Rearrangement of martensitic variants in Ni<Subscript>2</Subscript>MnGa studied with the phase-field method

A phase-field model is introduced to simulate the magnetic shape memory effect, i.e. the solid-state rearrangement of the boundaries of a martensitic microstructure using an external magnetic field, in the shape memory material Ni<Subscript>2</Subscript>MnGa. The model is derived from an existing phase-field model that has proven well in several applications in materials science, based on the interpolation of free energies. The micromagnetic and elastic energy contributions entering the constitutive free energy functional are given, and the coupled kinetic equations of motion for the phase fields that describe the microstructure geometry, the spontaneous magnetization and the elastic displacement field are derived from the principle of minimization of free energy. The concept of representative volume elements is applied for the microstructure simulations carried out to analyze the material behavior, and the relevant boundary conditions are discussed. Stress vs. strain and strain vs. applied magnetic field curves are shown for Ni<Subscript>2</Subscript>MnGa. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013