Hysteresis During Stress-Induced Variant Rearrangement

This paper represents an attempt to understand, from basic principles, the origins of hysteresis during variant rearrangement. As a framework for this study, we focus on the biaxial loading experiments conducted in 171 on single crystals of 7; martensite, oriented so that two compound twinned variants of martensite have least energy. Our analysis supports the idea that hysteresis (at least in these slow cyclic experiments) is due to metastability: as the loads are changed, the current state goes from stable to metastable to unstable. The idea we explore is that the metastability is essentially caused by geometric incompatibility. That is, even though there is a state of lower energy than the metastable state, it is necessarily geometrically incompatible with it, and this gives rise to an energy barrier. We show that this concept of metastability (based on calculating relative minimizers of energy) has a close relation with the Schmid Law and reveals an interesting dependence on the shape of the specimen. Further details and background for the ideas presented here can be found in [4], forthcoming. 1. BIAXIAL LOADING EXPERIMENTS To test any idea of metastability as it relates to hysteresis, it is helpful to have a set of experiments for which the beginning and ending states are single-variant (so that one need only assess the metastability of of the single variant state) and for which there are several independent control parameters, so that the idea is rigorously tested. The experiments of Chu and James [1,7,8] are of this type. They are orthogonal biaxial loading experiments on single crystals of Cu14.0wt.%Al-3.9wt.%Ni in the fully transformed yi martensitic phase. The loading device in these experiments was specifically designed to be governed by the free energy, where y (x) is the deformation (defined on the reference configuration a) and T is a constant 3 x 3 matrix of the form