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

Abstract

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 ε = 0.75 for the geometry of a Berkovich indenter and for any kind of material, whereas the reality is that ε 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 γ 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 quartz are presented that show the variation of ε 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 γ, as predicted in some recent articles. Effects of both ε and γ on harness and modulus measurements are also shown.