Tip radius variation with elastic indentation depth

Abstract

The reduced elastic modulus of a material is measured with a nanoindenter probe that is operated in the tapping mode. The resonant frequency of a freely oscillating cantilever is reduced when contact is made between the indenter tip and surface under investigation. It’s shown using elasticity theory that the elastic deformation is a function of the indenter tip radius. A deeper penetration within the elastic range can change the tip radius, and introduce an error of 10% in calculating the reduced elastic modulus.