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Mixed mode I/II fracture criterion to anticipate cracked composite materials based on a reinforced kinked crack along maximum shear stress path

  • Shahsavar, Sadra (Faculty of New Sciences and Technologies, University of Tehran) ;
  • Fakoor, Mahdi (Faculty of New Sciences and Technologies, University of Tehran) ;
  • Berto, Filippo (Norwegian University of Science and Technology)
  • Received : 2020.11.04
  • Accepted : 2021.05.18
  • Published : 2021.06.25

Abstract

In this paper, a fracture criterion for predicting the failure of the cracked composite specimens under mixed mode I/II loading is provided. Various tests performed on composite components reveal that cracks always grow along the fibers in the isotropic media. Using a new material model called reinforcement isotropic solid (RIS) concept, it is possible to extend the isotropic mixed mode fracture criteria into composite materials. In the proposed criterion, maximum shear stress (MSS) theory which is widely used for failure investigation of un-cracked isotropic materials will be extended to composite materials in combination with RIS concept. In the present study, cracks are oriented along the fibers in the isotropic material. It is assumed that at the onset of fracture, crack growth will be in a path where the shear stress has the highest value according to the MSS criterion. Investigating the results of this criterion and comparing with the available experimental data, it is shown that, both the crack propagation path and the moment of crack growth are well predicted. Available mixed mode I/II fracture data of various wood species are used to evaluate and verify the theoretical results.

Keywords

References

  1. Aghaei, M., Forouzan, M.R., Nikforouz, M. and Shahabi, E. (2015), "A study on different failure criteria to predict damage in glass/polyester composite beams under low velocity impact", Steel Compos. Struct., 18(5), 1291-1303. https://doi.org/10.12989/scs.2015.18.5.1291.
  2. Akbas, S.D. (2019), "Nonlinear behavior of fiber reinforced cracked composite beams", Steel Compos. Struct., 30(4), 327-336. https://doi.org/10.12989/scs.2019.30.4.327.
  3. Al-Fasih, M.Y., Kueh, A.B.H., Abo Sabah, S.H. and Yahya, M.Y. (2018), "Tow waviness and anisotropy effects on Mode II fracture of triaxially woven composite", Steel Compos. Struct., 26(2), 241-253. https://doi.org/10.12989/scs.2018.26.2.241.
  4. Altunisik, A.C., Gunaydin, M., Sevim, B. and Adanur, S. (2017), "System identification of arch dam model strengthened with CFRP composite materials", Steel Compos. Struct., 25(2), 231-244. https://doi.org/10.12989/scs.2017.25.2.231.
  5. Anaraki, A.G. and Fakoor, M. (2010), "General mixed mode I/II fracture criterion for wood considering T-stress effects", Mater. Design, 31(9), 4461-4469. https://doi.org/10.1016/j.matdes.2010.04.055.
  6. Anaraki, A.G. and Fakoor, M. (2011), "A new mixed-mode fracture criterion for orthotropic materials, based on strength properties", J. Strain Anal. Eng., 46(1), 33-44. https://doi.org/10.1243/03093247JSA667.
  7. Ataabadi, K., Ziaei-Rad, S. and Hosseini-Toudeshky, H. (2012), "Compression failure and fiber-kinking modeling of laminated composites", Steel Compos. Struct., 12(1), 53-72. http://dx.doi.org/10.12989/scs.2011.12.1.053.
  8. Berto, F. (2014), "A brief review of some local approaches for the failure assessment of brittle and quasi-brittle materials", Adv. Mater. Sci. Eng., (2014). https://doi.org/10.1155/2014/930679.
  9. Chen, S., Shi, X. and Qiu, Z. (2011), "Shear bond failure in composite slabs-a detailed experimental study", Steel Compos. Struct., 11(3), 233-250. http://dx.doi.org/10.12989/scs.2011.11.3.233.
  10. D'Angela, D., Ercolino, M., Bellini, C., Di Cocco, V. and Iacoviello, F. (2020), "Characterisation of the damaging micromechanisms in a pearlitic ductile cast iron and damage assessment by acoustic emission testing", Fatigue Fract. Eng. M., 43(5), 1038-1050. https://doi.org/10.1111/ffe.13214.
  11. Dall'Asta, A., Dezi, L. and Leoni, G. (2002), "Failure mechanisms of externally prestressed composite beams with partial shear connection", Steel Compos. Struct., 2(5), 315-330. https://doi.org/10.12989/scs.2002.2.5.315.
  12. Daneshjoo, Z., Shokrieh, M.M. and Fakoor, M. (2018), "A micromechanical model for prediction of mixed mode I/II delamination of laminated composites considering fiber bridging effects", Theor. Appl. Fract. Mech., 94, 46-56. https://doi.org/10.1016/j.tafmec.2017.12.002.
