Thermomechanical discrete dislocation-transformation model of single-crystal shape memory alloy

The interaction between martensitic phase transformation and plastic deformation affects the response of shape memory alloys (SMAs) during cyclic loading, in particular in terms of their pseudoelasticity characteristics and the shape memory effect. This interaction, which occurs at a sub-micron length scale inside single crystal grains, influences the reversibility and the actuation capacity of SMAs. In order to capture the sub-grain interactions while keeping the simulations tractable, a suitable modeling compromise between length scale resolution and computational effort is required. To this end, a model originally developed for multiphase steels assisted by transformation-induced plasticity is extended for shape memory alloys. Two new features, relevant for shape memory alloys, are introduced in the model, namely (i) the modeling of crystallographically reversible transformations and (ii) the thermal contribution in the free energy and the thermal effects on the transformation driving force. The two-dimensional model uses discrete dislocations to simulate plastic deformation due to slip and discrete regions to explicitly take into account the evolution of the martensitic phase. Through representative numerical simulations, the microscale coupling between phase transformation and plasticity is investigated with a view of elucidating (i) the effect of dislocations on the martensitic transformation, (ii) the effect of the phase transformation on dislocation slip and (iii) the interaction of both phenomena on the total reversibility of SMAs during cyclic loading. The results provide valuable information for the understanding of the interaction mechanism in shape memory alloys at the level of single crystals, which may be extended to an aggregate of grains.