A Unified Statistical Methodology for Modeling Fatigue Damage

Introduction and Motivation of the Fatigue Problem An Integrated Overview of Fatigue 1.1 Introduction 1.2 Models with dimensionless variables 1.3 S-N or Wohler curves 1.3.1 Compatibility condition of NlAo and AalN 1.3.2 Statistical considerations 1.4 E-N curves 1.5 Stress-level effect 1.5.1 Compatibility condition of S-N curves for constant o;T, and S-N curves for constant a& 1.6 Crack-growth curves 1.6.1 Crack-growth curves for a constant stress pair T 1.6.2 Crack-growth curves for a varying stress pair T 1.6.3 Compatibility of crack-growth and S-N models 1.7 Crack-growth rate curves 1.8 Size effect 1.9 Normalization 1.9.1 Percentilebased normalizations 1.9.2 Stress range and lifetimebased normalizations 1.9.3 Extended percentile normalization 1.10 Damage measures and damage accumulation 11 Models Used in the Stress-Based Approach 2 S-N or Wohler Field Models 2.1 Introduction 2.2 Dimensional analysis 2.3 Extreme models in fatigue 2.3.1 The Weibull model 2.3.2 The minimal Gumbel model 2.4 Model for constant stress-level and range 2.4.1 Derivation of the model 2.4.2 Parmeter estimation 2.4.3 Alternative methods for dealing with run-outs 2.5 Model for a given stress-level and varying range 2.5.1 Derivation of the model 2.5.2 Some weaknesses of the proposed model 2.5.3 Parameter estimation 2.5.4 Use of the model in practice 2.5.5 Examples of application 2.6 Model for varying stress-level and range 2.7 Dimensional Weibull and Gumbel models 2.8 Properties of the model 2.8.1 Parameter estimation 2.8.2 Use of the model in practice 2.8.3 Example of applications 2.9 Concluding remarks 2.10 Appendix A: Derivation of the general model 2.11 Appendix B: S-N curves for the general model 3 Length Effect 3.1 Introduction 3.2 Modeling the S-N field for different lengths 3.2.1 A previous example 3.2.2 General model for different lengths 3.2.3 Parameter estimation 3.3 Examples of applications 3.3.1 Prestressing wires 3.3.2 Prestressing strands I11 Models Used in the Strain-Based Approach 4 Log-Weibull e-N Model 4.1 Introduction 4.2 Model for a constant strain level and range 4.2.1 Practical example 4.3 Model for a varying strain level and range 4.4 Converting strain into stress-life curves 4.4.1 Practical example 4.5 Concluding remarks IV Models Used in the Fracture-Mechanics Approach 5 Crack-Growth Models 5.1 Introduction and motivation 5.2 Building crack growth models 5.3 Crack-growth curves approach I 5.3.1 Crack-growth curves for constant Aa and a 5.3.2 Crack-growth curves for varying AD and a 5.3.3 Compatibility of crack-growth and S-N models 5.4 crack-growth curves approach I1 5.4.1 crack-growth curves for constant Aa and a; 5.4.2 crack-growth curves for varying Aa and a 5.4.3 Statistical distributions of aI N and Nla 5.4.4 Learning and estimating the mode1 5.4.5 Compatibility of approaches I and I1 5.5 Example of application 5.6 Summary and future work V Damage and Damage Accumulation Models 6 Damage Measures 6.1 Introduction 6.2 Normalization 6.3 Damage measures 6.3.1 Some requirements for a damage measure 6.3.2 Some damage measures 6.4 Concluding remarks 7 Damage-Accumulation 7.1 Damage-accumulation 7.1.1 Accumulated damage after a constant