A Thermodynamic Approach to Modeling of Stress-Induced Phase-Transition Front Propagation in Solids

Abstract

A number of continual models for describing the dynamics of phase boundaries has been developed in order to understand evolving phase transitions (cf., for example, [1]). All these models take the basic balance laws of continuum mechanics as a starting point. However, the propagation speed of phase-transition fronts is not completely determined by the balance of momentum in the dynamic problems involving phase boundaries. As a result, an additional constitutive criterion is needed for the determination of the dynamics of phase boundaries. In the sharp-interface theory, phase boundaries are treated as discontinuity surfaces of zero thickness. The canonical formalism of continuum mechanics with a full exploitation of the balance of so called pseudo- or canonical momentum leads to the balance of “ material” forces at the phase-transition front. The surface “balance” equation plays an essential role in the description of phase-transition front propagation. However, in all the theories, the constitutive relation for free energy is assumed to be able to describe the states in both sides of the phase-transition front simultaneously.