Simple method and critical comparison of frame compliance and indenter area function for nanoindentation
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Michael V. Swain Biomaterials, Faculty of Dentistry, University of Sydney, United Dental Hospital, Surry Hills, NSW 2010, Australia (Received 11 May 2004; accepted 12 July 2004)
A simple method has been proposed for an independent determination of the frame compliance Cf and the area function of a Berkovich indenter. Cf was determined from the unloading compliance of very large indentations in four test materials (fused silica, silicon nitride, high-carbon steel, and copper-zinc alloy) with known elastic properties, following the Oliver–Pharr method by assuming the ideal shape of Berkovich indenter. For a specific value of Cf (⳱ 0.3 nm/mN in our case) all the specimens showed an hc (contact depth)-independent modulus, which agreed well with the expected value when the pile-up effect was taken into account. The contact area A(hc) was then estimated using fused silica as the standard specimen, according to two different procedures, i.e., the Oliver–Pharr method and the Field–Swain method. Both methods gave almost identical area functions over the whole range of the measurement. It was also found that such area functions can be described by two separate equations: A ⳱ 2Rehc for hc < ⌬h and A ⳱ g(hc + ⌬h)2 for hc 艌 ⌬h, where Re is the effective tip radius, ⌬h the truncation depth, and g the geometrical factor for a Berkovich indenter. Based on the spherically truncated cone model, a simple procedure is presented to determine all these parameters from the analysis of a multiple partial unloading P-h curve.
I. INTRODUCTION
Nanoindentation testing has become a widely used technique for the evaluation of mechanical properties of thin films and surface layers of submicron thickness. The most commonly used approach is with a pointed indenter, typically a Berkovich diamond pyramid, and the resulting load–displacement data plots are generally analyzed according to the procedure proposed by Oliver and Pharr.1 The technique does not rely upon any direct observations of the residual impression to measure its characteristic dimensions that are often too small to be determined precisely by conventional techniques. Instead, the test involves only the continuous measurement of load (P) and displacement (h) during loading and unloading of the indenter. This allows us to estimate both the elastic and plastic properties of very small volumes of material. However, no pointed indenter is geometrically
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2004.0449 3490
J. Mater. Res., Vol. 19, No. 12, Dec 2004
perfect, and the blunting of the indenter tip seriously affects these values, especially at a very small contact depth. Thus, the shape of the indenter should be evaluated before the analysis of P-h curves, and the accuracy of this estimate ultimately determines the accuracy of the properties of the specimen tested. In addition, commercial nanoindentation machines generally have a finite frame compliance, which affects the precise measurement of the penetration depth of the
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