Dislocation propagation in and work hardening of γ channels and directional coarsening (rafting) of γ' precipitates are the major microscopic processes taking place during high temperature deformation of single crystal Ni-base superalloys. Understanding of those processes is crucial for developing improved models of creep and fatigue of turbine blades in aircraft engines. Recent investigations of rafting in superalloys demonstrate clearly the importance of elastic modulus difference between the γ and γ' phases and dislocation-level activities in the γ-channels in determining the kinetic pathway of the processes. The elastic modulus difference can lead to the non-uniform distribution of stresses through the interaction with the lattice misfit and external load. While work hardening in the γ channels has a direct effect on differentiation of the stress state in the vertical and horizontal channels and on γ/γ' interface coherency and energy, and hence influences the diffusive flow and morphological changes of the γ/γ' microstructure. In turn, changes in particle shape and coherency of the interface alter the local stress state and thereby the Peach-Koehler force on dislocations. Although existing models treating these processes separately can offer a qualitative explanation about the direction of rafting for typical superalloys, a complete quantitative understanding of rafting phenomena requires these processes to be treated simultaneously in a common framework because of their intimate coupling.
The objective of this thesis is to develop an integrated computational approach in simulating simultaneous evolution of both γ/γ' microstructure and dislocations in an elastically anisotropic and inhomogeneous system by using a single, consistent phase field methodology. In particular, the phase field dislocation model is used to simulate the initial dislocation γ channel filling process and calculate stress distribution associated with complex three-dimensional (3D) dislocation configurations in the γ-channels. The relative contributions from elastic modulus inhomogeneity and γ-channel plasticity are quantified by the dislocation-level simulations through the analysis of the spatial variation of solute atoms' chemical potential, which show that γ-channel plasticity plays the dominant role in controlling the rafting process (rafting type and kinetics). Micrometer-scale simulations are carried out that takes into account plastic deformation in γ-channels described by local channel dislocation densities from individual active slip systems. The rafting kinetics and the corresponding creep deformation are characterized at different values of applied stress, lattice misfit and precipitate volume fraction. The simulation predictions agree well with experimental observations and the models developed can be utilized in design of new superalloys and optimization of existing ones.