The use of shape correction factors for elastic indentation measurements

Elastic properties of small volumes of materials can be measured from the unloading of small indentations using the so-called nanoindenters The analytic elastic solutions for axisymmetric indenters are currently used to calculate modulus from the unloading curve, sometimes using corrections derived for flat, rigid punches. It is shown that these corrections represent an upper limit for the correction. More realistic corrections are derived for the Vickers, Berkovich, and Knoop indenter shapes, using the assumption of a uniformly loaded area. Results show that the axisymmetric solution overestimates the elastic compliance of the Vickers indenter by a factor of 1.0055, of the Berkovich indenter by a factor of 1.0226, and of the Knoop indenter by a factor of 2.682.