Modeling thermomechanical phase transformations between austenite and a two variant martensite

Both austenite/martensite transformations and martensite/martensite variant reorientation are central to shape memory actuation and pseudoelasticity. The approach is to augment conventional continuum mechanical descriptions with internal variables that track fractional partitioning of the material between austenite and the various martensite variants. A three-species model involving austenite and two complementary martensite variants provides sufficient generality to capture the variant distributions that underlie shape memory, and the strain-accommodation associated with pseudoelasticity. Transformations between any of these species can be tracked on the basis of triggering algorithms and kinetic continuation that reflect both transformation hysteresis and the variation of triggering stress and temperature, as given by the Clausius-Clapeyron relation. The particular algorithm that we describe here is for temperature-and stress-dependent response. It requires only the following experimental parameters: the four transformation temperatures {dollar}Msb{lcub}f{rcub}, Msb{lcub}s{rcub}, Asb{lcub}s{rcub}, Asb{lcub}f{rcub},{dollar} the crystallographic transformation strain, the Young's modulus and the transformation latent heat. The martensite flow and finish stresses are also introduced. As an application of the model, Two Element Thermal Engine (TSTE) is investigated to predict a reciprocal movement upon thermal heating/cooling pulses controlled for example by an electrical signal.