CONTINUUM ANALYSIS OF DISLOCATION PILE-UPS - INFLUENCE OF SOURCES

One explanation of the Hall-Fetch relationship is that dislocation pil e-ups serve to enhance the stress felt at grain boundaries. This dislo cation pile-up model results in a d(-1/2) dependence of the yield stre ngth, with d the grain size. In fact, this dependence is observed ofte n. However, the traditional pile-up picture neglects two important asp ects of pile-up formation: firstly the existence of a threshold stress for dislocation production, and secondly the necessity of a finite-si zed dislocation-fi-ee region in which a source may operate. In this pa per, both of these aspects are addressed within a continuum model of t he dislocation pile-ups. A closed-form expression is obtained for the dependence of yield stress on grain size and source characteristics. T he continuum model agrees closely with the corresponding discrete disl ocation model even when the pile-up contains as few as ten dislocation s.