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Simulate of edge and an internal crack problem and estimation of stress intensity factor through finite element method

  • Yaylaci, Murat (Department of Civil Engineering, Recep Tayyip Erdogan University)
  • 투고 : 2021.09.11
  • 심사 : 2022.02.08
  • 발행 : 2022.04.25

초록

In this study, the elastic plane problem of a layered composite containing an internal or edge crack perpendicular to its boundaries in its lower layer is examined using numerical analysis. The layered composite consists of two elastic layers having different elastic constants and heights. Two bonded layers rest on a homogeneous elastic half plane and are pressed by a rigid cylindrical stamp. In this context, the Finite Element Method (FEM) based software called ANSYS is used for numerical solutions. The problem is solved under the assumptions that the contacts are frictionless, and the effect of gravity force is neglected. A comparison is made with analytical results in the literature to verify the model created and the results obtained. It was found that the results obtained from analytical formulation were in perfect agreements with the FEM study. The numerical results for the stress-intensity factor (SIF) are obtained for various dimensionless quantities related to the geometric and material parameters. Consequently, the effects of these parameters on the stress-intensity factor are discussed. If the FEM analysis is used correctly, it can be an efficient alternative method to the analytical solutions that need time.

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참고문헌

  1. Adibelli, H. (2010), "Contact and crack problems at the bonded double layers resting on an elasitc half plane", Ph.D. Thesis, Karadeniz Technical University, Trabzon, Turkey.
  2. Adiyaman, G., Yaylaci, M. and Birinci, A. (2015), "Analytical and finite element solution of a receding contact problem", Struct. Eng. Mech., 54(1), 69-85. https://doi.org/10.12989/sem.2015.54.1.069.
  3. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/ 10.12989/sem.2019.71.5.485.
  4. Al-Furjan, M.S.H., Habibi, M., Ni, J., Jung, D.W. and Tounsi, A. (2020a), "Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM", Eng. Comput., 1-24. https://doi.org/10.1007/s00366-020-01144-2.
  5. Al-Furjan, M.S.H., Safarpour, H., Habibi, M., Safarpour, M. and Tounsi, A. (2020b), "A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method", Eng Comput., 1-18. https://doi.org/ 10.1007/s00366-020-01088-7.
  6. Al-Furjan, M.S.H., Habibi, M., Rahimi, A., Chen, G., Safarpour, H., Safarpour, M. and Tounsi, A. (2020c), "Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems", Eng Comput., 1-17. https://doi.org/10.1007/s00366-020-01200-x.
  7. Al-Furjan, M.S.H., Habibi, M., Ghabussi, A., Safarpour, H., Safarpour, M., and Tounsi, A. (2021a), "Non-polynomial framework for stress and strain response of the FG-GPLRC disk using three-dimensional refined higher-order theory", Eng. Struct., 228, 111496. https://doi.org/10.1016/j.engstruct.2020.111496.
  8. Al-Furjan, M.S.H., Hatami, A., Habibi, M., Shan, L. and Tounsi, A. (2021b), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 257, 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
  9. Al-Osta, M.A., Saidi, H., Tounsi, A., Al-Dulaijan, S.U., AlZahrani, M.M., Sharif, A. and Tounsi, A. (2021), "Influence of porosity on the hygro-thermo-mechanical bending response of an AFG ceramic-metal plates using an integral plate model", Smart Struct. Syst., 28(4), 499-513. https://doi.org/ 10.12989/sss.2021.28.4.499.
  10. ANSYS (2013), Mechanical APDL, ANSYS Contact Technology Guide, Ansys, Inc., Pennsylvania, U.S.A.
  11. Azizkhani, M., Kadkhodapour, J., Anaraki, A.P., Hadavand, B.S. and Kolahchi, R. (2020), "Study of body movement monitoring utilizing nano-composite strain sensors contaning Carbon nanotubes and silicone rubber", Steel Comp. Struct., 35(6), 779-788. https://doi.org/10.12989/scs.2020.35.6.779.
  12. Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H., Tounsi, A. and Mahmoud, S.R. (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method ", Comput. Concrete, 27(1), 73-83. https://doi.org/10.12989/CAC.2021.27.1.073.
