A relaxed-constraint model for the tensile behavior of polycrystal shape-memory alloy wires

This article provides a micromechanics-based theory to elucidate that the t hermomechanical behavior of a polycrystal shape-memory alloy (SMA) wire is different from that of a bulk material. The study is based on the observati on that a polycrystal wire cannot retain any significant amount of internal stress in the transverse direction; thus, the internal stress of its const ituent grains is predominantly tensile and the transverse components can be relaxed to zero. The heterogeneous tensile internal stress is then calcula ted from a self-consistent relation. By this internal stress and an irrever sible thermodynamic principle, the decrease of Gibbs free energy and the th ermodynamic driving force for martensitic transformation in the grain is es tablished. This leads to a kinetic equation for the evolution of the marten site phase in each constituent grain and then, by an orientational average process, the evolution of the overall phase-transformation strain of the po lycrystal SMA wire. Applications of the theory to a Ti-Ni wire under a ther mal cycle and under a stress cycle have led to results that are consistent with experimental data. As compared to the bulk behavior, the range of tran sformation temperatures for the wire is substantially narrower, and the tan gent modulus of its stress-strain curves is much lower. These characteristi cs point to the superiority of an SMA wire over the bulk in smart-material applications and are both attributable to its reduced geometrical constrain t in the transverse direction.