38978262 Fatigue and Fracture Mechanics of Offshore Structures

Fatigue and Fracture Mechanics of OffshoreStructures

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E N G I N E E R I N G R E S E A R C H S E R I E S

Fatigue and Fracture Mechanics ofOffshore Structures

L S Etube

Series EditorDuncan Dowson

Professional Engineering Publishing Limited,London and Bury St Edmunds, UK

First published 2001

This publication is copyright under the Berne Convention and the International Copyright Convention.All rights reserved. Apart from any fair dealing for the purpose of private study, research, criticism, orreview, as permitted under the Copyright Designs and Patents Act 1988, no part may be reproduced,stored in a retrieval system, or transmitted in any form or by any means, electronic, electrical, chemical,mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owners.Unlicensed multiple copying of this publication is illegal. Inquiries should be addressed to: ThePublishing Editor, Professional Engineering Publishing Limited, Northgate Avenue, Bury St Edmunds,Suffolk, IP32 6BW, UK. Fax: +44 (1)284 705271.

© Etube

ISBN 1 86058 312 1

ISSN 1468-3938ERS 4

A CIP catalogue record for this book is available from the British Library.

Printed and bound in Great Britain by St. Edmundsbury Press Limited, Suffolk, UK

The publishers are not responsible for any statement made in this publication. Data, discussion, andconclusions developed by the Author are for information only and are not intended for use withoutindependent substantiating investigation on the part of the potential users. Opinions expressed are thoseof the Author and are not necessarily those of the Institution of Mechanical Engineers or its publishers.

About the Author

Dr Linus Etube (BEng, PhD, CEng, MIMechE) joined theDepartment of Mechanical Engineering at the University ofLondon in October 1991 as an undergraduate. After completinghis BEng in 1994, he started his PhD research programme as aresearch student. He was appointed a lecturer in December 1997and obtained his PhD in September 1998.

His research interests include:• fatigue and the applications of fracture mechanics to engineering structures

under realistic loading and environmental conditions;• development of novel fracture mechanics models for engineering applications;• variable amplitude fatigue behaviour of offshore and related structures;• structural mechanics and failure analysis of offshore and related structures;• offshore safety, structural integrity, and reliability;• risk analysis.

Dr Etube has worked closely with a wide range of both UK-based and globalorganizations in the offshore oil and gas sector, including regulatory bodies such as theUK Health and Safety Executive (HSE), in expanding the knowledge and understandingof structural steels used offshore and in related industry sectors.


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Contents

Series Editor's Foreword

Foreword

Acknowledgements

Notation

Chapter 1 Literature Review1.1 Introduction and background1.2 Review1.3 Stress analysis of tubular joints

1.3.1 Definition of stresses in welded connections1.3.2 Definition of hot spot stress1.3.3 Methods of stress analysis

1.4 Fatigue design1.4.1 S-N approach1.4.2 The Fracture Mechanics (FM) approach

1.5 Summary

Chapter 2 Service Load Simulation2.1 Introduction2.2 Fatigue loading in Jack-up structures2.3 Review of previous loading models

2.3.1 COLOS/C 12-20 series2.3.2 UKOSRP II double-peaked spectrum2.3.3 Hart/Wischung algorithm2.3.4 WASH sequence

2.4 The JOSH model2.5 Generation of JOSH

2.5.1 The pseudo random binary sequence technique2.5.2 The Morkov chain technique

2.6 Jack-up dynamic response2.6.1 The transfer function approach2.6.2 Modelling of structural parameters2.6.3 Modelling of soil-structure interaction

xiii

xv

xvii

xxi

145569

16163640

434447484848494949505052525557

Contents

2.7 Modelling of wave loading2.8 Selection of sea states2.9 Discussion2.10 Summary

Chapter 3 Large-scale Fatigue Testing3.1 Introduction3.2 Test specimen consideration

3.2.1 Properties of SE 7023.2.2 Consideration of test specimen geometry3.2.3 Fabrication of SE 702 specimens

3.3 Experimental set-up3.3.1 Details of test rig3.3.2 Test control and data acquisition3.3.3 Simulation of environmental conditions

3.4 Stress analysis of Y joints3.4.1 Experimental stress analysis procedure3.4.2 Use of parametric equations

3.5 Experimental fatigue testing3.5.1 Test parameters and the JOSH sequence

3.6 Fatigue test results3.6.1 Fatigue crack initiation3.6.2 Crack growth curves3.6.3 Crack aspect ratio evolution3.6.4 S-N data

3.7 Discussion3.8 Summary

Chapter 4 Fracture Mechanics Analysis4.1 Introduction4.2 The stress intensity factor concept4.3 Experimental results4.4 Use of empirical SIF solutions

4.4.1 The average stress model4.4.2 The two-phase model (TPM)4.4.3 The modified average stress model

4.5 Adapted plate solutions4.5.1 Newman-Raju SIF solution for surface cracks

4.6 New semi-empirical Y factor solution4.7 Variable amplitude crack growth models

4.7.1 Equivalent stress range approach4.7.2 Equivalent crack growth concept

60626476

7778788082828282838484858787919194969898103

105106108114114115116117118122127127128

x

Contents

4.8 Consideration of sequence effects4.9 Fast assessment of offshore structures

4.9.1 New normalized PSD equation4.10 Sea state probability model

4.10.1 Use of sea state probability distribution model4.10.2 Formulation of the sea state equivalent stress concept

4.11 Discussion4.12 Summary

Chapter 5 Conclusion5.1 Summary5.2 Conclusions and recommendations

References

Index

130132134136138139140147

149149

153

161

xi


Series Editor's Foreword

The nature of engineering research is such that many readers of papers in learnedsociety journals wish to know more about the full story and background to the workreported. In some disciplines this is accommodated when the thesis or engineeringreport is published in monograph form - describing the research in much more completeform than is possible in journal papers. The Engineering Research Series offers thisopportunity to engineers in universities and industry and will thus disseminate wideraccounts of engineering research progress than are currently available. The volumes willsupplement and not compete with the publication of peer-reviewed papers in journals.

Factors to be considered in the selection of items for the Series include the intrinsicquality of the thesis, its comprehensive nature, the novelty of the subject, potentialapplications, and the relevance to the wider engineering community.

Selection of volumes for publication will be based mainly upon one of the following;single higher degree theses; a series of theses on a particular engineering topic;submissions for higher doctorates; reports to sponsors of research; or comprehensiveindustrial research reports. It is usual for university engineering research groups toundertake research on problems reflecting their expertise over several years. In suchcases it may be appropriate to produce a comprehensive, but selective, account of thedevelopment of understanding and knowledge on the topic in a specially prepared singlevolume.

Authors are invited to discuss ideas for new volumes with Sheril Leich, CommissioningEditor in the Books Department, Professional Engineering Publishing Limited, or withthe Series Editor.

The fourth volume in the Series comes from London University and is entitled

Fatigue and Fracture Mechanics of Offshore Structuresby

Linus Sone EtubeDepartment of Mechanical Engineering, University College, London.

The development and operation of the North Sea oil and gas fields represents a trulyremarkable technological achievement. Many new engineering challenges have beenencountered at various stages in the development and operation of the fields, and thepresent volume illustrates an engineering science approach to one of them. Animportant factor affecting the integrity of these huge offshore structures is the fatiguebehaviour of welded tubular joints.

Fatigue and Fracture Mechanics of Offshore Structures

The author has studied many aspects of the fatigue characteristics of such joints in Jack-up offshore structures. The application of millions of cycles of variable amplitudeloading is related to sea states and wave motion. The development of a standard loadinghistory is described and realistic environmental conditions are considered. An account isgiven of large-scale fatigue testing and the detailed analysis of fatigue crack initiationand growth; bringing together a balance of experimental and theoretical approaches tothe problem.

This latest contribution to the Engineering Research Series enlarges the scope of topicscovered by the early volumes. Topics covered to date deal with aspects of design,surface inspection techniques, and wettability characteristics of engineering materials.

Professor Duncan DowsonSeries Editor

Engineering Research Series

xiv

Foreword

The tubular welded joints used in the construction of offshore structures can experiencemillions of variable amplitude load cycles during their service life. Such fatigue loadingrepresents a main cause of degradation of structural integrity in these structures. As aresult, fatigue is an important consideration in their design.

Jack-up legs are made from a range of high-strength steels with yield strengths up to700 MPa. These steels were thought to exhibit fatigue resistance properties which aredifferent when compared with conventional fixed platform steels such as BS 4360 50Dand BS 7191 355D. The perceived difference in their behaviour was heightened by thediscovery, in the late 1980s and early 1990s, of extensive cracking around the spud-canregions of several Jack-ups operating in the North Sea. It was thought that these steelsmight be more susceptible to hydrogen cracking and embrittlement. This enhanced theneed to study their behaviour under representative service loading conditions.

This book contains results of an investigation undertaken to assess the performance of atypical high-strength weldable Jack-up steel under realistic loading and environmentalconditions. Details of the methodology employed to develop a typical Jack-up OffshoreStandard load History (JOSH) are presented. The factors that influence fatigueresistance of structural steels used in the construction of Jack-up structures arehighlighted. The methods used to model the relevant factors for inclusion in JOSH arepresented with particular emphasis on loading and structural response interaction.

Results and details of experimental Variable Amplitude Corrosion Fatigue (VACF) testsconducted using JOSH are reported and discussed, with respect to crack growthmechanisms in high-strength weldable Jack-up steels. Different fracture mechanicsmodels for VACF crack growth prediction are compared, and a novel improvedgeneralized methodology for fast assessment of offshore structural welded joints ispresented.


Acknowledgements

I wish to express my deep appreciation for the support offered by the followingindividuals and organizations.

First, I would like to thank Dr F. P. Brennan and Professor W. D. Dover for theinvaluable supervision and guidance given during the course of my PhD programme.Their stimulating discussions are invaluable. I would like to thank Professors L. F.Boswell and J. Sharp for taking the time to review the manuscript and for their finesuggestions and recommendations.

I would also like to thank everyone in the Department of Mechanical Engineering, atUniversity College London, especially my colleagues who all played an important rolein providing the conducive and intellectually stimulating environment under whichwork presented in this book was conducted.

I acknowledge financial support received from the Cameroon Government through theMinistry of Higher Education and Scientific Research in the form of an OverseasScholarship, which enabled me to acquire a solid grounding in the field of mechanicalengineering, subsequently developing a keen interest in structural integrity ofengineering structures.

The financial support of a number of organizations made the successful completion ofthe work reported in this book possible. I acknowledge the following organizations fortheir contribution (in-kind or financial): the UK Health and Safety Executive (HSE);British Steel (now The Corus Group, from a merger between British Steel andKoninklijke Hoogovens); Statoil; and Creusot Loire Industrie.

Dr L S EtubeDepartment of Mechanical Engineering

University College London, UK


To my family

This book is dedicated to my entire family. To my late father, Daniel Etube, who spentthe greater part of his life educating and encouraging people to aspire for a deeperunderstanding of the things around them. To my mother - Christina Etube - mybrothers, my sisters, and my wife - Delphine Ntube Etube. Their love, support, andguidance will always remain an inexhaustible source of inspiration for me.


Notation

Romana, c

ao, ai

afA, pAg/AgCl

C, mCD, CmCJ, mj

Cp, p

da/dNDDs

erf(x)E

f, fn, fp

fnB, fB, £2B

G

Hs ext, Tz ext

Hs, TD, Tz

Hr, Tr, fl

I

Kmax, Kmin

KIC

KISCC

L

MiMxd1

N, N1, N3

Crack depth (except where otherwise defined), half surface crack lengthInitial crack depthFinal crack depth (except where otherwise defined)Scaling parameters (except where otherwise defined)Silver/silver chloride reference electrode

Paris law material constantsDrag coefficient, mass coefficientParis law material constants for a multi-segment da/dN curveEmpirical retardation parameter, shaping parameter

Crack growth rateTubular joint chord diameterMiner's cumulative damage ratio

Error function of xYoung's modulus

Frequency, natural frequency, peak frequencyFrequency corrected non-dimensional parameters

Shear modulus

Extreme sea state parametersSignificant wave height, dominant period, mean zero crossing periodNon dimensional wave height, Period and frequency ratios

Irregularity factor

Maximum and minimum stress intensity factorsCritical mode I stress intensity factorStress intensity factor for stress corrosion cracking

Tubular joint chord length

ith spectral momentACPD crack depth modifier, one-dimensional ACPD solution

Life (number of cycles), initiation life, through thickness life

Notation

P(x), p(x)

VQBVQrR

S, AS, Aa

SB, tB ySh, Shi

S(f)N

tT

Y(a), Y

Exceedance of variable x, 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 rangeThickness effect parametersEquivalent stress, equivalent stress for sea state iNormalized response spectrum

Brace thickness or time or plate thickness (defined where applicable)Tubular joint chord thickness

Stress intensity factor correction function (Y factor)

Greek Symbolsa, p, Y, T, 0a

PYeeveaOop, Kop

Oy

T

or(x)AKAKth,AKeff

A, Vc, Vr,

D(f)

¥

AcronymsACPDAVSCP

Tubular joint dimensional parameters (except where otherwise defined)Twice the ratio of chord length to chord diameter (2L/D)Ratio of brace diameter to chord diameter (d/D)Ratio of chord diameter to twice chord thickness (D/2T)Spectral bandwidth parameterAngle around tubular joint chord/brace intersectionPoisson's ratioDamping ratioRoot mean square (RMS) valueCrack tip opening stress, stress intensity factor corresponding to aop

Yield strengthRatio of brace thickness to chord thickness (t/T)Angular position or angle of inclinationGamma function of xStress intensity factor rangeThreshold stress intensity factor rangeEffective stress intensity factor rangeACPD probe spacing, crack voltage, reference voltageStress spectrum given by Wirsching's equationCrack shape correction (CSC) factor

Aalternating current potential differenceAverage stressCathodic protection

xxii

Notation

CLIFEAIPBJOSHMAVSSCFTPMUKOSRPUEGUCLUKCSUTSOPBPSDSENBWASH

Creusot Loire IndustrieFinite element analysisIn-plane bendingJack-up offshore standard load historyModified average stressStress concentration factorTwo-phase modelUnited Kingdom Offshore Steels Research ProjectUnderwater engineering groupUniversity College LondonUnited Kingdom Continental ShelfUltimate tensile strengthOut-of-plane bendingPower spectral density (spectrum)Single edge notch bendWave action standard history

xxiii


Chapter 1

Literature Review

1.1 Introduction and backgroundIn recent years there has been considerable interest in the use of high-strength steels inthe construction of offshore structures. One main reason for this is to satisfy the desirefor lightweight constructions. This is particularly relevant to offshore structures,because a reduction in weight can lead to the achievement of considerable saving insupport substructure. There are other potential benefits to be derived from the use ofhigh-strength steels. Fabrication costs, for example, can be minimized through the useof reduced plate thicknesses.

Historically, there has been a great deal of interest in the use of high-strength steels forthe fabrication of Jack-up structures when compared with fixed platforms. However,the potential benefits of using high-strength steels have been recognized by theoffshore oil and gas industry, and a fairly recent review [1.1] showed that theproportion of higher strength steels used in fixed offshore structures had gone up to 40per cent by 1995. This is a five-fold increase when compared to 8 per cent in 1988. Itis important to note that most of the high-strength steels used in fixed structures arelimited to topside applications and other less critical parts of the structure wherefatigue damage is not a major concern.

This situation is, however, different for Jack-up platforms that have traditionally beenused for short-term drilling and maintenance operations. These structures are nowbeing increasingly used as production platforms for marginal field development. Inrecent designs, extended periods at the same elevation in their fatigue designphilosophy are included. BP Harding is a typical example of this new generation ofJack-up platforms. It is designed to operate in a water depth of 100 m with an intendedservice life of thirty-five years.

1


High-strength steels used in the construction of Jack-up structures are mainly limitedto the fabrication of the legs. Steels with nominal yield strength in the range of 450 to700 MPa have commonly been used. The detailed leg structure will vary from onetype of Jack-up to another. A review of different designs is presented in [1.2]. In thisreview the structures were classified according to the Jack-up design, some of whichinclude Le Toumeau, CFEM, MSC, Friede and Goldman, and Hitachi designs. Ingeneral, each leg (Fig. 1.1) is made of three or four longitudinal chord members thatmay contain a rack plate for elevating the hull and a series of interconnectinghorizontal and diagonal tubular members (Fig. 1.2). In some designs, supplementarybraces are frequently used between main brace midpoints to increase the bucklingresistance of the structure and to provide adequate structural redundancy.

Fig. 1.1 Typical lattice leg structure of a Jack-up platform

Fig. 1.2 Typical Jack-up leg chord with rack plate

2

Literature Review

There has recently been a remarkable increase in the overall size of these structures.The main reason for this is to satisfy the requirement to operate in deeper waters inpredominantly harsher sectors of the North Sea, and worldwide. Several Jack-ups arenow used for production. This role requires long-term deployment and, therefore,limits the opportunity for dry dock inspection and repair. This has increased the risk ofdeterioration from long-term problems such as fatigue.

The vast majority of research on the fatigue performance of tubular welded joints,carried out by the offshore oil and gas industry [1.3, 1.4] has focussed on conventionalfixed offshore platform steels such as BS 4360 50D [1.5] and BS 7191 355D [1.6]with typical yield strengths in the region of 350 MPa. Fatigue data on higher strengthtubular joints are, therefore, very limited and this has been highlighted in reviews [1.2,1.7]. Consequently the fatigue design guidance developed to date is not applicable tohigh-strength steels, and this is reflected in the guidance published in 1995 [1.8]. Thisdocument has now been withdrawn, but the basic design, curve is restricted to steelswith guaranteed yield strengths of up to 400 MPa for nodal joints and 500 MPa forwelded plate connections. Even the current draft ISO standard [1.9] only providesguidance for steels with yield strength less than 500 MPa.

The absence of sufficient guidance on the use of high-strength steels and the lack offatigue data is a matter for concern. This is all the more important due to theincreasing proportion of higher strength steel grades used in offshore applications.This concern was strengthened by the discovery of extensive cracking in the spud-canregion of Jack-ups operating in the United Kingdom Continental Shelf (UKCS) in theperiod of 1988-89 [1.10]. As a result, it was accepted that high-strength steels aremore susceptible to corrosion fatigue and hydrogen-induced stress corrosion cracking(HISCC) when compared with conventional fixed platform steels. The mainconclusion drawn from the investigation was that the generation of hydrogen from thesacrificial anode systems protecting high-strength steel structures at levels that areexcessively negative (i.e. <-850mV Vs Ag/AgCl) can enhance fatigue crack growthand should be avoided.

Fatigue performance of high-strength steels is subject to uncertainty and there is needto investigate their performance further. This will allow designers of high-strengthsteel marine structures to use these materials with greater confidence. Two principalsources of this uncertainty for high-strength steels lie in the effect of cathodicprotection and variable amplitude corrosion fatigue. An investigation of the effect ofcathodic protection on the fatigue performance of a typical high-strength Jack-up steelunder constant amplitude loading conditions is reported in [1.11]. This study wasaimed at investigating the fatigue performance of the same steel, SE 702 [1.12], underrealistic loading and environmental conditions, with particular emphasis on the effectsof stochastic service loading under cathodic protection conditions.

This book is laid out in five chapters. Chapter 1 contains a review of the current stateof knowledge in the fatigue design of offshore welded structures. Particular emphasisis given to design against fatigue failure under stochastic service loading andenvironmental conditions.

3


A Jack-up Offshore Standard load History (JOSH) was developed as part of thisinvestigation. The methodology adopted and how the different factors that affect thefatigue performance of Jack-up steels, as modelled and represented in JOSH, ispresented in Chapter 2.

Chapter 3 presents details of the large-scale fatigue testing programme conducted ontubular weld joints using the simulated service loading history, JOSH. The resultsobtained are presented in the form of fatigue crack initiation and propagationbehaviour and S-N data. The results obtained from SE 702 are compared with thoseobtained from other high-strength steels and conventional fixed offshore platformsteels, such as BS 4360 SOD.

Fracture Mechanics (FM) analyses of results are presented in Chapter 4. In thischapter, existing FM models are compared with experimental data and the inherentlimitations of the models, when applied under stochastic service loading conditions,are identified. This chapter also contains new developments in this field. A novelgeneralized fracture mechanics approach for the assessment of fatigue crack growth inoffshore installations is presented.

The book is concluded in Chapter 5 with a statement of the main findings andrecommendations. Further work, which will add to the existing body of knowledge inthis field, is also identified and highlighted in this final chapter.

1.2 ReviewStress analysis of an engineering component containing a crack or crack-like defectand a failure model hypothesis, which defines the events of crack extension, are thetwo central ingredients for a fracture theory. This emphasizes the importance of stressanalysis in the process of implementing any fracture mechanics methodology for theassessment of structural integrity of cracked components. Stress analysis is also a veryimportant step in the design process for engineering structures, as it provides vitalinformation on the level and distribution of critical stresses in each component of thestructure. 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 integrityassessment procedures.

This chapter is concerned with a literature review of appropriate topics related tostructural assessment. It is dedicated to the important subjects of stress analysis,fatigue design, and the role of variable amplitude corrosion fatigue in the failure ofwelded connections used in the fabrication of engineering structures, such as Jack-upplatforms. The main sources of stresses in welded joints are given, as well as a reviewof the different stress analysis techniques available to the designer for their estimation.The current practice on the design of offshore welded connections using both S-Nanalysis and FM is reviewed, and the implications of some of the recommendationsfrom the existing design codes are discussed.

4

Literature Review

1.3 Stress analysis of tubular jointsOffshore structures are made from welded tubular joints of varying complexity withrespect to size, shape, and load carrying capacity. These joints can be loaded in anycombination of three modes. These include axial loading, out-of-plane (OPB), and in-plane (IPB) bending, illustrated in Fig. 1.3. Due to the complexity of joint geometryand shell behaviour of welded tubular joints that govern load response, local stressesare non-uniformly distributed.

Fig. 1.3 Illustration of IPB, OPB, and axial loading

The non-uniform distribution of stress has been demonstrated to occur both on thetubular joint surface and also through the joint thickness. Non-uniform stressdistribution leads to the existence of stress gradients and sites of stress concentrations,mostly along the chord and brace weld toes. These stress concentration sites representregions where fatigue cracks can originate and propagate to cause structural failure. Asan integral step in the design and assessment of engineering structural components,stress analysis is carried out to determine both the location and magnitude of thesecritical stresses. This section presents a definition of the stresses involved and themethodologies employed in determining the characteristic stress, which is consideredto control the fatigue life of tubular welded joints. Great emphasis is placed onexperimental techniques and the use of parametric equations.

1.3.1 Definition of stresses in welded connectionsIn both stress-life (S-N) and FM based methodologies for fatigue crack growthanalysis critical stresses have to be determined for each component of the structure.Three main sources of stress have been identified in tubular welded joints: Nominalstresses, geometric stresses and notch stresses.

Nominal stresses arise due to the tubes of the welded joint behaving as beams andcolumns. These stresses can be calculated by considering the mechanism of loadtransfer through each tube and intersection using frame analysis and beam bendingtheory. The nature of such stresses will depend entirely on the dimensions of the jointand the mode of loading.

5


Geometric stresses, on the other hand, arise as a result of differences in the loadresponse of braces and chords under the loading configuration. It is known thatgeometric stresses may cause the tube wall to bend in order to ensure compatibility inthe deformation of the chord and brace around the intersection depending on the modeof loading. As a result, the concept of the geometric stress range (GSR) has evolved asa practical basis for the fatigue design of tubular welded joints as it places manydifferent structural geometries on a common basis and, therefore, allows for the use ofa single S-N curve in their design.

Notch stresses arise from the notch effect or geometric discontinuity of the tube wallsintroduced by an abrupt change in section at the weld toe. These stresses are alsocommonly referred to as local stresses and are a function of weld size and geometry.The greater the weld toe radius and the greater the overall angle of the weld toe, themore restraint there is on localized deformation and the higher the magnitude of localstresses. Unlike nominal and geometric stresses, notch or local stresses are notpropagated far through the wall thickness and, therefore, the resulting three-dimensional stress field is highly localized. Due to the complexity and the variety ofjoint geometries used in the construction of offshore structures, the weld toe geometry(i.e. the weld toe radius and angle) cannot be made identical for each jointconfiguration. It has been noted [1.13] that even with very tight quality controlstrategies in manufacturing yards, weld profiles in offshore structures cannot becontrolled to such a degree that will lead to consistency in the distribution of notchstress concentrations in tubular welded joints. These stresses are, therefore, difficult tomeasure in a reproducible manner by any criteria. The consequence of this has beenthe adoption of a characteristic stress range for the development of S-N curves. Thischaracteristic stress range is known as the hot spot stress range.

1.3.2 Definition of hot spot stressThe hot spot stress is considered to control the complete fatigue life of a tubularwelded joint. It is the stress at the weld toe calculated by manner of a linearextrapolation to the weld toe of the geometric stress. The definition is illustrated inFig. 1.4. The hot spot stress excludes the contribution to the stress concentrationcaused by the notch effect of the weld geometry. This definition is not stated veryclearly in many design codes [1.14] and, depending on the code used, can result inmisinterpretation of this important parameter.

The definition of hot spot stress is not clear cut in the DnV rules for the design andconstruction of offshore structures [1.15]. The document states that stressconcentration factors may be obtained from relevant tests or analyses. It also indicatesthat 'different stress components may be associated with different SCFs. Differentlocation of 'hot-spots' for the different stress components may be taken into account ifrelevant documentation on the locations is available'. This code also requires the SCFnot to be less than 2.5, but fails to emphasize the need for it to be calculable andexperimentally reproducible.

6

Literature Review

Another document that attempts to impose a limiting value to the minimum SCF isthat produced by Lloyd's Register (LR) of Shipping [1.16]. Compared to the minimumvalue of 2.5 recommended by DnV, this document requires that the SCF values arelimited to a minimum of 1.5. It also recommends the use of empirical formulaeproposed by Wordsworth and Smedley for calculating the brace and chord SCFs for Tand X joints, while the semi-empirical formulae due to Kuang are recommended for Kand KT joints. These have now been revised [1.17] and LR recommends the use ofEfthymiou equations for T, Y, X, and overlapped K joints, while the Lloyd's Registerequations [1.18] are recommended for K and KT joint configurations.

Fig. 1.4 Schematic definition of hot spot stress in tubular joints [1.42]

The original document, however, had its limitations regarding the definition of hotspot stress. It did not spell out the need for the hot spot stress to incorporate theeffects of the overall chord and brace geometry, including the stiffening effects of theweld without the influence of the region of rapidly increasing and highly variable non-experimentally determinable stress near the weld toe. For particular cases where, dueto the joint geometry or loading mode, or a combination of both, a particular joint falls

7


outside the validity limits for the formulae indicated above, LR recommends the use ofa conservative approach. This requires that the higher SCF is used where this increaseswith the parameter of interest and where this reduces the limiting value at theparameter limit.

The American Petroleum Institute-RP2A [1.19] defines hot spot stress as 'the stress inthe immediate vicinity of a structural discontinuity'. The definition of hot spot stress inthe United States is characterized by two main design codes. The API RP2A and AWSDl.1-92 [1.20], which defines the hot spot strain as The cyclic total range of strainwhich would be measured at the point of highest stress concentration in a weldedconnection ...'. This code, like API-RP2A, recommends the use of the finite elementanalysis (FEA) method to obtain hot spot stress and highlights the fact that 'Whenmeasuring hot-spot strain, the strain gauge should be sufficiently small to avoidaveraging high and low strains in the regions of steep gradients'. Using this definitionthe hot spot strain is taken as the absolute peak value obtained by a strain gauge placednear the weld toe. This value is clearly a combination of geometric and notch stressesand is bound to vary from joint to joint, depending on the mode of loading. Thisdefinition does not, therefore, offer the necessary consistency required for determiningSCFs in tubular welded joints.

The UK Department of Energy Guidance notes give a clearer definition of hot spotstress as [1.21], The greatest value around the brace/chord intersection of theextrapolation to the weld toe of the geometric stress distribution near the weld toe.This hot-spot stress incorporates the overall effects of joint geometry (i.e. the relativesizes of brace and chord) but omits the stress concentrating influence of the weld itselfwhich results in a local stress distribution'. This definition of hot spot stress was asubject of discussion in the UK Offshore Steels Research Project (UKOSRP) and wasdrafted by the review panel set up by the Department of Energy to asses the results ofthe research programme. It was used in the revised UK guidance notes. This definitionof hot spot stress is now accepted as an offshore standard for stress analysis ofoffshore tubular joints. This is the definition adopted in this book. The current draftISO standard maintains the concept of the geometric stress as the characterizing stressfor fatigue analysis of welded connections, but draws attention to the fact that theconcept of hot spot stress is applied differently in Europe and the US. In the US theemphasis is on the extrapolation of the maximum measured stress; the approach inEurope relies on the extrapolation of the maximum principal stress.

