Preface ...................................................... xiii
Acknowledgments ................................................ xv
1 Introduction ................................................. 1
1.1 Contextual Framework .................................... 2
1.2 Lessons Learned and Contextual Framework ................ 4
1.3 Crack Tolerance and Residual Strength ................... 5
1.4 Crack Growth Resistance and Subcritical Crack Growth .... 7
1.5 Objective and Scope of Book ............................. 7
REFERENCES ................................................... 8
2 Physical Basis of Fracture Mechanics ......................... 9
2.1 Classical Theories of Failure ........................... 9
2.1.1 Maximum Principal Stress (or Tresca [3])
Criterion ........................................ 9
2.1.2 Maximum Shearing Stress Criterion ............... 10
2.1.3 Maximum Principal Strain Criterion .............. 10
2.1.4 Maximum Total Strain Energy Criterion ........... 10
2.1.5 Maximum Distortion Energy Criterion ............. 11
2.1.6 Maximum Octahedral Shearing Stress Criterion
(von Mises [4] Criterion) ....................... 12
2.1.7 Comments on the Classical Theories of Failure ... 12
2.2 Further Considerations of Classical Theories ........... 12
2.3 Griffith's Crack Theory of Fracture Strength ........... 14
2.4 Modifications to Griffith's Theory ..................... 16
2.5 Estimation of Crack-Driving Force G from Energy Loss
Rate (Irwin and Kies [8, 9]) ........................... 17
2.6 Experimental Determination of G ........................ 20
2.7 Fracture Behavior and Crack Growth Resistance Curve .... 21
REFERENCES .................................................. 25
3 Stress Analysis of Cracks ................................... 26
3.1 Two-Dimensional Theory of Elasticity ................... 26
3.1.1 Stresses ........................................ 27
3.1.2 Equilibrium ..................................... 27
3.1.3 Stress-Strain and Strain-Displacement
Relations ....................................... 28
3.1.4 Compatibility Relationship ...................... 29
3.2 Airy's Stress Function ................................. 30
3.2.1 Basic Formulation ............................... 30
3.2.2 Method of Solution Using Functions of Complex
Variables ....................................... 32
Complex Numbers ............................................. 32
Complex Variables and Functions ............................. 32
Cauchy-Riemann Conditions and Analytic Functions ............ 33
3.3 Westergaard Stress Function Approach [8] ............... 34
3.3.1 Stresses ........................................ 34
3.3.2 Displacement (Generalized Plane Stress) ......... 35
3.3.3 Stresses at a Crack Tip and Definition of
Stress Intensity Factor ......................... 36
3.4 Stress Intensity Factors - Illustrative Examples ....... 38
3.4.1 Central Crack in an Infinite Plate under
Biaxial Tension (Griffith Problem) .............. 39
Stress Intensity Factor ......................... 39
Displacements ................................... 41
3.4.2 Central Crack in an Infinite Plate under
a Pair of Concentrated Forces [2-4] ............. 41
3.4.3 Central Crack in an Infinite Plate under Two
Pairs of Concentrated Forces .................... 43
3.4.4 Central Crack in an Infinite Plate Subjected
to Uniformly Distributed Pressure on Crack
Surfaces ........................................ 43
3.5 Relationship between G and К ........................... 45
3.6 Plastic Zone Correction Factor and Crack-Opening
Displacement ........................................... 47
Plastic Zone Correction Factor .............................. 47
Crack-Tip-Opening Displacement (CTOD) ....................... 48
3.7 Closing Comments ....................................... 48
REFERENCES .................................................. 49
4 Experimental Determination of Fracture Toughness ............ 50
4.1 Plastic Zone and Effect of Constraint .................. 50
4.2 Effect of Thickness; Plane Strain versus Plane
Stress ................................................. 52
4.3 Plane Strain Fracture Toughness Testing ................ 54
4.3.1 Fundamentals of Specimen Design and Testing ..... 55
4.3.2 Practical Specimens and the "Pop-in" Concept .... 58
