Modeling the martensite reorientation and resulting zero/negative thermal expansion of shape memory alloys

Recent experimental investigation shows that macroscopic overall zero/negative thermal expansion (TE) can be obtained through the martensite reorientation of NiTiPd shape memory alloy (SMA). In this work, a microstructure-based theoretical model is established to quantify such phenomenon. Based on the crystallographic symmetry, the microstructures and the coefficients of thermal expansion of the austenite and martensite lattices of NiTiPd SMA are analyzed. A crystal plasticity-type constitutive model at the individual grain level is constructed to describe the martensite transformation (MT) and martensite reorientation (MR) processes, and the evolution of thermal expansion coefficient. The nonlinear constitutive model is linearized by adopting the implicit backward Euler time discretization scheme and an incremental affine stress–strain–temperature relationship is obtained. An incremental self-consistent homogenization scheme is proposed to describe the interaction among the grains and calculate the elastic, inelastic (MT and MR) and thermal deformations of the polycrystalline aggregates. The established model is used to simulate the MR and the resulting zero/negative TE of polycrystalline NiTiPd SMA. It is shown that the observed quantitative features in experiments can be captured reasonably by the model.