A theoretical framework of one-dimensional sharp phase fronts in shape memory alloys

Abstract

In this paper, we propose a one-dimensional (1D) sharp phase front-based theoretical framework for shape memory alloys (SMAs). An assumption of equality of the chemical potential at the phase front leads to a generalized Clausius–Clapeyron equation, which then gives the condition for the evolution of the phase front during phase transformation. The theoretical framework is general enough to incorporate any Helmholtz free energy function, and for that reason, if the Helmholtz free energy function is completely characterized, then so is the entire system of equations (including the condition for the phase boundary evolution). The small strain, quasistatic approximation of the theory in conjunction with a trilinear Helmholtz free energy function is used to predict the following two experiments: (i) constant deformation-rate phase transformation in a SMA single crystal; and (ii) constant load, temperature-induced transformation in a SMA polycrystalline wire.