Though the guidance available on stress analysis of offshore welded tubular joints mayseem limited as presented above, there is a wide body of literature on stress analysis oftubular welded joints. The recommendations outlined in the codes above depend onthe methodologies employed and the degree of accuracy required for any particularjoint configuration and loading. These approaches to stress analysis range fromclassical theoretical methods, through experimental methods on steel and acrylicmodels, to numerical computer intensive methods such as finite element analysis andthose based on parametric equations. These categories are covered very briefly in thefollowing section.

8

Literature Review

1.3.3 Methods of stress analysisThrough careful examination and analysis of considerable experimental andtheoretical data that were obtained after major research projects into the behaviour ofoffshore structures (such as the UKOSRP), the hot spot stress at the intersection ofwelded tubular joints has been accepted to govern fatigue endurance of offshorestructures. Its determination and evaluation is, therefore, an important first step at thedesign stage and also during structural integrity assessment programmes.

Stress analysis of tubular welded connections is not the main subject of this book.However, extensive experimental stress analysis was carried out on the tubular weldedjoints used in the course of the study presented in this book, the results of which arepresented in Chapter 3. As a result, additional background and the basic principlesbehind the development of other methods are presented in this chapter. This isparticularly useful for the comparison of results presented in Chapter 3, as thisknowledge provides a suitable platform from which any discrepancies between resultsobtained using different methods can be adequately explained.

Due to the complexity of joint shapes and the shell behaviour governing load responseof tubular joints, stress analysis of tubular welded joint intersections is difficult.Nevertheless, a wide range of techniques have been developed and employed inassessing offshore structures. The methods vary in their degree of accuracy in modellingdifferent geometries and loading cases. This section presents a review of these analysistechniques used to evaluate stresses for fatigue assessment of offshore structures.

Several methods have been used over the years for the analysis of stresses in weldedjoints. For instance, the first attempts to analyse tubular joints using theoreticalmethods started in the early part of the 1950s and 1960s when Biljaard [1.22] andToprac [1.23], after studying cylinders subjected to diametrically opposedconcentrated loading, used Roark's results. These were in the form of empiricalequations developed for stresses and deflections. Although Roark's work was notdirectly concerned with tubular joints, his results were used by other researchers tomake important contributions.

Numerical methods were also used as early as 1955 through to the early 1960s. By thelate 1960s, the classical solution methods used by Kellogg [1.24] and Caulkins [1.25]were well established. Kellogg used an analogy of the behaviour of a circular cylinder,subjected to uniform circumferential loads and developed a method of obtainingstresses in the chord. This was employed by computing the nominal stresses in thebrace and treating this as a live load applied to the surface of the chord at theintersection. The stresses in the chord were then obtained by increasing the loadintensity on the chord due to the axial forces in the brace by an appropriate factor andadding this to the load intensity on the chord due to bending stresses in the chord. Thestresses obtained by using this method were limited to axial loads applied through thechord and under IPB conditions. Caulkins used a computer program FRAMETI, basedon membrane cylindrical bending stress theory, to evaluate brace and chord stressesfor T and Y joints under all three modes of loading and K joints under axial loading.

9


During stress analysis assessment of offshore structures for fatigue evaluation,distribution of stress around the intersection and also through the joint thickness maybe required. The determination of stresses in tubular welded joints, used in theconstruction of today's increasingly complex structures, is difficult through the use oftheoretical methods, even though these have been improved tremendously over theyears. As a result, these methods have been superseded by the use of FEA,experimental measurements, and parametric equations. This book focusses on thelatter two methods.

1.3.3.1 Experimental methodsMost of the early information on the performance of tubular joints and tubular jointstress behaviour was obtained by experimental measurements on steel models. Theincreased offshore activity in the North Sea in the 1970s lead to an increased need topredict stresses in tubular joints more accurately, and different approaches were beingused to determine stresses in tubular welded joints using experimental methods.Experimental methods rely on the measurement of strain and hence stressconcentration factors on scaled or full-scale models. Experimental methods can becategorized, depending on the modelling medium. These include methods based on theuse of steel models, acrylic models, and photoelastic models. Photoelasticity isparticularly useful for joints with rather complicated geometries. The method wasdeveloped in parallel with FEA. Bouwkamp carried out the first reported tests ontubular welded joints using this technique in 1966. Holliday and Graff [1.26] used it inthe early 1970s to conduct three-dimensional stress analysis on T joints. Morerecently, Fessler et al. [1.27, 1.28] used the technique to study a range of tubular jointgeometries and obtained detailed information on the distribution of stresses on thesurface and also through the chord and brace walls near the intersection. Thesetechniques are not covered in detail in this book. However, a discussion on the use ofstrain gauges for experimental determination of stress concentration factors ispresented.

The use of steel models for stress analysis of offshore structural components is a well-established technique. It is usually implemented by strain gauging scaled down modelsor full-scale replica of tubular welded joints. This method was used in the course ofthe UKOSRP to study a wide range of T and K joints and the effect of varying theirgeometric parameters on their behaviour under different modes of loading. The stressconcentration factors for the tubular joints presented in this book were based onexperimental measurements. The results are compared with those predicted usingparametric equations in Chapter 3.

In order to attain a high level of correlation with measurable stresses and strainsencountered in a typical offshore structure, steel tubular joints used for stress analysismust be fabricated to standard offshore procedures to obtain satisfactory results. It isalso recommended that tolerances on dimensions be based on current offshorestandards and the results interpreted in the light of actual specimen dimensions andgeometry. It is known that unrealistically large welds can produce unrepresentativeresults. Care must, therefore, be taken in the scaling down of weld sizes for scaleddown specimens.

10

Literature Review

The use of experimental stress analysis methods relies on the assumption that the two-dimensional strains measured on the surface of the steel model remain linear.Therefore, two-dimensional stresses on the surface of the specimen can be computedand transformed into principal stresses. This is achieved by multiplying the strains atthe gauge locations with the Young's modulus of the material and appropriately takinginto account any Poisson ratio effects. This should be done with caution to avoid anyunrepresentative results. The recommended practice in both AWS Dl.1-92 and APIRP2A, which considers the hot spot stress as the product of maximum measurablestrain and Young's Modulus, may lead to underestimation of hot spot stress by up to30 per cent. This is mainly due to the fact that a direct multiplication approach like thisdoes not take into account any deformation resulting from the Poisson ratio effect.

The stresses at the weld toe are obtained experimentally by linear extrapolation to theweld toe of the experimentally measured principal stresses. There are strict guidelinesregarding the location of strain gauges for this purpose and Fig. 1.5 shows a schematicrepresentation of the locations of the extrapolation gauges. Strain gauges should bepositioned in accordance with recommendations of UKOSRP. The relevant distancesand tolerances on positioning the gauges are shown in Fig. 1.6.

Fig. 1.5 Locations of strain gauges on tubular joints

11


Fig. 1.6 Recommended tolerances for locating strain gauges from the weld toe [1.40]

Experimental methods on steel models normally give representative and accurateresults, if precautions are taken. Results obtained using this technique are, therefore,commonly used as a benchmark for assessing the accuracy of other methods. Howeverdue to the physical size of the gauges, only average strains over the region of interestcan be measured. This may pose a serious problem where changes in strain are verysmall and difficult to measure or, on the other extreme, where a very steep straingradient exists. It is also a very time consuming and expensive method, becauseextensive strain gauging is required to give detailed information on the stressdistribution in the region of interest. In addition, high-capacity loading machines arerequired to provide measurable strains in full-scale and otherwise stiff specimens.There are other methods that have been successfully used in recent years, asalternatives to strain gauging large-scale steel specimens where possible. Theseinclude thermoelastic methods, the use of brittle lacquers, and conductingmeasurements on acrylic models.

In the 1970s, when offshore activity in the North Sea increased tremendously and themore cost-effective methods of stress analysis of offshore tubular joints were beingsought after, scaled-down acrylic models offered an alternative solution to full-scaletests carried out on steel models. Wordsworth and Smedley [1.29] used this method toinvestigate stresses in tubular welded joints.

12

Literature Review

Acrylic models offer some advantages over steel models. First, lower loads arerequired to produce measurable strains in acrylic models, since their Young's modulusis usually a lot lower than the typical values for steel models. As a result, the test rigsdesigned for applying these loads could be simpler, cheaper, and a lot lighter. Second,strain gauges can be fitted before assembly, making it possible for strains and stressesto be obtained at those locations that are normally inaccessible in conventional weldedsteel models. This makes it easier to use acrylic models to study stress distributions onvery complex geometries. They can also be used to investigate the effects of ringstiffeners and welds on stress concentration factors. For example, Smedley [1.30]employed this approach to produce a weld fillet correction factor for T and 90 degreeX joints based on the weld fillet leg length.

The main disadvantage of using acrylic models is that the tubing may be susceptible tosignificant residual stresses that affect the surface of the specimen. They can also bemore prone to deformation due to creep. However, with due precaution, accurate andrepresentative results can be obtained from acrylic models at a lower cost comparedwith steels models. Some of the precautions include making estimates of Young'smodulus at the same time at which the strain measurements are made, and taking duecare when selecting the length of tubing and the required model scale.

1.3.3.2 Parametric equationsBased on several independent studies, a few sets of parametric equations have beenpublished that have varying capabilities and degrees of accuracy in analysing variousjoint geometries. These equations include those of Wordsworth and Smedley [1.29]based on a study of acrylic models, equations of Kuang et al. [1.31] published in 1977,and Gibstein's equations [1.32] published in 1978 after the use of the finite elementprogram NV332 to study stresses in T joints. There are other parametric equationssuch as those proposed by Efthymiou and Durkin [1.33], Efthymiou [1.34], Lloyd'sRegister [1.17], and the Hellier Connolly and Dover [1.35-1.37] equations. Acomparison between experimental measurements and SCFs obtained using parametricequations is presented in Chapter 3. A general review of some of these parametricequations is presented here.

Lloyd's Register equationsLloyd's Register proposed a set of parametric equations, which were published in 1991.These were developed for simple tubular joints after completing a project sponsored bythe UK Department of Energy to assess methods for deriving stress concentrationfactors (SCFs) in simple tubular joints. These equations were based on an existingdatabase of SCFs previously derived from steel and acrylic models. The equationsproposed included design safety factors and influence factors for different loadingconfigurations.

Kuang et al.Kuang studied forty-six T and Y joints under the three modes of loading, thirty-nine Kjoints under balanced axial loading, thirty-seven K joints under in-plane bending, andsixteen KT joints under balanced axial loading conditions in the inclined braces, and a

13


single axial load in the 90 degree brace using a finite element program, TKJOINT.These equations are presented in reference [1.31].

In obtaining these equations, Kuang assumed fixed chord end conditions to providethe necessary torsional restraint. It should be noted that the SCF obtained using this setof equations is that at the intersection line of the mid-surface between the brace andchord for the Y joints, described in detail in Chapter 3.

Wordsworth and SmedleyThese parametric equations were developed for T, Y, KT, and X joints. Subsequentlymodified by Underwater Engineering Group (UEG) for joints with equal brace andchord diameters, they were based on results from acrylic models. The formulae aresummarized in [1.29].

For these sets of equations the effect of the welds was not included and they wereintended to yield the gross deformation SCF. The reason for the modification introducedby UEG was a recognition of the fact that the original equations underestimated the

SCFs for joints with B = 1.0. However, the modifying parameter VQB was assumed to

be valid only for DT, X, K, Y, and T joints for estimating the saddle point SCFs.

Another geometric modifying parameter, VQr, was introduced to ensure better

prediction for joints with y > 20 and it was assumed to be applicable to all joints.

GibsteinAfter using the finite element program NV332 to study stresses in T joints, Gibsteinproposed a set of parametric equations to predict SCFs in T joints. They were based ona study conducted on seventeen T joints with both chord ends rigidly fixed, the effectof which was also investigated by varying the end conditions in a separate test that hadsimply supported chord ends.

Gibstein regarded the Gaussian points closest to the brace chord intersection to berepresentative of the locations for the 'hot spot' stresses and did not investigate theeffect of the non-dimensional parameter, a. However, it should be noted that theinfluence of a was deduced from Kuang's formulation and is included in theformulation for axial loading of tubular T joints. The SCFs for the brace weremodified by a factor of 0.8 to ensure correlation between the predicted andexperimental results.

Efthymiou and DurkinIn Efthymiou and Durkin's paper which presented the set of equations for predictingSCFs for T, Y, and K joints [1.33], the equations were based on a three-dimensionalfinite element analysis using the program PMBSHELL. Three-dimensional curvedshell elements, capable of explicitly modelling the tube thickness and weld profile,were used and 150 joints under various loading configurations were studied. However,designers and classification authorities were still faced with a few problems. First,there was a significant difference between the predictions from these two sets ofequations for certain joints and loading configurations. Second, there was limited

14

Literature Review

information on SCFs in stiffened and multiplanar joints. Third, limited informationwas available for certain loading configurations in simple K and KT joints and also onjoints with overlapped braces. At the time of this publication, the most comprehensiveand widely used equations were those of Kuang and Wordsworth and Smedley.

The set of equations proposed by Efthymiou and Durkin was developed to close up thegap that existed between predicted results from the equations of Kuang and Wordsworthand Smedley and to offer better prediction of SCFs for certain simple K and KT jointsand for joints with overlapped braces. The formulae are summarized in reference [1.33]and were subsequently extended [1.34] to cover X and KT joints. They were used in thedevelopment of generalized influence functions for the prediction of SCFs in planar andmulti-planar joints subjected to arbitrary brace end loads and moments.

A fixity study was also carried out and the effects of chord end fixity were quantifiedwhere relevant, including the effect of chord length. It was noted that using short chordsinterrupts the natural decay of chord deformation resulting from brace loading. This leadsto a reduction in the deformation and stresses in the chord. The short chord correctionfactors were, therefore, developed to account for this. These equations are recommendedby most design guidance notes and are highly consistent in the prediction of SCFs.

Hellier Connolly and DoverHellier Connolly and Dover carried out extensive and systematic FEA to study stressesin T and Y joints. This involved nearly 900 thin shell FE models. Wide ranges of jointgeometries under various modes of loading were studied. The results were comparedwith those obtained from a range of other techniques. This lead to the development ofa comprehensive set of parametric equations for estimating SCFs in tubular welded Yand T joints. A complete summary of these equations is given in reference [1.36].

These set of equations were modified to give the first set of parametric equationscapable of predicting the stress distribution around the intersection of the brace andchord. For Y joints, for example under OPB, the distribution of SCF was found to besymmetrical about the saddle position and the following expression that predicts thedistribution of SCF was proposed

where S(0) is the characteristic formula for the stress concentration factor around thechord brace intersection with a hot spot value of KHS- The above equations wereadopted for other parametric equations to facilitate the comparison of experimentalresults with those based on other parametric equations in Chapter 3.

15


1.4 Fatigue designOne definition of fatigue given in reference [1.38] is 'Failure of a metal under a repeatedor otherwise varying load which never reaches a level sufficient to cause failure in asingle application'. Another definition given in reference [1.39] is The process ofprogressive localized permanent change occurring in a material subjected to conditionswhich produce fluctuating stresses and strains at some point or points and which mayculminate in cracks or complete fracture after a sufficient number of fluctuations'.

These two definitions are not the only variants of the numerous definitions found inthe vast literature available on fatigue and the behaviour of fatigue cracks. However,they give a clear indication that fatigue is a process of cumulative damage. This wasrecognized well over a hundred years ago and research in this area started as far backas 1838. Codification of the resulting data started around the 1850s when Wohlercarried out his now classic experiments, which lead to the development of S-N curves.Design for fatigue resistance and fatigue life prediction is an important aspect forconsideration in a wide range of industries and engineering applications today.

In the offshore industry, for example, steel offshore jackets and Jack-up legs consistmainly of tubular joints, which are formed by welding together intersecting brace andchord members. These welded intersections constitute regions of stress concentrations,which represent areas that are highly susceptible to crack initiation and subsequentpropagation. Crack propagation may lead to eventual failure of the structure. Thismakes fatigue analysis of such structures very important, both at the design stage andalso during structural integrity assessment programmes.

Fatigue analysis can be rigourous, but it is by no means an exact science. As a result ofthe idealizations and approximations employed in the analysis process, any fatigueanalysis approach adopted will almost always be associated with some degree ofidentifiable uncertainty. This will include uncertainties resulting from inadequateunderstanding of the complete effect on the structure of the operational environment,and the relationship between this and the actual forces, moments, and stressesexperienced by the structure. The implication of this uncertainty is to introduce apotential for error and, at the same time, reduce the level of confidence that may beassociated with any exact calculations resulting from any particular fatigue lifeprediction methodology.

Fatigue analysis, however, is a very important tool for designers to use in theprediction of relative magnitudes of fatigue lives of structures at potentially criticalpoints. Fatigue analysis methodologies have been shown to yield reliable estimates offatigue life and two distinct approaches have evolved for use in fatigue life assessmentof engineering structures, which are subjected to fatigue loading. These include the S-N approach and the fracture mechanics approach.

1.4.1 The S-N approachThe stress-life (S-N) approach is based on available fatigue test data. It has theadvantage that it provides an assessment methodology that is based on a single

16

Literature Review

parameter, the 'hot spot' stress. S-N refers to the life or number of cycles to failure ofthe joint.

Like 'hot spot' stress, S, the definition of life, N, used in S-N design curves has been asubject for consideration in the course of major research programmes such as theUKOSRP. Projects like this lead to the generation of vast amounts of experimentaldata that were used to formulate the S-N curves for the Department of Energy DesignGuidance notes and the Health and Safety Executive (HSE) design guidance.

The same definition of 'hot spot' stress used in the UKOSRP reports [1.40] wasmaintained in the Department of Energy's 'Background to new fatigue designguidance for steel welded joints in offshore structures', first published in 1984 [1.41]and the subsequent revision [1.42]. This definition, discussed in Section 1.3.2, is basedon a linear extrapolation to the weld toe, of the linear part of the stress distributionnear the weld toe but removed from the region of rapidly rising stress immediatelyadjacent to it.

On the other hand, the definition of fatigue life, or the number of fatigue cycles tofailure, N, was taken as that which denoted 'first through wall cracking. This isdetected either visually or, more accurately, by noting first loss of internally appliedair pressure to the damaged member, or by monitoring the output of strain gaugespositioned adjacent to the crack at its deepest part'. The reason for adopting thisdefinition is that it is appropriate to use a measure of life that will result in bothdetectable and reparable cracks in a structure that is capable of tolerating them withoutthe intervention of catastrophic fracture. Such cracks are also deemed necessary to be'...small enough for the structure not to have to shed load and thereby (possibly)damage other joints' [1.42]. This life, designated N3, (designated N2 in reference[1.41]) together with the 'hot spot' stress, S , are the two parameters used to formulateS-N design curves and are given as

1.4.1.1 Formulation of the basic S-N curvesThe S-N approach is well established for the design of offshore welded tubular jointsand connections. In the early 1970s, editions of both API RP2A and AWS Dl.lprovided the first guidance on the design of tubular joints against fatigue using S-Ncurves. Even though the API RP2A was influenced to a large extent by the experienceon the behaviour of platforms in the Gulf of Mexico, it has been used extensively todesign structures for the harsher environments of the North Sea. The curvesrecommended by the 1972 editions of API and AWS were developed on the basis oftwo concepts. The first was an attempt to correlate failure to brace nominal stress, andthe second was based on the 'hot spot' stress of the joint. Using data obtained fromsmall-scale specimens tested in air, under constant amplitude loading conditions, theS-N curve (called the 'X curve') was proposed with a note of caution from AWS. Theimplication was that calculated fatigue lives based on the proposed curves should be

17


viewed with a healthy amount of scepticism, more as design guidance than as anabsolute requirement.

The same data used in producing the API and AWS curves were also the basis of thecurves in BS 6235 [1.43], NPD [1.44], and DnV rules [1.15], including earlier editions ofthe UK Department of Energy guidance notes. The above statement of caution, however,is an indication that there were other factors at the time that were understood to governfatigue but which had not yet been addressed. To a large extent this constituted a drivingforce behind the initiation of extensive research programmes starting with UKOSRP I in1973. Following the increasing availability of experimental data, design codes have beenrevised and the guidance on fatigue design has been modified, based on available data.These revisions have not been given here in detail since they are available in respectivecodes and other relevant literature. However, an indication of how the fatigue guidanceoffered by the UK Department of Energy Guidance notes has evolved in more recentyears is presented with consideration of other relevant factors that affect fatigueperformance and how they have been incorporated into the S-N approach.

After the completion of the first phase of the United Kingdom Offshore SteelsResearch Project (UKOSRP I) in 1984, a major revision of the fatigue guidance noteswas carried out. Under the section on 'Fatigue-allowable fatigue stresses', a basic Tcurve was proposed for fatigue design of tubular joints. This curve was based on sixtyfour T, X, and K joint test results and recommended for joints having a chord wallthickness of 32 mm, see Table 1.1.

Table 1.1 The basic design T curve

CurveT

N < 107

Log10(K1)

12.164m

3.0

N<107

Log10 (K1)

15.61m

5.0

The document also addressed the modification to the basic curve for unprotected jointsin seawater, thickness effect, and effects of weld improvement and treatment for lowand high stress cycles.

Since 1984 when reference [1.21] was published, a substantial amount of data on thefatigue behaviour of offshore welded tubular joints was made available following thecompletion of other major research projects such as the UKOSRP II. The data wereassessed by a review panel for fatigue guidance, appointed by the Department ofEnergy to ensure that relevant data were used in the revision of the UK Department ofEnergy Fatigue Design Guidance.

After excluding some categories of the available data to ensure that the selected dataset covered the widest range of joint geometries and loading configurations, the designS-N curve given in Table 1.2 was proposed.

18

Literature Review

Table 1.2 The basic design T' curve

CurveT'

N < 107

Log10 (K1)

12.476m

3.0

N < 107

Log10(K1)

16.127m

5.0

This was based on 16 mm wall thickness (cf. 32 mm for earlier revision) andallowances were made for other relevant factors. This basic design S-N curve fortubular joints was taken to correspond to two times the standard deviation of theLog 10 (N) below the mean S-N line for the 16 mm data.

The slope of -1/3 was adopted for the T' curve, mainly to retain consistency withprevious guidance and other design codes. The existence of an endurance limit wasaccounted for by a change in slope of the basic curve from -1/3 to -1/5 at 107 cycles. Thecorresponding basic design S-N curves for flat or rolled plates is given in Table 1.3.

Table 1.3 The basic design P curve

Curve

P

N <107

Log10(K1)12.182

m

3.0

N <107

Log10(K1)

15.637

m

5.0

The current draft ISO standard recommends a new set of basic design S-N curvesbased on the joint type. It recommends the TJ curve for welded tubular joints that areexposed to constant or variable amplitude loading, the CJ curve for cast nodes, and theOJ curve for other welded connections, depending on the classification for theconnection. This could be (B, C, D, E, F, F2, and W') similar to the classes forwelded plates in the HSE guidance. These equations are given in Table 1.4.

Table 1.4 The basic design S-N curves from the ISO draft standard

Curve

TJCJ

OJ (Class B)OJ (Class C)OJ (Class D)OJ (Class E)OJ (Class F)OJ (Class F2)OJ (Class W)

N <108

Log10 (K1)

12.4815.1715.0113.6312.1812.0211.8011.6310.97

m

3.04.04.03.53.03.03.03.03.0

N <108

Log10(K1)

15.47

16.7616.0414.9714.6914.3314.0613.33

m

5.05.05.05.05.05.05.05.05.0

19


The draft ISO standard also recommends that the above curves should be used for bothair and seawater applications, with adequate cathodic protection. There are otherimportant factors that should be taken into consideration when using S-N curves.Some of these factors are discussed below.

1.4.1.2 The implication of other factors' fatigue performanceOther relevant factors effect the fatigue behaviour of welded connections, these needto be taken into consideration when using these curves for the design of weldedconnections. Even though a wide range of these factors had been studied, the dataavailable when the T' and P curves were proposed, were not considered adequate to beincorporated in the proposed design curves. As a result, some of the data that wereavailable were excluded from the statistical analysis carried out by the review panelfor fatigue guidance after the screening process. Some of the categories that wereexcluded include the database on variable amplitude loading and data obtained fromtests carried out on specimens with wall thickness less than 16 mm. The implication ofthis is that the design guidance is very limited for real engineering structures subjectedto variable amplitude loading. This book addresses part of this problem. It presentsnew data on high-strength steels and identifies the key issues to be considered whendealing with variable amplitude fatigue. This adds significantly to current knowledgeon variable amplitude corrosion fatigue performance of high-strength steels. The bookalso presents new methods for assessing fatigue damage under variable amplitudeloading conditions and identifies the likely differences in S-N behaviour of high-strength steels when compared with conventional fixed-platform steels.

Despite the exclusion of some of the data sets on the grounds that they were notadequate, allowances were made for these relevant factors to be considered whenusing the design S-N curves. These important considerations and the associated'penalties' applied to the basic design S-N curves are covered below.

Thickness effects on fatigue resistanceConsiderable research work into the effect of wall thickness on fatigue resistance of acomponent or structure has been carried out and documented. A great proportion ofthe fatigue life of tubular joints is spent in the propagation of fatigue cracks. It hasbeen demonstrated for a given 'hotspot' stress, that the average growth rate of thesecracks is higher in specimens with wall thickness in excess of 32 mm. It has also beendemonstrated that this effect could be operative for chord wall thickness as high as 75mm and the trend has equally been observed to occur in simpler welded connectionssuch as T butt welded plates.

The implication of this is that, instead of an increase in fatigue resistance as wallthickness is increased, a reduction may result for greater wall thickness. This effecthas been widely referred to as the 'thickness effect'. It was demonstrated by Wyldeand Mcdonald in 1979 [1.45] and different researchers have since put forwarddifferent arguments to explain this phenomenon.

Marshall [1.46] studied size effect on tubular welded joints in the early 1980s andsuggested that the phenomenon is not only related to plate thickness and that other

20

Literature Review

parameters, such as the weld toe and the associated size of the local notch zone couldbe more important. This view followed Haibach's findings [1.47] when heinvestigated the effect of fillet weld throat size on 50 mm thick plates in the late1970s. He noted that there was a fall in fatigue strength as a result of an increase in theweld size alone.

Webster et al. [1.48] noted a decrease in fatigue strength by about a third by increasingthe plate from 38 mm to 100 mm. They also observed increases in the weld toe stressconcentration factors for thicker joints. Based on this observation, another explanationbased on higher local stresses was proposed.

Other researchers [1.49-1.51] argue that size effect is due to a combination ofincreased weld toe stresses and, to some degree, the effect of a lower through-thickness stress gradient. This argument focussed the size effect on crack growth in thelow A.K region, which controls a high proportion of the fatigue life and moresignificantly so in smaller welded joints.

This is by no means an exhaustive review of studies conducted to quantify thicknesseffects on the fatigue strength of tubular joints. It is, however, widely accepted that theeffect can be detrimental to fatigue performance. After a review of experimental data,a correction factor was proposed. This is expressed as

SB is the stress range at the reference thickness, tB and 5, the stress range that results inthe same fatigue endurance at a thickness t, and y is the thickness correction exponent.This correction factor is applied as a penalty factor to thicknesses greater than thereference thickness.

In the earlier edition of the UK Department of Energy Fatigue Guidance notes [1.21],the reference thickness was taken as 32 mm for tubular joints and 22 mm for plates. Avalue of 0.25 was recommended for the thickness correction exponent, y.

After reviewing further fatigue test data, it was demonstrated that the thickness effectalso occurs in joints with chord wall thickness below the previous limiting thickness of32 mm. A new reference thickness of 16 mm was proposed for tubular joints andplates with a conservative thickness correction exponent of 0.3. The effect of thicknesson the design S-N curve is demonstrated in Fig. 1.7.

21


Fig. 1.7 Illustration of thickness effect on S-N curve

The argument that thickness effect is not just related to plate thickness and that otherparameters, such as the weld toe and the associated size of the local notch zone couldbe more important, cannot be dismissed. However, this does not explain the fact thatthis phenomenon is less pronounced for axial loading than has been observed undersituations where bending loads are involved.

