PARADISCYL:Cylinder-Surface cross slip

Surface cross slip

ill Ryu and Wei Cai

This tutorial describes how to implement cross slip mechanism from the cylinder surface. The theoretical background is published in Computing Image Stress in an Elastic Cylinder(Proceedings of the National Academy of Sciences, 105, 14304 (2008)http://micro.stanford.edu/~caiwei/papers/Weinberger08PNAS-bccpillar.pdf (PDF)])

How to select slip plane of the surface segments

To implement surface cross slip in cylinder code, we change the slip plane of the surface nodes with respect to the magnitude of the force on the surface nodes.To do that,dislocation character of the surface nodes should be screw-like.

If there is a screw dislocation in the BCC crystal in left figure, we can see that there are three possible slip planes(red, blue green planes in the figure). From the MD calculation, we knew the image stress generate the force to move dislocation in the direction along which the length of dislocation shortens.Therefore, image force points downward for the front node, while it points upward for the back node(Figure 1). However, P-K force points in same direction both front node and back node. Taking the summation of these forces into account, the slip plane is selected as the one

For simplicity, we In the first test case, image stress of a straight edge dislocation is considered, as shown in the Figure 1, where dislocation is offset($x0$) from the center of the cylinder. We have two cases of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x0} =0.5Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} and 0.9Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} .Here, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} is the radius of the cylinder.

(a)	(b)
Fig.1 (a) When the P-K force is dominant(blue plane is taken as a slip plane)(b) When the image force is dominant(green plane is taken as a slip plane) Since the image stress field of this configuration had been solved analytically[Eshelby, J.D., 1979],we compare the image force between the simulation result and analytic solution.The number of grids in circumferential direction is same as the one along the cylinder axis.To consider periodic images along the cylinder axis under PBC, analytical stress field of edge dislocation is implemented in the function of "AllSegmentStress_no_cell_test1".To use this function, modify makefile in ParaDiS/cylinder directory so that the following line is active. DEFS += -D_CYL_TEST1 Using Method I,the relative error in the image force is computed from the image stress calcualtion. Right plot clearly show exponential decay of the relative error with increasing number of grids. The convergence is slower when the location of the edge dislocation is close to the surface.