Phenomenological model for phase transformation characteristics of textured shape memory alloys

Abstract

In the present study, a new transformation criterion that includes the effect of tension- compression asymmetry and texture-induced anisotropy is proposed and combined with a thermodynamical model to describe the thermomechanical behavior of polycrystalline shape memory alloys. An altered Prager criterion has been developed, introducing a general transformation of the axes in the stress space. A convexity analysis of such criterion is included along with an identification strategy aimed at extracting the model parameters related to tension-compression asymmetry and anisotropy. These are identified from a numerical simulation of a SMA polycrystal, using a self-consistent micromechanical model previously developed by Patoor et al. (Patoor, E., Eberhardt, A., Berveiller, M., 1996. Micromechanical Modelling of Superelasticity in Shape Memory Alloys. Journal de Physique IV 6, C1 277) for several loading cases on isotropic, rolled and drawn textures. Transformation surfaces in the stress and transformation strain spaces are obtained and compared with those predicted by the micromechanical model. The good agreement obtained between the macroscopic and the microscopic polycrystalline simulations states that the proposed criterion and transformation strain evolution equation can capture phenomenologically the effects of texture on anisotropy and asymmetry in SMAs.