Plasticity Like Model of Martensite Phase Transition in Shape Memory Alloys

Abstract
Many models simulating the behavior of Shape Memory Alloys (SMA) exist nowadays, in the one or three dimensional situation. In most of the cases they are not able to describe the non isothermal behavior of SMA due to the thermomechanical loadings. Indeed, the influence of the stress on the product phase leads to an orientation of the variants, when the temperature creates a self-accomodating martensite. The result of these two different influences is that the oriented product phase creates large deformations of phase transition, although the self-accomodating one does not produce any macroscopical deformation. In this paper, we develop a model of phase transition which takes into account the two types of martensite. Using this model allows us to simulate the behavior of SMA in isothermal or non isothermal loadings. Thus, the pseudoelasticity, the orientation of self-accomodating variants, the recovery stress or the thermal cycling at constant stress or strain can be simulated with a good agreement with experiments.