Differential and integral hardness—new aspects of quantifying load–depth-data in depth-sensing nanoindentation experiments

The Meyer hardness H as load F over contact area AC: H=F/AC, has the physical meaning of the mean pressure inside the contact area. In addition to this we introduce a differential hardness Hd as Hd=dF/dAC. This quantity provides more information on the pressure, required to initiate plastic flow, than the conventional hardness does. Furthermore, an integral or energetic hardness is considered being the plastic work Wp divided by the volume Vp of irreversibly displaced material: He=Wp/Vp. Since the plastic work is the area encircled by the loading and the unloading curve, information from the entire loading curve is involved in the calculation of He, i.e. He integrates over the deformation states from the very beginning of loading up to the unloading procedure. It turns out that He is more surface sensitive than H, whereas Hd proves more sensitive to the material properties of the bulk. H, Hd and He are determined as continuous functions of penetration depth h derived from nanoindentations into fused quartz, single-crystalline CdS and amorphous diamond-like-carbon layers (DLC) onto silicon substrates. The calculation takes advantage of a newly developed iterative procedure to calculate the contact depth hC for every point of the loading curve of a single indent.