On the origin of the Hall?Petch law: A 3D-dislocation dynamics simulation investigation

3D-DD simulations are performed with cubic grains ranging from 1 to 10 ?m to investigate the physical mechanisms at the origin of the Hall?Petch law. In particular, the long-range stress (back stress) induced by the density of polarized dislocations (GNDs) accumulated at GBs is quantified separately from the short-range stress associated with the forest dislocation (SSDs) density. We show that the back stress and the associated strain hardening is independent of grain size at low strain. Hence, the grain size effect reproduced by 3D-DD simulations is controlled by an increase of the CRSS when decreasing grain size. Such evolution of the CRSS amplitude is controlled by two competing strengthening mechanisms justify? ing the generic 1 / d dependent form of the Hall?Petch law observed in simulations and experiments. ? 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Automated summary

The study revealed that the back stress and associated strain hardening are independent of grain size at low strain, while the grain size effect is controlled by increasing the critical resolved shear stress (CRSS) when decreasing grain size. The evolution of the CRSS amplitude is controlled by two competing strengthening mechanisms, justifying the generic 1/d dependent form of the Hall-Petch law observed in simulations and experiments.