states 1 and 2) were clipped to increase the effective equivalent stress and to ensure that the maximum stress did not exceed the yield strength of the material. These distributions are normalized with respect to the most probable occurring stress range in Fig.Fatigue and Fracture Mechanics of Offshore Structures Fig. together with the stress range distribution in part of the JOSH2C sequence used in the first corrosion test (LEYOPB2C). 3. 3.9. 3.9 Normalized SRPD curves for JOSH Figure 3.8 Stress range distribution curves for JOSH Fig.8 shows the distribution of stress ranges for both JOSH1A and JOSH2C. 90 . Fracture mechanics analysis of results is presented in Chapter 4. In this section the results are presented in the form of initiation data. 3. crack growth curves. Fig. This section presents the details of the large-scale fatigue tests carried out using.1 mm deep fatigue crack.6 Fatigue test results The results of the fatigue tests are presented here. The limited guidance available today on fatigue design of offshore structures under realistic variable amplitude loading conditions is a result of limited experimental data. The experimental Y factors and crack growth rates obtained are presented and compared with predictions using existing fracture mechanics models. These results are compared with those obtained from tests conducted on lower strength and other high-strength steels.Large-scale Fatigue Testing As highlighted in Chapter 1. Early crack growth data from the four tests conducted for this study are shown in Figs 3. JOSH.1 mm. crack aspect ratio evolution. 3. This is the primary justification for conducting these tests. This detection capability is important when it comes to determining the point of initiation of each defect. Most of the analysis presented in Chapter 2 is necessary to ensure that a representative loading history or sequence is produced. large-scale fatigue testing is a necessary requirement for understanding the fatigue behaviour of offshore structural steels under variable amplitude loading conditions. Ni is taken as the attainment of a 0. 3.1 Fatigue crack initiation Inspection of the ACPD data collected during the early portion of each test has shown the ACPD technique to be capable of detecting crack growth increments of less than 0. The definition of initiation.13. and the fatigue life of each specimen presented in S-N format.6.10 Early crack growth data for LEYOPB1A 91 .10 to 3. 12 Early crack growth data for LEYOPB3C 92 .11 Early crack growth data for LEYOPB2C Fig.Fatigue and Fracture Mechanics of Offshore Structures Fig. 3. 3. 3. From this figure it can be seen that the initiation life for the air test is about 620 500 cycles.13 respectively. The initiation lives were determined graphically from plots such as those shown in Figs 3.Large-scale Fatigue Testing Fig.10 shows results obtained from the air test.11-3. It was possible to monitor the progress of a fatigue crack from initiation through to failure. The initiation and S-N data obtained for the Y joints are summarized in Table 3. which also shows results obtained from constant amplitude tests [1. The corresponding results obtained for the corrosion tests (LEYOPB2C.1 mm deep crack. LEYOPB3C.10-3.291 0. and LEYOPB4C) are shown in Figs 3.032 0.158 93 .8 Summary of initiation and S-N data for Y joints Test No.11] conducted on Tjoints made from the same steel. Yl Y2 Y3 Y4 Conditions 180MPa(Airtest 260 MPa (-800 mV) 200 MPa (-800 mV) 200 MPa (-1000 mV) Ni 620 500 10000 50000 180000 N3 2 130000 380 000 1 545 000 1 140 000 Ni/N 3 0.8. which corresponds to the first data point collected after the attainment of a 0.13. Table 3.13 Early crack growth data for LEYOPB4C Figure 3. LEYOPB1A.026 0. Fatigue and Fracture Mechanics of Offshore Structures Summary of initiation and S-N data for T-joints [1. 94 . However. There is further difficulty involved when comparing the T joint results directly.192 <0.14 also shows that fatigue crack growth.8) for the same steel.11] (Table 3.14.1] carried out a series of variable amplitude tests on BS 4360 SOD steel using the WASH sequence. in terms of initiation to total life ratio. under variable amplitude loading conditions is not steady. In each case regions of accelerated growth were found to coincide with the 'storm' in the load sequence. This is further supported by results from T5 when compared with LEYOPB1A carried out at the same hot spot stress range. Figure 3. The sequence used in each case had significant variability in amplitude and frequency content. 13000 24000 115000 105 000 Run Out <10 000 N3 74000 180000 194 000 548 000 130 000 138 000 Ni/N3 0.292 0.1000 mV) 300 MPa (-1000 mV) 300 MPa (-800 mV) N. The tests carried out at a CP level of -1000 mV have a higher initiation to total life ratio in both cases when compared with those carried out at the CP level of -800 mV.2Crack growth curves The crack growth curves for all the tests are shown in Fig. This effect is not so clear from the results obtained from this study. The only discrepancy is from LEYOPB1A. SE 702. It is also apparent that the CP level has an effect on the initiation to total life ratio for both joint types. Austin [3. one would expect higher-strength steels to show higher N1/N3 ratios since fatigue crack initiation is controlled by plastic deformation. The trend noted from his study was for lower Ni/Nj ratios for higher equivalent stress levels.072 The initiation to total life ratio. This was anticipated since the variable amplitude load sequence used to conduct the tests (JOSH) consisted of multiple sea states with varying degrees of severity.11] Test No. 3.176 0. 3. Tl T2 T3 T4 T5 T5(retest) T6 Conditions 400 MPa (Air) 300 MPa (Air) 225 MPa (. is used to measure the significance of the initiation period to the overall fatigue life. The total number of data points is limited even when the results from the T joint tests are included. The results from Y joints are compared with those obtained from constant amplitude tests reported in [1. since the type of loading is different.1000 mV) 225 MPa (-800 mV) 180 MPa (.133 0. A 'stair case' type crack growth curve was consistently obtained for each of the tests.6. The main reason for the difference in initiation to total life ratios is the presence of very damaging stress ranges from severe sea states that are present in the JOSH sequence. Nj/Ns^. The values for Y joints under variable amplitude loading are lower than those for T joints. Welded tubular joints generally exhibit short initiation and long propagation lives. Crack growth behaviour is somewhat more complex in a corrosive environment (with CP) than in air. 3.14 Comparison of variable amplitude fatigue crack growth curves Fig.Large-scale Fatigue Testing Fig. The main difference is the existence of 95 . The crack growth curves obtained under constant amplitude conditions for the tests reported in [1.11] are shown in Fig. 3. This influences the mechanism by which cracks propagate and can lead to irregular behaviour.15.15 Comparison of constant amplitude fatigue crack growth curves The corrosive environment used for the seawater tests also plays an important role in the fatigue crack growth process. This is highlighted by the difference in the crack growth curves when variable amplitude tests are compared with those obtained from constant amplitude loading conditions in seawater with CP. 3. 3.3 Crack aspect ratio evolution Fig. where the crack growth curves take on different linear slopes for the corrosion tests.6.16 Crack aspect ratio data for LEYOPB1A Fig.17 Crack aspect ratio data for LEYOPB2C 96 . This behaviour was also found in a more pronounced manner and following a distinct pattern that could be linked to significant fatigue damage related events in the sequence for the variable amplitude tests. 3.Fatigue and Fracture Mechanics of Offshore Structures distinct regions. 3. 97 . The results obtained are shown in Figs 3.19 Crack aspect ratio data for LEYOPB4C The surface crack length was measured at similar intervals to crack depth measurements for each of the four tests conducted.18 Crack aspect ratio data for LEYOPB3C Fig.19 for LEYOPB1A. 3.Large-scale Fatigue Testing Fig.16-3. 3. This was obtained from crack shape evolution. 7.6.Fatigue and Fracture Mechanics of Offshore Structures LEYOPB2C. 3. where they are used to develop a new Y factor model that can be used in the analysis of fatigue crack growth in offshore structures.4 S-N data The end of each test was defined as the attainment of a through-wall fatigue crack. An interesting observation can be made when comparing Y joint results with those obtained from T joints made from the same steel. It is. LEYOPB3C. with other medium and high-strength steels tested both in air and seawater. This observation was also made by Vinas-Pich [1. 3. These results are discussed further in Chapter 4.64]. However.7 Discussion The results obtained from SE 702 large-scale tubular welded joints are compared with the T' curves for air and seawater under adequate cathodic protection conditions in Fig. It can be seen from Fig.as shown in Fig.8. The stress range indicated is the sequence equivalent stress range derived from rainflow counted fatigue cycles. 3.21. difficult to draw any conclusions from this observation as the T joints were tested under constant amplitude while the Y joints were tested under variable amplitude loading conditions. The experimental fatigue life (N3) of each specimen is given in Table 3. and LEYOPB4C respectively. however. 3.20 for comparison. The S-N data obtained for the study on the Y joints are compared with those obtained from T joints in Table 3. The mean line for data obtained from previous test programmes on lower strength steels (BS 4360 50D) is also shown in Fig. 3. This indicates that Y joints under out-of-plane bending may exhibit a nominally better fatigue resistance than T joints under axial loading. axially loaded T joints are known to exhibit a more severe response to fatigue loading when compared with Y joints under out-of-plane bending.8. It can be seen that all the Y joint data lie to the right of T joint data. 3.20 that the SE 702 data points all lie above the air design curve.20. 98 . The fatigue performance of SE 702 is further compared in Section 3. These results are later compared with the design S-N curves for air and seawater with CP conditions and the mean line for 16 mm thick specimens made from BS 4360 50D. and is reflected by the existing database for tests under different modes of loading. 20 Comparison of SE 702 data with design S-N curves Fig. 3. 3.21 Effect of loading mode on S-N data 99 .Large-scale Fatigue Testing Fig. For the constant amplitude loaded T joints at 225 MPa for example. and Vinas-Pich [1. 3. where results from air tests are compared with those from seawater tests CP. however. This comparison is shown in Fig.23. The geometry of the test specimens used by Austin was nominally identical to the SE 702 T joint test specimens reported in [1. The effect of CP is shown in Fig. 3. less severe when compared with a reduction factor of three in crack growth rate for the fatigue crack growth specimens (SENB) tested at Cranfield University [3. Both of these test programmes were conducted using variable amplitude loading under corrosion conditions with CP. The lowerstrength steel data points all lie below the air design curve while the SE 702 data points all lie above this line. A similar ratio of 73 per cent was obtained from the variable amplitude Y joint tests conducted at an equivalent hot spot stress range of 200 MPa. The data suggest that high-strength steel joints may have longer fatigue lives at lower stress levels.22 where SE 702 shows a tendency to lie at the upper end of the scatter band. The level of CP influences the fatigue performance of SE 702. Increasing the CP level from -800 mV to -1000 mV resulted in a shorter life at a given stress level for both T and Y joints. 