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Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

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Abstract

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis.

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References

  1. W. A. Curtin, “Stress-strain behavior of brittle matrix composites,” in: Comprehensive Composite Materials. Vol. 4, Elsevier Science Ltd. (2000), pp. 47–76.

    Google Scholar 

  2. V. Kostopoulos and Y. Z. Pappas, “Toughening mechanisms in long fiber ceramic matrix composites, ” in: Comprehensive Composite Materials. Vol. 4, Elsevier Science Ltd. (2000), pp. 95–114.

    Article  Google Scholar 

  3. J. Aveston, G. A. Cooper, and A. Kelly, “Single and multiple fracture,” in Proc. of Conference “Properties of Fiber Composites,” National Physical Laboratory, IPC, England (1971), pp. 15–26.

    Google Scholar 

  4. J. Aveston and A. Kelly, “Theory of multiple fracture of fibrous composites,” J. Mater. Sci., 8, No. 3, 352–362 (1973).

    Article  CAS  Google Scholar 

  5. B. Budiansky, J. W. Hutchinson, and A. G. Evans, “Matrix fracture in fiber-reinforced ceramics,” J. Mech. Phys. Solids, 34, No. 2, 167–189 (1986).

    Article  MATH  Google Scholar 

  6. M. Sutcu and W. B. Hillig, “The effect of fiber-matrix debond energy on the matrix cracking strength and the debond shear strength,” Acta Metall., 38, No. 12, 2653 (1990).

    Article  CAS  Google Scholar 

  7. Y. C. Chiang, “On fiber debonding and matrix cracking in fiber reinforced ceramics,” J. Compos. Sci. Technol., 61, No. 12, 1743–1756 (2001).

    Article  CAS  Google Scholar 

  8. Y. C. Gao, Y. W. Mai, and B. Cotterell, “Fracture of fiber-reinforced materials,” J. Appl. Math. Phys. (ZAMP), 39, No. 7, 550–572 (1988).

    Article  MATH  Google Scholar 

  9. J. W. Hutchinson and H. M. Jensen, “Models of fiber debonding and pull out in brittle composites with friction,” Mech. Mater., 9, 139–163 (1990).

    Article  Google Scholar 

  10. Y. C. Chiang, “On crack-wake debonding in fiber reinforced ceramics,” Eng. Fract. Mech. 65, No. 1, 15–28 (2000).

    Article  Google Scholar 

  11. W. Wu, I. Verpoest, and J. Varna, “A novel axisymmetric variational analysis of stress transfer into fibres through a partially debonded interface,” J. Com pos. Sci. Technol., 58, 1863–1877 (1998).

    Article  CAS  Google Scholar 

  12. J. A. Nairn and Y. C. Liu, “Stress transfer into a fragmented anisotropic fiber through an imperfect interface,” Int. J. Solids Struct., 34, 1255–1281 (1996).

    Article  Google Scholar 

  13. U. Mbanefo and R. A. Westmann, “Axisymmetric stress analysis of a broken debonded fiber,” ASME Trans. J. Appl. Mech., 57, 654–660 (1990).

    Article  MATH  Google Scholar 

  14. D. Hull and T. W. Clyne, An Introduction to Composite Materials, 2nd Ed., Cambridge University Press (1996).

  15. P. L. Lawrence, “Some theoretical considerations of fibre pull-out from an elastic matrix,” J. Mater. Sci., 7, No. 1, 1–6 (1972).

    Article  CAS  Google Scholar 

  16. A. Takaku and R. G. C. Arridge, “The effect of interfacial radial and shear stress on fibre pull-out in composite materials,” J. Phys. D: Appl. Phys., 6, No. 11, 2038–2047 (1973).

    Article  ADS  CAS  Google Scholar 

  17. H. Stang and S. P. Shah, “Failure of fibre-reinforced composites by pull-out fracture,” J. Mater. Sci., 21, No. 3, 953–957 (1986).

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Chinese Culture University No. 55, Hua-Kang Rd., Taipei, Taiwan

    Yih-Cherng Chiang

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  1. Yih-Cherng Chiang
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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.

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Chiang, YC. Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites. Mech Compos Mater 43, 113–126 (2007). https://doi.org/10.1007/s11029-007-0012-4

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  • DOI: https://doi.org/10.1007/s11029-007-0012-4

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