Micro-mechanic modeling of the stress–strain curves of a TiNiCu shape memory alloy

A micro-mechanic model based on Eshelby’s method and the minimization of the Gibbs free energy criterion, is proposed and used to predict the orientation angles of martensite variants in a single crystal TiNiCu shape memory alloy, which are in a good agreement with the observations by Saburi et al. Then, the stress–strain curve of a single crystal TiNiCu is predicted and is found to be dependent on the mode of applied stress, i.e. tension and compression. The above model is extended to the case of polycrystal TiNiCu system which is assumed to be composed of finite number of grains with several martensite variants being embedded in each grain. It turns out that use of only small number of grains are needed to simulate the smooth stress–strain curve of TiNiCu system. The stress–strain curves in both loading and unloading modes are correctly predicted at an equilibrium temperature. Finally this polycrystal model is applied for other temperatures, indicating the correct temperature dependance of the stress–strain curves.