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

Abstract

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 $\ensuremath{\gamma}$ 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 $1.9\phantom{\rule{4pt}{0ex}}\text{eV}$ when the core is represented by only two Shockley partials, while this value converges to $1.43\phantom{\rule{4pt}{0ex}}\text{eV}$ 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 $1.15\ifmmode\pm\else\textpm\fi{}0.37\phantom{\rule{4pt}{0ex}}\text{eV}$ [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 $0.62\phantom{\rule{4pt}{0ex}}\text{eV}$. 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.