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Extended JKR theory on adhesive contact of a spherical tip onto a film on a substrate

Published online by Cambridge University Press:  21 October 2011

Seung Tae Choi
Seung Tae Choi*
Affiliation:
School of Mechanical Engineering, University of Ulsan, Ulsan 680-749, Republic of Korea
*
a)Address all correspondence to this author. e-mail: stchoi@ulsan.ac.kr
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Abstract

The conventional JKR theory was extended to the adhesive contact of a rigid sphere onto an elastic film perfectly bonded to a rigid substrate. An elasticity problem of axisymmetric indentation on an elastic film was revisited, in which the force–depth relations for both flat and spherical indentations were obtained in a simple form. With the obtained force–depth relations, the energy release rate at the debonding of a spherical tip from an elastic film was expressed in terms of pull-off force, elastic constants, and geometric parameters. The adhesion energy between a spherical tip and an elastic film can be measured as the critical energy release rate at the instability of debonding. This study suggests that when the critical radius of contact is larger than the thickness of an elastic film, the extended JKR theory should be used in place of the conventional JKR theory to correctly evaluate the adhesion energy between the spherical tip and the elastic film.

Keywords

AdhesionFilmNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 1: Focus Issue: Instrumented Indentation , 14 January 2012 , pp. 113 - 120
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Johnson, K.L., Kendall, K., and Robert, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. London, Ser. A 324, 301 (1971).Google Scholar
2.Kendall, K.: The adhesion and surface energy of elastic solids. J. Phys. D: Appl. Phys. 4, 1186 (1971).CrossRefGoogle Scholar
3.Derjaguin, B.V., Muller, V.M., and Toporov, Y.P.: Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53, 314 (1975).Google Scholar
4.Tabor, D.: Surface forces and surface interactions. J. Colloid Interface Sci. 58, 1 (1977).CrossRefGoogle Scholar
5.Maugis, D.: Adhesion of spheres: The JKR-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150, 243 (1992).CrossRefGoogle Scholar
6.Maugis, D.: Contact, Adhesion and Rupture of Elastic Solids (Springer Series in Solid-State Sciences, New York, 2000).CrossRefGoogle Scholar
7.Barthel, E.: Adhesive elastic contacts: JKR and more. J. Phys. D: Appl. Phys. 41, 163001 (2008).CrossRefGoogle Scholar
8.Lebedev, N.N. and Ufliand, Ia.S.: Axisymmetric contact problem for an elastic layer. J. Appl. Math. Mech. 22, 320 (1958).CrossRefGoogle Scholar
9.Dhaliwal, R.S.: Punch problem for an elastic layer overlying an elastic foundation. Int. J. Eng. Sci. 8, 273 (1970).Google Scholar
10.Hayes, W.C., Keer, L.M., Herrmann, G., and Mockros, L.F.: A mathematical analysis for indentation tests of articular cartilage. J. Biomech. 5, 541 (1972).Google Scholar
11.Yu, 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).Google Scholar
12.Yang, F.: Indentation of an incompressible elastic film. Mech. Mater. 30, 275 (1998).CrossRefGoogle Scholar
13.Yang, F.: Thickness effect on the indentation of an elastic layer. Mater. Sci. Eng., A 358, 226 (2003).CrossRefGoogle Scholar
14.Choi, S.T., Lee, S.R., and Earmme, Y.Y.: Measurement of time-dependent adhesion between a polymer film and a flat indenter tip. J. Phys. D: Appl. Phys. 41, 074023 (2008).CrossRefGoogle Scholar
15.Mary, P., Chateauminois, A., and Fretigny, C.: Deformation of elastic coatings in adhesive contacts with spherical probes. J. Phys. D: Appl. Phys. 39, 3665 (2006).CrossRefGoogle Scholar
16.Sridhar, I., Johnson, K.L., and Fleck, N.A.: Adhesion mechanics of the surface force apparatus. J. Phys. D: Appl. Phys. 30, 1710 (1997).CrossRefGoogle Scholar
17.Johnson, K.L. and Sridhar, I.: Adhesion between a spherical indenter and an elastic solid with a compliant elastic coating. J. Phys. D: Appl. Phys. 34, 683 (2001).CrossRefGoogle Scholar
18.Sridhar, I. and Johnson, K.L.: On the adhesion mechanics of multi-layer elastic systems. Surf. Coat. Tech. 167, 181 (2003).CrossRefGoogle Scholar
19.Sridhar, I., Zheng, Z.W., and Johnson, K.L.: A detailed analysis of adhesion mechanics between a compliant elastic coating and a spherical probe. J. Phys. D: Appl. Phys. 37, 2886 (2004).CrossRefGoogle Scholar
20.Gladwell, G.M.L.: Contact Problems in the Classical Theory of Elasticity (Sijthoff & Noordhoff International Publishers, The Netherlands, 1980).Google Scholar
21.Sneddon, I.N.: The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
22.Hertz, H. R.: Über die Berührung fester elastischer Körper (On the contact of elastic solids). J. Reine Angew. Math. 92, 156 (1882).Google Scholar
23.Maugis, D. and Barquins, M.: Fracture mechanics and the adherence of viscoelastic bodies. J. Phys. D: Appl. Phys. 11, 1989 (1978).CrossRefGoogle Scholar
24.Christensen, R.M.: Theory of Viscoelasticity (Academic Press, New York, 1982).Google Scholar
25.Graham, G.A.C.: The correspondence principle of linear viscoelasticity theory for mixed boundary value problems involving time-dependent boundary regions. Q. Appl. Math. 26, 167 (1968).CrossRefGoogle Scholar