Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T16:16:09.182Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic Deformation of Coating/substrate Composites in Axisymmetric Indentation

Published online by Cambridge University Press:  01 August 2005

M. Sakai ,
J. Zhang  and
A. Matsuda
M. Sakai*
Affiliation:
Department of Materials Science, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441-8580, Japan
J. Zhang
Affiliation:
Department of Materials Science, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441-8580, Japan
A. Matsuda
Affiliation:
Department of Materials Science, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441-8580, Japan
*
a) Address all correspondence to this author. e-mail: [email protected] This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/publications/JMR/policy/html/
Get access

Abstract

Elastic deformation of coating/substrate composites was examined for axisymmetric indentations with three different geometries of flat-ended cylinder, sphere, and cone. Intensive theoretical considerations were made for the Boussinesq problems not only in its Fredholm integral equation of the second kind, but also in its Green function using the principle of superposition for the approximated contact stress distribution. The agreement and the disagreement between these two different numerical/analytical assessments for elastic surface deformations are discussed. Along with these theoretical considerations, experimental scrutiny was conducted for the theoretical predictions for spherical indentation by the use of a sol-gel-derived MeSiO3/2 film coated on a soda-lime glass plate. A novel technique is also proposed for estimating in a simultaneous manner the elastic moduli of both the coating film and of the substrate or the elastic modulus of the film and its thickness in spherical indentation tests.

Keywords

Elastic propertiesNanoindentationThin film
Type
Articles
Information
Journal of Materials Research , Volume 20 , Issue 8 , August 2005 , pp. 2173 - 2183
Copyright
Copyright © Materials Research Society 2005

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

1Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).Google Scholar
2Chechemin, N.G., Bøttiger, J. and Krog, J.P.: Nanoindentation of amorphous aluminum oxide film I. The influence of the substrate on the plastic properties. Thin Solid Films 261, 219 (1995).CrossRefGoogle Scholar
3Tsui, T.Y., Vlassak, J.J. and Nix, W.D.: Indentation plastic displacement field, Part I and II. J. Mater. Res. 14, 2196 (1999).CrossRefGoogle Scholar
4Gerberich, W.W., Strojny, A., Yoder, K. and Cheng, L-S.: Hard protective overlayers on viscoelastic-plastic substrates. J. Mater. Res. 14, 2210 (1999).CrossRefGoogle Scholar
5Sawa, T., Akiyama, Y., Shimamoto, A. and Tanaka, K.: Nanoindentation of a 10 nm thick thin film. J. Mater. Res. 14, 2228 (1999).Google Scholar
6Malzbender, J., de With, G. and Toonder, J.M.J. den: Determination of the elastic modulus and hardness of sol-gel coatings on glass; Influence of indenter geometry. Thin Solid Films 372, 134 (2000).Google Scholar
7Chen, X.I. and Vlassak, J.J.: Numerical study on the measurement of thin film mechanical properties by means of nanoindentations. J. Mater. Res. 16, 2974 (2001).Google Scholar
8Saha, R. and Nix, W.D.: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50, 23 (2002).CrossRefGoogle Scholar
9Atanacio, A.J., Latella, B.A., Barbé, C.J. and Swain, M.V.: Mechanical properties and adhesion characteristics of hybrid sol-gel thin films. Surf. Coat. Technol. 192, 354 (2005).Google Scholar
10Bückle, H.: Use of the hardness test to determine other material properties, in The Science of Hardness Testing and Its Research Application, edited by Westbrook, J.W. and Conrad, H. (ASM, Materials Park, OH, 1973), p. 453.Google Scholar
11Xu, Z-H. and Rowcliffe, D.: Finite element analysis of substrate effects on indentation behavior of thin films. Thin Solid Films 447–448, 399 (2004).Google Scholar
12Dhaliwal, R.S.: Punch problem for an elastic layer overlying an elastic foundation. Int. J. Eng. Sci. 8, 273 (1970).Google Scholar
13Dhaliwal, R.S. and Rau, I.S.: The axisymmetric Boussinesq problem for a thick elastic layer under a punch of arbitrary profile. Int. J. Eng. Sci. 8, 843 (1970).CrossRefGoogle Scholar
14Yu, H.Y., Sanday, S.C. and Rath, B.B.: The effect of substrate on the elastic properties of films determined by the indentation test; Axisymmetric Boussinesq problem. J. Mech. Phys. Solids 38, 745 (1990).CrossRefGoogle Scholar
15Hsueh, C-H. and Miranda, P.: Master curves for Hertzian indentation on coating/substrate systems. J. Mater. Res. 19, 94 (2004).CrossRefGoogle Scholar
16Hsueh, C-H. and Miranda, P.: Combined empirical-analytical method for determining contact radius and indenter displacement during Hertzian indentation on coating/substrate systems. J. Mater. Res. 19, 2774 (2004).CrossRefGoogle Scholar
17Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, U.K., 1985), Chap. 4 and 5.Google Scholar
18Gao, H., Chiu, C-H. and Lee, J.: Elastic contact versus indentation modeling of multi-layered materials. Int. J. Solids Struct. 29, 2471 (1992).Google Scholar
19Timoshenko, S.P. and Goodier, J.N.: Theory of Elasticity (McGraw-Hill, New York, 1951), Sec. 138 in Chap. 12.Google Scholar
20Brinker, C.J. and Scherer, G.W.: Sol-Gel Science (Academic Press, San Diego, CA, 1990).Google Scholar
21Matsuda, A. Sol-gel micropatterning, in Application of Sol-Gel Technology, Vol. III, edited by Sakka, S. (Kluwer Academic, Boston, MA, 2004), Chap. 30.Google Scholar
22El-Gendi, S.E.: Chebyshev solution of differential, integral and integro-differential equations. Comput. J. 12, 282 (1969).Google Scholar
23Yang, F.: Thickness effect on the indentation of an elastic layer. Mater. Sci. Eng. A358, 226 (2003).Google Scholar
24Menčik, J., Munz, D., Quandt, E., Weppelmann, E.R. and Swain, M.V.: Determination of elastic modulus of thin layers using naniondentation. J. Mater. Res. 12, 2475 (1997).CrossRefGoogle Scholar