4.3.3 Summary of Specimen Size Requirement ............ 60
4.3.4 Interpretation of Data for Plane Strain
Fracture Toughness Testing ...................... 61
4.4 Crack Growth Resistance Curve .......................... 67
4.5 Other Modes/Mixed Mode Loading ......................... 70
REFERENCES .................................................. 70
5 Fracture Considerations for Design (Safety) ................. 72
5.1 Design Considerations (Irwin's Leak-Before-Break
Criterion) ............................................. 72
5.1.1 Influence of Yield Strength and Material
Thickness ....................................... 74
5.1.2 Effect of Material Orientation .................. 74
5.2 Metallurgical Considerations (Krafft's Tensile
Ligament Instability Model [4]) ........................ 75
5.3 Safety Factors and Reliability Estimates ............... 78
5.3.1 Comparison of Distribution Functions ............ 81
5.3.2 Influence of Sample Size ........................ 82
5.4 Closure ................................................ 84
REFERENCES .................................................. 85
6 Subcritical Crack Growth: Creep-Controlled Crack Growth ..... 86
6.1 Overview ............................................... 86
6.2 Creep-Controlled Crack Growth: Experimental Support .... 87
6.3 Modeling of Creep-Controlled Crack Growth .............. 90
6.3.1 Background for Modeling ......................... 92
6.3.2 Model for Creep ................................. 93
6.3.3 Modeling for Creep Crack Growth ................. 94
6.4 Comparison with Experiments and Discussion ............. 97
6.4.1 Comparison with Experimental Data ............... 97
6.4.2 Model Sensitivity to Key Parameters ............. 99
6.5 Summary Comments ...................................... 101
REFERENCES ................................................. 101
7 Subcritical Crack Growth: Stress Corrosion Cracking and
Fatigue Crack Growth (Phenomenology) ....................... 103
7.1 Overview .............................................. 103
7.2 Methodology ........................................... 104
7.2.1 Stress Corrosion Cracking ...................... 106
7.2.2 Fatigue Crack Growth ........................... 108
7.2.3 Combined Stress Corrosion Cracking and
Corrosion Fatigue .............................. 110
7.3 The Life Prediction Procedure and Illustrations [4] ... 111
Example 1 - Through-Thickness Crack ........................ 111
Example 2 - For Surface Crack or Part-Through Crack ........ 114
7.4 Effects of Loading and Environmental Variables ........ 115
7.5 Variability in Fatigue Crack Growth Data .............. 118
7.6 Summary Comments ...................................... 118
REFERENCES ................................................. 119
8 Subcritical Crack Growth: Environmentally Enhanced Crack
Growth under Sustained Loads (or Stress Corrosion
Cracking) .................................................. 120
8.1 Overview .............................................. 120
8.2 Phenomenology, a Clue, and Methodology ................ 121
8.3 Processes that Control Crack Growth ................... 123
8.4 Modeling of Environmentally Enhanced (Sustained-
Load) Crack Growth Response ........................... 124
Modeling Assumptions ....................................... 126
8.4.1 Gaseous Environments ........................... 127
8.4.1.1 Transport-Controlled Crack Growth ..... 129
8.4.1.2 Surface Reaction and Diffusion-
Controlled Crack Growth ............... 130
8.4.2 Aqueous Environments .................... 131
8.4.3 Summary Comments ........................ 133
8.5 Hydrogen-Enhanced Crack Growth: Rate-Controlling
Processes and Hydrogen Partitioning ................... 133
8.6 Electrochemical Reaction-Controlled Crack Growth
(Hydrogen Embrittlement) .............................. 137
8.7 Phase Transformation and Crack Growth in Yttria-
Stabilized Zirconia ................................... 141
8.8 Oxygen-Enhanced Crack Growth in Nickel-Based
Superalloys ........................................... 143
8.8.1 Crack Growth ................................... 144
8.8.2 High-Temperature Oxidation ..................... 146
8.8.3 Interrupted Crack Growth ....................... 148
