Abstract
The traditional description of elastic field and energies of dislocations is based on continuum theory of linear elasticity that suffers from the long-standing problem of singularities at the dislocation core. Singular solutions are often circumvented by introducing an artificial core-cutoff radius. This limits the applicability of the theory to describe situations where it is important to know the strained state and nanoscopic details within a few atomic spacings surrounding the dislocation center, known as the dislocation core. In this paper, a computationally tractable multiscale approach is developed to calculate the nonsingular elastic fields of dislocations in both bulk and nano-layered materials. The approach is an extension of Peierls-Nabarro (PN) model, with the following features: (1) all three components of the displacement vector for atoms within the dislocation core are included; (2) the entire generalized stacking fault energy (GSFE or gamma-gamma) surface obtained from ab initio calculations is utilized; and (3) the method can be generalized to treat curved dislocations. We combine the parametric dislocation dynamics (DD) approach for the interaction and motion of dislocations with the ab initio calculations of the lattice restoring forces, which are extracted from the gamma surface. The method is used to study two important problems: (a) dislocation dissociation in bulk crystals (b) dislocation transmission across interfaces in elastic bi-materials. Dislocation core structures in bulk aluminum and silver are determined. The results from the model are shown to be in excellent agreement with experiments for both Al and Ag. For bi-materials system, the effects of the mismatch in the elastic properties, gamma surface and lattice parameters on the spreading of the dislocation onto the interface(s) and the transmission across the interface(s) are studied in detail.