Structural Engineering and Mechanics

  • 제33권4호
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  • Pages.429-446
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  • 2009
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Evaluation of homogenized thermal conductivities of imperfect carbon-carbon textile composites using the Mori-Tanaka method

  • Vorel, Jan (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague) ;
  • Sejnoha, Michal (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Centre for Integrated Design of Advances Structures)
  • 투고 : 2008.09.17
  • 심사 : 2009.08.25
  • 발행 : 2009.11.10
⟨ 이전 논문 다음 논문 ⟩

초록

Three-scale homogenization procedure is proposed in this paper to provide estimates of the effective thermal conductivities of porous carbon-carbon textile composites. On each scale - the level of fiber tow (micro-scale), the level of yarns (meso-scale) and the level of laminate (macro-scale) - a two step homogenization procedure based on the Mori-Tanaka averaging scheme is adopted. This involves evaluation of the effective properties first in the absence of pores. In the next step, an ellipsoidal pore is introduced into a new, generally orthotropic, matrix to make provision for the presence of crimp voids and transverse and delamination cracks resulting from the thermal transformation of a polymeric precursor into the carbon matrix. Other sources of imperfections also attributed to the manufacturing processes, including non-uniform texture of the reinforcements, are taken into consideration through the histograms of inclination angles measured along the fiber tow path together with a particular shape of the equivalent ellipsoidal inclusion proposed already in Sko ek (1998). The analysis shows that a reasonable agreement of the numerical predictions with experimental measurements can be achieved.

