Influence of tip defect and indenter shape on the mechanical properties determination by indentation of a TiB2–60%B4C ceramic composite

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Abstract

Instrumented indentation is very useful to determine the elastic modulus and hardness of materials. To obtain reliable values of the mechanical properties, the measurement of the indenter displacement into the material must be very precise. In practice, the frame compliance of the instrument and the indenter tip defect are among the most influential parameters. In microindentation, the frame compliance term must be calculated for each analysis. On the other hand, the tip defect can lead to a wrong estimation of the contact area, which is involved in both the elastic modulus and the hardness calculations. The present work is mainly focused on the influence of the tip defect on the determination of the mechanical properties of a composite TiB2–60% B4C hard material using Berkovich, Vickers, Knoop and spherical indenters. This composite system was obtained by sintering in vacuum, employing a pulsed electric current, without any sintering additives. It has been shown that the tip defect greatly affects the results related to the mechanical properties of the system under study, even for low defect sizes, which are usually neglected in practice. After correction, the elastic modulus of the TiB2–60% B4C is found to be equal to 490 GPa whatever the indenter shape used. This result corroborates the value of 500 GPa found for this system by employing the resonance frequency method according to the ASTM Standard e1876-99. For analyzing the hardness-load dependence, the representative parameter of the Proportional Specimen Resistance model becomes null when the tip defect is introduced into the hardness calculation. Additionally, this parameter is found to be directly proportional to the tip defect size, suggesting a special attention when characterizing the indentation size effect of materials. Finally, the Meyer hardness found for the TiB2–60% B4C is close to 20 GPa.

Highlights

► Instrumented indentation is used for determining the mechanical properties of TiB2–60%B4C. ► Berkovich, Vickers, Knoop and spherical indenters are employed. ► Methodology of Oliver and Pharr is applied considering the tip defect and the frame compliance. ► The tip defect is responsible of the indentation size effect (ISE) and connected to the magnitude of the ISE parameter. ► The elastic modulus and the Meyer hardness are 500 GPa and 20 GPa, respectively.

Introduction

Nowadays, the evaluation of the mechanical properties of materials is widely carried out by means of nanoindentation techniques, which allow a local determination of the elastic modulus and hardness in various types of materials, like metals [1], hard materials [2], cement [3] or biological samples such as bones [4]. However, to obtain consistent and exploitable values for the mechanical properties of these materials, very cautious calibrations of the instrument and of the displacement measurements are required. These mainly concern the adjustment of the frame compliance of the instrument [5], [6] and the correction of the contact area calculation [7], [8], [9].

With the objective of determining the mechanical behavior of a material at a macroscopic scale, nanoindentation is very useful and appropriate for homogeneous materials. However when the material is heterogeneous from a microstructural point of view or when it presents some defects like porosity or microcracks, nanoindentation could give results, which can vary to a large extent depending on the location of the indentation experiment [10], [11]. One way to avoid such a problem and reduce the standard deviation of the mechanical parameters values could be the application of higher loads, which can lead to the development of a plastic deformation volume large enough to represent the microstructure of the material.

For example, this can be achieved by instrumented indentation at a micrometric scale for which the load ranges between 1 and 20 N. But, at such scale of measurement under indentation, the problems related to the instrument calibration differ in comparison with nanoindentation. Indeed, the frame compliance term used to correct the indenter displacement by separating the contributions that arise from the material and from the deflection of the instrument, has no constant value [12], [13]. This could be due to the sample mounting system, indentation testing conditions, e.g. loading and unloading rate, dwell-time, multi-cycling test or simply it could result from the magnitude of the indentation loads [13].

As a consequence, the frame compliance must be taken into account as a free-parameter for each microindentation data analysis. On the contrary, at a microscopic scale, the indenter tip defect responsible of the variation of the contact area has been often and probably wrongly neglected regarding its size, in comparison with the indenter displacement values.

