Abstract
The mechanics of crack initiation and propagation beneath an axisymmetric flat punch are investigated. The stress tensor given by Sneddon in 1946 is described. Numerical integration along stress trajectories gives the strain energy release rate as a function of both the crack length and its position relative to the indenter. Comparison with Hertzian fracture is made. The initiation of crack outside the circle of contact is shown to be due to the steepest gradient of stresses along the flaws near the circle of contact. The meaning of Auerbach's law is discussed. The Auerbach range is shown to correspond to the relatively flat maximum of the envelope of theG againstc/a curves for various starting radii. The influence of subcritical crack growth is also discussed. The model proposed in 1978 by Maugis and Barquins for kinetics of crack propagation between punches and viscoelastic solids is used. It is assumed that the static fatigue limit corresponds to the true Griffith criterion with intrinsic surface energy γ, and that the critical strain energy release rateG c corresponds to a criterion for crack speed instability and velocity jump, so that no stress corrosion is needed to explain subcritical crack growth for 2γ<G<G c. The 1971 experimental results of Mikosza and Lawn are easily interpreted by this model. Finally, experiments performed on a borosilicate glass give results that agree satisfactorily with the theory. Due to kinetic effects, an apparent surface energy of about 4.5 J m−2 is obtained, larger than the intrinsic surface energy and slightly lower than the fracture energy derived from high-speed experiments.
