Thermodynamic Analysis of Anomalous Shape of Stress-Strain Curves for Shape Memory Alloys

In some shape-memory single crystals the stress-strain (σ~ε) curves, belonging to stress induced martensitic transformations from austenite to martensite at fixed temperature, instead of being the usual slightly increasing function or horizontal, have an overall negative slope with sudden stress drops in it. We discuss this phenomenon by using a local equilibrium thermodynamic approach and analysing the sign of the second derivative of the difference of the Gibbs free energy. We show that, considering also the possible nucleation and growth of two martensite structural modifications/variants, the stress-strain loops can be unstable. This means that the overall slope of the uploading branch of the stress-strain curve can be negative for smooth transformation if the second martensite, which is more stable with larger transformation strain, is the final product. We also show that local stress-drops on the stress-strain curve can appear if the nucleation of the second martensite is difficult, and the presence of such local stress-drops alone can also result in an overall negative slope of the stress-strain curves. It is illustrated that the increase of the temperature of the thermal recovery during burst-like transition is a measure of the change of the nucleation energy: the more stable martensite has larger nucleation energy.