Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys

Abstract

In shape-memory alloys a first-order martensitic phase transition is responsible for pseudo-elastic and for ferro-elastic stress-strain relations. To describe this behaviour a modified Landau theory is proposed in which the free energy of the crystal depends on the temperature and on the full strain tensor. The energy is invariant with respect to the cubic point group Oh of the high-temperature phase. To predict the cubic-to-monoclinic phase transition of beta -phase shape-memory alloys an expansion up to sixth order in strain is necessary for which, for the class of alloys considered, odd terms may be neglected. For a CuAlNi alloy the expansion coefficients are determined by comparison with experimental results. In contrast to classical Landau theory of second-order phase transitions, not only a single second-order but also a fourth-order expansion coefficient depend on temperature.