Pile-Up Based Hall-Petch Considerations at Ultra-Fine Grain Sizes

Abstract

AbstractThe dislocation pile-up explanation for the Hall-Petch (H-P) relation is re-examined for ultrafine grain sizes when only a few dislocations are involved in the pile-up, formed necessarily at applied stress levels near to the theoretical limit. Each dislocation added to the pile-up produces a step reduction in the H-P stress. Consequently, differences in dislocation configurations and types of pile-ups are easily recognized in the limit of small dislocation numbers. A significant reduction occurs in the H-P slope value (i.e., microstructural stress intensity) for the extreme case of only one dislocation loop being expanded against the grain boundary obstacle stress.