The concept of differential hardness in depth sensing indentation

Abstract

Since in-depth sensing indentation load-depth data of the entire loading-unloading cycle are available, more information than a single hardness value and an elastic modulus can be extracted from the experimental data. The conventional hardness H(h) = F(h)/AC(h) and the differential hardness Hd(h) = dF/dAC are calculated as continuous functions of depth h and compared to each other in this paper (F: load, AC: contact area). It turns out that Hd describes the momentary material resistance to deformation, whereas H integrates over deformation states from first tip-sample contact to current penetration h. This difference is particularly important for materials not homogeneous in depth (e.g. layer systems), and for situations where time-dependent external factors influence the momentary deformation resistance. Photoplasticity is considered as an example for the latter.