Avoiding or controlling fatigue damage is a major issue in the design and inspection of welded structures subjected to dynamic loading. Life predictions are usually used for safe life analysis, i.e. for verifying that it is very unlikely that fatigue damage will occur during the target service life of a structure. Damage tolerance analysis is used for predicting the behavior of a fatigue crack and for planning of in-service scheduled inspections. It should be a high probability that any cracks appearing are detected and repaired before they become critical.  In both safe life analysis and the damage tolerance analysis there may be large uncertainties involved that have to be treated in a logical and consistent manner by stochastic modeling. This book focuses on fatigue life predictions and damage tolerance analysis of welded joints and is divided into three parts. The first part outlines the common practice used for safe life and damage tolerance analysis with reference to rules and regulations. The second part emphasises stochastic modeling and decision-making under uncertainty, while the final part is devoted to recent advances within fatigue research on welded joints. Industrial examples that are included are mainly dealing with offshore steel structures. Spreadsheets which accompany the book give the reader the possibility for hands-on experience of fatigue life predictions, crack growth analysis and inspection planning. As such, these different areas will be of use to engineers and researchers.

Table of Contents:
Abbreviations xv PART I. Common Practice 1 Chapter 1. Introduction 3 1.1. The importance of welded joints and their fatigue behavior 3 1.2. Objectives and scope of the book 4 1.3. The content of the various chapters 5 1.4. Other literature in the field 7 1.5. Why should the practicing engineer apply reliability methods? 8 1.6. How to work with this book 9 1.7. About the authors 10 Chapter 2. Basic Characterization of the Fatigue Behavior of Welded Joints 11 2.1. Introduction and objectives 11 2.2. Fatigue failures 11 2.3. Basic mechanisms of metal fatigue 15 2.4. Parameters that are important to the fatigue damage process 17 2.4.1. External loading and stresses in an item 17 2.4.2. Geometry, stress and strain concentrations 19 2.4.3. Material parameters 20 2.4.4. Residual stresses 24 2.4.5. Fabrication quality and surface finish 25 2.4.6. Influence of the environment 25 2.5. Important topics for welded joints 26 2.5.1. General overview 26 2.6. Various types of joints 30 2.6.1. Plated joints 30 2.6.2. Tubular joints 34 2.7. References 35 Chapter 3. Experimental Methods and Data Analysis 37 3.1. Introduction and objectives 37 3.2. Overview of various types of tests 38 3.3. Stress-life testing (S-N testing) of welded joints 38 3.3.1. Test specimens and test setup 38 3.3.2. Preparations and measurements 41 3.3.3. Test results 46 3.4. Testing to determine the parameters in the strain-life equation 49 3.5. Crack growth tests – guidelines for test setup and specimen monitoring 50 3.6. Elementary statistical methods 55 3.6.1. Linear regression analyses 55 3.7. References 60 Chapter 4. Definition and Description of Fatigue Loading 61 4.1. Introduction and objectives 61 4.2. Constant amplitude loading 62 4.3. Variable amplitude loading 63 4.3.1. Overview 63 4.3.2. Rain-flow cycle counting of time series 64 4.3.3. The energy spectrum approach 69 4.4. References 73 Chapter 5. The S-N Approach 75 5.1. Introduction and objectives 75 5.2. Method, assumptions and important factors 76 5.2.1. Statistics for the S-N approach, median and percentile curves 76 5.2.2. Discussion of S-N curves-important factors 78 5.2.2.1. The threshold phenomenon 78 5.2.2.2. Mean stress and loading ratio 79 5.2.2.3. Stress relieving 79 5.2.2.4. The thickness effect 80 5.2.2.5. Misalignment 81 5.2.2.6. Post-weld improvement techniques 82 5.2.2.7. Corrosive environment 83 5.3. Mathematics for damage calculations 84 5.3.1. Linear damage accumulation; load spectrum on a histogram format 84 5.3.2. Discussion of the validity of the linear damage accumulation 86 5.3.3. Definition of the equivalent stress range 88 5.3.4. Load spectrum on the format of a Weibull distribution 88 5.4. S-N curves related to various stress definitions 91 5.4.1. Nominal stress, geometrical stress and weld notch stresses 92 5.4.2. Geometrical stresses in tubular joints 96 5.4.3. Fatigue life estimate based on the weld notch stress approach 98 5.4.4. Conclusions on the various stress approaches 101 5.5. Some comments on finite element analysis 104 5.6. Current rule and regulations 110 5.6.1. General considerations 110 5.6.2. The