Evolution of Phase Transitions: A Continuum Theory
Cambridge University Press
Edition: Illustrated, 7/6/2006
EAN 9780521661478, ISBN10: 0521661471
Hardcover, 260 pages, 25.4 x 17.8 x 1.5 cm
Language: English
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.
Part I. Introduction
1. What this monograph is about
2. Some experiments
3. Continuum mechanics
4. Quasilinear systems
5. Outline of monograph
Part II. Two-Well Potentials, Governing Equations and Energetics
1. Introduction
2. Two-phase nonlinearly elastic materials
3. Field equations and jump conditions
4. Energetics of motion, driving force and dissipation inequality
Part III. Equilibrium Phase Mixtures and Quasistatic Processes
1. Introduction
2. Equilibrium states
3. Variational theory of equilibrium mixtures of phases
4. Quasistatic processes
5. Nucleation and kinetics
6. Constant elongation rate processes
7. Hysteresis
Part IV. Impact-Induced Transitions in Two-Phase Elastic Materials
1. Introduction
2. The impact problem for trilinear two-phase materials
3. Scale-invariant solutions of the impact problem
4. Nucleation and kinetics
5. Comparison with experiment
6. Other types of kinetic relations
7. Related work
Part V. Multiple-Well Free Energy Potentials
1. Introduction
2. Helmholtz free energy potential
3. Potential energy function and the effect of stress
4. Example 1
the van der Waals fluid
5. Example 2
two-phase martensitic material with cubic and tetragonal phases
Part VI. The Continuum Theory of Driving Force
1. Introduction
2. Balance laws, field equations and jump conditions
3. The second law of thermodynamics and the driving force
Part VII. Thermoelastic Materials
1. Introduction
2. The thermoelastic constitutive law
3. Stability of a thermoelastic material
4. A one-dimensional special case
uniaxial strain
Part VIII. Kinetics and Nucleation
1. Introduction
2. Nonequilibrium processes, thermodynamic fluxes and forces, kinetic relation
3. Phenomenological examples of kinetic relations
4. Micromechanically-based examples of kinetic relations
5. Nucleation
Part IX. Models for Two-Phase Thermoelastic Materials in One Dimension
1. Preliminaries
2. Materials of Mie-Gruneisen type
3. Two-phase Mie-Gruneisen materials
Part X. Quasistatic Hysteresis in Two-Phase Thermoelastic Tensile Bars
1. Preliminaries
2. Thermomechanical equilibrium states for a two-phase material
3. Quasistatic processes
4. Trilinear thermoelastic material
5. Stress cycles at constant temperature
6. Temperature cycles at constant stress
7. The shape-memory cycle
8. The experiments of Shaw and Kyriakides
9. Slow thermomechanical processes
Part XI. Dynamics of Phase Transitions in Uniaxially Strained Thermoelastic Solids
1. Introduction
2. Uniaxial strain in adiabatic thermoelasticity
3. The impact problem
Part XII. Statics
Geometric Compatibility
1. Preliminaries
2. Examples
Part XIII. Dynamics
Impact-Induced Transition in a CuA1Nl Single Crystal
1. Introduction
2. Preliminaries
3. Impact without phase transformation
4. Impact with phase transformation
5. Application to austenite-B1 martensite transformation in CuA1Nl
Part XIV. Quasistatics
Kinetics of Martensitic Twinning
1. Introduction
2. The material and loading device
3. Observations
4. The model
5. The energy of the system
6. The effect of the transition layers
further observations
7. The effect of the transition layers
further modeling
8. Kinetics.
'Wherever possible, Abeyaratne and Knowles connect phenomenological and experimental results. Aside from comparisons between analytical predictions and experiments on shape-memory wires, the authors use their framework to model experiments involving phase transformations induced by high-speed impact. To some extent, links between atomistic and continuum models for kinetics are also explored. This book is a unique, valuable, and elegantly written contribution to the literature on phase transformations. It should be included in the library of any mechanician, applied mathematician, or material scientist interested in martensitic alloys. Others working on broader classes of phase transformations will also find this book to be worthwhile reading. It is physically well-motivated, mathematically sound, and eminently clear.' Theoretical and Computational Fluid Dynamics