Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part IV: modeling of minor hysteresis loops
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A thermomechanical model for the hysteretic response of Shape Memory Alloys (SMAs) is proposed in this paper by expanding a previous model developed by Bo and Lagoudas to include minor hysteresis loops. The constitutive model for SMAs previously developed by Bo and Lagoudas is reviewed first, and a simplification for the case of fully trained SMAs with a stable major hysteresis loop is then presented. An evolution equation for the energy dissipation is proposed based on the theoretical analysis and experimental observations. A connection between the Preisach hysteresis model and the present thermomechanical model is also investigated. The memory (wiping out) property for the present model is determined in a way similar to that of the Preisach model. Comparisons between the present model predictions and the experimental results show that the present model accurately predicts the minor loop hysteresis response of SMAs, even when such minor loops are close to the transformation start and finish points. Compared with the Preisach model, the present hysteresis model follows a thermodynamic formulation, which makes it easier to account for the effects of changing loading paths and two-way memory effect induced by cyclic loading. The developed numerical implementation algorithm can also be easily incorporated in conjunction with other existing thermomechanical constitutive models, thus providing a general scheme for the modeling of hysteretic response of SMAs, based on physical parameters.
