A distributed-dislocation method for treating free-surface image stresses in three-dimensional dislocation dynamics simulations

Abstract

This work reports on a recent advancement in three-dimensional dislocation dynamics modelling. A method is presented for the treatment of dislocation image stresses resulting from the presence of nearby traction-free surfaces. The image stress-field of a dislocation segment below a finite-sized free surface is obtained by the distribution of N generally prismatic rectangular or square dislocation loops padding the area (the external bounding surfaces of the simulation box). The unphysical tractions created at surface collocation points by sub-surface crystal dislocations are annulled by proper determination of the loops' Burgers vectors. The image stresses on a dislocation segment are simply those stresses resulting from the surface loops. The accuracy can be improved by increasing the number of collocation points (i.e. surface loop density).

Overview of Enhanced Continuum Theories for Thermal and Mechanical Responses of the Microsystems in the Fast-Transient Process

“…An alternative technique to address the mechanisms responsible for size and boundary effects in microstructures is the discrete dislocation method [16,35,[273][274][275][276][277][278][279][280]. An alternative technique to address the mechanisms responsible for size and boundary effects in microstructures is the discrete dislocation method [16,35,[273][274][275][276][277][278][279][280].…”

Numerical methodology for treating static and dynamic dislocation problems near a free surface

“…In a single crystal, El-Azab et al [16,17] formulated traction and dislocation flux boundary conditions. Khraishi et al developed several methods for the treatment of traction-free boundary conditions in 3D dislocation dynamics [18][19][20]. In these referenced works, the dislocation field stress formulation developed in an infinite medium was augmented by image stress and surface correction terms, i.e.…”

“…In the works mentioned earlier [18][19][20], correction terms to mitigate the surface traction was developed locally and then transformed into a global coordinate system to compute the stress field due to the presence of a dislocation segment. Moreover, for each dislocation segment, the works just-mentioned required the placing of image dislocations in all six directions (across six free surfaces), see figure 1.…”

A crystal plasticity analysis of length-scale dependent internal stresses with image effects

“…Of particular interest are the long-range GND-GND and GND-free surface interactions. While molecular dynamics (MD) and discrete dislocation dynamics (DDD) account for these internal stresses as a length-scale dependent entity (e.g., Fivel et al, 1996;Yan et al, 2004), coarser realizations based on continuum approaches, e.g., crystal plasticity, rely on augmenting the traditional kinematics and kinetics with additional lengthscale dependent features. A continuum crystal plasticity description of the internal stress due to long-range GND-GND curvature in the case of pure bending results in r g also being constant (Han et al, 2005).…”

“…Similar to the DD approaches (Lubarda et al, 1993;Van der Giessen and Needleman, 1995;Fivel et al, 1996;Yan et al, 2004), superposition of image stress fields due to dislocation ensembles described by a continuum density measure would be a natural way to satisfy the b.c. 's at free surfaces.…”