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Boundary integral equation fracture mechanics analysis of plane orthotropic bodies

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Abstract

In this paper, a quick and efficient means of determining stress intensity factors, K I and K II, for cracks in generally orthotropic elastic bodies is presented using the numerical boundary integral equation (BIE) method. It is based on the use of quarter-point singular crack-tip elements in the quadratic isoparametric element formulation, similar to those commonly employed in the BIE fracture mechanics studies in isotropic elasticity. Analytical expressions which enable K Iand K II to be obtained directly from the BIE computed crack-tip nodal traction, or from the computed nodal displacements, of these elements are derived. Numerical results for a number of test problems are compared with those established in the literature. They are accurate even when only a very modest number of boundary elements are used.

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References

  1. F.J. Rizzo and D.J. Shippy, Journal of Composite Materials 4 (1970) 36–61.

    Google Scholar 

  2. S.M. Vogel and F.J. Rizzo, Journal of Elasticity 3 (1973) 203–216.

    Google Scholar 

  3. G.R. Tomlin and R. Butterfield, Proceedings ASCE, 100-EM3 (1974) 511–529.

    Google Scholar 

  4. M.D. Snyder and T.A. Cruse, International Journal of Fracture 11 (1975) 315–328.

    Google Scholar 

  5. R.B. Wilson and T.A. Cruse, International Journal for Numerical Methods in Engineering 12 (1978) 1381–1397.

    Google Scholar 

  6. E. Mahajerin and D.L. Sikarskie, Journal of Composite Materials 20 (1986) 376–389.

    Google Scholar 

  7. K.S. Chan and T.A. Cruse, Engineering Fracture Mechanics 23 (1986) 863–874.

    Article  Google Scholar 

  8. M. Vable and D.L. Sikarskie, International Journal of Solids and Structures 24 (1988) 1–11.

    Article  Google Scholar 

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

    Google Scholar 

  10. J.C. Lachat and J.O. Watson, Computer Methods in Applied Mechanics and Engineering 10 (1977) 273–289.

    Article  Google Scholar 

  11. T.A. Cruse and R.B. Wilson, Nuclear Engineering and Design 46 (1978) 223–234.

    Article  Google Scholar 

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

    Google Scholar 

  13. C.L. Tan and R.T. Fenner, Proceedings Royal Society, London, A369 (1979) 243–260.

    Google Scholar 

  14. T.A. Cruse and R.B. Wilson, Boundary Integral Equation Method for Elastic Fracture Mechanics Analysis, AFOSR-TR-78-0305 Report (1977).

  15. G.E. Blandford, A.R. Ingraffea and J.A. Ligget, International Journal for Numerical Methods in Engineering 17 (1981) 387–404.

    Google Scholar 

  16. J. Martinez and J. Dominguez, International Journal for Numerical Methods in Engineering 20 (1984) 1941–1950.

    Google Scholar 

  17. Z.H. Jia, D.J. Shippy and F.J. Rizzo, International Journal for Numerical Methods in Engineering 26 (1988) 2739–2575.

    Google Scholar 

  18. C.L. Tan and Y.L. Gao, Engineering Fracture Mechanics 36 (1990) 919–932.

    Article  Google Scholar 

  19. C.L. Tan and Y.L. Gao, Computational Mechanics 7 (1991) 381–396.

    Google Scholar 

  20. C.L. Tan and Y.L. Gao, Journal of Strain Analysis 25 (1990) 197–206.

    Google Scholar 

  21. Y.L. Gao, C.L. Tan and A.P.S. Selvadurai, Computational Mechanics Communications (in press).

  22. T.A. Cruse, Mathematical Foundations of the Boundary Integral Equation Method in Solid Mechanics, AFOSR-TR-1002 Report (1977).

  23. G.C. Sih and H. Liebowitz, in Fracture — An Advance Treatise, vol. II, H. Liebowitz (ed.), Academic Press, New York (1968) 108–131.

    Google Scholar 

  24. S.G. Lekhnitskii, Theory of Elasticity of An Anisotropic Elastic Body, Holden-Day, San Francisco (1963).

    Google Scholar 

  25. B. Carnahan, H.A. Luther and J.O. Wilkes, Applied Numerical Methods, John Wiley, New York (1969).

    Google Scholar 

  26. O.L. Bowie and C.E. Freese, International Journal of Fracture 8 (1972) 49–58.

    Google Scholar 

  27. K.R. Gandhi, Journal of Strain Analysis 7 (1972) 157–162.

    Google Scholar 

  28. A.C. Kaya and F. Erdogan, International Journal of Fracture 16 (1980) 171–190.

    Article  Google Scholar 

  29. S.K. Cheong and C.S. Hong, Engineering Fracture Mechanics 31 (1988) 237–248.

    Article  Google Scholar 

Download references

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Authors and Affiliations

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

    C. L. Tan & Y. L. Gao

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  1. C. L. Tan
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  2. Y. L. Gao
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Tan, C.L., Gao, Y.L. Boundary integral equation fracture mechanics analysis of plane orthotropic bodies. Int J Fract 53, 343–365 (1992). https://doi.org/10.1007/BF00034182

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  • DOI: https://doi.org/10.1007/BF00034182

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