3.22 Comparison of SE 702 with lower strength steels SE 702 results are also compared with those of Austin [3. but there are insufficient data to identify a clear trend.11] while those of VinasPich were of the same geometry as the Y joints used for this study.1]. 100 .64] obtained on tubular welded joints made from BS4360 SOD steel.3]. Both Austin and Vinas-Pich used the WASH sequence. the life at -1000 mV corresponded to approximately 70 per cent of the life at -800 mV .Fatigue and Fracture Mechanics of Offshore Structures Fig. This is increasingly so for the tests conducted at lower stresses. This reduction factor on fatigue life observed for the large-scale tubular joint tests is. 3.11] involved tests on high-strength steels with yield strength in the region of 700 MPa.Large-scale Fatigue Testing Fig. In addition. and none appear to be directly relevant to the joint geometries frequently used in the fabrication of Jack-up platforms.23 shows that SE 702 results obtained from tubular joints lie well within the existing scatter with a tendency for better fatigue performance when compared directly with lower strength steels. There is a limited amount of S-N data for welded joints manufactured from higher strength steels. Figure 3.23 Comparison of SE 702 data with data from a database of protected joints The results from Cranfield showed that fatigue crack growth rates were increased by up to a factor of three when the CP level was increased from -830 mV to -1080 mV (Ag/AgCl). In both cases tests were performed on T butt joints in seawater with CP. 101 . a recent study [3. Data for welded plates with yield strengths up to 540 MPa are reported in [3. The results indicate that the performance of these joints is comparable to that of conventional structural steels.10]. relative to medium strength structural steels. Fatigue and Fracture Mechanics of Offshore Structures Fig. 3.24 SE 702 compared with other high-strength steels tested in air Fig. 3.25 SE 702 compared with high-strength steels tested in seawater 102 . crack aspect ratio evolution. and are seen to lie above the T' curve.24. The seawater temperature was maintained between 8°C and 10°C. These results have been compared with results from previous studies and those obtained from a parallel study on SE 702. representative of fabrication methods. The data have been thickness corrected to 16 mm using a thickness exponent of 0. This behaviour was attributed to the presence of manganese sulphide inclusions in the parent material.Large-scale Fatigue Testing Data from tests conducted on high-strength steel tubular joints in air. 3. 3. and S-N data. 3. 103 . crack growth curves. Some of the tests were conducted under free corrosion conditions and Fig. A comparatively smaller number of tests have been performed on high-strength steel tubular joints in seawater.24. rather than perpendicular to it.12]. It can be seen from Fig. and details of the materials used. Two welding methods. SE 702 is a typical high-strength steel used in the construction of Jack-up rig legs. The graph shows that some of the data points lie above the S-N curves.8 Summary This chapter has presented details of variable amplitude fatigue tests conducted on full-scale tubular welded Y joints fabricated from a 700 MPa yield strength steel.3. were used. with chord thicknesses ranging from 5 mm to 78 mm. A statistical analysis carried out on the SE 702 data showed that a best-fit mean curve has a slope of -5.3 [1. These conditions are similar to those used in Section 3.4 as a soak time of two weeks was equally employed prior to testing. SE 702. The mode of cracking in the in-air SMAW specimens differed from that observed in tubular joints of conventional structural steel in that the cracks propagated in a plane that was approximately parallel to the chord surface. The tests were conducted in air and in seawater at a CP level of -1000 mV Ag/AgCl under OPBatanR-ratioofO. yielding string welds.65]. namely flux cored arc welding (FCAW). and shielded metal arc welding (SMAW). JOSH. The objective of this study was to assess the effect of realistic variable amplitude loading and CP on the fatigue crack growth behaviour and subsequent fatigue life of high-strength steels. The HSE study included a programme of constant amplitude corrosion fatigue tests [1.2. 3. These results are compared with SE 702 data together with the T" design curve in Fig. The results obtained from the investigation.395 instead of -3 as recommended by the existing UK guidance notes. have been thickness corrected to 16 mm using a thickness exponent of 0. 3.24 that some points fall below the T' design line.13] were generated in a study funded by the UK Health and Safety Executive (HSE). have been presented in the form of initiation data. These results are also included in Fig.25. These results are compared with SE 702 data in Fig. 3. Data for tubular DT joints manufactured from Le Toumeau MM X85 high-strength steel with nominal yield strength of 590 MPa [3.25 shows that their performance is not necessarily poorer than that of CP joints. A total of one air test and three corrosion fatigue tests with CP were carried out under simulated environmental conditions using.05. 3. entailing weave welding. especially Jack-up platforms used for production. However there is no evidence to suggest that SE 702 is any more susceptible to hydrogen embrittlement than other high-strength steels of similar grade. It is also possible that. There are potential benefits to be gained by using high-strength steels in the fabrication of offshore structures. They have the potential for better performance and may offer the benefit of longer fatigue lives at lower stress levels.Fatigue and Fracture Mechanics of Offshore Structures The fatigue life results from the current investigation suggest that tubular joints fabricated from SE 702 are at least as good as conventional fixed platform steels. The limited number of tests conducted show that SE 702 may be used under these applications without necessarily increasing the risk of fatigue failure due to hydrogen induced stress corrosion cracking and embrittlement. increasing the cathodic protection level from -800 mV to -1000 mV may lead to a shorter fatigue life. The results show that highstrength steels are no worse than conventional fixed platform steels such as BS 4360 50D. due to limited data on high-strength steels. in order to adequately quantify the potential benefits and to formulate appropriate guidance on their use in the fabrication of engineering structures. For hot spot stress levels of around 200225 MPa a factor on life of around 30 per cent was observed for tests conducted using variable amplitude loading and this was consistent with results obtained from a separate investigation on the same steel under constant amplitude loading conditions. However. 104 . It is strongly recommended that further tubular joint fatigue tests should be carried out on SE 702 and other high-strength steels. it is difficult to draw firm conclusions on any existing trends in the fatigue behaviour of high-strength steels. obtained from these models. depending on the interaction between the loading and the environment. The accuracy of these models in the prediction of fatigue crack growth in welded tubular joints. for instance. with experimental results.1 Introduction The S-N approach has been used extensively to design welded offshore tubular joints and other welded connections. Some of the existing FM models. and those based on results obtained from finite element analysis. subjected to service loading. However. to make important decisions on inspection scheduling and repair strategies. It provides the basis for fatigue life prediction. Service loading in offshore structures. 105 . are presented in this chapter. is mainly due to wave and wind action with variable amplitude and frequency content. Emphasis is placed on the effect of service loading. adapted flat plate solutions. used in the prediction of fatigue crack growth in offshore welded tubular joints. FM is also used during the operational stage of a structure. steel selection. As a result. is assessed by comparing the predicted results. It can also be used as a tool for establishing limits on operational conditions. the S-N approach cannot be used in assessing the structural integrity of cracked components under service conditions.Chapter 4 Fracture Mechanics Analysis 4. and consideration is given to the sequence effects on the accuracy of existing models when used for fatigue crack growth prediction in engineering structures. and tolerance setting on allowable weld imperfections. it is the most powerful and useful technological tool available for describing and solving fatigue crack problems. at present. The process of fatigue is influenced by many factors that may be different in each application area. Fatigue failure of structural components under these conditions is a major concern in the maintenance of offshore structures. fracture mechanics (FM) is used and. These models include empirical and semi-empirical models. Fracture mechanics is currently used at the design stage of offshore facilities. A different and more realistic FM based approach is required. the use of the overall sequence equivalent stress range needs to be applied with caution. Perhaps his most significant contribution came in the mid 1950s [4.2 The stress intensity factor concept Irwin has made a great contribution to the development of FM concepts. Based on the philosophy of the crack driving force and the crack tip stresses.4] proposed the following expression for the SIF for an embedded elliptical crack in a uniform tensile stress field (Fig. generally rely on using the overall equivalent stress range. This chapter seeks to address this problem. are taken into account. It also presents a proposed FM based model for predicting fatigue crack growth in offshore structures. These effects can be significant under service loading conditions as crack growth is largely dependent on SEF range that is a function of stress range and crack size. per unit increase in crack length. observed in service. It is possible that the use of the overall sequence equivalent stress concept in a fracture mechanics analysis procedure may have significant limitations in dealing with the high degree of variability. per unit thickness. as crack growth acceleration and retardation cannot be accounted for using this approach.2]. 4. to ensure that any significant sequence. and postulated that energy due to plastic deformation should be taken into account in evaluating the energy associated with the creation of a new crack surface.1) after accounting for the flaw shape 106 .3].Fatigue and Fracture Mechanics of Offshore Structures Existing FM models. It presents a fast assessment procedure for the determination of load spectra for fatigue analysis of offshore structures. Irwin [4. for FM crack growth prediction employed after an in-service inspection schedule. For S-N type analysis. or interaction effects. However. for fatigue crack growth prediction under variable amplitude loading. together with a suitable crack growth law. G. when he showed that the local stresses near the crack tip can be expressed in the form where r and 9 are the cylindrical co-ordinates of a point with respect to the crack tip. He extended Griffith's theory [4. 4.1] (crack propagation will occur if the change in elastic strain energy due to crack extension is larger than the energy required to create new crack surfaces) for ductile materials [4. which is the total energy absorbed during cracking. this method is by far the best when dealing with variable amplitude sequences. and fatigue crack growth prediction methods. the strain energy release rate or 'crack driving force'. He also defined a quantity. 