Thermal effects in the superelasticity of crystalline shape-memory materials

Abstract

This paper develops a three-dimensional theory for the superelastic response of single-crystal shape-memory materials. Since energetic considerations play a major role in the phase transformations associated with the superelastic response, we have developed the theory within a framework that accounts for the laws of thermodynamics. We have implemented a special set of constitutive equations resulting from the general theory in a finite-element computer program, and using this program have simulated the superelastic response of a single crystal Ti–Ni shape-memory alloy under both isothermal and thermo-mechanically coupled situations. Both manifestations of superelasticity—stress–strain response at fixed temperature and strain–temperature response at fixed stress—are explored. The single-crystal constitutive-model is also used to discuss the superelastic response of a polycrystalline aggregate with a random initial crystallographic texture. The overall features of the results from the numerical simulations are found to be qualitatively similar to existing experimental results on Ti–Ni.