Determination of the effective zero point of contact for spherical nanoindentation
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Accurate determination of the “zero point,” the first contact between an indenter tip and sample surface, has to date remained elusive. In this article, we outline a relatively simple, objective procedure by which an effective zero point can be determined accurately and reproducibly using a nanoindenter equipped with a continuous stiffness measurement option and a spherical tip. The method relies on applying a data shift, which ensures that curves of stiffness versus contact radius are linear and go through the origin. The method was applied to fused silica, sapphire single crystals, and polycrystalline iron with various indenter sizes to a zero-point resolution of ≈2 nm. Errors of even a few nanometers can drastically alter plots and calculations that use the data, including curves of stress versus strain.
I. INTRODUCTION
Instrumented indentation is a valuable method for characterizing the mechanical behavior of materials, especially that of single crystals and thin films. Field and Swain,1,2 and Oliver and Pharr3 have made significant progress in developing the technique, but recognize the significant hurdles yet to overcome. One such obstacle is the accurate and reliable determination of the zero point, where the indenter tip makes first contact with the sample surface.3–9 At this point, both the applied indentation load, P, and the total displacement, ht, or indentation depth, should be zero, though the sample stiffness, S, may appear positive. Inset 1 in Fig. 1(a) shows the conundrum, wherein a curve of P versus ht has no clear zero point. To date, methods of various sophistication have been proposed to qualitatively or quantitatively determine the zero point.10–17 For example, one is to simply plot P versus ht and choose a point where P first exceeds a certain threshold, while another uses a video camera.14,16 For instruments with continuous stiffness measurement (CSM) capabilities, Oliver and Pharr3 have suggested using the point at which S reaches a local minimum before increasing steadily. Alternatively, they suggested using abrupt changes in CSM harmonic displacement or phase angle if they are clearer, but all three options require some subjectivity, however small. They claim the method has an accuracy of 2 nm, but we have found that
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0012 204 J. Mater. Res., Vol. 23, No. 1, Jan 2008 http://journals.cambridge.org Downloaded: 09 Apr 2015
it identifies the zero point too early, sometimes by as much as 14 nm. This may seem insignificant, but as we show below, the difference can be quite important. Chudoba and colleagues10,11 and Ullner17 have suggested using regression on the P-versus-ht plots. The former advocates an iterative numerical method to fit the data to a variation of the Hertzian model, replacing the conventional parameters of tip radius and effective modulus with an optimized proportionality constant, and forcing the data to go through zero.10,11 The latter advocates optimizing the terms of a second-o
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