4. and </> is the angle of orientation. Cracks in welded tubular joints are usually in a complex stress field that is different from the case of a uniform stress field in an infinite plate. in the absence of all boundaries. in an infinite plate subjected to a uniform stress field. The elliptical integral. therefore. O.4) gives the SEF. such that the SIF is given by 107 . SEF solutions for cracks in tubular welded joints must. 4. (Fig. and specimen and crack geometries.2) is given by Equation (4. the mode 7 SIF for a centre crack of length 2a. of a form applicable to the mode of loading and specimen geometry. is given by In general. cr.1 Embedded elliptical crack in a uniform tensile stress field where the crack dimensions are described by a for crack depth.Fracture Mechanics Analysis Fig. include various correction functions to account for boundary effects due to loading. and c for crack surface length. it is possible to determine experimental stress intensity Y factors with reasonable accuracy. 4. This method has been used in the past to develop empirical Y factor models.5] form given by Ys Yw Ye Yg = Correction for a free front surface = Correction for finite plate width = Correction for crack geometry = Correction for non-uniform stress field Yk = Correction for the presence of geometrical discontinuity Ym = Correction for changes in structural restraint Different analysis methods have been used to determine the Y factors for cracked tubular welded joints. These experimental values are used as a benchmark for comparing the accuracy of other models presented in this chapter. Fatigue crack growth data presented in Chapter 3 have been used to determine experimental Y factors.Fatigue and Fracture Mechanics of Offshore Structures Fig. 108 . This has led to the development of several SIF solutions for semi-elliptical surface cracks. The procedure adopted in determining the experimental Y factors is presented here.2 Crack in an infinite plate under a uniform stress field where Fis the SIF correction function with a general recommended [4.3 Experimental results Calculation of experimental SIF can be carried out using experimental crack growth data. 4. Some of these are semi-empirical and empirical solutions obtained from experimental results. using data from ACPD crack depth measurements. and those based on finite element analysis results. With the increasing accuracy in the measurement of experimental fatigue crack growth rates. experimental Y factors may be obtained from The experimental crack growth rates. LEYOPB3C.Fracture Mechanics Analysis The determination of experimental Y factor relies on the use of a suitable crack growth law. 4. and AS is the hot spot stress range. LEYOPB2C. such as Paris law (4. By assuming that Paris law applies. respectively. Fig. are shown in Figs 4. A.K" is the stress intensity factor range.3 to 4. and LEYOPB4C.6 for tests LEYOPB1A.7) where a is the crack size. obtained from the fatigue tests conducted for this study.3 Experimental fatigue crack growth rate for LEYOPB1A 109 . 4.Fatigue and Fracture Mechanics of Offshore Structures Fig. 4.4 Experimental fatigue crack growth rate for LEYOPB2C Fig.5 Experimental fatigue crack growth rate for LEYOPB3C 110 . 10. respectively.6 Experimental fatigue crack growth rate for LEYOPB4C The corresponding experimental Y factor curves obtained for the tests are shown in Figs 4. Fig.Fracture Mechanics Analysis Fig.7 Experimental Y factors for LEYOPB1A 111 . 4.7 to 4. 4. 8 Experimental Y factors for LEYOPB2C Fig.9 Experimental Y factors for LEYOPB3C 112 . 4.Fatigue and Fracture Mechanics of Offshore Structures Fig. 4. is given in Table 4.1687 Table 4. for both parent plate and the heat affected zone. the use of arbitrary values from PD 6493 [4.5320 3.715 x 10"y 3. Comparing the results from CLI with those from other tests [3. used in the tests conducted to generate the data. 113 . 4.6].1687 Where appropriate data are not available.2 Paris law seawater data for SE 702 (CP: -830 mV/ECS. as misleading results can be obtained. Table 4. A summary of the data supplied.872 x 10'9 m 3.1.2.2 shows other values of C and m.872 x 10'9 m 3. Table 4. Temperature: 20°C) Parent Metal (PM) Heat Affected Zone (HAZ) C 2.3] suggests that there is scatter on the C and m values.5320 3.Fracture Mechanics Analysis Fig. It is important to note that the accuracy of the experimental Y factors presented. were obtained from compact tension tests performed on parent plate in air by CLI [4.10 Experimental Y factors for LEYOPB4C The accuracy of the experimental Y factors depends on the Paris law material constants C and m.1 Paris law air data for SE 702 Parent Metal (PM) Heat Affected Zone (HAZ) C 2. The values used in the sample calculation above.5] is not recommended. depends greatly on the values of C and m used in analysing the experimental results. As shown in Table 4. are not identical to those used for the large-scale tests in this study.715 x 10'9 3. the CP levels. for free corrosion and for corrosion tests conducted with CP. results show that under variable amplitude loading conditions there can be discrepancies across a wider range (Fig. to the hot spot stress concentration factor.11). 4. This model made use of stress intensity modification (Y) factors and assumed a thickness correction for joints other than 16 mm.7] was proposed after testing large-scale 16 mm tubular joints. and have been successfully used for fast assessment of crack growth in tubular welded joints. with discrepancies only occurring during early growth where the crack depth is less than 25 per cent of the chord wall thickness. 114 . 4. which include the two phase model (TPM). These models. at any location of the joint intersection. SCF#s. Some of these models have gained wide acceptance.1 The average stress model The average stress (AVS) model [4. and the modified average stress models. However. The Y factor predicted by this model is given by 5 is a non-dimensional parameter. This model has been used to predict crack growth rates in tubular welded joints under constant amplitude loading conditions.4 Use of empirical SIF solutions Empirical models were developed for rapid and accurate analysis of crack growth data. the average stress. It is given by and where T is the chord wall thickness and a is the crack depth.Fatigue and Fracture Mechanics of Offshore Structures 4. SCFav. which is the ratio of the average stress concentration factor. are presented here and their performance is compared with experimental results.4. Fracture Mechanics Analysis Fig.25). MI is taken as one for the propagation phase (o/T >0. and Q. S.11 Comparison of experimental Y factors with AVS prediction 4. to consider crack growth affected by joint size.8] was based on published crack growth data and was developed. and p is the early crack growth phase controlling parameter. 4.25T/o~p for the early crack growth phase (o/T<0. mainly. 115 . It is given in the form where B and k are functions of size and AVS parameter.2 The two phase model The two phase model (TPM) [4.25).4. which required that the Y factor predicted by the AVS model be reduced by 15 per cent. Austin [3. It was developed by applying a 15 per cent reduction factor to the original AVS model. 4. is such that it imposes a very severe dependence of crack growth on thickness.1] suggested the 15 per cent reduction factor. The Y factor predicted by this model is given as 116 . The thickness correction exponent that determines the value of the early crack growth phase controlling parameter. for the representative double-peaked spectrum originally used to develop the AVS model.15. as shown in Fig. A modification to the AVS model was then proposed based on this difference.3 The modified average stress model The modified average stress (MAYS) model [3. 4. The reduction factor was based on the assumption that rainflow cycle counting provided a higher degree of correlation.12 Comparison of experimental and TPM Y The early crack growth phase controlling parameter was produced by assuming that early crack growth behaviour can be treated as an extrapolation of the propagation phase. 4. p.Fatigue and Fracture Mechanics of Offshore Structures Fig. modified by an exponentially decaying effect. determined by the wall thickness. This makes the model more sensitive to thickness effects than has been observed experimentally.1] was proposed after testing largescale 16 mm tubular joints. and the hot spot stress. the diameter ratio. after noting that the equivalent stress determined from rainflow counting was higher than could be obtained using simple range counting.12. than range counting on which the original AVS model was based. This factor was found to be 1. with constant amplitude data.4. one such solution is that due to Newman and Raju. For instance. flat plate solutions may be used to obtain SIF for semi-elliptical cracks in T plates by introducing a correction function to account for the influence of the weld detail and the attached plate. Under variable amplitude conditions this may equally be affected by the method of cycle counting used.13 shows the predicted Y factor based on this model compared with experimental data. however. important in that they can be used to provide estimates of stress intensity factors for other geometries by applying the appropriate boundary condition correction functions. 4.Fracture Mechanics Analysis All the variables are as defined for the AVS model. and the detail contained in the crack growth data. The degree of accuracy obtainable from this model depends. Different researchers have used different approaches over the years to model the effect of the weld detail on the flat plate solutions and develop SIF solutions for welded connections. numerical methods. 117 . This is as a result of the differences in boundary conditions. They are. These range from methods based on weight functions to those based on finite element analysis.13 Comparison of experimental Y factor with MAYS prediction 4. Fig. These approaches fall within three broad categories of methods. and semi-empirical solutions based on a combination of experimental and analytical data. Figure 4. For instance.5 Adapted plate solutions SIF solutions for plates cannot be applied directly to tubular welded joints. generally used to determine stress intensity factors. largely. These include classical solutions for idealized geometries. on the accuracy of the original experimental data on which it is based. Fatigue and Fracture Mechanics of Offshore Structures 4. are the correction functions for the tension and bending stresses. The NR solution has been shown [4. w. The solution gives the stress intensity factor for a surface crack of depth.. respectively. 118 .9] to yield results that agree closely with experimental tubular joint Y factors for cracks of o/T >0.5. by applying the moment release function to account for the stress redistribution that accompanies crack propagation in tubular joints.15. 2c. om and Ob. in that it can be used to provide estimates of stress intensity factors for other geometries by applying the appropriate boundary correction functions. it is very important.. a. O is an elliptical integral approximated by The correction functions for tension. in the form Fm and Ft. are given as fw is the plate width correction function for a plate with a finite width.1 Newman-Raju SIF solution for surface cracks Newman and Raju (NR) derived a stress intensity factor solution for a semi-elliptical crack in a flat plate. Even though this flat plate solution cannot be applied directly to tubular welded joints.. F. Fb. and surface length. and for bending. a linear moment release (LMR) to account for load shedding. 