Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Multiple unequal cracks between an FGM orthotropic layer and an orthotropic substrate under mixed mode concentrated loads

  • M. Hassani (Department of Mechanical Engineering, Doroud Branch, Islamic Azad University) ;
  • M.M. Monfared (Department of Mechanical Engineering, Hashtgerd Branch, Islamic Azad University) ;
  • A. Salarvand (Department of Mechanical Engineering, Doroud Branch, Islamic Azad University)
  • Received : 2023.01.09
  • Accepted : 2023.04.15
  • Published : 2023.05.25
⟨ Previous Next ⟩

Abstract

In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

Keywords

References

  1. Ayatollahi, M. and Monfared, M.M. (2012), "Anti-plane transient analysis of planes with multiple cracks", Mech. Mater., 50, 36-46 .https://doi.org/10.1016/j.mechmat.2012.03.002.
  2. Ayatollahi, M., Monfared, M.M. and Nourazar, M. (2017), "Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane", J. Intel. Mater. Syst. Struct., 28(19), 2823-2834 . https://doi.org/10.1177/1045389X17698593.
  3. Bagheri, R. and Monfared, M.M. (2018), "Magneto-electro-elastic analysis of a strip containing multiple embedded and edge cracks under transient loading", Acta Mechanica, 229(12), 4895-4913 .https://doi.org/10.1007/s00707-018-2289-x.
  4. Chen, Y.F. and Erdogan, F. (1996), "The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate", J. Mech. Phys. Solid., 44(5), 771-787 . https://doi.org/10.1016/0022-5096(96)00002-6.
  5. Dag, S. and Ilhan, K.A. (2008), "Mixed-mode fracture analysis of orthotropic functionally graded material coatings using analytical and computational methods", J. Appl. Mech., 75(5), 051104. https://doi.org/10.1115/1.2932098.
  6. Dag, S., Yildirim, B. and Erdogan, F. (2004), "Interface crack problems in graded orthotropic media: Analytical and computational approaches", Int. J. Fract., 130(1), 471-496. https://doi.org/10.1023/B:FRAC.0000049497.81105.c4.
  7. Dag, S., Yildirim, B. and Sarikaya, D. (2007), "Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads", Int. J. Solid. Struct., 44(24), 7816-7840. https://doi.org/10.1016/j.ijsolstr.2007.05.010.
  8. Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech., 50(3), 609-614. https://doi.org/10.1115/1.3167098.
  9. Delale, F. and Erdogan, F. (1988), "Interface crack in a nonhomogeneous elastic medium", Int. J. Eng. Sci., 26(6), 559-568. https://doi.org/10.1016/0020-7225(88)90054-7.
  10. Ding, S.H., Zhou, Y.T. and Li, X. (2014), "Interface crack problem in layered orthotropic materials under thermomechanical loading", Int. J. Solid. Struct., 51(25-26), 4221- 4229. https://doi.org/10.1016/j.ijsolstr.2014.08.007.
  11. Guo, L.C., Wu, L. and Ma, L. (2004), "The interface crack problem under a concentrated load for a functionally graded coating-substrate composite system", Compos. Struct., 63(3-4), 397-406. https://doi.org/10.1016/S0263-8223(03)00188-0.
  12. Guo, L.C., Wu, L.Z., Zeng, T. and Ma, L. (2004), "Mode I crack problem for a functionally graded orthotropic strip", Eur. J. Mech.-A/Solid., 23(2), 219-234. https://doi.org/10.1016/j.euromechsol.2003.12.006.
  13. Hassani, A. and Monfared, M.M. (2017), "Analysis of an orthotropic circular bar weakened by multiple radial cracks under torsional transient loading", Eng. Fract. Mech., 186, 300-315. https://doi.org/10.1016/j.engfracmech.2017.10.015.
