Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Equivalent reinforcement isotropic model for fracture investigation of orthotropic materials

  • Fakoor, Mahdi (Faculty of New Sciences & Technologies, University of Tehran) ;
  • Rafiee, Roham (Faculty of New Sciences & Technologies, University of Tehran) ;
  • Zare, Shahab (Faculty of New Sciences & Technologies, University of Tehran)
  • Received : 2018.01.14
  • Accepted : 2018.12.31
  • Published : 2019.01.10
⟨ Previous Next ⟩

Abstract

In this research, an efficient mixed mode I/II fracture criterion is developed for fracture investigation of orthotropic materials wherein crack is placed along the fibers. This criterion is developed based on extension of well-known Maximum Tensile Stress (MTS) criterion in conjunction with a novel material model titled as Equivalent Reinforced Isotropic Model (ERIM). In this model, orthotropic material is replaced with an isotropic matrix reinforced with fibers. A comparison between available experimental observations and theoretical estimation implies on capability of developed criterion for predicting both crack propagation direction and fracture instance, wherein the achieved fracture limit curves are also compatible with fracture mechanism of orthotic materials. It is also shown that unlike isotropic materials, fracture toughness of orthotic materials in mode $I(K)_{IC}{\mid})$ cannot be introduced as the maximum load bearing capacity and thus new fracture mechanics property, named here as maximum orthotropic fracture toughness in mode $I(K_{IC}{\mid}^{ortho}_{max})$ is defined. Optimum angle between crack and fiber direction for maximum load bearing in orthotropic materials is also defined.

