Study On Micromechanics-based Thermodynamic Constitutive Relation Of NiMnGa Ferromagnetic Shape Memory Alloys

NiMnGa ferromagnetic shape memory alloys, as a new kind of functional material and potential smart material with high ferromagnetism, large magnetic field induced-strain, thermoelastic and magnetic shape memory effect, high response frequency and large strain-stress output, have attracted considerable interests from material and physical scientists.NiMnGa alloys, which are non-homogeneous materials, tend to show high mechanical and magnetic anisotropic effects due to the field-induced motion of the twin boundaries between the different martensite variants. Considering the anisotropic martensite consisted of two kinds of isotropic materials with different material constants based on the micro-mechanics point of view, a microscopic-thermodynamic constitutive model of NiMnGa ferromagnetic shape memory alloys is presented based on the classical Eshelby equivalent inclusion theory, Mori-Tanaka mean field method and thermodynamic theory. In order to describe the micro mechanism of the martensitic variant rearrangement, the alloy is considered as two-phase material, one martensitic phase can be regard as inclusion, and the other can be regard as matrix in this model, and the relationship between the volume fraction of martensite and the macroscopic strain is obtained.The martensitic variant reorientation behavior induced by magnetic and stress field and magnetic flied-induced strain effect of NiMnGa alloys are taken into account here. The magneto-mechanical coupled characteristics of the NiMnGa alloys with the inclusions in spherical and ellipsoidal forms are modeled, meanwhile, the inclusion with different shape and material anisotropy effects on the martensitc variant reorientation are also considered here. The numerical simulations show better agreement with the experimental results than the former model without considering the inclusion with different shape and material anisotropy effects.