Theoretical consideration of the time-dependent deformation of ferromagnetic Ni-Mn-Ga martensite

A statistical model describing the time-dependent deformation of twinned Ni-Mn-Ga martensite under a stationary magnetic field or/and mechanical loading is reported. The fluctuating stress that affects the twin structure and causes its time evolution was considered and related then to the amplitudes of thermal phonons. The thermal phonons that effectively interact with the twinned martensite have been considered and the temperature dependence of the twinning stress value has been computed. This dependence proved to be caused by the softening of the elastic modulus and the increase of the strain fluctuations in the vicinity of the martensitic transformation temperature. A strong dependence of the twinning stress on the twin width has been predicted. The deformation curves have been computed for the twin widths to be about 45 nm and 250 nm.