A: Illustration of stress gradient for pure bending

B: Effect of thickness on AK and mode of fracture

Fig. 1.8 Schematic illustration of thickness effects [1.52]

22

Literature Review

As illustrated in Fig. 1.8, there are two likely causes for thickness effect under bendingconditions. The first of these is the existence of a lower through-thickness stressgradient in a thicker plate. This implies that a fatigue crack of a given size will besubjected to a higher stress in a thicker specimen, which may also exhibit a low criticalstress intensity factor range. This higher stress level will lead to a higher crack growthrate in the thicker specimen.

The second reason for this behaviour is that, for a given crack size, a larger surfacearea or volume of material is subjected to a higher stress level in the thicker specimen.As a result, there is a greater probability of initiating a fatigue crack in the thickerspecimen, which also has a higher probability of containing inherent manufacturingflaws - assuming that their distribution per unit volume is uniform. The consequenceof these two aspects is that, even though a fatigue crack has a longer propagation pathin a thicker specimen, the probability of initiation is higher in thicker specimens wherethey can also propagate faster, due to the presence of a more severe stress field.

Environmental effects on fatigue resistanceThe environmental conditions experienced for welded connections in service can vary,depending on the location of the connection in the structure. This will depend onfactors such as whether the joint is in the splash zone, fully immersed and also on thelevel of any cathodic protection (CP) applied. This section presents importantdiscussion on some of the key issues relating to corrosion fatigue and the likely impactof CP. In particular, the way this is incorporated in the use of design S-N.

It was recognized that the environment could have detrimental effects on fatigueperformance of tubular joints relative to air. Based on this, and also due to the lack ofsufficient experimental data, three recommendations were made in earlier codesregarding the use of design S-N curves and the environment.

A penalty factor of two on design fatigue life was recommended for unprotectedjoints. It was also recommended that the air curve be used for adequately protectedjoints. The change in slope at 107 cycles was not to be applicable to joints under freecorrosion. The main reason for this decision was that free corrosion may lead topitting. Corrosion pits act as stress concentration sites where crack initiation andsubsequent propagation can take place. This effectively removes the fatigue limit,which may exist at low stress levels in a non-corrosive environment.

The following curves (Table 1.5) were proposed for use in the design of protectedjoints and for those under free corrosion conditions and are the latest proposedrevisions to fatigue guidance [1.42].

23


Table 1.5 The basic design S-N curves for protected and freely corroding joints

CurveN<10 7

Log10(K1) mN<107

Log10 (K1) m

Free corrosionTubulars

Plates12.00

11.7053.03.0

--

--

Protected jointsTubulars

Plates12.17511.784

3.53.0

16.12715.637

5.05.0

These curves effectively represent a factor of two on design fatigue life, even foradequately protected joints. The main reason for this change in approach to the designof protected joints was that further fatigue tests carried out before the 1990 revision tothe design guidance notes [1.42] under adequate cathodic protection levels did notshow trends in fatigue lives comparable to air tests. The current draft ISO standard[1.9], however, recommends the use of the same basic S-N curves for both air andseawater with adequate protection for steels with a yield strength of less than500MPa. Results from tests conducted as part of the study presented in this book forhigher strength steels and newly generated data on high-strength steels, show that anenvironmental factor may still be applicable even for adequately protected joints.

Fatigue under CP conditions is influenced by many factors, some of which have beendemonstrated to be different from material to material. Corrosion fatigue crack growthrates under cathodic protection conditions also depend on the level of cathodicprotection, among other variables. The degree of susceptibility of a particular materialwill largely depend on the complex interaction between the hydrogen equilibrium inthe vicinity of the crack tip and the stress intensity factor. Since the effect of hydrogenproduced under cathodic protection conditions varies for different grades of steel, it ispossible that the current reduction factor of two on fatigue life may not be directlyrelevant in the design of structures made from higher strength steels. This implicationis discussed in greater detail in Chapter 3 where results of the fatigue tests carried outin this study are compared with those from previous tests on conventional fixedplatform steels such as BS 4360 50D.

Corrosion fatigueOne definition of fatigue quoted earlier is 'Failure of a metal under a repeated orotherwise varying load, which never reaches a level sufficient to cause failure in asingle application'. Corrosion, on the other hand, could be defined simply as a processby which a metal's chemical structure is changed resulting in gradual deterioration bybeing slowly 'eaten' away in a chemical oxidation-reduction reaction. The occurrenceof corrosion under fatigue loading conditions leads to a situation where the damageprocess depends on the severity of the fatigue loading, the rate of materialdeterioration due to corrosion, and the interaction between these two damageprocesses. This phenomenon is known as corrosion fatigue.

24

Literature Review

Corrosion fatigue involves unique failure mechanisms that are very complex anddepend on the stage of the fatigue process. Different ideas have been proposed toexplain the basic mechanism of corrosion fatigue during the initiation stage. However,the mechanism that operates during the crack propagation stage is very complicatedand not well understood for high-strength steels.

Predicting the behaviour of a structural crack entails estimating the load states that thestructure will have to withstand. Obtaining representative loading conditions for suchstructures is, therefore, very important. This can be adequately modelled by use ofwave power spectra, together with the transfer function approach in the frequencydomain as discussed in Chapter 2. However, if this simulation is carried out in anunrepresentative environment, then misleading results can be obtained. Environmentassisted fatigue is a major cause for concern and contributes significantly towards thefailure of structures. The early work of Gough and Sopwith [1.53] has shown that airdoes decrease fatigue life relative to tests in vacua. They demonstrated that thecombined presence of water vapour and oxygen was the cause of atmospheric effects.For tests in aqueous environments the presence of oxygen was demonstrated to benecessary to induce corrosion fatigue. The dissolution of iron in an aqueous solutioncan be represented as follows

The resulting free electrons from the above process reacted with water and dissolvedoxygen to give hydroxide ions as shown in the following equation

The corrosion process is effected when the iron ions react with the hydroxide ionsresulting in the formation of iron(II) hydroxide as follows

The above reaction is shown schematically in Fig. 1.9. Iron(II) hydroxide is not a verystable compound due to the presence of iron(II) ions (Fe2+). This form of thehydroxide is, therefore, quickly oxidized to produce the more stable iron(III)hydroxide Fe(OH)3, which is precipitated as a reddish brown substance, the mainconstituent of rust.

25


Fig. 1.9 Illustration of the corrosion process

Oxygen is not an absolute requirement for the inducement of corrosion fatigue, and thepossible role of hydrogen is now thought to play a more significant part in theembrittlement of high-strength steels.

The processes of corrosion fatigue and hydrogen embrittlement of high-strength steelsare a complex combination of chemical reactions. But the overall process can berepresented by the following simple reduction-oxidation reaction.

Corrosion fatigue involves unique failure mechanisms, that are very complex anddepend on the stage of the corrosion fatigue process. Various models have beenproposed to explain the basic mechanism of corrosion fatigue during the initiation stage.However, the mechanism that operates during the crack propagation stage is verycomplicated and not well understood for high-strength steels, but increased crack growthrates under CP conditions help to provide an explanation that hydrogen embrittlement isa possible mechanism. In a fairly recent review [1.54], five main theories that have beenproposed to explain this phenomenon were highlighted. Three of the more plausibletheories include the pressure, decohesion, and surface energy.

The pressure theory is based on the assumption that atomic hydrogen generated duringcathodic protection is absorbed into the microstructure of the steel, and diffusesthrough the metal lattice structure collecting into voids and/or defects within the metal.Subsequent combination of atomic hydrogen at these voids forms hydrogen gas, thenleads to the formation of 'pockets' of high pressure within the metal. There is evidenceto support this theory, but the occurrence of hydrogen embrittlement in high-strengthsteels in a relatively low-pressure environment [1.55] has led to the view that othermechanisms may be involved in the process of hydrogen embrittlement.

26

Literature Review

The surface energy and decohesion theories are similar. The decohesion theorysuggests that the presence of hydrogen will tend to lower the inter-atomic energy and,therefore, make it easier for the inter-atomic bonds to be broken, resulting in higher-than-expected crack growth rates. The surface energy theory, on the other hand,suggests that the presence of hydrogen will decrease the surface energy of newlyformed surfaces. This means that the energy required to produce a new surface, i.e. toproduce a fatigue crack, is less than expected and, therefore, higher-than-expectedcrack growth rates will prevail in the presence of hydrogen.

Other theories that have been proposed to explain hydrogen embrittlement in high-strength steels include the hydride formation and the local plasticity theories. There islittle evidence to support the hydride formation theory. This suggests that the presenceof hydrogen will favour the formation of brittle hydrides in the vicinity of the crack tipleading to the embrittlement of the steel. There is even less evidence to support thelocal plasticity theory. This suggests that the presence of hydrogen tends to reduce thetotal stress required for dislocation movement. Easy movement of dislocations in thepresence of hydrogen implies that high-strength steels will show a greater tendency toductile behaviour, thereby reducing the possibility of cleavage fracture. Thiscontradicts the surface energy and decohesion, theories and there is little evidence toindicate this kind of behaviour in high-strength steels.

One of the difficulties in quantifying corrosion fatigue and hydrogen embrittlement inhigh-strength steels is the large number of variables involved. These variables includealloying elements in the structural member, local flow velocity, salt content, andchemical composition of the corrosive environment, temperature, pH, degree ofaeration, and the loading frequency. Some of these aspects and their effects on thefatigue resistance of offshore structures are covered in greater detail in the followingsections. The way they can be controlled during fatigue testing is presented in Chapter 3.

Initiation of corrosion fatigue cracksThe fatigue life of smooth polished specimens is dominated by fatigue crack initiation.For this type of specimen, crack initiation and associated mechanisms are veryimportant. Typically 90 per cent of the air fatigue life of smooth polished specimensmay be associated with the initiation of fatigue cracks and only 10 per cent with theirgrowth [1.56]. However, the presence of a corrosive environment can drasticallyreduce fatigue life by reducing the fatigue crack initiation life to about 10 per cent ofthe total life.

This is very significant for offshore structures in that most of the fatigue life of thestructural components is characterized by crack propagation. For this reason initiationmechanisms for these structures are considered not to be as important as in the case ofsmooth polished specimens. However, under variable amplitude loading conditions,crack arrest is possible. This is possible due to a combination of sequence effects andcrack tip blunting that may arise from the electrochemical action of the environment.Under these circumstances, it is important to distinguish between crack arrest and theabsence of initiation.

27


One of the basic mechanisms of corrosion fatigue during the initiation stage can beexplained thus: a corrosive environment attacks the surface of a metal producing anoxide film. Localized cracking of the oxide layer under cyclic loading exposes freshmetal surfaces that subsequently undergo the same process. This can cause localizedpitting of the metal surface resulting in the production of stress concentration sites.Corrosion fatigue crack initiation and the role of pitting has been the subject of muchdiscussion, Laird and Duquette [1.57] concluded that for steels, 'perhaps pits observedat failure were not the cause of corrosion fatigue but rather the result of it'.

This conclusion is not applicable to all cases of corrosion fatigue, as it is justifiable insome cases and unjustifiable in others. The effect of pitting on the initiation ofcorrosion fatigue cracks is dependent upon details of pit formation. It is also importantto recognize the fact that different mechanisms of initiation are possible, and that themechanism with the fastest kinematics will dominate the fatigue crack initiationprocess. For example, grain boundary attack, hydrogen-assisted cracking, andlocalized attack at protruding slip steps are all possible mechanisms for corrosionfatigue crack initiation.

Considerable research has been carried out on structural steels used for jacketstructures, and some of the corrosion fatigue crack initiation data for steels such as BS4360 (50D), BS 7191 (355D), 450F, and API X85 are now available. Depending onthe operative initiation mechanism, it is possible that high-strength steels wouldexhibit an entirely different behaviour under realistic loading and environmentalconditions. This comparison is covered in greater detail in Chapter 3.

Propagation of corrosion fatigue cracksThe fatigue life of offshore welded tubular joints is dominated by fatigue crackpropagation, which often represents well over 80 per cent of total life. For offshorewelded tubular joints, therefore, crack growth data are of practical significance forcorrosion fatigue since these joints are assumed to have fabrication defects when theyare commissioned. Even under circumstances where this is not the case, defects aredeveloped in these structures relatively quickly and their service life is determined byhow fast they propagate through individual components under the relatively lowfrequency loading that characterizes corrosion fatigue in offshore structures.

Four factors have been highlighted to be the most significant influences on the fatiguelife of welded tubular joints. These include specimen characteristics, environmentaleffects, component stress state, and stress-time interaction effects. The most relevantaspects of specimen characteristics, and how these affect the fatigue life of offshorewelded tubular joints, are discussed in Chapter 3. The effects of stress states andstress-time interactions are determined by the loading mode and a combination ofwave loading, wave excitation frequency, and structural response for any particularstructure. These aspects are covered in Chapter 2. The following two sections reviewthe effects of cathodic protection and variable amplitude loading on the fatigueperformance characteristics of welded tubular joints. The way these conditions aremodelled for tests conducted as part of the study presented in this book are discussedfurther in Chapters 2 and 3.

28

Literature Review

Effects of cathodic protection on fatigue crack growthA great deal of effort has been concentrated over a period of several years on studyingthe effect of the environment on fatigue resistance of engineering materials. In general,air fatigue data are used as a basis for comparing the performance of steels in differentenvironments, although it is known that air is not inert with respect to fatigue crackgrowth. Fatigue crack propagation rates in vacua have been observed [1.57] to belower than those in air at lower stress levels, and it is now well established that acorrosive environment could have serious detrimental effects on the performance ofsteel components subjected to fatigue. This section presents a general review ofcorrosion fatigue and examines some of the mechanisms that have been identified inthe more recent years.

Cathodic protection (CP) is the most widely used method for preventing corrosion. Itis a remedial measure that was originally thought to improve corrosion fatigue life to alevel comparable to that in air. CP is achievable in two ways. One of the methodsinvolves attaching a sacrificial anode to the structure to be protected. The otherrequires the application of a cathodic potential or current to the structure to beprotected by use of an external current generator. This impressed current method wasused for the corrosion fatigue tests carried out as part of this study and it is describedin greater detail in Chapter 3.

Depending on the method adopted, the difficulty in maintaining a uniform CP over theentire structure, and the actual levels of these potentials, are known to haveconsiderable effect on the fatigue crack propagation rates of materials exposed tocorrosive environments under CP conditions. This behaviour is important for high-strength steels and is discussed further in Chapter 3.

The levels of CP used can be classed into three categories: under-protection or freecorrosion, adequate protection, and over-protection. These categories are a function ofthe relative magnitudes of the protection potential and the equilibrium potential for thefree corrosion of bare steel in seawater. This dependence of fatigue behaviour onelectrode potential is shown schematically in Fig. 1.10.

The equilibrium potential for free corrosion of bare steel in seawater is approximately-650mV with respect to Ag/AgCl reference electrode.

29


Fig. 1.10 Effect of electrode potential on fatigue [1.57]

Adequate CP is said to be achieved when the protection potential reaches a level thatis just sufficient to prevent dissolution of iron ions in the aqueous solution. Thisadequate CP level has been identified to be around -850 mV and has been used in awide range of fatigue tests as part of the UKOSRP programmes. The fatigue testresults in this book have assessed the effect of CP on high-strength steels, and arepresented in Chapter 3.

Fatigue tests carried out under free corrosion potentials (-600 mV to -700 mV) havebeen shown to produce shorter fatigue lives when compared to air tests [1.58-1.62].These tests show similar environmental reduction factors between two and three withthe larger reduction factors occurring at lower stresses, suggesting a possible effectfrom a greater exposure time characteristic of tests carried out at lower stress ranges.

There seems to be general agreement that the use of adequate cathodic protection canproduce corrosion fatigue performance of initially smooth specimens of the lowerstrength structural steels comparable to that in air. However, the effect of moderate CPpotentials on welded tubular joints is far less conclusive, as data for tubular jointsseem to exhibit inconsistency. For example, there was some discrepancy between theseawater tests carried out as part of the UKOSRP II programme when compared interms of environmental reductions factors with results obtained from the UKOSRP Iplate joint tests. However, individual welded tubular joint test programmes show atrend towards longer lives at low stresses with a CP level of -850 mV.

The influence of cathodic over-protection on fatigue crack growth rates is even lessconclusive, as the data for tests conducted using cathodic potentials in excess of-1000 mV are limited, especially on high-strength steels and primarily on medium-strength steel plate specimen tests. Previous research, however, suggests that verynegative cathodic potentials may have a detrimental effect on the fatigue performanceof BS 4360 50D in seawater. Tests on API-X65 steel also show that cathodic over-protection can result in accelerated crack growth rates when compared to freecorrosion and air fatigue crack growth data [1.63, 1.64].

30

Literature Review

The effects of both under-protection and over-protection are of considerable importancefor crack growth in a corrosive environment under CP conditions, especially due to thefact that different materials may show different responses to these two extremeconditions. For instance, it is known that some steels are susceptible to hydrogenembrittlement cracking depending on the level of protection potential used. There isevidence that cathodic polarization may be of little benefit in reducing corrosion fatiguecrack growth rates and that cathodic over-protection may be detrimental, especially forhigh-strength steels. A review of UK and other design guidance suggests that CPpotentials more negative than -850 mV may be detrimental to steels with strength levelsabove 700 MPa and that in some instances even -800 mV may be detrimental to steelswith yield strengths higher than 800 MPa [1.65]. This dependence of crack growth ratesis discussed further in Chapters 3 and 4, where the effects of CP on both fatigue crackinitiation and propagation are examined for a typical high-strength steel, SE 702.

Tests on API X65 pipeline steel have shown that high CP potentials can increase crackgrowth rates by as much as fifty times over those observed in air. This effect may beworse for higher strength steels, which are thought to be more susceptible to hydrogenembrittlement cracking, depending on the loading. Although data on the effects ofvariable amplitude loading are limited for this class of steels, the following sectionpresents a discussion on the likely impact of service loading conditions on fatigueperformance.

Variable amplitude fatigueThe current guidance on fatigue assessment and design of welded connections is stillrather limited with respect to the variable amplitude loading. The available design S-Ncurves are largely based on constant amplitude tests, while in-service loading experiencedby most engineering structures has both variable amplitude and frequency content. Anumber of tests have been conducted [1.4, 1.66, 1.67] under variable amplitude loadingconditions. However, the data were not incorporated in design S-N curves proposed byHSE, for example. The effect of environmental loading (variable amplitude loading) onfatigue performance and crack propagation in high-strength steels is an important aspectof the material presented in this book, and it is covered in greater detail in Chapters 2 and3. However, a brief review of current guidance on the design of offshore structuressubjected to variable amplitude fatigue using S-N curves is given here.

The current edition of API RP2A, under the section on fatigue analysis, recommendsthat the wave climate should be derived as the aggregate of all sea states to beexpected over the long period. This may be condensed into representative sea statescharacterized by wave energy spectra. The stress response calculated for each locationis combined into the long-term stress distribution used in calculating the cumulativedamage ratio. The approach outlined does not make any allowances for any sequenceor sea state interaction effects that may be present under service loading conditionswhere several sea states of different significant wave heights may characterize thelong-term distribution of stresses in a structure. This aspect of variable amplitudecorrosion fatigue in offshore structures is reported in greater detail in Chapters 3 and 4where the results of fatigue tests are presented in terms of a sea state sequence and thevariations in crack growth rates accounted for.

31


The earlier editions of the Norwegian Petroleum Directorate Design Rules do notprovide any specific guidance on the effect of variable amplitude loading. Thedocument recommends a similar damage summation model to that in API RP2A. i.e.

The damage summation level Ds recommended by this code is however, unlike API,'taken equal to 1.0 for any part of the structure unless otherwise specified by the NPD'.

The same damage summation rule was recommended by AWS with a damagesummation level of one third for critical joints. Similarly, DnV recommends the use ofMiner's rule for the determination of cumulative damage. It indicates that thecalculated damage summation failure limit should range from 0.1 to 1.0. This is a veryconservative level and is relevant to practical situations were inspection andmaintenance operations are limited. The DnV rules also require that, in establishingthe long-term distribution of stress range, variable loads arising from influences suchas waves, wind, current, and so on should be accounted for.

Lloyd's Register of Shipping also recommends the use of Miner's rule with asummation level 'normally taken as 1.0'.

The recommendations proposed by UK Department of Energy guidance notes werebased on variable amplitude tests carried out on welded plates with respect to a best-fitconstant amplitude curve from tests on similar joints. The document recommends theuse of a damage summation level of unity for both tubulars and plates.

The effect of Miner's rule on an S-N curve is shown in Fig. 1.11. Constant amplitudeloading is generally assumed when analysing the behaviour of tubular joints. Atpresent, Miner's rule is generally accepted. Any other fatigue damage predictionmethod requires an assumption on the accumulation of damage resulting from variableamplitude stress cycles of any stress sequence.

Fig. 1.11 Effect of Miner's damage rule on S-N curves

32

Literature Review

Variable amplitude used within the context of existing methods and codes based on S-N curves makes a fundamental assumption that individual fatigue cycles from avariable amplitude loading process cause the same damage as if each cycle were partof a constant amplitude series. The implications of this assumption are discussedfurther in Chapter 4.

The effect of loading conditions on corrosion fatigue crack growth can be understoodonly by studying the effect this has on the crack tip, a region of rapidly deformingmaterial where new surfaces are being created at a rate that is not easily definable.This approach is very difficult and not well understood for conditions where the stresstime behaviour and the crack tip stress intensity factor range both determine crackgrowth rate.

For example, by calculating the relevant strain rate for the crack tip, using the crackopening displacement for each cycle, it has been shown that the strain rate willinitially be very high but decreases with increasing load for monotonic loading.Triangular wave forms also give an initially high strain rate that decreases as themaximum load is approached. Unloading is, however, affected by factors such asreversed plastic flow, crack closure, crack extension, and crack tip profile. Forsinusoidal loading, the strain rate will be zero at the minimum stress, reaches amaximum during the loading cycle, and falls to zero again at the maximum stress.Hence in a cyclic loading situation the region at the crack tip will experience highstrain rates with the continual generation of new surface if the crack is growing.

The relationship between crack tip strain rate and variable amplitude loading fatiguecycles is not as clear as the case for constant amplitude waveforms due to possiblesequence effects, or load interaction effects, which could be quite significant. Anumber of possible models have been proposed to explain the variability in crackgrowth rates observed under variable amplitude loading and to predict fatigue crackgrowth under these conditions. In each of these models, discussed in Chapter 4,separate mechanisms involved are not necessarily exclusive, as a number of them maybe operating simultaneously. One thing that is commonly encountered when dealingwith variable amplitude fatigue analysis for both S-N and fracture mechanicsapproaches is the requirement for cycle counting. This is very important as it is used inidentifying significant events in the sequence, that are directly relevant to fatiguedamage. Cycle counting methods can be broadly classified into two categories -conventional and theoretical methods. The following section presents details ofestablished methods used in analysing variable amplitude load sequences.

Conventional methods of cycle countingCycle counting is the process of reducing a complex variable amplitude load historyinto a number of constant amplitude stress excursions, that can be related to availableconstant amplitude test data. This is a necessary step, that needs to be carried out inorder to predict fatigue crack growth in components subjected to variable amplitudeloading. The method of cycle counting used often depends on the occurrences in theparticular sequence that are considered to be significant in terms of fatigue damage.Several cycle counting methods have been developed. The more commonly used

33


include rainflow, range, and peak counting. One of the most important considerationsin cycle counting is that the basis of the counting method needs to be compatible withthe understanding of the relevance of stress fluctuations to the fatigue process. Someof these methods are discussed below.

Rainflow counting The rainflow counting method derived its name from an analogyused by Matsuishi and Endo in their early work [1.68] on cycle counting. It has sincebecome a generic term that describes any cycle counting method that identifies closedhysteresis loops in the stress-strain response of a material subjected to cyclic loadingand represents the most accurate method for local strain type analysis. When used inconjunction with the predicted stress-strain response of a material, this method ofcycle counting provides insight into the effect of a given strain history on thematerial's response. When the stress-strain response of the material is considered, themean stress of the hysteresis loops can also be determined. A number of differentrainflow counting techniques can be identified that vary in principle from the originalrainflow method [1.69-1.71]. These include methods such as range-pair counting,hysteresis loop counting and ordered overall range counting.

Peak counting Peak counting can be implemented in a number of ways. These dependon how the significant events (load peaks) are counted. The method is based on theidentification of local maximum and minimum stresses or strains in the sequence.Positive and negative peak counting is implemented, for example, by counting positivepeaks above and negative troughs below zero which fall into prescribed increments.Using this technique implies that troughs which are negative peaks above or positivepeaks below zero are not taken into account directly.

Peak counting can also be implemented by setting a datum at the lowest stress in thesequence and counting only the positive peaks present. This method is known aspositive peak counting. This approach assumes that all minima occur at the datumlevel. This method will amplify small variations in stress and increase overallexcursions of stresses in the sequence. The distortion introduced by using positivepeak counting can be avoided by using net peak counting. To implement net peakcounting, peaks are measured from the preceding trough root, which is taken as thedatum. When the positive and negative peak counting method is used in conjunctionwith this method, the zero stress line is taken as the datum when it is reached.

In an alternative peak counting method, only one count of the highest peak, positive ornegative, is made between two successive zero crossings. This is known as the zero-crossing peak counting and ignores all peaks smaller than the highest between zero-crossings. This means that using this method will lead to considerable distortion of theoriginal sequence as significant load excursions may be ignore.

Range counting Simple range counting requires that only the stress or strain rangesbetween successive reversals are counted. This method can be used to recordinformation on the actual stress ranges that have occurred. However, it does not giveany information on the actual peaks unless the stress returns to zero between cycles. Indetermining the number of cycles in a sequence, if both positive and negative rangesare included, each range is assumed to form one half cycle. In this way positive and

34

Literature Review

negative ranges are paired to form complete cycles that are assumed to have the samemean. This method of cycle counting will not retain the sequence of stress variations.It may also be difficult to pair negative and positive ranges.

The difficulty of assuming a mean level in the simple range counting method can beovercome by also counting the mean value associated with each range. When rangecounting is implemented in this way it is referred to as range mean counting.

An alternative implementation of range counting is range-pair counting. Unlike simplerange counting and range-mean counting methods, range-pair counting is independentof the smallest variations neglected. Also, the inability to pair all ranges is removed asa count is not made unless the ranges pair. This means that the overall sequence maybe heavily distorted by using this method, although a great part of the sequence canalso be retained due to the pairing conditions.

Range counting is quite popular because it can easily be implemented to extract therequired load ranges from any known sequence. However, although range paircounting, for example, is capable of showing good agreement with total excursion ofthe original sequence by retaining a great part of the sequence as a result of the pairingconditions, it can also lead to loss of a considerable part of the overall sequence. Themain disadvantage of this counting method is that it can produce a large number ofsmall cycles for wide band sequences. Since fatigue damage is largely influenced bylarger fluctuations in stress, any analysis based on range counting may beunconservative for long-term fatigue damage assessment.

Level crossing counting This is a cycle counting method where a count is made whenthe load, stress, or strain in the sequence crosses a specified level. The stress axis ofthe sequence is divided into a number of increments as required. A count is made eachtime a positively sloped portion of the stress history crosses an increment locatedabove the reference level. Similarly, a count is made each time a negatively slopedportion of the sequence crosses an increment located below the reference stress level.The reference level can be arbitrarily selected, but when zero is used as the referencelevel it is known as zero crossing counting. Like the previous methods, the individualcrossings have to be combined to form complete cycles. In this way, the mostdamaging combination in terms of fatigue are obtained by first forming the largestcycles. Zero crossing counting is significant for offshore structures as it is used toestablish sea state statistics. It is also more conservative in terms of fatigue damage asit leads to the identification of large cycles.

Like other cycle counting methods, level crossing counting does not lead to a completereproduction of the original sequence and will lead to a misplacement of loadexcursions in the sequence. The implication of this is that the effect of a particularcycle, or half-cycle, may be incorporated into a fatigue damage analysis before itactually occurs. This is particularly relevant for the counting methods like rainflowthat aim to be more conservative by combining the most damaging fatigue cycles first.Where sequence effects are insignificant, this will have very few implications on theaccuracy of fatigue crack growth prediction. However, this is not always the case,

35


especially for offshore structures where sea state interaction effects are most likely tobe too significant to be ignored in any crack growth prediction model.

