Acta Mechanica Solida Sinica

, Volume 26, Issue 5, pp 519–535 | Cite as

Interaction of Three Parallel Cracks in Rectangular Plate under Cyclic Loads

  • Changqing Miao
  • Xiangqiao Yan


This paper presents a numerical approach for modeling the interaction between multiple cracks in a rectangular plate under cyclic loads. It involves the formulation of fatigue growth of multiple crack tips under mixed-mode loading and an extension of a hybrid displacement discontinuity method (a boundary element method) to fatigue crack growth analyses. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, remeshing of existing boundaries is not necessary for each increment of crack extension. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, the numerical approach is used to analyze the fatigue growth of three parallel cracks in a rectangular plate. The numerical results illustrate the validation of the numerical approach and can reveal the effect of the geometry of the cracked plate on the fatigue growth.


mixed-mode crack fatigue crack growth crack-tip element displacement discontinuity method 


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  1. 1.
    Ingraffea, A.R., Blandford, G. and Liggett, J.A., Automatic Modeling of Mixed-Mode Fatigue and Quasi-Static Crack Propagation Using the Boundary Element Method. 14th Natl Symp on Fracture, ASTM STP 791, 1987, 1407–1426.Google Scholar
  2. 2.
    Blandford, G.E., Ingraffea, A.R. and Liggett, J.A., Two-dimensional stress intensity factor computations using the boundary element method. Int J Num Methods Eng, 1981, 17: 387–404.CrossRefGoogle Scholar
  3. 3.
    Grestle, W.H., Finite and boundary element modeling of crack propagation in two and three-dimensions using interactive computer graphics. Ph.D Thesis, Cornell Univ, Ithaca, NY, 1986.Google Scholar
  4. 4.
    Doblare, M., Espiga, F., Garcia, L. and Alcanmd, M., Study of crack propagation in orthotropic materials by using the boundary element method. Eng. Fract. Mech., 1990, 37: 953–967.CrossRefGoogle Scholar
  5. 5.
    Aliabadi, M.H., Boundary element formulation in fracture mechanics. Applied Mechanics Review, 1997, 50: 83–96.CrossRefGoogle Scholar
  6. 6.
    Portela, A., Aliabadi, M.H. and Rooke, D.P., Dual boundary element incremental analysis of crack propagation. Int. J. Comput. Struct., 1993, 46: 237–247.CrossRefGoogle Scholar
  7. 7.
    Mi, Y. and Aliabadi, M.H., Three-dimensional crack growth simulating using BEM. Int. J. Comput. Struct., 1994, 52: 871–878.CrossRefGoogle Scholar
  8. 8.
    Mi, Y. and Aliabadi, M.H., Automatic procedure for mixed-mode crack growth analysis. Commun. Numer. Methods Eng, 1995, 11: 167–177.CrossRefGoogle Scholar
  9. 9.
    Yan, X., An efficient and accurate numerical method of SIFs calculation of a branched crack. ASME J Appl. Mech. 2005, 72(3): 330–340.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Sih, G.C. and Barthelemy, B.M., Mixed mode fatigue crack growth prediction. Engineering Fracture Mechanics, 1980, 13: 439–451.CrossRefGoogle Scholar
  11. 11.
    Erdogan, F. and Sih, G.C., On the crack extension in plates under plane loading and transverse shear. J. Basic Engineering, 1963, 85: 519–527.CrossRefGoogle Scholar
  12. 12.
    Khan, A.S. and Paul, T.K.A., New model for fatigue crack propagation in 4340 steel. Int. J. Plasticity, 1994, 10: 957–972.CrossRefGoogle Scholar
  13. 13.
    Khan, A.S. and Paul, T.K., A centrally crack thin circular disk, Part II: mixed mode fatigue crack propagation. Int. J. Plasticity, 1998, 14: 1241–1264.CrossRefGoogle Scholar
  14. 14.
    Shi, H.J., Niu, L.S., Mesmacque, G. and Wang, Z.G., Branched crack growth behavior of mixed mode fatigue for an austenitic 304L steel. Int. J. Fatigue, 2000, 22: 457–465.CrossRefGoogle Scholar
