The micromechanical theory that we recently developed (LuZK andWengGJ 1997J.Mech.Phys.Solids451905-28) forthe stress-induced martensitic transformation is extended to studythe thermally induced phase transformation of shape memory alloys. This further development makes use of two martensitemorphologies: one with aligned plates and the other with randomlyoriented plates, intended respectively for the presence of asuperimposed applied stress and for a pure thermally inducedprocess. Inherent in the adoption of these two simple morphologiesis the assumption of scale-invariant transition from the singlecrystal to the homogenized polycrystal level without going throughthe calculation of the individual contributions of the constituentgrains. In the presence of an applied stress the orientation of thealigned martensite plates is chosen to maximize the transformationwork, while for a pure thermally induced setting the randomlyoriented plates are used to reflect the variously oriented variantsin the constituent grains. The theory developed is found to havetwo important characteristics: (i)the rate of transformation tendsto decrease during the cooling process and increase upon heating;and (ii)in the presence of an applied stress the hysteresis loopduring cooling and heating in the martensiteconcentration-temperature (cM-T) space translatesrigidly to the right, with a magnitude given by the transformationwork divided by the entropy change. The uncovered autoretardednature of theAMtransformation and theautocatalytic nature of theMAtransformation arefound to be in good quantitative accord with the experimental datafor a Ni-Ti system under a superimposed tension and of a Cu-Al-Nisystem undergoing a pure thermally induced process.
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