  13. Di Cocco, V., Iacoviello, F. and Cavallini, M. (2010), "Damaging micromechanisms characterization of a ferritic ductile cast iron", Eng. Fract. Mech., 77(11), 2016-2023. https://doi.org/10.1016/j.engfracmech.2010.03.037.
  14. Di Cocco, V., Iacoviello, F., Rossi, A. and Iacoviello, D. (2014), "Macro and microscopical approach to the damaging micromechanisms analysis in a ferritic ductile cast iron", Theor. Appl. Fract. Mech., 69, 26-33. https://doi.org/10.1016/j.tafmec.2013.11.003.
  15. Edlund, J., Lindstrom, H., Nilsson, F. and Reale, M. (2006), "Modulus of elasticity of Norway spruce saw logs vs. structural lumber grade", Holz als Roh-und Werkstoff, 64(4), 273-279. https://doi.org/10.1007/s00107-005-0091-7.
  16. Fakoor, M. (2017), "Augmented Strain Energy Release Rate (ASER): a novel approach for investigation of mixed-mode I/II fracture of composite materials", Eng. Fract. Mech., 179, 177-189. https://doi.org/10.1016/j.engfracmech.2017.04.049.
  17. Fakoor, M. and Farid, H.M. (2019), "Mixed-mode I/II fracture criterion for crack initiation assessment of composite materials", Acta Mechanica, 230(1), 281-301. https://doi.org/10.1007/s00707-018-2308-y.
  18. Fakoor, M. and Ghoreishi, S.M.N. (2018), "Experimental and numerical investigation of progressive damage in composite laminates based on continuum damage mechanics", Polymer Testing, 70, 533-543. https://doi.org/10.1016/j.polymertesting.2018.08.013.
  19. Fakoor, M. and Khansari, N.M. (2016), "Mixed mode I/II fracture criterion for orthotropic materials based on damage zone properties", Eng. Fract. Mech., 153, 407-420. https://doi.org/10.1016/j.engfracmech.2015.11.018.
  20. Fakoor, M. and Khansari, N.M. (2018), "General mixed mode I/II failure criterion for composite materials based on matrix fracture properties", Theor. Appl. Fract. Mech., 96, 428-442. https://doi.org/10.1016/j.tafmec.2018.06.004.
  21. Fakoor, M. and Khezri, M.S. (2020), "A micromechanical approach for mixed mode I/II failure assessment of cracked highly orthotropic materials such as wood", Theor. Appl. Fract. Mech., 109, 102740. https://doi.org/10.1016/j.tafmec.2020.102740.
  22. Fakoor, M. and Rafiee, R. (2013), "Fracture investigation of wood under mixed mode I/II loading based on the maximum shear stress criterion", Strength Mater., 45(3), 378-385. https://doi.org/10.1007/s11223-013-9468-8.
  23. Fakoor, M., Rafiee, R. and Zare, S. (2019), "Equivalent reinforcement isotropic model for fracture investigation of orthotropic materials", Steel Compos. Struct., 30(1), 1-12. https://doi.org/10.12989/scs.2019.30.1.001.
  24. Fakoor, M. and Shahsavar, S. (2020), "Fracture assessment of cracked composite materials: Progress in models and criteria", Theoretical and Applied Fracture Mech., 105, 102430. https://doi.org/10.1016/j.tafmec.2019.102430.
  25. Farid, H.M. and Fakoor, M. (2019), "Mixed mode I/II fracture criterion for arbitrary cracks in orthotropic materials considering T-stress effects", Theor. Appl. Fract. Mech., 99, 147-160. https://doi.org/10.1016/j.tafmec.2018.11.015.
  26. Farid, H.M. and Fakoor, M. (2020), "Mixed mode I/II fracture criterion to anticipate behavior of the orthotropic materials", Steel Compos. Struct., 34(5), 671-679. https://doi.org/10.12989/scs.2020.34.5.671.
  27. Fernandino, D.O., Boeri, R.E., Di Cocco, V., Bellini, C. and Iacoviello, F. (2020a), "Damage evolution during tensile test of austempered ductile iron partially austenized", Mater. Design Process. Commun., 2(4), e157. https://doi.org/10.1002/mdp2.157.
  28. Fernandino, D.O., Di Cocco, V., Boeri, R.E. and Iacoviello, F. (2020b), "Microstrain measurements and damage analysis during tensile loading of intercritical austempered ductile iron", Fatigue Fract. Eng. M., 43(11), 2744-2755. https://doi.org/10.1111/ffe.13346.
