A phase-field model on the hysteretic magneto-mechanical behaviors of ferromagnetic shape memory alloy

A phase-field model with a friction-type resistance in the kinetic equation for the martensite reorientation is proposed to simulate the coupled magneto-mechanical behaviors of ferromagnetic shape memory alloy (FSMA). The phase-field simulation is able to capture the evolution of the microstructures (martensite twins and magnetic domains) and the rate-independent hysteresis in the associated responses under various quasi-static loading paths of controlling a mechanical stress or/and a magnetic field. Phase diagrams are constructed, by summarizing many simulation cases, to demonstrate the dependence of the material state (martensite variant state and the level of magnetization along the external magnetic field) on the magneto-mechanical loading. Particularly, the critical levels of the stress/field to trigger the martensite reorientation in the cases like Magnetic-Field Induced Strain (MFIS) and field-assisted quasi-plasticity/pseudoelasticity (superelasticity) can be predicted, which agree with experimental observations.