Zhenduo Guan

Examination of the indentation size effect in low-load Vickers hardness testing of ceramics

Abstract The indentation size effect (ISE) in Vickers hardness for several ceramic materials was observed in a relatively wider range of applied test load. It was shown that the proportional specimen resistance (PSR) model proposed by Li and Bradt is insufficient for describing the experimental data. By considering the effect of the machining-induced plastically deformed surface on the hardness measurements, the PSR model was modified and the empirical equation proposed originally by Buckle was proven to be more suitable for correlating the measured indentation dimension to the applied test load. ©

Analysis of the indentation size effect on the apparent hardness for ceramics

Abstract Based on a reasonable assumption that Meyers law gives an accurate description for the variation of the apparent hardness with indentation size for ceramics, the empirical equation proposed originally by Buckle: P = a 0 + a 1 d + a 2 d 2 , is proved sufficiently suitable for representing the original data from the conventional hardness testing. The physical meanings of the parameters included in this equation are discussed in detail. It is shown that the energy–balance relationship can be evaluated completely with this equation, in which the extra energy dissipation and the experimental errors are considered properly. Further analysis reveals that the origin of the indentation size effect on the apparent hardness of ceramics lies in the fact that the traditional definition of hardness, i.e., the ratio of the applied load to the resulting indentation area, is an incomplete description for the energy–balance relationship during indentation.

Load-dependence of the measured hardness of Ti(C,N)-based cermets

The Vickers hardnesses of a series of Ti(C,N)-based cermets were measured in the indentation load range from 1.47 to 40.67 N. It was found that the examined materials exhibit a reversed indentation size effect, i.e. the measured hardness increases with increasing indentation load. Both Meyers law and the energy balance model can not provide a proper description for the observed experimental phenomena, while the polynomial series representation can describe the experimental data very well. A possible explanation for the cause of the observed reverse indentation size effect was also proposed.

Load-dependence of Knoop hardness of Al2O3-TiC composites

Abstract Nine samples of Al2O3–30 wt.% TiC composites were prepared by hot-pressing the Al2O3 powder mixed with TiC particles. The average sizes of the TiC particles used for preparing the nine samples were different with each other. Knoop hardness measurements were conducted on these nine samples, respectively, in the indentation load range from 1.47 to 35.77 N. For each sample, the measured Knoop hardness decreases with the increasing indentation load. The classical Meyers power law and an empirical equation proposed originally by Buckle were verified to be sufficiently suitable for describing the observed load-dependence of the measured hardness. Analysis based on Meyers law can not provide any useful information about the cause of the observed ISE while true hardness values, which are load-independent, can be deduced from the Buckles equation. It was found that the deduced true hardness increases with the average size of TiC particles existing in the sample.

A comparison between Knoop and Vickers hardness of silicon nitride ceramics

Abstract The hardness values of seven silicon nitride ceramics were measured at an applied load of 2.45 N for both Vickers and Knoop indenter geometries. It was found that the measured Knoop hardness, H K , is generally lower than the corresponding Vickers hardness, H V . There is a strong correlation between ( H V / H K ) and ( a / d ), where a and d are the measured lengths of the minor and the major diagonals of the Knoop indentation, respectively. Such a correlation indicates that the difference between H V and H K may be attributed to the elastic recovery occurring at the indentation.

Load dependence of low-load Knoop hardness in ceramics: a modified PSR model

Utilizing experimental data of the Knoop hardness versus applied load for several ceramics, the applicability of the proportional specimen resistance (PSR) model proposed by Li and Bradt to describing the indentation size effect (ISE) observed in a relatively wide range of applied load was examined. The PSR model was proven to be insufficient for representing the experimental data and was modified based on the consideration of the effect of machining-induced residually stressed surface on the hardness measurements.

Indentation toughness of ceramics: A modified approach

The indentation toughness equation proposed by Anstis et al. was re-examined with a particular emphasis on the definition of the hardness parameter used. It was shown that, because of the existence of the well-known indentation size effect (ISE), the apparent hardness defined as the ratio of the applied load to the projected area of the resultant indentation usually varies with the applied load and seems not to be suitable for use in indentation toughness determination. A new equation for determining indentation toughness, in which a load-independent hardness number was incorporated, was proposed.

Load dependence of the apparent hardness of silicon nitride in a wide range of loads

Abstract The load dependence of the apparent hardness of Si 3 N 4 ceramics is investigated in a wide range of applied loads. It is found that the proportional specimen resistance (PSR) model proposed by Li and Bradt is not suitable for describing the experimental data. A new semi-empirical equation is proposed to correlate the indentation size to the applied test load.

Effect of TiC particle size on the toughness characteristics of Al2O3-TiC composites

Abstract The effect of TiC particle size on the toughness of Al 2 O 3 –30 wt.% TiC composites was examined by quantitatively analyzing the R -curves measured with direct indentation method for four samples having different TiC particle sizes. It was shown that the toughening effect in the composite is strongly dependent on the size of the TiC particles.

Effect of load-dependence of hardness on indentation toughness determination for soda-lime glass

By analyzing the indentation data on soda-lime glass, it was found that, in the indentation toughness determination with the basic equation proposed by Anstis et al. [G.R. Anstis, P. Chantikul, B.R. Lawn, D.B. Marshall, J. Am. Ceram. Soc. 64 (1981) 533], treating the measured hardness as a constant would result in an indentation-load-dependent toughness number. A modified toughness equation was then proposed in which a load-independent hardness number was incorporated.