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Limited Input Benzeggagh and Kenane delamination failure criterion for mixed-mode loaded fiber reinforced composite laminates

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Abstract

Bilinear delamination failure criteria proposed by Reeder for mixed-mode (I–II) fracture of composite laminates has four limitations: require mixed-mode (I–II) fracture data by the more complex MMB test; determination of bilinear constants by two independent curve fits; failure of bilinear equations to intersect at \(\hbox {G}_{\mathrm{I}}^{\mathrm{m}}/\hbox {G}_{\mathrm{II}}^{\mathrm{m}}=1\); and the data representation by \(\hbox {G}_{\mathrm{I}}^{\mathrm{m}}\) versus \(\hbox {G}_{\mathrm{II}}^{\mathrm{m}}\) instead of the conventional \(\hbox {G}_{\mathrm{c}}^{\mathrm{m}}\) versus \(\hbox {G}_{\mathrm{II}}^{\mathrm{m}}/\hbox {G}_{\mathrm{T}}\). Some of these limitations were overcome by limited input bilinear criteria (LIBC) proposed by Davidson and Zhao by replacing the MMB test data by DCB, ENF, and SLB (single leg beam) test data. But the LIBC retained the two discontinuous forms of the equations for no specific reason in a continuous material system. This paper eliminates the two equations by a single power law equation that covers the whole domain of fracture as in Benzeggagh and Kenane’s empirical equation. This simplified mixed-mode delamination fracture criterion we call “Limited Input B–K (LIBK) criterion in recognition of the works of Davidson and Zhao, and Benzeggagh and Kenane. The criterion was validated by a large number of test data in the literature.

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References

  1. Adeyemi NB, Shivakumar KN, Avva VS (1999) Delamination fracture toughness of woven-fabric composites under mixed-mode loading. AIAA J 37(4):517–520

  2. ASTM D5528-13 (2013) Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. ASTM International

  3. Benzeggagh ML, Kenane M (1996) Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos Sci Technol 56(4):439–449

  4. Bonhomme J, Viña J, Argüelles A, Viña I, Mollón V (2013) Influence of the matrix toughness in carbon-epoxy composites subjected to delamination under modes I, II, and mixed I/II. Mech Adv Mater Struct 20(4):679–686

  5. Boni L, Fanteria D, Lazzeri L, Panettieri E, Mariani U, Rigamonti M (2018) Influence of environment conditioning on the interlaminar fracture toughness of a graphite/epoxy unidirectional material. Compos Part B Eng 153:97–107

  6. Crews Jr JH, Reeder JR (1988) A mixed-mode bending apparatus for delamination testing. NASA-TM-100662

  7. D6671/D6671M-19 (2019) Standard test method for mixed mode I–mode II interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites. ASTM International

  8. D7905M-14 (2014) Standard test method for determination of the mode II interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. ASTM International

  9. Daneshjoo Z, Shokrieh M, 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

  10. Davidson BD, Sun X (2005) Effects of friction, geometry, and fixture compliance on the perceived toughness from three-and four-point bend end-notched flexure tests. J Reinf Plast Compos 24(15):1611–1628

  11. Davidson BD, Zhao W (2006) An accurate mixed-mode delamination failure criterion for laminated fibrous composites requiring limited experimental input. J Compos Mater 41(2):679–702

  12. Davidson BD, Zhao W (2007) An accurate mixed-mode delamination failure criterion for laminated fibrous composites requiring limited experimental input. J Compos Mater 41(2):679–702

  13. De Morais A, Pereira A, De Moura M, Silva F, Dourado N (2015) Bilinear approximations to the mixed-mode I–II delamination cohesive law using an inverse method. Compo Struct 122:361–366

  14. Ducept F, Davies P, Gamby D (1997) An experimental study to validate tests used to determine mixed mode failure criteria of glass/epoxy composites. Compos Part A Appl Sci Manuf 28(4):719–729

