Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-14T18:46:21.800Z Has data issue: false hasContentIssue false
  • English
  • Français

Conformal Map on Rough Boundaries Application to Fracture

Published online by Cambridge University Press:  10 February 2011

Stéphane Roux and
Damien Vandembroucq
Stéphane Roux
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, ESPCI, 10 rue Vauquelin, 75231 Pans, France.
Damien Vandembroucq
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, ESPCI, 10 rue Vauquelin, 75231 Pans, France.
Get access

Abstract

A conformai mapping technique is presented which allows to solve efficiently harmonic and bi-harmonic problems in semi-infinite domains limited by a rough boundary. This technique is applied to obtain the statistical distribution of flux and elastic stress in the vicinity of a self-affine boundary. This computation justifies the occurence of Weibull statistics for the strength of glass fibers, with Weibull modulus depending on the roughness amplitude. Another application concerns the determination of the local mode III stress intensity factor ahead of a rough crack. Extension of the method to surface stress-corrosion, and interfacial crack propagation are discussed.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

1. Vandembroucq, D. and Roux, S., “Conformai mapping on rough boundaries I: Applications to harmonie problems”, preprint;Google Scholar
2. Vandembroucq, D. and Roux, S., “'Conformai mapping on rough boundaries II: Applications to bi-harmonic problems”, preprint;Google Scholar
3. Vandembroucq, D. and Roux, S., “Harmonic field distributions on self-affine boundaries”, preprint;Google Scholar
4. Vandembroucq, D. and Roux, S., “Mode III stress intensity factor ahead of a rough crack”, to appear in J. Mech. Phys. Sol.Google Scholar
5. Sivashinsky, G.I., Acta Astronautica, 4, 1177, (1977)Google Scholar
6. Guilloteau, E., Ph. D. dissertation, Univ. Paris-Sud, (1995)Google Scholar
7. Weibull, W., J. Appl. Mech. 18, 293, (1951)Google Scholar
8. Davidge, R. W., “Mechanical behaviour of ceramics”, Cambridge Univ. Press, (1980)Google Scholar
9. Barabási, A.L. and Stanley, H.E., “Fractal concepts in surface growth”, Cambridge Univ. Press, (1995)Google Scholar
10. Olami, Z., Galanti, B., Kuppervasser, O. and Procaccia, I., “Random noise and pole dynamics in unstable front propagation”, preprintGoogle Scholar
11. Schmittbuhl, J., Roux, S., Vilotte, J.P. and Måløy, K.J., Phys. Rev. Lett. 74, 10, 1787, (1995)Google Scholar