Abstract:
Conventionally, the use of continuous distributions of dislocations to model plasticity has been confined to the analysis of crack tip plasticity using linear arrays of dislocations, within the framework of plane analysis. By expanding this technique into a distribution of dislocation over an area, a method is developed to model the plasticity at stress raising features such as notches or holes under plane strain conditions. The method explicitly takes account of the boundary conditions by using a dislocation solution which accounts for the presence of the stress-raise itself. Other free boundaries may be modelled more approximately using boundary elements which also correctly include the presence of the stress raiser. The dislocations are distributed over finite sized cells, and the solutions found for the strain fields compare favourably with both finite element and bounding Neuber and Glinka results.