Similar content being viewed by others
References
F. Auerbach,Ann. Phys. Chem. 43 (1891) 61.
M. T. Huber,Ann. Physik 14 (1904) 153.
A. E. H. Love,Phil. Trans. 228 (1929) 377.
F. C. Frank andB. R. Lawn,Proc. Roy. Soc. A299 (1967) 291.
B. R. Lawn andT. R. Wilshaw,J. Mater. Sci. 10 (1975) 1049.
R. Warren,Acta Metall. 26 (1978) 1759.
F. C. Roesler,Proc. Phys. Soc B 69 (1956) 981.
C. J. Culf,J. Soc. Glass. Techn. 41 (1957) 157.
J. J. Benbow,Proc. Phys. Soc B 75 (1960) 697.
M. V. Swain andB. R. Lawn,Int. J. Fract. 9 (1973) 481.
B. R. Lawn andE. R. Fuller,J. Mater. Sci. 10 (1975) 2016.
J. S. Nadeau andA. S. Rao,J. Can. Ceram. Soc. 41 (1972) 63.
I. N. Sneddon,Proc. Camb. Phil. Soc. 42 (1946) 29.
M. Barquins andD. Maugis,J. Méch. Théor. Appl. 1 (1982) 331.
B. R. Lawn,J. Appl. Phys. 39 (1968) 4828.
S. Way,J. Appl. Mech. 7 (1940) 147.
B. R. Lawn andM. V. Swain,J. Mater. Sci. 10 (1975) 113.
G. I. Barenblatt,Adv. Appl. Mech. 7 (1962) 55.
J. R. Rice, “Fracture”, Vol. 2, edited by H. Liebovitz (Academic, New York, 1968) p. 222.
M. K. Kassir andG. C. Sih,J. Appl. Mech. 33 (1966) 601.
F. B. Langitan andB. R. Lawn,J. Appl. Phys 40 (1969) 4009.
T. R. Wilshaw,J. Phys. D: Appl. Phys. 4 (1971) 1567.
J. P. A. Tillet,Proc. Phys. Soc B 69 (1956) 47.
A. S. Argon, Y. Hori andE. Orowan,J. Amer. Ceram. Soc. 43 (1960) 86.
E. W. Sucov,ibid. 45 (1962) 214.
B. Hamilton andH. Rawson,J. Mech. Phys. Solids 18 (1970) 127.
K. L. Johnson, J. J. O'Connor andA. C. Woodward,Proc. Roy. Soc A334 (1973) 95.
H. Conrad, M. K. Keshavan andG. A. Sargent,J. Mater. Sci. 14 (1979) 1473.
H. L. Oh andI. Finnie,J. Mech. Phys. Solids 15 (1967) 401.
J. S. Nadeau,J. Amer. Ceram. Soc. 56 (1973) 467.
B. R. Lawn, T. R. Wilshaw andN. E. W. Hartley,Int. J. Fract. 10 (1974) 1.
B. D. Powell andD. Tabor,J. Phys. D: Appl. Phys. 3 (1970) 783.
Y. M. Tsai andH. Kolsky,J. Mech. Phys. Solids 15 (1967) 29.
F. C. Roesler,Proc. Roy. Soc. B69 (1956) 55.
G. M. C. Fisher,J. Appl. Phys. 38 (1967) 1781.
J. Harrison andJ. Wilks,J. Phys. D: Appl. Phys. 11 (1978) 73.
M. K. Keshavan, G. S. Sargent andH. Conrad,J. Mater. Sci. 15 (1980) 839.
J. V. Lewis andH. Rawson,Glass Technol. 17 (1976) 128.
H. Matzke, T. Inoue andR. Warren,J. Nucl. Mater. 91 (1980) 205.
H. Matzke andR. Warren,J. Mater. Sci. Lett. 1 (1982) 441.
U. C. B. O. Ejike,J. Elast. 11 (1981) 359.
D. Maugis andM. Barquins,J. Phys. D: Appl. Phys. 16 (1983) 1843.
R. E. Mould,J. Amer. Ceram. Soc. 43 (1960) 160.
R. E. Mould andR. D. Southwick,ibid. 42 (1959) 582.
E. K. Pavelchek andR. H. Doremus,J. Mater. Sci. 9 (1974) 1803.
D. N. Turner, P. D. Smith andW. B. Rotsey,J. Amer. Ceram. Soc. 50 (1967) 594.
M. M. Chaudhri andE. H. Yoffe,Phil. Mag. A44 (1981) 667.
H. Matzke,J. Mater. Sci. 15 (1980) 739.
J. A. Greenwood andJ. H. Tripp,J. Appl. Mech. 89 (1967) 153.
F. C. Yip andJ. E. S. Venart,J. Phys. D: Appl Phys. 4 (1971) 1470.
K. L. Johnson, “The mechanics of the contact between deformable bodies”, edited by A. D. De Pater and J. J. Kalker (Delft University Press, Rotterdam, 1975) p. 26.
B. D. Hughes andL. R. White,Trans. ASME 47 (1980) 194.
J. Kagami, K. Yamada andT. Hatazawa,Wear 87 (1983) 93.
F. B. Langitan andB. R. Lawn,J. Appl. Phys. 41 (1970) 3357.
A. G. Mikosza andB. R. Lawn,ibid. 42 (1971) 5540.
B. R. Lawn, “The science of hardness testing and its research applications”, edited by J. H. Westbrook and H. Conrad (ASM, Metals Park, 1973) p. 418.
D. Maugis,J. Mater. Sci. 20 (1985) in press.
D. Maugis andM. Barquins,J. Phys. D: Appl. Phys. 11 (1978) 1989.
Idem, “Adhesion and adsorption of polymers”, Part A, edited by L. H. Lee (Plenum, New York, 1980) p. 203.
A. N. Gent andJ. Schultz,J. Adhes. 3 (1972) 281.
E. H. Andrews andJ. A. Kinloch,Proc. Roy. Soc. A332 (1973) 385.
D. Maugis, “Microscopic aspects of adhesion and lubrification”, edited by J. M. Georges (Elsevier, Amsterdam, 1982) p. 221.
S. M. Wiederhorn, E. R. Fuller andR. Thomson,Met. Sci. 14 (1980) 450.
S. M. Wiederhorn,J. Amer. Ceram. Soc. 52 (1969) 99.
S. M. Wiederhorn, H. Johnson, A. M. Diness andA. H. Heuer,ibid. 57 (1974) 336.
S. M. Wiederhorn andL. H. Boltz,ibid. 53 (1970) 543.
S. M. Wiederhorn, “Fracture Mechanics of Ceramics”, Vol 2, edited by R. C. Bradt, D. P. H. Hasselman and F. F. Lange (Plenum, New York, 1974) p. 613.
A. J. Holland andW. E. S. Turner,Glass Technol. 24 (1940) 46T.
M. V. Swain, J. S. Williams, B. R. Lawn andJ. J. H. Beek,J. Mater. Sci. 8 (1973) 1153.
A. G. Metcalfe andG. K. Schmitz,Glass Technol. 13 (1972) 5.
T. P. Dabbs andB. R. Lawn,J. Amer. Ceram. Soc. 65 (1982) C37.
S. M. Wiederhorn, A. G. Evans andD. E. Roberts, “Fracture Mechanics of Ceramics”, Vol. 2, edited by R. C. Bradt, D. P. H. Hasselman and F. F. Lange (Plenum, 1974) p. 829.
L. R. F. Rose,Int. J. Fract. 17 (1981) 45.
W. E. Swindlehurst andT. R. Wilshaw,J. Maler. Sci. 11 (1976) 1653.
A. G. Evans andM. Linzer,J. Amer. Ceram. Soc. 56 (1973) 575.
A. G. Evans, M. Linzer andL. R. Russel,Mater. Sci. Engng 15 (1974) 253.
J. S. Nadeau,J. Amer. Ceram. Soc. 64 (1981) 585.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mouginot, R., Maugis, D. Fracture indentation beneath flat and spherical punches. J Mater Sci 20, 4354–4376 (1985). https://doi.org/10.1007/BF00559324
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00559324