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

Dislocation Pile-Ups in the Presence of Stress Gradients. J.P.Hirth: Philosophical Magazine, 2006, 86[25-26], 3959-63