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Effect of modulus and cohesive energy on critical fibre length in fibre-reinforced composites

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Abstract

The effect of fibre modulus and cohesive energy on critical fibre length and radius in ceramic-fibre-reinforced brittle composites has been investigated employing both analytical theory and computer simulation. The theory consists of a shear-lag analysis in which an energy failure criterion is incorporated. The simulation consists of a two-dimensional computer model based upon a discrete network of grid points. Failure is also defined in terms of an energy criterion, where the energy is calculated on the basis of a two- and three-body interaction between the grid points. Both theory and simulation show that a minimum critical aspect ratio is found as a function of the elastic moduli ratio, E f/E m, with a divergence occurring at both low- and high-modulus values. As the modulus ratio is increased, there is a transition in failure mechanism from tensile-dominated failure in the matrix to shear-dominated failure at the fibre-matrix interface. In addition, families of critical aspect ratio curves are obtained as a function of the cohesive energy ratio, U f/U m. Larger cohesive energy ratios shift the critical aspect ratio curve to larger values. These features potentially explain trends in the experimental results reported by Asloun et al., where the critical fibre aspect ratio was measured for fibre/matrix systems having different modulus and toughness ratios.

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References

  1. A. Kelly and G. J. Davies, Metall. Rev. 10 (1965) 37.

    Google Scholar 

  2. G. S. Holister and C. Thomas, “Fibre Reinforced Materials” (Elsevier, London, 1966) p. 16.

    Google Scholar 

  3. B. W. Rosen and N. F. Dow, in “Fracture”, Vol. 7, edited by H. Leibowitz (Academic, New York, 1972) p. 1.

    Google Scholar 

  4. M. R. Piggott, in “Load Bearing Fibre Composites” (Pergamon, Oxford, 1980) p. 83.

    Book  Google Scholar 

  5. D. Hull, “An Introduction to Composite Materials” (Cambridge University Press, Cambridge, 1981) p. 142.

    Google Scholar 

  6. H. L. Cox, Brit. J. Appl. Phys. 3 (1952) 72.

    Article  Google Scholar 

  7. A. S. Carrara and E. J. McGarry, J. Compos. Mat. 2 (1968) 222.

    Article  CAS  Google Scholar 

  8. R. A. Larder and C. W. Beadle, ibid. 10 (1976) 21.

    Article  Google Scholar 

  9. E. D. Reedy, ibid. 18 (1984) 595.

    Article  CAS  Google Scholar 

  10. S. R. Nutt and A. Needleman, Scripta Metall. 21 (1987) 705.

    Article  CAS  Google Scholar 

  11. W. R. Tyson and G. J. Davies, Brit. J. Appl. Phys. 16 (1965) 199.

    Article  Google Scholar 

  12. D. M. Schuster and E. Scala, Trans. Met. Soc. AIME 230 (1965) 1491.

    Google Scholar 

  13. B. W. Rosen, AIAA J. 2 (1964) 1985.

    Article  Google Scholar 

  14. Idem, “Fiber Composite Materials” (ASM, Metals Park, OH, 1965) p. 1.

    Google Scholar 

  15. C. Galiotis, R. J. Young, P. H. J. Heung and D. N. Batchelder, J. Mater. Sci. 19 (1984) 3640.

    Article  CAS  Google Scholar 

  16. Y. Termonia, ibid. 22 (1987) 504.

    Article  CAS  Google Scholar 

  17. Idem, ibid. 22 (1987) 1733.

    Article  CAS  Google Scholar 

  18. E. M. Asloun, M. Nardin and J. Schultz, ibid. 24 (1989) 1835.

    Article  CAS  Google Scholar 

  19. A. Kelly and W. R. V. Tyson, Mech. Phys. Solids 13 (1965) 329.

    Article  CAS  Google Scholar 

  20. M. J. Folkes and W. K. Wong, Polymer 28 (1987) 1309.

    Article  CAS  Google Scholar 

  21. W. D. Bascom and R. M. Jensen, J. Adhesion 19 (1986) 219.

    Article  CAS  Google Scholar 

  22. P. D. Beale and D. J. Srolovitz, Phys. Rev. B 37 (1988) 5500.

    Article  CAS  Google Scholar 

  23. W. H. Yang, D. J. Srolovitz, G. N. Hassold and M. P. Anderson, in “Simulation and Theory of Evolving Microstructures”, edited by M. P. Anderson and A. D. Rollett (TMS, Warrendale, PA, 1990) p. 277.

