Skip to main content
Log in

The determination of crack bridging forces

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

A method is presented for determining the bridging tractions acting on the fracture surfaces of cracks from measurements of the crack opening profile. The tractions may be expressed either as a function ϕ(x) of position in the crack or a function p(u) of the crack opening displacement. The feasibility of deducing ϕ(x) or p(u) from noisy displacement data is demonstrated by numerical simulations. It is found that the most complete information is contained in profiles of cracks growing from notches. Improved estimates of p(u) can also be found by analzying data from several cracks at different stress levels simultaneously.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D.B. Marshall and A.G. Evans, Journal of the American Ceramic Society 68 (1985) 225–231.

    Google Scholar 

  2. L.S. Sigl, P.A. Mataga, B.J. Dalgleish, R.M. McMeeking and A.G. Evans, Acta Metallurgica 36 (1988) 945–953.

    Google Scholar 

  3. D.B. Marshall, B.N. Cox and A.G. Evans. Acta Metallurgica 33 (1987) 2013–2021.

    Google Scholar 

  4. Y.-W. Mai and B.R. Lawn, Journal of the American Ceramic Society 70 (1987) 289–294.

    Google Scholar 

  5. L.R.F. Rose, International Journal of Fracture 33 (1987) 145–152.

    Google Scholar 

  6. J. Aveston, G.A. Cooper and A. Kelly, in The Properties of Fiber Composites, Conference Proceedings, National Physical Laboratory, IPC Science and Technology Press Ltd. (1971) 15–26.

  7. D.B. Marshall and B.N. Cox, Acta Metallurgica 35 (1987) 2607–2619.

    Google Scholar 

  8. D.B. Marshall and B.N. Cox, Mechanics of Materials 7 (1988) 127–133.

    Google Scholar 

  9. B.N. Cox, D.B. Marshall and M.D. Thouless, Acta Metallurgica 37 (1989) 1933–1943.

    Google Scholar 

  10. L.R.F. Rose, Journal of the Mechanics and Physics of Solids 34 (1987) 383–405.

    Google Scholar 

  11. B. Budiansky, J.W. Hutchinson and A.G. Evans, Journal of the Mechanics and Physics of Solids 34 (1986) 167–189.

    Google Scholar 

  12. B. Budiansky, J.C. Amazigo and A.G. Evans, Journal of the Mechanics and Physics of Solids 36 (1988) 167–187.

    Google Scholar 

  13. L.N. McCartney, Proceedings of the Royal Society of London, Series A 409 (1987) 329–350.

    Google Scholar 

  14. A. Kelly and L.N. McCartney, Proceedings 6th International Conference on Composite Materials, F.L. Matthews, N.C.R. Buskell and J.M. Hodgkinson (eds.), Elsevier, London (1987) 3.210–3.222.

    Google Scholar 

  15. B.N. Cox and D.B. Marshall, “Stable and Unstable Solutions for Bridged Cracks in Various Specimens,” Acta Metallurgica et Materialia, in press.

  16. V.C. Li and R.J. Ward, in Proceedings of the International Workshop on Fracture Toughness and Fracture Energy-Test Methods for Concrete and Rock, Sendai, Japan, October 1988, A.A. Mihashi (ed) Balhema, Publishers, The Netherlands (1989).

    Google Scholar 

  17. H. Tada, The Stress Analysis of Cracks Handbook, 2nd ed., Paris Productions, Inc., St. Louis, Missouri (1985).

    Google Scholar 

  18. I.N. Sneddon and M. Lowengrub, Crack Problems in the Classical Theory of Elasticity, Wiley, New York (1969).

    Google Scholar 

  19. A.N. Tihonov, Soviet Mathematics (Crovidence) 4 (1963) 1035–1038.

    Google Scholar 

  20. M. Sutcu, Acta Metallurgica 37 (1989) 651–661.

    Google Scholar 

  21. M.D. Thouless and A.G. Evans, Acta Metallurgica 36 (1988) 517–522.

    Google Scholar 

  22. R.F. Cook, C.J. Fairbanks, B.R. Lawn and Y.-W. Mai, Journal of Materials Research 2 (1987) 345–356.

    Google Scholar 

  23. D.R. Williams, D.L. Davidson and J. Lankford, Experimental Mechanics 20 (1980) 134–139.

    Google Scholar 

  24. B.N. Cox, W.L. Morris and M.R. James, in Proceedings of Nondestructive Testing and Evaluation of Advanced Materials and Composites, Colorado Springs, CO, August, 1986 (U.S. Department of Defense) 25–39.

  25. M.R. James, W.L. Morris and B.N. Cox, Experimental Mechanics 30 (1990) 60–67.

    Google Scholar 

  26. I.D. Parsons, J.F. Hall and A.J. Rosakis, “A Finite Element Investigation of the Elastostatic State Near a Three-Dimensional Edge Crack,” Caltech Report SM 86.29 (1986).

  27. J.C. Newman, Jr., NASA Langley Research Center, Hampton, VA, U.S.A., and D.E. McCabe, Materials Engineering Associates, Lanham, MD, U.S.A., private communications (1989).

  28. Z. Gao, Virginia Polytechnic Institute, Blacksburg, VA, U.S.A., and L.R.F. Rose, Aeronautical Research Laboratories, Melbourne, Australia, private communications (1989).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cox, B.N., Marshall, D.B. The determination of crack bridging forces. Int J Fract 49, 159–176 (1991). https://doi.org/10.1007/BF00035040

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00035040

Keywords

Navigation