  13. Banh, T.T., Lee, J., Kang, J. and Lee, D. (2020), "Multi material topology optimization for crack problems based on eXtended isogeometric analysis", Steel Comp. Struct., 37(6), 629-640. https://doi.org/10.12989/scs.2020.37.6.663 663.
  14. Barenblatt, G.I. (1962), "Mathematical theory of equilibrium cracks in brittle fracture", Adv. Appl. Mech., 7, 55-129. https://doi.org/10.1016/S0065-2156(08)70121-2.
  15. Belinha, J., Azevedo, J.M.C., Dinis, L.M.J.S. and Natal Jorge R.M. (2018), "Simulating fracture propagation in brittle materials using a meshless approach", Eng. Comput., 34, 503-522. https://doi.org/10.1007/s00366-017-0555-5.
  16. Bellifa, H., Selim, H.M., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Al-Zahrani, M.M. and Tounsi, A. (2021), "Influence of porosity on thermal buckling behavior of functionally graded beams", Smart Struct. Syst., 27(4), 719-728. https://doi.org/ 10.12989/sss.2021.27.4.719.
  17. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H. and Al-Zahrani, M. M. (2020), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concrete, 26(5), 439-450. https://doi.org/10.12989/CAC.2020.26.5.439.
  18. Bhattacharya, S., Singh. I.V. and Mishra, B.K. (2013), "Fatigue-life estimation of functionally graded materials using XFEM", Eng Comput., 29, 427-448. https://doi.org/10.1007/s00366-012-0261-2.
  19. Birinci, A. and Cakiroglu, F.L. (2003), "Partial closure of a crack located in an infinite elastic layer", Eur. J. Mech. A Solids, 22, 583-590. https://doi.org/10.1016/s0997-7538(03)00053-6.
  20. Birinci, A. and Erdol, R. (2004), "A layered composite containing a crack in its lower layer loaded by a rigid stamp", Eur. J. Mech. A Solids, 23, 909-924. https://doi.org/10.1016/j.euromechsol.2004.05.008.
  21. Birinci, A., Birinci, F., Cakiroglu F.F. and Erdol, R. (2010), "An internal crack problem for an infinite elastic layer", Arch. Appl. Mech., 80, 997-1005. https://doi.org/10.1007/s00419-009-0355-5.
  22. Bouafia, H., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Hussain, M. (2021), "Natural frequencies of FGM nanoplates embedded in an elastic medium", Adv. Nano Res., 11(3), 239-249. https://doi.org/10.12989/anr.2021.11.3.239.
  23. Erdol, R. and Erdogan, F. (1976), "A note on the bending of a cracked strip", Report NGR 39-007-011; Lehigh University, Pensilvenia, U.S.A.
  24. Farrokhian, A. and Kolahchi, R. (2020), "Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs", Struct. Eng. Mech, 73(5), 555-563. https://doi.org/10.12989/SEM.2020.73.5.555.
  25. Figueira, D., Sousaa, C. and Neves, A.S. (2018), "Winkler spring behavior in FE analyses of dowel action in statically loaded RC cracks", Comput. Concrete, 21(5), 593-605. https://doi.org/10.12989/cac.2018.21.5.593.
  26. Griffith, A.A. (1920), "The phenomena of rupture and flow in solids", Phil. Trans. Roy. Soc. London, A, 1221, 163-198.
  27. Griffith, A.A, (1924), "The theory of rupture", Proceedings of the 1st International Congress on Applied Mechanics, 55, Delft, Netherlands.
  28. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M, Hussain, M. and Mahmoud, S.R. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. https://doi.org/ 10.12989/scs.2021.38.1.001.
  29. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. https://doi.org/ 10.12989/scs.2021.39.1.051.
  30. Hajmohammad, M.H., Zarei, M.S., Farrokhian, A. and Kolahchi, R. (2018), "A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment", Adv. Nano Res., 6(4), 299-321. https://doi.org/10.12989/anr.2018.6.4.299.
  31. Huang, Y., Karami, B., Shahsavari, D. and Tounsi, A. (2021), "Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels", Archiv. Civ. Mech. Eng, 21. https://doi.org/ 10.1007/s43452-021-00291-7.
  32. Huang, X., Hao, H., Oslub, K., Habibi, M. and Tounsi, A. (2021), "Dynamic stability/instability simulation of the rotary size-dependent functionally graded microsystem", Eng. Comput.,1-17. https://doi.org/ 10.1007/s00366-021-01399-3.
