Application of a partially relaxed shape memory free energy function to estimate the phase diagram and predict global microstructure evolution

Abstract

In this work recent results regarding bounds of the relaxed free energy functions of a broad class of shape memory materials of arbitrary symmetry are leveraged to develop a simple and efficient numerical method to analyze several aspects of the thermomechanical response of such materials. This approach is shown to be useful for construction of the austenitic phase diagram used in many early phenomenological models. It is also demonstrated that the resulting implementation is suitable for finite element analysis, has desirable numerical properties, and makes realistic quantitative predictions regarding the evolution of the lattice correspondence variants, transformation stress and strain levels, and orientation dependence.