Simplified Area Function for Sharp Indenter Tips in Depth-sensing Indentation

A two-parameter “area function” characterizing the depth-dependent projected area of an indenter was introduced and applied to a Berkovich tip. The two parameters have physical meaning, corresponding to the effective tip radius and effective cone angle. The indenter tip was calibrated on a commercial load-controlled Nano Indentert® XP (MTS Systems Corp., Eden Prairie, MN). All calibrations were carried out using the procedure of Oliver and Pharr [J. Mater. Res. 7, 1564 (1992)] using several homogeneous materials. Plane-strain modulus and hardness values deconvoluted from indentation load–displacement traces using the calibrated two-parameter area function compared well with the values determined using the empirical eight-parameter area function of Oliver and Pharr.