A stochastic thermodynamic model for the gradual thermal transformation of SMA polycrystals
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The martensitic-austenitic phase transformation of a polycrystalline shape memory alloys (SMA) occurs gradually over a range of temperatures even though the monocrystal undergoes a first-order transition (at a single temperature). Factors such as material inhomogeneities and internal stresses in a polycrystal are believed to cause the spread in transformation temperatures. In this work, we assume that the local regions of a polycrystal transform at a single temperature, characteristic of a first-order transition; this temperature is taken to vary from one region to another. The first-order transition of a generic local region is modeled with the Boyd-Lagoudas thermodynamic theory and a simple averaging process is used to derive the overall response of the polycrystal. The concept of a statistical distribution in the first-order transition temperatures is then introduced. By reducing the proposed stochastic thermodynamic theory to the special case of a pure thermal transformation in a polycrystal, it becomes possible to obtain the parameters of the statistical distribution from calorimetric data. This new approach renders unnecessary the customary practice in the SMA literature to artificially assign 'start' and 'finish' transformation temperatures to a SMA polycrystal. The statistical distribution is also used as a basis to correlate strain recovery against temperature measurements from repetitive cycles of a thermally induced transformation in untrained polycrystalline SMA wires.
