The physics and mathematics of adiabatic shear bands / T.W. Wright.

Format:

Book

Author/Creator:

Wright, T. W.

Series:

Cambridge monographs on mechanics

Language:

English

Subjects (All):

Shear (Mechanics).

Flexure.

Materials--Thermal properties.

Materials.

Physical Description:

xviii, 241 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2002.

Contents:

1 Introduction: Qualitative description and one-dimensional experiments 1

1.1 Qualitative features of adiabatic shear bands 2

1.1.1 Basic morphology 2

1.1.2 Occurrence 7

1.1.3 Importance 11

1.1.4 Qualitative mechanics 14

1.1.5 Reviews and symposiums on adiabatic shear 15

1.1.6 Implications for computations 17

1.2 One-dimensional experiments 18

1.2.1 Dynamic testing with uniform fields 19

1.2.2 Formation of adiabatic shear bands in thin-walled tubes and other geometries 26

2 Balance laws and nonlinear elasticity: A brief summary 35

2.1 Balance laws 36

2.1.1 Balance of mass 37

2.1.2 Balance of momentum 37

2.1.3 Balance of angular momentum 38

2.1.4 Balance of energy 38

2.1.5 The Clausius-Duhem inequality 39

2.2 Thermoelasticity 40

2.2.1 Objectivity and implications of the Clausius-Duhem inequality 40

2.2.2 Helmholz and Gibbs functions 42

2.2.3 Specific heat, thermal stress, and thermal expansion 44

3 Thermoplasticity 47

3.1 General structure 50

3.1.1 Kinematics 50

3.1.2 Thermodynamic potentials 53

3.1.3 Entropy and energy 55

3.2 Yield, plastic flow, and constitutive equations 58

3.2.1 The intermediate configuration and the local elastic reference configuration 58

3.2.2 Elastically isotropic materials with scalar internal variables only 60

3.2.3 Plastic stretching in elastically isotropic materials 62

3.2.4 Plastic yield 64

3.2.5 Constitutive laws for plastic flow 65

3.2.6 Flow potentials 68

3.3 One-dimensional forms 69

3.3.1 Specializations and approximations 69

3.3.2 Isotropic work hardening and the stored energy of cold work: An example 73

4 Models for thermoviscoplasticity 77

4.1 Work hardening 78

4.1.1 Work hardening without history effects 81

4.1.2 Quasi-static, isothermal stress-strain curves 81

4.1.3 Thermodynamic consistency of cold work and work hardening 84

4.2 Plastic flow: Simple phenomenological and physical models 85

4.2.1 Power law model 86

4.2.2 Litonski's model 87

4.2.3 Johnson-Cook model 88

4.2.4 Zerilli-Armstrong models 89

4.2.5 Bodner-Partom model 92

4.2.6 MTS model 93

4.2.7 Anand's model 95

5 One-dimensional problems, part I: General considerations 98

5.1 Homogeneous solutions and the reduction to rigid-plastic material 98

5.1.1 Initial boundary layer: General description 99

5.1.2 Initial boundary layer: A simple example 100

5.2 Steady solutions 103

5.3 Change of type, regularization, and embedded change of type 106

5.4 Typical numerical results 108

6 One-dimensional problems, part II: Linearization and growth of perturbations 115

6.1 Perturbations from homogeneous solutions: Linearized equations 116

6.1.1 Frozen coefficients 116

6.1.2 The initial-boundary value problem for perturbations 118

6.2 Quasi-static solutions for special cases on a finite interval 122

6.2.1 Perfect plasticity with finite thermal conductivity 122

6.2.2 Work hardening without thermal conductivity: The early response 124

6.2.3 Work hardening without thermal conductivity: The response near peak homogeneous stress 129

6.2.4 Finite thermal conductivity and work hardening 131

6.2.5 Discussion of quasi-static solutions 133

6.2.6 Scaling laws and scaling parameters 136

6.3 Infinite domain: Band spacing and patterning 141

7 One-dimensional problems, part III: Nonlinear solutions 150

7.1 Adiabatic cases; k = 0 150

7.1.1 Stress boundary condition 150

7.1.2 Velocity boundary condition; Wright (1990a, 1990b) 151

7.1.3 Graphical interpretation of solutions 152

7.2 Finite thermal conductivity; k [not equal] 0 156

7.2.1 An exact solution 156

7.2.2 Approximate solution with no work hardening 158

7.2.3 Further approximations and qualitative interpretation 160

7.3 Multiple-length scales: Structure of a fully formed band and the evolution of stress in a special case 163

7.4 Canonical structure of a fully formed band in the general case 168

7.5 Thermal and mechanical length scales 176

7.6 DiLellio and Olmstead's theory of shear band evolution 177

8 Two-dimensional experiments 183

8.1 Kalthoff's experiment 183

8.1.1 Stable-brittle-ductile behavior 184

8.1.2 Brittle behavior 185

8.1.3 Ductile behavior 187

8.1.4 Other results and discussion 187

8.2 Thick-walled torsion experiments 189

8.3 Collapse of a thick-walled cylinder 193

9 Two-dimensional solutions 201

9.1 Mode III: Antiplane motion 202

9.1.1 Inertial solution 203

9.1.2 Core solution 208

9.2 Mode II: In-plane motion 211

9.3 The leading boundary layer 218.

Notes:

Includes bibliographical references (pages 229-238) and index.

ISBN:

0521631955

OCLC:

47927632