Modeling of the reorientation behavior of a single crystalline shape-memory alloy by a micromechanical approach

A Helmholtz free energy for a martensitic transformation of a single crystalline shape-memory alloy is obtained by a micromechanical approach. 24 variants of the single crystal are taken into account. In the framework of irreversible thermodynamics, a kinetic relation, a martensitic nucleation criterion and the reorientation criterion of martensitic variants are obtained. These relations are valid for a three-dimensional proportional or non-proportional mechanical loading or a combination of mechanical and thermal loading. Reorientation behavior of a single crystalline shape-memory alloy CuZnAl is simulated. When a tensile load is applied to a thermally-induced martensite, 24 self-accommodated martensitic variants are reoriented to the most favorable variant. In the following unloading and compression load, the most favorable variant in the tensile load is reoriented to the most favorable variant in this loading condition.