Nanomechanics of Hall–Petch relationship in nanocrystalline materials

Classical Hall–Petch relation for large grained polycrystals is usually derived using the model of dislocation pile-up first investigated mathematically by Nabarro and coworkers. In this paper the mechanical properties of nanocrystalline materials are reviewed, with emphasis on the fundamental physical mechanisms involved in determining yield stress. Special attention is paid to the abnormal or ‘inverse’ Hall–Petch relationship, which manifests itself as the softening of nanocrystalline materials of very small (less than 12 nm) mean grain sizes. It is emphasized that modeling the strength of nanocrystalline materials needs consideration of both dislocation interactions and grain-boundary sliding (presumably due to Coble creep) acting simultaneously. Such a model appears to be successful in explaining experimental results provided a realistic grain size distribution is incorporated into the analysis. Masumura et al. [Masumura RA, Hazzledine PM, Pande CS. Acta Mater 1998;46:4527] were the first to show that the Hall–Petch plot for a wide range of materials and mean grain sizes could be divided into three distinct regimes and also the first to provide a detailed mathematical model of Hall–Petch relation of plastic deformation processes for any material including fine-grained nanocrystalline materials. Later developments of this and related models are briefly reviewed.Prof. Frank Nabarro was a physicist by training, a metallurgist by profession and a genius by nature, blessed with a unique ability to treat everyone as his equal. During his later years he was very much interested in the mechanical properties of nanocrystalline materials. This review on that topic is our contribution to the special issue of Progress in Materials Science honoring him.