Keywords

References

  1. Al-Fasih, M.Y., Kueh, A.B.H., Sabah, S.H. and Yahya, M.Y. (2018), "Tow waviness and anisotropy effects on Mode II fracture of triaxially woven composite", Steel Compos. Struct., Int. J., 26(2), 241-253.
  2. Aliha, M.R.M., Bahmani, A. and Akhondi, S. (2015), "Determination of mode III fracture toughness for different materials using a new designed test configuration", Mater. Des., 86, 863-871. https://doi.org/10.1016/j.matdes.2015.08.033
  3. Anaraki, A.G. and Fakoor, M. (2010a), "General mixed mode I/II fracture criterion for wood considering T-stress effects", Mater. Des., 31(9), 4461-4469. https://doi.org/10.1016/j.matdes.2010.04.055
  4. Anaraki, A.G. and Fakoor, M. (2010b), "Mixed mode fracture criterion for wood based on a reinforcement micro-crack damage model", Mater. Sci. Eng.: A, 527(27), 7184-7191. https://doi.org/10.1016/j.msea.2010.08.004
  5. Anaraki, A.G. and Fakoor, M. (2011), "A new mixed-mode fracture criterion for orthotropic materials, based on strength properties", J. Strain Anal. Eng. Des., 46(1), 33-44. https://doi.org/10.1243/03093247JSA667
  6. Buczek, M.B. and Herakovich, C.T. (1985), "A normal stress criterion for crack extension direction in orthotropic composite materials", J. Compos. Mater., 19(6), 544-553. https://doi.org/10.1177/002199838501900606
  7. Cetisli, F. and Kaman, M.O. (2014), "Numerical analysis of interface crack problem in composite plates jointed with composite patch", Steel Compos. Struct., Int. J., 16(2), 203-220. https://doi.org/10.12989/scs.2014.16.2.203
  8. Chow, C.L. and Woo, C.W. (1979), "Orthotropic and mixed mode fracture in wood", Proceedings of the 1st International Conference of Wood Fracture, Vancouver, Canada, pp. 39-52.
  9. Deretic-Stojanovic, B. and Kostic, S.M. (2017), "A simplified matrix stiffness method for analysis of composite and prestressed beams", Steel Compos. Struct., Int. J., 24(1), 53-63. https://doi.org/10.12989/scs.2017.24.1.053
  10. Ehart, R.J.A., Stanzl-Tschegg, S.E. and Tschegg, E.K. (1998), "Crack face interaction and mixed mode fracture of wood composites during mode III loading", Eng. Fract. Mech., 61(2), 253-278. https://doi.org/10.1016/S0013-7944(98)00033-2
  11. Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plates under plane loading and transverse shear", J. Basic Eng., 85(4), 519-525. https://doi.org/10.1115/1.3656897
  12. Faal, R.T., Aghsam, A. and Milani, A.S. (2015), "Stress intensity factors for cracks in functionally graded annular planes under anti-plane loading", Int. J. Mech. Sci., 93, 73-81. https://doi.org/10.1016/j.ijmecsci.2015.01.006
  13. 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
  14. 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
  15. 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
  16. Fakoor, M., Rafiee, R. and Sheikhansari, M. (2015), "The influence of fiber-crack angle on the crack tip parameters in orthotropic materials", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(3), 418-431. https://doi.org/10.1177/0954406215617195
  17. 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
  18. Golewski, G.L. (2017a), "Effect of fly ash addition on the fracture toughness of plain concrete at third model of fracture", J. Civil Eng. Manag., 23(5), 613-620. https://doi.org/10.3846/13923730.2016.1217923
  19. Golewski, G.L. (2017b), "Generalized fracture toughness and compressive strength of sustainable concrete including low calcium fly ash", Materials, 10(12), 1393. https://doi.org/10.3390/ma10121393
  20. Golewski, G.L. (2017c), "Determination of fracture toughness in concretes containing siliceous fly ash during mode III loading", Struct. Eng. Mech., Int. J., 62(1), 1-9. https://doi.org/10.12989/sem.2017.62.1.001
  21. Gregory, M.A. and Herakovich, C.T. (1986), "Predicting crack growth direction in unidirectional composites", J. Compos. Mater., 20(1), 67-85. https://doi.org/10.1177/002199838602000105
  22. 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
  23. Jernkvist, L.O. (2001a), "Fracture of wood under mixed mode loading: I. Derivation of fracture criteria", Eng. Fract. Mech., 68(5), 549-563. https://doi.org/10.1016/S0013-7944(00)00127-2
  24. Jernkvist, L.O. (2001b), "Fracture of wood under mixed mode loading: II. Experimental investigation of Picea abies", Eng. Fract. Mech., 68(5), 565-576. https://doi.org/10.1016/S0013-7944(00)00128-4
  25. Lazzarin, P., Campagnolo, A. and Berto, F. (2014), "A comparison among some recent energy-and stress-based criteria for the fracture assessment of sharp V-notched components under Mode I loading", Theor. Appl. Fract. Mech., 71, 21-30. https://doi.org/10.1016/j.tafmec.2014.03.001
  26. Leicester, R.H. (1974), "Application of Linear Fracture Mechanics in the Design of Timber Structures", Proceedings, Conference Australian Fractured Group 23, Melbourne, Australia, October, pp. 156-164.
  27. Li, J., Meng, S., Tian, X., Song, F. and Jiang, C. (2012), "A nonlocal fracture model for composite laminates and numerical simulations by using the FFT method", Compos. Part B: Eng., 43(3), 961-971. https://doi.org/10.1016/j.compositesb.2011.08.055
  28. Lim, W.K. (2012), "Mixed-mode crack extension in orthotropic materials under biaxial load", Int. J. Fract, 173(1), 71-77. https://doi.org/10.1007/s10704-011-9668-9
  29. 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)
  30. Merzoug, M., Boulenouar, A. and Benguediab, M. (2017), "Numerical analysis of the behaviour of repaired surface cracks with bonded composite patch", Steel Compos. Struct., Int. J., 25(2), 209-216.
  31. Motamedi, D. and Mohammadi, S. (2012), "Fracture analysis of composites by time independent moving-crack orthotropic XFEM", Int. J. Mech. Sci., 54(1), 20-37. https://doi.org/10.1016/j.ijmecsci.2011.09.004
  32. Nobile, L. and Carloni, C. (2005), "Fracture analysis for orthotropic cracked plates", Compos. Struct., 68(3), 285-293. https://doi.org/10.1016/j.compstruct.2004.03.020
  33. 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
  34. Sadowski, T. and Golewski, G.L. (2018), "A failure analysis of concrete composites incorporating fly ash during torsional loading", Compos. Struct., 183, 527-535. https://doi.org/10.1016/j.compstruct.2017.05.073
  35. 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
  36. Serier, N., Mechab, B., Mhamdia, R. and Serier, B. (2016), "A new formulation of the J integral of bonded composite repair in aircraft structures", Struct. Eng. Mech., Int. J., 58(5), 745-755. https://doi.org/10.12989/sem.2016.58.5.745
  37. 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
  38. Sih, G.C., Chen, E.P., Huang, S.L. and McQuillen, E.J. (1975), "Material characterization on the fracture of filament-reinforced composites", J. Compos. Mater., 9(2), 167-186. https://doi.org/10.1177/002199837500900207
  39. Tsai, S.W. and Wu, E.M. (1971), "A general theory of strength for anisotropic materials", J. Compos. Mater., 5(1), 58-80. https://doi.org/10.1177/002199837100500106
  40. 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
  41. Williams, J.G. and Birch, M.W. (1976), "Mixed mode fracture in anisotripic media", ASTM STP, p. 125-137.
  42. Wu, E.M. (1967), "Application of fracture mechanics to anisotropic plates", J. Appl. Mech., 34(4), 967-974. https://doi.org/10.1115/1.3607864

Cited by

  1. Mixed mode I/II fracture criterion to anticipate behavior of the orthotropic materials vol.34, pp.5, 2019, https://doi.org/10.12989/scs.2020.34.5.671