EBOOK - The Theory of Materials Failure (Richard M. Christensen)


The technical and scholarly interest in materials failure goes back almost to the beginnings of classical mechanics and deformable body mechanics. The effort to put order and organization into the field of failure characterization and failure criteria has been unflagging over the ensuing time span, measured in decades and even centuries. Despite the high level of sustained activity, the long time rate of progress was agonizingly slow.

By many measures of difficulty, the treatment of failure in solids (materials) is comparable to that of turbulence in fluids, both being controlled by non-linear physical effects. It is only in the modern era that the elements needed for constructing a complete, three-dimensional theory of failure for homogeneous materials have coalesced into meaningful forms. This book presents the derivation and a detailed examination of the resultant general theory of failure for materials science and materials engineering.

CONTENTS:

Technical Status and Challenges xii
1 The Perspective on Failure and Direction of Approach 1
1.1 Materials Failure Problem 1
1.2 Direction and Scope 2
1.3 Guides for Utility 4
References 5
2 History, Conditions, and Requirements 6
2.1 Historical Review 7
2.2 Conditions and Requirements of Study 12
References 14
3 Isotropic Baselines 16
3.1 Failure Characterization 16
3.2 Stress versus Strain 17
3.3 Mises and Tresca Failure Criteria 19
3.4 Drucker–Prager Failure Criterion 23
3.5 Coulomb–Mohr Failure Criterion 25
3.6 The Bottom Line 28
References 29
4 The Failure Theory for Isotropic Materials 30
4.1 Theoretical and Testing Problems 30
4.2 Properties or Parameters 31
4.3 The Organizing Principle 32
4.4 The Constitutive Equations of Failure, Part A:
Polynomial-Invariants Criterion 34
4.5 The Constitutive Equations of Failure, Part B:
Fracture Criterion 39
4.6 Ductile and Brittle Limits 42
4.7 Problem Sets Purpose 46
Problem Areas for Study 48
References 49
viii Contents
5 Isotropic Materials Failure Behavior 50
5.1 Failure Behavior in Two Dimensions 51
5.2 Failure in Principal Stress Space 51
5.3 Ductile-versus-Brittle Failure 57
5.4 TandCversusSandD 61
Problem Areas for Study 68
References 69
6 Experimental and Theoretical Evaluation 70
6.1 Evaluation Problem 70
6.2 Theoretical Assessment 72
6.3 Experimental Evaluation 76
6.4 Isotropy Conclusion 83
Problem Areas for Study 84
References 85
7 Failure Theory Applications 87
7.1 Very Ductile Polymers 88
7.2 Brittle Polymers 89
7.3 Glasses 91
7.4 Ceramics 92
7.5 Minerals 93
7.6 Geo-Materials 95
Problem Areas for Study 97
References 97
8 The Ductile/Brittle Transition for Isotropic
Materials 98
8.1 Introduction 98
8.2 Conventional Difficulty with Characterizing Ductility 100
8.3 The Ductile/Brittle Transition 103
8.4 The Failure Number for Gauging Ductility Levels 108
Problem Areas for Study 115
References 117
9 Defining Yield Stress and Failure Stress (Strength) 118
9.1 Yield Stress and Strength as Historically and
Currently Practiced 118
9.2 A Rational Definition of Yield Stress 119
9.3 A Rational Definition of Failure Stress 124
Contents ix
9.4 Significance and Conclusions 130
Problem Areas for Study 131
References 132
10 Fracture Mechanics 133
10.1 Fracture Mechanics Development 133
10.2 The Two Distinct Failure Theories 136
10.3 Fracture Mechanics Example 137
10.4 Failure Criterion Example 139
10.5 Assessment 141
Problem Areas for Study 142
References 143
11 Anisotropic Unidirectional Fiber
Composites Failure 144
11.1 Transversely Isotropic Polynomial Invariants 144
11.2 The Matrix-Controlled Failure Criterion 146
11.3 The Fiber-Controlled Failure Criterion 147
11.4 Hashin Failure Criterion 149
11.5 Tsai–Wu Failure Criterion 150
11.6 Comparisons 151
Problem Areas for Study 154
References 155
12 Anisotropic Fiber Composite Laminates Failure 157
12.1 Introduction 157
12.2 Progressive Damage in Laminates 161
12.3 Testing Results 166
12.4 Polynomial Invariants for Laminates 168
Problem Areas for Study 175
References 175
13 Micromechanics Failure Analysis 177
13.1 General Considerations 177
13.2 Transverse Shear Strength for Aligned
Fiber Composites 180
13.3 Spherical Inclusion in an Infinite Elastic Medium 187
13.4 Load Redistribution in Aligned Fiber Composites 192
Problem Areas for Study 198
References 199
14 Nanomechanics Failure Analysis 200
14.1 Graphene Nanostructure 200
14.2 A Hypothetical Nanostructure 206
14.3 Comparison and Discussion 207
14.4 Are the Elements Ductile or Brittle? 210
14.5 A Ductility Scale for the Elements 219
Problem Areas for Study 222
References 222
15 Damage, Cumulative Damage, Creep
and Fatigue Failure 223
15.1 Damage 223
15.2 Cumulative Damage 226
15.3 Four Models 229
15.4 Residual Strength 236
15.5 Life Prediction 238
15.6 Residual Life 241
15.7 Conclusion 242
Problem Areas for Study 243
References 244
16 Probabilistic Failure and Probabilistic
Life Prediction 245
16.1 Variability and Extreme Cases of Variability 245
16.2 Power-Law Failure Interpretation 247
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