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Prediction of thermal conductivities of laminated composites using penny-shaped fillers

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Abstract

A new model is proposed to predict the thermal conductivities of laminated composites, where the Eshelby method modified with Mori-Tanaka’s mean field approach is employed to consider the interaction effect. Based on the equivalency of composites with penny-shaped fillers and composites with layers of components, each lamina is considered as a penny-shaped filler and its thermal conductivities are computed by modified Eshelby method. The laminated composites are then simulated as the matrix and penny-shaped fillers of different thermal conductivities. By comparing the results of the laminated composites predicted by the present model and conventional approach combined with the potential theory and electrical analogy, the applicability of the present model to predict the thermal conductivities of the laminated composites is validated.

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References

  1. H. Hatta and M. Taya, Effective thermal conductivity of a misoriented short fiber composite, J. Appl. Phys., 58 (1985) 2478–2486.

    Article  Google Scholar 

  2. H. Hatta and M. Taya, Equivalent inclusion method for steady state heat conduction in composites, Int. J. Engng Sci., 24 (1986) 1159–1172.

    Article  MATH  Google Scholar 

  3. D. P. H. Hasselman and L. F. Johnson, Effective thermal conductivity of composites with interfacial thermal barrier resistance, J. Comp. Mater., 21 (1987) 508–515.

    Article  Google Scholar 

  4. C. L. Choy, W. P. Leung, K. W. Kowk and F. P. Lau, Elastic moduli and thermal conductivity of injection-molded short-fiber-reinforced thermoplastics, Poly. Comp., 13 (1992) 69–80.

    Article  Google Scholar 

  5. H. Hatta, M. Taya, F. A. Kulacki and J. F. Harder, Thermal diffusivities of composites with various types of filler, J. Comp. Mater., 26 (1992) 612–625.

    Article  Google Scholar 

  6. R. Rolfes and U. Hammerschmidt, Transverse thermal conductivity of CFRP laminates: A numerical and experimental validation of approximation formulae, Comp. Sci. Tech., 54 (1995) 45–54.

    Article  Google Scholar 

  7. C. H. Chen and Y. C. Wang, Effective thermal conductivity of misoriented short-fiber reinforced thermoplastics, Mech. Mater., 23 (1996) 217–228.

    Article  Google Scholar 

  8. M. R. Kulkarni and R. P. Brady, A model of global thermal conductivity in laminated carbon/carbon composites, Comp. Sci. Tech., 57 (1997) 277–285.

    Article  Google Scholar 

  9. S. Okamoto and H. Ishida, A new theoretical equation for thermal conductivity of two-phase systems, J. App. Poly. Sci., 72 (1999) 1689–1697.

    Article  Google Scholar 

  10. S. Y. Fu and Y. W. Mai, Thermal conductivity of misaligned short-fiber-reinforced polymer composites, J. App. Poly. Sci., 88 (2003) 1497–1505.

    Article  Google Scholar 

  11. D. Kumlutas, I. H. Tavman, and M. T. Coban, Thermal conductivity of particle filled polyethylene composite materials, Comp. Sci. Tech., 63 (2003) 113–117.

    Article  Google Scholar 

  12. J. K. Carson, S. J. Lovatt, D. J. Tanner and A. C. Cleland, Thermal conductivity bounds for isotropic, porous materials, Int. J. Heat and Mass Transfer, 48 (2005) 2150–2158.

    Article  MATH  Google Scholar 

  13. P. K. Samantray, P. Karthikeyan and K. S. Reddy, Estimating effective thermal conductivity of two-phase materials, Int. J. Heat and Mass Transfer, 49 (2006) 4209–4219.

    Article  MATH  Google Scholar 

  14. J. Wang, J. K. Carson, M. F. North and D. J. Cleland, A new approach to modelling the effective thermal conductivity of heterogeneous materials, Int. J. Heat and Mass Transfer, 49 (2006) 3075–3083.

    Article  MATH  Google Scholar 

  15. L. N. McCartney and A. Kelly, Effective thermal and elastic properties of [+θ/−θ]s laminates, Comp. Sci. Tech., 67 (2007) 646–661.

    Article  Google Scholar 

  16. J. D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. of the Royal Society of London, A241 (1957) 376–396.

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Mori and K. Tanaka, Average stress in the matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., 21 (1973) 571–574.