  33. Ismail, A.E., Ariffin, A.K., Abdullah, S., and Ghazali, M.J. (2017), "Finite element analysis of J-integral for surface cracks in round bars under combined mode I loading", Int. J. Integr. Eng., 9(2), 1-8.
  34. Javani, R., Bidgoli, M.R. and Kolahchi, R. (2019), "Buckling analysis of plates reinforced by Graphene platelet based on Halpin-Tsai and Reddy theories", Steel Comp. Struct., 31(4), 419-426. https://doi.org/ 10.12989/SCS.2019.31.4.419.
  35. Jiang, Z. and Xiang, J. (2020), "Method using XFEM and SVR to predict the fatigue life of plate like structures", Struct. Eng. Mech., 73(4), 455-462. https://doi.org/10.12989/sem.2020.73.4.455.
  36. Knott, J.F. (1973), "Fundamentals of fracture mechanics", Butterworth and Co Ltd, London, U.K.
  37. Krenk, S. (1973), "The problem of an inclined crack in an elastic strip", Report No. IFSM-73-52; Lehigh University, Pensivenia, U.S.A.
  38. Kumar, Y., Gupta, A. and Tounsi, A. (2021), "Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model", Adv. Nano Res., 11(1), 1-17. https://doi.org/ 10.12989/anr.2021.11.1.001.
  39. Malekan, M., Khosravi, A. and St-Pierre, L, (2021), "An Abaqus plug-in to simulate fatigue crack growth", Eng. Comput., 1-25. https://doi.org/10.1007/s00366-021-01321-x.
  40. Maleki, M., Bidgoli, M.R. and Kolahchi, R. (2019), "Earthquake response of nanocomposite concrete pipes conveying and immersing in fluid using numerical methods", Comput. Concrete, 24(2), 125-135. https://doi.org/10.12989/CAC.2019.24.2.125.
  41. Memarzadeh, P., Mousavian, S., Ghehi, M.H. and Zirakian, T. (2020), "Effect of crack location on buckling analysis and SIF of cracked plates under tension", Steel Compos. Struct., 35(2), 629-640. https://doi.org/10.12989/scs.2020.35.2.215.
  42. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. https://doi.org/ 10.12989/scs.2021.39.5.631.
  43. Minguez, L.M. (1993), "Study of elastic behaviour of plates containing cracks by finite element analysis", Comput. Concrete, 47(6), 917-925. https://doi.org/10.1016/0045-7949(93)90296-P.
  44. Moallemia, S. and Pietruszczak, S. (2018), "Numerical analysis of propagation of macrocracks in 3D concrete structures affected by ASR", Comput. Concrete, 22(1), 1-10. https://doi.org/10.12989/cac.2018.22.1.001.
  45. Mudhaffar, I.M., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Structures, 33, 2177-2189. https://doi.org/ 10.1016/j.istruc.2021.05.090.
  46. Nojumi, M.M. and Wang, X. (2020), "Analysis of crack problems in functionally graded materials under thermomechanical loading using graded finite elements", Mech. Res. Commun., 106, 103534. https://doi.org/10.1016/j.mechrescom.2020.103534.
  47. Nguyen, A.P., Banh, T.T., Lee, D., Lee, J., Kang, J. and Shin, S. (2018), "Design of multiphase carbon fiber reinforcement of crack existing concrete structures using topology optimization", Steel Comp. Struct., 29(5), 635-645. https://doi.org/10.12989/scs.2018.29.5.635.
  48. O ner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.607.
  49. O ner, E., Sengul Sabano, B., Uzun Yaylaci, E., Adiyaman, G., Yaylaci, M. and Birinci, A., (2022), "On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods", ZAMM, e202100287. https://doi.org/10.1002/zamm.202100287.
  50. Pajand, M.R. and Moghaddam, N.G. (2018), "Two new triangular finite elements containing stable open cracks", Struct. Eng. Mech., 65(1), 99-110. https://doi.org/10.12989/sem.2018.65.1.099.
  51. Saberi, S., Memarzadeh, P. and Zirakian, T. (2019), "Study of buckling stability of cracked plates under uniaxial compression using singular FEM", Struct. Eng. Mech., 69(4), 417-426. https://doi.org/10.12989/sem.2019.69.4.417 417.
