Three-dimensional thermomechanical modeling of pseudoelasticity in shape memory alloys with different elastic properties between austenite and martensite

In the present work, a three-dimensional micromechanical model has been developed based on Gall and Lim's expression for Gibbs free energy, which can reproduce the pseudoelastic behavior of NiTi shape memory alloys. The emphasis was put on the difference of elastic properties between austenite and martensite. The formulations for the evolution of volume fraction of the 24 martensite variants are derived. The discrete evolutionary equations are presented, with the expression of the mechanical Jacobian matrix. The model is implemented as User Material subroutine (UMAT) into ABAQUS. The model formulations and finite element method (UMAT) have been validated by numerical method. As an example, pseudoelastic response of a polycrystal NiTi shape memory alloy under uniaxial loading has been simulated. The distributions of the martensite and Mises stress are quite uniform. The Mises stresses are higher during loading than unloading, while the volume fractions during loading are lower than that during unloading at the same strain level. The results show that the model can predict experiments better than that without considering different elastic properties between austenite and martensite.