A Simplified Multivariant SMA Model Based on Invariant Plane Nature of Martensitic Transformation

The Multivariant model describing shape memory alloy (SMA) constitutive behavior is further developed in this paper for improved prediction of thermomechanical response. In the original formulation of the Multivariant model, an interaction energy, representative of the incompatibility of an inclusion to the matrix, was calculated by a micromechanics model in which every variant group (inclusion) was embedded in the austenite phase with numerous other inclusions. However, experiments show that martensite variants tend to form large plates most of which have an invariant plane interface with the austenite and reach the grain boundary. Hence, to better simulate material behavior, in the revised model the micromechanical interaction energy is replaced by a small, constant term. The predictions by the new model for different uniaxial tension directions on a single CuAlNi crystal have excellent agreement with the experimental results. Furthermore, the counterintuitive results for a polycrystal CuZnAl under triaxial loading are also well captured by the new model. As the revised model removes an iterative procedure for interaction energy, calculations are simplified, making the Multivariant model more suitable for larger scale computations.