An analysis of the pile-up of infinite periodic walls of edge dislocations

• Numerical simulations of pile-up of discrete dislocation walls show two regimes.
• Near the obstacle, the classical single glide plane solution holds.
• Transition to linear density profile at larger distance.
• Both parts can be predicted quantitatively.
• They are characterised by different length scales.

We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two distinct regions, for each of which we provide an interpretation and an analytical prediction. Near the obstacle, the influence of neighbouring slip planes may be neglected and the classical solution for a single slip plane applies. At a larger distance a linear decay is obtained. The characteristic length scales of the two parts of the pile-up are shown to depend differently on the parameters of the problem.