Three-dimensional phase field model and simulation of cubic → tetragonal martensitic transformation in polycrystals

Abstract

Abstract The phase field microelasticity theory is used to formulate a three-dimensional phase field model of proper cubic → tetragonal martensitic transformation in a polycrystalline material under an external load. The model is based on the exact solution of the elasticity problem for the material with an arbitrary phase pattern in the homogeneous and isotropic modulus approximation. The transformation-induced coherency strain, strain coupling between grains, and applied stress are explicitly taken into account in this solution. Computer simulations are performed for the martensitic transformation with crystallographic parameters corresponding to the transformation in Fe-31 at.% Ni alloy. The polycrystalline systems with a periodically repeated motif of three, five and seven grains of the parent phase with different orientations are studied. The development of the martensitic transformation through nucleation, growth and coarsening of orientation variants is simulated at different levels of the applied stress. The simulated martensitic structure has a complex polytwinned morphology. The simulation has shown that the martensitic transformation in polycrystals drastically differs from the transformation in single crystals. The simulation has predicted that the deformation curve of a polycrystalline material has a hysteretic effect.