Open Access

ARTICLE

The Influence of Crystal Surfaces on Dislocation Interactions in Mesoscopic Plasticity: A Combined Dislocation Dynamics- Finite Element Approach

R. Martinez¹, N. M. Ghoniem²

1 TRW Space and Electronics, Defense Systems Division, Redondo Beach, CA
2 Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA 90095-1597

Computer Modeling in Engineering & Sciences 2002, 3(2), 229-244. https://doi.org/10.3970/cmes.2002.003.229

Abstract

We focus here on the direct coupling of Dislocation Dynamics (DD) computer simulations with the Finite Element Method (FEM) to simulate plastic deformation of micro-scale structures, and investigate the influence of crystal surfaces on dislocation motion. A series of three-dimensional (3-d) DD simulations of BCC single crystals with a single shear loop in the (101)-[111] slip system are first presented. The purpose of these simulations is to explore the relationship between loop force distributions and the proximity of the loop to the crystal boundary. Traction boundary conditions on a single crystal model are satisfied through the superposition of the "image'' stress field computed by FEM, and the elastic stress field of dislocations computed by DD. The force distribution on a prototypical shear loop is shown to consist of the superposition of Peierls, image, applied, and self forces. Force distributions are explored as a function of loop proximity to the boundary of the single crystal model. The deformation of the loop under the influence of these force distributions is computed using a Galerkin variational energy method, and the equilibrium geometry is determined. Additionally, the deformation of a Frank-Reed (FR) source in a single crystal model under the influence of image forces, applied stress, and Peierls forces with varying screw/edge mobility ratios is determined. The results indicate that image forces play a significant role in dislocation force distributions and deformation to a depth from the surface, which is proportional to the loop radius. Large out-of-plane image force distributions on closed loops in ``oblique'' slip plane/free surface orientations are verified. These forces act in such a way as to repel loop motion from the intersection of the slip plane with the free surface, while causing deformation through the mechanism of cross-slip. Expansion or contraction of shear loops is found to be dependent on the critical applied stress, the radius of curvature, and the proximity/orientation of the loop with respect to the boundary.

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