Evolution of phase transitions : a continuum theory / Rohan Abeyaratne, James K. Knowles.

Format:

Book

Author/Creator:

Abeyaratne, Rohan.

Contributor:

Knowles, James K. (James Kenyon), 1931-

Language:

English

Subjects (All):

Phase transformations (Statistical physics).

Continuum mechanics.

Kinetic theory of matter.

Physical Description:

xv, 242 pages : illustrations ; 27 cm

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2006.

Summary:

This work began with the authors' exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of the energy or ellipticity of the field equations of equilibrium are relinquished. When generalized to thermoelasticity, this theory turns out to be a natural vehicle for the study of phase transitions in solids. This is a valuable work for those interested in the development and application of continuum-mechanical models that describe the macroscopic response of materials capable of undergoing stress- or temperature-induced transitions between two solid phases. The focus is on the evolution of phase transitions, which may be either dynamic or quasi-static, controlled by a kinetic relation that in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory. The book should be of interest to mechanicians, material scientists, geophysicists, and applied mathematicians.

Contents:

1.1 What this monograph is about 3

1.2 Some experiments 7

1.3 Continuum mechanics 9

1.4 Quasilinear systems 10

1.5 Outline of monograph 11

Part II Purely Mechanical Theory

2 Two-Well Potentials, Governing Equations and Energetics 19

2.2 Two-phase nonlinearly elastic materials 20

2.3 Field equations and jump conditions 25

2.4 Energetics of motion, driving force and dissipation inequality 27

3 Equilibrium Phase Mixtures and Quasistatic Processes 32

3.2 Equilibrium states 33

3.3 Variational theory of equilibrium mixtures of phases 37

3.4 Quasistatic processes 42

3.5 Nucleation and kinetics 44

3.6 Constant elongation rate processes 47

3.7 Hysteresis 53

4 Impact-Induced Transitions in Two-Phase Elastic Materials 59

4.2 The impact problem for trilinear two-phase materials 61

4.2.1 The constitutive law 61

4.2.2 The impact problem 64

4.3 Scale-invariant solutions of the impact problem 66

4.3.1 Solutions without a phase transition 66

4.3.2 Solutions with a phase transition: The two-wave case 67

4.3.3 Solutions with a phase transition: The one-wave case 68

4.3.4 The totality of solutions 69

4.4 Nucleation and kinetics 71

4.5 Comparison with experiment 74

4.6 Other types of kinetic relations 77

Part III Thermomechanical Theory

5 Multiple-Well Free Energy Potentials 85

5.2 Helmholtz free energy potential 86

5.3 Potential energy function and the effect of stress 88

5.4 Example 1: The van der Waals Fluid 90

5.5 Example 2: Two-phase martensitic material with cubic and tetragonal phases 95

6 The Continuum Theory of Driving Force 105

6.2 Balance laws, field equations and jump conditions 106

6.2.1 Balances of momentum and energy in integral form 106

6.2.2 Localization of the balance laws 106

6.3 The second law of thermodynamics and the driving force 108

6.3.1 Entropy production rate 108

6.3.2 Driving force and the second law 110

6.3.3 Driving force in the case of mechanical equilibrium 111

7 Thermoelastic Materials 113

7.2 The thermoelastic constitutive law 113

7.2.1 Relations among stress, deformation gradient, temperature and specific entropy 113

7.2.2 The heat conduction law 116

7.2.3 The partial differential equations of nonlinear thermoelasticity 116

7.2.4 Thermomechanical equilibrium 117

7.3 Stability of a thermoelastic material 118

7.4 A one-dimensional special case: uniaxial strain 120

8 Kinetics and Nucleation 124

8.2 Nonequilibrium processes, thermodynamic fluxes and forces, kinetic relation 124

8.3 Phenomenological examples of kinetic relations 127

8.4 Micromechanically based examples of kinetic relations 128

8.4.1 Viscosity-strain gradient model 130

8.4.2 Thermal activation model 131

8.4.3 Propagation through a row of imperfections 133

8.4.4 Kinetics from atomistic considerations 134

8.4.5 Frenkel-Kontorowa model 136

8.5 Nucleation 139

Part IV One-Dimensional Thermoelastic Theory and Problems

9 Models for Two-Phase Thermoelastic Materials in One Dimension 149

9.2 Materials of Mie-Gruneisen type 151

9.3 Two-phase Mie-Gruneisen materials 153

9.3.1 The trilinear material 153

9.3.2 Stability of phases of the trilinear material 156

9.3.3 Other two-phase materials of Mie-Gruneisen type 159

10 Quasistatic Hysteresis in Two-Phase Thermoelastic Tensile Bars 163

10.2 Thermomechanical equilibrium states for a two-phase material 164

10.3 Quasistatic processes 166

10.4 Trilinear thermoelastic material 167

10.5 Stress cycles at constant temperature 169

10.6 Temperature cycles at constant stress 173

10.7 The shape-memory cycle 175

10.8 The experiments of Shaw and Kyriakides 176

10.9 Slow thermomechanical processes 178

11 Dynamics of Phase Transitions in Uniaxially Strained Thermoelastic Solids 181

11.2 Uniaxial strain in adiabatic thermoelasticity 182

11.2.1 Field equations, jump conditions and driving force 182

11.2.2 The trilinear Mie-Gruneisen thermoelastic material 183

11.3 The impact problem 185

11.3.1 Formulation: Scale-invariant solutions 185

11.3.2 Solutions with no phase transition 186

11.3.3 Solutions with a phase transition 188

Part V Higher Dimensional Problems

12 Statics: Geometric Compatibility 197

13 Dynamics: Impact-Induced Transition in a CuAlNi Single Crystal 209

13.3 Impact without phase transformation 212

13.4 Impact with phase transformation 214

13.5 Application to austenite-[beta superscript r subscript 1] martensite transformation in CuAlNi 217

13.5.1 Experimental data 217

13.5.2 Phase boundary speed 218

13.5.3 Driving force 218

13.5.4 Kinetic law 219

14 Quasistatics: Kinetics of Martensitic Twinning 221

14.2 The material and loading device 222

14.3 Observations 223

14.4 The model 225

14.5 The energy of the system 226

14.5.1 Elastic energy of the specimen 226

14.5.2 Loading device energy 227

14.6 The effect of the transition layers: Further observations 229

14.7 The effect of the transition layers: Further modeling 230

14.8 Kinetics 231.

Notes:

Includes bibliographical references and indexes.

ISBN:

0521661471

OCLC:

62342046

Publisher Number:

9780521661478

Online:

Publisher description