Modeling of the stress–strain responses and deformation patterns of superelastic NiTi tubes subjected to biaxial loadings

Nearly equiatomic NiTi shape memory alloy exhibits superelasticity, i.e., it can be strained up to ~ 7% and recover completely upon unloading, and consequently, the stress–strain response forms a closed hysteresis. The mechanical behavior of superelastic NiTi is characterized by significant tension–compression asymmetry, which leads to complexity in the stress–strain responses and deformation patterns of thin-walled superelastic NiTi tubes loaded by axial force and internal pressure simultaneously. In the reported biaxial experiments, the NiTi tube exhibits hardening responses and essentially homogeneous deformation in a neighborhood of equibiaxiality. In other cases, its stress–strain responses trace stress plateaus associated with localized deformation patterns, and the level of plateaus, magnitude of transformation strains, and orientation of the localization bands are strongly dependent on the axial-to-hoop stress ratio. In this paper, finite element modeling is performed to analyze numerically the mechanical response of biaxially loaded superelastic NiTi tube. A numerical feedback control scheme is developed to maintain the stress ratio to follow the target value. The simulations reproduce successfully the observed phenomena in the experiments, such as the localization of helical bands, the variation of band angles with stress ratio, as well as the hardening and uniform deformation near the state of equibiaxial stress. In addition, the variation of axial and hoop stress–strain responses with different stress ratios are also studied, which are reasonably close to the experimental ones. The presented work demonstrates the validity of the developed finite element analysis framework and paves the way for analysis of superelastic shape memory alloy structures under multiaxial loading.