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A new macro-mechanical approach for investigation of damage zone effects on mixed mode I/II fracture of orthotropic materials

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Abstract

In this paper a new criterion for fracture investigation of orthotropic materials with cracks under mixed mode I/II loading is presented. In this fracture criterion, orthotropic material will be considered as a reinforced isotropic material. It is supposed that the crack will grow in the matrix of the orthotropic material. A new definition named here as “isotropic–orthotropic stress reduction factor” (IO-SRF) is utilized to consider the effects of the fracture process zone by a macro-mechanics approach. Also, the stress reduction factors will present a valuable relationship between the orthotropic and isotropic fracture toughness. Experimental and finite element methods will be introduced for computing the stress reduction factors. The SRFs are calculated for samples of glass–epoxy as an orthotropic material and samples of epoxy as a related isotropic one. Experimental tests under mixed mode I/II are performed on glass–epoxy composite samples to evaluate the validity of the presented mixed mode fracture criterion. The results of experimental tests on composite samples show a good agreement with the results of the presented criterion. Thus, the proposed criterion could be utilized as an efficient criterion for investigating the fracture of orthotropic materials under mixed mode I/II loading.

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References

  1. Talreja, R.: Assessment of the fundamentals of failure theories for composite materials. Compos. Sci. Technol. 105, 190–201 (2014)

    Article  Google Scholar 

  2. Benveniste, Y., Aboudi, J.: Crack propagation in a laminated composite material modeled by a two-dimensional mixture theory. Acta Mech. 29(1), 213–227 (1978)

    Article  MATH  Google Scholar 

  3. Li, Y.D., Xiong, T., Zhao, H.: Interfacial fracture analysis of a piezoelectric-polythene composite cylindrical shell patch under axial shear. Acta Mech. 225(2), 543 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Li, Y.D., Xiong, T., Cai, Q.G.: Coupled interfacial imperfections and their effects on the fracture behavior of a layered multiferroic cylinder. Acta Mech. 226(4), 1183–1199 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Sih, G.C.: Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fract. 10(3), 305–321 (1974)

    Article  Google Scholar 

  6. Hussain, M.A., Pu, S.L., Underwood, J.: Strain energy release rate for a crack under combined mode I and mode II. In: Fracture Analysis: Proceedings of the 1973 National Symposium on Fracture Mechanics, Part II. ASTM International (1974)

  7. Erdogan, F., Sih, G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 85(4), 519–525 (1963)

    Article  Google Scholar 

  8. Fakoor, M., Khansari, N.M.: Mixed mode I/II fracture criterion for orthotropic materials based on damage zone properties. Eng. Fract. Mech. 153, 407–420 (2016)

    Article  Google Scholar 

  9. Lin, W.H., Tsai, Y.M.: Fracture of hybrid laminates containing a pair of collinear cracks in the central layer. Acta Mech. 82(3), 159–173 (1990)

    Article  MATH  Google Scholar 

  10. Wu, E.M.: Application of fracture mechanics to anisotropic plates. J. Appl. Mech. 34(4), 967–74 (1967)

    Article  Google Scholar 

  11. Leicester, R.H.: Applications of linear fracture mechanics in the design of timber structures. In: Conference of the Australian Fracture Group, Melbourne, pp. 156–164 (1974)

  12. Williams, J.G., Birch, M.W.: Mixed mode fracture in anisotropic media. ASTM STP 601, 125–37 (1976)

    Google Scholar 

  13. Woo, C.W., Chow, C.L.: Mixed mode fracture in orthotropic media. In: Sih, G.C., Valluri, S.R. (eds.) Fracture Mechanics in Engineering Application, pp. 387–96. Sijthoff and Noordhoff, Rockville (1979)

    Google Scholar 

  14. Hunt, D.G., Croager, W.P.: Mode II fracture toughness of wood measured by a mixed-mode test method. J. Mater. Sci. Lett. 1(2), 77–9 (1982)

    Article  Google Scholar 

  15. Mall, S., Murphy, J.F., Shottafer, J.E.: Criterion for mixed mode fracture in wood. J. Eng. Mech. 109(3), 680–690 (1983)

    Article  Google Scholar 

  16. Jernkvist, L.O.: Fracture of wood under mixed mode loading: I. Derivation of fracture criteria. Eng. Fract. Mech. 68(5), 549–563 (2001)

