Improving method for deterministic treatment of double cross-slip in FCC metals under low homologous temperatures

Abstract

Despite its importance in crystal plasticity, cross-slip has not yet been completely understood. The widely accepted approach understands cross-slip as a thermally-activated stochastic process, especially at higher homologous temperatures. An alternative approach is based on an experimentally supported observation that, especially at lower homologous temperatures, cross-slip becomes a deterministic stress-driven process governed by the line tension, by the applied stress, and by the short-range interactions among dislocations. The current challenge remains in understanding how the tip of the screw dislocation segment of changes the primary slip plane for the secondary slip plane. We suggest an explanation of this problem available by the mathematical theory of moving parametrized curves. For the dynamical change between the primary plane and the cross-slip plane, two methods are introduced and compared. They are referred to as the tilting projection method (denoted as TPM) and the vertical projection method (denoted as VPM). Main difference between them is how they regularize the motion of the dislocation across the edge between the primary and the cross-slip plane. After the motion strategy is set, this article explains that dislocation motion laws can be treated numerically by means of the flowing finite-volume method, including the redistribution of the discretization points ensuring a long-term stability of the algorithm. Particular computational results of cross-slip obtained by both approaches are mutually compared and evaluated. For the considered material setup of the FCC copper and nickel crystals, good agreement has been observed.