Dislocation pile-ups in stress gradients revisited

The complete fields for a double-ended dislocation pile-up, or equivalently a crack, are derived for the situation where there is a gradient in applied stress. The dislocation content is smeared into a continuous, infinitesimal distribution. The effect of the gradient is to intensify the dislocation content near the pile-up tip and weaken it (or reverse it) near the center of the pile-up. For the same tip stress the thermodynamic force to propagate the pile-up/crack is less in the gradient cases. The results can be qualitatively understood in terms of superdislocation poles.