A simple method for the determination of contact area for nanoindentation tests

The contact area is a key parameter for the mechanical property characterization via the nanoindentation technique. In the conventional Oliver-Pharr (OP) method, the contact area was calculated based on an empirical area function precalibrated with a standard sample. However, the procedure for precalibrating the area function is rather complex and concerns about its reliability still exist. In this paper, the efficiency of the precalibrated OP area function was evaluated based on the expression derived by Malzbender et al. [J Mater Res, 2000, 15: 1209-1212] to describe the nanoindentation loading behavior. It was shown for the first time that, for a relatively small contact depth, the loading segment of the measured load-displacement cannot be described sufficiently using the mechanical properties determined via the conventional OP method, implying that the method may not yield reliable results for small indentations. To overcome these limitations while using the OP area function, based on the consideration of a self-consistent description for the measured load-displacement curve, a simple method was proposed in the present study to directly determine the contact area without precalibration. The two parameters involved in this new method for calculating the contact area, the contact depth hc, and the so-called "truncation distance of a rounded indenter tip" hd, can be obtained directly and easily by analyzing the unloading and the loading segments of the same load-displacement curve, respectively. Compared with the conventional OP method, the main advantage of this method is that the contact area can be determined directly using the data measured with the test material, and the results may reflect the material responses to nanoindentation directly and accurately. The efficiency and reliability of this newly proposed method were confirmed by the nanoindentation data measured on typical materials.