A model considering mechanical anisotropy of magnetic-field-induced superelastic strain in magnetic shape memory alloys

Highlights: ► The model analyzes mechanical anisotropy of magnetic shape memory alloy. ► The numerical evaluation of Eshelby tensor of shape memory alloy is obtained. ► Interaction energy of magnetic shape memory alloy is analyzed. - Abstract: Under applied mechanical load and magnetic field, a micromechanics-based thermodynamic model taking account of mechanical anisotropy of magnetic shape memory alloys (MSMAs) is developed in this work. Considering the crystallographic and magnetic microstructure, the internal state variables are chosen and the model can capture the magnetic shape memory effect caused by the martensitic variant reorientation process. It is assumed that the Gibbs free energy is consisted of the mechanical potential energy of anisotropic matrix, the Zeeman energy and the magnetocrystalline anisotropy energy in the model. In terms of the balance between the thermodynamic driving force derived from the reduction of Gibbs free energy and the resistive force for the variant reorientation, the kinetic equation is established and the Eshelby tensor of anisotropic MSMAs is then obtained by using numerical evaluation. At last, the effects of the anisotropy on interaction energy and macroscopic strain are discussed. The assumption of isotropy tends to underestimate interaction energy and macroscopic strain. The results considering mechanical anisotropy are in good agreement with the experimental data.