  15. 15.
    Lida, S. and Kabayashi, A.S., Crack propagation rate in 7075-T6 plates under cyclic tension and transverse shear loading. J. Basic Engineering, 1969, 91: 764–769.CrossRefGoogle Scholar
  16. 16.
    Tanaka, K., Fatigue crack propagation from a crack inclined to the cyclic tension axis. Engineering Fracture Mechanics, 1974, 6: 493–507.CrossRefGoogle Scholar
  17. 17.
    Otsoka, A., Mori, K. and Miyata, T., The condition of fatigue crack growth in mixed mode condition. Engineering Fracture Mechanics, 1975, 7: 429–439.CrossRefGoogle Scholar
  18. 18.
    Yan, X., Du, S. and Zhang, Z., Mixed-mode fatigue crack growth prediction in biaxially stretched sheets. Eng. Fract. Mech., 1992, 43 (3): 471–475.CrossRefGoogle Scholar
  19. 19.
    Charalambides, P.G. and McMeeking, R.M., Finite element method simulation of a crack propagation in a brittle microcracked solid. Mechanics of Materials, 1987, 6: 71–87.CrossRefGoogle Scholar
  20. 20.
    Yan, X., Analysis of the interference effect of arbitrary multiple parabolic cracks in plane elasticity by using a new boundary element method. Computer Methods in Applied Mechanics and Engineering, 2003, 192(47–48): 5099–5121.CrossRefGoogle Scholar
  21. 21.
    Yan, X., A numerical analysis of perpendicular cracks under general in-plane loading with a hybrid displacement discontinuity method. Mechanical Research Communications, 2004, 31(2): 175–183.CrossRefGoogle Scholar
  22. 22.
    Yan, X., An effective method of stress intensity factor calculation for cracks emanating form a triangular or square hole under biaxial loads. Fatigue and Fracture of Engineering Materials and Structures, 2003, 26: 1127–1133.CrossRefGoogle Scholar
  23. 23.
    Yan, X., A numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loads. Eng Fracture Mech., 2004, 71(11): 1615–1623.CrossRefGoogle Scholar
  24. 24.
    Yan, X., Interaction of arbitrary multiple cracks in an infinite plate. J Strain Analysis for Engineering Design, 2004, 39(3): 237–244.CrossRefGoogle Scholar
  25. 25.
    Yan, X., Analysis for a crack emanating form a corner of a square hole in an infinite plate using the hybrid displacement discontinuity method. Appl Mathematics Modeling, 2004, 28(9): 835–847.CrossRefGoogle Scholar
  26. 26.
    Yan, X., Cracks emanating from circular hole or square hole in rectangular plate in tension. Eng Fracture Mech, 2006, 73, 12: 1743–1754.CrossRefGoogle Scholar
  27. 27.
    Yan, X., Stress intensity factors for asymmetric branched cracks in plane extension by using crack-tip displacement discontinuity elements. Mechanics Research Communications, 2005, 32(4): 375–384.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Yan, X., A numerical analysis of stress intensity factors at bifurcated cracks. Engineering Failure Analysis, 2006, 13(4): 629–637.MathSciNetCrossRefGoogle Scholar
  29. 29.
    Yan, X., Microdefect interacting with a finite main crack. J Strain Analysis for Engineering Design, 2005, 40(5): 421–430.CrossRefGoogle Scholar
  30. 30.
    Yan, X., A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate. European J of Mechanics-A, 2006, 25(1): 142–153.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Crouch, S.L. and Starfield, A.M., Boundary Element Method in Solid Mechanics, with Application in Rock Mechanics and Geological Mechanics. London, George Allon & Unwin, Bonton, Sydney, 1983.zbMATHGoogle Scholar
  32. 32.
    Murakami, Y., Stress Intensity Factors Handbook, Pergamon Press, Oxford, 1987.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  1. 1.Research Laboratory for Composite MaterialsHarbin Institute of TechnologyHarbinChina

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