키워드

참고문헌

  1. Benveniste, Y. (1987), "A new approach to the application of Mori-Tanaka theory in composite materials",Mech. Mater., 6, 147-157 https://doi.org/10.1016/0167-6636(87)90005-6
  2. Benveniste, Y., Chen, T. and Dvorak, G. (1990), "The effective thermal conductivity of composites reinforced by coated cyllindrically orthotropic fibers", J. Appl. Phys., 67(6), 2878-2884 https://doi.org/10.1063/1.345463
  3. Chen, T. and Yang, S.H. (1995), "The problem of thermal conduction for two ellipsoidal inhomogeneities in an anisotropic medium and its relevance to composite materials", Acta Mech., 111, 41-58 https://doi.org/10.1007/BF01187726
  4. Dvorak, G. and Sejnoha, M. (1996), "Initial failure maps for ceramic and metal matrix composites", Model. Simul. Mater. Sci. Eng., 4, 553-580 https://doi.org/10.1088/0965-0393/4/6/002
  5. Eshelby, J. (1957), "The determination of the elastic field of an ellipsoidal inclusion and related problems", Proc. Royal Soc., Series A, 241, 376-396 https://doi.org/10.1098/rspa.1957.0133
  6. Gommers, B., Verpoest, I. and Van Houtte, P. (1998), "The Mori-Tanaka method applied to textile composite materials", Acta Mater., 46(6), 2223-2235 https://doi.org/10.1016/S1359-6454(97)00296-6
  7. Hatta, H. and Taya, M. (1986), "Equivalent inclusion method for steady state heat conduction in composites", Int. J. Eng. Sci., 24, 1159-1170 https://doi.org/10.1016/0020-7225(86)90011-X
  8. Hellmich, C. and Ulm, F.J. (2005), "Drained and undrained poroelastic properties of healthy and pathological bone: a poro-micromechanical investigation", Transport. Porous Med., 58, 243-268 https://doi.org/10.1007/s11242-004-6298-y
  9. Huysmans, G., Verpoest, I. and Van Houtte, P. (1998), "A poly-inclusion approach for the elastic modelling of knitted fabric composites", Acta Mater., 46(9), 3003-3013 https://doi.org/10.1016/S1359-6454(98)00021-4
  10. Jeong, H., Hsu, D. and Liaw, P. (1998), "Anisotroic conductivities of multiphase particulate metal-matrix composites", Compos. Sci. Technol., 58, 65-76 https://doi.org/10.1016/S0266-3538(97)00093-6
  11. Kanari, M., Tanaka, K., Baba, S. and Eto, M. (1997), "Nanoindentation behavior of a two-dimensional carboncarbon composite for nuclear applications", Carbon, 35(10-11), 1429-1437 https://doi.org/10.1016/S0008-6223(97)00042-0
  12. Košková, B. and Vopi ka, S. (2001), "Determination of yarn waviness parameters for C/C woven composites", in: Proceedings of International Conference CARBON '01, Lexington (KY, USA), 1-6
  13. Kubi ár, L., Bohá , V. and Vretenár, V. (2002), "Transient methods for the measurement of thermophysical properties: The pulse transient method", High Temp. - High Pressures, 34, 505-514 https://doi.org/10.1068/htjr053
  14. Kuhn, J.L. and Charalambides, P.G. (1999), "Modeling of plain weave fabric composite geometry", J. Compos. Mater., 33(3), 188-220
  15. Lackner, R., Spiegl, M., Blab, R. and Eberhardsteiner, J. (2005), "Is low-temperature creep of asphalt mastic independent of filler shape and mineralogy? - arguments from multiscale analysis", J. Mater. Civil Eng., ASCE, 15, 485-491
  16. LIM, System Lucia G, User guide, LUCIA - Laboratory Universal Computer Image Analysis, http://www.laboratory-imaging.com
  17. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metallurgica, 21, 571-574 https://doi.org/10.1016/0001-6160(73)90064-3
  18. Ohlhorst, C.W. (1997), Thermal Conductivity Database of Various Strutural Carbon Carbon Composite Materials, NASA Technical Memorandum 4787, Lanley Research Center, Hampton, Virginia
  19. Piat, R., Tsukrov, I., Mladenov, N., Guellali, M., Ermel, R., Beck, E. and Hoffman, M. (2007), "Material modeling of the CVI-infiltrated carbon felt II. Statistical study of the microstructure, numerical analysis and experimental validation", Compos. Sci. Technol., 66(15), 2769-2775 https://doi.org/10.1016/j.compscitech.2006.03.003
  20. Piat, R., Tsukrov, I., Mladenov, N., Verijenko, M., Guellali, M., Schnack, E. and Hoffman, M. (2007), "Material modeling of the CVI-infiltrated carbon felt I. Basic formulae, theory and numerical experiments", Compos. Sci. Technol., 66(15), 2997-3003
  21. Rektorys, K. (Ed.) (1994), Survey of Applicable Mathematics: Volume II, second revised Edition, Vol. 281 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht
  22. Sko ek, J., Zeman, J. and Šejnoha, M. (2008), "Effective properties of Carbon-Carbon textile composites: application of the Mori-Tanaka method", Model. Simul. Mater. Sci. Eng., (accepted) https://doi.org/10.1088/0965-0393/16/8/085002
  23. Tomková, B. (2004), Study of porous structure of C/C composites, in: International Conference ICAPM, Evora,Portugal, 379-387
  24. Tomková, B. and Košková, B. (2004), "The porosity of plain weave C/C composite as an input parameter for evaluation of material properties", in: International Conference Carbon 2004, Providence, USA, 50
  25. Tomková, B., Šejnoha, M., Novák, J. and Zeman, J. (2008), "Evaluation of effective thermal conductivities of porous textile composites", Int. J. Multiscale Comput. Eng., 6(2), 153-168 https://doi.org/10.1615/IntJMultCompEng.v6.i2.40
  26. TORAYCA, Technical Data Sheet, Toroyca T800H, Toray Carbon Fibers America, http://www.torayusa.com
  27. Tsukrov, I., Piat, R., Novak, J. and Schnack, E. (2005), "Micromechanical modeling of porous carbon/carbon composites", Mech. Adv. Mater. Struct., 12, 43-54 https://doi.org/10.1080/15376490490492034
  28. Vopi ka, S. (2004), Popis geometrie vyztužujícího systému v tkaninových kompozitech [Description of geometry of textile composites reinforcing system], Ph.D. thesis, Technical University of Liberec, in Czech
  29. Zeman, J. and Šejnoha, M. (2001), "Numerical evaluation of effective properties of graphite fiber tow impregnated by polymer matrix", J. Mech. Phys. Solids, 49(1), 69-90 https://doi.org/10.1016/S0022-5096(00)00027-2
  30. Zeman, J. and Šejnoha, M. (2004), "Homogenization of balanced plain weave composites with imperfect microstructure: Part I - theoretical formulation", Int. J. Solids Struct., 41(22-23), 6549-6571 https://doi.org/10.1016/j.ijsolstr.2004.05.011
  31. Šejnoha, M. and Zeman, J. (2002), "Overall viscoelastic response of random fibrous composites with statistically quasi uniform distribution of reinforcements", Comput. Meth. Appl. Mech. Eng., 191(44), 5027-5044 https://doi.org/10.1016/S0045-7825(02)00433-4
  32. Šejnoha, M. and Zeman, J. (2008), "Micromechanical modeling of imperfect textile composites", Int. J. Eng. Sci., 46, 513-526 https://doi.org/10.1016/j.ijengsci.2008.01.006
  33. Šejnoha, M., Valenta, R. and Zeman, J. (2004), "Nonlinear viscoelastic analysis of statistically homogeneous random composites", Int. J. Multiscale Comput. Eng., 2(4), 645-673 https://doi.org/10.1615/IntJMultCompEng.v2.i4.80
  34. Šmilauer, V. and Bittnar, Z. (2006), "Microstructure-based micromechanical prediction of elastic properties in hydrating cement paste", Cement Concrete Res., 36(9), 1708-1718 https://doi.org/10.1016/j.cemconres.2006.05.014

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