Russian Journal of Earth Sciences
Vol. 4, No. 2, April 2002
Thermomechanics of Phase Transitions of the First Order in Solids
V. I. Kondaurov
Abstract
Methods of nonequilibrium thermodynamics and continuum mechanics are
used for studying phase transitions of the first order in deformable
solids with elastic and viscoelastic rheology. A phase transition of
the first order is treated as the transition from one branch of the
response functional to another as soon as state parameters reach
certain threshold values determined by thermodynamic phase potentials
and boundary conditions of the problem. Notions of kinematic and
rheological characteristics of a phase transition associated with the
change of the symmetry group due to the structural transformation and
with the difference between thermodynamic potentials in undistorted
phase configurations are introduced. In a quasi-thermostatic
approximation, when inertia forces and temperature gradients are small,
a close system of equations on the interface between deformable solid
phases is formulated using laws of conservation. The system of the
latter includes, in addition to the traditional balance equations of
mass, momentum and energy, the divergence equation ensuring the
compatibility of finite strains and velocities. As distinct from the
classical case of the liquid (gas) phase equilibrium, the phase
transition in solids is supposed to be irreversible due to the presence
of singular sources of entropy of the delta function type whose carrier
concentrates on the interface between the phases. The relations on the
interface including the continuity conditions of the displacement
vector, temperature, mass flux and the stress vector, as well as a
certain restraint imposed on the jump of the normal component of the
chemical potential tensor, are discussed. The latter restraint makes
the resulting relations basically distinct from the classical
conditions of the phase equilibrium.
A generalized Clapeyron-Clausius equation governing the differential
dependence of the phase transition temperature on the initial phase
deformation is formulated. The paper presents a new relation of the
phase transformation theory, namely, the equation describing the
differential dependence of the phase transition temperature on the
interface orientation relative to the anisotropy axes and the principal
axes of the initial phase strain tensor. Based on the relations derived
in this study, the phase transformation temperature of an initially
isotropic material is shown to assume extreme values if the normal to
the interface coincides with the direction of a principal axis of the
initial phase strain tensor. The phase transition of the first order in
a linear thermoelastic material with small strain values and small
deviations of the temperature from its initial value is discussed in
detail. A class of materials is distinguished in which an increase in
the initial phase strain necessarily changes the character of the phase
transformation (a normal phase transition becomes an anomalous one and
vice versa). The equilibrium of a compressed viscoelastic layer
admitting melting and the effect of stress relaxation in the solid
phase on the fluid boundary motion are examined.