A multi-physics, multi-scale and finite strain crystal plasticity-based model for pseudoelastic NiTi shape memory alloy

A crystal plasticity-based constitutive model is developed to describe the thermomechanical behavior of pseudoelastic NiTi single crystal. The model includes, for the first time in the literature, all inelastic mechanisms influencing the fatigue behavior of NiTi SMAs in a finite strain framework: martensite transformation, deformation slip in austenite at high-temperature, deformation twinning in martensite at large strain, transformation-induced plasticity (TRIP) as well as thermomechanical coupling. Furthermore, new internal variables and evolution laws are introduced in the monocycle model (referred as basic model in the remainder of the paper) to reproduce the main features of anisotropic cyclic deformation of pseudoelastic NiTi single crystal. The numerical implementation of the constitutive model is performed in the CAST3M (2019) finite element software through a user-defined UMAT subroutine. A series of simulations were performed to verify the basic and generalized cyclic models under various conditions. Moreover, the robustness of the model is attested by comparing the simulation results with the reported data of the pseudoelastic NiTi single crystal. The effect of crystallographic orientation and anisotropic cyclic deformation behavior are revealed and shown to be quantitatively in a good agreement with experimental results. Finally, the evolution of dislocation density and stored energy is discussed from the perspective of fatigue analysis of SMAs.