Structural Engineering and Mechanics

Techno-Press (테크노프레스)
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T-stress solutions for cracks in rectangular plates with multiple holes

  • Yu, Jackie (Dept. of Mechanical and Aerospace Engineering, Carleton University) ;
  • Wang, Xin (Dept. of Mechanical and Aerospace Engineering, Carleton University) ;
  • Tan, Choon-Lai (Dept. of Mechanical and Aerospace Engineering, Carleton University)
  • Received : 2006.09.08
  • Accepted : 2007.02.08
  • Published : 2007.07.30
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Abstract

The elastic T-stress is increasingly being recognized as an important second parameter to the stress intensity factor for fracture and fatigue assessments. In this paper, the mutual or M-contour integral approach is employed in conjunction with the Boundary Element Method (BEM) to determine the numerical T-stress solutions for cracks in plates with multiple holes. The problems investigated include plates of infinite width with multiple holes at which single or double, symmetric cracks have grown from. Comparisons of these results are also made with the corresponding solutions of finite plates with a single hole. For completeness, stress intensity factor solutions for the cracked geometries analyzed are presented as well. These results will be useful for failure assessments using the two-parameter linear elastic fracture mechanics approach.

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References

  1. Ainsworth, R.A., Bannister, A.C. and Zerbst, U. (2002), 'An overview of the european flaw assessment procedure sintap and its validation', Int. J. Pressure Vessel & Piping, 77, 869-876
  2. Ainsworth, R.A., Sattari-Far, I., Sherry, A.H., Hooten, D.G. and Hadley, I. (2000), 'Methods of including constraint effects within SINTAP procedures', Eng. Fract. Mech., 67, 563-571 https://doi.org/10.1016/S0013-7944(00)00074-6
  3. Aliabadi, M.H. and Rooke, D.P. (1986), Numerical Fracture Mechanics. Kluwer Academic Publishers, Dordrecht
  4. Betegon, C. and Hancock, J.W. (1991), 'Two-parameter characterization of elastic-plastic crack tip field', J. Appl. Mech., ASME, 58, 104-110 https://doi.org/10.1115/1.2897135
  5. Bilby, B.A., Cardew, G.E., Goldthorpe, M.R. and Howard, I.C. (1986), 'A finite element investigation of the effect of specimen geometry on the fields of stress and strains at the tips of stationary cracks', In: Size Effects in Fracture, Mechanical Engineering Publications, London, 37-46
  6. Broberg, K.B. (2004), 'A note on T-stress determination using dislocation arrays', Int. J. Fracture, 131, 1-14 https://doi.org/10.1007/s10704-004-3637-5
  7. Du, Z.Z. and Hancock, J.W. (1991), 'The effect of non-singular stresses on crack tip constraint', J. Mech. Physics Solids, 39, 555-567 https://doi.org/10.1016/0022-5096(91)90041-L
  8. Kfouri, A.P. (1986), 'Some evaluations of the elastic T-stress using Eshelby's method', Int. J. Fract., 20, 301-315
  9. Larsson, S.G and Carlsson, A.J. (1973), 'Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack-tips in elastic-plastic materials', J. Mech. Physics Solids, 21, 263-277 https://doi.org/10.1016/0022-5096(73)90024-0
  10. Lewis, T. (2005), 'T-stress solutions for cracks at notches and in cylinders', M.A.Sc. Thesis, Carleton University, Ottawa, ON, Canada
  11. Li, J., Tan, C.L. and Wang, X. (2004), 'T-stress solutions for a radial edge crack in a thick-walled cylinder by the boundary element method', In: Leitao, V.M.A. and Aliabadi, M.H. (eds.) Advances in Boundary Element Techniques V, Proceedings of BETEQ 2004 Conference, Lisbon, EC Ltd., U.K., 141-146
  12. Murakami, Y. (2003), Stress Intensity Factors Handbook. Pergamon Press, Elmsford, New York
  13. Rice, J.R. (1974), 'Limitations to small scale yielding approximation for crack tip plasticity', J. Mech. Physics Solids, 22, 17-26 https://doi.org/10.1016/0022-5096(74)90010-6
  14. Rooke, D.P. and Cartwright, D.J. (1976), Compendium of Stress Intensity Factors. Hillington Press, Uxbridge, Middx (UK)
  15. Roychowdhury, S. and Dodds, R.H. (2004), 'Effects of T-stress on fatigue crack closure in 3-D small scale yielding', Int. J. Solids Struct., 41, 2581-2606 https://doi.org/10.1016/j.ijsolstr.2003.11.004
  16. Shah, P.D., Tan, C.L. and Wang, X. (2005), 'T-stress solutions for two-dimensional crack problems in anisotropic elasticity using the boundary element method', Fatigue Fract. Engng. Mater. Struct., 29, 343-356
  17. Sladek, J., Sladek, V. and Fedelinski, P. (1997), 'Contour integrals for mixed-mode crack analysis: effect of nonsingular terms', Theo. Appl. Fract. Mech., 27, 115-127 https://doi.org/10.1016/S0167-8442(97)00013-X
  18. Tong, J. (2002), 'T-stress and its implications for crack growth', Eng. Fract. Mech., 69, 1325-1337 https://doi.org/10.1016/S0013-7944(02)00002-4
  19. Wang, X., Lewis, T. and Bell, R. (2006), 'Estimations of the T-stress for small cracks at notches', Eng. Fract. Mech., 73, 366-375 https://doi.org/10.1016/j.engfracmech.2005.06.009
  20. Williams, M.L. (1957), 'On the stress distribution at the base of a stationary crack', J. Appl. Mech., ASME, 24, 109-114
  21. Yu, J., Tan, C.L. and Wang, X. (2006), 'T-stress solutions for cracks emanating from a circular hole in a finite plate', Int. J. Fract., 140, pp. 293-298 https://doi.org/10.1007/s10704-006-0110-7

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