Strengthening mechanism in micro-polycrystals with penetrable grain boundaries by discrete dislocation dynamics simulation and Hall–Petch effect

The grain-size effect on the yield stress and the flow strength in micro-polycrystals relates closely to the penetrability of grain boundary (GB) to dislocations. To simulate the dislocation transmission across grain boundary, a dislocation–grain boundary penetration model is proposed and then integrated into the two-dimensional discrete dislocation dynamics (DDD) framework by Giessen and Needleman (1995). By this extended DDD technology, the Hall–Petch effect in micro-polycrystals and the strengthening mechanism are computationally studied, with the main focus on the significant influence of the dislocation transmission across grain boundary that is not fully considered formerly. Results indicate that the Hall–Petch type relation is still applicable, but depends strongly on the GB-penetrability to dislocations, especially for the flow strength at large offset strains. The fitting values of Hall–Petch grain-size sensitive exponents n for initial yield stress and flow stress basically agree with experimentally measured data in published literatures.