Analytical Models of Stress Transfer in Unidirectional Composites and Cross-Ply Laminates, and Their Application to the Prediction of Matrix/Transverse Cracking

  • L. N. McCartney
Part of the IUTAM Symposia book series (IUTAM)

Summary

Many unidirectional composites are made using carbon fibres which have anisotropic thermo-mechanical properties. There is a need, therefore, to take account of this anisotropy when making predictions of the properties of damaged composites. For the more general case when the fibres and matrix are both transverse isotropic solids, a relatively simple shear-lag approach to understanding stress transfer between fibres and matrix is presented. A similar approach is used to develop a shear-lag model of stress transfer between neighbouring plies in a cross-ply laminate containing transverse cracks. As to be expected stress transfer is governed by second order ordinary differential equations which are easily solved. It is shown how a more realistic model of stress transfer for unidirectional composites must be modified when the fibres and matrix of the composite are transverse isotropic solids. Reference is made to more realistic models of stress transfer in cross-ply laminates containing transverse cracks in the 90 ply. The more realistic models lead to fourth order differential equations. Such models are thus more flexible than shear lag models in that a greater variety of boundary conditions can be satisfied.

A procedure is described which enables the matrix cracking stress for unidirectional composites, and the transverse cracking stress for cross-ply laminates, to be calculated from the various micromechanical models of stress transfer. The models are also used to predict the dependence of the thermoelastic constants on the density of matrix cracks in unidirectional composites, and on the density of transverse cracks in cross-ply laminates. An attempt is made to predict the stress-strain curves of damaged composites based on two approximations that can be used to estimate the density of cracking as a function of applied stress.

Using the shear-lag and more realistic models of stress transfer for unidirectional and laminated composites, comparisons are made of the predictions of the thermoelastic constants and of the stress-strain curves.

Keywords

Anisotropy Carbide Brittle Tungsten Kelly 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D.B. Marshall, B.N. Cox and A.G. Evans, Acta Metall. 1985, 33, 2013–2021.CrossRefGoogle Scholar
  2. 2.
    L.N. McCartney, Proc. Roy. Soc. Lond. 1987, A409, 329–350.CrossRefGoogle Scholar
  3. 3.
    L.N. McCartney, ‘Mechanics for the growth of bridged cracks in composite materials’ NPL Report DMM(A)28, June 1991.Google Scholar
  4. 4.
    A. Kelly and L.N. McCartney, Proc. 6th Int. Conf. on Composite Materials, 1987, vol 3, pp 210–222. Elsevier Applied Science, London, NY.Google Scholar
  5. 5.
    H.L. Cox, Brit. J. Appl. Phys. 1952, l3, 72–79.CrossRefGoogle Scholar
  6. 6.
    J. Aveston, G.A. Cooper and A. Kelly, Conf. on ‘Properties of fibre composites’ 1971, NPL, pp 15–26, IPC Science and Technology, Guildford, Surrey.Google Scholar
  7. 7.
    J. Aveston and A. Kelly, J.Mater. Sci. 1973, 8, 352–362.CrossRefGoogle Scholar
  8. 8.
    A.H. Nayfeh, Fibre Sci. and Tech. 1977, 10, 195–209.CrossRefGoogle Scholar
  9. 9.
    P.S. Steif, J. Comp. Mater. 1984, 17, 153–172.CrossRefGoogle Scholar
  10. 10.
    C-H Hsueh, J. Amer. Ceram. Soc. 1988, 71 490–493.CrossRefGoogle Scholar
  11. 11.
    Y-C Gao, Y-W Mai and B. Cotterell, J. Appl. Math & Phys. (ZAMP) 1988, 39 550–572.CrossRefMATHGoogle Scholar
  12. 12.
    T.W. Clyne, Mater. Sci. Engng. 1989, A122, 183–192.CrossRefGoogle Scholar
  13. 13.
    K.W. Garrett and J.E. Bailey, J. Mater. Sci. 1977, 12, 157–168.CrossRefGoogle Scholar
  14. 14.
    S.L. Ogin, P.A. Smith and P.W.R. Beaumont, Comp. Sci & Tech. 1985, 22, 23–31.CrossRefGoogle Scholar
  15. 15.
    P.A. Smith and J.R. Wood, Comp. Sci & Tech. 1990, 38, 85–93.CrossRefGoogle Scholar
  16. 16.
    L.N. McCartney, Proc. Roy. Soc. Lond. 1989, A425, 215–244.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Z. Hashin, Mech of Mater. 1985, 4, 121–136.CrossRefGoogle Scholar
  18. 18.
    Z. Hashin, J. Appl. Mech. 1987, 54, 872–879.CrossRefMATHGoogle Scholar
  19. 19.
    L.N. McCartney, Proc. Inst. Mech. Eng. 4th Int. Conf. FRC’ 90 Fibre Reinforced Composites, 1990, pp 19–26. Mechanical Engineering Publications, Bury St Edmunds, UK.Google Scholar
  20. 20.
    L.N. McCartney, ‘Theory of stress transfer in a cross-ply laminate containing a parallel array of transverse cracks’, NPL Report DMA(A)189, March 1990. (Modified version accepted for publication in J. Mech. Phys. Solids).Google Scholar
  21. 21.
    R.J. Nuismer and S.C. Tan J. Comp. Mater. 1988 22 306–321.Google Scholar
  22. 22.
    L.N. McCartney 1991, to be published.Google Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1992

Authors and Affiliations

  • L. N. McCartney
    • 1
  1. 1.Division of Materials MetrologyNational Physical LaboratoryTeddingtonUK

Personalised recommendations