Thus, the objective of this work is the determination of consistent values of the elastic modulus and hardness of a TiB2–60% B4C massive ceramic material, which has a large volume fraction of pores. For this reason, microindentation tests using various indenter shapes have been conducted, in order to verify the convergence of the results obtained for the mechanical properties and to analyze the influence of the tip defect, since the indenters employed have different bluntness levels. Particularly, a Vickers indenter with a highly pronounced rounded tip, commonly used in this kind of experiments, is employed. For this indenter, the objective is twofold: on the one hand, it is important to show that, even if the indenter tip is highly blunted, it can be used to obtain consistent results. On the other hand, it is also important to demonstrate that the appropriate determination of both the elastic modulus and hardness requires the consideration of the tip defect.

The second indenter employed is a Berkovich type, which is the most widely used in nanoindentation. It has the advantage of being similar to the Vickers indenter, in the sense that the tip angle of the equivalent or effective conical indenter has the same value. The Berkovich indenter employed for this purpose has an indenter tip bluntness less than that of the Vickers indenter.

To confirm the methodology proposed in the present work, a low tip bluntness Knoop indenter is also used. In addition, the Knoop indenter presents some relevant differences in comparison with the Vickers and Berkovich ones. For example, the tip angle of the equivalent conical indenter has a higher value [14]. Moreover, it is recognized that under the same applied load, both the indenter displacement and plastic deformation zone size obtained with the Knoop indenter are significantly less than those obtained with the Vickers and Berkovich indenters [15]. These three types of indenters are classified as pyramidal indenters. For this reason, a WC spherical indenter was also employed. For this indenter, the contact theory and associated mathematical development for the determination of the elastic modulus and hardness are totally different in comparison with the diamond pyramidal indenters.

As a main result, it has been confirmed that, independently of the indenter shape and magnitude of the tip defect, the consideration of the latter as well as the frame compliance of the instrument, into the indentation data analysis is absolutely necessary for determining reliable values of the elastic modulus and hardness of the massive TiB2–60% B4C ceramic material, i.e. 490 GPa and 20 GPa, respectively.

Section snippets

Instrumented indentation analysis

By analyzing the unloading part of a load–depth curve obtained by instrumented indentation, Oliver and Pharr [16] proposed the determination of the reduced modulus, ER, from the computation of the contact area, AC, and the compliance term of the sample, C, as follows:ER=π21AC1Cwhere ER is expressed as a function of the elastic modulus and Poisson's ratio of the material and of the indenter, Em, Ei, νm and νi, respectively. For a diamond indenter, Ei = 1140 GPa and νi = 0.07 [17]. Therefore, the

Material

The TiB2–60% B4C particulate composite material investigated in the present work was made by pulsed electric current sintering (PECS). The detailed description of the experiments has been presented elsewhere [32]. The sintered discs produced by PECS were sand blasted and had a thickness of 4 mm and a diameter of 30 mm. After a careful metallographic preparation, the average roughness of the sample achieved a value of ~ 0.1 μm. The complete characterization was performed using different methods such

Results and discussion

From an experimental point of view, the lowest maximum indentation load of 100 mN gives rise to Vickers and Berkovich indenters' displacements of around 300 nm. On the basis of the indent geometrical diagonal to depth ratio, which can be calculated from the half-angle of the tip indenters and based on the plastic zone radius to the indent diagonal ratio [35], the lowest diameter of the plastic deformation zone formed by a sharp indentation is found to be around 5 μm. This value is higher than the

Conclusions

As a main conclusion, the instrumented indentation at a microscopic scale is a valuable tool for determining the elastic modulus and hardness of a material if the frame compliance term is considered as a free-parameter and if the calculation of the contact area takes into account the tip defect. It has been shown that the same values for the mechanical properties can be obtained independently on the indenter shape. However, for the Knoop indenter, the maximum indenter displacement must be

Acknowledgements

Professor Puchi-Cabrera gratefully acknowledges the financial support of the Conseil Régional Nord-Pas de Calais, France, through the International Chair program 2011 and Professor Staia acknowledges the financial support from Ghent University (BOF).

References (42)

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