4.23) and showed that *¥ could be approximated by the following equation 119 .10]. as shown in Fig. Yg is the NSC factor. and B/T is the bending to total stress ratio.11]. and a crack shape correction (CSC) factor. This factor can be obtained using a method proposed by Albrecht and Yamada[4.14. The CSC factor. that remains symmetrical about the crack centre line. introduced by Monahan.Fracture Mechanics Analysis A semi-analytical model based on the NR flat plate solution for predicting Y factors in welded tubular joints was proposed by Monahan [4. It included the following modifications: a non-uniform stress correction (NSC) to account for weld geometry. The proposed equation is given by where T. <7(x). This is for a non-uniform stress distribution. was included to account for the influence of crack aspect ratio. T. which accounts for the influence of the stress concentration produced by the weld detail. the CSC factor. This factor was obtained by comparing experimental Y factors with those obtained by the NR flat plate solution that included a NSC factor and the linear moment release model such that Monahan used curve fitting through the values given by equation (4. Fatigue and Fracture Mechanics of Offshore Structures Fig. Myers [1. This would make it difficult to use this type of semi-empirically derived solution for other joint geometries. 4. depending on the geometry of the specimens. is unity for the range of crack aspect ratios obtained for the Y joints tested for this study. The first part of the correction function can be considered to represent an upper boundary for a/2c < 0. 4.05. 120 . shown above. and obtained a CSC factor applicable to T ioints under axial loading given by The data from which this correction factor was derived are shown in Fig. The reason for this is that the crack shape evolution curve depends greatly on both the joint geometry and the mode of loading.15. is outside the scatter band for the data used.05. 4.15. This is also demonstrated by the fact that the crack shape correction. the CSC function used for a/2c > 0. However.14 Schematic illustration of Albrecht's method for determining Yg The above CSC function was derived from experimental data obtained from tests conducted on a combination of X and multi-braced tubular joints. This means that it may not be directly applicable to other joint geometries.11] used a similar approach adopted by Monahan. as shown in Fig. It is possible that a wide range of CSC factors are obtainable. 16 Comparison of crack shape evolution curves for Y and T joints 121 .16. 4. where the best fit curves obtained for the two geometries are compared. 4. 4. This sensitivity is due to the semi-empirical nature of the model. used in this study. The implication of this is that. However. As a result. This is shown in Fig. the crack shape evolution curves obtained from the two studies are different.Fracture Mechanics Analysis Fig. the Y factor curve obtained will depend on the CSC function used.15 Myers' data used in deriving CSC factors for NR solution The brace and chord thickness of the Y joints. are the same as those used by Myers. Fig. both the geometry and mode of the loading are different. and the adapted flat plate solution based on the NR equations.17 shows that the experimental Y factors obtained for this study are all below those predicted by the above equations. The use of this method for the prediction of Y factors in welded joints is not discussed any further in this book. a CSC function that also accounts for the effect of joint dimensional parameters.13] is based on the use of a root mean square (RMS) stress intensity factor for the transverse and longitudinal directions of crack growth. The new semi-empirical model accounts for the effect of crack aspect ratio. There is a lack of solutions available for predicting crack aspect ratio evolution.15] in analysing fatigue cracks in pipes. 4. Those shown in Fig. One approach highlighted by Brennan [4. there is some degree of uncertainty in the applicability of the model.14].17 shows the Y factor curves predicted by various existing Y factor models. and it has been used by Dedhia and Harris [4. 4. AVS.12] to represent the greatest hindrance to good predictions of remaining fatigue life of cracked components. MAYS. Fig. 4. for cases other than those from which the CSC factors were derived. needs to be introduced. In order to avoid this uncertainty.Fatigue and Fracture Mechanics of Offshore Structures As a result. but a new approach is introduced in the next section. Different researchers have used different approaches to incorporate the effect of crack aspect ratio into SEF models used for fatigue crack growth prediction.17 include the TPM.6 New semi-empirical Y factor solution Figure 4. This has been identified [4. Figure 4. and the mode of loading employed. to the prediction of Y factors.17 Comparison of Y factors from different models with Y joint data 122 . This approach was proposed by Cruse and Besuner [4. 16. therefore.18. The main reason for this is that both joint geometry and mode of loading. 123 .Fracture Mechanics Analysis The previous section highlights the importance of crack shape evolution in the accurate prediction of crack growth in cracked components.18 shows the crack shape evolution curves for the Y joint tests conducted for this study. to obtain the mean best crack shape evolution curve for Y joint under OPB. in the welded joint of interest. The difference in the two curves is. most likely. is representative of those originally used in deriving the respective equations. The TPM. possible that their accuracy in predicting Y factors in tubular welded joints will depend on whether the crack shape evolution. with the data. AVS.11]. Figure 4. for axial T joints tested under constant amplitude loading conditions in Fig. as shown in Fig. therefore. and MAYS models do not account for this effect. Fig. will influence crack shape evolution. It is. The best fit curve is given by This curve has been compared with that obtained for data presented in reference [1. 4. important that a suitably flexible model is developed that also accounts for these observed effects due to differences in the mode of loading and joint geometry. due to the differences in the mode of loading and joint geometry.18 Experimental crack shape data It is. 4. as discussed in the previous section. 4. Curve fitting was used. of the predicted results from the experimental data. to obtain the results shown in Fig.20 and is given by where A = 0.19 shows how the best-fit experimental Y factors compare with the predicted values based on the modified NR equations. 8. 4. This prediction method is used as a basis for comparison.0. is used. given in equation (4. This deviation is shown in Fig. The appropriate CSC function.24).26).19 Comparison of best-fit curve with the modified NR solution 124 . 4. Fig. 4.56 . because it has been identified to give the best correlation with experimental results obtained for the investigation reported in [4.19.185 and the rest of the variables are as previously defined for the AVS model.Fatigue and Fracture Mechanics of Offshore Structures Figure 4.10]. together with equation (4. The Gumbel distribution is then used to model the deviation. The prediction of crack aspect ratio has been identified to represent a major source of uncertainty in the fatigue crack growth prediction.22 + 0. 4. is then obtained by combining the modified solution with the deviation from the experimental data.20 Modeled deviation (5) of predicted results from experimental data The flat plate solution was then modelled using curve fitting to obtain an equation that is similar to the AVS model.185" and j = 0.56 -0. 4. This is illustrated for the Y joint results in Fig. This is mainly as a result of the large scatter on crack aspect ratio obtainable from experimental data. YVA. It also takes into account the effect of crack aspect ratio. This MAYS solution is given by A = 0. such that This proposed solution is more accurate in predicting the average Y factor for the Y joints used for this study.Fracture Mechanics Analysis Fig. It is compared with the experimental data and predictions from existing models in Fig. 4.065 The proposed Y factor solution. 125 .22.21. The reason for using this form of equation is because it is a function of parameters that have been established to be important in influencing the predicted Y factor. Fatigue and Fracture Mechanics of Offshore Structures Fig. 4.21 Comparison of proposed Y factor solution with other solutions Fig. 4.22 Effect of wide scatter on crack shape evolution data 126 Fracture Mechanics Analysis Fig. 4.23 Effect of ±25 per cent error in predicted crack length on Y factor As shown in Fig. 4.22, a ±25 per cent error in the predicted crack length is still within the scatter obtained from the experimental results. In absolute terms, this is quite significant. However, this level of error leads to very little change in the predicted Y factor, as shown in Fig. 4.23. In this figure, the curve from the proposed equation, and those for ±25 per cent error, are indistinguishable since they are almost coincident. 4.7 Variable amplitude crack growth models The derivation of accurate SIF solution is imperative for reliable crack growth prediction. However, there are other important factors that are often ignored, partly due to the lack of sufficient data, and partly due to the inherent difficulty that is often encountered in reducing the level of uncertainty to a reasonable level. One of these factors is the effect of variable amplitude loading and the associated sequence effects. Different statistical models have been developed for the prediction of crack growth rates under variable amplitude loading conditions. These models do not account for sequence effects and have been shown to be applicable to load spectra in which such effects are minimal. Some of the more popular statistical models, which have been applied to crack growth prediction in engineering structures, are discussed below. 4.7.1 Equivalent stress range approach The equivalent stress range approach is an extension of the equivalent fatigue damage concept, first proposed by Paris, to relate the effects of variable amplitude stress histories to constant amplitude fatigue crack growth data. This extension was proposed by Dover [4.16], as the weighted AVS range, or the equivalent stress range approach, for the fatigue crack growth analysis of tubular welded joints subjected to variable amplitude loading. Like the original equivalent fatigue damage concept, this method 127 Fatigue and Fracture Mechanics of Offshore Structures does not account for any load interaction effects in the random sequence, as it relies on the assumption that such effects are negligible. Using this approach, and assuming that Paris law applies, variable amplitude fatigue crack growth rates can be predicted from where Sh, is the equivalent or weighted AVS range, an individual stress range, m Paris crack growth exponent, p(A5) the probability density of AS, and .P(AS) is the probability of occurrence of AS. This approach, and definition of the equivalent stress range concept is procedurally equivalent, and applicable, for both crack growth analysis and conventional S-N approach using Miner's cumulative damage summation method. It has been successfully used, together with the rainflow counting method, to predict variable amplitude fatigue crack growth in air. However, despite the successful application of this model to air fatigue crack growth data, it was thought that it required modification for corrosion fatigue, where crack growth is controlled mainly by two competing factors. Corrosion fatigue, unlike air fatigue, crack growth is controlled by a combination of the mechanical action, due to cyclic stressing, and the electrochemical action of the corrosive environment. Also, the 'no load interaction assumption' has not been established for typical multi-sea state load spectra. For these sort of load sequences, with very high clipping ratios (in excess of seven), it is possible that sequence effects may become more significant and, hence, important for crack growth prediction. The implication for not adequately modelling sequence effects, is that unconservative results may be obtained under variable amplitude conditions. This aspect of crack growth prediction in offshore structures is discussed further in a later section in this chapter, where a new model that predicts crack growth under realistic loading conditions and accounts for sea state interaction effects are presented. 