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

Abstract

A theoretical model is developed to describe the influence of recovery and recrystallization on the macroelastic limit, the yield strength, and the grain-boundary hardening coefficient of the submicrocrystalline (SMC) metals fabricated by severe plastic deformation. The anomalous hardening and the increase in the grain-boundary hardening coefficient upon annealing of the SMC metals are shown to be related to defect accumulation in migrating grain boundaries in them. Equations are derived to relate the Hall–Petch relation parameters to the grain-boundary migration velocity, the nonequilibrium state of grain boundaries, the lattice dislocation density, and the annealing temperature and time. The results of the numerical calculations performed using the developed model are compared with the experimental results obtained in part I of this work.