Skip to main content
Top
Published in:
Cover of the book

2011 | OriginalPaper | Chapter

1. Contact Mechanics

Author : Anthony C. Fischer-Cripps

Published in: Nanoindentation

Publisher: Springer New York

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Footnotes
1
In this section only, δ is the indentation depth measured from the contact circle, not below the original free surface.
 
Literature
1.
go back to reference 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 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.
2.
go back to reference 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. 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.
3.
go back to reference S. Timoshenko and J.N. Goodier, Theory of Elasticity, 2nd Ed. McGraw-Hill, N.Y. 1951.MATH S. Timoshenko and J.N. Goodier, Theory of Elasticity, 2nd Ed. McGraw-Hill, N.Y. 1951.MATH
4.
go back to reference 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.CrossRef 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.CrossRef
5.
go back to reference M.M. Chaudhri, “A note on a common mistake in the analysis of nanoindentation test data”, J. Mater. Res. 16 2, 2001, pp. 336–339.CrossRef M.M. Chaudhri, “A note on a common mistake in the analysis of nanoindentation test data”, J. Mater. Res. 16 2, 2001, pp. 336–339.CrossRef
6.
go back to reference A.C. Fischer-Cripps, “The use of combined elastic modulus in depth-sensing indentation with a conical indenter,” J. Mat. Res. 18 5, 2003, pp.1043–1045.CrossRef A.C. Fischer-Cripps, “The use of combined elastic modulus in depth-sensing indentation with a conical indenter,” J. Mat. Res. 18 5, 2003, pp.1043–1045.CrossRef
7.
go back to reference Y.P. Cao, M. Dao, J. Lu, “A precise correcting method for the study of the superhard material using nanoindentation tests,” J. Mater. Res. 22 5, 2007, pp. 1255–1264.CrossRef Y.P. Cao, M. Dao, J. Lu, “A precise correcting method for the study of the superhard material using nanoindentation tests,” J. Mater. Res. 22 5, 2007, pp. 1255–1264.CrossRef
9.
go back to reference 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.CrossRefMATH 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.CrossRefMATH
10.
11.
go back to reference P.-L. Larsson, A.E. Giannakopolous, E. Soderlund, D.J. Rowcliffe and R. Vestergaard, “Analysis of Berkovich Indentation,” Int. J. Structures, 33 2, 1996, pp.221–248.CrossRefMATH P.-L. Larsson, A.E. Giannakopolous, E. Soderlund, D.J. Rowcliffe and R. Vestergaard, “Analysis of Berkovich Indentation,” Int. J. Structures, 33 2, 1996, pp.221–248.CrossRefMATH
12.
go back to reference A.C. Fischer-Cripps, Introduction to Contact Mechanics, 2nd Ed. Springer-Verlag, New York, 2007.CrossRefMATH A.C. Fischer-Cripps, Introduction to Contact Mechanics, 2nd Ed. Springer-Verlag, New York, 2007.CrossRefMATH
13.
go back to reference D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951. D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951.
14.
go back to reference 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.CrossRef 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.CrossRef
15.
go back to reference E. Meyer, “Untersuchungen über Harteprufung und Harte,” Phys. Z. 9, 1908, pp. 66–74. E. Meyer, “Untersuchungen über Harteprufung und Harte,” Phys. Z. 9, 1908, pp. 66–74.
16.
go back to reference S.L. Hoyt, “The ball indentation hardness test,” Trans. Am. Soc. Steel Treat. 6, 1924, pp. 396–420. S.L. Hoyt, “The ball indentation hardness test,” Trans. Am. Soc. Steel Treat. 6, 1924, pp. 396–420.
17.
go back to reference 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.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.
18.
go back to reference 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.CrossRef 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.CrossRef
19.
go back to reference M.T. Huber, “Contact of solid elastic bodies,” Ann. D. Physik, 14 1, 1904, pp. 153–163.CrossRefMATH M.T. Huber, “Contact of solid elastic bodies,” Ann. D. Physik, 14 1, 1904, pp. 153–163.CrossRefMATH
