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Kaupp and Naimi-Jamal (2010) claimed that the analysis of published loading curves reveals the exponent 3/2 to the depth for nanoindentations with sharp pyramidal or conical tips. To demonstrate this, they plotted the load vs. the penetration depth to the power 3/2. We show, through examples, the authors' assertion is not credible because the methodology used is misleading and it cannot be asserted that the exponent 3/2 has a universal validity that applies to all kinds of materials.

Dimensional analysis is used to show that the maximum penetration depth and the tip radius affect the β correction factor appearing in the Sneddon relationship between unloading contact stiffness, contact area, and elastic modulus. A simple analytical model based on elasticity theory is derived that predicts the variation of β with penetration depth. This model shows that β increases at low penetration depth and decreases with the tip radius. The β(h) curve given by the model is compared with that calculated by finite element analysis for an elastic material and also with that deduced from experimental measurements performed on fused quartz with two Berkovich indenters: a sharp one and a blunted one. It is also demonstrated that the correction factor can be expressed as two multiplicative contributions, a contribution related to the mechanical properties of the material and a contribution related to the indenter geometry. Implications of these findings on nanoindentation test are also discussed.