On the pseudo-elastic hysteresis

It is often considered that in solids a non-monotone load-deformation characteristic of the "van der Waals type" may give rise to hysteretic behaviour in a phase transition. Here we consider a pseudo-elastic hysteresis that occurs in the austenitic-martensitic phase transition of shape memory alloys. For demonstrative purposes we let the non-monotone characteristic first be defined by the Landau-Devonshire model, later we even use straight lines. We ask the following questions: (i) How wide is the hysteresis loop? (ii) How does the width of the hysteresis loop change with temperature? (iii) What are the possible processes inside the hysteresis loop? Answers are provided for all three questions, viz. On (i) The width is determined by the interfacial energy of the phases. On (ii) There is no significant dependence on temperature. On (iii) The hysteresis loop contains metastable states that loose their (meta-)stability on a line defining phase equilibrium. The theoretical predictions are qualitative results. They are supported by tensile experiments on a CuZnAl single crystal.