This article reports on a study of the microstructure and mechanical response of copper polycrystals with grain sizes in the micrometer range. Three-dimensional dislocation dynamics simulations are used for the first time to investigate grain boundary strengthening and the Hall-Petch law. The methodology, which involves constructing a microcrystalline representative volume element with periodic boundary conditions, is briefly presented. Simulation results show that the initial density of dislocation sources and the cross-slip mechanism are two key factors controlling the heterogeneity of plastic deformation within the grains. At yield, the smaller the grains size, the more plastic deformation is heterogeneously distributed between grains and homogeneously distributed inside the grains. A size effect is reproduced and it is shown that the Hall-Petch exponent decreases from the very beginning of plastic flow and may reach a stable value at strains larger than the conventional proof stress.