Effect of the structural factor on the inverse Hall-Petch dependence in nanocrystals

Abstract

A gradated dislocation-disclination model of plastic shear in nanocrystals is generalized allowing for the structural factor (the distribution of the grain size in a polycrystalline ensemble) in the context of the three-dimensional problem when describing the mechanical behavior of nanocrystals in the region of the effect of the inverse Hall-Petch relation. The critical size of the crystal that corresponds to the change of the deformation mode, and the value of which for pure copper nanocrystals agrees with the experimental data without allowing for the structural factor is found using an analytical function calculated with the Mathematica 5.2 computer system. It is shown that the critical grain size increases rather than decreases as the standard deviation grows. The requirements for the form of the function describing the inverse Hall-Petch dependence are formulated.