The first indenter-sample contact and the indentation size effect in nano-hardness measurement

The problem of appropriately defining the First Indenter-Sample Contact (FISC) is known to be a major problem in hardness measurement and particularly in nano-indentation. Another difficulty arises from the determination of the real indentation area when a piled up occurs near the indentation print. This phenomenon is known as the Indentation Size Effect (ISE). The indentation piles up can be particularly heavy for low loads which affects the nano-indentation measurements. The Loading Displacement Curves (LDC) with ISE can be modelled by the PSR law (Proportional Specimen Resistance). We show that an error on the FISC validates PSR law even if no ISE occurs meaning that it is illusory to quantify the ISE with only one loading curve. To overcome this difficulty, a statistical protocol is proposed that consists in simultaneously analysis a fixed number of loading curves. With this approach, a new equation of LDC is proposed that allows determination of Hardness, ISE coefficient and the FISC position on each curve (98 LDC are recorded from a fused silica standard). The uncertainty on each coefficient is determined by a bootstrap protocol.