On the description of indentation size effect in hardness testing for ceramics: Analysis of the nanoindentation data

Abstract The nanoindentation hardnesses of a commercially available soda-lime glass, a tetragonal ZrO 2 polycrystalline and a hot-pressed Si 3 N 4 were measured in the peak load range from 7.5 to 500 mN. The experimental results revealed that, for each material, the measured hardness exhibits a peak-load- dependence, i.e., indentation size effect (ISE). Such a peak-load-dependence was then analyzed using the Meyer’ law, the Hay–Kendall approach, the proportional specimen resistance (PSR) model, the elastic recovery model and the modified PSR model. The analyses revealed that: (1) Meyer's law provides a satisfactory description for the experimental data for each material but cannot provide any knowledge of the origin of the observed ISE; (2) the Hays–Kendall approach, the elastic recovery model and the PSR model yield meaningless values of the parameters included in the corresponding equations, invalidating the applicability of these models in analyzing the ISE in the nanoindentation region; (3) the modified PSR model is sufficient for describing the observed ISE but the physical meaning of this model seems to be more complex than those proposed originally. For each material, the true hardness was also determined based on the PSR model, the elastic recovery model and the modified PSR model, respectively. It was found that the true hardness values deduced based on different models are similar with each other and this similarity was attributed to the similarity between the empirical equations adopted in these models.