The mechanism of the anomalous behavior of the Hall-Petch relationship in micro- and nano-crystalline materials was considered. The theoretical analysis was based upon the dislocation-kinetic model; according to which this relationship arose because of the effect of grain boundaries upon the strain-hardening of polycrystalline material. In the case of ultra-fine granular aggregates, the grain boundaries not only acted as barriers which limited the mean free path of dislocations, but also acted as barriers and locations where dislocations were annihilated.

Breakdown of the Hall-Petch Law in Micro- and Nanocrystalline Materials. G.A.Malygin: Fizika Tverdogo Tela, 1995, 37[8], 2281-92 (Physics of the Solid State, 1995, 37[8], 1248-53)