Dislocation Pile-up in Two-Phase Materials

Based on the theory of continuously distributed dislocations, the equilibrium equations for both edge-and screw-dislocation pile-ups in materials composed of soft and hard phases are formulated in terms of a singular integral equation. The integral equation is solved exactly by using the Wiener-Hopf technique with Mellin transforms. The dislocation distribution function is found in explicit form. It is shown that the number of dislocations in the piled-up array can be determined directly from the Mellin transform of the distribution function without its inverse transform.