Dislocation pileups in the presence of stress gradients

Abstract

A solution is obtained for the field of a dislocation pileup in the presence of a linear stress gradient by means of Hilbert transforms. The method can be extended to stress contours that are general power laws as a function of position. The forces on the pileup tip are somewhat weaker than those for the constant stress case for pileups of the same width and with the same maximum stress.

Acknowledgment

Contributions from J. Lothe, G. Saada, H. M. Zbib and F. Akasheh are gratefully acknowledged.