An improved energy method for determining Young’s modulus by instrumented indentation using a Berkovich tip

Abstract

We previously proposed a method for estimating Young’s modulus from instrumented nanoindentation data based on a model assuming that the indenter had a spherical-capped Berkovich geometry to take account of the bluntness effect. The method is now further improved by releasing the constraint on the tip shape, allowing it to have a much broader arbitrariness to range from a conical-tipped shape to a flat-ended shape, whereas the spherical-capped shape is just a special case in between. This method requires two parameters to specify a tip geometry, namely, a volume bluntness ratio Vr and a height bluntness ratio hr. A set of functional relationships correlating nominal hardness/reduced elastic modulus ratio (Hn/Er) and elastic work/total work ratio (We/W) were established based on dimensional analysis and finite element simulations, with each relationship specified by a set of Vr and hr. Young’s modulus of an indented material can be estimated from these relationships. The method was shown to be valid when applied to S45C carbon steel and 6061 aluminum alloy.