Indentation Size Effect and the Hall-Petch ‘Law’
The flow of material out from under regions in compression must occur by the operation of many slip systems, which together produce rotational flow. Such flow requires the accumulation of geometrically necessary dislocations, and leads to the indentation size effect: smaller indents produce higher hardness, a component of the hardness being inversely proportional to the square-root of the indenter size. A pattern of flow in polycrystals which satisfies both continuity of normal stress and continuity of matter at boundaries can be achieved by rotational flow, and it leads to a grain-size effect. Under most circumstances, the flow stress has a component which is inversely proportional to the square-root of the grain size, the Hall-Petch law. The flow is accompanied by the build-up of internal stress which can be relieved by intercrystalline cracking, thereby limiting the cohesive strength of polycrystals. The relationship between these ideas and traditional views is briefly explained, and an analysis is given of recent experimental results.
M. Munawar Chaudhri
L.M. Brown "Indentation Size Effect and the Hall-Petch ‘Law’", Materials Science Forum, Vol. 662, pp. 13-26, 2011