Skip to main content
SpringerLink
Log in

Extensions of the pseudo tractions technique for friction in cracks, circular cavities and external boundaries; effect of the interactions on the homogenised stiffness

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

Abstract

This paper deals with interactions in a two-dimensional cracked and porous medium. Interactions are computed using a semi analytical method based on ‘pseudo tractions’, in order to quantify the global behaviour of cracked materials. The number of singularities induced by cracks shows that the analytical pseudo tractions based on linear elastic fracture mechanics can be used to solve problems involving interactions. It is explained how the original technique of computation of interactions between cracks can be extended to finite media containing both circular cavities and cracks, with a Coulomb model for friction in cracks. The ability of the method to give accurate results is illustrated with some examples. The effects of interactions and presence of boundaries, introduced at a mesoscale, are illustrated here by some examples considering the global stiffness of the cracked media under tensile loading. The necessity of the computation of the interactions is related to the density of the cracks. Some simple expressions a vailable in the cases of weak interactions, and allowing friction in cracks, are developed. The pseudo tractions results are compared to those given by self consistent and differential techniques. Results involving porosity and crack closure with friction were shown in a previous paper [7].

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Gambarotta and S. Lagomarsino, International Journal of Solids and Structures 30 (1993) 177–198.

    Article  Google Scholar 

  2. H.P. Yin, PhD thesis, Ecole Nationale des Ponts et Chaussées, France (1992).

  3. A. Chudnovsky, A. Dolgopolsky and M. Kachanov, International Journal of Solids and Structures 23 (1987) 1–10.

    Article  Google Scholar 

  4. Y. Benveniste, G.J. Dvorak, J. Zarzour and E.C. Wung, On interacting cracks and comples configurations in linear elastic media, Department of Civil Engineering, Rensselaer Institute, Troy, NY 12180, USA (1988).

    Google Scholar 

  5. M. Kachanov, Advances in Applied Mechanics 30 (1993) 229–445.

    Google Scholar 

  6. S. Ramtani, Y. Berthaud and J. Mazars, Nuclear Engineering and Design 133 (1992) 97–111.

    Article  Google Scholar 

  7. C. Fond, J.L. Fléjou and Y. Berthaud, European Journal of Mechanics A/Solids 14 (1995).

  8. M. Kachanov, International Journal of Fracture 28 (1985) R11-R19.

    Google Scholar 

  9. M. Kachanov, International Journal of Solids and Structures 1 (1987) 23–43.

    Article  Google Scholar 

  10. E. Montagut and M. Kachanov, International Journal of Fracture 37 (1988) R55-R62.

    Google Scholar 

  11. N.I. Muskhelishvili, Some Basics Problem of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1953).

    Google Scholar 

  12. J.W. Ju and K.H. Tseng, ASME 34 (1992) 69–82.

    Google Scholar 

  13. J.N. Goodier, ASME Transactions 55 (1933) 39–44.

    Google Scholar 

  14. L.G. Ting and Z.R. Zhong, Engineering Fracture Mechanics 35 (1990) 67–78.

    Article  Google Scholar 

  15. Y. Berthaud, C. Fond and P. Brun, Mechanics Research Communications 21 (1994) 525–533.

    Article  Google Scholar 

  16. C. Fond, PhD thesis, Université de Paris 6, France (1992).

  17. J.P. Henry and F. Parsy, Cours d'élasticité, Dunod Université (1982).

  18. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill (1951).

  19. H. Horii and S. Nemat-Nasser, International Journal of Solids and Structures 21 (1985) 731–745.

    Article  Google Scholar 

  20. Y. Belkacemi, Méthode des discontinuités de déplacement en champ complexe, Thèse de Doctorat de l'Université de Lille Flandres Artois (1990).

  21. A. Bouhaddane, Application de l'intégrale de Cauchy à la méthode des discontinuités de déplacement et autres méthodes de collocation, Thèse de Doctorat de l'Université de Lille Flandres Artois (1987).

  22. Y. Murakami, Stress Intensity Factors Handbook, Pergamon Press (1988).

  23. C.A. Brebbia, J.C.F. Telles and L.C. Wrobel, Boundary Element Technique—Theory and Applications in Engineering, Springer-Verlag (1984).

  24. R.E. Peterson, Stress Concentration Factors, John Wiley & Sons (1974).

  25. J.D. Eshelby, Proceedings of the Royal Society of London/A 241 (1957) 376–396.

    Article  Google Scholar 

  26. J. Mazars, Y. Berthaud and S. Ramtani, Engineering Fracture Mechanics 35 (1990) 629–635.

    Article  Google Scholar 

  27. M. Kachanov and J.P. Laures, International Journal of Fracture 41 (1989) 289–313.

    Article  Google Scholar 

  28. N. Laws and J.R. Brockenborough, International Journal of Solids and Structures 23 (1992) 56.

    Google Scholar 

  29. P. Brun, Private communication (1993).

  30. B. Budiansky and R. O'Conell, International Journal of Solids and structures 12 (1976) 81–97.

    Article  Google Scholar 

  31. M. S. Wu, Engineering Fracture Mechanics 48 (1994) 177–198.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Charles Sadron, 6 rue Boussingault, F-67083, Strasbourg, France

    C. Fond

  2. Laboratoire de Mécanique et Technologie, E.N.S. de Cachan/C.N.R.S./Université de Paris 6, 61, avenue du Président Wilson, F94235, Cachan, France

    Y. Berthaud

Authors
  1. C. Fond
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Berthaud
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fond, C., Berthaud, Y. Extensions of the pseudo tractions technique for friction in cracks, circular cavities and external boundaries; effect of the interactions on the homogenised stiffness. Int J Fract 74, 1–28 (1996). https://doi.org/10.1007/BF00018572

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00018572

Keywords

Search

Navigation