A bi-crystal aggregate model of pseudoelastic behaviour of shape-memory alloy polycrystals

A multi-scale model of stress-induced phase transformation and martensite variant reorientation in shape memory alloy (SMA) polycrystals is developed. It is proposed to include neighbouring-grain interaction in a simple manner by introducing an intermediate bi-crystal level into the sequential averaging scheme for SMA. The constitutive relationships are defined by specifying the free energy and dissipation functions. At the level of a single grain, the rate-independent dissipation function is used that incorporates the dissipation due to forward and reverse austenite-to-martensite transformation as well as reorientation of martensite variants. The global response of the model is simulated numerically by minimizing the total incremental energy supply. Specific examples are calculated for a NiTi polycrystal for proportional and non-proportional loading paths.