Nanomechanics of Hall-Petch relationship in nanocrystalline materials

Classical Hall–Petch relation for large grained polycrystals isusually derived using the model of dislocation pile-up first investi-gated mathematically by Nabarro and coworkers. In this paper themechanical properties of nanocrystalline materials are reviewed,with emphasis on the fundamental physical mechanisms involvedin determining yield stress. Special attention is paid to the abnor-mal or ‘inverse’ Hall–Petch relationship, which manifests itself asthe softening of nanocrystalline materials of very small (less than12 nm) mean grain sizes. It is emphasized that modeling thestrength of nanocrystalline materials needs consideration of bothdislocation interactions and grain-boundary sliding (presumablydue to Coble creep) acting simultaneously. Such a model appearsto be successful in explaining experimental results provided a real-istic grain size distribution is incorporated into the analysis.Masumura et al. [Masumura RA, Hazzledine PM, Pande CS. ActaMater 1998;46:4527] were the first to show that the Hall–Petchplot for a wide range of materials and mean grain sizes could bedivided into three distinct regimes and also the first to provide adetailed mathematical model of Hall–Petch relation of plasticdeformation processes for any material including fine-grainednanocrystalline materials. Later developments of this and relatedmodels are briefly reviewed.Prof. Frank Nabarro was a physicist by training, a metallurgist byprofession and a genius by nature, blessed with a unique ability totreat everyone as his equal. During his later years he was verymuch interested in the mechanical properties of nanocrystallinematerials. This review on that topic is our contribution to the spe-cial issue of Progress in Materials Science honoring him.Published by Elsevier Ltd.