original fatigue classes and S-N curves from DoE 112 5.6.3. S-N life predictions according to Eurocode 3-Air environment 117 5.6.4. S-N life predictions according to HSE 119 5.6.5. S-N life predictions according to NORSOK and DNV 120 5.6.6. S-N life predictions for ship structures 122 5.7. The industrial case: an offshore loading buoy 130 5.8. References 136 Chapter 6. Applied Fracture Mechanics 139 6.1. Introduction 139 6.2. Objectives of this chapter 142 6.3. Basic concepts of linear elastic fracture mechanics 142 6.3.1. The local stress field ahead of the crack front 142 6.4. Fracture criterion due to extreme load 152 6.4.1. Mixed mode rupture 153 6.4.2. The R6 criterion and critical crack size 154 6.5. Fatigue threshold and fatigue crack growth 156 6.5.1. Crack growth models 156 6.5.2. Parameters C and m 159 6.5.3. Residual stresses 160 6.5.4. Some notes on the size of the initial cracks 161 6.6. Geometry function and growth parameters given in BS7910 161 6.6.1. The geometry function 162 6.6.2. Parameters C and m 163 6.7. Fracture mechanics model for a fillet welded plate joint 165 6.7.1. Basic assumptions and criteria for the model 165 6.7.2. Data for crack growth measurements (database 1) 166 6.7.3. Data for fatigue lives at low stress levels (database 2) 167 6.7.4. Procedure and curve fitting 167 6.7.5. Growth parameters C and m 169 6.7.6. The initial crack depth a0 172 6.7.7. Prediction of crack growth histories and construction of S-N curves 173 6.7.8. Conclusions for fillet joints with cracks at the weld toe 175 6.8. Fatigue crack growth in tubular joints 176 6.8.1. Discussion of current models 179 6.8.2. Conclusion on the empirical fracture mechanics model 183 6.8.3. Proposal for model improvements 183 6.9. A brief overview of stiffened panels 184 6.10. Units and conversion for fracture mechanics parameters 186 6.11. Industrial case: fatigue re-assessment of a welded pipe 186 6.11.1. Introduction 186 6.11.2. Description of the loading buoy with steel pipe 187 6.11.3. Replacement and inspection strategy 189 6.11.4. Re-assessment based on the S-N approach 190 6.11.5. Re-assessment based on fracture mechanics 191 6.12. References193 PART II. Stochastic Modeling 197 Chapter 7. Stochastic Modeling 199 7.1. Introduction and objectives 199 7.2. Overview of models and methodology 200 7.2.1. Sources of uncertainty 200 7.2.2. Introduction to the random variable model and related methods 201 7.2.3. Requirements for a stochastic model 203 7.2.4. The concept of the limit state function and the safety margin 204 7.2.5. The first and second order reliability methods (FORM/SORM) 206 7.3. Elementary reliability models 207 7.3.1. General considerations 207 7.3.2. The Lognormal distribution 208 7.3.3. The Weibull distribution  209 7.4. The random variable model using simulation methods 212 7.4.1. General considerations 212 7.4.2. The realization of a random variable by the Monte Carlo method 213 7.5. Random variable models based on the S-N approach 215 7.5.1. The lognormal format for the S-N fatigue life 215 7.5.1.1. Example: full-penetration butt joint in an offshore structure 217 7.5.2. Monte Carlo Simulation of the S-N fatigue life 219 7.6. Random variable models based on fracture mechanics 220 7.6.1. General considerations 220 7.6.2. Taking account for future inspections and inspection results 221 7.6.3. Characterization of the performance of the non-destructive inspection technique 223 7.6.4. Simulation with account for future planned inspections 225 7.6.4.1. A first approximation to the inspection problem 225 7.6.4.2. Full stochastic simulation 226 7.6.5. Simulation of planned inspections for a fillet welded joint 229 7.6.6. Updating based on inspections results 231 7.7. The Markov chain model 235 7.7.1. Basic concepts 235 7.7.2. Simple illustration on how the model works 235 7.7.3. Elaboration of the model 242 7.7.4. Influence of scheduled inspection and repair 244 7.7.5. Parameter estimation  246 7.7.6. Hybrid model to account for additional scatter 248 7.7.7. Analysis of a fillet welded joint 249 7.7.7.1. Short review and elaboration of database 1 250 7.7.7.2. Determination of parameters in the Markov model 251 7.7.7.3. Reliability results and discussion 253 7.8. A damage tolerance supplement to rules and regulation 255 7.8.1. Introduction 255 7.8.2. An industrial case study: single anchor loading system 260 7.8.2.1. Example 1: butt weld in upper pipeline 262 7.8.2.2. Example 2: welded brackets on the main plates 263 7.8.3. Conclusions for the damage tolerance supplement 263 7.9. Risk assessments and cost benefit analysis 264 7.10. Reliability and risk assessment for the riser