A Constitutive Model of the Zero/Negative Thermal Expansion Response during Phase Transformation and Martensite (Re)Orientation in Shape Memory Alloys

Recent experiments demonstrated that the macroscopic thermal expansion (TE) response of bulk SMAs can be tailored via martensite (re)orientation, phase transformation, and crystallographic texture by taking advantage of the significant anisotropy in coefficients of thermal expansion (CTEs) of the martensite variants. Here, a phenomenological constitutive model, developed within the framework of irreversible thermodynamics with internal state variables, is proposed that can efficiently describe the TE evolution in SMAs during phase transformation and (re)orientation of martensite variants. The calibration of the model and its numerical implementation in an efficient scheme are described in detail. The model is validated by comparing simulations with available experimental data on the zero/negative TE of a polycrystalline NiTiPd SMA during deformation processing.