Journal of Materials Science

, Volume 28, Issue 24, pp 6799–6808 | Cite as

Dilatational bands in rubber-toughened polymers

  • A. Lazzeri
  • C. B. Bucknall


A theory is advanced to explain the effects of rubber particle cavitation upon the deformation and fracture of rubber-modified plastics. The criteria for cavitation in triaxially-stressed particles are first analysed using an energy-balance approach. It is shown that the volume strain in a rubber particle, its diameter and the shear modulus of the rubber are all important in determining whether void formation occurs. The effects of rubber particle cavitation on shear yielding are then discussed in the light of earlier theories of dilatational band formation in metals. A model proposed by Berg, and later developed by Gurson, is adapted to include the effects of mean stress on yielding and applied to toughened plastics. The model predicts the formation of cavitated shear bands (dilatational bands) at angles to the tensile axis that are determined by the current effective void content of the material. Band angles are calculated on the assumption that all of the rubber particles in a band undergo cavitation and the effective void content is equal to the particle volume fraction. The results are in satisfactory agreement with observations recorded in the literature on toughened plastics. The theory accounts for observed changes in the kinetics of tensile deformation in toughened nylon following cavitation and explains the effects of particle size and rubber modulus on the brittle-tough transition temperature.


Rubber Cavitation Shear Modulus Shear Band Tensile Deformation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. B. Bucknall, “Toughened Plastics” (Applied Science Publishers, London, 1977).Google Scholar
  2. 2.
    P. Beahan, A. Thomas and M. Bevis, J. Mater. Sci. 11 (1976) 1207.Google Scholar
  3. 3.
    A. M. Donald and E. J. Kramer, J. Appl. Polym. Sci. 27 (1982) 3729.Google Scholar
  4. 4.
    G. H. Michler, Acta Polymerica 36 (1985) 285.Google Scholar
  5. 5.
    R. A. Bubeck, D. J. Buckley, E. J. Kramer and H. Brown, J. Mater. Sci. 26 (1991) 6249.Google Scholar
  6. 6.
    A. S. Argon and M. M. Salama, Mater. Sci. Engng 23 (1977) 219.Google Scholar
  7. 7.
    H. Breuer, F. Haaf, and J. Stabenow, J. Macromol. Sci.-Phys. B14 (1977) 387.Google Scholar
  8. 8.
    G. H. Michler, Colloid Polym. Sci. 267 (1989) 377.Google Scholar
  9. 9.
    A. F. Yee and R. A. Pearson, J. Mater. Sci. 21 (1869) 2462.Google Scholar
  10. 10.
    Idem., ibid. 21 (1986) 2475.Google Scholar
  11. 11.
    H.-J. Sue, ibid. 27 (1992) 3098.Google Scholar
  12. 12.
    A. Lazzeri, PhD thesis, Cranfield Institute of Technology, Cranfield, UK (1991)Google Scholar
  13. 13.
    A. F. Yee and R. A. Pearson, in “Fractography and Failure Mechanisms of Polymers and Composites ” edited by A. C. Roulin-Moloney (Elsevier Applied Science, London, 1989) p. 291.Google Scholar
  14. 14.
    R. J. M. Borggreve, R. J. Gaymans and H. M. Eichenwald, Polymer 30 (1989) 78.Google Scholar
  15. 15.
    A. J. Oostenbrink, L. J. Molenaar and R. J. Gaymans, Third European Symposium on Polymer Blends, Cambridge, 24–26 July 1990 (Plastics and Rubber Institute, London, 1990) paper E3.Google Scholar
  16. 16.
    F. Ramsteiner, Kunststoffe 73(3) (1983) 148.Google Scholar
  17. 17.
    F. Ramsteiner and W. Heckmann, Polym. Commun. 26 (1985) 199.Google Scholar
  18. 18.
