Dislocation pileups in small grains

While the grain size effect (GSE) is universally observed in polycrystalline metals and alloys, extended dislocation pileups (DPUs) at grain boundaries (GBs) are rarely observed. Although this discrepancy was noticed over 50 years ago, DPUs are still widely accepted as the explanation for the GSE, often expressed as the Hall-Petch (HP) relationship. To provide a quantitative assessment of the pileup hypothesis, four classical pileup models were compared to three sets of numerical calculations, spanning a grain size range from 25 nm to 25mm. To do so, the stress field and Peach-Köhler force for short dislocation segments and circular dislocation loops were calculated as closed-form expressions and simplified to the case of pileups. Published values for the Hall-Petch constant provide the reference for estimating the critical tip stress for transmission of plastic strain from one grain to its neighbour. The results are compared in terms of consistency between models and between models and experiments. Different assumptions on the pileup geometry induce important variations in the results. Tendencies found in the numerical models resemble the trends marked in compilations of experimental results; predicted values for dislocation density and plastic shear upon yielding disagree with commonly accepted values. Added to the scarceness of experimental observation, the analysis indicates that DPUs play a role in polycrystal plasticity but do not consistently explain the GSE.