Simplified method for analyzing nanoindentation data and evaluating performance of nanoindentation instruments
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Nanoindentation is a simple and effective means for evaluating the mechanical properties of thin films. In such circumstances, nanoindentation testers have been developed and commercialized by some companies. In this study, we tested the standard four specimens using six different types of testers and established a method to evaluate the nanoindentation data. The method requires only two correction factors; one is the frame compliance, Cf, of the testers, and the other is the error of the detection of the original surface which includes both the truncation of the indenter apex and the damage of the surface caused by the preloading of the indenter. The latter correction is conducted by adding a correction length, ⌬hC, to the measured penetration depth, h. It was found that the values ⌬hC increase with decrease in the hardness of material and are very sensitive to the performance of the testers.
I. INTRODUCTION
Nanoindentation, a type of hardness test, is a technique that measures load and displacement continuously during the process that the indenter is loaded and unloaded on a sample surface at submicron depths. We estimate the mechanical property, hardness and elastic modulus of the very surface of materials by analyzing the resultant load–penetration depth curve (P–h curve), which is schematically illustrated in Fig. 1. The information obtained from the P–h curve is the maximum applied load, Pmax, the maximum penetration depth, hmax, final penetration depth, hf, gradient of initial unloading curve (stiffness), S, and the depth extrapolated stiffness to the h axis, hS. We should estimate the values of hardness and the elastic modulus from such a limited number of values. Assuming that the contact area remains constant during the initial unloading stage, an approximate elastic contact solution can be obtained by using the flat-ended punch model with an equivalent contact area.1 The solution for an axisymmetric punch derived by Sneddon2 gives S=
dP = dh
2
公
E*
公A
,
(1)
where A is the real projected contact area. E* is the composite Young’s modulus and is expressed by 1 − S2 1 − I2 1 + , = E* ES EI
(2)
where E and are Young’s modulus and Poisson’s ratio of the materials and subscripts S and I mean sample and indenter, respectively. A triangular indenter is commonly 3084
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J. Mater. Res., Vol. 16, No. 11, Nov 2001 Downloaded: 18 Mar 2015
used for nanoindentation measurement for the reason that the three facets theoretically converge to a single point. In this study, we use the Berkovich triangular indenter which has the same area–depth function as that of a Vickers indenter. We usually make use of Eq. (1) for estimating Young’s modulus of material, since the deviations from Eq. (1) for flat-ended punches with square and triangular cross sectional are only 1.2% and 3.4%, respectively.3 Assuming that the real contact area remains constant during indentation, hardness H can be defined by dividing the maximum applied load Pmax by A.3 Thus, this hardness will be related to th
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