Continuum Modeling of Phase Transitions in Solids

Abstract

In this paper, we describe a simple phenomenological thermoelastic model for stress-induced solid-solid phase transitions in a tensile bar. In this model, the bar is treated as a one-dimensional continuum, and the phase transition is assumed to take place quasi-statically and isothermally at a temperature θ. By accounting for temperature effects solely in the kinetics of the phase transition, we show that some of the qualitative features of the experimental observations in [1] can be predicted, even though the effects of temperature on the nucleation of the transition and on the stress-strain relation have been neglected. A purely mechanical counterpart of the theory described here has been given in [2]; the latter work, as well as a mechanical theory of fast phase transitions in solids, is reviewed in [3].