Determining the Area Function of Spherical Indenters for Nanoindentation.
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Determining the Area Function of Spherical Indenters for Nanoindentation. Andrew J.Bushby1 and Nigel M. Jennett2 1 Department of Materials, Queen Mary, University of London, UNITED KINGDOM 2 NPL Materials Centre, National Physical Laboratory, Teddington, UNITED KINGDOM. ABSTRACT Nanoindentation with spherical tipped indenters provides a powerful technique for exploring surface mechanical properties through the application of Hertzian mechanics. The full range of mechanical response can be obtained from elastic, through the yield point to a range of permanent deformation. However, the successful application of the technique requires accurate calibration of the indenter tip geometry. In this paper methods based on indentation into a number of reference materials are used to characterise a range of spherical tipped indenters with nominal radii from 5 to 50 microns. A traceably calibrated metrological AFM is also used to determine the actual shape of one of the indenters. The sensitivity of each method to test parameters is discussed. Coincidence of the data from both methods validates the determined shape of the indenter and offers the opportunity to cross-correlate the calibration of both instruments with high sensitivity. INTRODUCTION Spherical indenters are a useful weapon in the armoury of nanoindentation. They allow the determination of a wide range of mechanical behaviour and can provide complementary information to experiments with pointed indenters (pyramids and cones)[1]. Specifically they can provide: material responses exclusively in the elastic regime for both bulk and thin film materials[2]; yield behaviour, in the form of the elastic limit[3]; indentation stress-strain curves can be generated, using appropriate techniques[4]; data for comparison with axisymetric numerical models; and, the geometry can be used for certain critical instrument calibration issues such as the determination of instrument frame compliance. The successful application of spherical nanoindentation techniques requires accurate calibration of the indenter tip geometry. In nanoindentation diamond indenters tend to be used for their high hardness and elastic modulus. However, the indenters often deviate from an ideal spherical shape due to the difficulty of polishing an anisotropic crystal into a spherical shape. Calculation of the effective shape, or area function, for pointed indenters is often based on indentation into reference materials[5]. Methods using two reference materials have shown good agreement with direct imaging using atomic force microscope (AFM) techniques[6]. In this paper we discuss similar methods for calibrating the effective radius of spherical indenters, Reff, by indentation into reference materials with known properties using Hertzian contact mechanics and by directly imaging the indenter on a traceably calibrated metrological atomic force microscope (AFM). DEPTH SENSING INDENTATION (DSI) METHOD For elastic contact between a sphere and a planar surface, the total elastic displacement, he, from Hertzian contact
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