A microscopic phase field (MPF) model is formulated to describe quantitatively the core structure and energy of dislocations using ab initio data as input. Based on phase-field microelasticity theory implemented in the slip plane using Green’s function to describe the long-range elastic interaction, the MPF is a three-dimensional generalization of the Peierls model. Using the same generalized stacking fault energy as input, the core structure and energy predicted for straight dislocations by the MPF model showed complete agreement with those predicted by the Peierls model. The ability of the MPF model in treating dislocations of arbitrary configurations is demonstrated by calculating the structure and energy of twist grain boundaries in Al and by studying dislocation-precipitate interactions in Ni-base superalloys. After discrete lattice sampling a la Nabarro, the grain boundary energy manifests Read-Shockley behavior for low-angle boundaries as well as deep cusps for high-angle special boundaries, indicating a “Peierls torque friction” effect for grain boundaries that has the same physical origin as the Peierls lattice friction for dislocation cores. With ab initio calculations of generalized stacking fault (GSF) energies as input, the MPF predicts automatically the formation of various faults in both the ordered ?’(L12) precipitate phase and the disordered ? (FCC) matrix phase and the dominant deformation modes under various microstructural and loading conditions.
Back to Workshop III: Mesoscale and Continuum Scale Modeling of Materials Defects