Modeling and numerical simulation of the pseudoelastic behavior of shape memory alloy circular rods under tension-torsion combined loading

Most research on the behavior of shape memory alloys (SMAs) under tension-torsion combined loading has focused on tubular materials. In contrast to tubular SMAs, SMA rods have unique characteristics. When an SMA rod is twisted, the central region remains elastic while the outer layer undergoes a martensite transformation. The nonlinear stress distribution of an SMA rod through the radial direction gives the SMA rod peculiarities, and this is the primary factor that makes analysis of the stress-strain behavior difficult. The authors suggest a material model that can represent the stress-strain behavior of an SMA rod under tension-torsion combined loading. The proposed model is based on Brinson's phase transformation kinetics and the plastic flow rules. Furthermore, the yield is assumed to be in accordance with the Von Mises criterion and the effect of thermal expansion is not considered. The authors also present some numerical solutions of the proposed model in the context of isothermal strain and stress processes ( proportional and nonproportional loading) in the pseudoelastic region. According to simulation results, the stress-strain behavior of an SMA solid rod under biaxial loading differs from that of a thin-walled tube or a rod under one-dimensional loading.