    Article  Google Scholar 

  17. Jernkvist, L.O.: Fracture of wood under mixed mode loading: II. Experimental investigation of Picea abies. Eng. Fract. Mech. 68(5), 565–576 (2001)

    Article  Google Scholar 

  18. Romanowicz, M., Seweryn, A.: Verification of a non-local stress criterion for mixed mode fracture in wood. Eng. Fract. Mech. 75(10), 3141–60 (2008)

    Article  Google Scholar 

  19. Gowhari Anaraki, A.R., Fakoor, M.: General mixed mode I/II fracture criterion for wood considering T-stress effects. Mater. Des. 31, 4461–4469 (2010)

    Article  Google Scholar 

  20. Van der Put, T.A.C.M.: A new fracture mechanics theory for orthotropic materials like wood. Eng. Fract. Mech. 74, 771–781 (2007)

    Article  Google Scholar 

  21. Gowhari Anaraki, A.R., Fakoor, M.: Mixed mode fracture criterion for wood based on a reinforcement microcrack damage model. Mater. Sci. Eng. A 527, 7184–7191 (2010)

    Article  Google Scholar 

  22. Gowhari-Anaraki, A.R., Fakoor, M.: A new mixed-mode fracture criterion for orthotropic materials, based on strength properties. J. Strain Anal. IMechE (2010). https://doi.org/10.1243/03093247JSA667

    Google Scholar 

  23. Fakoor, M., Rafiee, R.,: Fracture investigation of wood under mixed mode I/II loading based on the maximum shear stress criterion. Strength Mater. 45(3), 378–385 (2013)

  24. Carraro, P.A., Zappalorto, M., Quaresimin, M.: A comprehensive description of interfibre failure in fibre reinforced composites. Theor. Appl. Fract. Mech. 79, 91–97 (2015)

    Article  Google Scholar 

  25. Buczek, M.B., Herakovich, C.T.: A normal stress criterion for crack extension direction in orthotropic composite materials. J. Compos. Mater. 19(6), 544–553 (1985)

    Article  Google Scholar 

  26. Gregory, M.A., Herakovich, C.T.: Predicting crack growth direction in unidirectional composites. J. Compos. Mater. 20(1), 67–85 (1986)

    Article  Google Scholar 

  27. Saouma, V.E., Ayari, M.L., Leavell, D.A.: Mixed mode crack propagation in homogeneous anisotropic solids. Eng. Fract. Mech. 27(2), 171–184 (1987)

    Article  Google Scholar 

  28. Buczek, M.B., Herakovich, C.T.: A normal stress criterion for crack extension direction in orthotropic composite materials. J. Compos. Mater. 19(6), 544–53 (1985)

    Article  Google Scholar 

  29. Wei-yang, Y., Shao-qin, Z., Yuan-duo, J.: On J-integrals in the plane fracture of composite materials. Appl. Math. Mech. 13(3), 281–287 (1992)

    Article  Google Scholar 

  30. Saucedo, L., Rena, C.Y., Ruiz, G.: Fully-developed FPZ length in quasi-brittle materials. Int. J. Fract. 178(1–2), 97–112 (2012)

    Article  Google Scholar 

  31. Fakoor, M., Rafiee, R., Sheikhansari, M.: The influence of fiber-crack angle on the crack tip parameters in orthotropic materials. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 0954406215617195 (2015)

  32. He, Q.L., Wu, L., Li, M., Yu, H.: Prediction of mode I crack growth resistance based on a comparative investigation of J-integral and energy dissipation rate concept. Acta Mech. 215(1–4), 175–191 (2010)

    Article  MATH  Google Scholar 

  33. Agarwal, B.D., Broutman, L.J., Chandrashekhara, K.: Analysis and Performance of Fiber Composites. Wiley, Hoboken (2006)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of New Sciences and Technologies, University of Tehran, 1439955941, Tehran, Iran

    Mahdi Fakoor & Maryam S. Shokrollahi

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  1. Mahdi Fakoor
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  2. Maryam S. Shokrollahi
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Correspondence to Mahdi Fakoor.

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Fakoor, M., Shokrollahi, M.S. A new macro-mechanical approach for investigation of damage zone effects on mixed mode I/II fracture of orthotropic materials. Acta Mech 229, 3537–3556 (2018). https://doi.org/10.1007/s00707-018-2132-4

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  • DOI: https://doi.org/10.1007/s00707-018-2132-4

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