Theoretical methods of cycle counting Conventional cycle counting methods describedabove require the generation of the variable amplitude sequence of interest. This isusually a lengthy process, but it is not a problem when dealing with sequences used invariable amplitude fatigue testing programmes, as these are readily available for cyclecounting. This approach is, however, difficult to implement when dealing with serviceloading experienced by offshore structures in the North Sea, for example. The need tocalculate equivalent stresses under conditions like this, without a pre-knowledge of theloading sequence, leads to the development of fast assessment methods for use duringstructural integrity assessment procedures. These methods are not covered in detail inthis book, but the way they can be incorporated into a more robust methodology forfatigue crack growth assessment in offshore structures is presented and discussed inChapter 4 both for S-N and fracture analysis.

1.4.2 The fracture mechanics (FM) approachThe S-N approach has been used extensively to design welded connections foroffshore applications. This approach, however, has its limitations. One of the mostsignificant shortcomings of the method is that it cannot be used in assessing thestructural integrity of cracked tubular joints in service.

Fracture mechanics analysis is, at present, the most powerful and useful technologicaltool available for describing and solving fatigue crack problems. It is a simulation withcrack growth models for mechanical evaluation of the strengths of cracked bodies or thebehaviour of fatigue cracks. The practical use of FM has been established for use onlarge turbine and electric generator rotor components, atomic power generation, and theaircraft industry. Application areas in the offshore industry have also been identified andreported in the literature [1.72-1.74]. The use of FM in the analysis of structuralcomponents subjected to fatigue loading is increasing, in the offshore oil and gasindustry and other sectors. This trend will continue with increasing interest and advancesin structural integrity monitoring technology. Some of the existing FM models arediscussed in Chapter 4 and compared with experimental results. This section of the bookpresents basic concepts of FM analysis of cracked bodies.

1.4.2.1 Fatigue crack growth modellingIn the various practical uses of fracture mechanics, such as design life prediction andfailure analysis, fatigue crack propagation rates or curves in a particular environmentand operating conditions have to be determined. Often this relies on the use of FMfatigue tests to determine the values of certain material constants. Figure 1.12 shows thecharacteristic sigmoid shape of the do/dN versus AK curve [1.75] in logarithmic scale.This is the typical shape of this curve exhibited by crack growth in air. Unlike corrosionfatigue crack growth where the environment influences crack propagation mechanisms,crack growth in air is mainly governed by deformation-controlled mechanisms.

36

Fig. 1.12 Characteristic da/dN Vs AK curve [1.76]

The curve is characterized by three distinctive regions within which the fatigue crackgrowth rate exhibits distinctively different dependencies on the stress intensity factor(SIF) range, AK.

Region 1 is characterized by a rapid decrease in crack growth rate with decreasingcyclic plastic zone size. The behaviour of crack growth in this region is attributed totwo forms of resistance to crack growth, extrinsic and intrinsic resistance. Behaviourin this region is dependent on microstructural features and it is of considerableimportance in service components.

The rate of crack propagation in region 3 increases rapidly until fracture. This regioncorresponds to the onset of unstable and rapid crack growth and is characterized byeither the material's fracture toughness or, in the case of ductile materials, by plasticinstability. Environment has little effect in this region and deformation mechanismsare similar to that characteristic of monotonic loading.

Crack growth in region 2, on the other hand, has been described as a continuumprocess not strongly dependent on the microstructure. Region 2 is characterized bystable crack growth and can be described by the Paris equation

37

Literature Review


is the crack growth rate, AM is the SIF range, and C and m are material constants.

Cracks in region 2 have been observed to grow by the formation of striations thatrange in size from 0.05 to 2.5 micrometers [1.76, 1.77]. In 1962, Forsyth [1.78]suggested that striation formation was the result of a cleavage fracture ahead of thecrack tip, while other researchers suggested that the striations are formed as a result ofalternate blunting and sharpening of the crack tip during cyclic loading. Secondarymechanisms such as brittle intergranular or transgranular microfractures that result indiscrete growth increments, have also been observed [1.78].

This review on fatigue crack growth only cites early views that were proposed toexplain crack growth and the observed striations. There is abundant literature on crackadvance and crack propagation mechanisms in the literature on fatigue. This cannot bepresented here exhaustively, but it is important to note that fatigue crack growth inregion 2 forms the basis for linear elastic FM analysis. The majority of crack growth inengineering structures can be considered to lie in this region and may represent morethan 80 per cent of the fatigue life of tubular joints and welded connections.

1.4.2.2 Fatigue life assessment based on FMThe fatigue life of a welded tubular joint is characterized by the propagation of fatiguecracks. This has lead to what has now become common thinking that defects arealways inherently present in welded structures and that crack propagation represents asubstantial per centage of total fatigue life of welded joints. The use of the damagetolerant design philosophy for welded connections is, therefore, well accepted.

Fatigue life assessment based on FM involves calculating the number of fatigue cyclesrequired for a given increase in crack size. This is implemented by assuming a suitablecrack growth law such as the Paris equation. Using this technique the number offatigue cycles required to extend a fatigue crack from an initial depth ai to any depth afis given as

The stress intensity factor range, AK, is a parameter that expresses the effect of loadrange on the crack. It describes the stress field associated with the cracked body at thecrack tip. Y is the modifying shape parameter that depends on the crack geometry andthe geometry of the specimen.

In practice, calculations depicted in the above equations may be more complex, but thegeneral FM approach to fatigue life prediction will require: the selection of a suitablecrack growth law; the use of suitable crack growth material constants (C and m);

38

Literature Review

determination of the appropriate stress ranges, considerations for environmentaleffects; determination of stress intensity factors; and subsequent integration of theselected crack growth law for the applied loads.

This methodology can be heavily dependent on the nature of the load sequence used inthe analysis and whether a cycle-by-cycle approach is preferred in order to account forany sequence effects that may be present. This is discussed in greater detail inChapters 4 where the equivalent stress concept is linked to sea state spectra and usedto model interaction effects on fatigue crack growth in offshore structures. In thissection the main stages involved in any FM approach to fatigue crack growthprediction are reviewed.

7.4.2.3 Determination of SIFsThe concept of SCF becomes inapplicable in the analysis of stresses near the crack tip.This is due to the existence of a stress singularity. To overcome this problem, fracturemechanics relies on analysing the stress field in the vicinity of the crack tip, ratherthan the infinite stress due to the stress singularity at the crack tip. The nature of thisstress field depends on the mode of crack extension, loading, deformation, ordisplacement of crack faces.

Fig. 1.13 Modes of crack deformation or extension

Cracks are extended or deformed in one or a combination of modes. These includemodes I (opening mode), II (sliding mode), and III (tearing mode). These modes areshown schematically in Fig. 1.13. Mode I is characterized by tension normal to thecrack faces. It is the predominant mode for most practical applications. Modes II andIII tend to be less significant with negligible contributions to crack growth.

The SEF is the parameter adopted to describe the elastic stress field in a cracked bodyaround the crack tip for any given mode of crack extension. It is a function of appliedstress, the size and shape of the crack, and the geometry of the cracked component.For mode I, for example, it is given as

For surface cracks in engineering structures, various correction factors have to beused to account for boundary effects, crack shape, and loading geometry. The overallcorrection function, Y(a), may account for aspects such as a free front surface, finite

39


plate width, crack shape, a non-uniform stress field, presence of geometricaldiscontinuity, and effects arising from changes in structural restraint in thecomponent. A variety of solutions have been proposed to model this parameter butthese are not discussed in detail in this book. However, an illustration is given inChapter 4 on how it can be derived for tubular welded joints using flat platesolutions.

1.5 SummaryStress analysis and fatigue design of tubular welded connections have been reviewedin this chapter. Despite the availability of all the methods discussed for determiningthe stresses and SCFs in tubular welded joints, the method adopted for any particulardesign will depend on the constraints of time, cost, and the accuracy required.

Photoelastic methods have largely been superseded by finite element analysis (FEA).This is a potentially expensive technique, depending on the element formulation usedin the analysis and the computational time required for the accuracy needed. The useof strain gauge measurements on steel models is known to be the most reliable way ofdetermining SCFs. However, this method can be time consuming where detail isimportant for large number of specimens and it can also represent an expensive way ofcalculating SCFs.

The use of parametric equations, based on either acrylic models or FEA validated byexperimental results, can represent a very quick way of checking SCFs before anydetailed analysis is carried out. A summary of the recommended parametric equationsfor the sample joint geometry used in this book is shown Table 1.6.

Table 1.6 Recommended parametric equations for Y joints under OPB

LocationChord sideBrace side

WordsVV

EfthyVV

KuangX

X*

UEGVV

LRVV

KeyWordsEfthy

KuangUEGLR

UCLV

Vc

N/AX

X*

UCLVV

Wordsworth and Smedley equationsEfthymiou and Durkin equationsKuang equationsUEG equationsLloyd's Register equationsUCL Equations (HCD)Recommend the parametric equationRecommend the parametric equation - note equation isgenerally conservativeThere is no parametric equation for this load caseNot recommend the parametric equation,the acceptance criteria

since it fails to meet

The equation cannot be recommended since there are less than15 steel and acrylic joints in the SCF database

40

Literature Review

Parametric equations provide an expedient analysis route for obtaining SCFs.However, available recommended equations are only suitable for simple planar joints,and FEA may be required for more complicated three-dimensional geometriescommonly found in engineering structures.

Each set of parametric equations is limited in application in one of three ways. Thereare restrictions in the types of joint geometry that can be analysed using theseequations, restrictions on parametric validity range, and restrictions on the loadingconfiguration covered by any particular set of parametric equations. These restrictionsconstitute a limitation in the use of parametric equations to determine SCF in tubularwelded joints. As a result, the design of more complex joint geometries still requiresthe use of some form of FEA, since currently available parametric equations arelimited in applicability. Different parametric equations will yield results that vary inaccuracy, depending on the joint geometry and the validity range. However,consistency in the predicted results is also important. Recent studies [1.79, 1.80]concluded that when compared with other parametric equations, Efthymiou equationsand the Lloyd's design equations have considerable advantages in consistency andcoverage. Efthymiou equations also provided a better fit to the SCF databaseexamined when compared to the Lloyd's equations. Based on the SCF database, theLloyd's equations were found to be more conservative (41 per cent) than Efthymiouequations (19 per cent). The Efthymiou equations are recommended by the currentdraft ISO standard partly for this reason and also because they offer the best, or a verygood, option for the prediction of SCFs for all joint types. In addition they areapplicable to overlapped K and KT joints.

On the subject of fatigue design, the two approaches available are the S-N and the FMapproach. The S-N method relies on the use of available experimental data. However,due to the inherent scatter associated with the limited experimental data available,large factors of safety or reduction factors on fatigue life are still applied to giveconservative results and also to account for different factors that are known to controlthe fatigue performance of welded joints. Currently there is no guidance available onthe use of high-strength steels (ay >500 MPa), but as more reliable experimental databecome available, this method of fatigue design will also become increasingly morereliable and cost effective, even for use in the design of high-strength steelinstallations. This is demonstrated by the modification of the reduction factors onfatigue life as more data have become available to give less conservative estimates andnarrow down the largely unnecessary safety margins. These are often used due to lackof adequate understanding of the fatigue performance characteristics of a particularmaterial [1.81]. At the same time, as more material data become available, thepotential for using FM analysis for both design and also for structural integrityanalysis and inspection scheduling for offshore structures will gain more ground. Atpresent, fracture mechanics remains the most powerful and useful scientific tool fordescribing and solving fatigue crack problems. This is an important aspect for thisbook. The use of fracture mechanics and the different models available for the analysisof engineering structures subjected to variable amplitude fatigue will be discussed ingreater detail in Chapter 4.

41


Through this review it is apparent that one of the difficulties in trying to quantifyvariable amplitude corrosion fatigue is the large number of variables involved thatoperate together to influence fatigue crack growth at any one time. These variablesinclude: material properties determined by the alloying elements present; the nature ofthe corrosive environment determined by its chemical composition; and, additionalfactors such as flow velocity, temperature, pH, and degree of aeration, the magnitudeof cyclic loads applied, and also the loading frequency. These factors can, however, beadequately controlled in a laboratory to carry out tests under realistic loading andenvironmental conditions as described in Chapter 3. A considerable amount of data isnow available for fixed platform structural steels such as 50D. There are significantlyless fatigue data available on high-strength steels.

42

Chapter 2

Service Load Simulation

2.1 IntroductionJack-up platforms are self-elevating platforms that have conventionally been usedextensively in the North Sea to drill exploratory and production wells and for othershort-term offshore operations. As highlighted in Chapter 1, many of these platformsare now designed to operate in deeper waters as production platforms. The TPG 500production Jack-up design [2.1] and the production platform used for the marginal Sirifield [2.2] are examples. Their use as production platforms for marginal fielddevelopment means long-term deployment. This change of use increases the potentialrisk of eventual fatigue failure. Typical examples of fatigue failures are represented byincidents such as Ranger 1 (1979) where the mat/column connection failed due tofatigue 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 UKContinental Shelf (UKCS) is designed, in part, to minimize such risk of structuralfailure. It requires the owner or operator of an offshore installation to demonstrate thatall hazards, with the potential to cause an accident, have been identified and sufficientmeasures taken to reduce the risk to a level that is reasonably practicable. This riskmay be associated with potential material failure due to fatigue. As a result, bothmaterial selection for critical parts and in-service inspection are integral parts of therisk reduction process. This can only be satisfactorily achieved through adequateguidance. As highlighted in Chapter 1, however, fatigue design guidance for high-strength steels under sustained North Sea conditions is limited. There is, therefore, aneed for adequate understanding of their fatigue behaviour under realistic variableamplitude loading and environmental conditions.

In-service loading of offshore structures, such as Jack-up platforms, is mainly due towave and/or wind action with variable amplitude and frequency content. As Jack-ups

43


move into deeper waters fatigue loading becomes more sensitive to the dynamicresponse of the structure. This means that the effects of dynamics and structuralresponse become more important and must be modelled if realistic results are to beobtained.

It has since been recognized that predicted fatigue lives for offshore structures shouldbe confirmed by large-scale tests under simulated service loading. This providesimportant information on the crack growth mechanisms under realistic loading andenvironmental conditions. Such knowledge contributes significantly towards thedevelopment of appropriate design codes for use by offshore designers. It also enablesdesigners to assess the validity of the adaptation of the damage calculation procedureand for in-service integrity assessment.

This chapter covers the relevant methodology used [2.4] in the assessment of high-strength steels used in offshore structures. It looks at the influences on fatigueresistance of structural steels used in the construction of offshore structures such as aJack-up platform. The environmental loading and structural response interaction arediscussed and emphasis is placed on how the relevant factors were modelled toproduce the Jack-up Offshore Standard load History (JOSH). These factors especiallyinclude wave loading, Jack-up structural dynamic response, and the effect of acorrosive environment. As a benchmark for validating the analytical results presented,model results are compared with service measurements made on a typical Jack-upplatform operating at two different locations in the North Sea. This chapter alsopresents and discusses the advantages and disadvantages of previous simulated loadhistories and further emphasizes the significance of JOSH in the fatigue analysis ofhigh-strength steel Jack-up structures.

2.2 Fatigue loading in Jack-up structuresFatigue is the main source of structural degradation of offshore structures and this hasbeen the focus of many major research programmes. Fatigue is sensitive to manyfactors that may be different in each application area. As a result, previous researchexperience and understanding of the fatigue performance of conventional fixedplatform steels such BS 4360 50D and BS 7191 355D, which have been heavilyresearched, cannot be easily extrapolated to predict the behaviour of high-strengthsteels. In order to increase the understanding of the fatigue performance of these steelsunder realistic service loading conditions, it is important that the relevant factors thatinfluence their performance in service are identified and included in the analysis.

Jack-up platforms exhibit non-linear dynamic response in different sea states and canbe 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 formoving from one location to another can be very important.

This led to the proposal [2.5] that transit loads should be included in any simulatedservice load history. Four simulation options were envisaged, as shown in Fig. 2.1.The most suitable simulation option for production Jack-up platforms containstransportation loading at the beginning of the loading sequence. This is relevant to

44


Jack-ups used for production since it is representative of a situation where thetransportation loads are experienced by the structure while it is towed to theinstallation site.

Fig. 2.1 Options for simulating transit loading in Jack-ups

Fig. 2.2 Wet transport of a self-propelling Jack-up

45


Fig. 2.3 Dry transport of a Jack-up using a low loader

Data on typical transit loads experienced by Jack-up platforms are very limited as thisdepends on the method of transportation to the installation site. Figures 2.2 and 2.3show typical Jack-up transportation modes. Self-propelling Jack-ups are transported asshown in Fig. 2.2, whereas dry toe is implemented by transporting the Jack-up on acarrier, as shown in Fig. 2.3. In both cases the Jack-up rig legs may be fully elevated,as shown in Figs 2.2 and 2.3. Depending on the weather conditions and the turbulenceof the sea, large bending moments can be induced on the legs during transportation.For production Jack-ups, this would represent only a small per centage of total fatiguedamage experienced by the structure during its design life, except under circumstanceswhere transportation loads are severe enough to cause leg failure or plasticdeformation. This type of loading is, however, difficult to quantify for inclusion in atypical load history for a production Jack-up.

The characteristics of fatigue loading under service conditions that apply to offshorestructures such as Jack-up platforms, are dependent on three broad categories ofinfluences: the wave loading regime, structural features, and environmental conditions.These features are covered in detail in this chapter with an illustration of the analysisprocedure using a Jack-up platform.

46


2.3 Review of previous loading modelsFatigue testing of specimens and structures started in the mid-19th century, asdemonstrated in a comprehensive review on fatigue [1.38]. Codification of theresulting data can be said to have started around the 1850s, when Wohler carried outhis now classic experiments that lead to the determination of S-N curves. Repeatedloading tests were carried out and laboratory testing of specimens continued since thenthrough the 1920s and 1940s, resulting in the accumulation of a considerable amountof empirical data.

By the mid-1950s, which is considered by most as the beginning of the era of modernfatigue testing, three main trends had emerged. These included structural fatiguetesting, fatigue crack growth testing, and the development of design codes from thedata available.

Research work on fatigue behaviour of different structures continued. The Comet jetairliner accidents of 1954 had a very significant effect, since they stimulated extensivefatigue testing of aircraft structures. With the development of servo-hydraulicactuators and microprocessors, the whole art of fatigue testing entered a new phase.This saw an era with the potential for testing structural components by applyingincreasingly complex loads. Since then, the ultimate aim has been to simulate serviceloading conditions and to conduct fatigue tests under realistic service loadingconditions.

The objective then, as it is today, was to produce standardized load histories intendedfor use in fatigue testing. Conducting tests under simulated service conditions allowsfor comparison of results obtained from different laboratories across the world. Thisalso supports the provision of guidance for laboratories undertaking the tests. Thiscontributes tremendously to increasing the general understanding of variableamplitude fatigue testing and the development of prediction methods for fatigue crackgrowth analysis.

The development of standardized load histories for fatigue testing of offshore structuralcomponents had progressed rather slowly and had not received great attention untilfairly recently. On the other hand, standardized load spectra were developed for theaircraft and automotive industries in the late 1960s. By the early 1970s aircraftcomponents were being tested using standardized load sequences. A well knownexample is FALSTAFF (Fighter Aircraft Loading Standard For Fatigue) [2.6].

Attention was turned to the development of standardized load histories for testingwelded offshore tubular structures in the early 1980s and through into the 1990s. Thisperiod saw the development of the COLOS (Common Load Sequence) for theEuropean Coal and Steel Community Research Programme II [2.7] and the associatedC-12-20 series, the double peaked spectrum, developed for UKOSRP [2.8], theHart/Wirsching algorithm [2.9, 2.10], and the WASH (Wave Action Standard History)sequence [2.11]. Some of these models, including their advantages and disadvantages,are covered in greater detail in this section, highlighting the main differences betweenthese models and the JOSH model.

47


2.3.1COLOS/C-12-20 seriesCOLOS was developed for the European Coal and Steel Community ResearchProgramme III. This sequence, and the associated C-12-20 series, represent a singlenarrow band stress spectrum with constant RMS. The overall spectrum was built upusing seven stationary Gaussian spectra of different RMS values. All stationaryspectra were stepped by about 5 per cent of the peak load in order to produce a randomdistribution of peaks. This type of load history has peaks that can be defined by aRayleigh distribution.

The main drawback with COLOS is the fact that only the forcing loads are taken intoaccount, while dynamic effects are ignored. For structures operating under conditionswith significant resonance effects, COLOS was not representative of real-life loading,and the frequency control was far from accurate. This type of spectrum would,therefore, not be appropriate for use in the variable amplitude corrosion fatigue testingof Jack-up steel tubular joints since the frequency content under realistic conditions isvery important.

2.3.2 UKOSRPII double-peaked spectrumThis double-peaked spectrum was developed for random load fatigue testing in theUKOSRP II. It was based on data obtained from the Forties Bravo platform and otherrelevant data. The UCL double-peak spectrum and the frequency content of theresulting load history was represented by the double-peak power spectrum. Like theCOLOS/C-12-20, this sequence did not completely model the realistic load history,since it was based on a single stormy sea state, and some features that could berepresented by other sea states were missing. The resulting time history from thisspectrum could be pseudo-random, since a suitable pseudo-random generator wasdeveloped at UCL using a binary shift register. However, this sequence did not modelthe long-term variation in sea state RMS and, therefore, was not representative of real-life wave-induced stress history. As a result, it could not be used directly for thefatigue testing of Jack-up steels without introducing the necessary modifications thatwould allow for Jack-up specific response characteristics to be accounted for.

2.3.3 Hart/Wirsching algorithmThis was the most sophisticated simulation of North Sea stress histories available inearly 1986 that modelled the long-term variation in sea state RMS. It was amodification of the fatigue loading spectrum, proposed by Wirsching, to produce aspectrum similar in appearance to the long-term stress history of deep-water structures.This was based upon the original relationship proposed by Wirsching and given as

48


where o(f) is the stress spectral density function expressed as a function of wavefrequency, f. The natural frequency of the structure is given by fn and £ is the dampingfactor while A and (p are scaling factors. Hs is the significant wave height of a wavewith dominant period TD.

For this spectrum the three lowest sea states for the original spectrum were omittedand the highest three were combined. The long-term random history was simulated byuse of a discrete Markov chain model that allowed the sequence of sea states to beadequately modelled. A realistic sequencing of sea states represented the majordifference between this model and previous models that relied on using power spectrabased on the extreme stormy sea conditions.

2.3.4 WASH sequenceThe Hart proposal was, by the end of 1986, the most realistic simulation for the fatiguetesting of offshore structures. Around this same period, research work undertaken todevelop WASH was in progress.

The basic philosophy of the WASH model [2.11-2.13] is the same as the Hartproposal but there are three main features that are unique to the WASH model.

The signal generation mechanism in WASH was designed as a 'standard'. Therandomness in the generated load history was produced using the pseudo-randombinary sequence technique (PRBS). The duration of each sea state was also taken intoaccount. This was achieved by defining a state transition matrix containing theprobabilities for each sea state to move up or down one state, or to remain at thecurrent state. This makes the modelled sea state sequence a more realistic andconsistent simulation of the monitored service behaviour.

2.4 The JOSH modelThe WASH model is the state of the art in the simulation of realistic service loadingfor fatigue testing of fixed offshore structural materials. However, it cannot be applieddirectly to Jack-ups, since resonance effects tend to dominate the power spectraldensity (PSD) functions for typical Jack-up platforms [2.14].

The main differences between these two models is that the JOSH takes into accountthe dynamic response characteristics of the more dynamically sensitive Jack-upplatforms. It also relies on the use of a representative combination of sea state dataobserved in service from a typical Jack-up site in the North Sea. The Jack-up structuralresponse data, used in the generation of JOSH, were also modelled and validated withdata obtained from service measurements.

2.5 Generation of JoshThe JOSH model, like the WASH model, relies on the use of advanced simulationtechniques to generate the realistic loading history. These include the Markov chaintechnique for simulating the random sea state sequence, and the pseudo random binarysequence technique (PRBS)for simulating the stationary random load history for eachsea state. Both these techniques and their implementation are discussed below.

49


2.5.1 PRBSThe random load history, within the duration of any particular sea state, is generatedfrom the corresponding power spectral density function for that sea state. Fourdifferent methods can be used in this process. These include: the random rangegenerator; the Markovian load range generator; Fourier summation random walktechnique; and PRBS. The last method was used in the WASH framework and thesame procedure was adapted for the development of JOSH. This has the advantageover other methods in that it makes use of a shift register of a certain length. Althoughonly discrete frequencies occur in the pseudo random binary signal generated in thisway, they are so closely spaced that the characteristics of broad band random loading,typical for offshore structures, can be preserved. This superior frequency control is themajor advantage of this technique since this is very important for corrosion fatigue.

The detailed procedure used in implementing this technique is not given in this book.Further details can be found in [2.15]. In its mathematical form it relies on usingoutput points from a shift register that is filtered through a filter function, hx(T). Thiscontains weights that are used to amplify the desired frequency content for any givensea state PSD function. In order to reproduce any relevant loading characteristics fromany particular PSD function, the filter function is taken as the inverse discrete Fouriertransform of the transfer function, Hx(f), obtained from the white noise spectrum,SE(f), relevant to the PSD, Sx(f). This is expressed as

The second step involves the generation of the filter function that is given in theangular frequency domain as

The white noise signal generated by the shift register is then finally filtered to give therequired loading history, nx(t), such that

This method gives very good simulation for any given power spectrum. Previousstudies have also shown that the feedback loop size does not show any significanteffect on either the sequence root mean square value or the weighted average stressrange ratio. It, therefore, offers a considerable advantage over other simulationtechniques, not only in reproducing the frequency content of the power spectrum, butalso in maintaining the long-term statistics so that they are representative of the PSD.

2.5.2The Markov chain techniqueThe Markov chain is used in reproducing the long-term sequencing of a combinationof naturally occurring sea states. For offshore applications, the long-term distribution

50


of naturally occurring sea states can be analysed as a stochastic process, thecharacteristics of which are determined by the long-term probability distribution of seastates. For example, suppose this process {Sn,n = 1,2,3...} takes on a finite orcountable number of possible values, then each value can be considered to be adefined state. For offshore applications these defined states may consist of a range oftypically occurring sea states characterized by their probability of occurrence andmean zero crossing period. Such data are commonly available for typical sites and areoften presented as scatter diagrams. If at time n, Sn=i, then the process is said to be instate i. However, whenever the process is in state i, there is always a chance orprobability Pij that it will move to state j such that

for all states i0, i1, i2, . . . in, i, j and for all n>0. This type of stochastic process is knownas a Markov chain. It can be used in the implementation of service load simulation forany engineering structure, as long as the individual states are defined. The value Pij

represents the probability that the process will make a transition from state i to state j.Considering that probabilities are non negative and that the process must make atransition from one state into another, the following conditions will always beapplicable

Based on this representation, a state transition matrix can be defined that contains theprobabilities for each state to either move up ( j= i+1) or down (j=i-1) one state, orto remain (j=i) in its original state. For offshore applications, the occurrence ofindividual sea states does not affect the long-term probability distribution of all the seastates. As a result, it can be stated mathematically that

Where H(n) is a matrix containing the probability of occurrence of each sea state aftern transitions. Ti is the transpose of the Markov chain matrix that allows the statetransition matrix, after a large number of transitions, to represent the long-termprobability distribution of sea states, such that

The state transition matrix is obtained from the individual sea state characteristics,such as the significant wave height and their average duration, represented by discreteapproximations of their exponential conditional distribution.

51


2.6 Jack-up dynamic responseCategories of influences for the fatigue performance of structural steels used in theconstruction of offshore structures have been identified. These include wave loadingregime, structural features, and environmental conditions. The way these features canbe modelled to produce realistic results is presented in this section. The methodologyused to ensure that the above factors, or influences, are accounted for is discussed.

2.6.1 The transfer function approachFigure 2.4 shows a typical Jack-up platform. Figure 2.5 shows a simplified Jack-upmodel. Detailed mathematical modelling was carried out to investigate the behaviourof this theoretical model under wave excitation. As a benchmark for comparison ofresults, modelled results have been compared with service measurements carried outon a typical Jack-up platform operating at typical North Sea sites [2.14, 2.16]. Themethodology used to determine model response is presented here.

Fig. 2.4 Typical Jack-up platform

52


Fig. 2.5 Simplified model of Jack-up platform

It is important at this stage to distinguish between dynamic loading and dynamicresponse. Dynamic loading varies with time and/or direction. Dynamic response,which results from this, depends on the stiffness, mass, and overall damping of thestructure. Both of these affect the transfer function given as

where H ( j w ) i s the complex transfer (or receptance) matrix. It is important to considerthe physical interpretation of the transfer function matrix. Each element H(ij) relatesthe deflection in freedom i on the structure due to an excitation force in freedom jwhen all others are unrestrained and unforced

For random loading such as that experienced by offshore structures, the response ineach of the n degrees of freedom may be calculated as

53


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.

