DISLOCATION MULTIPLICATION AND TRANSMISSION IN A BICRYSTAL
Random sources are introduced in a closed grain (lower dodecahedron). A tensile applied stress is applied along the vertical axis. Sources are then activated and a pile up is observed on the grain boundary. When the stress at the head dislocation in the pile up is high enough, a dislocation crosses the grain boundary and enters the upper grain.
Such a situation naturally leads to the Hall-Petch relationship between the grain size and the yield stress.