  15. Ducept F, Davies P, Gamby D (2000) Mixed mode failure criteria for a glass/epoxy composite and an adhesively bonded composite/composite joint. Int J Adhes Adhes 20(3):233–244

  16. Fanteria D, Lazzeri L, Panettieri E, Mariani U, Rigamonti M (2017) Experimental characterization of the interlaminar fracture toughness of a woven and a unidirectional carbon/epoxy composite. Compos Sci Technol 142:20–29

  17. Hansen P, Martin R (1999) DCB, 4ENF and MMB delamination characterisation of S2/8552 and IM7/8552, Material Engineering Research Lab LTD Hertford (United Kingdom)

  18. Juntti M, Asp LE, Olsson R (1999) Assessment of evaluation methods for the mixed-mode bending test. J Compos Technol Res 21(1):37–48

  19. Karnati SR (2014) A mixed-mode (I–II) fracture criterion for AS4/8552 carbon/epoxy composite laminate. North Carolina Agricultural and Technical State University, North Carolina

  20. Liu Y, Zhang C, Xiang Y (2015) A critical plane-based fracture criterion for mixed-mode delamination in composite materials. Compos Part B Eng 82:212–220

  21. Mathews MJ, Swanson SR (2007) Characterization of the interlaminar fracture toughness of a laminated carbon/epoxy composite. Compos Sci Technol 67(7–8):1489–1498

  22. Naghipour P, Bartsch M, Chernova L, Hausmann J, Voggenreiter H (2010) Effect of fiber angle orientation and stacking sequence on mixed mode fracture toughness of carbon fiber reinforced plastics: numerical and experimental investigations. Mater Sci Eng A 527(3):509–517

  23. Ozdil F, Carlsson L (1999) Beam analysis of angle-ply laminate mixed-mode bending specimens. Compos Sci Technol 59(2):937–945

  24. Pereira A, De Morais A (2008) Mixed mode I + II interlaminar fracture of carbon/epoxy laminates. Compos Part A Appl Sci Manuf 39(2):322–333

  25. Reeder JR (1992) An evaluation of mixed-mode delamination failure criteria, NASA-TM-104210

  26. Reeder JR, Crews Jr JH (1991) Nonlinear analysis and redesign of the mixed-mode bending delamination test. NASA TM-102777

  27. Shivakumar KN, Crews JH Jr, Avvat VS (1998) Modified mixed-mode bending test apparatus for measuring delamination fracture toughness of laminated composites. J Compos Mater 32(5):804–828

  28. Shokrieh M, Zeinedini A, Ghoreishi SM (2017) On the mixed mode I/II delamination R-curve of E-glass/epoxy laminated composites. Comp Struct 171:19–31

  29. Singh S, Partridge I (1995) Mixed-mode fracture in an interleaved carbon-fibre/epoxy composite. Compos Sci Technol 55(4):319–327

  30. Treber D, Haspel B, Elsner P, Weidenmann K (2017) Delamination fracture toughness of continuous glass-fiber/epoxy composites for structural applications. Int J Plast Technol 21(1):39–54

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Acknowledgements

The first author thanks the staff and faculty of the Center for Composite Materials Research and the Department of Mechanical Engineering for their financial support during this research. Special thanks to Mr. Matthew Sharpe, Composite Materials Lab Manager, for his support in fabricating composite laminates and preparation of the test specimens and testing. The first author also thanks the support from the Joint School of Nanoscience and Nanoengineering at North Carolina A&T State University through the National Science Foundation (ECCS-1542174) grant. The second author acknowledges the financial support of NASA through URC Grant Number NNX09AV08A.

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Correspondence to Kunigal Shivakumar.

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Karnati, S.R., Shivakumar, K. Limited Input Benzeggagh and Kenane delamination failure criterion for mixed-mode loaded fiber reinforced composite laminates. Int J Fract (2020). https://doi.org/10.1007/s10704-019-00418-1

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Keywords

  • Mixed-mode stress state
  • Delamination failure criterion
  • Fracture toughness
  • LIBK