steel pipe 267 7.11. References 268 PART III. Recent Advances 271 Chapter 8. Proposal for a New Type of S-N Curve 273 8.1. Introduction and objectives 273 8.2. General considerations for the conventional S-N approach 275 8.2.1. Basic assumptions 275 8.2.2. The S-N approach based on BS5400 and Eurocode 3 275 8.3. S-N curves based on a random fatigue limit model 277 8.4. Experimental data for model calibration 278 8.4.1. Data for fatigue life at high stress levels (database 1) 278 8.4.2. Data for fatigue lives at low stress levels (database 2) 279 8.5. Comparison between the F-class curve, the RFLM-based curve and the data 279 8.6. Conclusions 284 8.7. References 284 Chapter 9. Physical Modeling of the Entire Fatigue Process 287 9.1. Introduction and objectives 287 9.2. Modeling the fatigue crack initiation period 289 9.2.1. Basic concept and equations for the local stress-strain approach 289 9.2.2. Definition of the initiation phase and determination of parameters 292 9.2.3. Local toe geometry and stress concentration factor 292 9.2.4. Transition depth 294 9.2.5. Cyclic mechanical properties and parameters in Coffin-Manson equation 295 9.3. Constructing the S-N curve from the two-phase model 297 9.4. Damage accumulation using the TPM 301 9.5. The practical consequences of the TPM 302 9.5.1. General considerations 302 9.5.2. Life predictions and dimensions 302 9.5.3. Predicted crack evolution and inspection planning 303 9.6. Conclusions 306 9.7. Suggestions for future work 307 9.8. References 308 Chapter 10. A Notch Stress Field Approach to the Prediction of Fatigue Life 309 10.1. A modified S-N approach 309 10.1.1. General considerations 309 10.1.2. The basic theory for the notch stress intensity factor 311 10.1.3. S-N data analysis for fillet welded joints 313 10.2. A modified crack growth approach 315 10.3. References 317 Chapter 11. Multi-Axial Fatigue of Welded Joints 319 11.1. Introduction and objectives 319 11.2. Overview of theory and crack-extension criteria 321 11.3. The crack box technique 322 11.3.1. General considerations for finite element analysis and element mesh 322 11.3.2. Methodology 322 11.3.3. Examples 324 11.4. Tentative mixed-mode model to crack propagation in welded joints 325 11.4.1. Modeling the effect of the loading mode on the crack growth rate 327 11.4.2. Modeling the effect of the residual stress due to the weld on the crack growth rate 328 11.4.3. Measured effect of the loading angle on the crack growth rate 329 11.4.4. Measured effect of weld on the crack growth rate 331 11.4.5. Measured crack extension angle under mixed mode loading 332 11.5. Validation of the model 333 11.5.1. Verification of the models for non-welded steel specimens under mixed-mode loading 334 11.5.2. Verification of the models for non-welded and welded steel specimens under mode I loading 336 11.5.3. Verification of the models for welded steel specimens under mixed-mode loading 337 11.5.4. Verification of the effect of the welded residual stress on the fatigue life 338 11.5.5. Discussion and conclusions 339 11.6. Extension to full test 340 11.6.1. Modeling methodology 341 11.6.2. Global calculation scheme 341 11.6.3. The crack box technique 343 11.6.4. Crack-propagation rate 344 11.6.5. Description of experiments carried out 345 11.6.6. Results 345 11.6.7. Weld toe geometry 346 11.6.8. Numerical calculations 347 11.6.8.1. Crack initiation 347 11.6.8.2. Crack growth 349 11.7. References 351 Chapter 12. The Effect of Overloads on the Fatigue Life 355 12.1. Introduction and objectives 355 12.2. Residual stress opening approach at the crack tip following an overload during fatigue 359 12.3. Numerical modeling 362 12.3.1. Modeling aspects 362 12.3.2. Finite element modeling choices 363 12.4. Proposed deterministic approach to fatigue crack growth following an overload 366 12.5. Reliability modeling including the effect of an overload 370 12.6. Application of the reliability model to a fillet welded joint 371 12.7. References 375 Appendix A. Short Overview of the Foundations of Fracture Mechanics 381 A1. Introduction 381 A2. Elementary failure modes and stress situations 383 A3. Foundations of fracture mechanics 383 A4. Parameters characterizing the singular zone 385 A4.1. The stress intensity factor (SIF), K. 385 A4.2. The energy release rate, G 387 A4.3. The J-integral 388 A4.4. The crack-opening displacement (COD) 389 A5. Asymptotic stress field in elastic-plastic media 390 A5. References 391 Appendix B. Spreadsheet for Fatigue Life Estimates 393 Appendix C. CG – Crack Growth Based on Fracture Mechanics 395 Appendix D. CI – Crack Initiation Based on Coffin-Manson 399 Index 403