  29. Fernandino, D.O., Tenaglia, N., Di Cocco, V., Boeri, R.E. and Iacoviello, F. (2020c), "Relation between microstructural heterogeneities and damage mechanisms of a ferritic spheroidal graphite cast iron during tensile loading", Fatigue Fract. Eng. M., 43(6), 1262-1273. https://doi.org/10.1111/ffe.13221.
  30. Golewski, G.L. (2017a), "Effect of fly ash addition on the fracture toughness of plain concrete at third model of fracture", J. Civil Eng. Management, 23(5), 613-620. https://doi.org/10.3846/13923730.2016.1217923.
  31. Golewski, G.L. (2017b), "Determination of fracture toughness in concretes containing siliceous fly ash during mode III loading", Struct. Eng. Mech., 62(1), 1-9. https://doi.org/10.12989/sem.2017.62.1.001.
  32. Golewski, G.L. (2017c), "Improvement of fracture toughness of green concrete as a result of addition of coal fly ash. Characterization of fly ash microstructure", Mater. Characterization, 134, 335-346. https://doi.org/10.1016/j.matchar.2017.11.008.
  33. Golewski, G.L. (2018), "An assessment of microcracks in the Interfacial Transition Zone of durable concrete composites with fly ash additives", Compos. Struct., 200, 515-520. https://doi.org/10.1016/j.compstruct.2018.05.144.
  34. Golewski, G.L. (2019a), "The influence of microcrack width on the mechanical parameters in concrete with the addition of fly ash: Consideration of technological and ecological benefits", Constr. Build. Mater., 197, 849-861. https://doi.org/10.1016/j.conbuildmat.2018.08.157.
  35. Golewski, G.L. (2019b), "Physical characteristics of concrete, essential in design of fracture-resistant, dynamically loaded reinforced concrete structures", Mater. Design Process. Commun., 1(5), e82. https://doi.org/10.1002/mdp2.82
  36. Golewski, G.L. (2020), "Changes in the fracture toughness under mode II loading of low calcium fly ash (LCFA) concrete depending on ages", Materials, 13(22), 5241. https://doi.org/10.3390/ma13225241.
  37. Golewski, G.L. (2021), "The Beneficial Effect of the Addition of Fly Ash on Reduction of the Size of Microcracks in the ITZ of Concrete Composites under Dynamic Loading", Energies, 14(3), 668. https://doi.org/10.3390/en14030668.
  38. Golewski, G.L. and Gil, D.M. (2021), "Studies of Fracture Toughness in Concretes Containing Fly Ash and Silica Fume in the First 28 Days of Curing", Materials, 14(2), 319. https://doi.org/10.3390/ma14020319.
  39. Hunt, D.G. and Croager, W.P. (1982), "Mode II fracture toughness of wood measured by a mixed-mode test method", J. Mater. Sci. Lett., 1(2), 77-79. https://doi.org/10.1007/BF00731031.
  40. Jernkvist, L.O. (2001a), "Fracture of wood under mixed mode loading: I. Derivation of fracture criteria", Eng. Fracture Mech., 68(5), 549-563. https://doi.org/10.1016/S0013-7944(00)00127-2.
  41. Jernkvist, L.O. (2001b), "Fracture of wood under mixed mode loading: II. Experimental investigation of Picea abies", Eng. Fracture Mech., 68(5), 565-576. https://doi.org/10.1016/S0013-7944(00)00128-4.
  42. Kaman, M.O. and Cetisli, F. (2012), "Numerical analysis of center cracked orthotropic fgm plate: Crack and material axes differ by θ", Steel Compos. Struct., 13(2), 187-206. https://doi.org/10.12989/scs.2012.13.2.187.
  43. Khansari, N.M., Fakoor, M. and Berto, F. (2019), "Probabilistic micromechanical damage model for mixed mode I/II fracture investigation of composite materials", Theor. Appl. Fract. Mech., 99, 177-193. https://doi.org/10.1016/j.tafmec.2018.12.003.
  44. Kollmann, F.F., Kuenzi, E.W. and Stamm, A.J. (2012), Principles of Wood Science and Technology: II Wood Based Materials. Springer Science & Business Media.
  45. Leicester, R.H. (2006), "Application of linear fracture mechanics to notched timber elements", Progress Struct. Eng. Mater., 8(1), 29-37. https://doi.org/10.1002/pse.210.
  46. Mall, S., Murphy, J.F. and Shottafer, J.E. (1983), "Criterion for mixed mode fracture in wood", J. Eng. Mech., 109(3), 680-690. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:3(680).
  47. Marsavina, L., Pop, I.O. and Linul, E. (2019), "Mechanical and fracture properties of particleboard", Frattura Ed., Integrita Strutturale, 13(47), 266-276. https://doi.org/10.3221/IGFESIS.47.20.
