Further analysis of indentation loading curves: Effects of tip rounding on mechanical property measurements
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Further analysis of indentation loading curves: Effects of tip rounding on mechanical property measurements Yang-Tse Chenga) Physics and Physical Chemistry Department, General Motors Global Research and Development Operations, Warren, Michigan 48090
Che-Min Cheng (Zheng Zhemin)b) Laboratory for Non-linear Mechanics of Continuous Media, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China (Received 10 July 1997; accepted 15 October 1997)
The effects of indenter tip rounding on the shape of indentation loading curves have been analyzed using dimensional and finite element analysis for conical indentation in elastic-perfectly plastic solids. A method for obtaining mechanical properties from indentation loading curves is then proposed. The validity of this method is examined using finite element analysis. Finally, the method is used to determine the yield strength of several materials for which the indentation loading curves are available in the literature.
I. INTRODUCTION
Indentation experiments have been performed for nearly one hundred years for measuring the hardness of materials.1 Recent years have seen increased interest in indentation because of the significant improvement in indentation equipment and the need for measuring the mechanical property of materials on small scales. With the improvement in indentation instruments, it is now possible to monitor, with high precision and accuracy, both the load and displacement of an indenter during indentation experiments in the respective microNewtons and nanometer ranges.2–4 In addition to hardness, basic mechanical properties of materials, such as the Young’s modulus, yield strength, and work hardening exponent, may be deduced from the indentation load versus displacement curves for loading and unloading. For example, the hardness and Young’s modulus may be calculated from the peak load and the initial slope of the unloading curves using the method of Oliver and Pharr5 or that of Doerner and Nix.6 Finite element methods have also been used successfully to extract the mechanical properties of materials by matching the simulated loading and unloading curves with that of the experimentally determined ones.7–10 Recently, many attempts have been made to better understand indentation loading curves. For example, several empirical formulae have been proposed for the loading curves in terms of Young’s modulus and hardness.11,12 Loading curves have also been discussed using energetic considerations of reversible and irre-
a)
Electronic mail: Yang T. [email protected] Electronic mail: [email protected]
b)
J. Mater. Res., Vol. 13, No. 4, Apr 1998
versible parts of the indentation-induced deformations.13 Using dimensional analysis and finite element calculations, we have recently derived scaling relationships for indentation into elastic-perfectly plastic solids using conical indenters.14,15 In this paper, we apply the scaling relationships of indentation to determine the mechanical properties of
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