Phase-field modeling of microstructure evolution in elastically inhomogeneous polycrystalline materials

This study focuses on modeling microstructure evolution in elastically inhomogeneous polycrystalline materials using the phase-field approach. Phase-field models for the diffusional processes and the structural transformations are successfully integrated with the inhomogeneous elasticity model of polycrystalline materials. By employing the Voigt notation scheme of the mechanical equilibrium equation, the computational efficiency for obtaining elastic solutions in polycrystalline materials is improved. The developed phase-field models are then applied to investigate the kinetic processes taking place in polycrystals.;To describe the diffusional processes in an elastically anisotropic polycrystalline binary solid solution, the chemical free energy model of the solid solution is integrated with the elastic strain energy model. The elastic interactions due to coherency elastic strain are incorporated by solving the mechanical equilibrium equation using an iterative-perturbation scheme taking into account elastic modulus inhomogeneity stemming from the grain orientation. The elastic strain energy of the solid solution itself of an elastically anisotropic polycrystal is also formulated based on Khachaturyan's theory, and discussed from the theoretical point of view. By applying the model, the precipitate-precipitate interaction across a grain boundary and the grain boundary segregation-precipitate interaction are microscopically investigated.;We then study strain-induced solute segregation at a grain boundary and solute drag effect on boundary migration using a phase-field model integrating grain boundary segregation and grain structure evolution. Strain-induced grain boundary segregation at a static planar boundary is studied numerically and the equilibrium segregation composition profiles are validated using analytical solutions. In addition, we systematically study the effect of misfit strain on grain boundary migration with solute drag. The drag force is theoretically analyzed based on Cahn's analytic theory. The simulation results are discussed based on our theoretical analysis in terms of elastic and chemical drag forces. The optimum condition for solute diffusivity to maximize the drag force under a given driving force is identified.;The developed phase-field model for structural change in polycrystals is modified and applied to the deformation twinning process in fcc materials. A phase-field model for modeling the microstructure evolution during deformation twinning in fcc crystals is firstly proposed. The order parameters are proportional to the shear strains defined in terms of twin plane orientations and twinning directions. The deformation energy as a function of shear strain is obtained using the first-principle calculations. The gradient energy coefficients are fitted to the twin boundary energies along the twinning planes and to the dislocation core energies along the directions that are perpendicular to the twinning planes. The elastic strain energy of a twinned structure is included using the Khachaturyan's elastic theory. The model is then extended to modeling the deformation twinning processes in polycrystals. We simulate the twinning processes and microstructures evolution under a number of fixed deformations and predicted the twinning plane orientations and microstructures in single- or polycrystals. Moreover, the hierarchical twinning process in a fcc crystal (Cu) is simulated by applying the phase-field model for twinning processes in polycrystals. The possibility of secondary and tertiary twinning processes under the proper deformation condition is identified from the simulations.;The developed models for both diffusional processes and structural transformations are also applied to modeling phase transformations in one of realistic materials systems, Ti alloys in which the phase transformation takes place through solute diffusion processes as well as bcc to hcp structural changes. First of all, the possible kinetic pathways during the phase transformation from the high temperature beta phase to the low temperature (alpha+beta) two-phase Ti alloys are investigated based on the thermodynamic stability analyses using a Ti-V binary alloy system. We demonstrate and discuss the proposed phase transformation sequences employing phase-field simulations. We then study the morphological evolution during the phase transformations in polycrystalline Ti alloy by applying the phase-field model for polycrystals to the system. The mechanisms of the alpha phase formation as well as the variant selection at or near a grain boundaries are investigated using the phase-field simulations.