Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: simulation of ζ′2 martensite in AuCd alloys

A three-dimensional phase field model of the martensitic transformation that produces a low symmetry phase in polycrystals is developed. The transformation-induced strain mostly responsible for the specific features of the martensitic transformation is explicitly taken into account. The high computational efficiency of the model turns out to be almost independent of the complexity of the polycrystal geometry. An example of the cubic→trigonal transformation in AuCd alloys producing ζ′2 martensite is considered. The development of the transformation through nucleation, growth and coarsening of orientation variants is simulated for both single crystal and polycrystalline materials. The effect of an external load on the martensitic microstructure in the polycrystalline material is studied. It is shown that the elastic coupling between different transformed grains of the polycrystal drastically affects the microstructure and its response to the applied stress. The obtained self-accommodating morphologies of the multivariant martensitic structure are in agreement with those observed in the experiments.