Mean-field framework for the characterization of SMA polycrystals with material uncertainties
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abstract
Single crystals of Shape Memory Alloys are known to undergo a first order transition; the transformation from one phase into another occurs at the same temperature. Transformation of a polycrystalline SMA however occurs over a range of temperatures. Factors such as defect structure and internal stresses in a polycrystal are believed to cause the spread in transformation temperatures (also referred to as material uncertainties). In this work), we extend the Boyd-Lagoudas thermomechanical model (1995) to include the effect of an assumed first-order transition for the local regions of the polycrystal undergoing transformation and a statistical distribution of the temperatures at which these regions transform. Reducing the model to the special case of pure thermal transformation of the polycrystal, it is possible to get the parameters of the statistical distribution after getting a good comparison with experimental calorimetric data. The statistical distribution is proposed to be used in future work on stress-induced transformation behavior of the polycrystal.
