An analysis of equilibrium dislocation distributions

Equilibrium distributions of collections of discrete dislocations are analyzed, with the dislocations modelled as line defects in a linear elastic medium. The dislocated equilibrium configuration is determined by finding a minimum potential energy configuration, with respect to variations in the dislocation positions, for a fixed number and type of dislocations. Numerical results are presented for finite and infinite bodies with distributions of edge dislocations under plane strain conditions. Calculations involving doubly periodic arrays of cells, within which there is a single set of parallel slip planes, show a strong tendency for sharp dislocation walls to form. Perturbations of the wall structure due to the presence of pinned dislocations, vacant slip planes and free surfaces are illustrated. The stress fields due to the dislocation walls are calculated and large shear stress values are found away from any dislocation core. Pileups involving dislocations on two sets of intersecting slip planes are found to give rise to equilibrium configurations involving dislocation free regions. The response of dislocation patterns in an infinite medium to an imposed shear stress is also analyzed.