[SY-C8] Stress-Dependent Activation Parameters for Cross-Slip in FCC Metals
Cross-slip is a thermally activated process by which screw dislocations can change their glide plane. Quantifying the activation parameters for cross-slip in a general stress field is imperative to model cross-slip in dislocation-based simulations. In most discrete dislocation dynamics (DDD) simulations, only the contribution of the resolved shear stress is considered. Recently, the contributions of Escaig stresses on the primary and cross-slip planes were accounted for. In this work, we propose a model for cross-slip of screw dislocations in Face-Centered Cubic (FCC) metals by employing the line-tension model to calculate the free-energy barrier under a general stress field.
When only Escaig stresses are applied, we show that cross-slip is favorable only when Escaig stress in the primary plane is larger than in the cross-slip plane. The free-energy barrier decreases nonlinearly with Escaig stresses, whereas it decreases stronger with Eacsig stress in the primary plane. Using our model, we show that there is typical length for cross-slip, which is a means to quantify the region that bows-in towards constriction. The typical length scale varies when applying different Escaig stresses on both the primary and the cross-slip planes.
Schmid stresses in the cross-slip plane break the symmetry of the solution, and the partial dislocations bow-out in the cross-slip plane after constricting. The application of Schmid stresses is shown to remove the divergence in the free-energy barrier and cross-slip is possible for all combination of Escaig stress. We propose an Escaig and Schmid stress-dependent closed-form expression for the free-energy barrier for a cross slip in a large range of stresses without any fitting parameters. The proposed expression captures qualitatively the essentials found in atomistic simulations and is in good agreement with previous models. This closed-form activation energy function can be easily implemented in DDD simulations, owing to its simplicity and universality.
Malka-Markovitz A. and Mordehai D., Philos. Mag. 98 (2018) 347-370.
When only Escaig stresses are applied, we show that cross-slip is favorable only when Escaig stress in the primary plane is larger than in the cross-slip plane. The free-energy barrier decreases nonlinearly with Escaig stresses, whereas it decreases stronger with Eacsig stress in the primary plane. Using our model, we show that there is typical length for cross-slip, which is a means to quantify the region that bows-in towards constriction. The typical length scale varies when applying different Escaig stresses on both the primary and the cross-slip planes.
Schmid stresses in the cross-slip plane break the symmetry of the solution, and the partial dislocations bow-out in the cross-slip plane after constricting. The application of Schmid stresses is shown to remove the divergence in the free-energy barrier and cross-slip is possible for all combination of Escaig stress. We propose an Escaig and Schmid stress-dependent closed-form expression for the free-energy barrier for a cross slip in a large range of stresses without any fitting parameters. The proposed expression captures qualitatively the essentials found in atomistic simulations and is in good agreement with previous models. This closed-form activation energy function can be easily implemented in DDD simulations, owing to its simplicity and universality.
Malka-Markovitz A. and Mordehai D., Philos. Mag. 98 (2018) 347-370.