Abstract
There has been considerable recent interest in the mechanical characterisation of thin film systems and small volumes of material using depth-sensing indentation tests with either spherical or pyramidal indenters. Usually, the principal goal of such testing is to extract elastic modulus and hardness of the specimen material from experimental readings of indenter load and depth of penetration. These readings give an indirect measure of the area of contact at full load, from which the mean contact pressure, and thus hardness, may be estimated. The test procedure, for both spheres and pyramidal indenters, usually involves an elastic—plastic loading sequence followed by an unloading. The validity of the results for hardness and modulus depends largely upon the analysis procedure used to process the raw data. Such procedures are concerned not only with the extraction of modulus and hardness, but also with correcting the raw data for various systematic errors that have been identified for this type of testing. The forces involved are usually in the millinewton (10−3 N) range and are measured with a resolution of a few nanonewtons (10−9 N). The depths of penetration are on the order of microns with a resolution of less than a nanometre (10−9 m). In this chapter, we consider the general principles of elastic and elastic—plastic contact and how these relate to indentations at the nanometre scale.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Hertz, “On the contact of elastic solids,” J. Reine Angew. Math. 92, 1881, pp. 156–171. Translated and reprinted in English in Hertz’s Miscellaneous Papers, Macmillan & Co., London, 1896, Ch. 5.
H. Hertz, “On hardness,” Verh. Ver. Beförderung Gewerbe Fleisses 61, 1882, p. 410. Translated and reprinted in English in Hertz’s Miscellaneous Papers, Macmillan & Co, London, 1896, Ch. 6.
A.C. Fischer-Cripps, “The use of combined elastic modulus in the analysis of depth sensing indentation data,” J. Mater. Res., 16 11, 2001, pp. 3050–3052.
I.N. Sneddon, “Boussinesq’s problem for a rigid cone,” Proc. Cambridge Philos. Soc. 44, 1948, pp. 492–507.
J.R. Barber and D.A. Billings, “An approximate solution for the contact area and elastic compliance of a smooth punch of arbitrary shape,” Int. J. Mech. Sci. 32 12, 1990, pp. 991–997.
G.G. Bilodeau, “Regular pyramid punch problem,” J. App. Mech. 59, 1992, pp. 519–523.
A.C. Fischer-Cripps, Introduction to Contact Mechanics, Springer-Verlag, New York, 2000.
D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951.
F. Auerbach, “Absolute hardness,” Ann. Phys. Chem. (Leipzig) 43, 1891, pp.61–100. Translated by C. Barus, Annual Report of the Board of Regents of the Smithsonian Institution, July 1, 1890–June 30 1891, reproduced in “Miscellaneous documents of the House of Representatives for the First Session of the Fifty-Second Congress,” Government Printing Office, Washington, D.C., 43, 1891–1892, pp.207-236.
E. Meyer, “Untersuchungen über Harteprufung und Harte,” Phys. Z. 9, 1908, pp. 66–74.
S.L. Hoyt, “The ball indentation hardness test,” Trans. Am. Soc. Steel Treat. 6, 1924, pp. 396–420.
M.C. Shaw, “The fundamental basis of the hardness test,” in The Science of Hardness Testing and its Research Applications, J.H. Westbrook and H. Conrad, Eds. American Society for Metals, Cleveland, OH, 1973, pp. 1–15.
M.V. Swain and J.T. Hagan, “Indentation plasticity and the ensuing fracture of glass,” J. Phys. D: Appl. Phys. 9, 1976, pp. 2201–2214.
M.T. Huber, “Contact of solid elastic bodies,” Ann. D. Physik, 14 1, 1904, pp. 153–163.
A.C. Fischer-Cripps, “Elastic-plastic response of materials loaded with a spherical indenter,” J. Mater. Sci. 32 3, 1997, pp. 727–736.
S.Dj. Mesarovic and N. A. Fleck, “Spherical indentation of elastic-plastic solids,” Proc. R. Soc. Lond. A455, 1999, pp. 2707–2728.
R. Hill, E.H. Lee and S.J. Tupper, “Theory of wedge-indentation of ductile metals,” Proc. R. Soc. London, A188, 1947, pp. 273–289.
R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 1950.
D.M. Marsh, “Plastic flow in glass,” Proc. R. Soc. London, A279, 1964, pp. 420–435.
L.E. Samuels and T.O. Mulhearn, “An experimental investigation of the deformed zone associated with indentation hardness impressions,” J. Mech. Phys. Solids, 5, 1957, pp. 125–134.
T.O. Mulhearn, “The deformation of metals by Vickers-type pyramidal indenters,” J. Mech. Phys. Solids, 7, 1959, pp. 85–96.
