Macroscopic Modeling of Shape Memory Alloys Under Non-Proportional Thermo-Mechanical Loadings

A new continuum model for the description of the general mechanical behavior of polycrystalline Shape Memory Alloys (SMA) is introduced in order to represent some particular 3D-effects not described by usual plasticity-like macroscopic models (e.g., reorientation under general loadings). The model describes the one-way and the pseudoelasticity shape memory effects as well as their transient behavior under reorientation of the martensite by arbitrary thermo-mechanical loadings. The main idea for the description of phase change and martensite reorientation consists of the assumption that the driving forces of the phase transformation depend on both the actual stress state and the transformation induced strain (TIS) tensor. In order to describe the change of the martensite structure both, the TIS as a tensorial internal variable together with a scalar valued variable which describes the phase fraction of thermally induced martensite, are used. The evolution of the TIS tensor is described by a new evolution equation without plastic analogy. The problem of modeling the evolution direction and the thermodynamical consistency are discussed in details.