4.7.2Equivalent crack growth concept The equivalent crack growth concept was proposed by Kam [4.17] as a modification to the equivalent stress range concept, for the prediction of variable amplitude corrosion fatigue crack growth in offshore structures This model was based on multiple segment Paris-type linear representation of corrosion fatigue crack growth, as shown in Fig. 4.24. Each segment, shown in Fig. 4.24, is taken to represent the material response that covers all relevant stress intensity factor ranges for which the material's constants, C and m, are pertinent. It assumes that the average crack growth rate for a multi-segment crack growth rate curve, such as that depicted in Fig. 4.24, that has k segments with material constants C, and mj, over segment y can be given as 128 from this equation. It has. possible that a better prediction procedure may be obtained which is based on a more appropriate distribution relevant to a particular sequence. 4.Fracture Mechanics Analysis The equivalent crack growth concept has been shown to give good agreement with the experimental results. It is. however. The main drawback with this model is that it involves the lengthy procedure of signal generation and cycle counting before any analysis can be carried out. To overcome this. not been possible to assess the accuracy of this model due to the lack of Paris law data for SE 702. without going through the cycle counting process. It is not clear whether all representative sequences for offshore structures will exhibit a distribution of peaks that can be sufficiently described by these two distributions combined in this way. for the distribution of peaks can be expressed as the sum of the Gaussian and Rayleigh equations.24 Typical multi-segment corrosion fatigue crack growth rate curve 129 . Fig. therefore. This modified version was based on the original idea behind the Chaudhury and Dover equation for predicting the equivalent stress range directly from the PSD. The solution. an alternative prediction procedure was proposed in the form of an extended version of the Kam and Dover equation. and bypass the signal generation and cycle counting before analysis. ap is the sum of overload crack length and overload plastic zone size. This model was proposed for analysing crack growth on a cycle-by-cycle basis and it can be used to obtain the defect size after r cycles as follows where a0 and ar are the initial crack length and crack length after r cycles.. Some of these models are based on crack tip plasticity. the implementation of which has been covered in Chapter 1. respectively. There is a lack of suitable fatigue crack growth prediction models that account for all the relevant effects that are unique to variable amplitude loading conditions. 4. associated with the rth cycle is given by (da/dN)cA. The retardation parameter is taken to be a function of the ratio of the current plastic zone size to the overload plastic zone size.18] model predicts that crack growth following an overload may be estimated by modifying the constant amplitude growth rate using an empirical retardation parameter. is the crack length at zth loading cycle.8 Consideration of sequence effects As discussed in the previous section. and assume that crack growth rates can be related to the evolution of the crack tip plastic zones. Apart from the statistical models. a. the prediction of fatigue crack growth under variable amplitude loading conditions is still in its infancy. AAT. other models have been proposed for use in analysing variable amplitude loading. such that The constant amplitude growth rate appropriate to the stress intensity factor range. presented above. The Wheeler [4. and is given by where ryi is the *th loading cyclic plastic zone size. all the models discussed above rely on one form of cycle counting or another. Cp. 130 .. are those of Wheeler and Willenborg. The more popular models that have attempted to explain the variability in crack growth rates observed under variable amplitude loading conditions using crack tip plasticity.Fatigue and Fracture Mechanics of Offshore Structures Apart from the fast assessment equations that can be used to calculate equivalent stresses directly. One of the main disadvantage is that it relies on the use of an empirically determined constant. Its cycle-by-cycle approach. The Willenborg model [4.20] is based on the assumption that retardation in crack growth rate. who suggested that the driving force for crack extension is reduced by the development of plasticity induced crack closure. that is the applied stress. The model. Hence. oxide-induced. p. not considered appropriate. required to shape the constant amplitude crack growth retardation parameter. whether based on plasticity-induced. such as those experienced by offshore structures. it uses only constant amplitude crack growth data and does not require the derivation of any empirical shaping constants. contrasts with the phenomenon of delayed retardation observed during overloads [4. resulting from an overload. relies on the use of an effective stress. or crack closure 131 . Other approaches to analysing crack growth retardation rely on the use of the crack closure concept. to give the crack growth rate for the jth cycle as The main difference between this model and the Wheeler model is that. makes it inappropriate for use in structural integrity assessment procedures. Crack closure models. He proposed the effective stress intensity factor range concept that allowed fatigue crack growth rates to be estimated under crack closure conditions. Based on this effective stress concept. reduced by the compressive residual stress component. developed around the crack tip as a result of the elastic body surrounding the overload plastic zone. is practically similar to using the effective stress concept developed by Willenborg. occurs immediately after the application of the overload as the retardation parameter turns to zero. together with an appropriate crack growth law. however.19]. is caused by compressive residual stresses acting on the crack tip. such as those experienced by engineering structures. it also predicts maximum retardation. under such conditions. typical for offshore structures. following an overload. the Willenborg model is also limited in its application to fatigue loads. to obtain the summation of crack extensions. therefore. This was first proposed by Elber. therefore. The Wheeler model also predicts that maximum retardation. Hence. roughness-induced. the calculated effective stress intensity factor range can be used. The use of this method for analysing the results obtained from this study was. The model also neglects the counteracting effect of negative peak loads in crack retardation. it has some inherent disadvantages. immediately after the application of an overload. the model has very limited capability in analysing variable amplitude loading sequences. This. on a cycle-by-cycle basis. The fact that it also relies on an empirically determined parameter. Determining the crack opening stress. makes it very difficult to account for any retardation effects that may be present in very long sequences. like the Wheeler model. and fails to predict the observed retardation effects and the decrease in retardation observed due to the application of underloads.Fracture Mechanics Analysis Although this model can be used to predict the effect of overloads. However. with emphasis on the offshore oil gas sector. for example. is negligible for any chosen output range normally determined by the load requirement for any particular test. experimental results have shown that there are fundamental differences between crack propagation. This method was used to compare the model transfer function with the service measurements obtained from the Maersk Guardian Jack-up platform. under variable amplitude loading conditions. when compared to behaviour under constant amplitude loading conditions. the effect on the SRPD. 4. It is. This procedure can be adopted. crack growth under variable amplitude conditions is nonuniform. The non-uniform crack propagation under variable amplitude loading conditions makes the prediction of fatigue crack growth difficult and calls for the need to develop appropriate models for use under these conditions. This experimental observation suggests that. therefore. that normally corresponds to the extreme sea state. In addition. therefore.Fatigue and Fracture Mechanics of Offshore Structures mechanisms resulting from the effect of calcareous deposits on the crack surfaces. The results presented in Chapter 3 show characteristic 'staircase'-type crack growth curves. because normalized spectra maintain the frequency content of loading. important that these differences are taken into consideration when attempting to predict crack propagation under variable amplitude loading conditions using the FM approach. have fundamental problems on grounds of practicality similar to the Wheeler and the Willenborg models. The output scales used to generate the distribution of turning points are. This depends on the fourth and second spectral moments of the power spectrum and is given by 132 . for implementing test conditions for material characterization. These differences have been observed for both air and seawater tests. However. and presents a generalized procedure for the assessment of engineering structures. outlined in Chapter 2. The scale for any sea state i is then given as where A is the calibration factor determined by the required maximum output amplitude and fp is the peak frequency for sea state i. The advantage of using normalized spectra is that it can facilitate the process of comparison of PSDs resulting from different sea states. due to any changes in the magnitude of the scaling factor. The rest of this chapter deals with this in greater detail. weighted with respect to the parameters of the extreme PSD. and allow the flexibility for scaling.9 Fast assessment of offshore structures The sea state PSDs generated from the structural dynamic transfer function approach. can be presented in normalized form. therefore. 133 . and Q. for any structure under wave excitation in the North Sea for any given set of sea states. The basic form of this equation is given as where fn is the natural frequency of the structure and £. Based on this philosophy. 