Differential Equation of Hysteresis : Application to Partial Martensitic Transformation in Shape-Memory Alloys

Abstract
Because the martensitic transformations, as a rule, are first order transitions, a special attention should be attracted to a hysteretic behavior of shape-memory alloys. The most important characteristics of the temperature-or stress-induced martensitic transformation, have been studied in detail up to date. It has been shown that such macroscopic state variables as inelastic strain or volume fraction of the martensite are always complex multi-valued functions of the temperature and external stress. Some phenomenological approaches for the thermomechanical state equations for shape memory alloys were recently published. In particular, a special type of differential equations describing evolution of the inelastic macroscopic strain and volume fraction of martensite as a functions of the temperature have been proposed in our recent papers [11 - 12]. These and some other problems associated with the irreversible processes caused by hysteresis will be discussed in the present paper. The main aim is to consider a simplest application of these equations to a strain evolution during the multiple temperature cycling in small temperature intervals.