Fatigue Life Analyses of Welded Structures

Tom Lassen is from Agder University College in Grimstad, Norway. He also teaches aircraft maintenance for the Norwegian Royal Air Force and has recently been a visiting Professor at University Blaise Pascal, Clermont-Ferrand, France. Naman Recho has worked extensively with conceptual and applied aspects of fracture mechanics, with welded offshore structures and reliability analysis of cracked structures. He also teaches at Centre des Hautes Etudes de la Construction, Paris, and is guest Professor at Hefei University of Technology in China.

• Abbreviations xvPART I. Common Practice 1Chapter 1. Introduction 31.1. The importance of welded joints and their fatigue behavior 31.2. Objectives and scope of the book 41.3. The content of the various chapters 51.4. Other literature in the field 71.5. Why should the practicing engineer apply reliability methods? 81.6. How to work with this book 91.7. About the authors 10Chapter 2. Basic Characterization of the Fatigue Behavior of Welded Joints 112.1. Introduction and objectives 112.2. Fatigue failures 112.3. Basic mechanisms of metal fatigue 152.4. Parameters that are important to the fatigue damage process 172.4.1. External loading and stresses in an item 172.4.2. Geometry, stress and strain concentrations 192.4.3. Material parameters 202.4.4. Residual stresses 242.4.5. Fabrication quality and surface finish 252.4.6. Influence of the environment 252.5. Important topics for welded joints 262.5.1. General overview 262.6. Various types of joints 302.6.1. Plated joints 302.6.2. Tubular joints 342.7. References 35Chapter 3. Experimental Methods and Data Analysis 373.1. Introduction and objectives 373.2. Overview of various types of tests 383.3. Stress-life testing (S-N testing) of welded joints 383.3.1. Test specimens and test setup 383.3.2. Preparations and measurements 413.3.3. Test results 463.4. Testing to determine the parameters in the strain-life equation 493.5. Crack growth tests – guidelines for test setup and specimen monitoring 503.6. Elementary statistical methods 553.6.1. Linear regression analyses 553.7. References 60Chapter 4. Definition and Description of Fatigue Loading 614.1. Introduction and objectives 614.2. Constant amplitude loading 624.3. Variable amplitude loading 634.3.1. Overview 634.3.2. Rain-flow cycle counting of time series 644.3.3. The energy spectrum approach 694.4. References 73Chapter 5. The S-N Approach 755.1. Introduction and objectives 755.2. Method, assumptions and important factors 765.2.1. Statistics for the S-N approach, median and percentile curves 765.2.2. Discussion of S-N curves-important factors 785.2.2.1. The threshold phenomenon 785.2.2.2. Mean stress and loading ratio 795.2.2.3. Stress relieving 795.2.2.4. The thickness effect 805.2.2.5. Misalignment 815.2.2.6. Post-weld improvement techniques 825.2.2.7. Corrosive environment 835.3. Mathematics for damage calculations 845.3.1. Linear damage accumulation; load spectrum on a histogram format 845.3.2. Discussion of the validity of the linear damage accumulation 865.3.3. Definition of the equivalent stress range 885.3.4. Load spectrum on the format of a Weibull distribution 885.4. S-N curves related to various stress definitions 915.4.1. Nominal stress, geometrical stress and weld notch stresses 925.4.2. Geometrical stresses in tubular joints 965.4.3. Fatigue life estimate based on the weld notch stress approach 985.4.4. Conclusions on the various stress approaches 1015.5. Some comments on finite element analysis 1045.6. Current rule and regulations 1105.6.1. General considerations 1105.6.2. The original fatigue classes and S-N curves from DoE 1125.6.3. S-N life predictions according to Eurocode 3-Air environment 1175.6.4. S-N life predictions according to HSE 1195.6.5. S-N life predictions according to NORSOK and DNV 1205.6.6. S-N life predictions for ship structures 1225.7. The industrial case: an offshore loading buoy 1305.8. References 136Chapter 6. Applied Fracture Mechanics 1396.1. Introduction 1396.2. Objectives of this chapter 1426.3. Basic concepts of linear elastic fracture mechanics 1426.3.1. The local stress field ahead of the crack front 1426.4. Fracture criterion due to extreme load 1526.4.1. Mixed