Temperature-induced phase transformation in a shape memory alloy: Phase diagram based kinetics approach

In this article we develop a general framework to model the one dimensional thermomechanical behavior of shape memory alloys (SMAs) based on phase diagram kinetics and a phenomenological constitutive law with martensite fraction as an internal variable. As part of this framework, we construct a consistent mathematical description for martensite fraction evolution to be used in conjunction with an experimentally defined phase diagram; the kinetics formalism is illustrated with examples of isostress and isothermal cycling. As an application, we consider the thermo-induced martensite transformation of a 1D prestressed SMA polycrystalline body which proceeds by migration of the austenite-martensite two-phase zone from the cooled boundary, converting the SMA body from an austenite (A) to a detwinned martensite (M) state. The mathematical model for the two-phase zone migration is based on the nonstationary equation of energy balance and the quasistationary approximation for the linear momentum equation and utilizes a quasistatic kinetic law, a macroscale constitutive law and an incompressibility constraint. To close the formulated system of equations, the internal energy of an A/M mixture in the two-phase zone is heuristically derived. The mixed initial-boundary value problem is then solved numerically and compared to analytical results for a simplified model. The results stress the significance of the stress dependency in the kinetic law and the transformation heat to the progress of transformation.