Thermo-magneto-mechanical coupling dynamics of magnetic shape memory alloys

This paper is to improve our previous phase-transformable material constitutive model (Chen et al., 2014) and implement it in a mass-spring configuration to study the recently discovered dynamic phenomena in (Zhang et al., 2018a, 2018b): the harmonic oscillator of the cyclic magnetic-field-induced deformation in Magnetic Shape Memory Alloys (MSMA) is modulated by a thermo-magneto-mechanical coupling feedback loop where the cyclic field-induced Martensite Reorientation (MR) provides cyclic dissipative deformation whose dissipation heat influencing the material temperature modifies the temperature-dependent MR process and/or triggers the martensite-to-austenite Phase Transformation (PT) to modify the martensite volume fraction so as to change the deformation oscillation amplitude. Such a feedback loop causing the amplitude modulation was ignored in the existing models. This paper develops a dynamic model to include the feedback loop by considering the heat balance (i.e. the interactions among heat generation due to MR, the latent heat release/absorption of PT and the heat transferred to the ambient), by introducing proper kinetics of the temperature-dependent MR and PT processes, and by taking into account the inertial dynamic effect with a simple mass-spring configuration. The simulation based on the model captures all the main features of the experimental phenomena and provides the relations between the macroscopic responses (the deformation amplitude and temperature evolution) and the microscopic physical mechanisms (the kinetics of MR and PT). The study reveals that, with the coupling effects, the MSMA system can be smart to keep its temperature constant by self-organized microstructures under varying external thermo-magneto-mechanical boundary conditions. Moreover, the forward and reverse martensitic phase transformations influenced by the coupling dynamics show little hysteresis, contrasting to the usual hysteretic kinetics of the quasi-static martensitic phase transformation.