mode rupture 1536.4.2. The R6 criterion and critical crack size 1546.5. Fatigue threshold and fatigue crack growth 1566.5.1. Crack growth models 1566.5.2. Parameters C and m 1596.5.3. Residual stresses 1606.5.4. Some notes on the size of the initial cracks 1616.6. Geometry function and growth parameters given in BS7910 1616.6.1. The geometry function 1626.6.2. Parameters C and m 1636.7. Fracture mechanics model for a fillet welded plate joint 1656.7.1. Basic assumptions and criteria for the model 1656.7.2. Data for crack growth measurements (database 1) 1666.7.3. Data for fatigue lives at low stress levels (database 2) 1676.7.4. Procedure and curve fitting 1676.7.5. Growth parameters C and m 1696.7.6. The initial crack depth a0 1726.7.7. Prediction of crack growth histories and construction of S-N curves 1736.7.8. Conclusions for fillet joints with cracks at the weld toe 1756.8. Fatigue crack growth in tubular joints 1766.8.1. Discussion of current models 1796.8.2. Conclusion on the empirical fracture mechanics model 1836.8.3. Proposal for model improvements 1836.9. A brief overview of stiffened panels 1846.10. Units and conversion for fracture mechanics parameters 1866.11. Industrial case: fatigue re-assessment of a welded pipe 1866.11.1. Introduction 1866.11.2. Description of the loading buoy with steel pipe 1876.11.3. Replacement and inspection strategy 1896.11.4. Re-assessment based on the S-N approach 1906.11.5. Re-assessment based on fracture mechanics 1916.12. References193PART II. Stochastic Modeling 197Chapter 7. Stochastic Modeling 1997.1. Introduction and objectives 1997.2. Overview of models and methodology 2007.2.1. Sources of uncertainty 2007.2.2. Introduction to the random variable model and related methods 2017.2.3. Requirements for a stochastic model 2037.2.4. The concept of the limit state function and the safety margin 2047.2.5. The first and second order reliability methods (FORM/SORM) 2067.3. Elementary reliability models 2077.3.1. General considerations 2077.3.2. The Lognormal distribution 2087.3.3. The Weibull distribution  2097.4. The random variable model using simulation methods 2127.4.1. General considerations 2127.4.2. The realization of a random variable by the Monte Carlo method 2137.5. Random variable models based on the S-N approach 2157.5.1. The lognormal format for the S-N fatigue life 2157.5.1.1. Example: full-penetration butt joint in an offshore structure 2177.5.2. Monte Carlo Simulation of the S-N fatigue life 2197.6. Random variable models based on fracture mechanics 2207.6.1. General considerations 2207.6.2. Taking account for future inspections and inspection results 2217.6.3. Characterization of the performance of the non-destructive inspection technique 2237.6.4. Simulation with account for future planned inspections 2257.6.4.1. A first approximation to the inspection problem 2257.6.4.2. Full stochastic simulation 2267.6.5. Simulation of planned inspections for a fillet welded joint 2297.6.6. Updating based on inspections results 2317.7. The Markov chain model 2357.7.1. Basic concepts 2357.7.2. Simple illustration on how the model works 2357.7.3. Elaboration of the model 2427.7.4. Influence of scheduled inspection and repair 2447.7.5. Parameter estimation  2467.7.6. Hybrid model to account for additional scatter 2487.7.7. Analysis of a fillet welded joint 2497.7.7.1. Short review and elaboration of database 1 2507.7.7.2. Determination of parameters in the Markov model 2517.7.7.3. Reliability results and discussion 2537.8. A damage tolerance supplement to rules and regulation 2557.8.1. Introduction 2557.8.2. An industrial case study: single anchor loading system 2607.8.2.1. Example 1: butt weld in upper pipeline 2627.8.2.2. Example 2: welded brackets on the main plates 2637.8.3. Conclusions for the damage tolerance supplement 2637.9. Risk assessments and cost benefit analysis 2647.10. Reliability and risk assessment for the riser steel pipe 2677.11. References 268PART III. Recent Advances 271Chapter 8. Proposal for a New Type of S-N Curve 2738.1. Introduction and objectives 2738.2. General considerations for the conventional S-N approach 2758.2.1. Basic assumptions 2758.2.2. The S-N approach based on BS5400 and Eurocode 3 2758.3. S-N