A self-consistent model for the stress–strain behavior of shape-memory alloy polycrystals

Abstract

In spite of the recent progress in the development of constitutive theory for shape-memory alloys (SMAs), no micromechanical model has been developed to calculate the stress–strain behavior of a SMA polycrystal from the behavior of its constituent grains. A self-consistent model is developed for such a purpose. Using a recently developed micromechanical theory to describe the behavior of single crystals (Lu and Weng, J. Mech. Phys. Solids, 1997, 45, 1905), the model provides a self-consistent relation to connect the stress and phase transformation strain on the grain level with those on the polycrystal level. This relation allows the phase transformation strain in each grain to be calculated in accordance with its stress, and then, by an orientational averaging process, the overall phase transformation strain of the polycrystal is determined. To further test the validity of the single crystal theory, a micromechanical, crystallographic procedure is developed to calculate the anisotropic phase transformation strains of a Ni–Ti crystal under various directions of tensile loading; the computed results were found to be in general accord with the experimentally measured values. The self-consistent model is then applied to derive the stress–strain behavior of a Ni–Ti polycrystal at three different levels of temperature, first above A f, then between A f and A s, and finally between A s and M s, to illustrate its pseudoelastic behavior, shape-memory effect and ferroelasticity, respectively. In each case the theoretical phase transformation strain of the polycrystal was in very good agreement with experiments. The “work-hardening” nature of the stress–strain curve at the later stage of phase transformation is also vividly displayed by both theory and experiment.