4. normalizing the PSDs for each sea state with respect to the extreme. Hr. is the damping ratio.25. are non-dimensional parameters given by The derivation of this equation is based on the assumption that. such as those shown in Fig. Tr.25 Sea state PSDs obtained using proposed equation This is applicable to power spectra of similar shape. an equation is proposed that uses non-dimensional parameters to estimate the normalized PSD. 4. does not change the stress range probability distribution for that particular structure under the given set of sea states. This is demonstrated below. or most severe sea state.Fracture Mechanics Analysis Fig. The response can.Tzext.41) and (4. outlined in Chapter 2. with known natural frequency. can be calculated from equation (4.9. therefore. under an extreme sea state with significant wave height. given by In a similar manner.44) with Hs and Tz. Sxx(f)i. the response spectrum for any other sea state with significant wave height Hs.1 New normalized PSD equation The derivation starts with the structural dynamic transfer function and the wave excitation spectrum given by equations (4. can be obtained by replacing Hsext and Tzext in equation (4. be normalized with respect to the resonant peak that is a maximum when f=fn.43) to give The natural frequency of the structure is a property of the structure.43).42) respectively. and mean zero crossing period. the response spectrum for a structure.Fatigue and Fracture Mechanics of Offshore Structures 4. to give the sea state response. The resonant response is. and uses the generalized solution given by equation (4. Hsext . for sea state i such that 134 . respectively. By applying the transfer function approach. therefore.. and mean zero crossing period Tz. It will. for any sea state.42). S u ( f )ext. be modified by introducing the same variable. to give the normalized PSD for that sea state as By substituting the response. with respect to the extreme resonant peak response obtained from equation (4. to obtain 135 . therefore. is that the variable /. The main advantage of the proposed normalized PSD equation is that it relies only on the use of non-dimensional parameters and the natural frequency of the structure to predict its PSD. between the above equation and equation (4. The solution given by equation (4.25. using this equation and the JOSH sea states. B.42). presented in Chapter 2. therefore. in Chapter 2.45). in equation (4. 4. to be more accurate in predicting the measured wave energy spectrum after introducing a frequency correction parameter. The difference. This equation simplifies to the form The PSDs obtained for a typical Jack-up platform. instead of using equation (4. S x x ( f ) i .42). It can also be adapted very easily for different locations by using the appropriate wave energy spectrum for the location of interest. is replaced by / .Fracture Mechanics Analysis This is then normalized. can be used. and the resonant response. the normalized PSD can be obtained.|f=fn. are shown in Fig.48) can. 7.of the structure into equation (4. represent a fast analytical tool for evaluating the behaviour of structures in the North Sea.47). the peak frequency corrected version. For example. This equation given below was demonstrated.49).B in equation (4. Observed sea state data have been demonstrated [2. It can also be written for all sea states with wave heights up to Hs. are used in determining the normalized PSDs.54) is that it can be integrated over specified limits such that 136 . Hs.10Sea state probability model A detailed examination of oceanographic data for the North Sea.Fatigue and Fracture Mechanics of Offshore Structures where fnB. its overall sensitivity is reduced and depends largely on the extreme sea state. given by The rest of the variables are as previously defined. since it only uses non-dimensional sea state parameters. This is discussed below.53) gives the sea state exceedance. However. given as where P (x) is the exceedance of the variable x. for any particular sea state exceeds a certain value. can be accurately described by the Gumbel distribution. Hs. The accuracy of this model depends on the accuracy of the sea state data used. has shown that the distribution of significant wave height. where available. observed over a period of several years. a suitable theoretical sea state distribution model can be used. 4. However. It is. recommended that service data. This is the probability that the significant wave height. where service data are not available. such that The implication of equation (4. therefore. and £B are all frequency corrected non-dimensional parameters. fB.11] to be well fitted by the following expression This modelled distribution agrees closely with sea state data from typical locations in the North Sea. Equation (4. based on the Gumbel distribution. show that a and P are 1. Constants a and (3 will vary for typical sites.55) can also be expressed as a function of y. sea states used for any fatigue analysis of offshore structures will depend on oceanographic data based on measurements and observations carried out over a finite length of time. respectively.55) represents a continuous probability distribution function for an infinite range of possible wave heights. Under this scenario. such that Equation (4. That is. 137 . often the total probability of occurrence of sea states is known. This gives a probability distribution function of the form Where a. P. There is always a constant y. over an infinite range. and can be expressed such that P(H S )T is the known cumulative probability. This can also be written as a discontinuous function for n discrete sea states.56) will give the exact solution for the long-term probability distribution of sea states. for which the integral of its product with the probability function is always unity. is normally taken as one while y is a constant which has to be evaluated. the long-term probability distribution of wave heights across the entire range of likely occurring sea states is not used. such that The cumulative probability P(//Or. Data from the Silver Pit and Ekofisk regions of the North Sea. The reason for this being that.06. In practice. and y are site-dependent parameters.Fracture Mechanics Analysis Equation (4. equation (4.55 and 1. This method would normally allow for the overall sequence equivalent stress. First. However. have been demonstrated. This is a function of crack geometry. the element of time is very important. oh. the overall long-term equivalent stress can be determined using the following procedure. used in the testing of structural materials in the laboratory. or the block equivalent stress. Therefore. or the overall long-term equivalent stress. using the overall equivalent stress range to characterize crack growth within an individual sea state may lead to inaccurate results. Using the overall equivalent stress concept excludes this element of time. This approach does not require cycle counting and can be applied directly to structures in service. Suppose a sea state. as described in Chapter 1.1 Use of sea state probability distribution model The use of fast assessment equations to determine sea state equivalent stresses was discussed in Chapter 1. especially for offshore structures where frequency effects. An alternative approach is to use conventional cycle counting. 138 . Where necessary. the fatigue crack growth rate at any time is dependent on the SIF range. can then be given by When AHsi is infinitesimally small. then its long-term contribution to fatigue damage. such that The overall equivalent stress. Another reason for caution is that the equivalent stress concept is inapplicable as long as it is applied to an entire sequence that may never be fully utilized before a structural integrity assessment exercise is carried out. will be largely different from the overall equivalent stress range. and equivalent stress Sh. loading mode. under corrosion fatigue conditions. has a long-term probability of occurrence P(Hs).10. with a significant wave height HSi. and stress range. can be given by ohi. i. within an individual sea state.. for three reasons.Fatigue and Fracture Mechanics of Offshore Structures 4. to be determined. this approach can equally be applied. it is important to note that. the use of the overall equivalent stress concept in the prediction of fatigue crack growth in structures under variable amplitude loading conditions may lead to inaccuracies in the results. then the long-term equivalent stress is give as For simulated service load histories (SLH). Second. The actual stress range applied to the fatigue crack. This sequence of sea states will be determined. however. mainly. characterized by k. This is implemented by assuming an appropriate crack growth law.Fracture Mechanics Analysis Third. using a similar approach to that on which the overall equivalent stress approach is based. Most of these sources of error associated with fatigue crack growth prediction using the overall equivalent stress approach will be minimized by adopting a sea state equivalent stress approach for offshore structures..10. there is the need to identify key fatigue damaging features for use in a block analysis procedure. within a particular sea state. It. i— are as previously defined. This concept is presented in the following section.. for example. a0. S/. With other engineering structures. with equivalent stress. Using this information. by their long-term probability of occurrence. i. duration. The overall sequence equivalent stress approach can be used to determine crack growth under variable amplitude loading conditions based on equation (4. relies on using sea state parameters to determine the sea state equivalent stress range that is then used to calculate fatigue crack growth associated with that sea state. N. stress ranges can be calculated. required to propagate a fatigue crack from an initial depth. and the necessary interaction between different sea states. can be calculated from The number of fatigue cycles. af.. it does not provide the necessary capability to model any interaction effects.2 Formulation of the sea state equivalent stress concept The sea state equivalent stress concept is introduced here. the total number of fatigue cycles. 4. Using Paris law. This procedure is then carried out over the entire sequence of expected sea states. and transition period. to a final depth.63). the crack growth rate within a particular sea state. The sea state equivalent stress range concept is based on the same philosophy as that of the overall equivalent stress range approach. Nh. required to propagate a fatigue crack after n sea state transitions can be calculated where 139 . because this approach does not include the element of time. . and illustrated for application to offshore structures. 4. This comparison is shown in Fig. are based on the simulated JOSH. The sea state equivalent stress approach is compared with the conventional overall equivalent stress range approach and experimental data obtained under variable amplitude loading conditions. with those calculated from the measured data used to generate the JOSH sequence. than the equivalent variation in the overall sequence put together. Sea state interaction effects are omitted when other conventional approaches to fatigue crack growth prediction under variable amplitude loading conditions are employed in determining crack growth in offshore structures.26. The sea state exceedance and cumulative probability obtained from this distribution are shown in Fig. 4. within any particular sea state. 140 .26.11 Discussion The results of fatigue crack growth predictions under variable amplitude conditions. 4. presented here. The sea state equivalent stress concept relies on the use of a suitable sea state probability distribution function.Fatigue and Fracture Mechanics of Offshore Structures The sea state equivalent stress range concept is more accurate in predicting fatigue crack growth under variable amplitude loading conditions in offshore structures than the overall equivalent stress range approach. The main reason for this is that the variability in the instantaneous stress range or stress intensity factor range is far less. The method also has the added advantage of allowing the inclusion of any sequence or sea state interaction effects. The probability distribution used to derive this function is the Gumbel distribution. and exceedance curves obtained from the Gumbel distribution. This was done by comparing sea state cumulative probability. The agreement between the variation in the predicted and measured curves is good. It was necessary to ascertain the accuracy of this distribution used to develop the model. 4. for three of the four tests carried out. was calculated for the different variants of JOSH used in the fatigue testing programme. The exceedance curves for the sea state. 