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Spherical indentation of an elastic bilayer: A modification of the perturbation approach

Published online by Cambridge University Press:  31 January 2011

Jae Hun Kim ,
Chad S. Korach  and
Andrew Gouldstone
Jae Hun Kim
Affiliation:
Department of Materials Science and Engineering, Stony Brook University, Stony Brook, New York 11794-2275
Chad S. Korach
Affiliation:
Department of Mechanical Engineering, Stony Brook University, Stony Brook, New York 11794-2275
Andrew Gouldstone*
Affiliation:
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115-5000
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

Accurate mechanical property measurement of films on substrates by instrumented indentation requires a solution describing the effective modulus of the film/substrate system. Here, a first-order elastic perturbation solution for spherical punch indentation on a film/substrate system is presented. Finite element method (FEM) simulations were conducted for comparison with the analytic solution. FEM results indicate that the new solution is valid for a practical range of modulus mismatch, especially for a stiff film on a compliant substrate. It also shows that effective modulus curves for the spherical punch deviates from those of the flat punch when the thickness is comparable to contact size.

Keywords

Elastic propertiesThin film
Type
Articles
Information
Journal of Materials Research , Volume 23 , Issue 11 , November 2008 , pp. 2935 - 2943
Copyright
Copyright © Materials Research Society 2008

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References

REFERENCES

1Doerner, M.F., Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 1986Google Scholar
2King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, 1657 1987Google Scholar
3Jung, Y.G., Lawn, B.R., Martyniuk, M., Huang, H., Hu, X.Z.: Evaluation of elastic modulus and hardness of thin films by nanoindentation. J. Mater. Res. 19, 3076 2004CrossRefGoogle Scholar
4Gao, H.J., Chiu, C.H., Lee, J.: Elastic contact versus indentation modeling of multilayered materials. Int. J. Solids Struct. 29, 2471 1992Google Scholar
5Mencik, J., Munz, D., Quandt, E., Weppelmann, E.R., Swain, M.V.: Determination of elastic modulus of thin layers using nanoindentation. J. Mater. Res. 12, 2475 1997Google Scholar
6Xu, H.T., Pharr, G.M.: An improved relation for the effective elastic compliance of a film/substrate system during indentation by a flat cylindrical punch. Scr. Mater. 55, 315 2006CrossRefGoogle Scholar
7Perriot, A., Barthel, E.: Elastic contact to a coated half-space: Effective elastic modulus and real penetration. J. Mater. Res. 19, 600 2004Google Scholar
8Clifford, C.A., Seah, M.P.: Modelling of nanomechanical nanoindentation measurements using an AFM or nanoindenter for compliant layers on stiffer substrates. Nanotechnology 17, 5283 2006Google Scholar
9Hsueh, C.H., Miranda, P.: Master curves for Hertzian indentation on coating/substrate systems. J. Mater. Res. 19, 94 2004CrossRefGoogle Scholar
10Johnson, K.: Contact Mechanics Cambridge University Press New York 1985Google Scholar
11Pane, I., Blank, E.: Response to loading and stiffness of coated substrates indented by spheres. Surf. Coat. Technol. 200, 1761 2005Google Scholar
12Maugis, D.: Contact, Adhesion, and Rupture of Elastic Solids Springer Berlin 2000Google Scholar
13Neuber, H.: Theory of Notch Stresses—Principles for Exact Stress Calculation Springer Berlin 1937Google Scholar
14Hamilton, G.M.: Explicit equations for the stresses beneath a sliding spherical contact. Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 197, 53 1983CrossRefGoogle Scholar
15Hamilton, G.M., Goodman, L.E.: Stress field created by a circular sliding contact. J. Appl. Mech. 33, 371 1966Google Scholar
16Sneddon, I.N.: Boussinesq’s problem for a flat-ended cylinder. Proc. Cambridge Philos. Soc. 42, 60 1946Google Scholar
17Hibbitt, , Karlsson, , Sorensen, : ABAQUS Theory Manual version 6.2 Hibbitt, Karlsson and Sorensen Inc., Pawtucket, RI 2001Google Scholar
18Hsueh, C.H., 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 2004Google Scholar