Fatigue loading in offshore structures is such that many forces on the structure arecaused by the same basic wave and wind action. This implies that the cross-correlationfunctions will not be zero. However, analysis that superimposes responses in such away that the cross correlation functions and hence the cross spectral densities areassumed negligible leads to satisfactory and conservative estimates. Using thisapproach gives the following simplified equation

This is a realistic approach and represents the effect due to each individual randomforce. When applied directly to an offshore structure, with a well-defined transferfunction H(f), which is a summation of the overall nodal effect for the n degrees offreedom, together with a relevant forcing spectrum Syy(f), a representative responsespectrum, Sxx(f), of the structure can be obtained thus

This approach, depicted in Fig. 2.6, yields a frequency domain solution that can betransformed into a time sequence using the approach [2.17] presented in Section 2.5.The time domain is the more useful form for fatigue testing of offshore structures. Forthe work presented in this book, it was important that a representative Jack-up transferfunction was obtained. To ensure this, results obtained by analysing the model werecompared with data obtained from in-service field measurements. The model transferfunction agreed very closely with the service data obtained for the same Jack-upoperating at two different sites in the North Sea. The following sections present theway the important parameters that affect the dynamic response of Jack-ups wereaccounted for in the analysis. An alternative approach, based on a direct integration-type analysis to obtaining a generalized representative spectrum, was also considered.This method was not studied further because it was thought that the approximationerrors were significant and did not reproduce service conditions adequately.

54


Fig. 2.6 Schematic illustration of the transfer function approach

2.6.2Modelling of structural parametersThe characteristics and influences of fatigue loading that apply to offshore structures,such as Jack-up platforms, have already been highlighted. In order to obtain realisticresults it is important that these effects are adequately modelled. The importance of thewave-loading regime used in the analysis is discussed in greater detail in Chapter 4.This section of the book covers the effects of structural features and how these can bemodelled to generate representative results. Consideration of a typical in-service Jack-up platform, used as a benchmark to validate model results, is a necessary startingpoint for the analysis and this is introduced in this section.

2.6.2.1 Study of an in-service Jack-up platformThe in-service Jack-up considered for comparison and validation of results is theMaersk Guardian. This Jack-up was built in 1986 and is owned by Maersk Drilling. Itis an independent three-legged, self-elevating, cantilever Jack-up with a leg length of156.77 m. Its legs are triangular and it can operate in a maximum water depth of about106 m. The Maersk Guardian has an electric rack and pinion jacking system. It has anhelideck just over 25 m in diameter with a refuelling system of 14440 gallons andprovides accommodation for ninety-four persons [2.18].

55


The Maersk Guardian Jack-up platform has features that are representative of a widerange of Jack-up platforms deployed in the North Sea and worldwide. Acomprehensive structural measurement programme was carried out on this platformduring the winter of 1988-89 in the southern North Sea (Silver Pit) [2.14] and duringthe winter of 1990-91 in the central North Sea (Ekofisk complex) [2.16]. Due to theavailability of these service data, the Maersk Guardian Jack-up platform was selectedas a benchmark for comparing modelled structural response characteristics withservice measurements made on a typical Jack-up under wave excitation in the NorthSea.

The most important parameters determining dynamic effects of a structure are: (1)excitation frequency; (2) natural frequency; (3) effective mass of structure; (4)effective stiffness of structure; and (5) the overall damping of the structure.

The first parameter depends on the nature of the excitation spectrum and is discussedin Chapter 4. The second parameter is a function of the third and fourth. The nature ofa structure's complex transfer function depends on all these parameters. The last threeare of particular interest as they represent physical properties of the structure. Theseare covered in greater detail in the following sections.

2.6.2.2 Effective mass of structure and mass matrixThe mass matrix was modelled by considering the details of structural mass and itsdistribution. This included the topside mass (or deck mass) and the distribution ofmass per unit length of legs. These details were obtained from the Maersk companyand represented typical structural data on the Maersk Guardian Jack-up platform. Theactual values are not given in this book because of confidentiality.

An important addition to the normal structural mass, the added mass, was alsoconsidered. Because of the uncertainty, and variability, of the increase in massresulting from marine growth, the effect of increase in mass due to marine growth wasnot modelled. This is assumed to be negligible compared to the overall mass of atypical Jack-up platform.

The added mass was, therefore, taken to consist of two components: (1) mass of watercontained within the submerged part of the structure, Mam and (2) mass of externallyentrained water, Mem.

These components were determined using the method of equivalent Jack-up legsections. This relies on using an equivalent cylindrical leg section, which has the samestructural and hydrodynamic properties as the actual Jack-up legs. Using thisapproach, the two components of added mass were obtained as follows

56


Cm, is the mass coefficient of the structure. This was taken as 2 for this analysis. Thisvalue was based on information supplied by the Maersk Company on the MaerskGuardian Jack-up. The density of seawater is p and a is the equivalent radius.

2.6.2.3 Stiffness of structure and stiffness matrixThis was derived from the generalized stiffness matrix, based on the equivalent legstructure, with coupled springs at the relevant nodes to model the effect of legstructure-soil interaction. The details of the approach adopted in selecting the stiffnessof the linear springs used in the model are presented in Section 2.6.3.

2.6.2.4 Damping of structure and damping matrixThe overall damping of the structure was considered to have two contributingcomponents, namely structural damping and hydrodynamic damping.

Structural damping is difficult to determine and cannot be determined analytically.However there are documented values and typical values for spring steel, for example,range from 0.4 per cent to 0.8 per cent [2.17].

Hydrodynamic damping is also important and the methodology used is based onobtaining damping due to motion in-line with the flow. Hydrodynamic damping isnon-linear and complete modelling requires non-linear analysis. However,linearization yields satisfactory results for large structures under the action of smallwaves. This is more applicable to inertia, rather than drag dominated loading. Non-linear effects are more severe in the latter.

The damping matrix, used in this analysis, was obtained using Rayleigh dampingcoefficients, the first two natural modes of vibration and a damping ratio of 4 per cent(Silver Pit location). Previous research [2.19] has shown that estimates of dampingcalculated using the spectral peaks and the half power bandwidth method range from 2per cent to 5 per cent over a wide range of representative sea states.

2.6.3 Modelling of soil-structure interactionSoil structure interaction is a very important aspect in Jack-up dynamic response andthis area has and continues to attract a lot of research interest [2.14, 2.16, 2.19, 2.20,2.21, 2.22, 2.23, 2.24]. A site assessment is recommended in order to determine thesoil properties. Even after a site assessment the values obtained are subject tovariability, and it is common practice to consider a parametric study to ensure that theworst combination of values are chosen to produce conservative solutions.

There are two established methods for modelling the soil to study the problem of soil-structure interaction. One of these relies on the use of a finite element approach. Thismethod is more expensive but has the advantage in that, variation of soil propertieswith depth can be analysed.

The second approach relies on the use of a lumped mass model. For this method, thefoundation is assumed to be rigid, and the springs representing the soil are assumed toperform as uncoupled elements. This method is satisfactory and is the more popular

57


approach used in modelling soil structure interaction. Based on this approach,formulae have been derived using elastic theory, which relate spring constants to theshear modulus, G, and Young's Modulus, E of the soil. The derived formulae arebased on the spring constant of a rigid circular base on an elastic half space and givenby

Kv, Kh, K0, and K0 are the vertical, horizontal, rotational, and torsional stiffnessesrespectively, v is Poisson's ratio and R, the radius of circular base. This can be takenas the spud-can radius.

The second approach was adopted for this analysis. The horizontal and rotationalsprings were considered sufficient to model the soil structure interaction. Poisson'sratio is known to vary between 0.3 for dry granular soils to 0.5 for soft saturated clays[2.17]. It is also known that any errors caused by using a value of Poisson's ratio equalto 0.5 for all calculations is small compared to other uncertainties. This is becausethere is very little variation as the Poisson's ratio changes from 0.1 to 0.5. This trend isshown in Figs 2.7 and 2.8. The variation of vertical and horizontal stiffness withPoisson's ratio is shown in Fig. 2.7, while the effect of Poisson's ratio on the rotationalstiffness is shown in Fig. 2.8. In both cases the sensitivity of stiffness to changes inPoisson's ratio between 0.1 and 0.5 is minimal.

58

Fig. 2.7 Variation of vertical and horizontal stiffness with Poisson's ratio

Fig. 2.8 Variation of rotational stiffness with Poisson's ratio

Some of the in-service results used in the validation of the model were measured onthe Maersk Guardian Jack-up while at the Silver Pit location. This site has a sandy soilstructure. A Poisson's ratio of 0.4 was considered representative of the soil type.Quoted values of Young's moduli for different soil types are given in reference [2.17]and the value assumed for this analysis is typical of loose sandy soil that lies in therange of 40 MPa to 80 MPa.

59



2.7 Modelling of wave loadingIn-service loading of Jack-ups is mainly due to wave and/or wind action; these aredynamic in nature. More generally, dynamic loading is all loading that has anappreciable variation with time. For many design purposes, it is adequate to considervariable loads in terms of an equivalent static load. The validity of such an approachdepends on two main factors. The first factor is the form of the structure and thesecond is the nature of the load.

The design wave approach is based on this methodology and is applied by defining awave, of large height and period range, whose probability of occurrence is such that itrepresents the maximum wave that the structure will encounter within the returnperiod. This approach is only realistic from the viewpoint of designing against staticstructural failure due to a large wave, and does not permit fatigue damage to beconsidered within the design. The design wave approach is not satisfactory for smallerwaves with excitation frequencies that can lead to structural resonance.

Another approach is based on a design to a statistical wave description. In thisapproach, the occurrence of waves incident on the structure is expressed in terms of aprobability of occurrence of waves with specific wave heights, periods, and directions.This method allows for adequate characterization of fatigue-inducing loads. It relies,however, on the linearity of superposition of wave components.

Due to a combination of the form of the Jack-up structure and the nature of the loads itexperiences in service, any analysis using an equivalent static load, without taking intoaccount the variability in the service loads, would be unrepresentative. Themethodology used here is a frequency domain analysis, using spectral densityfunctions and the transfer function approach. The main reasons for using this approachare: (1) the successful use of wave power spectra to describe water surface elevation;(2) the existence of short periods, during which wave statistics of the random sea maybe stationary (sea states); (3) the ease of handling non-linear effects; and (4) theresulting physically interpretable solution.

Considerable research work has been done on modelling ocean waves. Some of thebetter-known, one-dimensional wave spectra that have been developed to describeocean waves include the Bretchneider spectrum, JONSWAP spectrum, Pierson-Moskowitz (PM) spectrum [2.25], and the modified version of the PM spectrum. Themodified PM spectrum was chosen for the study presented in this book and a newlymodified version of the spectrum is given in Chapter 4. The PM spectrum was adoptedby several design codes and it has been successfully used to analyse threaded tensionleg platform tethers in the North Sea [2.26]. It expresses the wave PSD, Syy(f), as afunction of significant wave height Hs, mean zero crossing period Tz, and wavefrequency f, such that

60


This spectrum is based on extensive oceanographic data, and has been adopted as themost 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.This method of analysis relies on the use of the transfer function approach. Thismethod was preferred over the alternative method, based on the linear wave theory,and a direct integration-type analysis.

The main advantage of this approach is that it allows for a site-independent transferfunction to be determined. The transfer function can then be subsequently used toobtain the response spectrum, which can be transformed into a load history in the timedomain.

Fig. 2.9 Comparison of measured wave spectrum at Silver Pit with modified PMspectrum

61


Fig. 2.10 Comparison of measured wave spectrum at Ekofisk with modified PMspectrum

However, using this approach directly with the PM spectrum, as given above, can leadto an inaccurate representation of the frequency content of the generated time history.This is due to the fact that most of the wave energy in wave spectra measured attypical Jack-up sites is concentrated at frequencies slightly higher than that predictedby equation (2.21). This peak frequency effect is shown clearly in Figs 2.9 and 2.10for data obtained from the Silver Pit and Ekofisk locations, respectively.

A peak frequency correction parameter, B, was, therefore, incorporated into the PMspectrum to account for this effect, giving an alternative form of equation (2.21) as

Equation (2.22) is more accurate and yields a wave energy spectrum closer to themeasured spectra for both locations used in this study. The relationship between B and thepeak frequency of the wave energy spectrum is a linear one. It is a site-dependentparameter and its magnitude depends on sea state parameters, such as the significant waveheight and the mean zero crossing period. The values of B for the Ekofisk and Silver Pitlocations were found, using a curve fitting method, to be 0.016 and 0.044 respectively.

2.8 Selection of sea statesThis section introduces a study of the environmental influences on the stress PSD andhighlights the importance of using representative sea states, and modelling the effectsof the corrosive environment, to study the variable amplitude corrosion fatiguebehaviour of high-strength Jack-up steels.

62


A detailed examination of oceanographic data for the North Sea, observed over aperiod of five years, has shown that the distribution of significant wave height, Hs, ismore accurately described by the Gumbel distribution. The Gumbel distribution isgiven as

where P(x) is the exceedance of the variable x.

Observed sea state data was found [2.11] to be well fitted by the following expression

The associated mean zero crossing period Tz for a wave of significant height Hs isgiven as

This modelled distribution agrees very closely with sea state data, observed at typicalJack-up locations in the North Sea. The sea states used for the JOSH model arepresented in Table 2.1.

Table 2.1 Summary of sea states used for JOSH

Sea state number

123456789101112

Significant waveheight (m)

1.251.752.252.753.253.754.254.755.256.257.258.00

Mean zero crossingperiod (s)

5.55.96.26.56.87.17.47.77.98.48.99.2

63


2.9 DiscussionThe Jack-up transfer function H(f), used to generate the response spectrum, Sxx(f),was obtained using the procedure outlined in Section 2.6.1. As shown in Figs 2.13 and2.16 there is a very close match in the model and service transfer functions for 4 percent and 5.5 per cent damping, respectively, using data obtained from the Silver Pitand the Ekofisk complex in the North Sea. The sensitivity of the normalized transferfunction to changes in damping is not very high, as seen in Figs 2.11-2.13 for the dataobtained from the Silver Pit location. The corresponding results for the Ekofiskcomplex are shown in Figs 2.14-2.16.

Fig. 2.11 Model and measured service NTF for the Silver Pit location with 2 per centdamping

64


Fig. 2.12 Model and measured service NTF for the Ekofisk complex with 2 per centdamping


65


Fig. 2.14 Model and measured service NTF for the Ekofisk complex with 4 per centdamping


66


Fig. 2.16 Model and measured service NTF for the Ekofisk complex with 5.5 per centdamping

Peak frequency matching of the transfer functions was carried out by varying thestiffness of the rotational and translational springs used to model the effect of leg-foundation interaction. For this investigation three cases were studied: fixed, pinned,and model, based on a rotational and translational spring system.

A rotational spring stiffness of 5.576xl010Nm/rad was seen to give the best agreementbetween the service and peak frequency of about 0.24 Hz for the data obtained fromthe Silver Pit location, as shown in Fig. 2.13.

For the data obtained at the Ekofisk complex, a rotational spring stiffness of2.365xl010 Nm/rad was used, together with a damping ratio of 5.5 per cent. Both thesevalues compare very well with those presented in references [2.14] and [2.16],respectively. In reference [2.16] a similar approach was used with values of2.7xl010Nm/rad for rotational stiffness and a mean damping ratio of 5.5 per cent. Thisvalue was obtained with a standard deviation confidence range of 1.2 per cent,implying that the most likely damping estimates were between 4.3 and 6.7 per cent.This is confirmed by the model results obtained for this study for both cases with 4.0per cent and 5.5 per cent damping for the Silver Pit location and Ekofisk complex,respectively.

The service transfer functions were obtained, in each case, from the measured waveelevation and response spectra for each site considered. These are shown in Figs 2.9and 2.17 for the Silver Pit location and in Figs 2.10 and 2.18 for the Ekofisk complex.Figures 2.9 and 2.10 show the measured wave elevation spectra for the respectivelocations compared with those predicted by the PM and modified PM spectra. The

67


measured service response spectra for the Silver Pit and Ekofisk locations are shownin Figs 2.17 and 2.18, respectively.

Fig. 2.17 Measured service response spectrum at the Silver Pit location

Fig. 2.18 Measured service response spectrum at the Ekofisk complex

68


Using these spectra it was possible to obtain the corresponding service transferfunctions for the two sites. These were compared with service transfer functionspredicted by using the PM spectrum with a peak frequency correction. Thiscomparison is shown in Figs 2.19 and 2.20 for the Silver Pit and Ekofisk locations,respectively.

Fig. 2.19 NTF for measured and modified PM spectra for Silver Pit

Fig. 2.20 NTF for measured and modified PM spectra for Ekofisk complex

69


The agreement in the NTFs is especially good for frequencies higher than 0.1 Hz.Below 0.1 Hz the discrepancy in the transfer functions was greater. This effect iseither due to inaccuracies in measuring the energy of the ocean waves at very lowfrequencies, and/or as a result of non-linear effects.

It was observed that the effect of the translational spring constant on the transferfunction is negligible. This is illustrated in Fig. 2.21, which shows that the modeltransfer function is identical for cases 2 and 3 using identical rotational springs. Theoverall effect of varying the rotational spring stiffness on the NTF is shown in Fig.2.22. This figure also shows that, as the spring constant is increased, the normalizedtransfer function for case 2 approaches that for case 1 as expected.

Fig. 2.21 Effect of rotational and translational stiffness on the transfer function

70


Fig. 2.22 Convergence of transfer function to fixed case

A sensitivity analysis was carried out to quantify the effect of water depth on themodel transfer function. Results obtained from this study show that the nature of thetransfer function is very sensitive to the operating water depth. For the Silver Pitlocation, the results obtained from the sensitivity study on the rotational transferfunction (RTF) are shown in Fig. 2.23. Overall, the magnitude of the rotationaltransfer function was found to increase exponentially with water depth, as shown inFig. 2.24.

71


Fig. 2.23 Effect of water depth on rotational TF

Fig. 2.24 Sensitivity of rotational TF to water depth

72


The results obtained on the sensitivity of the translational transfer to changes in waterdepth are shown in Fig. 2.25. Figure 2.25 also shows that the effect on the magnitudeof the translational transfer function is less severe as the water depth is increased. Forthe rotational transfer function (RTF), a 5 per cent and 30 per cent increase in waterdepth lead to about 25 per cent and 250 per cent increase in the magnitude of RTF,respectively. The effect of increasing water depth on the TTF, on the other hand, is notas significant as the effect on the rotational transfer function. This is shown in Fig.2.26. It can be seen from this figure that the TTF exhibits an approximately lineardependence on water depth. An equivalent increase in water depth of 5 per cent and 30per cent only leads to an increase in magnitude of about 9 per cent and 45 per cent,respectively.

Fig. 2.25 Effect of water depth on TTF

73


Fig. 2.26 Sensitivity of TTF to water depth

It was observed that, although the magnitudes of the rotational and translationaltransfer functions increase with depth at different rates, they are equivalent whennormalized for any particular water depth. In a similar manner, normalizing the PSDpreserves the frequency content of any resulting time history, but allows for themagnitude of the peaks to be varied, as required, by applying a suitable scaling factorto meet the needs of any testing conditions. This is the best way of varying the testingtime for a particular joint, instead of altering the frequency content of the load history,which is important for corrosion fatigue behaviour of offshore structures.

74


Fig. 2.27 Measured and model PSD for the Silver Pit Location

Fig. 2.28 Measured and model PSD for the Ekofisk complex

The response spectra, used to generate JOSH, were based on the model transferfunction and the modified PM spectra for the different sea states used. In a similarmanner the predicted response spectra for the Maersk Guardian Jack-up platform atthe Silver Pit and Ekofisk locations were compared with those measured at the

75


respective locations. Figures 2.27 and 2.28 show this comparison. The overallprediction of the distribution of energy across the frequency range of interest in bothcases is good. However, there are slight discrepancies in both cases, possibly due to acombination non-linear effects, that are not accounted for in the model, and noise inthe measured data.

2.10 SummaryThis chapter has introduced, and discussed, the relevant analytical work that wascarried out to ensure that realistic results are obtained for this study. The influences onfatigue resistance of structural steels used in the construction of a typical Jack-up legstructure have been presented. The methodology used for the work presented in thisbook to model these relevant influences, has also been presented. This chapter hasintroduced and discussed the results of a comparative study between model andservice data and demonstrated the level of agreement between the two sets of data.

Further details of JOSH are presented in Chapter 3, together with the large-scalefatigue testing programme undertaken in this study using the simulated sequence.

76

Chapter 3

Large-scale Fatigue Testing

3.1 IntroductionFatigue tests on large-scale tubular welded joints have been performed, for manyyears, to characterize the fatigue behaviour of steels used offshore. Conducting thesetests can be very expensive. The expense is justified on the grounds that crack growthbehaviour in tubular welded joints is complex and cannot be reproduced by conductingtests on simple welded specimens.

A large number of these tests have been conducted on conventional fixed platform steelssuch as BS 4360 50D and BS 7191 355D. However, in recent years, there has been asteady increase in the use of high-strength steels in the construction of offshore structures.

The lack of fatigue data on high-strength steels under these applications was highlightedin Chapter 1, and this acted as an incentive for carrying out this investigation. The mainobjective of the study was to investigate the fatigue performance of high-strength steelsused in the construction of offshore structures under realistic loading and environmentalconditions. This was done firstly by developing a simulated service loading history for atypical Jack-up platform operating in the North Sea environment. This aspect of thestudy was covered in Chapter 2. Secondly the simulated history was used to carry outvariable amplitude fatigue tests using large-scale welded tubular Y joints made from atypical high-strength steel, SE 702.

The objective of this study was to assess the effect of realistic variable amplitudeloading and cathodic protection (CP) on the fatigue crack growth behaviour, andsubsequent fatigue life, of SE 702 - a typical high-strength steel used in theconstruction of Jack-up rig legs. One air and three seawater fatigue tests under CPwere carried out under simulated environmental loading conditions.

77


This chapter presents details of the testing programme and the results obtained fromthe study. The results are presented in the form of initiation behaviour, fatigue crackgrowth rates, and stress life (S-N) data. These results are compared with results fromprevious studies [1.3, 1.4, 1.64, 1.65, and 3.1] on lower strength steels, those obtainedfrom a parallel study [1.11] on SE 702, and other high-strength steels. The parallelstudy investigated the effect of CP on the same steel under constant amplitude loadingconditions on large-scale welded T joints.

3.2 Test specimen considerationLarge-scale welded Y joints made from SE 702 were used for this study. This sectiondescribes the geometry in detail. The mechanical and chemical properties of SE 702are also presented.

3.2.1 Properties of SE 702The steel, SE 702, is a member of the Super Elso (SE) family of steels. It is CreusotLoire Industrie's (CLI) equivalent of the A517GrQ standard. The chemical propertiesof the material are given in Table 3.1.

Table 3.1 Chemical composition of SE 702

Element

CMnSiSPNiCrMoBVCuSnAlTiCoNbAsPb

Specified

<0.14<0.9<0.3

< 0.004<0.01<1.5<0.7

<0.55< 0.003<0.05

--------

CLIanalysis0.125

1.10.256

<0.00050.0071.4040.4670.474

0.00120.0080.1850.0030.0690.0030.0110.0040.0070.003

UCLanalysis

0.121.050.25

<0.0010.0091.340.510.48

0.020.19

0.08<0.010.01

<0.01

In Table 3.1 the specified chemical composition is compared with independentchemical analysis results [3.2] carried out on a piece of the material cut from one ofthe Y joints used during the tests. As shown from Table 3.1, the chemical properties ofthe batch of steel from which the joints were made meets the specified standard for

78


each of the alloying elements, except for manganese which is higher than theguaranteed maximum. This difference in the percentage of manganese present in thesteel was not thought to be particularly relevant to its fatigue performance sincemanganese acts as a de-oxidizing agent.

The specified mechanical properties for SE 702 are given in Table 3.2. These werealso compared with results from tensile tests, carried out at Cranfield University [3.3],using specimens made from the same batch of steel used in the fabrication of large-scale Y joint specimens. The results from Cranfield are given in Table 3.3.

Table 3.2 Quoted mechanical properties of SE 702

Material

SE 702

ay (MPa)

700 (minimum)

UTS (MPa)

790 / 940

Elongation (percent)

16

These results compare well with the specified mechanical properties, but theygenerally show that the actual mechanical properties of the steel are better than thosespecified in Table 3.2.

Table 3.3 Measured mechanical properties of SE 702

SpecimenNo.

12345

Average

oy (MPa)

755744744750750748

UTS(MPa)

823813807816815815

Reductionin area

(per cent)666165646463

Elongation(per cent)

212020202020

Yield ratio(oy/UTS)

0.920.910.920.920.920.92

One of the conclusions made from the results obtained from Cranfield University, wasthat SE 702 has a uniform fine-grained microstructure, with a good combination ofmechanical properties. It is of high strength, and it was noted that it has good ductilityand excellent low-temperature toughness. Other measurements were made on the parentmetal, weld metal, and the heat affected zone obtained from the qualification weldsample. These included hardness measurements. The results obtained for parent, weldmetal, and the heat affect zone (HAZ) are compared with specified values in Table 3.4.

Vickers hardness values for the parent plate were approximately 250 HV. This valuewas considered acceptable for SE 702, and it has been suggested [1.12] that carbonsteel with Vickers hardness values in this range, should have an ultimate tensilestrength in the region of 800 MPa. This agrees with the values shown in Table 3.3.

79


Table 3.4 Hardness data for SE 702

Average

Range

SampleSize

Specimen12121

2

Weld metalCAP305305

276-336260-336

10

10

ROOT249253

245-251247-258

4

4

CGHAZCAP392389

373-409363^01

8

9

ROOT311300

262-363272-345

10

10

Parentplate253260

242-268243-274

11

11

3.2.2 Consideration of test specimen geometryA typical Jack-up leg structure is made from steel tubes formed into a three-dimensional space frame. The tubes are, normally, welded together at the intersectionsor joints. These tubular welded joints are usually made from materials of generallyhigh strength. Each lattice leg may be composed of longitudinal chord members thatmay contain a rack plate for elevating the hull with interconnecting horizontal anddiagonal tubular members.

Depending on the overall structural requirements, and the degree of structuralredundancy, a complex combination of joint geometries may result. These geometrieswill usually be a combination of planar and multiplanar joints, as shown in Fig. 3.1.Due to the practical difficulties involved in testing full-scale multiplanar joints in thelaboratory, planar joints are more commonly used.

Fig. 3.1 Typical planar and multi-planar joints used offshore

However, it has been established that the magnitude and the distribution of hot spotstresses around the intersection governs the fatigue performance of these joints. Thisinvariably implies that once the fatigue behaviour of simple planar joints under knownhot spot stresses is understood and the stress distribution in the more complex jointsknown, it is possible to relate them and, therefore, have a good understanding of theperformance of more complex joint geometries.

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Fig. 3.2 Detailed geometry of Y joint used for large-scale fatigue testing

Fig. 3.3 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 2figure 3.3 shows the welded intersection for one of the joints.

A summary of the detailed dimensions of the joint is given in Table 3.5 The Y jointdimensional parameters are also given in Table 3.5. The specimen dimensions werechosen to allow direct comparison with earlier tubular joint test programmesperformed at University College London using lower strength steels.

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Table 3.5 Detailed dimensions of Y joint

ChordBrace

Length(mm)24801390

Diameter(mm)457324

Thickness(mm)

1616

Brace angle = 35 degrees

3.2.3 Fabrication ofSE 702 specimensIt is important that the welded joints are representative of those used in the constructionof offshore structures, as this is known to have an effect on the resulting fatigue life ofthe joints. The joints were fabricated by a welding contractor (PAUMECA S. A. of LeBreuil, France) with experience in the fabrication of offshore structures.

The chord and brace tubes were made by seam welding two halves of rolled 16 mmthick plate. The welding was carried out using a gas metal arc welding (GMAW)process with a heat input of less than 2.5 kJ/mm. Post weld heat treatment (PWHT)was applied to the seam welds with preheating temperature of 125°C. Figure 3.3shows the seam weld on the brace and the brace/chord intersection string weld. Asshown in Fig. 3.3, the weld quality was good and no weld toe grinding was employed.

All welds successfully passed a full ultrasonic inspection, in accordance with theFrench standard NFP22-471 [3.4]. The dime test was performed on all welds and noweld failed the test.

