A Generalized Load-Penetration Relation for Sharp Indenters and the Indentation Size Effect

A dimensional analysis has been made of elastic-plastic indentation of an anisotropic solid, and of a solid showing pressure-sensitive yield behavior. It is found that, $P∝δ2,$ for indentation with sharp, self-similar indenters, where $P$ is the load applied by the indenter and δ is the corresponding distance of penetration of the indenter into the solid. This extends and generalizes a similar result obtained for isotropic solids showing conventional plastic behavior. When a strain-gradient plasticity is incorporated into the material model, then it is found that $P$ is no longer proportional to $δ2.$ Implications of the results for the indentation size-effect and for the determination of stress-strain curves from indentation are discussed.