Journal of Materials Science

, 45:1086 | Cite as

Influence of fibre taper on the work of fibre pull-out in short fibre composite fracture



A model has been formulated to determine the work of pull-out, U, of an elastic fibre as it shear-slides out of a plastic matrix in a fractured composite. The fibres considered in the analysis have the following shapes: uniform cylinder and ellipsoidal, paraboloidal or conical tapers. Energy transfer at the fibre–matrix interface is described by an energy density parameter which is defined as the ratio of U to the fibre surface area. The model predicts that the energy required to pull out a tapered fibre is small because the energy transfer at the fibre–matrix interface to overcome friction is small. In contrast, the pull-out energy of a uniform cylindrical fibre is large because the energy transfer is large. The pull-out energies of the paraboloidal and ellipsoidal fibres lay between those for the uniform cylindrical and the conical fibres. With the exception of the uniform cylindrical fibre which yields a constant energy density, tapered fibres yield expressions for the energy density which depend on the fibre axial ratio, q. In particular, the energy density increases as q increases but converges at large q. By defining the critical axial ratio, q 0, as the limit beyond which u is independent of the fibre slenderness, our model predicts the value of q 0 to be about 10. These results are applied to explain the mechanisms regulating fibre composite fracture.


Axial Stress Elastic Fibre Critical Length Matrix Interface Interfacial Shear Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Kim JK, Mai YW (1991) Compos Sci Technol 41:333CrossRefGoogle Scholar
  2. 2.
    Lawrence P (1972) J Mater Sci 7:1. doi: 10.1007/BF00549541 CrossRefADSGoogle Scholar
  3. 3.
    Piggott MR (1980) Load bearing fibre composites, 1st edn. Pergamon Press, OxfordMATHGoogle Scholar
  4. 4.
    Kelly A, MacMillan NH (1986) Strong solids: monographs on physics and chemistry of materials, 3rd edn. Clarendon Press, OxfordGoogle Scholar
  5. 5.
    Suemasu H, Kondo A, Itatani K, Nozue A (2001) Compos Sci Technol 61:281CrossRefGoogle Scholar
  6. 6.
    Bilteryst F, Marigo JJ (2003) Eur J Mech A 22:55MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Quek MY (2002) Int J Adhesion Adhesives 22:303CrossRefGoogle Scholar
  8. 8.
    Schuster DM, Scala E (1964) Trans Metall Soc AIME 230:1635Google Scholar
  9. 9.
    Carrara AS, McGarry FJ (1968) J Compos Mater 2:222CrossRefGoogle Scholar
  10. 10.
    Goh KL, Aspden RM, Mathias KJ, Hukins DWL (1999) Proc R Soc Lond A 455:3351MATHCrossRefADSGoogle Scholar
  11. 11.
    Goh KL, Mathias KJ, Aspden RM, Hukins DWL (2000) J Mater Sci 35:2493. doi: 10.1023/A:1004725903966 CrossRefGoogle Scholar
  12. 12.
    Goh KL, Aspden RM, Hukins DWL (2004) Compos Sci Technol 64:1091CrossRefGoogle Scholar
  13. 13.
    Goh KL, Aspden RM, Mathias KJ, Hukins DWL (2004) Proc R Soc Lond A 460:2339MATHCrossRefADSGoogle Scholar
  14. 14.
    Goh KL, Huq AMA, Aspden RM, Hukins DWL (2008) Adv Compos Lett 17:131Google Scholar
  15. 15.
    Cox HL (1952) Br J Appl Phys 3:72CrossRefADSGoogle Scholar
  16. 16.
    Gent AN, Chang YW, Nardin M, Schultz J (1996) J Mater Sci 31:1707. doi: 10.1007/BF00372182 CrossRefADSGoogle Scholar
  17. 17.
    Goh KL, Meakin JR, Aspden RM, Hukins DWL (2005) Proc R Soc Lond B 272:1979CrossRefGoogle Scholar
  18. 18.
    Goh KL, Meakin JR, Aspden RM, Hukins DWL (2007) J Theor Biol 245:305CrossRefPubMedGoogle Scholar
  19. 19.
    Gent AN, Wang C (1993) J Mater Sci 28:2494. doi: 10.1007/BF01151685 CrossRefADSGoogle Scholar
  20. 20.
    Chiang YC (2007) J Mech 23:95Google Scholar
  21. 21.
    Kelly A, Tyson WR (1965) J Mech Phys Solids 13:329CrossRefADSGoogle Scholar
  22. 22.
    Wisnom MR, Green D (1995) Composites 26:499CrossRefGoogle Scholar
  23. 23.
    Hosseinkhani H, Hosseinkhani M, Kobayashi H (2006) J Bioactive Compat Polym 21:277CrossRefGoogle Scholar
  24. 24.
    Leo AJ, Grande DA (2006) Cells Tissues Organs 183:112CrossRefPubMedGoogle Scholar
  25. 25.
    Holmes DF, Chapman JA, Prockop DJ, Kadler KE (1992) Proc Natl Acad Sci USA 89:9855CrossRefPubMedADSGoogle Scholar
  26. 26.
    Holmes DF, Watson RB, Chapman JA, Kadler KE (1996) J Mol Biol 261:93CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.School of Mechanical EngineeringUniversity of BirminghamEdgbastonUK
  3. 3.School of EngineeringMonash UniversitySelangor Darul EhsanMalaysia

Personalised recommendations