A micromechanical constitutive model for grain size dependent thermo-mechanically coupled inelastic deformation of super-elastic NiTi shape memory alloy

A micromechanical constitutive model is constructed to describe the grain size dependent thermo-mechanically coupled inelastic deformation of polycrystalline super-elastic NiTi shape memory alloys (SMAs). In the proposed model, the polycrystalline aggregate is regarded as a composite material, i.e., each grain-interior (GI) phase is assumed to be a spherical inhomogeneity embedded in a matrix of grain-boundary (GB). The constitutive relationship of GI phase is deduced in the framework of irreversible thermodynamics, and the driving force of martensite transformation and the internal heat production caused by transformation latent heat and mechanical dissipation are obtained by the Clausius's dissipative inequality and energy-balance equation, respectively. But, the stress-strain relationship of GB phase is assumed to be linearly elastic without energy dissipation. To describe the interaction between the GI and GB phases, a new incremental non-isothermal Mori-Tanaka's homogenization method is developed and the Eshelby's tensor of a spherical inclusion embedded in a finite spherical domain is introduced. Moreover, the continuous tangent moduli of GI and GB phases are deduced and the computational algorithms of the proposed micromechanical model are developed from fully implicit backward Euler's integration method. Finally, the proposed micromechanical model is verified by comparing the simulated results with the corresponding experimental ones. It is shown that the grain size dependent thermo-mechanically coupled inelastic deformation of NiTi SMAs can be well captured by the proposed model.