Pile-up of dissociated dislocations and the strength-grain size relationship

Abstract

The equilibrium positions of all the partial dislocations in a pile-up of dissociated dislocations are calculated numerically. As expected, the equilibrium width of the stacking fault varies along the length of the pile-up-being smaller near the tip than farther away from the tip. However, the stress concentration at the tip is found independent of the stacking-fault energy and so is the Hall-Petch slope. The observed effect of stacking-fault energy on the Hall-Petch slope reported by Ku, McEvily, and Johnston is interpreted by suggesting that the pile-up model is only applicable in the range of low stacking-fault energy. In the range of high stacking-fault energy, a forest model of yielding seems more appropriate.