A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

Experimental data of forward and reverse martensitic transformations of some single crystalline shape memory alloys are available in the literature. For example, the uniaxial tensile tests of CuZnAl single crystals (transformation from 3 DO austenite to 18R