Jianghong Gong

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. ©

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) Meyers 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.

An energy-balance analysis for the size effect in low-load hardness testing

The size effect in low-load hardness testing is analyzed theoretically using an energy-balance approach. A new semi-empirical equation is proposed to correlate the hardness test load and the resulting indentation size. The validity of this new equation is verified by analyzing the previously reported experimental data. It is found that the value of true hardness of material estimated with this new equation is independent of the indentor geometry as well as indentation size.

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.

Preparation of Ni/YSZ materials for SOFC anodes by buffer-solution method

NiO/YSZ composites were fabricated using mixed nickel oxideyttria stabilized zirconia powders (NiO/YSZ) with different Ni contents prepared by an improved co-precipitation technique, named the buffer-solution method. The composites were then exposed in a reducing gas mixture of CO and CO2 to form Ni/YSZ cermets which may be used as anode materials in solid oxide fuel cell (SOFC) technology. The conductivities of the resultant cermets were measured over the temperature range from 800 to 1200 degreesC and were found to be always much higher than those of samples with the same Ni contents but prepared by the traditional mechanical mixing method. This may be owing to the fact that the buffer-solution method can assure more homogeneous distribution of Ni in YSZ matrix

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.

Effect of peak load on the determination of hardness and Young's modulus of hot-pressed Si3N4 by nanoindentation

Abstract The indentation load–displacement curves of a hot-pressed silicon nitride were measured under different peak load levels. The unloading segments of these curves were analyzed using the widely adopted Oliver–Pharr method. It was found that both the hardness, H , and the Youngs modulus, E , exhibit significant peak-load-dependence. Empirical approaches were then proposed to determine the load-independent hardness and modulus. The hardness and modulus deduced from these empirical approaches were proven to be comparable with the literature reported data measured with conventional methods.

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.

Statistical analysis of fracture toughness of soda-lime glass determined by indentation

Vickers indentation tests were conducted on a commercial soda-lime glass to determine the fracture toughness. The resultant fracture toughness data were then analyzed statistically. It was found that there always exists a somewhat large scatter in the indentation toughness measured at each applied load level. The variability of the measured indentation toughness was modeled by the well-known Weibull statistics. For different sets of indentation toughness data measured at different load levels, the resultant Weibull moduli are nearly identical with each other, indicating that the statistical variability of the indentation toughness is load-independent.

On the energy balance model for conventional Vickers microhardness testing of brittle ceramics

It has been well known that, for many engineering materials, the microhardnesses calculated from Equation 1 are load dependent [1–3]. In general, the higher the applied load, the lower the measured hardness. Such a phenomenon is sometimes referred to as the ind ntation size effect (ISE). Several possible explanations for the ISE have been proposed and one of them is based on a general energy balance model which was established originally by Fröhlich et al. [1]. The basic assumption in the energy balance model is that, during an indentation process, the external work applied by the indenter is converted into a strain energy component, proportional to the volume of the resultant impression, and a surface energy component, proportional to the area of the resultant impression. This assumption results in the following general formula to relate the indentation size, d, with the applied load, P,