    Google Scholar 

  24. W. H. Yang, unpublished (1989).

  25. G. N. Hassold and D. J. Srolovitz; Phys. Rev. B 39 (1989) 9273.

    Article  CAS  Google Scholar 

  26. Y. Termonia, J. Mater. Sci. 25 (1990) 4644.

    Article  CAS  Google Scholar 

  27. M. R. Piggott, Compos. Sci. Tech. 30 (1987) 295.

    Article  CAS  Google Scholar 

  28. “Engineering Property Data on Selected Ceramics”, Vols 1–3, edited by J. F. Lynch (Metals and Ceramics Information Center, Columbus, OH, 1981).

    Google Scholar 

  29. “Handbook of Materials Science”, Vol. 3, edited by C. T. Lynch (CRC Press, Boca Raton, Florida, 1975).

    Google Scholar 

  30. T. W. Clyne, Mater. Sci. Engng A122 (1989) 183.

    Article  Google Scholar 

  31. C. R. Barrett, W. D. Nix and A. S. Tetelman, “The Principles of Engineering Materials” (Prentice-Hall, Englewood, NJ, 1973) p. 540.

    Google Scholar 

  32. F. W. Billmeyer Jr, “Textbook of Polymer Science” (Wiley, New York, London, Sydney, Toronto, 1971) p. 185.

    Google Scholar 

  33. H. Simon, PhD thesis, Université de Haute-Alsace, Mulhouse, France (1984).

    Google Scholar 

  34. H. Simon, F. Bomo and J. Schultz, in “Proceedings of the European Plastics Conference”, Paris, France, Vol. IV(9) (1982) pp. 1–5.

    Google Scholar 

  35. J. Schultz, L. Lavielle and C. Martin, J. Adhesion 23 (1987) 45.

    Article  CAS  Google Scholar 

  36. T. Ohsawa, A. Nakayama, M. Miwa and A. Hasegawa, J. Appl. Polym. Sci. 22 (1978) 3203.

    Article  CAS  Google Scholar 

  37. J. M. Robinson, R. J. Young, C. Galiotis and D. N. Batchelder, J. Mater. Sci. 22 (1987) 3642.

    Article  CAS  Google Scholar 

  38. J. Schultz, L. Lavielle and H. Simon, in “Proceedings of the International Symposium on Science and New Applications of Carbon Fibres”, Toyohashi, Japan, November 1984 (Toyohashi University of Technology, Japan, 1984) p. 125.

    Google Scholar 

  39. G. Guilpain and J. B. Donnet, personal communications (1987).

  40. L. T. Drzal, M. J. Rich, M. F. Koenig and P. F. Lloyd, J. Adhesion 16 (1983) 133.

    Article  CAS  Google Scholar 

  41. L. Ongchin, W. K. Olender and F. H. Ancker, in “Proceedings of the 27th Annual Technical Conference”, SPI/ Reinforced Plastics — Composite Institute, Washington (1972) Section 11-A.

    Google Scholar 

  42. M. Xie, PhD thesis, Institut National des Sciences Appliquées, Lyon, France (1987).

    Google Scholar 

  43. M. J. Folkes and W. K. Wong, Polymer 28 (1987) 1309.

    Article  CAS  Google Scholar 

  44. F. Bomo, PhD thesis, Université de Haute-Alsace, Mulhouse, France (1983).

    Google Scholar 

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Authors and Affiliations

  1. Corporate Research Science Laboratory, Exxon Research and Engineering Company, 08801, Annandale, NJ, USA

    L. Monette, M. P. Anderson, S. Ling & G. S. Grest

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  1. L. Monette
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  2. M. P. Anderson
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  3. S. Ling
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  4. G. S. Grest
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Monette, L., Anderson, M.P., Ling, S. et al. Effect of modulus and cohesive energy on critical fibre length in fibre-reinforced composites. J Mater Sci 27, 4393–4405 (1992). https://doi.org/10.1007/BF00541572

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