The nanoindentation loading curves measured on fused silica were analyzed based on the theoretical relationship derived by Malzbender et al. (J Mater Res 2000, 15: 1209-1212). It was found that the ratio of the applied load to the square of the displacement, P/(h + h_d)², does not keep constant during loading segment of the nanoindentation test. Considering the existence of the indentation size effect, an empirical method for the determination of the load-independent hardness by analyzing the nanoindentation loading curves was proposed.

Accurate estimation of Weibull parameters is an important issue for the characterization of the strength variability of brittle ceramics with Weibull statistics. In this paper, a simple method was established for the determination of the Weibull parameters, Weibull modulus m and scale parameter ${\sigma }_0$, based on Monte Carlo simulation. It was shown that an unbiased estimation for Weibull modulus can be yielded directly from the coefficient of variation of the considered strength sample. Furthermore, using the yielded Weibull estimator and the mean value of the strength in the considered sample, the scale parameter ${\sigma }_0$ can also be estimated accurately.

An abnormal displacement change observed during the holding period in nanoindentation tests on a zirconia dental ceramic was reported in this paper. It was found that, at the initial stage of the holding period, the measured displacement versus time curves were similar in shape with the typical indentation creep curve reported in previous studies. As the holding lasted for long time, however, an evident reduction in displacement was observed for tests with high loading rate, implying that another unknown process, which might result in a decrease in displacement, would co-exist with creep during holding period. Elastic recovery was suggested to be one of the possible sources for such a displacement reduction. An empirical method was also proposed to eliminate the effect of this displacement reduction on the determination of hardness and Young’s modulus.

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.