Determination of the Real Indenter Shape for Nanoindentation/Nanotribology Tests by Surface Metrological and Analytical
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DETERMINATION OF THE REAL INDENTER SHAPE FOR NANOINDENTATION/NANOTRIBOLOGY TESTS BY SURFACE METROLOGICAL AND ANALYTICAL INVESTIGATIONS
S. Enders, P. Grau*, H. M. Hawthorne NRC Innovation Centre, Surface Technology-Tribology Group, Vancouver, Canada *Martin-Luther-University Halle-Wittenberg, FB Physik-ExPh I, D-06108 Halle, Germany
ABSTRACT In this paper a critical comparison of different kinds of surface metrological methods like atomic force microscopy (AFM), scanning electron microscopy (SEM) and optical interferometric profilometry is made, as well as analytical investigations based on both Hertz and Sneddon theories of pure elastic contact, to qualify the real indenter shape function. The results obtained show the advantages and disadvantages of the respective methods by describing a rounded indenter tip. INTRODUCTION In contact experiments under high local loading, knowledge of the shape and the expansion of the developing stress field is vitally important for the exact determination and proper interpretation of the mechanical properties of the material under study. To deduce the latter’s properties from the stress field it is thus necessary to know with precision the actual shape of the indenter used. We make the assumption that as more tests are made, the indenter will not be evenly abraded and this infringes the indenter self-similarity needed for analysis. This happens not only during scratching experiments but also for the indentation test when uneven indenter wear occurs. To estimate the real indenter shape, various metrological and analytical methods can be used. However, each of these has its own aberrations, which can lead to incorrect determination of the real indenter shape and, thus, to inaccurate material property evaluations. A critical comparison of some of the widely used methods to qualify the real indenter shape should help to minimize these difficulties. THEORY There are many analytical approaches discussed in the literature to determining the indenter shape function, for example [1]. All are based on the fact that the indenter diverges from its ideal shape by some type of rounded blunting, especially for indentation depth h < 200 nm. This divergence can be determined by making indentation experiments on standard materials. For this, the materials must be of homogenous microstructure, isotropic in their mechanical properties and there must not be any change in their structure or phase under pressure. In this paper fused silica was used. In the following the calculations based on both Hertz and Sneddon theories of pure elastic contact will be discussed. Calculation based on Hertzian theory These calculations are based on the assumption that the tip of the indenter is an ideal sphere as this is the precondition of Hertz’s theory. Therefore, a statistically sufficient number of indentations in the pure elastic range was evaluated. For pure elastic contact the following power law describes, with the help of two parameters “C” and “n”, the relationship of the applied normal force FN and the res
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