Hall–Petch behaviour induced by plastic strain gradients

A very simple one-dimensional cellular automaton numerical model of plastic deformation that takes into account the local heterogeneity of strains, stresses and dislocation density predicts a realistic polycrystalline work hardening behaviour as well as a convincing Hall–Petch effect for the flow stress versus grain size relationship. In the model, the plastic strain gradients are resolved through the storage of geometrically necessary dislocations (GND). The results presented in the paper correspond to low-temperature deformation (no long-range diffusion, no account for the influence of spatial strain rate fluctuations) of materials not suffering from dislocation locking from solute atoms. The predicted Hall–Petch constants and their plastic strain dependence agree well with values of FCC metals or interstitial-free low-carbon steels at low temperatures and for small plastic strains.