About the importance of introducing a correction factor in the Sneddon relationship for nanoindentation measurements

In the Sneddon relationship between unloading contact stiffness, elastic modulus and contact area, it is absolutely necessary to introduce a correction factor alpha to perform good elastic modulus and hardness measurements by nanoindentation. This is verified by comparing the contact area determined from the Sneddon equation in the usual way to the projected area of the residual indent measured by atomic force microscopy (AFM). For fused quartz indented by a sharp Berkovich indenter, the tip radius of which is 180 nm, an alpha value as high as 1.17 - 1.19 is evaluated for a load of 10 mN corresponding to a penetration depth of about 300 nm. This correction factor is not a constant having a single value valid for any Berkovich indenter, but strongly depends on the blunting state of the indenter when measurements are performed in the nanoindentation regime, i.e. penetration depths of the order of a few hundreds nanometres.