Ab initio continuum model for the influence of local stress on cross-slip of screw dislocations in fcc metals

We develop a model of cross-slip in face-centered cubic (fcc) metals based on an extension of the Peierls-Nabarro representation of the dislocation core. The dissociated core is described by a group of parametric fractional Volterra dislocations, subject to their mutual elastic interaction and a lattice-restoring force. The elastic interaction between them is computed from a nonsingular expression, while the lattice force is derived from the gamma surface obtained directly from ab initio calculations. Using a network-based formulation of dislocation dynamics, the dislocation core structure is not restricted to be planar, and the activation energy is determined for a path where the core has three-dimensional equilibrium configurations. We show that the activation energy for cross-slip in Cu is 1.9 eV when the core is represented by only two Shockley partials, while this value converges to 1.43 eV when the core is distributed over a bundle of 20 Volterra partial fractional dislocations. The results of the model compare favorably with the experimental value of 1.15 +/- 0.37 eV [J. Bonneville and B. Escaig, Acta Metall. 27, 1477 (1979)]. We also show that the cross-slip activation energy decreases significantly when the core is in a particular local stress field. Results are given for a representative uniform Escaig stress and for the nonuniform stress field at the head of a dislocation pileup. A local homogeneous stress field is found to result in a significant reduction of the cross-slip energy. Additionally, for a nonhomogeneous stress field at the head of a five-dislocation pileup compressed against a Lomer-Cottrell junction, the cross-slip energy is found to decrease to 0.62 eV. The relatively low values of the activation energy in local stress fields predicted by the proposed model suggest that cross-slip events are energetically more favorable in strained fcc crystals.