On the Hysteresis in Martensitic Transformations

Abstract

The paper proposes an explanation of the hysteresis in shape memory alloys using energy minimization in nonlinear elasticity and the entropy criterion. The stored energy has two wells describing the two phases. At elongations from some interval, the minimum energy is realized on two-phase mixtures. If the loaded phases are incompatible, that minimum energy is a concave function, and so we have a phase equilibrium curve of negative slope. The quasistatic evolution during loading experiments is realized in the class of mechanically, but not thermodynamically, equilibrated mixtures. This family contains states of elongation and force covering the whole area of the hysteresis loop. The evolution must satisfy the entropy criterion for moving phase interfaces which implies that, in the region above the phase equilibrium line, only processes with nondecreasing amount of the second phase are possible while below the situation is the opposite. This picture provides all the elements necessary for the explanation of the hysteresis, including the internal hysteresis loops.