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Computational analysis of the thermal conductivity of the carbon–carbon composite materials

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Abstract

Experimental data for carbon–carbon constituent materials are combined with a three-dimensional stationary heat-transfer finite element analysis to compute the average transverse and longitudinal thermal conductivities in carbon–carbon composites. Particular attention is given in elucidating the roles of various micro-structural defects such as de-bonded fiber/matrix interfaces, cracks and voids on thermal conductivity in these materials. In addition, the effect of the fiber precursor material is explored by analyzing PAN-based and pitch-based carbon fibers, both in the same type pitch-based carbon matrix. The finite element analysis is carried out at two distinct length scales: (a) a micro scale comparable with the diameter of carbon fibers and (b) a macro scale comparable with the thickness of carbon–carbon composite structures used in the thermal protection systems for space vehicles. The results obtain at room temperature are quite consistent with their experimental counterparts. At high temperatures, the model predicts that the contributions of gas-phase conduction and radiation within the micro-structural defects can significantly increase the transverse thermal conductivity of the carbon–carbon composites.

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Abbreviations

α:

Thermal accommodation factor

C p :

Solid-phase mass heat capacity

d :

Gas collision diameter

δ:

Characteristic length scale for gas molecules in the porous medium

ɛ:

Emissivity

K B :

Boltzmann’s constant

Kn :

Knudsen number

k :

Thermal conductivity

λ:

Gas molecular mean field path

P :

Pressure

Pr :

Prandtle number

q :

Heat flux

ρ:

Density

σ:

Stefan–Boltzmann constant

T :

Temperature

x, y, z :

Spatial coordinates

x−y :

Quantity in the transverse plane

high:

Graphene in-plane quantity

low:

Graphene out-of-plane quantity

matrix:

Matrix-phase quantity

fiber:

Fiber-phase quantity

gas:

Gas-phase quantity

r:

Radiation related quantity

References

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Acknowledgements

The material presented in this paper is based on work sponsored by the U.S. Air Force through Touchstone Research Laboratory, Ltd. The authors acknowledge valuable discussions with Professors Don Beasley, Richard Miller and Jay Ochterbeck of Clemson University.

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Authors and Affiliations

  1. Program in Materials Science and Engineering, Department of Mechanical Engineering, Clemson University, 241 Engineering Innovation Building, Clemson, SC, 29634-0921, USA

    M. Grujicic, C. L. Zhao, E. C. Dusel, R. S. Miller & D. E. Beasley

  2. Touchstone Research Laboratory, Inc., Triadelphia, WV, 26059, USA

    D. R. Morgan

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  1. M. Grujicic
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  2. C. L. Zhao
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  3. E. C. Dusel
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  4. D. R. Morgan
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  5. R. S. Miller
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  6. D. E. Beasley
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Correspondence to M. Grujicic.

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Grujicic, M., Zhao, C.L., Dusel, E.C. et al. Computational analysis of the thermal conductivity of the carbon–carbon composite materials. J Mater Sci 41, 8244–8256 (2006). https://doi.org/10.1007/s10853-006-1003-x

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  • DOI: https://doi.org/10.1007/s10853-006-1003-x

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