3.3 Experimental set-upThis section describes the experimental facilities used in this study. This includesdetails of test rigs used, fatigue testing software, and data acquisition system.Information on the instrumentation used for the control of load and environmentalconditions is also presented.

3.3.1 Details of test rigA purpose-built reaction frame was available and this was used for the entire testprogramme. This was designed to allow for out-of-plane bending (OPB) tests on Yjoints. The load was applied using a 250 KN hydraulic actuator.

3.3.2 Test control and data acquisitionThe actuator was controlled with an INSTRON mini-controller via an advancedfatigue testing software, FLAPS [3.5]. All tests conducted were performed under loadcontrol. In this mode the specimen is subjected to load cycles of a pre-definedamplitude, as contained in the relevant sequence file. The FLAPS system is able togenerate different types of wave forms and also has the necessary capability to playback any developed realistic load sequence.

82

a (2L/D) = 10.85, B (d/D) = 0.71,y(D/2T) = 14.28, t(t/T) = 1.0 and 0 = 35o


FLAPS also has the facility for obtaining crack growth data in the course of a fatiguetest. Fatigue crack development was monitored by taking alternating current potentialdifference (ACPD) [3.6] crack depth measurements at fixed points around the chordbrace intersection where the fatigue crack was expected to occur. This technique is anestablished non-destructive inspection technique. It has been successfully applied tothe non-destructive inspection of welded joints of varying geometry, including othercomponents [3.7]. By choosing suitable inspection intervals it was possible to use thistechnique to follow crack growth from initiation, N1, to through-wall penetration, N3.

ACPD measurements were performed using a U10 crack microguage [3.6], togetherwith a 144-channel ACM3 switching unit. Two channels were used for eachmeasurement site, one channel for measuring the crack voltage and the other formeasuring the reference voltage. It was, therefore, possible to monitor crack growth atseventy-two sites around the chord brace intersection.

3.3.3 Simulation of environmental conditionsPrevious research and understanding of the effect of a corrosive environment on thefatigue performance of structural steels was introduced and reviewed in Chapter 1.Fatigue performance is a function of the severity of the corrosive environment and theinteraction of cyclic loading. As a result, it is important that tests are conducted underconditions that are representative of the environment loading system for relevantapplications. This section reiterates the importance of modelling both the loading andenvironmental conditions.

The loading is modelled, by use of wave power spectra, together with the transferfunction approach described in Chapter 2. However, if the simulated loading is appliedto test specimens in an unrepresentative environment, then misleading results can beobtained. The processes of corrosion fatigue and hydrogen embrittlement of Jack-upsteels are a complex combination of chemical reactions. The effects of these chemicalreactions, service loading, and the influences of any cathodic protection system haveto be modelled in the laboratory to obtain representative results.

3.3.3.1 Seawater environmentAll the corrosion fatigue tests were carried out under simulated environmentalconditions. The welded intersection, where the fatigue crack was expected to grow,was immersed in seawater. This was achieved by the use of an environment chamberaround the chord/brace intersection. Artificial seawater made to ASTM D1141 [3.8]was circulated from a reservoir through a closed loop passing through the environmentchamber. The fully aerated seawater was maintained between temperature limits of8°C and 10°C using an external refrigeration system. The pH of the seawater was alsomonitored in the course of each test and maintained between 7.8-8.2.

3.3.3.2 Cathodic protection systemCathodic protection is normally used in service to reduce the rate of corrosion to alevel that will allow the structure to attain its design life. This was applied andmaintained at a steady level (-800 mV and -1000 mV) with respect to Ag/AgClreference electrode for all the corrosion fatigue tests.

83


Prior to the application of fatigue loading, each joint was subjected to a 'soak time'where the joint was immersed in seawater with the CP applied and maintained at theappropriate level. A soak time of two weeks was implemented to achieve polarizationof the specimen and allow hydrogen to diffuse through the steel. The length of timerequired to achieve a uniform through-thickness hydrogen concentration is dependenton the diffusion coefficient for the material and the thickness of the specimens used.The two-week soak time was used to allow results to be compared with those fromprevious studies that employed a similar soak time. An important consideration whenconducting tests on tubular welded joints is the likely duration of the test. For large-scale tests, which may last several weeks, the soak time is less critical whencompared with that for a test on a simple specimen. A fatigue test on a simplespecimen may only last a day or two, and the soak time for such a test will have asignificant impact on its resulting life. The overall longer exposure period for large-scale tests, on the other hand, makes the through-thickness hydrogen concentrationgradient at the commencement of loading less critical, since the surface of thespecimen is still charged with hydrogen for a further period before crack initiationafter the soak time.

The effect of soak time on the fatigue performance of SE 702 was investigated atCranfield University [3.3] by carrying out tests employing a soak time of two andeight weeks. Although other researchers have noted that there can be significantdifferences, the study concluded that varying the soak time from two to eight weekshad very little effect on the results obtained for SE 702.

3.4 Stress analysis of Y jointsExtensive stress analysis of the joints used for this study was carried out before eachtest. Two methods were used in this process. Experimental stress analysis using straingauges and parametric equations. This section presents the procedure employed andcompares the results obtained

3.4.1 Experimental stress analysis procedureThe hot spot stress concentration factor for each joint was measured experimentallyusing strain gauges. In order to obtain accurate results for the stress concentrationfactors, 2 mm rosette gauges were used for all the tubular joints tested. The gaugeswere placed around the brace/chord intersection, in accordance with recommendationsof UKOSRP II, to obtain strains and stresses on the surface of the joint near theintersection.

At each measurement site the gauges were placed 10 and 20 mm from the chord weldtoe and the measurements from these two positions at each site were linearlyextrapolated to the weld toe to obtain the appropriate hot spot stresses.

Three rosette gauges were also placed on the brace. One close enough to the brace toeto measure the effect of the stress field determined by the combined deformation of thechord/brace intersection. The other two gauges were placed 500 mm and 800 mm fromthe brace toe, away from the region of rapidly increasing stress influenced by acombination of loading and chord/brace deformation. These two gauges were used to

84


measure the experimental nominal stresses and the extrapolated value to the braceweld toe. The stresses measured by these gauges were used to obtain the appropriatestress concentration factors.

Using these three gauges, it was possible to measure the variation of stress along thebrace with applied load, and this was compared with results from simple beambending type analysis. Three different sets of measurements were taken for each siteand average values of stress concentration factors were determined.

The effect of load path on the measured stress concentration factors was alsoinvestigated. This was considered very important since it was the only way ofchecking for any stress hysteresis effects. This was also used as a measure of the chordend fixity, and to ensure that there was no rotation of the chord within the fixed endcastilations. This was carried out by increasing the applied load from 0 per cent to 10per cent, from 10 per cent back to 0 per cent and up again to 10 per cent. For the firsttwo stages of loading intermediate measurements were made at 6 per cent load. For allthree stages of loading the measured stresses were checked to ensure repeatability andconsistency in all cases.

A summary of SCFs obtained for the joints is given in Table 3.6 where they arecompared with values predicted using parametric equations. The experimental resultswere very consistent and an average SCF of 4.47 was obtained. This value is typicalfor Y joints under out-of-plane bending with the dimensions shown in Fig. 3.2.

Table 3.6 Summary of measured Y joint SCFs

Method

HCDW&SE&D

KuangMeasured

PredictedSCF

4.535.045.433.57

Test ID/Percentage difference in measured and predicted SCF

LEYOPB1A(Yl)-2.208.1314.73-29.694.63

LEYOPB2C(Y2)5.0714.6820.81-20.45

4.3

LEYOPB3C(Y3)-1.548.7315.29-28.85

4.6

LEYOPB4C(Y4)2.8612.7018.97-23.25

4.4

3.4.2 Use of parametric equationsFigure 3.4 shows how the SCFs predicted by the various parametric equationscompare with the experimental values obtained for all the Y joints tested.

The parametric equations of Efthymiou and Durkin, Kuang, Wordsworth, andSmedley, and the UEG modified versions of Wordsworth and Smedley do not predictthe variation of stress concentration factors around the intersection. These equationsonly give the hot spot SCF. The Hellier Connolly Dover (HCD) equation for thevariation of SCF around the intersection for a given chord saddle hot spot, SCF is usedin all cases to produce the trends shown in Fig. 3.4.

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Fig. 3.4 Comparison of measured and predicted SCFs for Y joints

For all the parametric equations used, the HCD equation gives the best agreement withthe experimental results (for Y joints) after considering the scatter shown in Fig. 3.5.The HCD equation predicts a hot spot SCF of 4.54 compared with the measured valueof 4.6 for the first joint LEYOPB1A. The Efthymiou and Durkin equation and theequations of Wordsworth and Smedley overpredict by 18 per cent and 9.5 per cent,respectively. The only equation which underpredicts the chord saddle hot spot SCF isKuang's equation, which gives a value of 3.57, 22.4 per cent less than the measuredaverage value of 4.6.

The SCFs measured on the other three Y joints varied very slightly from the first. Thevalues obtained were 4.3, 4.6, and 4.4 for LEYOPB2C, LEYOPB3C, and LEYOPB4Crespectively. The percentage differences of these values from the first are 6.52 percent, 0 per cent, and 4.34 per cent, respectively. These results are consistent with avery small scatter.

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Fig. 3.5 Deviation of predicted SCFs from experimental values

3.5 Experimental fatigue testingThree major variables in the test programme were the hot spot stress and the CP levelapplied. All tests were conducted under variable amplitude loading conditions.

The effect of CP on hydrogen embrittlement is particularly relevant to high-strengthsteels. It is thought that CP could have a greater effect on the corrosion fatiguebehaviour of SE 702 steel than on lower-strength steels such as BS 4360 50D and BS7191 355D. A review of UK and other design guidance suggests that negativepotentials in excess of -850 mV (Ag/AgCl) may be detrimental to steels with strengthlevels above 700 MPa. In a recent study it was highlighted that, in some instances,even -800 mV may be harmful to steels with strength levels above 800 MPa [1.66]. Astudy on the effect of CP on the fatigue performance of SE 702 has been carried out[1.11] using constant amplitude loading. Later in this chapter, results from reference[1.11] are compared with those obtained from variable amplitude tests [3.9], to assessthe effect of environmental loading under CP conditions.

3.5.1 Test parameters and the JOSH sequenceA summary of the test parameters for the entire test programme undertaken is given inTable 3.7. The equivalent stresses indicated were obtained after rainflow cyclecounting of the sequence used in each case.

In each case the sequence was simulated from 4000 transitions of twelve sea states.Each transition was taken to last for a period of ten minutes. The output turning pointsfor the whole sequence were scaled to ±100 per cent. The sea states used aresummarized in Table 2.1, and their distribution in JOSH is shown in Figs 3.6 and 3.7.

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Table 3.7 Summary of parameters of JOSH

Sea states usedMax. stress (MPa)Min. stress (MPa)

RMS (MPa)Clipping ratio

Equiv. stress (MPa)Total number of

cyclesCP (mV)

Environment

LEYOP1A3-12

701.4821.2381.628.59

180.29280744

-Air

LEYOP2C1-12

975.3821.12111.758.73

250.0532025

-800Seawater

LEYOP3C1-12

783.4220.5389.348.76

200.0532025

-800Seawater

LEYOP4C1-12

783.4220.5389.348.76

200.0532025

-1000Seawater

Fig. 3.6 Distribution of sea states in JOSH2C

88


Fig. 3.7 Distribution of sea states in JOSH1A

All variants of JOSH are based on the same sea state PSDs. The normalized PSDfunctions, S(f)N for the JOSH sea states have been demonstrated [2.4] to be given as(see Chapter 4 for derivation)

Where fn is the natural frequency of the structure, £ is the damping ratio. Hr, Tr, and Q.are non dimensional parameters given as

The distribution of sea states in the sequence (JOSH1A), used for the air testCLEYOPB1A), is different from that in the sequence (JOSH2C) used for the corrosiontests. 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 themaximum stress did not exceed the yield strength of the material.

89


Fig. 3.8 Stress range distribution curves for JOSH

Fig. 3.9 Normalized SRPD curves for JOSH

Figure 3.8 shows the distribution of stress ranges for both JOSH1A and JOSH2C,together with the stress range distribution in part of the JOSH2C sequence used in thefirst corrosion test (LEYOPB2C). These distributions are normalized with respect tothe most probable occurring stress range in Fig. 3.9.

90


As highlighted in Chapter 1, large-scale fatigue testing is a necessary requirement forunderstanding the fatigue behaviour of offshore structural steels under variableamplitude loading conditions. The limited guidance available today on fatigue designof offshore structures under realistic variable amplitude loading conditions is a resultof limited experimental data. This is the primary justification for conducting thesetests. Most of the analysis presented in Chapter 2 is necessary to ensure that arepresentative loading history or sequence is produced. This section presents thedetails of the large-scale fatigue tests carried out using, JOSH.

3.6 Fatigue test resultsThe results of the fatigue tests are presented here. Fracture mechanics analysis ofresults is presented in Chapter 4. The experimental Y factors and crack growth ratesobtained are presented and compared with predictions using existing fracturemechanics models. In this section the results are presented in the form of initiationdata, crack growth curves, crack aspect ratio evolution, and the fatigue life of eachspecimen presented in S-N format. These results are compared with those obtainedfrom tests conducted on lower strength and other high-strength steels.

3.6.1 Fatigue crack initiationInspection of the ACPD data collected during the early portion of each test has shownthe ACPD technique to be capable of detecting crack growth increments of less than0.1 mm. This detection capability is important when it comes to determining the pointof initiation of each defect.

The definition of initiation, Ni is taken as the attainment of a 0.1 mm deep fatiguecrack. Early crack growth data from the four tests conducted for this study are shownin Figs 3.10 to 3.13.

Fig. 3.10 Early crack growth data for LEYOPB1A

91


Fig. 3.11 Early crack growth data for LEYOPB2C


92



Figure 3.10 shows results obtained from the air test, LEYOPB1A. From this figure itcan be seen that the initiation life for the air test is about 620 500 cycles, whichcorresponds to the first data point collected after the attainment of a 0.1 mm deepcrack. The corresponding results obtained for the corrosion tests (LEYOPB2C,LEYOPB3C, and LEYOPB4C) are shown in Figs 3.11-3.13 respectively.

It was possible to monitor the progress of a fatigue crack from initiation through tofailure. The initiation lives were determined graphically from plots such as thoseshown in Figs 3.10-3.13. The initiation and S-N data obtained for the Y joints aresummarized in Table 3.8, which also shows results obtained from constant amplitudetests [1.11] conducted on Tjoints made from the same steel.

Table 3.8 Summary of initiation and S-N data for Y joints

Test No.YlY2Y3Y4

Conditions180MPa(Airtest

260 MPa (-800 mV)200 MPa (-800 mV)

200 MPa (-1000 mV)

Ni620 5001000050000180000

N3

2 130000380 000

1 545 0001 140 000

Ni/N3

0.2910.0260.0320.158

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Summary of initiation and S-N data for T-joints [1.11]

Test No.TlT2T3T4T5

T5(retest)T6

Conditions400 MPa (Air)300 MPa (Air)

225 MPa (- 1000 mV)225 MPa (-800 mV)180 MPa (- 1000 mV)300 MPa (-1000 mV)300 MPa (-800 mV)

N,13000

24000115000105 000Run Out

-<10 000

N3

74000180000194 000548 000

-130 000138 000

Ni/N3

0.1760.1330.2920.192

--

<0.072

The initiation to total life ratio, Nj/Ns^, is used to measure the significance of theinitiation period to the overall fatigue life. Welded tubular joints generally exhibitshort initiation and long propagation lives. Austin [3.1] carried out a series of variableamplitude tests on BS 4360 SOD steel using the WASH sequence. The trend notedfrom his study was for lower Ni/Nj ratios for higher equivalent stress levels. Thiseffect is not so clear from the results obtained from this study. The total number ofdata points is limited even when the results from the T joint tests are included. There isfurther difficulty involved when comparing the T joint results directly, since the typeof loading is different. However, one would expect higher-strength steels to showhigher N1/N3 ratios since fatigue crack initiation is controlled by plastic deformation.

The results from Y joints are compared with those obtained from constant amplitudetests reported in [1.11] (Table 3.8) for the same steel, SE 702, in terms of initiation tototal life ratio. The values for Y joints under variable amplitude loading are lower thanthose for T joints. The only discrepancy is from LEYOPB1A. The main reason for thedifference in initiation to total life ratios is the presence of very damaging stress rangesfrom severe sea states that are present in the JOSH sequence. This is further supportedby results from T5 when compared with LEYOPB1A carried out at the same hot spotstress range. It is also apparent that the CP level has an effect on the initiation to totallife ratio for both joint types. The tests carried out at a CP level of -1000 mV have ahigher initiation to total life ratio in both cases when compared with those carried outat the CP level of -800 mV.

3.6.2Crack growth curvesThe crack growth curves for all the tests are shown in Fig. 3.14. Figure 3.14 alsoshows that fatigue crack growth, under variable amplitude loading conditions is notsteady. This was anticipated since the variable amplitude load sequence used toconduct the tests (JOSH) consisted of multiple sea states with varying degrees ofseverity. The sequence used in each case had significant variability in amplitude andfrequency content. A 'stair case' type crack growth curve was consistently obtainedfor each of the tests. In each case regions of accelerated growth were found to coincidewith the 'storm' in the load sequence.

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Fig. 3.14 Comparison of variable amplitude fatigue crack growth curves

Fig. 3.15 Comparison of constant amplitude fatigue crack growth curves

The corrosive environment used for the seawater tests also plays an important role inthe fatigue crack growth process. This influences the mechanism by which crackspropagate and can lead to irregular behaviour. This is highlighted by the difference inthe crack growth curves when variable amplitude tests are compared with thoseobtained from constant amplitude loading conditions in seawater with CP. The crackgrowth curves obtained under constant amplitude conditions for the tests reported in[1.11] are shown in Fig. 3.15. Crack growth behaviour is somewhat more complex in acorrosive environment (with CP) than in air. The main difference is the existence of

95


distinct regions, where the crack growth curves take on different linear slopes for thecorrosion tests. This behaviour was also found in a more pronounced manner andfollowing a distinct pattern that could be linked to significant fatigue damage relatedevents in the sequence for the variable amplitude tests.

3.6.3 Crack aspect ratio evolution

Fig. 3.16 Crack aspect ratio data for LEYOPB1A

Fig. 3.17 Crack aspect ratio data for LEYOPB2C

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The surface crack length was measured at similar intervals to crack depthmeasurements for each of the four tests conducted. This was obtained from crackshape evolution. The results obtained are shown in Figs 3.16-3.19 for LEYOPB1A,

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LEYOPB2C, LEYOPB3C, and LEYOPB4C respectively. These results are discussedfurther in Chapter 4, where they are used to develop a new Y factor model that can beused in the analysis of fatigue crack growth in offshore structures.

3.6.4 S-N dataThe end of each test was defined as the attainment of a through-wall fatigue crack. Theexperimental fatigue life (N3) of each specimen is given in Table 3.8. The stress rangeindicated is the sequence equivalent stress range derived from rainflow countedfatigue cycles. The S-N data obtained for the study on the Y joints are compared withthose obtained from T joints in Table 3.8. These results are later compared with thedesign S-N curves for air and seawater with CP conditions and the mean line for 16mm thick specimens made from BS 4360 50D. The fatigue performance of SE 702 isfurther compared in Section 3.7, with other medium and high-strength steels testedboth in air and seawater.

3.7 DiscussionThe results obtained from SE 702 large-scale tubular welded joints are compared withthe T' curves for air and seawater under adequate cathodic protection conditions inFig. 3.20. The mean line for data obtained from previous test programmes on lowerstrength steels (BS 4360 50D) is also shown in Fig. 3.20 for comparison. It can beseen from Fig. 3.20 that the SE 702 data points all lie above the air design curve. Aninteresting observation can be made when comparing Y joint results with thoseobtained from T joints made from the same steel.

It can be seen that all the Y joint data lie to the right of T joint data. This indicates thatY joints under out-of-plane bending may exhibit a nominally better fatigue resistancethan T joints under axial loading. It is, however, difficult to draw any conclusionsfrom this observation as the T joints were tested under constant amplitude while the Yjoints were tested under variable amplitude loading conditions. However, axiallyloaded T joints are known to exhibit a more severe response to fatigue loading whencompared with Y joints under out-of-plane bending. This observation was also madeby Vinas-Pich [1.64], and is reflected by the existing database for tests under differentmodes of loading,as shown in Fig. 3.21.

98


Fig. 3.20 Comparison of SE 702 data with design S-N curves

Fig. 3.21 Effect of loading mode on S-N data

99


Fig. 3.22 Comparison of SE 702 with lower strength steels

SE 702 results are also compared with those of Austin [3.1], and Vinas-Pich [1.64]obtained on tubular welded joints made from BS4360 SOD steel. Both of these testprogrammes were conducted using variable amplitude loading under corrosionconditions with CP. The geometry of the test specimens used by Austin was nominallyidentical to the SE 702 T joint test specimens reported in [1.11] while those of Vinas-Pich were of the same geometry as the Y joints used for this study. Both Austin andVinas-Pich used the WASH sequence. This comparison is shown in Fig. 3.22 whereSE 702 shows a tendency to lie at the upper end of the scatter band. The lower-strength steel data points all lie below the air design curve while the SE 702 datapoints all lie above this line. This is increasingly so for the tests conducted at lowerstresses. The data suggest that high-strength steel joints may have longer fatigue livesat lower stress levels, but there are insufficient data to identify a clear trend.

The effect of CP is shown in Fig. 3.23, where results from air tests are compared withthose from seawater tests CP. The level of CP influences the fatigue performance ofSE 702. Increasing the CP level from -800 mV to -1000 mV resulted in a shorterlife at a given stress level for both T and Y joints. For the constant amplitude loaded Tjoints at 225 MPa for example, the life at -1000 mV corresponded to approximately70 per cent of the life at -800 mV . A similar ratio of 73 per cent was obtained fromthe variable amplitude Y joint tests conducted at an equivalent hot spot stress range of200 MPa. This reduction factor on fatigue life observed for the large-scale tubularjoint tests is, however, less severe when compared with a reduction factor of three incrack growth rate for the fatigue crack growth specimens (SENB) tested at CranfieldUniversity [3.3].

100


Fig. 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 byup to a factor of three when the CP level was increased from -830 mV to -1080 mV(Ag/AgCl). Figure 3.23 shows that SE 702 results obtained from tubular joints lie wellwithin the existing scatter with a tendency for better fatigue performance whencompared directly with lower strength steels.

101

There is a limited amount of S-N data for welded joints manufactured from higherstrength steels, relative to medium strength structural steels, and none appear to bedirectly relevant to the joint geometries frequently used in the fabrication of Jack-upplatforms. Data for welded plates with yield strengths up to 540 MPa are reported in[3.10]. In addition, a recent study [3.11] involved tests on high-strength steels withyield strength in the region of 700 MPa. In both cases tests were performed on T buttjoints in seawater with CP. The results indicate that the performance of these joints iscomparable to that of conventional structural steels.


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

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Data from tests conducted on high-strength steel tubular joints in air, with chordthicknesses ranging from 5 mm to 78 mm, have been thickness corrected to 16 mmusing a thickness exponent of 0.3 [1.2, 3.12]. These results are compared with SE 702data together with the T" design curve in Fig. 3.24. It can be seen from Fig. 3.24 thatsome points fall below the T' design line. Data for tubular DT joints manufactured fromLe Toumeau MM X85 high-strength steel with nominal yield strength of 590 MPa[3.13] were generated in a study funded by the UK Health and Safety Executive (HSE).These results are also included in Fig. 3.24, and are seen to lie above the T' curve.

A comparatively smaller number of tests have been performed on high-strength steeltubular joints in seawater. The HSE study included a programme of constantamplitude corrosion fatigue tests [1.65]. Two welding methods, representative offabrication methods, were used, namely flux cored arc welding (FCAW), entailingweave welding, and shielded metal arc welding (SMAW), yielding string welds. Thetests were conducted in air and in seawater at a CP level of -1000 mV Ag/AgCl underOPBatanR-ratioofO.05.

The seawater temperature was maintained between 8°C and 10°C. These conditions aresimilar to those used in Section 3.4 as a soak time of two weeks was equally employedprior to testing. The mode of cracking in the in-air SMAW specimens differed from thatobserved in tubular joints of conventional structural steel in that the cracks propagated ina plane that was approximately parallel to the chord surface, rather than perpendicular toit. This behaviour was attributed to the presence of manganese sulphide inclusions in theparent material. These results are compared with SE 702 data in Fig. 3.25. The data havebeen thickness corrected to 16 mm using a thickness exponent of 0.3. The graph showsthat some of the data points lie above the S-N curves. Some of the tests were conductedunder free corrosion conditions and Fig. 3.25 shows that their performance is notnecessarily poorer than that of CP joints. A statistical analysis carried out on the SE 702data showed that a best-fit mean curve has a slope of -5.395 instead of -3 asrecommended by the existing UK guidance notes.

3.8 SummaryThis chapter has presented details of variable amplitude fatigue tests conducted onfull-scale tubular welded Y joints fabricated from a 700 MPa yield strength steel, SE702. SE 702 is a typical high-strength steel used in the construction of Jack-up riglegs. A total of one air test and three corrosion fatigue tests with CP were carried outunder simulated environmental conditions using, JOSH.

The objective of this study was to assess the effect of realistic variable amplitudeloading and CP on the fatigue crack growth behaviour and subsequent fatigue life ofhigh-strength steels.

The results obtained from the investigation, and details of the materials used, havebeen presented in the form of initiation data, crack growth curves, crack aspect ratioevolution, and S-N data. These results have been compared with results from previousstudies and those obtained from a parallel study on SE 702.

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The fatigue life results from the current investigation suggest that tubular jointsfabricated from SE 702 are at least as good as conventional fixed platform steels. Theyhave the potential for better performance and may offer the benefit of longer fatiguelives at lower stress levels. However, due to limited data on high-strength steels, it isdifficult to draw firm conclusions on any existing trends in the fatigue behaviour ofhigh-strength steels.

It is also possible that, increasing the cathodic protection level from -800 mV to-1000 mV may lead to a shorter fatigue life. For hot spot stress levels of around 200-225 MPa a factor on life of around 30 per cent was observed for tests conducted usingvariable amplitude loading and this was consistent with results obtained from aseparate investigation on the same steel under constant amplitude loading conditions.However there is no evidence to suggest that SE 702 is any more susceptible tohydrogen embrittlement than other high-strength steels of similar grade.

There are potential benefits to be gained by using high-strength steels in thefabrication of offshore structures, especially Jack-up platforms used for production.The limited number of tests conducted show that SE 702 may be used under theseapplications without necessarily increasing the risk of fatigue failure due to hydrogeninduced stress corrosion cracking and embrittlement. The results show that high-strength steels are no worse than conventional fixed platform steels such as BS 436050D. It is strongly recommended that further tubular joint fatigue tests should becarried out on SE 702 and other high-strength steels, in order to adequately quantifythe potential benefits and to formulate appropriate guidance on their use in thefabrication of engineering structures.

104

Chapter 4

Fracture Mechanics Analysis

4.1 IntroductionThe S-N approach has been used extensively to design welded offshore tubular jointsand other welded connections. However, the S-N approach cannot be used inassessing the structural integrity of cracked components under service conditions. As aresult, fracture mechanics (FM) is used and, at present, it is the most powerful anduseful technological tool available for describing and solving fatigue crack problems.

Fracture mechanics is currently used at the design stage of offshore facilities. Itprovides the basis for fatigue life prediction, steel selection, and tolerance setting onallowable weld imperfections. FM is also used during the operational stage of astructure, to make important decisions on inspection scheduling and repair strategies.It can also be used as a tool for establishing limits on operational conditions.

Some of the existing FM models, used in the prediction of fatigue crack growth inoffshore welded tubular joints, are presented in this chapter. These models includeempirical and semi-empirical models, adapted flat plate solutions, and those based onresults obtained from finite element analysis. The accuracy of these models in theprediction of fatigue crack growth in welded tubular joints, subjected to serviceloading, is assessed by comparing the predicted results, obtained from these models,with experimental results. Emphasis is placed on the effect of service loading, andconsideration is given to the sequence effects on the accuracy of existing models whenused for fatigue crack growth prediction in engineering structures.

Service loading in offshore structures, for instance, is mainly due to wave and wind actionwith variable amplitude and frequency content. Fatigue failure of structural componentsunder these conditions is a major concern in the maintenance of offshore structures. Theprocess of fatigue is influenced by many factors that may be different in each applicationarea, depending on the interaction between the loading and the environment.

