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A general relation for contact stiffness including adhesion in indentation analysis

Published online by Cambridge University Press:  02 June 2011

Pin Lu ,
Yong L. Foo ,
Lu Shen ,
Davy W.C. Cheong  and
Sean J. O’Shea
Pin Lu*
Affiliation:
Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), Singapore 117602
Yong L. Foo
Affiliation:
Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), Singapore 117602
Lu Shen
Affiliation:
Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), Singapore 117602
Davy W.C. Cheong
Affiliation:
Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), Singapore 117602
Sean J. O’Shea
Affiliation:
Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), Singapore 117602
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

The Maugis–Barquins (MB) solutions for the adhesive contact between an axisymmetric indenter and an elastic half-space are modified by incorporating the interfacial energy defined by the real area of contact. With the modified MB solutions, general relations for contact stiffness including adhesive effects in indentation analysis are derived. Numerical calculations showed that the difference in expected stiffness for the modified MB model compared to the standard MB results can be significant at low loads of interest in atomic force microscopy measurements and also for indentation tests at high load if the interfacial energy is large (∼0.1 J/m2) and the material is soft (Young’s modulus ≤100 MPa).

Keywords

AdhesionElastic propertiesNano-indentation
Type
Articles
Information
Journal of Materials Research , Volume 26 , Issue 11 , 14 June 2011 , pp. 1406 - 1413
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Pharr, G.M., Oliver, W.C., and Brotzen, F.R.: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613 (1992).CrossRefGoogle Scholar
2.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
3.Schwarz, U.D.: A generalized analytical model for the elastic deformation of an adhesive contact between a sphere and a flat surface. J. Colloid Interface Sci. 261, 99 (2003).CrossRefGoogle Scholar
4.Ebenstein, D.M. and Pruitt, L.A.: Nanoindentation of biological materials. Nano Today. 1, 26 (2006).CrossRefGoogle Scholar
5.Cao, Y.F., Yang, D.H., and Soboyejoy, W.: Nanoindentation method for determining the initial contact and adhesion characteristics of soft polydimethylsiloxane. J. Mater. Res. 20, 2004 (2005).Google Scholar
6.Johnson, K.L., Kendall, K., and Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. London, Ser. A 324, 301 (1971).Google Scholar
7.Barthel, E.: Adhesive elastic contacts: JKR and more. J. Phys. D: Appl. Phys. 41, 163001 (2008).Google Scholar
8.Maugis, D. and Barquins, M.: Adhesive contact of sectionally smooth-ended punches on elastic half-spaces: Theory and experiment. J. Phys. D: Appl. Phys. 16, 1843 (1983).CrossRefGoogle Scholar
9.Maugis, D.: Adhesion of spheres: The JKR-DMT transition using a Dugdale model. J. Colloid Interface Sci. 150, 243 (1992).Google Scholar
10.Maugis, D.: Contact, Adhesion and Rupture of Elastic Solids (Springer, Heidelberg, 2000).Google Scholar
11.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).Google Scholar
12.Yang, F.Q.: Effect of adhesion energy on the contact stiffness in nanoindentation. J. Mater. Res. 21, 2683 (2006).Google Scholar
13.Sirghi, L. and Rossi, F.: Adhesion and elasticity in nanoscale indentation. Appl. Phys. Lett. 89, 243118 (2006).CrossRefGoogle Scholar
14.Maugis, D. and Barquins, M.: Fracture mechanics and the adherence of viscoelastic bodies. J. Phys. D: Appl. Phys. 11, 1989 (1978).CrossRefGoogle Scholar
15.Tabor, D.: Surface forces and surface interactions. J. Colloid Interface Sci. 58, 2 (1977).Google Scholar
16.Lawn, B.: Fracture of Brittle Solids, 2nd ed. (Cambridge University Press, Cambridge, 1993).Google Scholar
17.Vallet, D. and Barquins, M.: Adhesive contact and kinetics of adherence if a rigid conical punch on an elastic half-space (natural rubber). Int. J. Adhes. Adhes. 22, 41 (2002).CrossRefGoogle Scholar
18.Kendall, K.: The adhesion and surface energy of elastic solids. J. Phys. D: Appl. Phys. 4, 1186 (1971).Google Scholar
19.Yang, F.Q.: Thickness effect on the indentation of an elastic layer. Mater. Sci. Eng., A 358, 226 (2003).Google Scholar
20.Yang, F.Q.: Adhesive contact between a rigid axisymmetric indenter and an incompressible elastic thin film. J. Phys. D: Appl. Phys. 35, 2614 (2002).Google Scholar
21.Hertz, H.: On the contact of elastic solids, in Miscellaneous Papers by Heinrich Hertz, English translated by Jones, D.E. and Schott, G.A. (Macmillan and Co., Ltd., new York, 1896), p. 146.Google Scholar
22.Fischer-Cripps, A.C.: Review of analysis and interpretation of nanoindentation test data. Surf. Coat. Tech. 200, 4153 (2006).CrossRefGoogle Scholar
23.Olah, A. and Vancso, G.J.: Characterization of adhesion at solid surfaces: Development of an adhesion-testing device. Eur. Polym. J. 41, 2803 (2005).CrossRefGoogle Scholar
24.Korsunsky, A.M.: The influence of punch blunting on the elastic indentation response. J. Strain Anal. Eng. Des. 36, 391 (2001).Google Scholar
25.Dimitriadis, E.K., Horkay, F., Maresca, J., Kachar, B., and Chadwick, R.S.: Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys. J. 82, 2798 (2002).Google Scholar
26.Withers, J.R. and Aston, D.E.: Nanomechanical measurements with AFM in the elastic limit. Adv. Colloid Interface Sci. 120, 57 (2006).Google Scholar