Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-15T20:43:25.971Z Has data issue: false hasContentIssue false
  • English
  • Français

Master curves for Hertzian indentation on coating/substrate systems

Published online by Cambridge University Press:  03 March 2011

Chun-Hway Hsueh  and
Pedro Miranda
Chun-Hway Hsueh
Affiliation:
Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
Pedro Miranda
Affiliation:
Departamento Electrónica e Ingeniería Electromecánica, Escuela de Ingenierías Industriales, Universidad de Extremadura, 06071 Badajoz, Spain
Get access

Abstract

An analytical model was developed to derive an approximate closed-form solution for indenter displacement when a rigid spherical indenter is pressed onto a coating/substrate system. Finite element analyses were also performed to verify the analytical solution. The results showed that the solution could be obtained from the analytical expression for Hertzian indentation on a homogeneous semi-infinite elastic medium multiplied by a modification term. This modification term is a function of two ratios: (i) Young’s modulus ratio between the coating and the substrate and (ii) the ratio between the coating thickness and the contact radius. Based on this modification term, master curves for Hertzian indentation on coating/substrate systems were plotted.

Keywords

IndentationLayeredCoating
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 1 , January 2004 , pp. 94 - 100
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

1.Hertz, H., Miscellaneous Papers by H. Hertz (Macmillan, London, U.K., 1896).Google Scholar
2.Johnson, K.L., Contact Mechanics (Cambridge University Press, London, U.K., 1985).CrossRefGoogle Scholar
3.Pharr, G.M., Oliver, W.C. and Brotzen, F.R., J. Mater. Res. 7 613 (1992).CrossRefGoogle Scholar
4.Swain, M.V. and Mencik, J., Thin Solid Films 253 204 (1994).CrossRefGoogle Scholar
5.Lawn, B.R., J. Am. Ceram. Soc. 81 1977 (1998).CrossRefGoogle Scholar
6.Djabella, H. and Arnell, R.D., Thin Solid Films 213 205 (1992).CrossRefGoogle Scholar
7.Djabella, H. and Arnell, R.D., Thin Solid Films 223 87 (1993).CrossRefGoogle Scholar
8.Sun, Y., Bloyce, A. and Bell, T., Thin Solid Films 271 122 (1995).CrossRefGoogle Scholar
9.Jaffar, M.J., J. Mech. Phys. Solids 36 401 (1988).CrossRefGoogle Scholar
10.Yu, H.Y.Sanday, S.C. and Rath, B.B.J. Mech. Phys. Solids 38, 745 1999CrossRefGoogle Scholar
11.Yang, F., Mech. Mater. 30 275 (1998).CrossRefGoogle Scholar
12.Schwarzer, N., Richter, F. and Hecht, G., Surf. Coat. Technol. 114 292 (1999).CrossRefGoogle Scholar
13.Waters, N.E., Br. J. Appl. Phys. 16 557 (1965).CrossRefGoogle Scholar
14.Boussinesq, J., Application des Potentials à l’etude de l’équilibre et du Mouvment des Solids élastiques (Gauthier-Villars, Paris, 1885).Google Scholar
15.Timoshenko, S.P. and Goodier, J.N., Theory of Elasticity (McGraw-Hill, New York, 1951).Google Scholar
16.Stone, D.S., J. Mater. Res. 13 3207 (1998).CrossRefGoogle Scholar
17.Schwarzer, N., J. Tribol. 122 672 (2000).CrossRefGoogle Scholar
18.Hsueh, C.H., Kim, J.H. and Kim, D.K., J. Mater. Res. 18 1481 (2003).CrossRefGoogle Scholar
19.Miranda, P., Pajares, A., Guiberteau, F., Cumbrera, F.L. and Lawn, B.R., J. Mater. Res. 16 115 (2001).CrossRefGoogle Scholar
20.Hsueh, C.H. and Miranda, P., J. Mater. Res. 18 1275 (2003).CrossRefGoogle Scholar