The piling-up of screw dislocations against a rigid inclusion

This paper determines the stress and displacement distributions near the tip of an array of continuously distributed screw dislocations piled-up against a rigid cylindrical inclusion; the inclusion-matrix interface near the pile-up tip is inclined at an angle β(≠ $\text{1}\text{2}$π) to the slip plane and the solid deforms in an anti-plane strain mode. The local stresses are a power function of the distance r from the pile-up tip, and both the radial and angular dependencies of the stresses are the same irrespective of whether or not there exists a shear stress σ within the interval containing the dislocations. This state of affairs contrasts markedly with that for the special case β = $\text{1}\text{2}$π discussed by E. Smith (1972), when the local stresses are independent of r if σ = 0 and have a logarithmic form when σ ≠ 0. The similarity of the model with that of two intersecting screw dislocation pile-ups in a homogeneous solid is also demonstrated.