  48. McKinney, J.M. (1972), "Mixed-mode fracture of unidirectional graphite/epoxy composites", J. Compos. Mater., 6(1), 164-166. https://doi.org/10.1177%2F002199837200600115. https://doi.org/10.1177%2F002199837200600115
  49. Mirsayar, M.M., Razmi, A. and Berto, F. (2018), "Tangential strain-based criteria for mixed-mode I/II fracture toughness of cement concrete", Fatigue Fract. Eng. M., 41(1), 129-137. https://doi.org/10.1111/ffe.12665.
  50. Nobile, L., Piva, A. and Viola, E. (2004), "On the inclined crack problem in an orthotropic medium under biaxial loading", Eng. Fract. Mech., 71(4-6), 529-546. https://doi.org/10.1016/S0013-7944(03)00051-1.
  51. Razavi, S.M.J. and Berto, F. (2019), "A new fixture for fracture tests under mixed mode I/II/III loading", Fatigue Fract. Eng. M., 42(9), 1874-1888. https://doi.org/10.1111/ffe.13033,
  52. Reynolds, T.P., Sharma, B., Serrano, E., Gustafsson, P.J. and Ramage, M.H. (2019), "Fracture of laminated bamboo and the influence of preservative treatments", Compos. Part B: Eng., 174, 107017. https://doi.org/10.1016/j.compositesb.2019.107017.
  53. Rizov, V.I. (2017), "Non-linear study of mode II delamination fracture in functionally graded beams", Steel Compos. Struct., 23(3), 263-271. https://doi.org/10.12989/scs.2017.23.3.263.
  54. Romanowicz, M. (2019), "A non-local stress fracture criterion accounting for the anisotropy of the fracture toughness", Eng. Fract. Mech., 214, 544-557. https://doi.org/10.1016/j.engfracmech.2019.04.033.
  55. Romanowicz, M. and Seweryn, A. (2008), "Verification of a nonlocal stress criterion for mixed mode fracture in wood", Eng. Fract. Mech., 75(10), 3141-3160. https://doi.org/10.1016/j.engfracmech.2007.12.006.
  56. Ross, R.J. (2010), Wood handbook: wood as an engineering material. USDA Forest Service, Forest Products Laboratory. General Technical Report FPL-GTR-190, 509(5).
  57. Scorza, D., et al. (2019), "Size-effect independence of particleboard fracture toughness", Compos. Struct., 229, 111374. https://doi.org/10.1016/j.compstruct.2019.111374.
  58. Saouma, V.E., Ayari, M.L. and Leavell, D.A. (1987), "Mixed mode crack propagation in homogeneous anisotropic solids", Eng. Fract. Mech., 27(2), 171-184. https://doi.org/10.1016/0013-7944(87)90166-4.
  59. Shahsavar, S., Fakoor, M. and Berto, F. (2020), "Verification of reinforcement isotropic solid model in conjunction with maximum shear stress criterion to anticipate mixed mode I/II fracture of composite materials", Acta Mechanica, 1-20. https://doi.org/10.1007/s00707-020-02810-8.
  60. Sih, G.C., Paris, P.C. and Irwin, G.R. (1965), "On cracks in rectilinearly anisotropic bodies", Int. J. Fract. Mech., 1(3), 189-203. https://doi.org/10.1007/BF00186854.
  61. Su, R.K.L. and Sun, H.Y. (2003), "Numerical solutions of two-dimensional anisotropic crack problems", Int. J. Solids Struct., 40(18), 4615-4635. https://doi.org/10.1016/S0020-7683(03)00310-X.
  62. Toribio, J. and Ayaso, F.J. (2003), "A fracture criterion for high-strength steel structural members containing notch-shape defects", Steel Compos. Struct., 3(4), 231-242. https://doi.org/10.12989/scs.2003.3.4.231.
  63. Van der Put, T.A.C.M. (2007), "A new fracture mechanics theory for orthotropic materials like wood", Eng. Fract. Mech., 74(5), 771-781. https://doi.org/10.1016/j.engfracmech.2006.06.015.
  64. Wang, D., Lin, L., Fu, F. and Fan, M. (2019), "The softwood fracture mechanisms at the scales of the growth ring and cell wall under bend loading", Wood Sci. Technol., 53(6), 1295-1310. https://doi.org/10.1007/s00226-019-01132-w.
  65. Williams, M.L. (1961), The bending stress distribution at the base of a stationary crack. https://doi.org/10.1115/1.3640470
  66. Wu, E.M. (1967), Application of fracture mechanics to anisotropic plates. https://doi.org/10.1115/1.3607864