Hysteresis During Stress-Induced Variant Rearrangement

Abstract
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 on single crystals of γ' 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, forthcoming.