20.
go back to reference A.C. Fischer-Cripps, “Elastic–plastic response of materials loaded with a spherical indenter,” J. Mater. Sci. 32 3, 1997, pp. 727–736.CrossRef A.C. Fischer-Cripps, “Elastic–plastic response of materials loaded with a spherical indenter,” J. Mater. Sci. 32 3, 1997, pp. 727–736.CrossRef
21.
go back to reference S.Dj. Mesarovic and N. A. Fleck, “Spherical indentation of elastic–plastic solids,” Proc. R. Soc. A455, 1999, pp. 2707–2728. S.Dj. Mesarovic and N. A. Fleck, “Spherical indentation of elastic–plastic solids,” Proc. R. Soc. A455, 1999, pp. 2707–2728.
22.
go back to reference R. Hill, E.H. Lee and S.J. Tupper, “Theory of wedge-indentation of ductile metals,” Proc. R. Soc. A188, 1947, pp. 273–289.CrossRefMathSciNet R. Hill, E.H. Lee and S.J. Tupper, “Theory of wedge-indentation of ductile metals,” Proc. R. Soc. A188, 1947, pp. 273–289.CrossRefMathSciNet
23.
go back to reference R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 1950.MATH R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 1950.MATH
24.
go back to reference D.M. Marsh, “Plastic flow in glass,” Proc. R. Soc. A279, 1964, pp. 420–435.CrossRef D.M. Marsh, “Plastic flow in glass,” Proc. R. Soc. A279, 1964, pp. 420–435.CrossRef
25.
go back to reference 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.CrossRef 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.CrossRef
26.
go back to reference T.O. Mulhearn, “The deformation of metals by Vickers-type pyramidal indenters,” J. Mech. Phys. Solids, 7, 1959, pp. 85–96.CrossRef T.O. Mulhearn, “The deformation of metals by Vickers-type pyramidal indenters,” J. Mech. Phys. Solids, 7, 1959, pp. 85–96.CrossRef
27.
go back to reference K.L. Johnson, “The correlation of indentation experiments,” J. Mech. Phys. Sol. 18, 1970, pp. 115–126.CrossRef K.L. Johnson, “The correlation of indentation experiments,” J. Mech. Phys. Sol. 18, 1970, pp. 115–126.CrossRef
28.
go back to reference 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. 469–479.CrossRef 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. 469–479.CrossRef
29.
go back to reference 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.CrossRef 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.CrossRef
30.
go back to reference 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.CrossRef 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.CrossRef
31.
go back to reference C.M. Perrott, “Elastic–plastic indentation: Hardness and fracture,” Wear 45, 1977, pp. 293–309.CrossRef C.M. Perrott, “Elastic–plastic indentation: Hardness and fracture,” Wear 45, 1977, pp. 293–309.CrossRef
32.
go back to reference 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.CrossRef 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.CrossRef
33.
go back to reference 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.CrossRef 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.CrossRef
35.
go back to reference J.H. Ahn and D. Kwon, “Derivation of plastic stress-strain relationship from ball indentations: Examination of strain definition and pileup effect,” J. Mater. Res. 16 11, 2001, pp. 3170–3178.CrossRef J.H. Ahn and D. Kwon, “Derivation of plastic stress-strain relationship from ball indentations: Examination of strain definition and pileup effect,” J. Mater. Res. 16 11, 2001, pp. 3170–3178.CrossRef
36.
go back to reference J. Thurn, D.J. Morris, and R.F. Cook, “Depth-sensing indentation at macroscopic dimensions,” J. Mater. Res. 17 10, 2002, pp. 2679–2690.CrossRef J. Thurn, D.J. Morris, and R.F. Cook, “Depth-sensing indentation at macroscopic dimensions,” J. Mater. Res. 17 10, 2002, pp. 2679–2690.CrossRef
37.
go back to reference F. Frölich, P. Grau, and W. Grellmann, “Performance and analysis of recording microhardness tests,” Phys. Stat. Sol. (a), 42, 1977, pp. 79–89.CrossRef F. Frölich, P. Grau, and W. Grellmann, “Performance and analysis of recording microhardness tests,” Phys. Stat. Sol. (a), 42, 1977, pp. 79–89.CrossRef
