ABSTRACT
Based on the load versus depth-of-penetration data generated, the parameters involved in a nanoindentation experiment (Figures 7.1a and 7.1b) are given by hf, the final depth of penetration; hmax, the maximum depth of penetration of the indenter when the load P = Pmax; and hc, the contact depth, i.e., the displacement where the indenter has maximum contact with the surface while unloading [1]. Any nanoindentation hardness calculation is also just like the conventional hardness calculation, i.e., load/load-bearing contact area. Now, there can be two area concepts used in nanoindentation evaluation. If the area is calculated from the contact depth, hc, it is generally denoted by the contact area, As. There is another area called Ap, which is the projected contact area of an ideal nanoindenter. Since the nanoindenters have very small tip radius, typically about 40-200 nm, and the load may be ultralow, from a few micronewtons to a few millinewtons, it is expected that the indentation imprints also will be very small. Therefore, to measure the contact area and the contact height directly experimentally is rather difficult because of the elastic recovery. Therefore, these are calculated based on the projected area, Ap. Assuming that a given nanoindenter (e.g., Vickers or Berkovich) has an ideal shape and the surfaces that it indents are perfectly flat, the contact depth (hc) is given by
=h
A 24.56c
and when hc is known, the contact area Ac is given by, e.g., Ac = 26.44 hc2, while the corresponding projected contact area Ap is given by, e.g., Ap(hc) = 24.56 hc2. The quantity Ap can be measured with sufficient accuracy from the images of the nanoindent, provided that the tangent height is set at typically about 90% below the surface height. Once Ap is known, hc can be calculated. When hc is calculated, the value of As can be easily predicted,
as mentioned previously. Because of the repeated contact events and friction with the surface being indented, the tip of the nanoindenter gets worn out and, as a result, it becomes rounded. Thereby, it physically shifts from its ideal shape. Hence, the calibration of the indenter area function is done to account for the deviation from the ideal shape.
