On the effect of the heat generated during a stress-induced thermoelastic phase transformation

In this paper we examine the stress-elongation response of a bar undergoing a thermoelastic phase transition. Attention is focussed on how this response is affected by the heat generated during the transformation. The analysis is based on a continuum model consisting of a two-well Helmholtz free-energy function, a kinetic relation and a nucleation criterion. The governing mathematical problem is related to one that describes a moving heat source, except that here, the strength and speed of the source are not known a priori and the energy field equation involves coupling between thermal and mechanical effects. A finite difference solution of this moving boundary-value problem is carried out. The heat generated by the transformation is found to have a significant effect on the mechanical response whenever the prescribed elongation-rate is moderately large.