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

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 V_r and a height bluntness ratio h_r. A set of functional relationships correlating nominal hardness/reduced elastic modulus ratio (H_n/E_r) and elastic work/total work ratio (W_e/W) were established based on dimensional analysis and finite element simulations, with each relationship specified by a set of V_r and h_r. 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.