A note on a common mistake in the analysis of nanoindentation data
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It is shown that to analyze the load versus displacement data obtained from a nanoindentation experiment on a flat surface, it is incorrect to use the so called “reduced modulus,” which includes the elastic properties of both the indenter and the test solid. It is suggested that, until correct analytical solutions become available, the indenter should always be of a much stiffer material than the test solid and it should be approximated to a rigid indenter in the analysis. Furthermore, when the indenter and the test surface are of comparable elastic moduli, the measured indenter displacement is the distance of mutual approach of the two contacting bodies rather than the penetration of the indenter below the original surface of the test solid.
During the last 20–30 years nanoindentation techniques have been increasingly used for determining the mechanical properties of solid surfaces and coatings.1–14 Nanoindentation experiments are usually carried out using instrumented machines with which indenter load and indenter displacement are continuously and simultaneously monitored during indenter loading and unloading. The most commonly used indenters are made of diamond and their usual shapes are pyramidal or spherical, though conical shapes are also employed. By analyzing a load-displacement curve obtained from an elastic-plastic indentation of a test solid, its Young’s modulus and hardness may be obtained. In some investigations, purely elastic loading with a spherical indenter has been carried out on a solid flat of a known Young’s modulus and Poisson’s ratio and from a typical loaddisplacement curve the radius of the indenter has been estimated. Despite the popularity and practical importance of the nanoindentation techniques, in most analyses of the loaddisplacement curves, a common mistake has been made. This mistake is that the theoretical expressions giving the depth of penetration of rigid indenters into an elastic half space are being modified and applied, without any theoretical justification, to data obtained using nonrigid indenters. By giving two examples below, it will be illustrated that such modifications lead to impossible results. To elucidate the point under consideration, first brief descriptions are given of a typical nanoindentation machine and a typical load versus displacement curve for an elastic/plastic indentation. Figure 1 shows a schematic diagram of such a machine. The indenter, usually made 336
http://journals.cambridge.org
J. Mater. Res., Vol. 16, No. 2, Feb 2001 Downloaded: 18 Mar 2015
of a very hard material such as diamond, is fixed firmly on one end of a stiff indenter shaft. The other end of the shaft is mounted firmly onto a sensitive load cell, which in turn is bolted onto a cross-beam. The latter can be moved up or down, using a sensitive drive mechanism, along a load frame in a controlled manner. On the indenter shaft is firmly mounted a stiff bracket, and a noncontact transducer is fixed to one end of the bracket, as shown in Fig. 1. The test sample is placed on a sample bas
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