A constitutive model for shape memory alloy in pure shear state

It is of engineering interest to establish a constitutive model which includes the equations describing the phase transformation and mechanical behaviors of shape memory alloys (SMA) in pure shear state. In this study, such a shape memory evolution equation is established using the shape memory factor and Brinson's relationship of phase transformation critical stress and temperature. A mechanical constitutive equation is also developed from 3D micro-mechanical constitutive equation based on the assumption that SMA is isotropic material to express the mechanical behaviors of SMA in pure shear state. All material constants in the shape memory evolution equation and mechanical constitutive equation can be determined through macroscopic experiments, so that they are more easily used in practical applications. Numerical simulation results show that this shape memory evolution equation could simulate truly the processes of phase transformations in austenite, twinned and detwinned martensites, and the mechanical constitutive equation could predict reasonably the mechanical behaviors of SMA in pure shear state.