K.L. Johnson, “The correlation of indentation experiments,” J. Mech. Phys. Sol. 18, 1970, pp. 115–126.
M.C. Shaw and D.J. DeSalvo, “A new approach to plasticity and its application to blunt two dimension indenters,” J. Eng. Ind. Trans. ASME, 92, 1970, pp. 469–79.
M.C. Shaw and D.J. DeSalvo, “On the plastic flow beneath a blunt axisymmetric indenter,” J. Eng. Ind. Trans. ASME 92, 1970, pp. 480–494.
C. Hardy, C.N. Baronet, and G.V. Tordion, “The elastic-plastic indentation of a half-space by a rigid sphere,” Int. J. Numer. Methods Eng. 3, 1971, pp. 451–462.
CM. Perrott, “Elastic-plastic indentation: Hardness and fracture,” Wear 45, 1977, pp. 293–309.
S.S. Chiang, D.B. Marshall, and A.G. Evans, “The response of solids to elastic/plastic indentation. 1. Stresses and residual stresses,” J. Appl. Phys. 53 1, 1982, pp. 298–311.
S.S. Chiang, D.B. Marshall, and A.G. Evans, “The response of solids to elastic/plastic indentation. 2. Fracture initiation,” J. Appl. Phys. 53 1, 1982, pp. 312–317.
K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985.
J.B. Pethica, “Microhardness tests with penetration depths less than ion implanted layer thickness in ion implantation into metals,” Third International Conference on Modification of Surface Properties of Metals by Ion-Implantation, Manchester, England, 23-26, 1981, V. Ashworth etal. eds., Pergammon Press, Oxford, 1982, pp. 147–157.
J.S. Field, “Understanding the penetration resistance of modified surface layers,” Surface and Coatings Technology, 36, 1988, pp. 817–827.
N.A. Stillwell and D. Tabor, “Elastic recovery of conical indentations,” Phys. Proc. Soc. 78 2, 1961, pp. 169–179.
R.W. Armstrong and W.H. Robinson, “Combined elastic and plastic deformation behaviour from a continuous indentation hardness test,” New Zealand Journal of Science, 17, 1974, pp. 429–433.
B.R. Lawn and V.R. Howes, “Elastic recovery at hardness indentations,” J. Mat. Sci. 16, 1981, pp. 2745–2752.
S.I. Bulychev, V.P. Alekhin, M. Kh. Shorshorov, and A.P. Ternorskii, “Determining Young’s modulus from the indenter penetration diagram,” Zavod. Lab. 41 9, 1975, pp. 11137–11140.
J.L. Loubet, J.M. Georges, O. Marchesini, and G. Meille, “Vicker’s indentation of magnesium oxide,” J. Tribol. 106, 1984, pp. 43–48.
M.F. Doerner and W.D. Nix, “A method for interpreting the data from depth-sensing indentation instruments,” J. Mater. Res. 14, 1986, pp. 601–609.
W.C. Oliver and G.M. Pharr, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7 4, 1992, pp. 1564–1583.
T.J. Bell, A. Bendeli, J.S. Field, M.V. Swain, and E.G. Thwaite, “The determination of surface plastic and elastic properties by ultra-micro indentation,” Metrologia, 28, 1991, pp. 463–69.
J.S. Field and M.V. Swain, “A simple predictive model for spherical indentation,” J. Mater. Res. 8 2, 1993, pp. 297–306.
A.C. Fischer-Cripps, “Study of analysis methods for depth-sensing indentation test data for spherical indenters,” J. Mater. Res. 16 6, 2001, pp. 1579–1584.
A.G. Atkins, “Topics in indentation hardness,” Metal Science, 16, 1982, pp. 127–137.
H.M. Pollock, “Nanoindentation”, ASM Handbook, Friction, Lubrication, and Wear Technology, 18, 1992, pp. 419–429.
J.L. Hay and G.M. Pharr, “Instrumented indentation testing,” ASM Handbook, Materials Testing and Evaluation, 8, 2000, pp. 232–243.
S.A. Syed, K.J. Wahl, and R.J. Colton, “Quantitative study of nanoscale contact and pre-contact mechanics using force modulation,” Mat. Res. Soc. Symp. Proc. 594, 2000, pp. 471–76.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fischer-Cripps, A.C. (2002). Contact Mechanics. In: Nanoindentation. Mechanical Engineering Series. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22462-6_1
Download citation
DOI: https://doi.org/10.1007/978-0-387-22462-6_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4899-0515-4
Online ISBN: 978-0-387-22462-6
eBook Packages: Springer Book Archive