The fundamentals and applications of phase field method in quantitative microstructural modeling

The key to predicting and therefore controlling properties of materials is the knowledge of microstructure. As computer modeling and simulation is becoming an important part of materials science and engineering, there is an ever-increasing demand for quantitative models that are able to handle microstructures of realistic complexity at length and time scales of practical interest. The phase field approach has become the method of choice for modeling complicated microstructural evolutions during various phase transformations, grain growth and plastic deformation. Using gradient thermodynamics of non-uniform systems and Langevin dynamics, the method characterizes arbitrary microstructures and their spatial-temporal evolution with field variables, and is capable of simulating microstructures and their evolution under various realistic conditions.; However, the adoption of the phase field method in practical applications has been slow because the current phase field microstructure modeling is qualitative in nature. In this thesis, recent efforts in developing the phase field method for quantitative microstructure modeling are presented. This includes extension of the phase field method to situations where nucleation, growth and coarsening occur concurrently, incorporation of anisotropic elastic energy into the nucleation activation energy, and comparison of phase field kinetics for diffusion-controlled phase transformations with Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. The most recent extensions of the phase field method to modeling dislocation networks, dislocation core structures and partial dislocations, and dislocation interactions with gamma/gamma' microstructures in superalloys are also presented. The length scale limitations and practical approaches to increase simulation length scales for quantitative modeling are discussed for a quite general category of phase field applications.; These extensions enable various new understandings of microstructure. For example, coherent precipitates are found to behave similar to dislocations and grain boundaries, causing solute segregation, correlated nucleation and autocatalytic effect. The overall kinetics in diffusion-controlled precipitation agrees with the JMAK prediction only at early stages, and due to soft-impingement and the Gibbs-Thomson effect the later kinetics could deviate considerably. The new formulations of the crystalline energy and gradient energy in phase field model of dislocations allow to study complex dislocation structures, including networks and dissociated nodes, in a self-consistent way. The introduction of gamma-surfaces for constituent phases enables treating dislocation motion in multi-phase microstructure in one model. Finally, the discussion on the length scale clarifies the applicability of the conventional approaches for increasing simulation length scales, and their respective consequence to the quantitative results.