Phase-field modeling of displacive phase transformations in elastically anisotropic and inhomogeneous polycrystals

We integrate the inhomogeneous elasticity model and the phase-field equations for displacive phase transformations in polycrystalline materials. The relaxation of the misfit strain between parent and transformed product phases or among different structural variants of transformed product phases near grain boundaries is taken into account. It is applied to the fcc to bcc martensitic transformation described by a Bain strain in a polycrystalline Fe-31at.%Ni metallic alloy. The focus is on the effect of grain boundaries on the displacive transformation behaviors. We first study nucleation of the bcc product phase at a grain boundary of a bicrystal. The predicted microstructures through nucleation near grain boundaries are compared to existing experimental observations in literature. The effects of grain boundary characteristics such as the degree and range of the misfit strain relaxation at the grain boundary and grain boundary curvature on the phase behaviors near a grain boundary are then examined for both a flat or a curved grain boundary. The model is also applied to polycrystals containing multiple grains. The effects of the misfit strain relaxation at grain boundaries, elastic anisotropy, and applied stress on the kinetics and the microstructures of displacive transformations are discussed.