Micromechanical theory for the thermally induced phase transformation in shape memory alloys

The micromechanical theory that we recently developed for the stress-induced martensitic transformation is extended to study the thermally induced phase transformation of shape memory alloys. This further development makes use of two martensite morphologies: one with aligned plates and the other with randomly oriented plates, intended respectively for the presence of a superimposed applied stress and for a pure thermally induced process. Inherent in the adoption of these two simple morphologies is the assumption of scale-invariant transition from the single crystal to the homogenized polycrystal level without going through the calculation of the individual contributions of the constituent grains. In the presence of an applied stress the orientation of the aligned martensite plates is chosen to maximize the transformation work, while for a pure thermally induced setting the randomly oriented plates are used to reflect the variously oriented variants in the constituent grains. The theory developed is found to have two important characteristics: (i) the rate of transformation tends to decrease during the cooling process and increase upon heating; and (ii) in the presence of an applied stress the hysteresis loop during cooling and heating in the martensite concentration-temperature (c_M-T) space translates rigidly to the right, with a magnitude given by the transformation work divided by the entropy change. The uncovered autoretarded nature of the A→M transformation and the autocatalytic nature of the M→A transformation are found to be in good quantitative accord with the experimental data for a Ni-Ti system under a superimposed tension and of a Cu-Al-Ni system undergoing a pure thermally induced process.