Evolution of Phase Transitions : A Continuum Theory (Reissue)

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Evolution of Phase Transitions : A Continuum Theory (Reissue)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 242 p.
  • 言語 ENG,ENG
  • 商品コード 9780521380515
  • DDC分類 532

Full Description


This 2006 work began with the author's exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of various energies or ellipticity of the field equations of equilibrium are relinquished. The finite deformation theory of elasticity turns out to be a natural vehicle for the study of phase transitions in solids where thermal effects can be neglected. This text will be of interest to 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 which in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory.

Table of Contents

Preface                                            xiii
Part I Introduction
1 Introduction 3 (16)
1.1 What this monograph is about 3 (4)
1.2 Some experiments 7 (2)
1.3 Continuum mechanics 9 (1)
1.4 Quasilinear systems 10 (1)
1.5 Outline of monograph 11 (8)
Part II Purely Mechanical Theory
2 Two-Well Potentials, Governing Equations 19 (13)
and Energetics
2.1 Introduction 19 (1)
2.2 Two-phase nonlinearly elastic 20 (5)
materials
2.3 Field equations and jump conditions 25 (2)
2.4 Energetics of motion, driving force 27 (5)
and dissipation inequality
3 Equilibrium Phase Mixtures and 32 (27)
Quasistatic Processes
3.1 Introduction 32 (1)
3.2 Equilibrium states 33 (4)
3.3 Variational theory of equilibrium 37 (5)
mixtures of phases
3.4 Quasistatic processes 42 (2)
3.5 Nucleation and kinetics 44 (3)
3.6 Constant elongation rate processes 47 (6)
3.7 Hysteresis 53 (6)
4 Impact-Induced Transitions in Two-Phase 59 (26)
Elastic Materials
4.1 Introduction 59 (2)
4.2 The impact problem for trilinear 61 (5)
two-phase materials
4.2.1 The constitutive law 61 (3)
4.2.2 The impact problem 64 (2)
4.3 Scale-invariant solutions of the 66 (5)
impact problem
4.3.1 Solutions without a phase 66 (1)
transition
4.3.2 Solutions with a phase 67 (1)
transition: The two-wave case
4.3.3 Solutions with a phase 68 (1)
transition: The one-wave case
4.3.4 The totality of solutions 69 (2)
4.4 Nucleation and kinetics 71 (3)
4.5 Comparison with experiment 74 (3)
4.6 Other types of kinetic relations 77 (1)
4.7 Related work 77 (8)
Part III Thermomechanical Theory
5 Multiple-Well Free Energy Potentials 85 (20)
5.1 Introduction 85 (1)
5.2 Helmholtz free energy potential 86 (2)
5.3 Potential energy function and the 88 (2)
effect of stress
5.4 Example 1: The van der Waals Fluid 90 (5)
5.5 Example 2: Two-phase martensitic 95 (10)
material with cubic and tetragonal phases
6 The Continuum Theory of Driving Force 105 (8)
6.1 Introduction 105 (1)
6.2 Balance laws, field equations and 106 (2)
jump conditions
6.2.1 Balances of momentum and energy 106 (1)
in integral form
6.2.2 Localization of the balance laws 106 (2)
6.3 The second law of thermodynamics and 108 (5)
the driving force
6.3.1 Entropy production rate 108 (2)
6.3.2 Driving force and the second law 110 (1)
6.3.3 Driving force in the case of 111 (2)
mechanical equilibrium
7 Thermoelastic Materials 113 (11)
7.1 Introduction 113 (1)
7.2 The thermoelastic constitutive law 113 (5)
7.2.1 Relations among stress, 113 (3)
