Abstract
The indentation strength of brittle solids is traditionally characterized by Auerbach's law, which predicts a linear relationship between the load required to initiate a Hertzian cone crack and the radius of a spherical indentor. This paper reviews both the energy balance and flaw statistical explanations of Auerbach's law. It is shown that Auerbach's law in the strictest sense only applies to well-abraded specimens. A novel application of Weibull statistics is presented which allows the distribution of fracture loads to be predicted for any specimen surface condition for a given indentor size. The indentation strength of a brittle solid, for both spherical and cylindrical indentors, is shown to be influenced by both its surface flaw statistics and the degree of interfacial friction. It is observed that the indentation strength of soda-lime glass is increased by a factor of about three times that expected for frictionless contact, and that for a fully bonded indentor, conical fractures cannot occur.
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H. Hertz,J. Reine Angew. Math. 92 (1881) 156; translated and reprinted in English in “Hertz's Miscellaneous Papers” (Macmillan, New York, 1896) Ch. 5.
Idem., Verhandlungen des Vereins zur Beforderung des Gewerbe Fleisses 61 (1882) 449; translated and reprinted in English in “Hertz's Miscellaneous Papers” (Macmillan, New York, 1896) Ch. 6.
Auerbach,Ann. Physik (Leipzig) 43 (1891) 61.
A. A. Griffith,Phil. Trans. R. Soc. A221 (1920) 163.
B. Hamilton andR. Rawson,J. Mech. Phys. Solids 18 (1970) 127.
F. C. Frank andB. R. Lawn,Proc. R. Soc. A229 (1967) 291.
R. Mouginot andD. Maugis,J. Mater. Sci. 20 (1985) 4354.
W. Weibull, “A Statistical Theory of the Strength of Materials”, Handlinger Nr 151 (Ingenious Vetenskaps Akademins, Stockholm, 1939).
K. L. Johnson, J. J. O'Connor andA. C. Woodward,Proc. R. Soc. A334 (1973) 95.
G. R. Irwin, in “Handbuch der Physik”6 (Springer, Berlin 1958) p. 551.
S. W. Freiman, T. L. Baker andJ. B. Wachtman Jr, in “Strength of Inorganic Glass”, edited by C. R. Kurkjian (Plenum Press, New York, 1985) p. 597.
H. L. Oh andI. Finnie,J. Mech. Solids 15 (1967) 401.
F. B. Langitan andB. R. Lawn,J. Appl. Phys. 40 (1969) 4009.
I. A. Sneddon,Proc. Camb. Philos. Soc. 42 (1946) 29.
M. Barquins andD. Maugis,J. Mecan. Theor. Appliq. 1 (1982) 331.
W. G. Brown, “A practicable formulation for the strength of glass and its special application to large plates”, Publication NRC 14372 (National Research Council of Canada, Ottawa, 1974).
W. L. Beason, “A Failure Prediction Model for Window Glass”, Institute for Disaster Research, Texas Tech University, Lubbock, Texas, NTIS Accession no. PB81-148421 (1980).
A. S. Argon, Y. Hori andE. Orowan,J. Am. Ceram. Soc. 43 (1960) 86.
D. A. Spence,J. Elast. 5 (1975) 297.
X.-Z. Hu, B. Cotterell andY.-W. Mai,Philos. Mag. Lett. 57(2) (1988) 69.
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Fischer-Cripps, A.C., Collins, R.E. The probability of hertzian fracture. J Mater Sci 29, 2216–2230 (1994). https://doi.org/10.1007/BF01154702
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DOI: https://doi.org/10.1007/BF01154702