8.8.3.1 Mechanically Based (Crack Growth)
Experiments ........................... 148
8.8.3.2 Chemically Based Experiments
(Surface Chemical Analyses) ........... 149
8.8.4 Mechanism for Oxygen-Enhanced Crack Growth in
the P/M Alloys ................................. 153
8.8.5 Importance for Material Damage Prognosis and
Life Cycle Engineering ......................... 154
8.9 Summary Comments ...................................... 155
REFERENCES ................................................. 155
9 Subcritical Crack Growth: Environmentally Assisted
Fatigue Crack Growth (or Corrosion Fatigue) ................ 158
9.1 Overview .............................................. 158
9.2 Modeling of Environmentally Enhanced Fatigue Crack
Growth Response ....................................... 158
9.2.1 Transport-Controlled Fatigue Crack Growth ...... 160
9.2.2 Surface/Electrochemical Reaction-Controlled
Fatigue Crack Growth ........................... 161
9.2.3 Diffusion-Controlled Fatigue Crack Growth ...... 162
9.2.4 Implications for Material/Response ............. 162
9.2.5 Corrosion Fatigue in Binary Gas Mixtures [3] ... 162
9.2.6 Summary Comments ............................... 164
9.3 Moisture-Enhanced Fatigue Crack Growth in Aluminum
Alloys [1, 2, 5] ...................................... 164
9.3.1 Alloy 2219-T851 in Water Vapor [1, 2] .......... 164
9.3.2 Alloy 7075-T651 in Water Vapor and Water [5] ... 167
9.3.3 Key Findings and Observations .................. 168
9.4 Environmentally Enhanced Fatigue Crack Growth in
Titanium Alloys [6] ................................... 169
9.4.1 Influence of Water Vapor Pressure on Fatigue
Crack Growth ................................... 169
9.4.2 Surface Reaction Kinetics ...................... 169
9.4.3 Transport Control of Fatigue Crack Growth ...... 171
9.4.4 Hydride Formation and Strain Rate Effects ...... 173
9.5 Microstructural Considerations ........................ 175
9.6 Electrochemical Reaction-Controlled Fatigue Crack
Growth ................................................ 177
9.7 Crack Growth Response in Binary Gas Mixtures .......... 180
9.8 Summary Comments ...................................... 180
REFERENCES ................................................. 181
10 Science-Based Probability Modeling and Life Cycle
Engineering and Management ................................. 183
10.1 Introduction .......................................... 183
10.2 Framework ............................................. 184
10.3 Science-Based Probability Approach .................... 185
10.3.1 Methodology .................................... 185
10.3.2 Comparison of Approaches ....................... 186
10.4 Corrosion and Corrosion Fatigue in Aluminum Alloys,
and Applications ...................................... 187
10.4.1 Particle-Induced Pitting in an Aluminum
Alloy .......................................... 187
10.4.2 Impact of Corrosion and Fatigue Crack Growth
on Fatigue Lives (S-N Response) ................ 191
10.4.3 S-N versus Fracture Mechanics (FM) Approaches
to Corrosion Fatigue and Resolution of
a Dichotomy .................................... 193
10.4.4 Evolution and Distribution of Damage in Aging
Aircraft ....................................... 193
10.5 S-N Response for Very-High-Cycle Fatigue (VHCF) ....... 194
10.6 Summary ............................................... 197
REFERENCES .................................................... 197
APPENDIX: Publications By R.P. Wei and Colleagues ............. 199
Overview/General ........................................... 199
Fracture ...................................................... 200
Stress Corrosion Cracking/Hydrogen-Enhanced Crack Growth ... 200
Deformation (Creep) Controlled Crack Growth ................ 203
Oxygen-Enhanced Crack Growth ............................... 203
Fatigue/Corrosion Fatigue .................................. 204
Fatigue Mechanisms ......................................... 206
Ceramics/Intermetallics .................................... 211
Material Damage Prognosis/Life Cycle Engineering ........... 211
Failure Investigations/Analyses ............................ 213
Analytical/Experimental Techniques ......................... 213
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