    Article  Google Scholar 

  18. D. Polder and J. H. van Santeen, The effective permeability of mixtures of solids, Physica, 12 (1946) 257–269.

    Article  Google Scholar 

  19. J. H. Huang, Micromechanics determinations of thermoelectroelastic fields and effective thermoelectroelastic moduli of piezoelectric composites, Mater. Sci. Eng., B39 (1996) 163–172.

    Article  Google Scholar 

  20. J. H. Huang, Y. H. Chiu and H. K. Liu, Magnetoelectro-elastic Eshelby tensors for a piezoelectricpiezomagnetic composite reinforced by ellipsoidal inclusions, J. App. Phys., 83 (1998) 5364–5370.

    Article  Google Scholar 

  21. J. Luo and R. Stevens, Micromechanics of randomly oriented ellipsoidal inclusion composites. Part II: Elastic moduli., J. App. Phys., 79 (1996) 9057–9063.

    Article  Google Scholar 

  22. A. Zhao and J. Yu, The overall elastic moduli of orthotropic composite and description of orthotropic damage of materials, Int. J. Solids and Struct., 37 (2000) 6755–6771.

    Article  MATH  Google Scholar 

  23. I. Sevostianov, N. Yilmaz, V. Kushch and V. Levin, Effective elastic properties of matrix composites with transversely-isotropic phases, Int. J. Solids and Struct., 42 (2005) 455–476.

    Article  MATH  Google Scholar 

  24. J. K. Lee, An analytical study on prediction of effective properties in porous and non-porous piezoelectric composites, J. Mechanical Science and Technology, 19(11) (2005) 2025–2031.

    Article  Google Scholar 

  25. J. K. Lee and J. G. Kim, An analytical study on prediction of effective elastic constants of perforated plate, J. Mechanical Science and Technology, 19(12) (2005) 2224–2230.

    Article  Google Scholar 

  26. J. Y. Kim and J. K. Lee, A new model to predict effective elastic constants of composites with spherical fillers, J. Mechanical Science and Technology, 20(11) (2006) 1891–1897.

    Article  Google Scholar 

  27. M. Taya and T. Mura, On stiffness and strength of an aligned short-fiber reinforced composite containing fiber-end cracks under uni-axial applied stress, ASME J. App. Mech., 48 (1981) 361–367.

    Article  MATH  Google Scholar 

  28. N. Laws, A note on penny-shaped cracks in transversely isotropic materials, Mech. Mater., 4 (1985) 209–212.

    Article  Google Scholar 

  29. Z. M. Xiao and K. D. Pae, Stress field and intensity factor due to crazes formed at the poles of a spherical inhomogeneity, ASME J. App. Mech., 61 (1994) 803–808.

    Article  MATH  Google Scholar 

  30. T. L. Wu and J. H. Huang, Critical volume fraction of multiple cracks for fracture in piezoelectric media, J. Thermoplastic Comp. Mater., 13 (2000) 21–39.

    Article  Google Scholar 

  31. H. M. Shodja, I. Z. Rad and R. Soheilifard, Interacting cracks and ellipsoidal inhomogeneities by the equivalent inclusion method, J. Mech. Phys. Solids, 51 (2003) 945–960.

    Article  MATH  Google Scholar 

  32. C. R. Chiang, Some crack problems in transversely isotropic solids, Acta Mech., 170 (2004) 1–9.

    Article  MATH  Google Scholar 

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Correspondence to Jae-Kon Lee.

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This paper was recommended for publication in revised form by Associate Editor Dongsik Kim

Jae-Kon Lee received a B.S. degree in Mechanical Engineering from Seoul National University in 1985. He then went on to receive his M.S. degree from KAIST and Ph.D. degrees from University of Washington in 1987 and 1996, respectively. Dr. Lee is currently a Professor at the School of Mechanical and Automotive Engineering at Catholic University of Daegu in Kyeongsan, Korea. Dr. Lee’s research interests are in the area of design and analysis of smart composite materials using mechanical, thermal, and piezoelectric properties.

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Lee, JK. Prediction of thermal conductivities of laminated composites using penny-shaped fillers. J Mech Sci Technol 22, 2481–2488 (2008). https://doi.org/10.1007/s12206-008-0815-9

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  • DOI: https://doi.org/10.1007/s12206-008-0815-9

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