Micromechanical Modelling of the Superthermoelastic Behavior of Materials Undergoing Thermoelastic Phase Transition

The superelasticity of the Shape Memory Alloys (SMA) is well known nowadays, but few models describe the non isothermal behavior of SMA. In this paper, we have developped a micromechanical modelling of the SMA's thermomechanical behavior based on a kinematical description of the strain mechanisms. In order to describe the microstructure evolution of the material, we define a thermodynamical potential in which volume fractions of the different variants of martensite used as the internal variables. This study allow us to determine the constitutive equations for the local behavior. Global one is then obtained using a scale transition method ; the self-consistent one. This model is able to predict not only the macroscopic behavior but also the evolution of the variants of martensite in the material. The results are in good agreement with experimental data and observations

EPS et culture : première partie

International audienceIn 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