Finite element modeling of phase transformation in Shape Memory Alloys

Modeling of shape memory alloys thermo-mechanical behavior has become a major requirement in order to design increasingly complex components utilizing shape memory alloys. In this research, a physically-based mathematical model was developed and coupled to finite elements, to predict the thermo-mechanical behavior, namely shape memory effect and pseudoelasticity, of shape memory alloys including Cu-Al-Ni. The model accounts for phase transformations occurring as a function of temperature, responsible for the unique properties of shape memory alloys. The phase transformation is described thermodynamically, by deriving an explicit free energy expression from micromechanics incorporating two state variables, namely: (i) the overall martensite volume fraction and (ii) the mean transformation strain. The chosen behavior is implemented using the commercial finite element software ABAQUS^TM, where the material properties were defined using UMAT subroutine. The predicted load-displacement and phase transformation as a function of temperature and applied stress is validated against experimental results obtained employing nano-indentation. The verified model will help in understanding the thermo-mechanical behavior of shape memory alloys at various loading conditions and temperatures.