105


Existing FM models, and fatigue crack growth prediction methods, generally rely onusing the overall equivalent stress range, together with a suitable crack growth law, forfatigue crack growth prediction under variable amplitude loading. For S-N typeanalysis, this method is by far the best when dealing with variable amplitudesequences. However, for FM crack growth prediction employed after an in-serviceinspection schedule, the use of the overall sequence equivalent stress range needs to beapplied with caution, to ensure that any significant sequence, or interaction effects, aretaken into account. These effects can be significant under service loading conditions ascrack growth is largely dependent on SEF range that is a function of stress range andcrack size. It is possible that the use of the overall sequence equivalent stress conceptin a fracture mechanics analysis procedure may have significant limitations in dealingwith the high degree of variability, observed in service, as crack growth accelerationand retardation cannot be accounted for using this approach. A different and morerealistic FM based approach is required.

This chapter seeks to address this problem. It presents a fast assessment procedure forthe determination of load spectra for fatigue analysis of offshore structures. It alsopresents a proposed FM based model for predicting fatigue crack growth in offshorestructures.

4.2 The stress intensity factor conceptIrwin has made a great contribution to the development of FM concepts. He extendedGriffith's theory [4.1] (crack propagation will occur if the change in elastic strainenergy due to crack extension is larger than the energy required to create new cracksurfaces) for ductile materials [4.2], and postulated that energy due to plasticdeformation should be taken into account in evaluating the energy associated with thecreation of a new crack surface. He also defined a quantity, G, the strain energyrelease rate or 'crack driving force', which is the total energy absorbed duringcracking, per unit increase in crack length, per unit thickness.

Perhaps his most significant contribution came in the mid 1950s [4.3], when heshowed 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.Based on the philosophy of the crack driving force and the crack tip stresses, Irwin[4.4] proposed the following expression for the SIF for an embedded elliptical crack ina uniform tensile stress field (Fig. 4.1) after accounting for the flaw shape

106


Fig. 4.1 Embedded elliptical crack in a uniform tensile stress field

where the crack dimensions are described by a for crack depth, and c for crack surfacelength, and </> is the angle of orientation. The elliptical integral, O, is given by

In general, the mode 7 SIF for a centre crack of length 2a, in an infinite plate subjectedto a uniform stress field, cr, (Fig. 4.2) is given by

Equation (4.4) gives the SEF, in the absence of all boundaries, of a form applicable tothe mode of loading and specimen geometry. Cracks in welded tubular joints areusually in a complex stress field that is different from the case of a uniform stress fieldin an infinite plate. SEF solutions for cracks in tubular welded joints must, therefore,include various correction functions to account for boundary effects due to loading,and specimen and crack geometries, such that the SIF is given by

107


Fig. 4.2 Crack in an infinite plate under a uniform stress field

where Fis the SIF correction function with a general recommended [4.5] form given by

Ys = Correction for a free front surface

Yw = Correction for finite plate width

Ye = Correction for crack geometry

Yg = 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 tubularwelded joints. This has led to the development of several SIF solutions for semi-ellipticalsurface cracks. Some of these are semi-empirical and empirical solutions obtained fromexperimental results, and those based on finite element analysis results.

4.3 Experimental resultsCalculation of experimental SIF can be carried out using experimental crack growthdata. With the increasing accuracy in the measurement of experimental fatigue crackgrowth rates, using data from ACPD crack depth measurements, it is possible todetermine experimental stress intensity Y factors with reasonable accuracy. This methodhas been used in the past to develop empirical Y factor models.

Fatigue crack growth data presented in Chapter 3 have been used to determineexperimental Y factors. These experimental values are used as a benchmark forcomparing the accuracy of other models presented in this chapter. The procedureadopted in determining the experimental Y factors is presented here.

108


The determination of experimental Y factor relies on the use of a suitable crack growthlaw, such as Paris law

(4.7)

where a is the crack size, A.K" is the stress intensity factor range, and AS is the hotspot stress range. By assuming that Paris law applies, experimental Y factors may beobtained from

The experimental crack growth rates, obtained from the fatigue tests conducted for thisstudy, are shown in Figs 4.3 to 4.6 for tests LEYOPB1A, LEYOPB2C, LEYOPB3C,and LEYOPB4C, respectively.

Fig. 4.3 Experimental fatigue crack growth rate for LEYOPB1A

109


Fig. 4.4 Experimental fatigue crack growth rate for LEYOPB2C


110



The corresponding experimental Y factor curves obtained for the tests are shown inFigs 4.7 to 4.10, respectively.

Fig. 4.7 Experimental Y factors for LEYOPB1A

111


Fig. 4.8 Experimental Y factors for LEYOPB2C


112



The accuracy of the experimental Y factors depends on the Paris law material constantsC and m. The values used in the sample calculation above, were obtained from compacttension tests performed on parent plate in air by CLI [4.6]. A summary of the datasupplied, for both parent plate and the heat affected zone, is given in Table 4.1.

Table 4.1 Paris law air data for SE 702

Parent Metal (PM)Heat Affected Zone (HAZ)

C2.715 x 10'9

3.872 x 10'9

m3.53203.1687

(CP: -830 mV/ECS, Temperature: 20°C)

Parent Metal (PM)Heat Affected Zone (HAZ)

C2.715 x 10"y

3.872 x 10'9

m3.53203.1687

Where appropriate data are not available, the use of arbitrary values from PD 6493 [4.5]is not recommended, as misleading results can be obtained. Table 4.2 shows othervalues of C and m, for free corrosion and for corrosion tests conducted with CP. Asshown in Table 4.2, the CP levels, used in the tests conducted to generate the data, arenot identical to those used for the large-scale tests in this study. Comparing the resultsfrom CLI with those from other tests [3.3] suggests that there is scatter on the C and mvalues. It is important to note that the accuracy of the experimental Y factors presented,depends greatly on the values of C and m used in analysing the experimental results.

113

Table 4.2 Paris law seawater data for SE 702


4.4 Use of empirical SIF solutionsEmpirical models were developed for rapid and accurate analysis of crack growthdata. Some of these models have gained wide acceptance, and have been successfullyused for fast assessment of crack growth in tubular welded joints. These models,which include the two phase model (TPM), the average stress, and the modifiedaverage stress models, are presented here and their performance is compared withexperimental results.

4.4.1 The average stress modelThe average stress (AVS) model [4.7] was proposed after testing large-scale 16 mmtubular joints. This model made use of stress intensity modification (Y) factors andassumed a thickness correction for joints other than 16 mm. The Y factor predicted bythis model is given by

5 is a non-dimensional parameter, which is the ratio of the average stress concentrationfactor, SCFav, to the hot spot stress concentration factor, SCF#s, at any location of thejoint intersection. It is given by

and

where T is the chord wall thickness and a is the crack depth.

This model has been used to predict crack growth rates in tubular welded joints underconstant amplitude loading conditions, with discrepancies only occurring during earlygrowth where the crack depth is less than 25 per cent of the chord wall thickness.However, results show that under variable amplitude loading conditions there can bediscrepancies across a wider range (Fig. 4.11).

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Fig. 4.11 Comparison of experimental Y factors with AVS prediction

4.4.2 The two phase modelThe two phase model (TPM) [4.8] was based on published crack growth data and wasdeveloped, mainly, to consider crack growth affected by joint size. It is given in theform

where B and k are functions of size and AVS parameter, S, and p is the early crackgrowth phase controlling parameter.

MI is taken as one for the propagation phase (o/T >0.25), and Q.25T/o~p for the earlycrack growth phase (o/T<0.25).

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Fig. 4.12 Comparison of experimental and TPM Y

The early crack growth phase controlling parameter was produced by assuming thatearly crack growth behaviour can be treated as an extrapolation of the propagationphase, modified by an exponentially decaying effect, determined by the wall thickness,the diameter ratio, and the hot spot stress. The thickness correction exponent thatdetermines the value of the early crack growth phase controlling parameter, p, is suchthat it imposes a very severe dependence of crack growth on thickness, as shown inFig. 4.12. This makes the model more sensitive to thickness effects than has beenobserved experimentally.

4.4.3 The modified average stress modelThe modified average stress (MAYS) model [3.1] was proposed after testing large-scale 16 mm tubular joints. It was developed by applying a 15 per cent reductionfactor to the original AVS model. The reduction factor was based on the assumptionthat rainflow cycle counting provided a higher degree of correlation, with constantamplitude data, than range counting on which the original AVS model was based.Austin [3.1] suggested the 15 per cent reduction factor, after noting that the equivalentstress determined from rainflow counting was higher than could be obtained usingsimple range counting, for the representative double-peaked spectrum originally usedto develop the AVS model. This factor was found to be 1.15. A modification to theAVS model was then proposed based on this difference, which required that the Yfactor predicted by the AVS model be reduced by 15 per cent. The Y factor predictedby this model is given as

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All the variables are as defined for the AVS model. The degree of accuracy obtainablefrom this model depends, largely, on the accuracy of the original experimental data onwhich it is based. Under variable amplitude conditions this may equally be affected bythe method of cycle counting used, and the detail contained in the crack growth data.Figure 4.13 shows the predicted Y factor based on this model compared withexperimental data.

Fig. 4.13 Comparison of experimental Y factor with MAYS prediction

4.5 Adapted plate solutionsSIF solutions for plates cannot be applied directly to tubular welded joints. This is as aresult of the differences in boundary conditions. They are, however, important in thatthey can be used to provide estimates of stress intensity factors for other geometries byapplying the appropriate boundary condition correction functions. For instance, flatplate solutions may be used to obtain SIF for semi-elliptical cracks in T plates byintroducing a correction function to account for the influence of the weld detail and theattached plate.

Different researchers have used different approaches over the years to model the effectof the weld detail on the flat plate solutions and develop SIF solutions for weldedconnections. These range from methods based on weight functions to those based onfinite element analysis. These approaches fall within three broad categories ofmethods, generally used to determine stress intensity factors. These include classicalsolutions for idealized geometries, numerical methods, and semi-empirical solutionsbased on a combination of experimental and analytical data. For instance, one suchsolution is that due to Newman and Raju.

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4.5.1 Newman-Raju SIF solution for surface cracksNewman and Raju (NR) derived a stress intensity factor solution for a semi-ellipticalcrack in a flat plate. The solution gives the stress intensity factor for a surface crack ofdepth, a, and surface length, 2c, in the form

Fm and Ft, are the correction functions for the tension and bending stresses, om and Ob,respectively. O is an elliptical integral approximated by

The correction functions for tension, F,,,, and for bending, Fb, are given as

fw is the plate width correction function for a plate with a finite width, w. Even thoughthis flat plate solution cannot be applied directly to tubular welded joints, it is veryimportant, in that it can be used to provide estimates of stress intensity factors forother geometries by applying the appropriate boundary correction functions.

The NR solution has been shown [4.9] to yield results that agree closely withexperimental tubular joint Y factors for cracks of o/T >0.15, by applying the momentrelease function to account for the stress redistribution that accompanies crackpropagation in tubular joints.

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A semi-analytical model based on the NR flat plate solution for predicting Y factors inwelded tubular joints was proposed by Monahan [4.10]. It included the followingmodifications: a non-uniform stress correction (NSC) to account for weld geometry, alinear moment release (LMR) to account for load shedding, and a crack shapecorrection (CSC) factor.

The proposed equation is given by

where T, the CSC factor, and B/T is the bending to total stress ratio. Yg is the NSCfactor, which accounts for the influence of the stress concentration produced by theweld detail. This factor can be obtained using a method proposed by Albrecht andYamada[4.11].

This is for a non-uniform stress distribution, <7(x), that remains symmetrical about thecrack centre line, as shown in Fig. 4.14.

The CSC factor, T, introduced by Monahan, was included to account for the influenceof crack aspect ratio. This factor was obtained by comparing experimental Y factorswith those obtained by the NR flat plate solution that included a NSC factor and thelinear moment release model such that

Monahan used curve fitting through the values given by equation (4.23) and showedthat *¥ could be approximated by the following equation

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Fig. 4.14 Schematic illustration of Albrecht's method for determining Yg

The above CSC function was derived from experimental data obtained from testsconducted on a combination of X and multi-braced tubular joints. This means that itmay not be directly applicable to other joint geometries. The reason for this is that thecrack shape evolution curve depends greatly on both the joint geometry and the modeof loading. This is also demonstrated by the fact that the crack shape correction, shownabove, is unity for the range of crack aspect ratios obtained for the Y joints tested forthis study. It is possible that a wide range of CSC factors are obtainable, depending onthe geometry of the specimens.

Myers [1.11] used a similar approach adopted by Monahan, and obtained a CSC factorapplicable to T ioints under axial loading given by

The data from which this correction factor was derived are shown in Fig. 4.15. The firstpart of the correction function can be considered to represent an upper boundary for a/2c< 0.05. However, as shown in Fig. 4.15, the CSC function used for a/2c > 0.05, isoutside the scatter band for the data used. This would make it difficult to use this type ofsemi-empirically derived solution for other joint geometries.

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Fig. 4.15 Myers' data used in deriving CSC factors for NR solution

The brace and chord thickness of the Y joints, used in this study, are the same as thoseused by Myers. However, both the geometry and mode of the loading are different. Asa result, the crack shape evolution curves obtained from the two studies are different.This is shown in Fig. 4.16, where the best fit curves obtained for the two geometriesare compared. The implication of this is that, the Y factor curve obtained will dependon the CSC function used. This sensitivity is due to the semi-empirical nature of themodel.

Fig. 4.16 Comparison of crack shape evolution curves for Y and T joints

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As a result, there is some degree of uncertainty in the applicability of the model, to theprediction of Y factors, for cases other than those from which the CSC factors werederived. In order to avoid this uncertainty, a CSC function that also accounts for theeffect of joint dimensional parameters, and the mode of loading employed, needs to beintroduced.

There is a lack of solutions available for predicting crack aspect ratio evolution. Thishas been identified [4.12] to represent the greatest hindrance to good predictions ofremaining fatigue life of cracked components. Different researchers have useddifferent approaches to incorporate the effect of crack aspect ratio into SEF modelsused for fatigue crack growth prediction. One approach highlighted by Brennan [4.13]is based on the use of a root mean square (RMS) stress intensity factor for thetransverse and longitudinal directions of crack growth. This approach was proposed byCruse and Besuner [4.14], and it has been used by Dedhia and Harris [4.15] inanalysing fatigue cracks in pipes. The use of this method for the prediction of Y factorsin welded joints is not discussed any further in this book, but a new approach isintroduced in the next section. The new semi-empirical model accounts for the effectof crack aspect ratio.

4.6 New semi-empirical Y factor solutionFigure 4.17 shows the Y factor curves predicted by various existing Y factor models.Those shown in Fig. 4.17 include the TPM, AVS, MAYS, and the adapted flat platesolution based on the NR equations. Figure 4.17 shows that the experimental Y factorsobtained for this study are all below those predicted by the above equations.

Fig. 4.17 Comparison of Y factors from different models with Y joint data

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The previous section highlights the importance of crack shape evolution in theaccurate prediction of crack growth in cracked components. The TPM, AVS, andMAYS models do not account for this effect. It is, therefore, possible that theiraccuracy in predicting Y factors in tubular welded joints will depend on whether thecrack shape evolution, in the welded joint of interest, is representative of thoseoriginally used in deriving the respective equations. The main reason for this is thatboth joint geometry and mode of loading, as discussed in the previous section, willinfluence crack shape evolution.

Figure 4.18 shows the crack shape evolution curves for the Y joint tests conducted forthis study. Curve fitting was used, with the data, to obtain the mean best crack shapeevolution curve for Y joint under OPB, as shown in Fig. 4.18. The best fit curve isgiven by

This curve has been compared with that obtained for data presented in reference[1.11], for axial T joints tested under constant amplitude loading conditions in Fig.4.16. The difference in the two curves is, most likely, due to the differences in themode of loading and joint geometry.

Fig. 4.18 Experimental crack shape data

It is, therefore, important that a suitably flexible model is developed that also accountsfor these observed effects due to differences in the mode of loading and jointgeometry.

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Figure 4.19 shows how the best-fit experimental Y factors compare with the predictedvalues based on the modified NR equations. This prediction method is used as a basisfor comparison, because it has been identified to give the best correlation withexperimental results obtained for the investigation reported in [4.10]. The appropriateCSC function, given in equation (4.24), is used, together with equation (4.26), toobtain the results shown in Fig. 4.19. The Gumbel distribution is then used to modelthe deviation, 8, of the predicted results from the experimental data. This deviation isshown in Fig. 4.20 and is given by

where A = 0.56 - 0.185 and the rest of the variables are as previously defined for theAVS model.

Fig. 4.19 Comparison of best-fit curve with the modified NR solution

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Fig. 4.20 Modeled deviation (5) of predicted results from experimental data

The flat plate solution was then modelled using curve fitting to obtain an equation thatis similar to the AVS model. The reason for using this form of equation is because it isa function of parameters that have been established to be important in influencing thepredicted Y factor. This MAYS solution is given by

A = 0.56 -0.185" and j = 0.22 + 0.065

The proposed Y factor solution, YVA, is then obtained by combining the modifiedsolution with the deviation from the experimental data, such that

This proposed solution is more accurate in predicting the average Y factor for the Yjoints used for this study. It also takes into account the effect of crack aspect ratio. It iscompared with the experimental data and predictions from existing models in Fig. 4.21.

The prediction of crack aspect ratio has been identified to represent a major source ofuncertainty in the fatigue crack growth prediction. This is mainly as a result of thelarge scatter on crack aspect ratio obtainable from experimental data. This is illustratedfor the Y joint results in Fig. 4.22.

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Fig. 4.21 Comparison of proposed Y factor solution with other solutions

Fig. 4.22 Effect of wide scatter on crack shape evolution data

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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 withinthe scatter obtained from the experimental results. In absolute terms, this is quitesignificant. However, this level of error leads to very little change in the predicted Yfactor, as shown in Fig. 4.23. In this figure, the curve from the proposed equation, andthose for ±25 per cent error, are indistinguishable since they are almost coincident.

4.7 Variable amplitude crack growth modelsThe derivation of accurate SIF solution is imperative for reliable crack growthprediction. However, there are other important factors that are often ignored, partly dueto the lack of sufficient data, and partly due to the inherent difficulty that is oftenencountered in reducing the level of uncertainty to a reasonable level. One of thesefactors is the effect of variable amplitude loading and the associated sequence effects.

Different statistical models have been developed for the prediction of crack growthrates under variable amplitude loading conditions. These models do not account forsequence effects and have been shown to be applicable to load spectra in which sucheffects are minimal. Some of the more popular statistical models, which have beenapplied to crack growth prediction in engineering structures, are discussed below.

4.7.1 Equivalent stress range approachThe equivalent stress range approach is an extension of the equivalent fatigue damageconcept, first proposed by Paris, to relate the effects of variable amplitude stresshistories to constant amplitude fatigue crack growth data. This extension was proposedby 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 variableamplitude loading. Like the original equivalent fatigue damage concept, this method

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does not account for any load interaction effects in the random sequence, as it relies onthe assumption that such effects are negligible. Using this approach, and assuming thatParis 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 Pariscrack growth exponent, p(A5) the probability density of AS, and .P(AS) is theprobability of occurrence of AS.

This approach, and definition of the equivalent stress range concept is procedurallyequivalent, and applicable, for both crack growth analysis and conventional S-Napproach using Miner's cumulative damage summation method. It has beensuccessfully used, together with the rainflow counting method, to predict variableamplitude fatigue crack growth in air.

However, despite the successful application of this model to air fatigue crack growthdata, it was thought that it required modification for corrosion fatigue, where crackgrowth is controlled mainly by two competing factors. Corrosion fatigue, unlike airfatigue, crack growth is controlled by a combination of the mechanical action, due tocyclic stressing, and the electrochemical action of the corrosive environment. Also, the'no load interaction assumption' has not been established for typical multi-sea stateload spectra. For these sort of load sequences, with very high clipping ratios (in excessof 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 unconservativeresults may be obtained under variable amplitude conditions. This aspect of crackgrowth prediction in offshore structures is discussed further in a later section in thischapter, where a new model that predicts crack growth under realistic loadingconditions and accounts for sea state interaction effects are presented.

4.7.2Equivalent crack growth conceptThe equivalent crack growth concept was proposed by Kam [4.17] as a modification tothe equivalent stress range concept, for the prediction of variable amplitude corrosionfatigue crack growth in offshore structures

This model was based on multiple segment Paris-type linear representation of corrosionfatigue crack growth, as shown in Fig. 4.24. Each segment, shown in Fig. 4.24, is taken torepresent the material response that covers all relevant stress intensity factor ranges forwhich the material's constants, C and m, are pertinent. It assumes that the average crackgrowth 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

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The equivalent crack growth concept has been shown to give good agreement with theexperimental results. It has, however, not been possible to assess the accuracy of thismodel due to the lack of Paris law data for SE 702.

The main drawback with this model is that it involves the lengthy procedure of signalgeneration and cycle counting before any analysis can be carried out. To overcomethis, and bypass the signal generation and cycle counting before analysis, analternative prediction procedure was proposed in the form of an extended version ofthe Kam and Dover equation. This modified version was based on the original ideabehind the Chaudhury and Dover equation for predicting the equivalent stress rangedirectly from the PSD, without going through the cycle counting process. Thesolution, from this equation, for the distribution of peaks can be expressed as the sumof the Gaussian and Rayleigh equations. It is not clear whether all representativesequences for offshore structures will exhibit a distribution of peaks that can besufficiently described by these two distributions combined in this way. It is, therefore,possible that a better prediction procedure may be obtained which is based on a moreappropriate distribution relevant to a particular sequence.

Fig. 4.24 Typical multi-segment corrosion fatigue crack growth rate curve

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Apart from the fast assessment equations that can be used to calculate equivalentstresses directly, all the models discussed above rely on one form of cycle counting oranother, the implementation of which has been covered in Chapter 1.

4.8 Consideration of sequence effectsAs discussed in the previous section, the prediction of fatigue crack growth under variableamplitude loading conditions is still in its infancy. There is a lack of suitable fatigue crackgrowth prediction models that account for all the relevant effects that are unique tovariable amplitude loading conditions. Apart from the statistical models, presented above,other models have been proposed for use in analysing variable amplitude loading.

Some of these models are based on crack tip plasticity, and assume that crack growthrates can be related to the evolution of the crack tip plastic zones. The more popularmodels that have attempted to explain the variability in crack growth rates observedunder variable amplitude loading conditions using crack tip plasticity, are those ofWheeler and Willenborg.

The Wheeler [4.18] model predicts that crack growth following an overload may beestimated by modifying the constant amplitude growth rate using an empiricalretardation parameter, Cp, such that

The constant amplitude growth rate appropriate to the stress intensity factor range,AAT,, associated with the rth cycle is given by (da/dN)cA.. The retardation parameter istaken to be a function of the ratio of the current plastic zone size to the overloadplastic zone size, and is given by

where ryi is the *th loading cyclic plastic zone size, ap is the sum of overload cracklength and overload plastic zone size, a, is the crack length at zth loading cycle.

This model was proposed for analysing crack growth on a cycle-by-cycle basis and itcan 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, respectively.

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Although this model can be used to predict the effect of overloads, on a cycle-by-cyclebasis, it has some inherent disadvantages. One of the main disadvantage is that it relieson the use of an empirically determined constant, p, required to shape the constantamplitude crack growth retardation parameter. The Wheeler model also predicts thatmaximum retardation, resulting from an overload, occurs immediately after theapplication of the overload as the retardation parameter turns to zero. This, however,contrasts with the phenomenon of delayed retardation observed during overloads[4.19]. The model also neglects the counteracting effect of negative peak loads incrack retardation. Hence, the model has very limited capability in analysing variableamplitude loading sequences, such as those experienced by offshore structures. Itscycle-by-cycle approach, to obtain the summation of crack extensions, makes it verydifficult to account for any retardation effects that may be present in very longsequences, typical for offshore structures. The fact that it also relies on an empiricallydetermined parameter, makes it inappropriate for use in structural integrity assessmentprocedures. The use of this method for analysing the results obtained from this studywas, therefore, not considered appropriate.

The Willenborg model [4.20] is based on the assumption that retardation in crackgrowth rate, following an overload, is caused by compressive residual stresses actingon the crack tip. The model, therefore, relies on the use of an effective stress, that isthe applied stress, reduced by the compressive residual stress component, developedaround the crack tip as a result of the elastic body surrounding the overload plasticzone.

Based on this effective stress concept, the calculated effective stress intensity factorrange can be used, together with an appropriate crack growth law, to give the crackgrowth rate for the jth cycle as

The main difference between this model and the Wheeler model is that, it uses onlyconstant amplitude crack growth data and does not require the derivation of anyempirical shaping constants. However, like the Wheeler model, it also predictsmaximum retardation, immediately after the application of an overload, and fails topredict the observed retardation effects and the decrease in retardation observed due tothe application of underloads. Hence, the Willenborg model is also limited in itsapplication to fatigue loads, such as those experienced by engineering structures.

Other approaches to analysing crack growth retardation rely on the use of the crackclosure concept. This was first proposed by Elber, who suggested that the drivingforce for crack extension is reduced by the development of plasticity induced crackclosure. He proposed the effective stress intensity factor range concept that allowedfatigue crack growth rates to be estimated under crack closure conditions. Determiningthe crack opening stress, under such conditions, is practically similar to using theeffective stress concept developed by Willenborg. Crack closure models, whetherbased on plasticity-induced, roughness-induced, oxide-induced, or crack closure

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mechanisms resulting from the effect of calcareous deposits on the crack surfaces,therefore, have fundamental problems on grounds of practicality similar to theWheeler and the Willenborg models.

However, experimental results have shown that there are fundamental differencesbetween crack propagation, under variable amplitude loading conditions, whencompared to behaviour under constant amplitude loading conditions. These differenceshave been observed for both air and seawater tests. It is, therefore, important that thesedifferences are taken into consideration when attempting to predict crack propagationunder variable amplitude loading conditions using the FM approach.

The results presented in Chapter 3 show characteristic 'staircase'-type crack growthcurves. This experimental observation suggests that, crack growth under variableamplitude conditions is nonuniform. The non-uniform crack propagation undervariable amplitude loading conditions makes the prediction of fatigue crack growthdifficult and calls for the need to develop appropriate models for use under theseconditions.

The rest of this chapter deals with this in greater detail, and presents a generalizedprocedure for the assessment of engineering structures, with emphasis on the offshoreoil gas sector.

4.9 Fast assessment of offshore structuresThe sea state PSDs generated from the structural dynamic transfer function approach,outlined in Chapter 2, can be presented in normalized form. The advantage of usingnormalized spectra is that it can facilitate the process of comparison of PSDs resultingfrom different sea states. This method was used to compare the model transfer functionwith the service measurements obtained from the Maersk Guardian Jack-up platform.This procedure can be adopted, because normalized spectra maintain the frequencycontent of loading, and allow the flexibility for scaling, for example, for implementingtest conditions for material characterization. In addition, the effect on the SRPD, due toany changes in the magnitude of the scaling factor, is negligible for any chosen outputrange normally determined by the load requirement for any particular test. The outputscales used to generate the distribution of turning points are, therefore, weighted withrespect to the parameters of the extreme PSD, that normally corresponds to the extremesea state. The scale for any sea state i is then given as

where A is the calibration factor determined by the required maximum outputamplitude and fp is the peak frequency for sea state i. This depends on the fourth andsecond spectral moments of the power spectrum and is given by

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Fig. 4.25 Sea state PSDs obtained using proposed equation

This is applicable to power spectra of similar shape, such as those shown in Fig. 4.25.Based on this philosophy, an equation is proposed that uses non-dimensional parametersto estimate the normalized PSD, for any structure under wave excitation in the NorthSea 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 £, is the damping ratio. Hr, Tr, andQ, are non-dimensional parameters given by

The derivation of this equation is based on the assumption that, normalizing the PSDsfor each sea state with respect to the extreme, or most severe sea state, does not changethe stress range probability distribution for that particular structure under the given setof sea states. This is demonstrated below.

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4.9.1 New normalized PSD equationThe derivation starts with the structural dynamic transfer function and the waveexcitation spectrum given by equations (4.41) and (4.42) respectively, and uses thegeneralized solution given by equation (4.43).