4.Fracture Mechanics Analysis Fig.27 shows the SRPD curves for three variants of the sequence used in the fatigue testing programme.26 Measured and predicted exceedance curves for JOSH sea states This agreement provided a suitable starting point in developing the sea state probability distribution model. The equivalent stresses due to each of the twelve sea states used. The JOSH sequence used was generated using advanced simulation techniques from twelve sea state PSDs. It consists of 1 064 050 turning points generated from 4000 transitions of the twelve sea states.29. Figure 4.28. These are plotted. Results from the fourth test are not shown because. for use in the prediction of fatigue crack growth in offshore structures under variable amplitude multi-sea state loading conditions. they are identical to those obtained from the third test. in Fig. 4. as they were conducted at the same overall equivalent stress range. are shown in Fig. 141 . Fatigue and Fracture Mechanics of Offshore Structures Fig. 4.28 Exceedance curves for JOSH sea states 142 .27 SRPD curves for JOSH Fig. 4. 4. together with the sea state equivalent stresses. 143 . 4. 4. with those obtained by using the conventional rainflow cycle counting method. to calculate the long-term contribution of each sea state to the overall sequence equivalent stress. The results shown in Fig. These values are compared.Fracture Mechanics Analysis Fig.30 are so close that the curves are virtually coincident. in Fig.30 Comparison of probability and cycle counting methods The probability of occurrence of each sea state was used. 4.30.29 Sea state equivalent stresses for different tests Fig. 4. for LEYOPB2C and LEYOPB3C. Fig.32 and 4. can be seen to follow a trend similar to the sea state transition sequence.33. As seen in these figures. respectively.32 Comparison of overall and sea state equivalent stresses for LEYOPB2C 144 . 4.32 and 4. shown in Figs 4.31 Sea state transition sequence for JOSH2C Fig.33 also compare the sea state equivalent stresses with the overall sequence equivalent stress.Fatigue and Fracture Mechanics of Offshore Structures The sequence of sea state transitions used to generate JOSH is shown in Fig. as expected. The calculated sea state equivalent stresses. This variation will have significant effects on fatigue crack growth and. therefore.31. 4. there is considerable variation in the sea state equivalent stress. needs to be adequately accounted for. Figures 4. 32 and 4.35.33. apart from tests LEYOPB3C and LEYOPB4C. for correlated data and an arbitrary sequence. 4. for the test conducted at an equivalent stress range levels of 250 MPa and 200 MPa. The way this difference affects the accuracy of crack growth rate predictions is very important. in Figs 4.Fracture Mechanics Analysis Fig. The crack growth curve obtained. is compared with experimental data for the air test. which were carried out at the same equivalent stress level. respectively. will be different for the cases where an overall equivalent stress range is used. The sea state equivalent stress concept was used to predict crack growth in the highstrength steel (SE 702) used in the fatigue testing programme. the individual tests were conducted under the required loading conditions by using different amplitude and load ranges. when compared with results obtained using a sea state equivalent stress. The variation in the sea state equivalent stress. From these results it is evident that the stress intensity factor range. This made the overall equivalent stresses different. together with results obtained using the overall equivalent stress range method. 145 . are shown in Figs 4. which is a function of crack geometry and stress range.34 and 4.33 Comparison of overall and sea state equivalent stresses for LEYOPB3C Even though the same sequence was used for the corrosion tests. 146 . The other two curves show the predicted crack growth curve. 4.35 Prediction with consideration for initiation and correlated initiation point for an arbitrary sequence In each of the figures the smooth curves are those obtained with the overall equivalent stress range method.Fatigue and Fracture Mechanics of Offshore Structures Fig. based on the sea state equivalent stress concept and experimental crack growth data. 4.34 Prediction with consideration for initiation and correlated initiation point Fig. 35. 4.33. shown in Fig. under variable amplitude loading conditions. This chapter has also introduced a fast assessment approach to the analysis of offshore structures. Some of these variables include material properties determined by the alloying elements present. The proposed semi-empirical function depends on crack aspect ratio and loading mode. This can be derived from oceanographic data. which almost always operate together to influence corrosion fatigue crack growth at any one time. have been assessed and possible areas for modification and improvement highlighted. is required for accurate prediction. is used to predict the fatigue crack growth for test LEYOPB1A. have been analysed using existing FM models. where the transition sequence. It can also be applied using an arbitrary sea state transition sequence. If this procedure is followed and the initiation period is appropriately taken into account. The methodology relies on the use of non-dimensional sea state parameters. is that information on the crack initiation point. 147 .Fracture Mechanics Analysis One of the problems encountered in predicting crack growth. however. Knowledge of the long-term distribution of sea states. which are important parameters thought to influence the nature of Y factors obtained. therefore. using this approach.12 Summary The results obtained from the variable amplitude fatigue tests. be used as long as a good approximation to the expected sea state transition sequence can be obtained. the nature of the corrosive environment determined mainly by its chemical composition. and their duration. like any other FM based method relies very much on the accuracy in the material constants used in the model. 4. Crack shape evolution has also been identified as an important parameter that influences the stress intensity factor. This is illustrated in Fig. conducted for this study. It should be noted that the individual sea state approach has the added capability of modelling interaction effects. The advantages associated with using the proposed equation have been highlighted and discussed. and other additional factors. The accuracy of this method. A new Y factor model has been proposed. The use of different FM models to predict fatigue crack growth. and to model the different observations of crack growth retardation and acceleration observed during variable amplitude loading conditions. within the sequence. a more accurate prediction can be obtained. The results shown in Fig.33 were obtained after accounting for the crack initiation life. is the large number of variables involved. together with the mode of structural response. This approach can. 4. It is apparent that one of the main difficulties involved in quantifying corrosion fatigue crack growth. 4. is important in the use of the sea state equivalent stress approach. which cannot be included if the overall sequence equivalent stress approach is used. This model relies on the Gumbel distribution. 148 .Fatigue and Fracture Mechanics of Offshore Structures A sea state probability distribution model has also been presented. A generalized FM approach for the assessment of fatigue crack growth in offshore installations is proposed. a sea state equivalent stress concept has been formulated and its mathematical background presented. Based on this model. and it has been verified with service measurements from a typical location in the North Sea. and it has been demonstrated to be more consistent with experimental observations of crack propagation under variable amplitude conditions. A sensitivity analysis carried out suggests that Jack-up response is very sensitive to water depth. Areas of further work. which can be considered to be representative of all service loading conditions for Jack-ups operating in different water depths and locations.1 Summary This book has presented results of an investigation undertaken to assess the performance of a typical high-strength weldable Jack-up steel under realistic loading and environmental conditions. Different fracture mechanics models for VACF crack growth prediction have also been compared in terms of the accuracy of predicted Y factors. which will contribute to the general body of knowledge in this field. with respect to results obtained from other high-strength steels and conventional fixed platform steels. it was concluded that there are difficulties associated with producing a single load history. are also identified. and a sea state equivalent stress concept formulated. Most importantly.2 Conclusions and recommendations One of the main objectives of this study was to simulate service loading on a typical Jack-up platform. an improved methodology for fast assessment of offshore structural welded joints has been proposed. 5.Chapter 5 Conclusion 5. Details of the methodology employed to develop a typical JOSH have been presented. This was successfully achieved by use of a representative Jack-up transfer function that was validated by use of service data obtained from a Jack-up platform operating under service conditions. most 149 . The following sections present the main conclusions that can be drawn from the work presented in the book. However. As a result of this sensitivity. Results and details of experimental variable amplitude corrosion fatigue (VACF) tests conducted using JOSH have been presented and discussed. the inherent limitations of the models. of any particular structure. applicable to all sites within a range of water depths. have been identified. In this regard. The added significance of these results is that. when applied under variable amplitude loading conditions. There was no evidence to suggest that SE 702 is more susceptible to corrosion fatigue. The fatigue life results suggest that tubular joints fabricated from SE 702. for any set of sea states. however. This approach relies on the use of non-dimensional parameters to describe the normalized stress PSD. a fast assessment approach has been proposed. the JOSH model provides a suitable framework for generating any representative service load history. and other high-strength steels. the results from the investigation presented in this book. will have wide implications on inspection scheduling for high-strength steel installations. Under CP conditions. any trends in the fatigue performance of high-strength steels can be clearly defined and quantified for incorporation into a suitable design guidance. This will lead to a reduction in operational costs. under variable amplitude conditions. After comparing existing FM models with experimental results. For these reasons. based on results obtained from this study. with longer fatigue lives at lower stress levels. introduce a certain degree of uncertainty when 150 . under simulated loading and environmental conditions. It is recommended that further fatigue tests be carried out on SE 702. the results show that an increase in the CP level from -800 mV to -1000 mV may lead to a reduction in fatigue life by up 30 per cent. especially for Jack-ups used as production platforms. such as. for example. These further tests are required. A new Y factor model has been proposed that accounts for important factors. and mode of loading.Fatigue and Fracture Mechanics of Offshore Structures operating sites in practice cover extensive areas of similar water depth. suggest that there may be advantages to be gained by using high-strength steels. so that. with a better understanding of high-strength Jack-up steels under realistic loading and environmental conditions. Based on this observation it can be concluded that there may be other important factors that affect crack propagation. in the presence of hydrogen produced under CP conditions. This implies that the existing slope of -3 for the T' curve may not be applicable to high-strength steels. the crack shape evolution (crack aspect ratio). to quantify the benefits associated with their use offshore. The existence of a more negative slope for the design curve. Jack-up structures used for short-term drilling operations may be designed with less safety margins when compared with those used for long-term operations. There was an apparent trend. geometry. are very encouraging. it will be possible to narrow down these safety margins during the design process. are at least as good as conventional fixed platform steels. On the whole. It was noted that the average experimental Y factor curve lies below the curves predicted by the existing solutions. than other high-strength steels of similar grade. Its semi-empirical nature may. that is expected to eliminate the lengthy analysis procedure normally required to generate the load PSDs for offshore structures. The results obtained from the large-scale fatigue testing programme on SE 702. that may have been ignored in previous models. but further tests at lower stress levels need to be performed to confirm any existing trends. showing a potential for better performance. therefore. This model relies on the use of a sea state probability distribution function that has been verified with service data. needs to be checked with further experimental data obtained from tests conducted under realistic loading conditions. it is important to check its accuracy against further service data from different locations. 