Screw dislocation pile-ups in two phase materials of finite rigidity

The arrangement of discrete screw dislocations piled-up under the action of a uniform applied stress against the welded interface between different elastically isotropic half-spaces has been determined by representing the pile-up as a continuous distribution of infinitesimal dislocations. The dislocation slip plane is inclined at an arbitrary angle $\text{1}\text{2}\text{aπ}$ to the normal to the interface, assuming a to be a rational number. The singular integral equation expressing the condition for static equilibrium of the dislocations under a constant applied stress is solved by a method based on the Wiener-Hoph technique with the Mellin transform, and from this solution the mean density of dislocations and the stress field of the pile-up are determined.