Relaxation in shape-memory alloys - Part I. Mechanical model

A variety of relaxation phenomena such as the stabilization of martensite, rubber-like behavior, evolving hysteresis loops and stabilization of interfaces have been observed in various shape-memory alloys. These effects adversely impact technological applications. Despite a great deal of experimental evidence, there is no consensus on the mechanism. However, there is universal agreement on certain fundamental aspects of these phenomena. Based on these areas of agreement, we propose a phenomenological, but predictive, model in this paper. This model is based on the framework of thermoelasticity augmented with an internal variable. In this part, we discuss the basic mechanical model and show that it reproduces the experimental observations remarkably well. In Part II of this paper, we extend this model to include thermal effects and use these models to propose new experiments in order to clarify longstanding issues.