38.
go back to reference 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 et al. eds., Pergammon Press, Oxford, 1982, pp. 147–157. 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 et al. eds., Pergammon Press, Oxford, 1982, pp. 147–157.
39.
go back to reference J.S. Field, “Understanding the penetration resistance of modified surface layers,” Surface and Coatings Technology, 36, 1988, pp. 817–827.CrossRef J.S. Field, “Understanding the penetration resistance of modified surface layers,” Surface and Coatings Technology, 36, 1988, pp. 817–827.CrossRef
40.
go back to reference N.A. Stilwell and D. Tabor, “Elastic recovery of conical indentations,” Phys. Proc. Soc. 78 2, 1961, pp. 169–179.CrossRefMathSciNet N.A. Stilwell and D. Tabor, “Elastic recovery of conical indentations,” Phys. Proc. Soc. 78 2, 1961, pp. 169–179.CrossRefMathSciNet
41.
go back to reference 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. 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.
42.
go back to reference B.R. Lawn and V.R. Howes, “Elastic recovery at hardness indentations,” J. Mat. Sci. 16, 1981, pp. 2745–2752.CrossRef B.R. Lawn and V.R. Howes, “Elastic recovery at hardness indentations,” J. Mat. Sci. 16, 1981, pp. 2745–2752.CrossRef
43.
go back to reference 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. 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.
44.
go back to reference J.L. Loubet, J.M. Georges, O. Marchesini, and G. Meille, “Vicker’s indentation of magnesium oxide,” J. Tribol. 106, 1984, pp. 43–48.CrossRef J.L. Loubet, J.M. Georges, O. Marchesini, and G. Meille, “Vicker’s indentation of magnesium oxide,” J. Tribol. 106, 1984, pp. 43–48.CrossRef
45.
go back to reference M.F. Doerner and W.D. Nix, “A method for interpreting the data from depth-sensing indentation instruments,” J. Mater. Res. 1 4, 1986, pp. 601–609.CrossRef M.F. Doerner and W.D. Nix, “A method for interpreting the data from depth-sensing indentation instruments,” J. Mater. Res. 1 4, 1986, pp. 601–609.CrossRef
46.
go back to reference 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.CrossRef 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.CrossRef
47.
go back to reference 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. 463–469.CrossRef 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. 463–469.CrossRef
48.
go back to reference J.S. Field and M.V. Swain, “A simple predictive model for spherical indentation,” J. Mater. Res. 8 2, 1993, pp. 297–306.CrossRef J.S. Field and M.V. Swain, “A simple predictive model for spherical indentation,” J. Mater. Res. 8 2, 1993, pp. 297–306.CrossRef
49.
go back to reference 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.CrossRef 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.CrossRef
50.
go back to reference A.G. Atkins, “Topics in indentation hardness,” Metal Science, 16, 1982, pp. 127–137.CrossRef A.G. Atkins, “Topics in indentation hardness,” Metal Science, 16, 1982, pp. 127–137.CrossRef
51.
go back to reference H.M. Pollock, “Nanoindentation”, ASM Handbook, Friction, Lubrication, and Wear Technology, 18, 1992, pp. 419–429. H.M. Pollock, “Nanoindentation”, ASM Handbook, Friction, Lubrication, and Wear Technology, 18, 1992, pp. 419–429.
52.
go back to reference J.L. Hay and G.M. Pharr, “Instrumented indentation testing,” ASM Handbook, Materials Testing and Evaluation, 8, 2000, pp. 232–243. J.L. Hay and G.M. Pharr, “Instrumented indentation testing,” ASM Handbook, Materials Testing and Evaluation, 8, 2000, pp. 232–243.
53.
go back to reference 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. 471–476. 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. 471–476.
Metadata
Title
Contact Mechanics
Author
Anthony C. Fischer-Cripps
Copyright Year
2011
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4419-9872-9_1

Premium Partners