Hall–Petch relation and boundary strengthening

The Hall–Petch relation is discussed separately for the yield stress of undeformed polycrystalline metals and for the flow stress of deformed metals. Key structural parameters are the boundary spacing, between grain boundaries in the former case and between dislocation boundaries and high angle boundaries in the latter. An analysis of experimental data supports the Hall–Petch relation for undeformed metals over a grain size range from about 20 nm to hundreds of micrometers. For deformed metals, boundary strengthening is not a constant and the Hall–Petch relation must be modified.