Three dimensional large deformation analysis of phase transformation in shape memory alloys

Shape memory alloys (SMAs) have been explored as smart materials and used as dampers, actuator elements, and smart sensors. An important character of SMAs is its ability to recover all of its large deformations in mechanical loading-unloading cycles without showing permanent deformation. This paper presents a stress-induced phenomenological constitutive equation for SMAs, which can be used to describe the superelastic hysteresis loops and phase transformation between Martensite and Austenite. The Martensite fraction of SMAs is assumed to be dependent on deviatoric stress tensor. Therefore, phase transformation of SMAs is volume preserving during the phase transformation. The model is implemented in large deformation finite element code and cast in the updated Lagrangian scheme. In order to use the Cauchy stress and the linear strain in constitutive laws, a frame indifferent stress objective rate has to be used. In this paper, the Jaumann stress rate is used. Results of the numerical experiments conducted in this study show that the superelastic hysteresis loops arising with the phase transformation can be effectively captured.