Three-dimensional constitutive model for magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy single crystals

Existing experimental results have shown that four types of physical mechanisms, namely, martensite transformation, martensite reorientation, magnetic domain wall motion and magnetization vector rotation, can be activated during the magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy (FSMA) single crystals. In this work, based on irreversible thermodynamics, a three-dimensional (3D) single crystal constitutive model is constructed by considering the aforementioned four mechanisms simultaneously. Three types of internal variables, i.e., the volume fraction of each martensite variant, the volume fraction of magnetic domain in each variant and the deviation angle between the magnetization vector, and easy axis are introduced to characterize the magneto-mechanical state of the single crystals. The thermodynamic driving force of each mechanism and the thermodynamic constraints on the constitutive model are obtained from Clausius's dissipative inequality and constructed Gibbs free energy. Then, thermodynamically consistent kinetic equations for the four mechanisms are proposed, respectively. Finally, the ability of the proposed model to describe the magneto-mechanical deformation of NiMnGa FSMA single crystals is verified by comparing the predictions with corresponding experimental results. It is shown that the proposed model can quantitatively capture the main experimental phenomena. Further, the proposed model is used to predict the deformations of the single crystals under the non-proportional mechanical loading conditions.