The effect of non-uniform stress distributions upon the concentrated stress by piled-up dislocations

The effect of non-uniformly applied stress distribution upon the stress concentration of piled-up dislocations was studied⁽¹⁾ in the case of linear or straight stress gradient. The result shows that the concentrated stress is determined by the averaged stress over the slip plane, independent of the maximum stress value of the applied stress distribution. In this note, we now consider a more general type of non-uniformly applied stress field.