curves based on a random fatigue limit model 2778.4. Experimental data for model calibration 2788.4.1. Data for fatigue life at high stress levels (database 1) 2788.4.2. Data for fatigue lives at low stress levels (database 2) 2798.5. Comparison between the F-class curve, the RFLM-based curve and the data 2798.6. Conclusions 2848.7. References 284Chapter 9. Physical Modeling of the Entire Fatigue Process 2879.1. Introduction and objectives 2879.2. Modeling the fatigue crack initiation period 2899.2.1. Basic concept and equations for the local stress-strain approach 2899.2.2. Definition of the initiation phase and determination of parameters 2929.2.3. Local toe geometry and stress concentration factor 2929.2.4. Transition depth 2949.2.5. Cyclic mechanical properties and parameters in Coffin-Manson equation 2959.3. Constructing the S-N curve from the two-phase model 2979.4. Damage accumulation using the TPM 3019.5. The practical consequences of the TPM 3029.5.1. General considerations 3029.5.2. Life predictions and dimensions 3029.5.3. Predicted crack evolution and inspection planning 3039.6. Conclusions 3069.7. Suggestions for future work 3079.8. References 308Chapter 10. A Notch Stress Field Approach to the Prediction of Fatigue Life 30910.1. A modified S-N approach 30910.1.1. General considerations 30910.1.2. The basic theory for the notch stress intensity factor 31110.1.3. S-N data analysis for fillet welded joints 31310.2. A modified crack growth approach 31510.3. References 317Chapter 11. Multi-Axial Fatigue of Welded Joints 31911.1. Introduction and objectives 31911.2. Overview of theory and crack-extension criteria 32111.3. The crack box technique 32211.3.1. General considerations for finite element analysis and element mesh 32211.3.2. Methodology 32211.3.3. Examples 32411.4. Tentative mixed-mode model to crack propagation in welded joints 32511.4.1. Modeling the effect of the loading mode on the crack growth rate 32711.4.2. Modeling the effect of the residual stress due to the weld on the crack growth rate 32811.4.3. Measured effect of the loading angle on the crack growth rate 32911.4.4. Measured effect of weld on the crack growth rate 33111.4.5. Measured crack extension angle under mixed mode loading 33211.5. Validation of the model 33311.5.1. Verification of the models for non-welded steel specimens under mixed-mode loading 33411.5.2. Verification of the models for non-welded and welded steel specimens under mode I loading 33611.5.3. Verification of the models for welded steel specimens under mixed-mode loading 33711.5.4. Verification of the effect of the welded residual stress on the fatigue life 33811.5.5. Discussion and conclusions 33911.6. Extension to full test 34011.6.1. Modeling methodology 34111.6.2. Global calculation scheme 34111.6.3. The crack box technique 34311.6.4. Crack-propagation rate 34411.6.5. Description of experiments carried out 34511.6.6. Results 34511.6.7. Weld toe geometry 34611.6.8. Numerical calculations 34711.6.8.1. Crack initiation 34711.6.8.2. Crack growth 34911.7. References 351Chapter 12. The Effect of Overloads on the Fatigue Life 35512.1. Introduction and objectives 35512.2. Residual stress opening approach at the crack tip following an overload during fatigue 35912.3. Numerical modeling 36212.3.1. Modeling aspects 36212.3.2. Finite element modeling choices 36312.4. Proposed deterministic approach to fatigue crack growth following an overload 36612.5. Reliability modeling including the effect of an overload 37012.6. Application of the reliability model to a fillet welded joint 37112.7. References 375Appendix A. Short Overview of the Foundations of Fracture Mechanics 381A1. Introduction 381A2. Elementary failure modes and stress situations 383A3. Foundations of fracture mechanics 383A4. Parameters characterizing the singular zone 385A4.1. The stress intensity factor (SIF), K. 385A4.2. The energy release rate, G 387A4.3. The J-integral 388A4.4. The crack-opening displacement (COD) 389A5. Asymptotic stress field in elastic-plastic media 390A5. References 391Appendix B. Spreadsheet for Fatigue Life Estimates 393Appendix C. CG – Crack Growth Based on Fracture Mechanics 395Appendix D. CI – Crack Initiation Based on Coffin-Manson 399Index 403