DOI QR코드

DOI QR Code

Energy release rate for kinking crack using mixed finite element

  • Salah, Bouziane (Department of Civil Engineering, University of 20 August 1955 Skikda) ;
  • Hamoudi, Bouzerd (Department of Civil Engineering, University of 20 August 1955 Skikda) ;
  • Noureddine, Boulares (Department of Civil Engineering, University of 20 August 1955 Skikda) ;
  • Mohamed, Guenfoud (Laboratory of Civil Engineering and Hydraulics, University of Guelma)
  • 투고 : 2013.12.27
  • 심사 : 2014.03.20
  • 발행 : 2014.06.10

초록

A numerical method, using a special mixed finite element associated with the virtual crack extension technique, has been developed to evaluate the energy release rate for kinking cracks. The element is two dimensional 7-node mixed finite element with 5 displacement nodes and 2 stress nodes. The mixed finite element ensures the continuity of stress and displacement vectors on the coherent part and the free edge effect. This element has been formulated starting from a parent element in a natural plane with the aim to model different types of cracks with various orientations. Example problems with kinking cracks in a homogeneous material and bimaterial are presented to assess the computational accuracies.

키워드

참고문헌

  1. Amestoy, M. and Leblond, J.B. (1992), "Crack paths in plane situations-II. Detailed form of expansion of the stress intensity factors", Int J. Solid Struct., 29, 465-501. https://doi.org/10.1016/0020-7683(92)90210-K
  2. Baker, M. (2008), "Finite element crack propagation calculation using trial cracks", Comput. Mater. Sci., 43, 179-183. https://doi.org/10.1016/j.commatsci.2007.07.027
  3. Baker, M. (2009), "Simulation of crack propagation in mixed mode and at biomaterial interfaces using trial cracks", Comput Mater. Sci., 45, 680-683. https://doi.org/10.1016/j.commatsci.2008.05.025
  4. Beghini, M, Benedetti, M., Fontanari, V. and Monelli, B.D. (2012), "Stress intensity factors of inclined edge cracks: A simplified approach", Eng. Fract Mech. , 81, 120-129. https://doi.org/10.1016/j.engfracmech.2011.11.005
  5. Bildy, B.A. (1975), "The crack with a kinked tip", Int. J. Fract. Mech., 11, 708-712. https://doi.org/10.1007/BF00116380
  6. Blonco, C, Martinez-Esnaola, J.M. and Atkinson, C. (1998), "Kinked cracks in an anisotropic elastic materials", Int. J. Fract., 93, 387-407. https://doi.org/10.1023/A:1007475627402
  7. Boulenouar, A, Benseddiq, N. and Mazari, M. (2013), "Strain energy density prediction of crack propagation for 2D linear elastic materials", Theor. Appl. Fract. Mech., 67-68, 29-37. https://doi.org/10.1016/j.tafmec.2013.11.001
  8. Bouzerd, H. (1992), "Element fini mixte pour interface coherente ou fissuree", These de doctorat en Genie Civil, Universite Claude Bemard Lyon I, France.
  9. Bouzerd, H., Boulares, N. and Bouchair, A (2011), "Un element fini mixte pour le calcul du taux de restitution d'energie du coudage (kinking) d'une fissure", XXIXe Rencontres Universitaires de Genie Civil, Tlemcen, Algerie.
  10. Bouziane, S., Bouzerd, H. and Guenfoud, M. (2009), "Mixed finite element for modelling interfaces", Euro. J. Comput. Mech., 18(2), 155-175. https://doi.org/10.3166/ejcm.18.155-175
  11. Chatterjee, S.N. (1975), "The stress field in the neighbour hood of a branched crack in a infinite elastic sheet", Int J. Solid Struct., 11, 512-538.
  12. Cotterel, B. and Rice, J.R (1980), "Slightly curved or kinking cracks", Int. J. Fract., 16, 155-159. https://doi.org/10.1007/BF00012619
  13. Hayashi, K. and Nemat-Nasser, S. (1981), "Energy release rate and crack kinking under combined loading", J. Appl. Mech., 13, 520-524.
  14. He, M. and Hutchinson, J.W (1989), "Kinking of crack out of an interface", J. Appl. Trans. ASME, 56(2), 270-278 https://doi.org/10.1115/1.3176078
  15. Hellen, T.K (1975), "On the method of virtual crack extensions", Int J. Numer. Meth. Eng, 9(1),187-208. https://doi.org/10.1002/nme.1620090114
  16. Jakobsen, J, Andreasen, J.H. and Bozhevolnaya, E. (2008), "Crack kinking of delamination at an inclined core junction interface in sandwich beam", Eng. Fract. Mech., 75, 4759-4773. https://doi.org/10.1016/j.engfracmech.2008.06.034
  17. Khrapkov, A.A. (1971), "The first problem for a notch at the apex of an infinite wedge", Int. J. Fract. Mech., 7,373-382.
  18. Li, D.F, Li, C.F, Qing, H. and Lu, J. (2010), "The elastic T-stress for slightly curved or kinked cracks", Int. J. Solid Struct., 47, 1753-1763. https://doi.org/10.1016/j.ijsolstr.2010.02.023
  19. Lo, K.K. (1978), "Analysis of branched cracks", J. Appl. Mech., 45, 797-802. https://doi.org/10.1115/1.3424421
  20. Maiti, S.K. (1990), "Finite element computation of strain energy release rate for kinking of a crack", Int. J. Fract., 43, 161-174. https://doi.org/10.1007/BF00018339
  21. Marsavina, L. and Sadowski, T. (2009), "Kinked crack at a bimaterial ceramic interface-numerical determination of fracture parameters", Comput. Mater. Sci., 44, 941-950. https://doi.org/10.1016/j.commatsci.2008.07.005
  22. Melin, S. (1986), "On singular integral equations for kinked cracks", Int J. Fract, 30, 57-65.
  23. Parks, D.M (1974), "A stiffness derivative finite element technique for determination of elastic crack tip stress intensity factors", Int. J. Fract., 10(4),487-502. https://doi.org/10.1007/BF00155252
  24. Petit, C (1990), "Modelisation des milieux composites multicouches fissures par la mecanique de la rupture", These de doctorat d'universite, Universite Blaise Pascal, France.
  25. Theocaris, P.S. and Makrakis, G.N. (1986), "The kinked crack solved by Mellin transform", J. Elasticity, 16, 393-411. https://doi.org/10.1007/BF00041764
  26. Theocaris, P.S. and Makrakis, G.N. (1987), "Crack kinking in anti-plane shear solved by Mellin transform", Int. J. Fract, 34, 251-262. https://doi.org/10.1007/BF00013081
  27. Vitek, V. (1977), "Plane strain intensity factors for branched cracks", Int. J. Fract., 13,481-501.
  28. Xie, D., Waas, A.M., Shahwan, K.W., Schroedre, J.A. and Boeman, R.G. (2004), "Computation of energy release rates for kinking cracks based on virtual crack closure technique", CMES, 6(6), 515-524.

피인용 문헌

  1. Evaluation of energy release rate of composites laminated with finite element method vol.55, pp.1, 2015, https://doi.org/10.12989/sem.2015.55.1.191
  2. Mixed Finite Element for Kinking Crack Analysis in an Orthotropic Media vol.33, pp.None, 2014, https://doi.org/10.1016/j.prostr.2021.10.110