Unified Statistical Methodology for Modeling Fatigue Damage (eBook)

I Introduction and Motivation of the Fatigue Problem 14
An Overview of Fatigue Problems 15
Introduction 16
Models with dimensionless variables 16
S-N or Wöhler curves 18
Compatibility condition of N*| and |N* 21
Statistical considerations 23
-N curves 24
Stress level effect 25
Compatibility condition of S-N curves for constant m* and S-N curves for constant M* 26
Crack growth curves 28
Crack growth curves for a constant stress pair T* 30
Crack growth curves for a varying stress pair T* 32
Compatibility of crack growth and S-N models 34
Crack growth rate curves 34
Size effect 37
Normalization 38
Percentile based normalizations 38
Stress range and lifetime based normalizations 41
Extended percentile normalization 42
Damage measures and damage accumulation 43
II Models Used in the Stress Based Approach 45
S-N or Wöhler Field Models 46
Introduction 47
Dimensional analysis 49
Extreme models in fatigue 52
The Weibull model 52
The minimal Gumbel model 53
Model for constant stress range and level 54
Derivation of the model 54
Parameter estimation 56
Alternative methods for dealing with run-outs 59
Model for varying range and given stress level 60
Derivation of the model 60
Some weaknesses of the proposed model 64
Parameter estimation 66
Use of the model in practice 67
Example of application 68
Model for varying stress range and level 70
Dimensional Weibull and Gumbel models 75
Properties of the model 76
Parameter estimation 80
Use of the model in practice 82
Example of applications 83
Concluding remarks 95
Appendix A: Derivation of the general model 96
Appendix B: S-N curves for the general model 100
Length Effect 102
Introduction 102
Modeling the S-N field for different lengths 106
A previous example 106
General model for different lengths 108
Parameter estimation 109
Examples of Application 111
Prestressing wires 111
Prestressing strands 116
III Models Used in the Strain Based Approach 121
Log-Weibull -N Model 122
Introduction 122
Model for constant strain range and level 125
Practical example 128
Model for varying strain range and level 128
Converting strain- into stress-life curves 130
Practical example 132
Concluding remarks 133
IV Models Used in the Fracture Mechanics Approach 135
Crack Growth Models 136
Introduction and motivation 136
Building crack growth models 138
Crack growth curves approach I 142
Crack growth curves for constant * and * 142
Crack growth curves for varying * and * 145
Compatibility of crack growth and S-N models 148
Crack growth curves approach II 151
Crack growth curves for constant * and * 151
Crack growth curves for varying * and * 153
Statistical distributions of a*|N* and N*|a* 156
Learning and estimating the model 159
Compatibility of approaches I and II 160
Example of application 161
Summary and future work 163
V Damage and Damage Accumulation Models 165
Damage Measures 166
Introduction 166
Normalization 170
Damage measures 172
Some requirements for a damage measure 172
Some damage measures 173
Concluding remarks 179
Damage Accumulation 180
Damage accumulation 180
Accumulated damage after a constant stress range load step 185
Accumulated damage after block loading 186
Fatigue under a general loading history 187
Random loading 191
Crack growth damage for any load history 191
VI Appendices 195
Models Used in Fatigue 196
Introduction 196
S-N curve models 199
The Wöhler model 199
The Basquin model 201
The Strohmeyer model 202
The Palmgren model 202
The Stüssi model 203
The Weibull model 203
The Spindel and Haibach model 203
The Kohout and Vechet model 204
Stress field models 205
The Pascual and Meeker model 205
The Bastenaire model 205
The Castillo et al. (1985) model 207
Fatigue limit models 208
The up-and-down method 208
Notation Used in This Book 216
Bibliography 216
Index 222