Abstract
3D -DD simulations are performed with cubic grains ranging from 1 to 10 μm 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 justifying the generic 1/√d dependent form of the Hall- Petch law observed in simulations and experiments.
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