A geometrical approach to determine reorientation start and continuation conditions in ferromagnetic shape memory alloys considering the effects of loading history

Ferromagnetic shape memory alloys (FSMAs) and magnetic shape memory alloys (MSMAs) are metallic alloys that can undergo inelastic responses when exposed to magnetic fields. Several constitutive models have been proposed so far to model the behaviors of FSMAs. In this work, the effects of loading history on reorientation start conditions are considered, and it is shown that reorientation start conditions are not fixed values; rather, they change with respect to the amount of loading history. To consider the effects of loading history on reorientation start conditions, an available phase diagram in stress-field space is generalized to reorientation surfaces in stress-field-loading history space. Correspondingly, kinetic laws are derived in a continuum framework to be used with the reorientation surfaces to determine the amount of the martensitic variant 2 volume fraction. Based on the geometry of the reorientation surfaces, conditions that must be satisfied to ensure the continuation of reorientations are obtained. Available experimental findings validate the proposed model and the reorientation surfaces.