Modeling phase fraction shakedown during thermomechanical cycling of shape memory materials

Shape memory actuation typically involves thermodynamic paths traversing regions of the stress–temperature phase diagram that support microstructures involving coexistence of austenite with multiple martensite variants. The fractional partitioning between these different phase/variant species depends on the previous path history. We discuss a simple model for the role that repeated stress–temperature cycling has on selecting the microstructural variants. The treatment is in terms of transitions between the austenite phase {A} and two martensite variants {M+} and {M−} with equal and opposing transformation strains. Purely temperature induced transitions then involve {M−, A, M+} mixtures with equal amounts of {M−} and {M+}. The {M+} variant is favored under positive stress, and positive stress transformation activity reflects this bias by a greater incremental gain in {M+} and/or a greater incremental loss in {M−}. Stress–temperature cycling then gives a {M−, A, M+}-partitioning that approaches a periodic limit cycle, giving rise to a limiting periodic strain response.