Abstract: The peculiarities of stress and deformation behavior of polycrystalline materials and unambiguous influence of a grain size on their strength are determined by a dual role of grain boundaries. On one part, they are sources and barriers for moving dislocations, on the other part, under certain conditions they may serve sinks of infinite capacity for them. As strong barriers grain boundaries limit the dislocations free path and thereby promote the process of more intensive accumulation of dislocations in grains and additional strain- hardening of a polycrystalline aggregate compared with a monocrystalline solid. As sinks and the places where dislocations annihilate they, opposite, favor decreasing the dislocation density in grains and promote thereby the process of strain-softening and falling deformation stresses. With the first role of grain boundaries are linked such characteristic features of the strength of poly-crystalline materials as the dependence of their yield stress $sigma$-0.2$/ and microhardness H on a grain size d (the Hall-Petch law, $sigma$-0.2$/, H approximately d$+$MIN$HLF$/) and the grain size dependence of a dimension of cells $Lambda in cell dislocation structure, $Lambda approximately d$+$HLF$/. !10
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