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Effective mechanical properties of unidirectional composites in the presence of imperfect interface

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Abstract

In this paper, the equivalent inclusion method is implemented to estimate the effective mechanical properties of unidirectional composites in the presence of an imperfect interface. For this purpose, a representative volume element containing three constituents, a matrix, and interface layer, and a fiber component, is considered. A periodic eigenstrain defined in terms of Fourier series is then employed to homogenize non-dilute multi-phase composites. In order to take into account the interphase imperfection effects on mechanical properties of composites, a stiffness parameter in terms of a matrix and interphase elastic modulus is introduced. Consistency conditions are also modified accordingly in such a way that only the part of the fiber lateral stiffness is to be effective in estimating the equivalent composite mechanical properties. Employing the modified consistency equations together with the energy equivalence relation leads to a set of linear equations that are consequently used to estimate the average values of eigenstrain in non-homogeneous phases. It is shown that for composites with both soft and hard reinforcements, largest stiffness parameter that indicates complete fiber–matrix interfacial debonding causes the same equivalent lateral properties.

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References

  1. Drechsler K., Geier M.H.: Quality handbook for composite materials. 1. Auflage, Chapman + Hull, London, 1994, 278 Seiten. Materialwissenschaft und Werkstofftechnik 25, 434 (1994)

    Article  Google Scholar 

  2. Summerscales J.: Manufacturing defects in fiber-reinforced plastics composites. Non Destruct. Test. Cond. Monit. 36, 936 (1994)

    Google Scholar 

  3. Månson, J.A.E., Wakeman, M.D., Bernet, N.: Composite processing and manufacturing-an overview. In: Talreja, R., Månson, J. A. E., Kelly, A., Zweben, C. (eds.) Comprehensive Composite Materials, vol. 2, p. 577. Elsevier Science Ltd., Oxford, UK (2000)

  4. Prakash R.: Significance of defects in the fatigue failure of carbon fibre reinforced plastics. Fibre Sci. Technol. 14, 171 (1981)

    Article  Google Scholar 

  5. Guerdal Z., Tomasino A.P., Biggers S.B.: Effects of processing induced defects on laminate response: inter laminar tensile strength. SAMPE J. 27, 3 (1991)

    Google Scholar 

  6. Bulsara V.N., Talreja R., Qu J.: Damage initiation under transverse loading of unidirectional composites with arbitrarily distributed fibers. Compos. Sci. Technol. 59, 673 (1999)

    Article  Google Scholar 

  7. Sorensen B.F., Talreja R.: Effects of nonuniformity of fiber distribution on thermally-induced residual stresses and cracking in ceramic matrix composites. Mech. Mater. 16, 351 (1993)

    Article  Google Scholar 

  8. Theocaris P.S.: The Mesophase Concept in Composites. Springer, Berlin (1987)

    Book  Google Scholar 

  9. Duan H.L., Yi X., Huang Z.P., Wang J.: A unified scheme for prediction of effective moduli of multiphase composites with interface effects: part II—application and scaling laws. Mech. Mater. 39, 94 (2007)

    Article  Google Scholar 

  10. Hashin Z.: Analysis of composite materials—a survey. J. Appl. Mech. 50, 481 (1983)

    Article  MATH  Google Scholar 

  11. Christensen R.M.: A critical evaluation for a class of micro-mechanics models. J. Mech. Phys. Solids 38, 379 (1990)

    Article  Google Scholar 

  12. Nemat-Nasser, S., Hori, M.: Micromechanics: overall properties of heterogeneous materials, vol. 2. Elsevier, Amsterdam (1999)

  13. Hill R.: Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour. J. Mech. Phys. Solids 12, 199 (1964)

    Article  MathSciNet  Google Scholar 

  14. Kanaun S.K., Kudryavtseva L.T.: Spherically layered inclusions in a homogeneous elastic medium. J. Appl. Math. Mech. 50, 483 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kanaun S.K., Kudryavtseva L.T.: Elastic and thermoelastic characteristics of composites reinforced with unidirectional fibre layers. J. Appl. Math. Mech. 53, 628 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  16. Hashin Z.: Thermoelastic properties of fiber composites with imperfect interface. Mech. Mater. 8, 333 (1990)

    Article  Google Scholar 

  17. Hashin Z.: Thermoelastic properties of particulate composites with imperfect interface. J. Mech. Phys. Solids 39, 745 (1991)

    Article  MathSciNet  Google Scholar 

  18. Qiu Y.P., Weng G.J.: Elastic moduli of thickly coated particle and fiber-reinforced composites. J. Appl. Mech. 58, 388 (1991)

    Article  MATH  Google Scholar 

  19. Shen L.X., Li J.: Homogenization of a fibre/sphere with an inhomogeneous interphase for the effective elastic moduli of composites. Proc. Roy. Soc. A. 461, 1475 (2005)

