Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T20:51:16.528Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic contact to a coated half-space: Effective elastic modulus and real penetration

Published online by Cambridge University Press:  03 March 2011

A. Perriot  and
E. Barthel
A. Perriot
Affiliation:
Laboratoire CNRS/Saint-Gobain Surface du Verre et Interfaces, 39, quai Lucien Lefranc, BP 135, F-93303 Aubervilliers Cedex, France
E. Barthel
Affiliation:
Laboratoire CNRS/Saint-Gobain Surface du Verre et Interfaces, 39, quai Lucien Lefranc, BP 135, F-93303 Aubervilliers Cedex, France
Get access

Abstract

A new approach to the contact to coated elastic materials is presented. A relatively simple numerical algorithm based on an exact integral formulation of the elastic contact of an axisymmetric indenter to a coated substrate is detailed. It provides contact force and penetration as a function of the contact radius. Computations were carried out for substrate to layer moduli ratios ranging from 10−2 to 102 and various indenter shapes. Computed equivalent moduli showed good agreement with the Gao model for mismatch ratios ranging from 0.5 to 2. Beyond this range, substantial effects of inhomogeneous strain distribution are evidenced. An empirical function is proposed to fit the equivalent modulus. More importantly, if the indenter is not flat-ended, the simple relation between contact radius and penetration valid for homogeneous substrates breaks down. If neglected, this phenomenon leads to significant errors in the evaluation of the contact radius in depth-sensing indentation on coated substrates with large elastic modulus mismatch.

Keywords

Thin filmIndentationElastic properties
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 2 , February 2004 , pp. 600 - 608
Copyright
Copyright © Materials Research Society 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Oliver, W.C. and Pharr, G.M.: J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
2Hertz, H.: J. Reine und angewandte Mathematik 92, 156 (1882).CrossRefGoogle Scholar
3Sneddon, I.N.: Fourier Transforms (McGraw-Hill, New York, 1951).Google Scholar
4Doerner, M.F. and Nix, W.D.: J. Mater. Res 1, 601 (1986).CrossRefGoogle Scholar
5Mencik, J., Munz, D., Quandt, E., Weppelmann, E.R. and Swain, M.V.: J. Mater. Res 12, 2475 (1997).CrossRefGoogle Scholar
6Gao, H.J., Chiu, C.H. and Lee, J.: Int. J. Solids Struct. 29, 2471 (1992).Google Scholar
7Yoffe, E.H.: Philos. Mag. Lett. 77, 69 (1998).Google Scholar
8Schwarzer, N.: J. Tribology 122, 672 (2000).Google Scholar
9Fabrikant, V.I.: Application of Potential Theory in Mechanics: A Selection of New Results (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989).Google Scholar
10Li, J. and Chou, T.W.: Int. J. Solids Struct. 34, 4463 (1997).CrossRefGoogle Scholar
11Sneddon, I.N.: Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
12Huguet, A. and Barthel, E.: J. Adhesion 74, 143 (2000).Google Scholar
13Haiat, G. and Barthel, E.: Langmuir 18, 9362 (2002).Google Scholar
14Hay, J.C., Bolshakov, A. and Pharr, G.M.: J. Mater. Res. 14, 2296 (1999).CrossRefGoogle Scholar
15El-Sherbiney, M. and Halling, J.: Wear 40, 325 (1976).CrossRefGoogle Scholar