  52. Sarfarazi, V., Haeri, H., Shemirani, A.B., Zhu, Z. and Marji, M.F. (2018), "Experimental and numerical simulating of the crack separation on the tensile strength of concrete", Struct. Eng. Mech., 66(5), 569-582. https://doi.org/10.12989/sem.2018.66.5.569.
  53. Sarfarazi, V. and Haeri, H. (2018), "Three dimensional numerical modeling of effect of bedding layer on the tensile failure behavior in hollow disc models using Particle Flow Code (PFC3D)", Struct. Eng. Mech., 68(5), 537-547. https://doi.org/10.12989/sem.2018.68.5.537.
  54. Seguini, M., Khatir, S., Boutchicha, D., Nedjar, D. and Wahab, M.A. (2021), "Crack prediction in pipeline using ANN-PSO based on numerical and experimental modal analysis", Smart Struct. Syst., 27(3), 507-523. https://doi.org/10.12989/sss.2021.27.3.507.
  55. Shariati, A., Habibi, M., Tounsi, A., Safarpour, H. and Safa, M. (2020), "Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties", Eng. Comput., 37(4), 3629-3648. https://doi.org/ 10.1007/s00366-020-01024-9.
  56. Tahir, S.I., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/ 10.1016/j.compstruct.2021.114030.
  57. Tiwari, P., Singh, N.N., and Sinha P.K. (2017), "Study and vibration analysisin elastic cracked beam by fem and ANSYS", Int. J. Eng. Sci. Technol., 6, 831-837.
  58. Uzun Yaylaci, E., Yaylaci, M., O lmez, H. and Birinci, A. (2020), "Artificial neural network calculations for a receding contact problem", Comput. Concrete, 25(6), 551-563. https://doi.org/10.12989/cac.2020.25.6.551.
  59. Vander, Z.H.D. and Grootenboer, H. (1986), "A finite element approach to interface cracks", J. Appl. Mech., ASME, 53, 573-578. https://doi.org/10.1115/1.3171813.
  60. Vinh, V.P., Tounsi, A. (2021), "The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates", Eng. Comput., 1-19. https://doi.org/ 10.1007/s00366-021-01475-8.
  61. Wang, H.T., Wu, G., Pang, Y.Y. and Zakari, H.M. (2019a), "Stress intensity factors for double-edged cracked steel beams strengthened with CFRP plates", Steel Comp. Struct., 33(5), 629-640. https://doi.org/10.12989/scs.2019.33.5.629.
  62. Wang, J., Chen, X., Bu, J. and Guo, S. (2019b), "Experimental and numerical simulation study on fracture properties of self-compacting rubberized concrete slabs", Comput. Concrete, 24(4), 283-293. https://doi.org/10.12989/cac.2019.24.4.283.
  63. Yaylaci, M. (2016). "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. https://doi.org/10.12989/sem.2016.57.6.1143.
  64. Yaylaci, M., Terzi, C. and Avcar, M. (2019), "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6), 775-783. https://doi.org/10.12989/sem.2019.72.6.775.
  65. Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete, 26(2), 107-114. https://doi.org/10.12989/cac.2020.26.2.107.
  66. Yaylaci, M., Adiyaman, E., O ner, E. and Birinci, A. (2020), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. https://doi.org/10.12989/sem.2020.76.3.325.
  67. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Uzun Yaylaci, E., O ner, E. and Birinci, A., (2021a), "Assessment of different solution methods for receding contact problems in functionally graded layered mediums", Mech. Mater., 154, 103730. https://doi.org/10.1016/j.mechmat.2020.103730.
  68. Yaylaci, M., Yayli, M., Uzun Yaylaci, E., O lmez, H. and Birinci, A. (2021b), "Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron", Struct. Eng. Mech., 78(5), 585-597. https://doi.org/10.12989/sem.2021.78.5.585.
  69. Zaitoun, M.W., Chikh, A., Tounsi, A., Sharif, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021), "An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects", Eng. Comput., 1-15. https://doi.org/ 10.1007/s00366-021-01498-1.
  70. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S.R. (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78(2), 117-124. https://doi.org/ 10.12989/sem.2021.78.2.117.
  71. Zhao, B. (2015), "The application of wavelet finite element method on multiple cracks identification of gear pump gear", Eng. Comput., 31, 281-288. https://doi.org/10.1007/s00366-013-0350-x.