Thermodynamic aspects of shape memory alloys

Phase transitions are universal phenomena which provide an important field of study for thermodynamics. It is therefore appropriate that thermodynamics should be applied to phase transitions and twinning processes of shape memory alloys. In this contribution, we develop thermodynamics and statistical thermodynamics of a simple one-dimensional model for a crystalline body which has an austenitic phase and martensitic twins. We recognize that the model permits the calculation of a free energy function which predicts martensite as the stable phase at low temperature and austenite as an entropically stabilized phase at high temperature. The phase transitions in shape memory alloys are hysteretic, and we consider hysteresis as a consequence of coherency between the phases. In this manner, it is possible to relate the size of the hysteresis to the interfacial energy and to predict the release of latent heat during the transition. A phase diagram can be constructed in the temperature-deformation plot and it is interesting to calculate the subtle changes which coherency predicts for the shape of the phase diagram. The Gibbs phase rule no longer applies in the usual form. The proper treatment of the metastability within the hysteresis loops is still a mystery. We discuss this point but do not resolve it. Our model permits the simulation of the response of a tensile specimen to a thermodynamic input. Thus, we are able to calculate the deformation and all phase fractions as functions of time if the load and the temperature are prescribed as functions of time. In particular, we can simulate isotherms in a load-deformation diagram that represent quasiplasticity at low temperature and pseudoelasticity at high temperature.