A coupled thermomechanical model for shape memory alloys—From single crystal to polycrystal

A number of shape memory alloys (SMAs), e.g., NiTi, exhibit a rate-dependent stress–strain behavior already at very low loading rates (10−4 to 10−2 s−1), leading to a considerable change in the shape of the stress–strain hysteresis. The reason for this phenomenon lies in the strong thermo-mechanical coupling due to the release and absorption of latent heats, and the high temperature sensitivity of the transformation stresses. A correct description of these mechanisms is important for, e.g., the simulation of electrically heated actuators or the dynamics of SMA-based damping elements. This paper presents a model which combines arguments from the theory of thermally activated processes and statistical thermodynamics to describe the kinetics of the martensite/austenite phase transformations responsible for the hysteretic SMA behavior. It starts out at the single-crystal level to introduce the concepts, and subsequently discusses a polycrystalline version based on a statistical homogenization. Finally, a computationally efficient implementation of the latter scheme by means of a parameterization method is derived and compared with results from tensile experiments with NiTi wires.