Simple method and critical comparison of frame compliance and indenter area function for nanoindentation

Abstract

A simple method has been proposed for an independent determination of the frame compliance Cf and the area function of a Berkovich indenter. Cf was determined from the unloading compliance of very large indentations in four test materials (fused silica, silicon nitride, high-carbon steel, and copper-zinc alloy) with known elastic properties, following the Oliver–Pharr method by assuming the ideal shape of Berkovich indenter. For a specific value of Cf (= 0.3 nm/mN in our case) all the specimens showed an hc (contact depth)-independent modulus, which agreed well with the expected value when the pile-up effect was taken into account. The contact area A(hc) was then estimated using fused silica as the standard specimen, according to two different procedures, i.e., the Oliver–Pharr method and the Field–Swain method. Both methods gave almost identical area functions over the whole range of the measurement. It was also found that such area functions can be described by two separate equations: A = 2πRehc for hc < Δh and A = g(hc + Δh)2 for hc ⩾ Δh, where Re is the effective tip radius, Δh the truncation depth, and g the geometrical factor for a Berkovich indenter. Based on the spherically truncated cone model, a simple procedure is presented to determine all these parameters from the analysis of a multiple partial unloading P-h curve.