A two-scale thermo-mechanically coupled constitutive model for grain size- and rate-dependent deformation of nano-crystalline NiTi shape memory alloy

In this paper, a two-scale thermo-mechanically coupled constitutive model is established to predict the grain size (GS)- and rate-dependent deformation of nano-crystalline super-elastic NiTi shape memory alloy (SMA). At the mesoscopic scale, the polycrystalline representative volume element (RVE) is considered as an aggregation of individual grains. Owing to the relatively large volume fraction (VF) of grain boundary in nano-crystalline NiTi SMA, an individual grain is further considered as a composite containing the grain interior (GI) and grain boundary (GB) phases. For the GI phase, a crystal plasticity-based model accounting for the internal heat generation is developed through the fundamental laws of irreversible thermodynamics. The constraint of GB phase on the martensite transformation in the GI phase is considered by introducing a scaling law between the transformation hardening modulus (THM) and GS. Owing to its un-transformable nature and relatively high yielding stress, the GB phase is assumed to behavior constitutively linear thermo-elasticity. To evaluate the thermo-mechanical interactions among the grains, GI phase and GB phase, and obtain the overall response of the polycrystalline RVE, a double inclusion self-consistent homogenization scheme involving the material nonlinearity and thermo-mechanical coupling effect is developed in an incremental form. At the macroscopic scale, the overall thermo-mechanical responses for the specimen of nano-crystalline NiTi SMA are obtained by solving the equations of force balance, deformation compatibility, and thermodynamic equilibrium through an approximation method. Finally, considering the specific texture measured in experiments, the proposed model is validated by predicting the GS- and rate-dependent deformation of nano-crystalline NiTi SMA sheet. Furthermore, the anisotropic thermomechanical responses of the sheet caused by the texture are predicted and discussed.