By applying the transfer function approach, outlined in Chapter 2, the responsespectrum for a structure, with known natural frequency, under an extreme sea statewith significant wave height, Hsext , and mean zero crossing period, Tzext. , can be

calculated from equation (4.43) to give

The natural frequency of the structure is a property of the structure. The response can,therefore, be normalized with respect to the resonant peak that is a maximum whenf=fn. The resonant response is, therefore, given by

In a similar manner, the response spectrum for any other sea state with significantwave height Hs, and mean zero crossing period Tz, can be obtained by replacingHsext and Tzext in equation (4.44) with Hs and Tz, respectively, to give the sea state

response, Sxx(f)i, for sea state i such that

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This is then normalized, with respect to the extreme resonant peak response obtainedfrom equation (4.45), to give the normalized PSD for that sea state as

By substituting the response, S x x ( f ) i , for any sea state, 7, and the resonant response,

S u ( f ) ext. |f=fn , of the structure into equation (4.47), the normalized PSD can be

obtained. This equation simplifies to the form

The PSDs obtained for a typical Jack-up platform, using this equation and the JOSHsea states, are shown in Fig. 4.25.

The main advantage of the proposed normalized PSD equation is that it relies only onthe use of non-dimensional parameters and the natural frequency of the structure topredict its PSD. It will, therefore, represent a fast analytical tool for evaluating thebehaviour of structures in the North Sea. It can also be adapted very easily fordifferent locations by using the appropriate wave energy spectrum for the location ofinterest. For example, instead of using equation (4.42), the peak frequency correctedversion, presented in Chapter 2, can be used. This equation given below wasdemonstrated, in Chapter 2, to be more accurate in predicting the measured waveenergy spectrum after introducing a frequency correction parameter, B.

The difference, between the above equation and equation (4.42), is that the variable /,in equation (4.42), is replaced by / - B in equation (4.49). The solution given byequation (4.48) can, therefore, be modified by introducing the same variable, to obtain

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where fnB, fB, and £B are all frequency corrected non-dimensional parameters, given by

The rest of the variables are as previously defined.

The accuracy of this model depends on the accuracy of the sea state data used.However, since it only uses non-dimensional sea state parameters, its overallsensitivity is reduced and depends largely on the extreme sea state.

It is, therefore, recommended that service data, where available, are used indetermining the normalized PSDs. However, where service data are not available, asuitable theoretical sea state distribution model can be used. This is discussed below.

4.10Sea state probability modelA detailed examination of oceanographic data for the North Sea, observed over a periodof several years, has shown that the distribution of significant wave height, Hs, can beaccurately described by the Gumbel distribution, given as

where P (x) is the exceedance of the variable x. Observed sea state data have been

demonstrated [2.11] to be well fitted by the following expression

This modelled distribution agrees closely with sea state data from typical locations inthe North Sea.

Equation (4.53) gives the sea state exceedance. This is the probability that thesignificant wave height, Hs, for any particular sea state exceeds a certain value. It canalso be written for all sea states with wave heights up to Hs, such that

The implication of equation (4.54) is that it can be integrated over specified limitssuch that

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Equation (4.55) represents a continuous probability distribution function for an infiniterange of possible wave heights. There is always a constant y, for which the integral ofits product with the probability function is always unity. That is, equation (4.55) canalso be expressed as a function of y, such that

Equation (4.56) will give the exact solution for the long-term probability distributionof sea states, over an infinite range, based on the Gumbel distribution. This gives aprobability distribution function of the form

Where a, P, and y are site-dependent parameters. In practice, the long-term probabilitydistribution of wave heights across the entire range of likely occurring sea states is notused. The reason for this being that, sea states used for any fatigue analysis of offshorestructures will depend on oceanographic data based on measurements and observationscarried out over a finite length of time. Under this scenario, often the total probabilityof occurrence of sea states is known, 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, such that

The cumulative probability P(//Or, is normally taken as one while y is a constant whichhas to be evaluated. Constants a and (3 will vary for typical sites. Data from the Silver Pitand Ekofisk regions of the North Sea, show that a and P are 1.55 and 1.06, respectively.

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4.10.1 Use of sea state probability distribution modelThe use of fast assessment equations to determine sea state equivalent stresses wasdiscussed in Chapter 1. This approach does not require cycle counting and can beapplied directly to structures in service. Where necessary, the overall long-termequivalent stress can be determined using the following procedure.

Suppose a sea state, i, with a significant wave height HSi, and equivalent stress Sh., has along-term probability of occurrence P(Hs), then its long-term contribution to fatiguedamage, or the overall long-term equivalent stress, can be given by ohi, such that

The overall equivalent stress, oh, can then be given by

When AHsi is infinitesimally small, then the long-term equivalent stress is give as

For simulated service load histories (SLH), used in the testing of structural materials inthe laboratory, this approach can equally be applied. An alternative approach is to useconventional cycle counting, as described in Chapter 1. This method would normallyallow for the overall sequence equivalent stress, or the block equivalent stress, to bedetermined. However, it is important to note that, the use of the overall equivalent stressconcept in the prediction of fatigue crack growth in structures under variable amplitudeloading conditions may lead to inaccuracies in the results, for three reasons.

First, the fatigue crack growth rate at any time is dependent on the SIF range. This is afunction of crack geometry, loading mode, and stress range. The actual stress rangeapplied to the fatigue crack, within an individual sea state, will be largely differentfrom the overall equivalent stress range. Therefore, using the overall equivalent stressrange to characterize crack growth within an individual sea state may lead toinaccurate results.

Second, the element of time is very important, especially for offshore structures wherefrequency effects, under corrosion fatigue conditions, have been demonstrated. Usingthe overall equivalent stress concept excludes this element of time. Another reason forcaution is that the equivalent stress concept is inapplicable as long as it is applied to anentire sequence that may never be fully utilized before a structural integrity assessmentexercise is carried out.

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Third, because this approach does not include the element of time, and the necessaryinteraction between different sea states, it does not provide the necessary capability tomodel any interaction effects. Most of these sources of error associated with fatiguecrack growth prediction using the overall equivalent stress approach will be minimizedby adopting a sea state equivalent stress approach for offshore structures. With otherengineering structures, there is the need to identify key fatigue damaging features foruse in a block analysis procedure. This concept is presented in the following section,and illustrated for application to offshore structures.

4.10.2 Formulation of the sea state equivalent stress conceptThe sea state equivalent stress concept is introduced here, using a similar approach tothat on which the overall equivalent stress approach is based.

The overall sequence equivalent stress approach can be used to determine crackgrowth under variable amplitude loading conditions based on equation (4.63).

i—

are as previously defined.

The sea state equivalent stress range concept is based on the same philosophy as thatof the overall equivalent stress range approach. It, however, relies on using sea stateparameters to determine the sea state equivalent stress range that is then used tocalculate fatigue crack growth associated with that sea state. This is implemented byassuming an appropriate crack growth law. Using Paris law, for example, the crackgrowth rate within a particular sea state, i, with equivalent stress, S/,., can be calculatedfrom

The number of fatigue cycles, Nh., , required to propagate a fatigue crack from aninitial depth, a0, to a final depth, af, within a particular sea state, characterized by k,stress ranges can be calculated. This procedure is then carried out over the entiresequence of expected sea states. This sequence of sea states will be determined,mainly, by their long-term probability of occurrence, duration, and transition period.Using this information, the total number of fatigue cycles, N, required to propagate afatigue crack after n sea state transitions can be calculated where

139


The sea state equivalent stress range concept is more accurate in predicting fatiguecrack growth under variable amplitude loading conditions in offshore structures thanthe overall equivalent stress range approach. The main reason for this is that thevariability in the instantaneous stress range or stress intensity factor range is far less,within any particular sea state, than the equivalent variation in the overall sequence puttogether. The method also has the added advantage of allowing the inclusion of anysequence or sea state interaction effects. Sea state interaction effects are omitted whenother conventional approaches to fatigue crack growth prediction under variableamplitude loading conditions are employed in determining crack growth in offshorestructures.

4.11 DiscussionThe results of fatigue crack growth predictions under variable amplitude conditions,presented here, are based on the simulated JOSH. The sea state equivalent stressapproach is compared with the conventional overall equivalent stress range approachand experimental data obtained under variable amplitude loading conditions.

The sea state equivalent stress concept relies on the use of a suitable sea stateprobability distribution function. The probability distribution used to derive thisfunction is the Gumbel distribution. The sea state exceedance and cumulativeprobability obtained from this distribution are shown in Fig. 4.26. It was necessary toascertain the accuracy of this distribution used to develop the model. This was done bycomparing sea state cumulative probability, and exceedance curves obtained from theGumbel distribution, with those calculated from the measured data used to generatethe JOSH sequence. This comparison is shown in Fig. 4.26. The agreement betweenthe variation in the predicted and measured curves is good.

140


Fig. 4.26 Measured and predicted exceedance curves for JOSH sea states

This agreement provided a suitable starting point in developing the sea stateprobability distribution model, for use in the prediction of fatigue crack growth inoffshore structures under variable amplitude multi-sea state loading conditions.

The JOSH sequence used was generated using advanced simulation techniques fromtwelve sea state PSDs. It consists of 1 064 050 turning points generated from 4000transitions of the twelve sea states. Figure 4.27 shows the SRPD curves for threevariants of the sequence used in the fatigue testing programme. The exceedance curvesfor the sea state, are shown in Fig. 4.28. The equivalent stresses due to each of thetwelve sea states used, was calculated for the different variants of JOSH used in thefatigue testing programme. These are plotted, in Fig. 4.29, for three of the four testscarried out. Results from the fourth test are not shown because, as they wereconducted at the same overall equivalent stress range, they are identical to thoseobtained from the third test.

141


Fig. 4.27 SRPD curves for JOSH

Fig. 4.28 Exceedance curves for JOSH sea states

142


Fig. 4.30 Comparison of probability and cycle counting methods

The probability of occurrence of each sea state was used, together with the sea stateequivalent stresses, to calculate the long-term contribution of each sea state to theoverall sequence equivalent stress. These values are compared, in Fig. 4.30, with thoseobtained by using the conventional rainflow cycle counting method. The results shownin Fig. 4.30 are so close that the curves are virtually coincident.

143

Fig.4.29 Sea state equivalent stresses for different tests


The sequence of sea state transitions used to generate JOSH is shown in Fig. 4.31. Thecalculated sea state equivalent stresses, shown in Figs 4.32 and 4.33, for LEYOPB2Cand LEYOPB3C, respectively, can be seen to follow a trend similar to the sea statetransition sequence, as expected. Figures 4.32 and 4.33 also compare the sea stateequivalent stresses with the overall sequence equivalent stress. As seen in thesefigures, there is considerable variation in the sea state equivalent stress. This variationwill have significant effects on fatigue crack growth and, therefore, needs to beadequately accounted for.

Fig. 4.31 Sea state transition sequence for JOSH2C

Fig. 4.32 Comparison of overall and sea state equivalent stresses for LEYOPB2C

144


Fig. 4.33 Comparison of overall and sea state equivalent stresses for LEYOPB3C

Even though the same sequence was used for the corrosion tests, the individual testswere conducted under the required loading conditions by using different amplitude andload ranges. This made the overall equivalent stresses different, apart from testsLEYOPB3C and LEYOPB4C, which were carried out at the same equivalent stresslevel. The variation in the sea state equivalent stress, for the test conducted at anequivalent stress range levels of 250 MPa and 200 MPa, are shown in Figs 4.32 and4.33.

From these results it is evident that the stress intensity factor range, which is a functionof crack geometry and stress range, will be different for the cases where an overallequivalent stress range is used, when compared with results obtained using a sea stateequivalent stress. The way this difference affects the accuracy of crack growth ratepredictions is very important.

The sea state equivalent stress concept was used to predict crack growth in the high-strength steel (SE 702) used in the fatigue testing programme. The crack growth curveobtained, is compared with experimental data for the air test, together with resultsobtained using the overall equivalent stress range method, in Figs 4.34 and 4.35, forcorrelated data and an arbitrary sequence, respectively.

145


Fig. 4.34 Prediction with consideration for initiation and correlated initiation point

Fig. 4.35 Prediction with consideration for initiation and correlated initiation point foran arbitrary sequence

In each of the figures the smooth curves are those obtained with the overall equivalentstress range method. The other two curves show the predicted crack growth curve,based on the sea state equivalent stress concept and experimental crack growth data.

146


One of the problems encountered in predicting crack growth, using this approach, isthat information on the crack initiation point, within the sequence, is required foraccurate prediction. If this procedure is followed and the initiation period isappropriately taken into account, a more accurate prediction can be obtained.

It should be noted that the individual sea state approach has the added capability ofmodelling interaction effects, which cannot be included if the overall sequenceequivalent stress approach is used. It can also be applied using an arbitrary seastate transition sequence. This is illustrated in Fig. 4.35, where the transitionsequence, shown in Fig. 4.33, is used to predict the fatigue crack growth for testLEYOPB1A. The results shown in Fig. 4.33 were obtained after accounting for thecrack initiation life.

This approach can, therefore, be used as long as a good approximation to the expectedsea state transition sequence can be obtained. This can be derived from oceanographicdata. Knowledge of the long-term distribution of sea states, and their duration, isimportant in the use of the sea state equivalent stress approach. The accuracy of thismethod, however, like any other FM based method relies very much on the accuracyin the material constants used in the model.

4.12 SummaryThe results obtained from the variable amplitude fatigue tests, conducted for thisstudy, have been analysed using existing FM models. The use of different FM modelsto predict fatigue crack growth, and to model the different observations of crackgrowth retardation and acceleration observed during variable amplitude loadingconditions, have been assessed and possible areas for modification and improvementhighlighted.

It is apparent that one of the main difficulties involved in quantifying corrosion fatiguecrack growth, under variable amplitude loading conditions, is the large number ofvariables involved, which almost always operate together to influence corrosionfatigue crack growth at any one time. Some of these variables include materialproperties determined by the alloying elements present, the nature of the corrosiveenvironment determined mainly by its chemical composition, and other additionalfactors. Crack shape evolution has also been identified as an important parameter thatinfluences the stress intensity factor.

A new Y factor model has been proposed. The proposed semi-empirical functiondepends on crack aspect ratio and loading mode, which are important parametersthought to influence the nature of Y factors obtained.

This chapter has also introduced a fast assessment approach to the analysis of offshorestructures. The methodology relies on the use of non-dimensional sea state parameters,together with the mode of structural response. The advantages associated with usingthe proposed equation have been highlighted and discussed.

147


A sea state probability distribution model has also been presented. This model relieson the Gumbel distribution, and it has been verified with service measurements from atypical location in the North Sea. Based on this model, a sea state equivalent stressconcept has been formulated and its mathematical background presented.

A generalized FM approach for the assessment of fatigue crack growth in offshoreinstallations is proposed, and it has been demonstrated to be more consistent withexperimental observations of crack propagation under variable amplitude conditions.

148

Chapter 5

Conclusion

5.1 SummaryThis book has presented results of an investigation undertaken to assess theperformance of a typical high-strength weldable Jack-up steel under realistic loadingand environmental conditions. Details of the methodology employed to develop atypical JOSH have been presented.

Results and details of experimental variable amplitude corrosion fatigue (VACF) testsconducted using JOSH have been presented and discussed, with respect to resultsobtained from other high-strength steels and conventional fixed platform steels.Different fracture mechanics models for VACF crack growth prediction have alsobeen compared in terms of the accuracy of predicted Y factors. Most importantly, animproved methodology for fast assessment of offshore structural welded joints hasbeen proposed, and a sea state equivalent stress concept formulated.

The following sections present the main conclusions that can be drawn from the workpresented in the book. Areas of further work, which will contribute to the general bodyof knowledge in this field, are also identified.

5.2 Conclusions and recommendationsOne of the main objectives of this study was to simulate service loading on a typicalJack-up platform. This was successfully achieved by use of a representative Jack-uptransfer function that was validated by use of service data obtained from a Jack-upplatform operating under service conditions. A sensitivity analysis carried out suggeststhat Jack-up response is very sensitive to water depth. As a result of this sensitivity, itwas concluded that there are difficulties associated with producing a single loadhistory, which can be considered to be representative of all service loading conditionsfor Jack-ups operating in different water depths and locations. However, most

149


operating sites in practice cover extensive areas of similar water depth. For thesereasons, the JOSH model provides a suitable framework for generating anyrepresentative service load history, applicable to all sites within a range of waterdepths. In this regard, a fast assessment approach has been proposed, based on resultsobtained from this study, that is expected to eliminate the lengthy analysis procedurenormally required to generate the load PSDs for offshore structures. This approachrelies on the use of non-dimensional parameters to describe the normalized stress PSD,of any particular structure, for any set of sea states.

The results obtained from the large-scale fatigue testing programme on SE 702, undersimulated loading and environmental conditions, are very encouraging. The fatiguelife results suggest that tubular joints fabricated from SE 702, are at least as good asconventional fixed platform steels. Under CP conditions, the results show that anincrease in the CP level from -800 mV to -1000 mV may lead to a reduction infatigue life by up 30 per cent.

There was no evidence to suggest that SE 702 is more susceptible to corrosion fatigue,in the presence of hydrogen produced under CP conditions, than other high-strengthsteels of similar grade. There was an apparent trend, showing a potential for betterperformance, with longer fatigue lives at lower stress levels. This implies that theexisting slope of -3 for the T' curve may not be applicable to high-strength steels.

On the whole, the results from the investigation presented in this book, suggest thatthere may be advantages to be gained by using high-strength steels, but further tests atlower stress levels need to be performed to confirm any existing trends. The existenceof a more negative slope for the design curve, for example, will have wideimplications on inspection scheduling for high-strength steel installations. This willlead to a reduction in operational costs, especially for Jack-ups used as productionplatforms. Jack-up structures used for short-term drilling operations may be designedwith less safety margins when compared with those used for long-term operations. Theadded significance of these results is that, with a better understanding of high-strengthJack-up steels under realistic loading and environmental conditions, it will be possibleto narrow down these safety margins during the design process. It is recommendedthat further fatigue tests be carried out on SE 702, and other high-strength steels, toquantify the benefits associated with their use offshore. These further tests arerequired, so that, any trends in the fatigue performance of high-strength steels can beclearly defined and quantified for incorporation into a suitable design guidance.

After comparing existing FM models with experimental results, the inherentlimitations of the models, when applied under variable amplitude loading conditions,have been identified. It was noted that the average experimental Y factor curve liesbelow the curves predicted by the existing solutions. Based on this observation it canbe concluded that there may be other important factors that affect crack propagation,under variable amplitude conditions, that may have been ignored in previous models.A new Y factor model has been proposed that accounts for important factors, such as,the crack shape evolution (crack aspect ratio), geometry, and mode of loading. Itssemi-empirical nature may, however, introduce a certain degree of uncertainty when

150

Conclusion

applied to other joint geometries. Its performance on other joint geometries, therefore,needs to be checked with further experimental data obtained from tests conductedunder realistic loading conditions. More accurate and reliable crack growth predictionin high-strength steels will have significant implications on the safety and reliability ofproduction Jack-ups. These structures are more susceptible to long-term fatigueproblems, when compared with Jack-ups used as mobile drilling units, with thepossibility of dry dock inspection. Inspection scheduling for production Jack-ups is,therefore, an important aspect in the risk reduction and safety enhancement processrequired for their reliable operation. It is especially in this area that some of the modelsdeveloped, as results of this study, can be used as tools for the assessment of high-strength steel offshore installations to enhance safety and structural reliability.

A generalized FM approach for the assessment of fatigue crack growth in offshoreinstallations has been proposed. This model relies on the use of a sea state probabilitydistribution function that has been verified with service data. However, the data usedin the development of the model were obtained from specific regions of the North Sea.In order to increase confidence in the use of this model and reduce the level ofuncertainty associated with its use, it is important to check its accuracy against furtherservice data from different locations. This will help in establishing the validity ofusing the proposed probability distribution model, to analyse structures at differentlocations other than the North Sea region.

A sea state equivalent stress concept has been mathematically formulated, for the firsttime, and used to predict fatigue crack growth in a typical high-strength offshore steel.This approach has been shown to have certain advantages over the conventionaloverall equivalent stress range approach, one of which is the potential to model seastate interaction effects. It can be used for more accurate inspection scheduling, andalso for the structural reliability analysis after an inspection schedule to ensure a highlevel of safety.

151


Chapter 6

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160

Index

Acrylic models 8, 10, 12-14, 40Adequate protection 24Anode, sacrificial 3, 29Artificial seawater 83Axial loading, balanced 13

Balanced axial loading 13Buckling resistance 2

Cantilever Jack-up 55Catastrophic fracture 17Cathodic protection (CP) 3, 20, 23, 29, 30, 83,

98, 104Chemical composition of SE 702 78Chord end fixity 15Construction of Jack-up structures 2Corrosion fatigue, variable amplitude 4, 20,

31, 48, 62, 128,149Crack:

arrest 27driving force 106extension 4,33, 106, 131mode of opening 39

Crack growth:early 91, 116law 38, 106, 109, 131, 139models 36rapid 38unstable 38

Crack propagation 27, 38, 106, 118non-uniform 132

Crack shape evolution 97, 120, 123, 147, 150Cracked components, structural integrity of 4,

105Cracking:

localized 27through-wall 17

Critical stresses 5Cross-correlation functions 54Crossing period, mean zero 60, 62, 63, 134Cumulative damage ratio 31Curves, exceedance 140, 142Cycle counting methods 34, 36

Damage ratio, cumulative 31Damage, fatigue 20, 34, 35, 46, 60Damage-tolerant design 38Damping 56, 64

hydrodynamic 57structural 57

Data, oceanographic 61, 63, 136, 137, 147Definition of initiation 91Design:

curves, S-N 17damage-tolerant 38wave approach 60

Development, marginal field 43Dislocation movement 27Distribution:

of sea states 89, 147Gumbel 63

Drilling unit, mobile 44, 151Dry dock 151

inspection 3Dynamic:

loading 53, 60response 44, 49, 53, 54, 57

Early crack growth 91, 116Effective:

mass of structure 56stiffness of structure 56

Efthymiou equations 7,41Elastic stress field 40Embrittlement, hydrogen 26, 83, 87, 104Environmental effects 28, 39Equilibrium potential 29Equivalent:

static load 60stress range 106, 127, 128, 138, 139, 140,

145Exceedance curves 140, 142Excitation frequency 56Extrapolation, linear 11

Fabrication defects 28Failure:

analysis 37structural 5, 60

Fatigue:corrosion, variable amplitude 42crack growth analysis 5, 47, 127crack initiation 4, 27, 28, 31, 94damage 20, 34, 35, 46, 60, 95, 127, 138definition of 16design guidance 3, 17, 18, 43design philosophy 1life prediction 16,39, 105loading, influences of 55resistance 20, 29, 44, 76, 98

161


strength 21testing, large-scale 4, 76, 81, 91, 150testing, variable amplitude 47, 77variable amplitude corrosion 20, 31, 42, 48,

62, 149variable amplitude 20, 31, 34, 36, 42, 103

Field development, marginal 1Finite element analysis (FEA) 8, 14, 40, 105,

108, 117Fixity, chord end 15Fluctuating stresses 16Fracture:

catastrophic 17toughness 38

Fracture mechanics:approach 16, 34linear elastic 38methodology 4

Frequency:excitation 56natural 49, 56

Geometric:parameters 10stresses 5, 8

Grain boundary attack 28Gross deformation SCF 13Growth analysis, fatigue crack 47, 127Guidance, fatigue design 17,18,43Gumbel distribution 63, 136, 137, 140

Hardness data of SE 702 80Heat affected zone 79Hot spot stress range 6, 94, 100, 109Hydrodynamic damping 57Hydrogen embrittlement 26, 31, 83, 87, 104Hydrogen-induced stress corrosion cracking 3

Influences of fatigue loading 55Initiation to total life ratio 94Initiation, definition of 91Inspection, dry dock 3Instability, plastic 38Installations, offshore 151Interaction effects 31, 33, 36, 38, 106, 128,

139, 140, 147, 151,stress-time 28

Jack-up design 2, 43Jack-up Offshore Standard load History

(JOSH) 4,44Jack-up structures, construction of 2Jack-up, cantilever 55

Joints:multiplanar 15, 80protected 24tubular welded 10, 41, 98, 100, 107, 108,

114,117, 118, 123, 127

Large-scale fatigue testing 76, 81, 91, 150Level crossing counting 35Linear elastic fracture mechanics 38Linear extrapolation 11Lloyd's design equations 41Lloyd's Register equations 7Loading conditions, variable amplitude 140,

147,150Loading:

dynamic 53variable amplitude 20, 138

Localized cracking 27Lumped mass model 57

Maintenance operations 1, 32Marginal field development 43Markov chain technique 49Mean zero crossing period 60, 62, 63, 134Measurement of strain 10Mechanical properties of SE 702 79Microfractures, transgranular 38Miner's rule 32Mobile drilling unit 44, 151Mode of crack extension 39Model, lumped mass 57Models:

acrylic 8, 10,12,13,14,40crack growth 36numerical 10photoelastic 10steel 10, 12, 13,40

Monitoring, structural integrity 37Multiplanar joints 80

Natural frequency 49, 56, 89, 133, 134Nominal stresses 5, 85Non-uniform:

crack propagation 132stress distribution 119

Notch stresses 6, 8Numerical:

methods 9, 117models 10

Ocean waves 60, 70Oceanographic data 61, 63, 136, 137, 147Offshore installation 43, 148, 151Operating water depth 71

162

Index

Parameter, peak frequency correction 62Parameters:

geometric 10sea state 62, 147

Parametric:equations 8, 10, 13, 14, 40, 41, 84, 85, 86validity range 41

Peak counting:negative 34positive 34zero-crossing 35

Peak frequency correction parameter 62Photoelastic models 10Pierson-Moskowitz (PM) spectrum 60Pitting 27Plastic instability 38Power spectral density 49, 50Principal stresses 11Production platform 43Protected joints 24Protection

adequate 29potential 29,31

Protruding slip steps 18

Rack plate 2, 80Rainflow counting 34, 116, 128Random range generator 50Random walk technique 50Range:

counting 35, 116generator, random 50

Range-pair counting 35Residual stresses 13Resistance:

buckling 2fatigue 20,29,44,76

Response, dynamic 44, 53, 54Risk of structural failure 43

Sacrificial anode 3, 29Safety Case Regulations 43SCF, gross deformation 14SE 702:

chemical composition of 78hardness data of 80mechanical properties of 79

Sea state parameters 62, 147Sea states, distribution of 89, 147Seawater, artificial 83Sequence 127

effects 27, 33, 36, 38, 105, 128equivalent stress 98,106, 138, 139, 143, 147

Service measurements 49, 52, 56, 132, 148Significant wave height 49, 51, 60, 62, 63, 136Simulated sequence 76Slip steps, protruding 18

S-N:approach 16, 17, 36, 128design curves 17

State transition matrix 49,51Static load, equivalent 60Statistical wave description 60Steel models 10,12, 13,40Strain, measurement of 10Strength, fatigue 21Stress:

corrosion cracking, hydrogen-induced 3distribution 15, 80

non-uniform 5, 119intensity factor 11, 23, 118, 128intensity factor range 39,109range, equivalent 106, 127, 128, 138, 139,

140, 145range, hot spot 6, 94, 100, 109singularity 39principal 8sequence equivalent 98, 106, 138, 139, 143,

147Stresses:

critical 5fluctuating 16geometric 6, 8nominal 5, 85notch 6, 8principal 11residual 13

Stress-time interaction effects 28Striations, formation of 38Structural:

damping 57discontinuity 8failure 5, 60

risk of 43integrity:

assessment 9, 16, 36, 131, 138monitoring 37of cracked components 4, 105

Structure:effective mass of 56effective stiffness of 56

Superposition of wave components 60

Thickness correction exponent 21, 116Thickness effect 18Through-thickness stress gradient 23Through-wall cracking 17Time domain 54, 61Transfer function 53, 149Transgranular microfractures 38Transit loads 44Transportation modes 46Tubular welded joints 3, 5, 41, 10, 77, 80, 84,

98, 100, 107, 108, 114, 117, 118, 123, 127

163


Under-protection 31 Wave:components, superposition of 60

Variable amplitude: description, statistical 60corrosion fatigue 4, 20, 31, 42, 48, 62, 128, height, significant 49, 51, 60, 62, 63, 136

149 Wave-loading regime 55fatigue 20, 31, 34, 36, 42, 103 Waves, ocean 70

testing 47 Welded joints, tubular 3, 5, 77, 80, 84, 98,tests 77 100, 107, 108, 114, 117, 118, 123, 127

loading 20, 138, 139loading conditions 140, 147, 150 Zero crossing counting 36

Vickers hardness 79 Zero-crossing peak counting 35

Walk technique, random 50Water depth, operating 71

164

38978262 Fatigue and Fracture Mechanics of Offshore Structures

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