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New Concepts of a Modified Hall - Petch Type Relationship
Abstract
A modified form of the Hall - Petch equation, where the average grain diameter is replaced by the surface to volume ratio of internal boundaries (Sv), is considered. Working with this model, a flow stress – Sv relationship dominated by geometrically necessary dislocations (GNDs) is derived for the low strain region.
At higher strains, a more complicated relationship between the flow stress and Sv is anticipated. The role of statically stored dislocations (SSDs) in the high strain region is emphasized. The Stacking fault energy (SFE), through the density of the SSDs may coetrol the character of the Hall - Petch slope Ky with increasing strain.
