Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques
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Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques A. Bolshakova) and G. M. Pharr Department of Materials Science, Rice University, 6100 Main Street, Houston, Texas 77005-1892 (Received 8 May 1997; accepted 16 October 1997)
Finite element simulation of conical indentation of a wide variety of elastic-plastic materials has been used to investigate the influences of pileup on the accuracy with which hardness and elastic modulus can be measured by load and depth-sensing indentation techniques. The key parameter in the investigation is the contact area, which can be determined from the finite element results either by applying standard analysis procedures to the simulated indentation load-displacement data, as would be done in an experiment, or more directly, by examination of the contact profiles in the finite element mesh. Depending on the pileup behavior of the material, these two areas may be very different. When pileup is large, the areas deduced from analyses of the load-displacement curves underestimate the true contact areas by as much as 60%. This, in turn, leads to overestimations of the hardness and elastic modulus. The conditions under which the errors are significant are identified, and it is shown how parameters measured from the indentation load-displacement data can be used to identify when pileup is an important factor.
I. INTRODUCTION
Numerous methods have been developed in recent years for measuring the mechanical properties of materials by means of load and depth sensing indentation testing.1–3 One of the great advantages of these methods is that it is not necessary to measure the area of the hardness impression by imaging; rather, the contact area and the material properties which can be derived from it are determined from analyses of indentation load-displacement data. The methods form the basis for nanoindentation testing, in which mechanical properties can be measured from very small indentations, sometimes only a few nanometers deep.4,5 Among the properties that can be measured in this way are the hardness, H, and the elastic modulus, E. One of the more commonly used methods for analyzing nanoindentation load-displacement data is that of Oliver and Pharr,3 which expands on ideas developed by Loubet et al.1 and Doerner and Nix,2 but is not constrained by the assumption of a flat punch indenter geometry. In the Oliver–Pharr method, hardness and elastic modulus are determined from indentation data obtained during one complete cycle of loading and unloading. The analysis begins by fitting the unloading curve to the power-law relation ¢m ° (1) P B h 2 hf , a)
Current address: Baker Hughes Inteq, P.O. Box 670968, Houston, Texas 77267-0968. J. Mater. Res., Vol. 13, No. 4, Apr 1998
where P is the indentation load, h is the displacement, B and m are empirically determined fitting parameters, and hf is the final displacement after complete unloading (also determined by curve fitting). The un
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