A multivariant model for single cystal shape memory alloy behavior

A general 3-D multivariant model based on thermodynamics and micromechanics for single crystal shape memory alloy (SMA) behavior is presented. This model is based on the habit plane and transformation directions for the variants of martensite in a given material. From this information, the single crystal behavior of the material to temperature and mechanical loads is derived using the concept of a thermodynamic driving force. The Eshelby-Kröner approach is utilized to determine the interaction energy between the variants, where it is assumed that variants can be subdivided into several self-accommodating groups in which variants can grow together compatibly. This model is examined initially for a simple 2-variant case and then extended to the typical 24 variant case. The multivariant model is shown to exhibit appropriate responses for uniaxial results on single crystals: the transformations occur instantaneously when the critical stress/temperature is reached; both pseudoelasticity and the shape memory effect are captured. The model is also examined for responses to multiaxial loadings and the distinction between perfectly compatible and imperfectly compatible variants (with nonzero volumetric transformation strain) is discussed.