Effect of Recovery and Recrystallization on the Hall–Petch Relation Parameters in Submicrocrystalline Metals: II. Model for Calculating the Hall–Petch Relation Parameters

A model is developed to calculate the Hall–Petch relation parameters for the submicrocrystalline (SMC) metals fabricated by severe plastic deformation (SPD) methods. The model is based on the assumption that the flow stress in SMC metals includes both conventional contributions (caused by lattice dislocations, impurity atoms, etc.) and a contribution related to the long-range internal stress fields created by the SPD-induced defects distributed over grain boundaries. Equations are derived to calculate the Hall–Petch relation parameters as functions of the strain and the strain rate. The results calculated by the derived equations agree well with the experimental data. The low resistance of grain boundaries to the motion of grain boundaries in SMC materials (see part I of this work) is found to be related to a violation of the Hall–Petch relation in SMC metals.