Skip to main content
SpringerLink
Log in

Three-dimensional contact mechanics analysis of crack problems using the boundary element method

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

Abstract

In this paper, a formulation based on the iterative-load incremental approach for the three-dimensional frictional contact mechanics analysis of fracture problems using the boundary element method (BEM), is presented. Special crack front elements are employed to provide a quick and direct means of obtaining the stress intensity factor. The veracity of the formulation is demonstrated with four crack problems. Three of these problems involve crack closure under bending loads, and the fourth is that of a pin-loaded rectangular plate with corner cracks at the pin-hole. The computed BEM solutions are compared, where possible, with those available in the literature, and there is generally good agreement between them. The numerical examples serve also to illustrate the need for a proper contact mechanics treatment to obtain accurate stress intensity factors for such problems.

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. D.S. Smith and C.W. Smith, International Journal of Fracture 6 (1970) 305–318.

    Google Scholar 

  2. P.C. Paris and H. Tada, International Journal of Fracture 11 (1975) R1070–1072.

    Article  Google Scholar 

  3. D.P. Jones and J.L. Swedlow, International Journal of Fracture 11 (1975) 897–914.

    Google Scholar 

  4. B. Fredriksson, Computers & Structures 6 (1976) 281–290.

    Article  Google Scholar 

  5. F.S. HemingJr., International Journal of Fracture 16 (1980) 298–303.

    Article  Google Scholar 

  6. R.S. Alwar and K.N.R. Nambissan, Engineering Fracture Mechanics 17 (1983) 223–333.

    Article  Google Scholar 

  7. G. Yagawa and H. Hirayama, International Journal for Numerical Methods in Engineering 20 (1984) 2175–2195.

    Article  Google Scholar 

  8. K. Kathiresan, T.M. Hsu and T.R. Brussat, Advanced Life Analysis Methods-Crack Growth Analysis Methods for Attachment Lugs, AFWAL-TR-84-3080 Report (1984).

  9. S. Thiagarajan and R.S. Alwar, Engineering Fracture Mechanics 24 (1986) 533–537.

    Article  Google Scholar 

  10. G. Karami and R.T. Fenner, International Journal of Fracture 30 (1986) 13–29.

    Google Scholar 

  11. Y.W. Kwon, Computers & Structures 32 (1989) 1439–1445.

    Article  Google Scholar 

  12. P.C. Bastias, G.T. Hahn and C.A. Rubin, Engineering Fracture Mechanics 20 (1989) 143–152.

    Article  Google Scholar 

  13. W.L. Zhang and P. Gudmundson, International Journal for Numerical Methods in Engineering 29 (1990) 847–860.

    Article  Google Scholar 

  14. S.B. Liu and C.L. Tan, Engineering Fracture Mechanics 42 (1992) 273–288.

    Article  Google Scholar 

  15. K.W. Man, M.H. Aliabadi and D.P. Rooke, in Proceedings of the 2nd International Conference on Computer Aided Assessment and Control-Localised Damage II '92, Vol. 2, M.H. Aliabadi, H. Nisitani and D.J. Cartwright (eds.) (1992) 213–227.

  16. S.B. Liu and C.L. Tan, Engineering Fracture Mechanics 48 (1994) 711–725.

    Article  Google Scholar 

  17. T. Andersson and B.G. Allan-Perrson, in The Boundary Element Method Applied to Two-dimensional Contact Problems. Chapter 5, Progress in Boundary Element Methods, Vol. II, C.A. Brebbia (ed.). Pentech Press London (1983) 136–157.

    Google Scholar 

  18. M.J. Abdulmishen, A.A. Bakr and A.P. Parker, Computers & Structures 23 (1986) 787–793.

    Article  Google Scholar 

  19. S.B. Liu, D. He and Y. Wang, in Proceedings of the International Conference on Boundary Elements Methods in Engineering, Beijing, Q.H. Du (ed.) (1986) 335–342.

  20. D.P. Gao and W.D. Wen, in Proceedings of the 3rd Japan-China Symposium on Boundary Element Methods, M. Tanaka and Q.H. Du (eds.) (1990) 135–143.

  21. F. Paris and J.A. Garrido, Engineering Analysis with Boundary Elements 6 (1989) 202–213.

    Article  Google Scholar 

  22. W.H. Chen and T.C. Chen, Computers & Structures 45 (1992) 431–438.

    Article  Google Scholar 

  23. S. Simunovic and S. Saigal, Journal of Engineering Mechanics 118 (1992) 1876–1891.

    Article  Google Scholar 

  24. B.W. Dandekar and R.J. Conant, International Journal for Numerical Methods in Engineering 33 (1992) 1513–1535.

    Article  Google Scholar 

  25. T.A. Cruse, Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, Dordrecht (1988).

    Book  Google Scholar 

  26. M.H. Aliabadi and D.P. Rooke, Numerical Fracture Mechanics, Kluwer Academic Publishers, Dordrecht (1991).

    Book  Google Scholar 

  27. A.P.S. Selvadurai and M.C. Au, in Proceeding of the 10th International Conference on BEM, BEM X, Vol. 3, C.A. Brebbia (ed.) (1988) 211–230.

  28. Z.Z. Cen, F. Qin and Q.H. Du, Acta Mechanica Solida Sinica (English Edition), 2 (1990) 189–202.

    Google Scholar 

  29. F. Paris, J.A. Garrido and A. Forces, Computers & Structures 43 (1992) 19–30.

    Article  Google Scholar 

  30. A. Forces, J.A. Garrido and F. Paris, in Proceedings of the 13th International Conference on BEM, BEM XII, C.A. Brebbia and G.S. Gipson (eds.) (1991) 663–676.

  31. A. Gakwaya, Engineering Analysis with Boundary Elements 10 (1992) 1–15.

    Article  Google Scholar 

  32. J.C. Lachat and J.O. Watson, International Journal for Numerical Methods in Engineering 10 (1976) 991–1005.

    Article  Google Scholar 

  33. F.J. Rizzo and D.J. Shippy, International Journal for Numerical Methods in Engineering 11 (1977) 1753–1768.

    Article  Google Scholar 

  34. C.L. Tan and R.T. Fenner, Proceedings of the Royal Society of London A 369 (1979) 243–260.

    Article  Google Scholar 

  35. M.L. Luchi and A. Poggialini, in Proceedings of the 5th International Conference on BEM, BEM V, C.A. Brebbia (ed.) (1983) 461–470.

  36. M.L. Luchi and S. Rizzuti, International Journal for Numerical Methods in Engineering 24 (1987) 2253–2271.

    Article  Google Scholar 

  37. Z.H. Jia, D.J. Shippy and F.J. Rizzo, International Journal for Numerical Methods in Engineering 28 (1989) 2257–2273.

    Article  Google Scholar 

  38. J.P. Benthem and W.T. Koiter, Mechanics of Fracture 1: Methods of Analysis and Solutions of Crack Problems, G.C. Sih (ed.) (1973) Chapter 3, 131–178.

  39. I.S. Raju and J.C. Newman Jr., Stress Intensity Factors for Corner Cracks at the Edge of a Hole, NASA Technical Memorandum 78728 (1978).

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Carleton University, K1S 5B6, Ottawa, Canada

    S. B. Liu & C. L. Tan

Authors
  1. S. B. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. L. Tan
    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

Liu, S.B., Tan, C.L. Three-dimensional contact mechanics analysis of crack problems using the boundary element method. Int J Fract 72, 39–67 (1995). https://doi.org/10.1007/BF00036928

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00036928

Keywords

Search

Navigation