The length of a pile-up containing a given number of dissociated dislocations

Abstract

A recent paper has described a numerical determination of the length of a pile-up containing a given number of dissociated edge dislocations subject to a uniform applied shear stress, the leading pertial of the first complete dislocation being fixed. The results for small numbers of dislocations were extrapolated to very large numbers, and it was concluded that the pile-up length was then independent of both the stacking-fault energy and the existence of the screw components. A very simple approach is developed here, the same result being deduced by employing upper and lower bound procedures, without resort to computational techniques. It is also readily shown that, even for smell numbers of dislocations, the pile-up length is relatively independent of the stacking-fault energy of the material. The general nature of the approach is emphasized.