[SY-C12] Comparison of two methods to cross-slip modeling by means of mathematical theory of moving curves
The contribution focuses on the comparison of two different methods of dislocation cross-slip modeling, both based on the theory of evolving curves. The cross-slip is understood as deterministic, stress-driven dislocation process. In certain geometrical configuration, the criterion based on evaluation of driving stresses in the primary plane and in the cross-slip plane is employed. As an illustrative example, we consider a scenario where the cross-slip is forced by the repulsive stress exerted by a spherical obstacle with realistic repulsive stress. The result of this scenario is the double cross-slip.
The employed model for the dislocation motion can be schematically written as the curvature driven flow in the form
normal velocity = curvature + force.
In the first method, the dislocation motion law is based on the isometric projection. The cross-slip plane is tilted to the primary plane so that dislocation motion remains planar. When the dislocation enters the cross-slip plane, the appropriate physical quantities are recalculated accordingly.
The second method is based on the exploitation of the model of curves evolving on smooth surfaces and driven by the geodesic curvature. The smoothness of the the glide surface is ensured by regularizing the sharp interfaces between the primary plane and the cross-slip plane.
For both methods, the dislocations are described as parametrized curves. In numerical simulations, the flowing finite volume method is used. The results of the numerical simulations for both methods are compared to demonstrate their agreement.
The employed model for the dislocation motion can be schematically written as the curvature driven flow in the form
normal velocity = curvature + force.
In the first method, the dislocation motion law is based on the isometric projection. The cross-slip plane is tilted to the primary plane so that dislocation motion remains planar. When the dislocation enters the cross-slip plane, the appropriate physical quantities are recalculated accordingly.
The second method is based on the exploitation of the model of curves evolving on smooth surfaces and driven by the geodesic curvature. The smoothness of the the glide surface is ensured by regularizing the sharp interfaces between the primary plane and the cross-slip plane.
For both methods, the dislocations are described as parametrized curves. In numerical simulations, the flowing finite volume method is used. The results of the numerical simulations for both methods are compared to demonstrate their agreement.