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A numerical code has been designed and implemented to find the stress at any material point in a holed wedge material due to any number of crystal or real screw dislocations in the wedge. The code implements the image dislocation method together with the collocation-point method to find stresses at any material point. We demonstrate that the combined analytical–numerical method (analytical with the image dislocations and numerical with the collocation-point method) is valid in that it produces stress fields giving rise to zero traction on free surfaces as well at an arbitrary number of collocation points on void surfaces. In addition, the method makes it possible to find the Peach–Koehler force (PKF) acting on a real screw dislocation at any point in the wedge, as well as to determine points of equilibrium, where the PKF is zero. Numerous and easy to interpret contour plots reveal the utility of this method which was carried out using the mathematical software MATLAB. [ABSTRACT FROM AUTHOR]

Standard text-book dislocation theory for the elastic fields of a dislocation is provided in an infinite medium. For problems involving free surfaces, or image stresses, the solution for such elastic fields is more complex. The current article extends the state of knowledge for problems with free surfaces to address the stress field of a screw dislocation in a plate (two planar free surfaces) containing a hole/void. Such surfaces interact and thus affect the stress field of a dislocation in deviation of the infinite medium solution. The numerical solutions provided herein, based on reflective image stresses and the collocation-point method, have been verified to the extent available and such solutions allow for further applied problems. One main finding of the paper is that the equilibrium location of a screw dislocation is always closer to the hole/void surface than the planar free surface. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]