Fundamental relations used in nanoindentation: Critical examination based on experimental measurements

The fundamental relations used in the analysis of nanoindentation load-displacement data to determine elastic modulus and hardness are based on Sneddon's solution for indentation of an elastic half-space by rigid axisymmetric indenters. It has been recently emphasized that several features that have important implications for nanoindentation measurements are generally ignored. The. first one concerns the measurement of the contact depth, which is actually determined by using a constant value epsilon = 0.75 for the geometry of a Berkovich indenter and for any kind of material,, whereas the reality is that epsilon is a function of the power law exponent deduced from the analysis of the unloading curve. The second feature-concerns the relation between contact stiffness, elastic modulus, and contact area, in which a correction factor gamma larger than unity is usually ignored leading to a systematic overestimation of the area function and thus to errors in the measured hardness and-modulus. Experimental measurements on fused quarto are presented that show the variation of epsilon with the geometry of the tip-sample contact; that is to say with the contact depth, as well as the existence of the correction factor gamma, as predicted in some recent articles. Effects of both epsilon and gamma on harness and modulus measurements are also shown.