Micromechanical model of polycrystalline shape memory alloys based on Reuss assumption

To understand the complicated thermodynamical behaviors of shape memory alloys (SMA) and to optimally design structures with SMA components, a simple yet micromechanical model of SMA was proposed based on Reuss assumption, namely, an assumption of uniform stress state in every grain. Since interaction between grains doesn't exist in Reuss assumption, we considered a specific distribution for phase interaction energy and also hardening due to the grain interaction. Choosing adequate distributions for both grain orientation and phase interaction energy, the model could describe the round shape around yielding stresses and the inner loops on a stress-strain hysteresis relationship and the temperature differences between transformation start and finish. They were in quantitative agreement with available experimental data for wires. Moreover, a heat balance equation was combined with the constitutive equation to take into account the effect of temperature change of the material. This combined model could capture quantitatively a temperature variation of about 20K in one cycle due to self heating and cooling as well as the effect of strain rate on stress-strain hysteresis loops. Finally, by reducing this proposed model to a model for unidirectional loading we showed that the proposed model became our previously developed macromechanical 1D model. Thus we could bridge the gap between a grain-based micromechanical model and a specimen-based macromechanical 1D model.