Advertisement

Appendices 1–7

  • Anthony C. Fischer-CrippsEmail author
Chapter
Part of the Mechanical Engineering Series book series (MES)

Abstract

The methods of analysis of nanoindentation test data rely heavily on the elastic unloading response of the system. It is of interest therefore to have some appreciation of the equations for elastic contact and the associated indentation stress fields. The following assumptions are an essential component of the analytical equations:
  • The radii of curvature of the contacting bodies are large compared with the radius of the circle of contact.

  • The dimensions of each body are large compared with the radius of the circle of contact. This allows indentation stresses and strains to be considered independently of those arising from the geometry, method of attachment, and boundaries of each solid.

  • The contacting bodies are in frictionless contact. That is, only a normal pressure is transmitted between the indenter and the specimen.

Keywords

Plastic Zone Contact Radius Spherical Indenter Thermal Drift Indentation Modulus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    A.C. Fischer-Cripps, Introduction to Contact Mechanics, 2nd Ed. Springer-Verlag, New York,2007.CrossRefzbMATHGoogle Scholar
  2. 2.
    J.E. Lennard-Jones and B.M. Dent, “Cohesion at a Crystal Surface,” Trans. Faraday Soc. 24, 1928, pp. 92–108.CrossRefGoogle Scholar
  3. 3.
    J.N. Israelachvili, Intermolecular and Surface Forces, 2nd Ed. 1992, Academic Press, London.Google Scholar
  4. 4.
    R.S. Bradley, “The cohesive force between solid surfaces and the surface energy of solids,” Phil. Mag. 13, 1932, pp. 853–862.zbMATHGoogle Scholar
  5. 5.
    B.V. Derjaguin, “Theorie des Anhaftens kleiner Teilchen,” Koll. Z. 69, 1934, pp. 155–164.CrossRefGoogle Scholar
  6. 6.
    B.V. Derjaguin, V.M. Muller, and Y.P. Toporov, “Effect of contact deformations on the adhesion of particles,” J. Coll. Interf. Sci. 53, 1975, pp. 314–326.CrossRefGoogle Scholar
  7. 7.
    K.L. Johnson, K. Kendall, and A.D. Roberts, “Surface energy and the contact of elastic solids,” Proc. R. Soc. A324, 1971, pp. 303–313.Google Scholar
  8. 8.
    K.L. Johnson, “Adhesion and Friction between a smooth elastic spherical asperity and a plane surface,” Proc. R. Soc. A453, 1997, pp. 163–179.CrossRefGoogle Scholar
  9. 9.
    K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge,1985.CrossRefzbMATHGoogle Scholar
  10. 10.
    J.A. Greenwood, “Contact of elastic spheres,” Proc. R. Soc. A453, 1997, pp. 1277–1297.CrossRefMathSciNetGoogle Scholar
  11. 11.
    V.M. Muller, V.S. Yushenko, and B.V. Derjaguin, “On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane,” J. Coll. Interf. Sci. 77, 1980, pp. 91–101.CrossRefGoogle Scholar
  12. 12.
    D. Maugis, “Adhesion of spheres: the JKR-DMT transition using a Dugdale model,” J. Coll. Interf. Sci. 150, 1992, pp. 243–269.CrossRefGoogle Scholar
  13. 13.
    N.A. Burnham and R.J. Colton, “Force Microscopy,” in Scanning Tunneling Microscopy and Spectroscopy: Theory, Techniques and Applications, 1993, D.A. Bonnell, ed., VCH Publishers, New York.Google Scholar
  14. 14.
    K.N.G. Fuller and D. Tabor, “The effect of surface roughness on the adhesion of elastic solids,” Proc. R. Soc. A324, 1975, pp. 327–342.CrossRefGoogle Scholar
  15. 15.
    D. Maugis, “On the contact and adhesion of rough surfaces,” J. Adhesion Sci. and Tech. 10, 1996, pp.161–175.CrossRefGoogle Scholar
  16. 16.
    K.L. Johnson, “Mechanics of adhesion,” Tribology International, 31 8, 1998, pp. 413–418.CrossRefGoogle Scholar
  17. 17.
    F.P. Bowden and D. Tabor, Friction and Lubrication of Solids, Clarendon Press, Oxford,1950.Google Scholar
  18. 18.
    J.F. Archard, “Elastic deformation and the laws of friction,” Proc. R. Soc. A243, 1957, pp. 190–205.CrossRefGoogle Scholar
  19. 19.
    K.L. Johnson, “The contribution of micro/nano-tribology to the interpretation of dry friction,” Proc. Instn. Mech. Engrs. 214 C, 2000, pp. 11–22.CrossRefGoogle Scholar
  20. 20.
    A.C. Fischer-Cripps, “The role of internal friction in indentation damage in a mica-containing glass-ceramic,” J. Am. Ceram. Soc. 84 11, 2001, pp. 2603–2606.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fischer-Cripps Laboratories Pty Ltd.Killarney HeightsAustralia

Personalised recommendations