  14. Hassani, A. and Monfared, M.M. (2017), "Analysis of cracked bars with rectangular cross-section and isotropic coating layer under torsion", Int. J. Mech. Sci., 128, 23-36. https://doi.org/10.1016/j.ijmecsci.2017.04.005.
  15. Ikeda, T., Miyazaki, N. and Soda, T. (1998), "Mixed mode fracture criterion of interface crack between dissimilar materials", Eng. Fract. Mech., 59(6), 725-735. https://doi.org/10.1016/S0013-7944(97)00177-X.
  16. Itou, S. (2001), "Stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes", Int. J. Fract., 110(2), 123-135. https://doi.org/10.1023/A:1010851732746.
  17. Korsunsky, A. and Hills, D. (1996), "The solution of crack problems by using distributed strain nuclei", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 210(1), 23-31. https://doi.org/10.1243/PIME_PROC_1996_210_166_02.
  18. Ming-Che, L. and Erdogan, F. (1983), "Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface-I. Analysis", Eng. Fract. Mech., 18(3), 491-506. https://doi.org/10.1016/0013-7944(83)90045-0.
  19. Monfared, M.M. (2017), "Mode III SIFs for interface cracks in an FGM coating-substrate system", Struct. Eng. Mech., 64(1), 71-79. https://doi.org/10.12989/sem.2017.64.1.071.
  20. Monfared, M.M. and Ayatollahi, M. (2011), "Dynamic stress intensity factors of multiple cracks in a functionally graded orthotropic half-plane", Theor. Appl. Fract. Mech., 56(1), 49-57. https://doi.org/10.1016/j.tafmec.2011.09.008.
  21. Monfared, M.M. and Ayatollahi, M. (2012), "Elastodynamic analysis of a cracked orthotropic half-plane", Appl. Math. Model., 36(6), 2350-2359. https://doi.org/10.1016/j.apm.2011.08.031.
  22. Monfared, M.M. and Bagheri, R. (2021), "In-plane stress analysis in a cracked functionally graded piezoelectric plane", Mech. Bas. Des. Struct. Mach., 1-27. https://doi.org/10.1080/15397734.2021.1967166.
  23. Monfared, M.M., Bagheri, R. and Yaghoubi, R. (2018), "The mixed mode analysis of arbitrary configuration of cracks in an orthotropic FGM strip using the distributed edge dislocations", Int. J. Solid. Struct., 130, 21-35. https://doi.org/10.1016/j.ijsolstr.2017.10.023.
  24. Monfared, M.M., Pourseifi, M. and Bagheri, R. (2019), "Computation of mixed mode stress intensity factors for multiple axisymmetric cracks in an FGM medium under transient loading", Int. J. Solid. Struct., 158, 220-231. https://doi.org/10.1016/j.ijsolstr.2018.09.010.
  25. Mottale, H., Monfared, M.M. and Bagheri, R. (2018), "The multiple parallel cracks in an orthotropic non-homogeneous infinite plane subjected to transient in-plane loading", Eng. Fract. Mech., 199, 220-234. https://doi.org/10.1016/j.engfracmech.2018.05.034.
  26. Pant, M., Singh, I. and Mishra, B. (2011), "Evaluation of mixed mode stress intensity factors for interface cracks using EFGM", Appl. Math. Model., 35(7), 3443-3459. https://doi.org/10.1016/j.apm.2011.01.010.
  27. Wang, S. and Choi, I. (1983), "The interface crack behavior in dissimilar anisotropic composites under mixed-mode loading", J. Appl. Mech., 50(1), 179-183. https://doi.org/10.1115/1.3166987.
  28. Wang, X. and Zhong, Z. (2003), "A cracked sliding interface between anisotropic bimaterials", Mech. Res. Commun., 30(4), 387-393. https://doi.org/10.1016/S0093-6413(03)00029-6.
  29. Zhou, Z.G., Wang, B. and Sun, Y.G. (2004), "Investigation of the behavior of a Griffith crack at the interface of a layer bonded to a half plane using the Schmidt method for the opening crack mode", Mech. Res. Commun., 31(5), 545-555. https://doi.org/10.1016/j.mechrescom.2004.03.010.