    F. Speroni, E. Castoldi, P. Fabbri and T. Casiraghi, J. Mater. Sci. 24 (1989) 2165.Google Scholar
  19. 19.
    C. B. Bucknall, P. Heather and A. Lazzeri, ibid. 24 (1989) 1489.Google Scholar
  20. 20.
    K. Dijkstra, PhD thesis, University of Twente, Netherlands (1993).Google Scholar
  21. 21.
    A. N. Gent and C. Wang, J. Mater. Sci. 26 (1991) 3392.Google Scholar
  22. 22.
    D. C. Edwards, ibid. 25 (1992) 4175.Google Scholar
  23. 23.
    H. Vangerko and L. R. G. Treloar, J. Phys. D Appl. Phys. 11 (1978) 1969.Google Scholar
  24. 24.
    P. F. Thomason, “Ductile Fracture of Metals” (Pergamon Press, Oxford, 1991).Google Scholar
  25. 25.
    A. L. Gurson, J. Eng. Mater. Technol., Trans. ASME 99 (1977) 2.Google Scholar
  26. 26.
    C. A. Berg, in “Inelastic Behaviour of Solids”, edited by M. F. Kanninen (McGraw-Hill, New York, 1970) p. 171.Google Scholar
  27. 27.
    I. M. Ward, J. Mater. Sci. 6 (1971) 1397.Google Scholar
  28. 28.
    N. Brown, in “Failure of Plastics”, edited by W. Brostow (Hanser Publishers, Munich, 1986).Google Scholar
  29. 29.
    R. J. Young and P. A. Lovell, “Introduction to Polymers”, 2nd Edn (Chapman & Hall, London, 1991).Google Scholar
  30. 30.
    A. L. Gurson, PhD thesis, Brown University (1975).Google Scholar
  31. 31.
    Idem., in Proceedings of the International Conference on Fracture, ICF4 Fracture 1977, Waterloo, Canada, Vol. 2A (Pergamon Press, Oxford, 1977) p. 357.Google Scholar
  32. 32.
    R. Hill, “The Mathematical Theory of Plasticity” (The University Press, Oxford, 1950).Google Scholar
  33. 33.
    H. Yamamoto, Int. J. Fract. 14 (1978) 347.Google Scholar
  34. 34.
    P. B. Bowden, in “The Physics of Glassy Polymers”, edited by R. N. Haward (Applied Science Publishers, London, 1973).Google Scholar
  35. 35.
    I. M. Ward, “Mechanical Properties of Solid Polymers” (Wiley, New York, 1983) p. 362.Google Scholar
  36. 36.
    J. F. W. Bishop and R. Hill, Phil. Mag. 42 (1951) 414.Google Scholar
  37. 37.
    Idem., ibid. 42 (1951) 1298.Google Scholar
  38. 38.
    J. C. Bauwens, J. Polym. Sci. A-2 5 (1967) 1145.Google Scholar
  39. 39.
    Idem., ibid. 8 (1970) 893.Google Scholar
  40. 40.
    P. B. Bowden and J. A. Jukes, J. Mater. Sci. 7 (1972) 52.Google Scholar
  41. 41.
    A. S. Argon, R. D. Andrews, J. A. Godrick and W. Whitney, J. Appl. Phys. 39 (1968) 1899.Google Scholar
  42. 42.
    R. P. Kambour, Nature 195 (1962) 1299.Google Scholar
  43. 43.
    Idem., Polymer 5 (1964) 143.Google Scholar
  44. 44.
    A. M. Donald and E. J. Kramer, J. Polym. Sci. Polym. Phys. 20 (1982) 899.Google Scholar
  45. 45.
    P. L. Fernando and J. G. Williams, Polym. Engng Sci. 20 (1980) 215.Google Scholar
  46. 46.
    O. F. Yap, Y.-W. Mai and B. Cotterell, J. Mater. Sci. 18 (1983) 657.Google Scholar
  47. 47.
    E. J. Kramer. Polym. Engng Sci. 24 (1984) 761.Google Scholar
  48. 48.
    S. Wu, Polymer 26 (1985) 1855.Google Scholar
  49. 49.
    Idem., J. Appl. Polym. Sci. 35 (1988) 349.Google Scholar
  50. 50.
    R. J. M. Borggreve, R. J. Gaymans, J. Schuijer and J. F. Ingen-Housz, Polymer 28 (1987) 1489.Google Scholar
  51. 51.
    R. J. M. Borggreve, R. J. Gaymans and J. Schuijer, ibid. 30 (1989) 71.Google Scholar

Copyright information

© Chapman & Hall 1993

Authors and Affiliations

  • A. Lazzeri
    • 1
  • C. B. Bucknall
    • 2
  1. 1.Materials Engineering CentreUniversity of PisaPisaItaly
  2. 2.Cranfield Institute of TechnologySIMSCranfieldUK

Personalised recommendations