A macro-mechanical constitutive model of shape memory alloys

It is of practical interest to establish a precise constitutive model which includes the equations describing the phase transformation behaviors and thermo-mechanical processes of shape memory alloy (SMA). The microscopic mechanism of super elasticity and shape memory effect of SMA is explained based on the concept of shape memory factor defined by the author of this paper. The conventional super elasticity and shape memory effect of SMA are further unified as shape memory effect. Shape memory factor is redefined in order to make clear its physical meaning. A new shape memory evolution equation is developed to predict the phase transformation behaviors of SMA based on the differential relationship between martensitic volume fraction and phase transformation free energy and the results of DSC test. It overcomes the limitations that the previous shape memory evolution equations or phase transformation equations fail to express the influences of the phase transformation peak temperatures on the phase transformation behaviors and the transformation from twinned martensite to detwinned martensite occurring in SMA. A new macro-mechanical constitutive equation is established to predict the thermo-mechanical processes realizing the shape memory effect of SMA from the expression of Gibbs free energy. It is expanded from one-dimension to three-dimension with assuming SMA as isotropic material. All material constants in the new constitutive equation can be determined from macroscopic experiments, which makes it more easily used in practical applications.