A simple framework of spherical indentation for measuring elastoplastic properties

Based on the indentation load–displacement curve, spherical indentation may deduce material elastoplastic properties from the measurements at several depths (which mimics the dual/plural sharp indentation method). The previous approaches, however, have very complex formulations and involve many fitting parameters that lack theoretical backgrounds; moreover, studies based on shallow indentation may not lead to unique solution. To close these gaps, we propose a simple framework of spherical indentation based on a new limit analysis-based representative strain analysis, which contains minimum number of fitting parameters. Two simple equations of the normalized loading work (at two different depths) are proposed, which can determine the material plastic properties accurately from the loading curve. In addition, by using either the established Fischer-Cripps method or an extra equation based on the contact stiffness, both the elastic and plastic properties are determined with reasonable accuracy. The simple framework may be useful for guiding the measurement of elastoplastic properties via spherical indentation.