deformation gradient, temperature and
specific entropy
7.2.2 The heat conduction law 116 (1)
7.2.3 The partial differential 116 (1)
equations of nonlinear thermoelasticity
7.2.4 Thermomechanical equilibrium 117 (1)
7.3 Stability of a thermoelastic material 118 (2)
7.4 A one-dimensional special case: 120 (4)
uniaxial strain
8 Kinetics and Nucleation 124 (25)
8.1 Introduction 124 (1)
8.2 Nonequilibrium processes, 124 (3)
thermodynamic fluxes and forces, kinetic
relation
8.3 Phenomenological examples of kinetic 127 (1)
relations
8.4 Micromechanically based examples of 128 (11)
kinetic relations
8.4.1 Viscosity-strain gradient model 130 (1)
8.4.2 Thermal activation model 131 (2)
8.4.3 Propagation through a row of 133 (1)
imperfections
8.4.4 Kinetics from atomistic 134 (2)
considerations
8.4.5 Frenkel-Kontorowa model 136 (3)
8.5 Nucleation 139 (10)
Part IV One-Dimensional Thermoelastic Theory
and Problems
9 Models for Two-Phase Thermoelastic 149 (14)
Materials in One Dimension
9.1 Preliminaries 149 (2)
9.2 Materials of Mie-Gruneisen type 151 (2)
9.3 Two-phase Mie-Gruneisen materials 153 (10)
9.3.1 The trilinear material 153 (3)
9.3.2 Stability of phases of the 156 (3)
trilinear material
9.3.3 Other two-phase materials of 159 (4)
Mie-Gruneisen type
10 Quasistatic Hysteresis in Two-Phase 163 (18)
Thermoelastic Tensile Bars
10.1 Preliminaries 163 (1)
10.2 Thermomechanical equilibrium states 164 (2)
for a two-phase material
10.3 Quasistatic processes 166 (1)
10.4 Trilinear thermoelastic material 167 (2)
10.5 Stress cycles at constant temperature 169 (4)
10.6 Temperature cycles at constant stress 173 (2)
10.7 The shape-memory cycle 175 (1)
10.8 The experiments of Shaw and 176 (2)
Kyriakides
10.9 Slow thermomechanical processes 178 (3)
11 Dynamics of Phase Transitions in 181 (16)
Uniaxially Strained Thermoelastic Solids
11.1 Introduction 181 (1)
11.2 Uniaxial strain in adiabatic 182 (3)
thermoelasticity
11.2.1 Field equations, jump conditions 182 (1)
and driving force
11.2.2 The trilinear Mie-Gruneisen 183 (2)
thermoelastic material
11.3 The impact problem 185 (12)
11.3.1 Formulation: Scale-invariant 185 (1)
solutions
11.3.2 Solutions with no phase 186 (2)
transition
11.3.3 Solutions with a phase transition 188 (9)
Part V Higher Dimensional Problems
12 Statics: Geometric Compatibility 197 (12)
12.1 Preliminaries 197 (3)
12.2 Examples 200 (9)
13 Dynamics: Impact-Induced Transition in a 209 (12)
CuAlNi Single Crystal
13.1 Introduction 209 (1)
13.2 Preliminaries 210 (2)
13.3 Impact without phase transformation 212 (2)
13.4 Impact with phase transformation 214 (3)
13.5 Application to austenite-β'1 217 (4)
martensite transformation in CuAlNi
13.5.1 Experimental data 217 (1)
13.5.2 Phase boundary speed 218 (1)
13.5.3 Driving force 218 (1)
13.5.4 Kinetic law 219 (2)
14 Quasistatics: Kinetics of Martensitic 221 (14)
Twinning
14.1 Introduction 221 (1)
14.2 The material and loading device 222 (1)
14.3 Observations 223 (2)
14.4 The model 225 (1)
14.5 The energy of the system 226 (3)
14.5.1 Elastic energy of the specimen 226 (1)
14.5.2 Loading device energy 227 (1)
14.5.3 Summary 228 (1)
14.6 The effect of the transition layers: 229 (1)
Further observations
14.7 The effect of the transition layers: 230 (1)
Further modeling
14.8 Kinetics 231 (4)
Author Index 235 (3)
Subject Index 238