Simplified Area Function for Sharp Indenter Tips in Depth-sensing Indentation
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A two-parameter “area function” characterizing the depth-dependent projected area of an indenter was introduced and applied to a Berkovich tip. The two parameters have physical meaning, corresponding to the effective tip radius and effective cone angle. The indenter tip was calibrated on a commercial load-controlled Nano Indenter威 XP (MTS Systems Corp., Eden Prairie, MN). All calibrations were carried out using the procedure of Oliver and Pharr [J. Mater. Res. 7, 1564 (1992)] using several homogeneous materials. Plane-strain modulus and hardness values deconvoluted from indentation load–displacement traces using the calibrated two-parameter area function compared well with the values determined using the empirical eight-parameter area function of Oliver and Pharr.
I. INTRODUCTION
Depth-sensing indentation (DSI) has become a common characterization tool for determining the mechanical properties of thin films and coatings. Conventional microhardness techniques require imaging of a residual indentation impression to estimate the projected contact area at peak load for hardness determination. However, to determine the mechanical properties of a film or coating from indentation experiments, the indententation depth must be at most a small fraction of the film or coating thickness. For such very small-scale indentations, measuring the residual impressions can be extremely difficult, requiring the use of sophisticated imaging techniques such as scanning electron microscopy (SEM), atomic force microscopy, or transmission electron microscopy. However, if the projected contact area is a known function of indentation depth (the “area function”), no imaging is required; the contact depth at peak load can be extracted from DSI load-displacement data recorded during a contact event and related to the area at peak load.1 Prior to deconvoluting a hardness or modulus from load-displacement data, the displacement contribution from “column compliance” must be removed. The indenter tip area function and the column compliance must be determined from calibrations on standard materials. There exist numerous methods of calibration to deduce the column compliance, area function,2 or both simultaneously1,3,4 for sharp pyramidal indenter tips (such as Vickers or Berkovich) that can be analytically approximated as cones with some effective included angle. In the analysis here, a physically meaningful two-parameter area function is introduced and compared to the J. Mater. Res., Vol. 17, No. 5, May 2002
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eight-parameter area function proposed by Oliver and Pharr.1 A two-parameter area function is used because it can be related directly to tip-blunting or tip-rounding, is easier to fit to experimental data than an eight-parameter function, and yet is not over-constrained (i.e., the indenter column compliance associated with the area function is not material- or load-dependent). II. ANALYSIS
Figure 1(a) shows a conical solid of revolution (indenter tip) of included angle 2␣ in contact wit
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