SUMMARY
The mechanical strengths of nano-scale individual crystal or nanopolycrystalline metals, and other dimensionally-related materials are increased by an order of magnitude or more as compared to those values measured at conventional crystal or polycrystal grain dimensions. An explanation for the result is attributed to the constraint provided at the surface of the crystals or, more importantly, at interfacial boundaries within or between crystals. The effect is most often described in terms either of two size dependencies: an inverse dependence on crystal size because of single dislocation behavior or, within a polycrystalline material, in terms of a reciprocal square root of grain size dependence, designated as a Hall-Petch relationship for the researchers first pointing to the effect for steel and who provided an enduring dislocation pile-up interpretation for the relationship. The current report provides an updated description of such strength properties for iron and steel materials, and describes applications of the relationship to a wider range of materials, including non-ferrous metals, nano-twinned, polyphase, and composite materials. At limiting small nm grain sizes, there is a generally minor strength reversal that is accompanied by an additional order-of-magnitude elevation of an increased strength dependence on deformation rate, thus giving an important emphasis to the strain rate sensitivity property of materials at nano-scale dimensions.