151 . to analyse structures at different locations other than the North Sea region. the data used in the development of the model were obtained from specific regions of the North Sea. However. Its performance on other joint geometries. Inspection scheduling for production Jack-ups is. More accurate and reliable crack growth prediction in high-strength steels will have significant implications on the safety and reliability of production Jack-ups. and also for the structural reliability analysis after an inspection schedule to ensure a high level of safety. It is especially in this area that some of the models developed. These structures are more susceptible to long-term fatigue problems. can be used as tools for the assessment of highstrength steel offshore installations to enhance safety and structural reliability. an important aspect in the risk reduction and safety enhancement process required for their reliable operation. one of which is the potential to model sea state interaction effects. as results of this study. In order to increase confidence in the use of this model and reduce the level of uncertainty associated with its use. and used to predict fatigue crack growth in a typical high-strength offshore steel. It can be used for more accurate inspection scheduling. when compared with Jack-ups used as mobile drilling units. with the possibility of dry dock inspection. A generalized FM approach for the assessment of fatigue crack growth in offshore installations has been proposed. therefore.Conclusion applied to other joint geometries. This approach has been shown to have certain advantages over the conventional overall equivalent stress range approach. for the first time. This will help in establishing the validity of using the proposed probability distribution model. A sea state equivalent stress concept has been mathematically formulated. This page intentionally left blank . BS 4360: 1990. 95/102. Corrosion Fatigue Fracture Mechanics of High Strength Jack-up Steels. D'Mello C. Myers P. and King R N. 'Current and Potential use of High Strength Steels in Offshore Structures'. Stacey A. London. Boswell L F.9] [1.12] Billingham J. United Kingdom Offshore Steels Research Project . 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Pook L P and Dover W D, 'Progress in the development of a Wave Action Standard History (WASH) for fatigue testing relevant to tubular structures in the North Sea', American Society for Testing and Materials: Symposium on the Development of Standard Load Spectra, 29 April 1987. 160 Index Acrylic models 8, 10, 12-14, 40 Adequate protection 24 Anode, sacrificial 3, 29 Artificial seawater 83 Axial loading, balanced 13 Balanced axial loading 13 Buckling resistance 2 Cantilever Jack-up 55 Catastrophic fracture 17 Cathodic protection (CP) 3, 20, 23, 29, 30, 83, 98, 104 Chemical composition of SE 702 78 Chord end fixity 15 Construction of Jack-up structures 2 Corrosion fatigue, variable amplitude 4, 20, 31, 48, 62, 128,149 Crack: arrest 27 driving force 106 extension 4,33, 106, 131 mode of opening 39 Crack growth: early 91, 116 law 38, 106, 109, 131, 139 models 36 rapid 38 unstable 38 Crack propagation 27, 38, 106, 118 non-uniform 132 Crack shape evolution 97, 120, 123, 147, 150 Cracked components, structural integrity of 4, 105 Cracking: localized 27 through-wall 17 Critical stresses 5 Cross-correlation functions 54 Crossing period, mean zero 60, 62, 63, 134 Cumulative damage ratio 31 Curves, exceedance 140, 142 Cycle counting methods 34, 36 Damage ratio, cumulative 31 Damage, fatigue 20, 34, 35, 46, 60 Damage-tolerant design 38 Damping 56, 64 hydrodynamic 57 structural 57 Data, oceanographic 61, 63, 136, 137, 147 Definition of initiation 91 Design: curves, S-N 17 damage-tolerant 38 wave approach 60 Development, marginal field 43 Dislocation movement 27 Distribution: of sea states 89, 147 Gumbel 63 Drilling unit, mobile 44, 151 Dry dock 151 inspection 3 Dynamic: loading 53, 60 response 44, 49, 53, 54, 57 Early crack growth 91, 116 Effective: mass of structure 56 stiffness of structure 56 Efthymiou equations 7,41 Elastic stress field 40 Embrittlement, hydrogen 26, 83, 87, 104 Environmental effects 28, 39 Equilibrium potential 29 Equivalent: static load 60 stress range 106, 127, 128, 138, 139, 140, 145 Exceedance curves 140, 142 Excitation frequency 56 Extrapolation, linear 11 Fabrication defects 28 Failure: analysis 37 structural 5, 60 Fatigue: corrosion, variable amplitude 42 crack growth analysis 5, 47, 127 crack initiation 4, 27, 28, 31, 94 damage 20, 34, 35, 46, 60, 95, 127, 138 definition of 16 design guidance 3, 17, 18, 43 design philosophy 1 life prediction 16,39, 105 loading, influences of 55 resistance 20, 29, 44, 76, 98 161 Fatigue and Fracture Mechanics of Offshore Structures strength 21 testing, large-scale 4, 76, 81, 91, 150 testing, variable amplitude 47, 77 variable amplitude corrosion 20, 31, 42, 48, 62, 149 variable amplitude 20, 31, 34, 36, 42, 103 Field development, marginal 1 Finite element analysis (FEA) 8, 14, 40, 105, 108, 117 Fixity, chord end 15 Fluctuating stresses 16 Fracture: catastrophic 17 toughness 38 Fracture mechanics: approach 16, 34 linear elastic 38 methodology 4 Frequency: excitation 56 natural 49, 56 Geometric: parameters 10 stresses 5, 8 Grain boundary attack 28 Gross deformation SCF 13 Growth analysis, fatigue crack 47, 127 Guidance, fatigue design 17,18,43 Gumbel distribution 63, 136, 137, 140 Hardness data of SE 702 80 Heat affected zone 79 Hot spot stress range 6, 94, 100, 109 Hydrodynamic damping 57 Hydrogen embrittlement 26, 31, 83, 87, 104 Hydrogen-induced stress corrosion cracking 3 Influences of fatigue loading 55 Initiation to total life ratio 94 Initiation, definition of 91 Inspection, dry dock 3 Instability, plastic 38 Installations, offshore 151 Interaction effects 31, 33, 36, 38, 106, 128, 139, 140, 147, 151, stress-time 28 Jack-up design 2, 43 Jack-up Offshore Standard load History (JOSH) 4,44 Jack-up structures, construction of 2 Jack-up, cantilever 55 Joints: multiplanar 15, 80 protected 24 tubular welded 10, 41, 98, 100, 107, 108, 114,117, 118, 123, 127 Large-scale fatigue testing 76, 81, 91, 150 Level crossing counting 35 Linear elastic fracture mechanics 38 Linear extrapolation 11 Lloyd's design equations 41 Lloyd's Register equations 7 Loading conditions, variable amplitude 140, 147,150 Loading: dynamic 53 variable amplitude 20, 138 Localized cracking 27 Lumped mass model 57 Maintenance operations 1, 32 Marginal field development 43 Markov chain technique 49 Mean zero crossing period 60, 62, 63, 134 Measurement of strain 10 Mechanical properties of SE 702 79 Microfractures, transgranular 38 Miner's rule 32 Mobile drilling unit 44, 151 Mode of crack extension 39 Model, lumped mass 57 Models: acrylic 8, 10,12,13,14,40 crack growth 36 numerical 10 photoelastic 10 steel 10, 12, 13,40 Monitoring, structural integrity 37 Multiplanar joints 80 Natural frequency 49, 56, 89, 133, 134 Nominal stresses 5, 85 Non-uniform: crack propagation 132 stress distribution 119 Notch stresses 6, 8 Numerical: methods 9, 117 models 10 Ocean waves 60, 70 Oceanographic data 61, 63, 136, 137, 147 Offshore installation 43, 148, 151 Operating water depth 71 162 143. 123. 147 Parametric: equations 8. 56.109 range. 109 singularity 39 principal 8 sequence equivalent 98. dynamic 44. 147 Sea states. 51. 119 intensity factor 11. 118. peak frequency correction 62 Parameters: geometric 10 sea state 62. 8 nominal 5. 116.44. gross deformation 14 SE 702: chemical composition of 78 hardness data of 80 mechanical properties of 79 Sea state parameters 62. 62. 148 Significant wave height 49. 36. formation of 38 Structural: damping 57 discontinuity 8 failure 5. random 50 Range-pair counting 35 Residual stresses 13 Resistance: buckling 2 fatigue 20. 127.106. 127 163 . 105. 86 validity range 41 Peak counting: negative 34 positive 34 zero-crossing 35 Peak frequency correction parameter 62 Photoelastic models 10 Pierson-Moskowitz (PM) spectrum 60 Pitting 27 Plastic instability 38 Power spectral density 49. 139.51 Static load. 80 Rainflow counting 34. 131. hot spot 6.29. 63. measurement of 10 Strength.31 Protruding slip steps 18 Rack plate 2. fatigue 21 Stress: corrosion cracking. 128 Random range generator 50 Random walk technique 50 Range: counting 35. 106. 147 Seawater. 114. 147 Stresses: critical 5 fluctuating 16 geometric 6. 128 equivalent stress 98.40 Strain. 14. 128 intensity factor range 39. 40. 52. 36. distribution of 89. 105 Structure: effective mass of 56 effective stiffness of 56 Superposition of wave components 60 Thickness correction exponent 21. 23. 118. 61 Transfer function 53. 8 principal 11 residual 13 Stress-time interaction effects 28 Striations. 41. 147 Service measurements 49. 94. 138. equivalent 106. 128. 85 notch 6. 117. 149 Transgranular microfractures 38 Transit loads 44 Transportation modes 46 Tubular welded joints 3. 10. 136 Simulated sequence 76 Slip steps. 132. 138. hydrogen-induced 3 distribution 15. 138 monitoring 37 of cracked components 4. 17. 13. 54 Risk of structural failure 43 Sacrificial anode 3. 108. 98. 143. 5. 107.12. 33. 139. equivalent 60 Statistical wave description 60 Steel models 10. 77. 145 range. 36. 10. protruding 18 S-N: approach 16. 140. 16. 84. 60 risk of 43 integrity: assessment 9. artificial 83 Sequence 127 effects 27. 38. 85. 80 non-uniform 5. 128 design curves 17 State transition matrix 49. 60.76 Response.Index Parameter. 116 Thickness effect 18 Through-thickness stress gradient 23 Through-wall cracking 17 Time domain 54. 139. 41. 50 Principal stresses 11 Production platform 43 Protected joints 24 Protection adequate 29 potential 29. 53. 138. 100. 100. 29 Safety Case Regulations 43 SCF. 116 generator. 84. 80. 13. random 50 Water depth. 127 Zero crossing counting 36 Zero-crossing peak counting 35 164 . 60.Fatigue and Fracture Mechanics of Offshore Structures Under-protection 31 Variable amplitude: corrosion fatigue 4. 62. 118. 84. ocean 70 Welded joints. 98. 20. 5. 123. 147. 42. 51. 100. 34. 77. 149 fatigue 20. 108. 36. 103 testing 47 tests 77 loading 20. 136 Wave-loading regime 55 Waves. 117. 62. 139 loading conditions 140. 31. 114. 63. statistical 60 height. 80. 107. operating 71 Wave: components. 31. 42. 150 Vickers hardness 79 Walk technique. tubular 3. 48. superposition of 60 description. 128. 138. significant 49.