Modeling of Double Cross-Slip by Means of Geodesic Curvature Driven Flow

Abstract

In this paper we develop a model for double cross-slip in fcc crystals. The double cross-slip mechanism is demonstrated by a simulation of an overcoming of a particle exerting spherically symmetric repulsive stress field. The cross-slip is treated as a deterministic, stress-controlled process. For the identification of the cross-slip, we use a criterion based on evaluation of stresses exerted on a tip of a screw part of a dislocation resolved in the primary plane and in the cross-slip plane. The motion of a dislocation is described by the geodesic curvature driven flow on surfaces, and treated by means of the parametric approach. The results of numerical simulations are validated by analytical calculations.

Expansions for the linear-elastic contribution to the self-interaction force of dislocation curves

“…In fact, our approach below reveals that an approximation by straight lines may cause a large error if not dealt with carefully. Another set of examples are the schemes used in [GTS00] and in the paper series by Beneš, Kratochvíl, Pauš et al (see [KBKP18] and references therein), which are based on the expansion in (7), but neglect the nonlocal contribution Ψ(x). This creates a relative discretization error of size O(1/| log ε|).…”