Recent progresses in the phenomenological description for the indentation size effect in microhardness testing of brittle ceramics

The indentation hardness of a given material is usually load-dependent and such a phenomenon is generally referred to as the indentation size effect (ISE). The existence of ISE means that, if hardness is used as a material selection criterion, it is clearly insufficient to quote a single hardness number. Several empirical or semi-empirical equations, including the Meyer's law, the Hays-Kendall approach, the energy-balance approach, the proportional specimen resistance (PSR) model and the modified PSR model, etc., have been proposed for the description of the variation of the indentation size with the applied test load and for determining the so-called load-independent hardness. This paper reviews these existing empirical equations, with a special emphasis on the analysis and the application of the modified PSR model.