A 3D thermo-mechanically coupled model for describing rate-dependent super-elastic degeneration of NiTi shape memory alloys

Abstract A 3D thermo-mechanically coupled constitutive model is constructed in the framework of continuum thermodynamics to describe the uniaxial and multiaxial rate-dependent cyclic super-elastic degeneration of NiTi shape memory alloys (SMAs). To capture the anisotropic martensitic transformation, a J 2 - J 3 type phase transformation surface with a correction tensor is introduced into the proposed constitutive model. As an internal variable, the residual martensitic volume fraction is introduced into the transformation kinetics equations to improve the simulation to the shape of hysteresis loop. A new evolution equation of residual martensitic volume fraction is constructed by introducing the saturated residual strain and maximum temperature rise. The accumulation of residual strain with the increasing number of cycles and loading rate can be reasonably described. Evolution equations of critical transformation temperatures during the cyclic loading are established by introducing a maximum temperature rise in current loading history, which reflects the evolutions of critical transformation stresses and the increasing transformation hardening modulus. Comparison of simulated and experimental results shows that the proposed model can reasonably describe the uniaxial and multiaxial rate-dependent cyclic stress-strain curves and temperature oscillations of NiTi SMAs.