Phase field-finite element analysis of magnetic-induced deformation in ferromagnetic shape memory alloy

Abstract

A phase field theory based model considering non-uniform demagnetizing field within ferromagnetic shape memory alloy and free space is established and realized by finite element method in a two-dimensional setting to save huge storage spaces and computational times. The martensite reorientation (contain nucleation and growth) from the stress field-favored martensite variant to magnetic field-favored martensite variant is numerically simulated. The simulation reasonably depicts the essence of magnetic-induced martensite reorientation and magnetization change for NiMnGa ferromagnetic shape memory alloy and their dependence on the loading level. Furthermore, the evolution and interaction of martensite domain structure, magnetic domain structure, magnetic potential and demagnetizing field are analyzed. And the dominant driving force generated by minimization of total Helmholtz free energy for loading level dependent martensite reorientation and magnetization change are revealed by addressing the influence of loading level. The simulation results show that the local demagnetizing field within ferromagnetic shape memory alloy and free space is the key to the local nucleation of new martensite variant. The dominant driving force of local nucleation and growth of new martensite variant are completely different: the local nucleation of new martensite variant is driven by local high magnetocrystalline anisotropy energy caused by local demagnetizing field; the local high Landau-type double well potential energy caused by local nucleation of new martensite variant has the largest impact on growth of the new martensite variant. The local high magnetocrystalline anisotropy energy caused by local nucleation and growth of new martensite variant has the largest impact on local rapid magnetization change within new martensite variant domain. When it comes to high loading level, the inhibition of martensite reorientation is attributed to the elastic strain energy, and the approximately uniform magnetization change is driven by Zeeman energy.