Modeling of latent heat effects on phase transformation in shape memory alloy thin structures

This paper presents a fully coupled thermo-mechanical constitutive model for shape memory alloys taking into account latent heat effects during forward and reverse martensitic phase transformations. This model is obtained as an extension of an original macroscopic model, derived from a micromechanical-inspired Gibbs free energy expression. The proposed formulation considers beside the constitutive equations describing the thermo-mechanical behavior of Shape Memory Alloys (SMAs), the heat equation with additional internal source terms related to the latent heat generated during phase transformation. Hence, the thermo-mechanical problem to be solved consists of the mechanical equilibrium and the established heat equations. A 2D specific plane stress continuum and isoparametric finite element with three degrees of freedom (dof) per node corresponding to in-plane displacements and temperature is developed to solve the derived thermomechanical problem. The developed 2D finite element is implemented in the Abaqus® finite element code through the UEL user's subroutine. The numerical simulations performed by using this new finite element show the delaying effect of the transformation latent heat on the forward and reverse phase transformations in SMA thin structures and the possible heterogeneous character of the phase transformation in this case. These effects are even more important as the strain rate is high.