Effect of matrix cracking on the overall thermal conductivity of fibre-reinforced composites

  • T. J. Lu
  • J. W. Hutchinson


The longitudinal thermal conductivity of a unidirectional fibre-reinforced composite containing an array of equally spaced transverse matrix cracks is calculated. The cracked composite is modelled by a cylindrical cell which accounts for altered heat transfer across the matrix cracks as well as through debonded portions of the fibre—matrix interface. Heat transfer mechanisms across the cracks and dedonded interfaces considered are contact, gaseous conduction, and radiation, and the relative importance of these mechanisms is discussed. Approximate closed form solutions to the cell model for the overall thermal conductivity are obtained using an approach reminiscent of the shear lag analysis of stiffness loss due to matrix cracking and debonding. Selected numerical results from a finite-element analysis of the cell model are presented to complement the analytical solutions. Both matrix cracking and interfacial debonding have the potential for significantly reducing the longitudinal thermal conductivity.


Biot Number Crack Density Matrix Crack Debonded Interface Gaseous Conduction 
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  1. Batchelor, G. K. 1974 A. Rev. Fluid Mech. 6, 227–251.CrossRefGoogle Scholar
  2. Beyerle, D., Spearing, S. M., Zok, F. W. & Evans, A. G. 1992 J. Am. Ceram. Soc. 75, 2719–2725.CrossRefGoogle Scholar
  3. Bhatt, H., Donaldson, K. Y., Hasselman, D. P. H. & Bhatt, R. T. 1990 J. Am. Ceram. Soc. 73, 312–316.CrossRefGoogle Scholar
  4. Benveniste, Y. 1987 J. appl. Phys. 61, 2840–2843.CrossRefGoogle Scholar
  5. Fadale, T. D. & Taya, M. 1991 J. Mater. Sci. Lett. 10, 682–684.CrossRefGoogle Scholar
  6. Hasselman, D. P. H. 1978 J. Comp. Mater. 12, 403–407.CrossRefGoogle Scholar
  7. Hasselman, D. P. H. & Johnson, L. F. 1987 J. Comp. Mater. 21, 508–512.CrossRefGoogle Scholar
  8. He, M. Y., Wu, B.-X., Evans, A. G. & Hutchinson, J. W. 1994 Mech. Mater. 18, 213–229.CrossRefGoogle Scholar
  9. Hoenig, A. 1983 J. Comp. Mater. 17, 231–237.CrossRefGoogle Scholar
  10. Hutchinson, J. W. & Jensen, H. M. 1990 Mech. Mater. 9, 139–163.CrossRefGoogle Scholar
  11. Laws, N. & Dvorak, G. J. 1988 J. Comp. Mater. 22, 900–916.CrossRefGoogle Scholar
  12. Leung, W. P. & Tam, A. C. 1988 J. appl. Phys. 63, 4505–4510.CrossRefGoogle Scholar
  13. Lu, T. J. & Hutchinson, J. W. 1995 Composites. (In the press.) McCartney, L. N. 1992 J. Mech. Phys. Solids 40, 27–68.Google Scholar
  14. Sears, F. W. 1967 Introduction to thermodynamics: the kinetic theory of gases and statistical mechanics, Cambridge, MA: Addison-Wesley.Google Scholar
  15. Swartz, E. T. & Pohl, R. O. 1989 Rev. mod. Phys. 61, 605–668.CrossRefGoogle Scholar
  16. Tzou, D. Y. 1991 J. Comp. Mater. 25, 1064–1084.Google Scholar
  17. Tzou, D. Y. & Li, J. 1993 Int. J. Heat Mass Transfer 36, 3887–3895.CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • T. J. Lu
  • J. W. Hutchinson

There are no affiliations available

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