Aspects on numerical integration of dislocation surface traction fields for discrete dislocation dynamics FEM coupling: the case of emerging dislocations

Abstract

In discrete dislocation dynamics frameworks for finite samples, the evaluation of surface tractions caused by dislocations requires special attention to capture the contributions of dislocations piercing through the surface. Here we focus on this aspect only, and the convergence of an empirically improved Gauss integration and the Duffy and Duffy distance integration schemes commonly used for 1/r singularities, is investigated for a finite element surface area. It is found, that traction from a dislocation, using singular segment stress fields, can be integrated with an error smaller than 1% with the distance Duffy integration using a total of 48 integration points only. This scheme was tested for a wide range of dislocation Burgers vectors and glide plane orientations with respect to the surface. Furthermore the FEM nodal forces behave smoothly during the motion of exit point of the dislocation (the singular point) to a neighbouring surface element in the mesh.