    Article  Google Scholar 

  20. Mura T.: Micromechanics of Defects in Solids. M. Nijhoff, Boston (1982)

    Book  Google Scholar 

  21. El Mouden M., Cherkaoui M., Molinari A., Berveiller M.: The overall elastic response of materials containing coated inclusions in a periodic array. Int. J. Eng. Sci. 36, 813 (1998)

    Article  Google Scholar 

  22. Dunn M.L., Ledbetter H.: Elastic moduli of composites reinforced by multiphase particles. J. Appl. Mech. 62, 1023 (1995)

    Article  MATH  Google Scholar 

  23. Hori M., Nemat-Nasser S.: Double-inclusion model and overall moduli of multi-phase composites. Mech. Mater. 14, 189 (1993)

    Article  Google Scholar 

  24. Shodja H.M., Roumi F.: Overall behavior of composites with periodic multi-inhomogeneities. Mech. Mater. 37, 343 (2005)

    Article  Google Scholar 

  25. Zohdi T.I., Wriggers P.: Aspects of the computational testing of the mechanical properties of microheterogeneous material samples. Int. J. Numer. Methods Eng. 50, 2573 (2001)

    Article  MATH  Google Scholar 

  26. Zohdi, T.I., Wriggers, P.: Computational micro-macro material testing. Arch. Comput. Methods Eng. 8, 131 (2001/06/01, 2001)

    Google Scholar 

  27. Wriggers P., Zavarise G., Zohdi T.I.: A computational study of interfacial debonding damage in fibrous composite materials. Comput. Mater. Sci. 12, 39 (1998)

    Article  Google Scholar 

  28. Kaminski M.: Boundary element method homogenization of the periodic linear elastic fiber composites. Eng. Anal. Bound. Elem. 23, 815 (1999)

    Article  MATH  Google Scholar 

  29. Schröder, J.: Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilitätsproblemen, A habilitation thesis of the University of Stuttgart, (2000)

  30. Oskay C., Fish J.: Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comput. Methods Appl. Mech. Eng. 196, 1216 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  31. Lebensohn R.A., Liu Y., Ponte Castañeda P.: On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta. Materialia 52, 5347 (2004)

    Article  Google Scholar 

  32. Klinge S., Hackl K.: Application of the multiscale fem to the modeling of nonlinear composites with a random microstructure. Int. J. Mult. Comp. Eng. 10, 213 (2012)

    Article  Google Scholar 

  33. Sevostianov I., Rodriguez-Ramos R., Guinovart-Diaz R., Bravo-Castillero J., Sabina F.J.: Connections between different models describing imperfect interfaces in periodic fiber-reinforced composites. Int. J. Solids Struct. 49, 1518 (2012)

    Article  Google Scholar 

  34. Würkner M., Berger H., Gabbert U.: Numerical study of effective elastic properties of fiber reinforced composites with rhombic cell arrangements and imperfect interface. Int. J. Eng. Sci. 63, 1 (2013)

    Article  Google Scholar 

  35. Berger H., Kurukuri S., Kari S., Gabbert U., Rodriguez-Ramos R., Bravo-Castillero J., Guinovart-Diaz R.: Numerical and analytical approaches for calculating the effective thermo-mechanical properties of three-phase composites. J. Thermal Stress. 30, 801 (2007)

    Article  Google Scholar 

  36. Guinovart-Dıaz R., Bravo-Castillero J., Rodrıguez-Ramos R., Sabina F.J.: Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: elastic and hexagonal symmetry. J. Mech. Phys. Solids 49, 1445 (2001)

    Article  MATH  Google Scholar 

  37. Nemat-Nasser S., Taya M.: On effective moduli of an elastic body containing periodically distributed voids. Q. Appl. Math. 39, 43 (1981)

    Google Scholar 

  38. Nemat-Nasser S., Iwakuma T., Hejazi M.: On composites with periodic structure. Mech. Mater. 1, 239 (1982)

    Article  Google Scholar 

  39. Iwakuma T., Nemat-Nasser S.: Composites with periodic microstructure. Comput. Struct. 16, 13 (1983)

    Article  MATH  Google Scholar 

  40. Miller B., Muri P., Rebenfeld L.: A microbond method for determination of the shear strength of a fiber/resin interface. Compos. Sci. Technol. 28, 17 (1987)

    Article  Google Scholar 

  41. Hazanov S., Amieur M.: On overall properties of elastic heterogeneous bodies smaller than the representative volume. Int. J. Eng. Sci. 33, 1289 (1995)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Center of Excellence in Aerospace Systems, Aerospace Engineering Department, Sharif University of Technology, Azadi Avenue, Tehran, Iran

    S. A. Hosseini Kordkheili & H. Toozandehjani

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  1. S. A. Hosseini Kordkheili
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  2. H. Toozandehjani
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Correspondence to S. A. Hosseini Kordkheili.

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Hosseini Kordkheili, S.A., Toozandehjani, H. Effective mechanical properties of unidirectional composites in the presence of imperfect interface. Arch Appl Mech 84, 807–819 (2014). https://doi.org/10.1007/s00419-014-0834-1

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  • DOI: https://doi.org/10.1007/s00419-014-0834-1

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