Modelling Discrete Dislocation Dynamics with Discontinuity-Enriched Finite Element Analysis

Abstract

Discrete Dislocation Dynamics concerns the analysis of microplasticity in which the dislocations, a line defect in the crystallographic periodicity, are treated as separate moving entities inside an elastic continuum. This analysis at the mesoscale can give valuable insights in the nature of dislocations and the behaviour of macroscopic plasticity. Although an analytical solution for dislocations exist, special measures are to be taken for the solution of boundary value problems. In this thesis a Discrete Dislocation Dynamic model in a two-dimensional plane-strain formulation for edge dislocations is proposed using DE-FEM, a finite element formulation enriched with discontinuities to model dislocations independent of the mesh. Although the modelling of a stationary field with dislocations is straightforward, the dynamic solution becomes much more complicated. It requires the accurate stress retrieval of the numerical stresses close to an artificial singularity and various attempts, such as eliminating the singularity by subtracting the analytical solution or incorporating a singular core enrichment, were proven to be ineffective. Recommendations are given for future attempts, but also an alternative numerical superposition approach is explained. Its results are comparable to existing methods in terms of accuracy, but the computation time is not optimal for the current implementation.