Initial Yield Surface of Shape Memory Alloy in Stress Induced Martensitic Phase Transformation

Abstract

Based on the critical conditions for nucleation and the actual eigenstrain of a given shape memory alloy in the stress induced martensitic phase transformation, the closed-form expression of its corresponding initial yield (nucleation) surface is obtained. Consequently, the underline mechanism for non-symmetry in the stress vs. strain relationship between uniaxial tension and uniaxial compression experimentally observed in many SMAs is revealed. Unlike that in many traditional criteria, such as the Von Mises and Tresca criteria, in which the yield surfaces are functions of stress only, the yield surface derived here is closely related to the crystal structures before and after the phase transformation. The initial yield surface of a polycrystalline CuZnAl shape memory alloy tube under combined loading of tension and torsion predicted by the formula developed here agrees well with the experimental results reported in the literature.