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

Abstract

This article provides a micromechanics-based theory to elucidate that the thermomechanical behavior of a polycrystal shape-memory alloy (SMA) wire is different from that of a bulk material. The study is based on the observation that a polycrystal wire cannot retain any significant amount of internal stress in the transverse direction; thus, the internal stress of its constituent grains is predominantly tensile and the transverse components can be relaxed to zero. The heterogeneous tensile internal stress is then calculated from a self-consistent relation. By this internal stress and an irreversible thermodynamic principle, the decrease of Gibbs free energy and the thermodynamic driving force for martensitic transformation in the grain is established. This leads to a kinetic equation for the evolution of the martensite phase in each constituent grain and then, by an orientational average process, the evolution of the overall phase-transformation strain of the polycrystal SMA wire. Applications of the theory to a Ti-Ni wire under a thermal 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 transformation temperatures for the wire is substantially narrower, and the tangent modulus of its stress-strain curves is much lower. These characteristics point to the superiority of an SMA wire over the bulk in smart-material applications and are both attributable to its reduced geometrical constraint in the transverse direction.