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Two-Scale Prediction of Effective Thermal Conductivity of 3D Braided C/C Composites Considering Void Defects by Asymptotic Homogenization Method

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Abstract

In order to predict the effective thermal conductivities of three-dimensional (3D) braided carbon/carbon (C/C) composites with randomly distributed void defects. Two-scale prediction model is developed based on the asymptotic homogenization method. Unit cell models both on fiber-scale and fiber bundle-scale are established according to the scanning electron microscopy observation of the material, and the randomly distributed void defects are considered. The effective thermal conductivities of fiber bundles with void defects are predicted firstly, then the effective thermal conductivities of the 3D braided C/C composites are predicted considering void defects in matrix pocket and interface by introducing the predicted thermal conductivities of fiber bundles. The predicted effective thermal conductivities agree well with the experimental results, demonstrating the validity of the two-scale prediction model. A parametric study is then conducted to analyze the effects of void volume fraction and interfacial thermal conductivity on the predictions of the developed model. The results show that the random distribution of void defects has a little effect on the effective thermal conductivities, while the void volume fraction has a significant effect on the effective thermal conductivities. The thermal conductivities decrease generally linearly with the increase of void volume fractions, and the effect of void volume fraction of matrix pocket is greater than that of fiber reinforcement. The effective thermal conductivities increase with the increase of interfacial thermal conductivity, and the effect of void volume fraction of interface becomes larger with the increase of interfacial thermal conductivity. A higher interfacial thermal conductivity have a greater effect on the effective thermal conductivities of the material than a smaller interfacial thermal conductivity.

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References

  1. Soydan, O., Jale, T., Peter, F.: Microstructure and elastic properties of individualcomponents of C/C composites. Carbon. 47, 3403–3414 (2009)

    Article  Google Scholar 

  2. Dagli, L., Remonf, Y.: Identification of the non-linear behaviour a 4D carbon-carbon material designed for aeronautic application. Appl. Compos. Mater. 9, 1–15 (2002)

    Article  Google Scholar 

  3. Luo, R., Liu, T., Li, J., Zhang, H., Chen, Z., Tian, G.: Thermophysical properties of carbon/carbon composites and physical mechanism of thermal expansion and thermal conductivity. Carbon. 42, 2887–2895 (2004)

    Article  CAS  Google Scholar 

  4. Grujicic, M., Zhao, C.L., Dusel, E.C.: Computational analysis of the thermal conductivity of the carbon-carbon composite materials. J. Mater. Sci. 41, 8244–8256 (2006)

    Article  CAS  Google Scholar 

  5. Yin, J., Zhang, H.B., Xiong, X., Zuo, J.L., Huang, B.Y.: Ablation performance of carbon/carbon composite throat after a solid rocket motor ground ignition test. Appl. Compos. Mater. 19, 237–245 (2012)

    Article  CAS  Google Scholar 

  6. Ning, Q.G., Chou, T.W.: Closed-form solutions of the in-plane effective thermal conductivities of woven-fabric composites. Compos. Sci. Technol. 55, 41–48 (1995)

    Article  CAS  Google Scholar 

  7. Chou, T.W., Ning, Q.G.: A general analytical model for predicting the transverse effective thermal conductivities of woven fabric composites. Composites Part A:Applied Science & Manufacturing. 29, 315–322 (1998)

    Article  Google Scholar 

  8. Ronghua, N.I.E., Guiqiong, J.I.A.O., Bo, W.A.N.G.: Prediction on coefficient of thermal conductivity for 2D braided C/SiC composites. Acta Meteriae compositae Sinica. 26, 169–174 (2009)

    Google Scholar 

  9. Marcos-Gómez, D., Ching-Lloyd, J., Elizalde, M.R., Clegg, W.J., Molina-Aldareguia, J.M.: Predicting the thermal conductivity of composite materials with imperfect interfaces. Compos. Sci. Technol. 70, 2276–2283 (2010)

    Article  Google Scholar 

  10. Gou, J.J., Ren, X.J., Fang, W.Z., Li, S.G., Tao, W.Q.: Two small unit cell models for prediction of thermal properties of 8-harness satin woven pierced composites. Composites Part B. 135, 218–231 (2018)

    Article  CAS  Google Scholar 

  11. Jiang, L., Xu, G., Cheng, S., Lu, X., Zeng, T.: Predicting the thermal conductivity and temperature distribution in 3D braided composites. Compos. Struct. 108, 578–583 (2014)

    Article  Google Scholar 

  12. Li, H., Li, S., Wang, Y.: Prediction of effective thermal conductivities of woven fabric composites using unit cells at multiple length scales. J. Mater. Res. 26, 384–394 (2011)

    Article  CAS  Google Scholar 

  13. Dong, K., Zhang, J., Jin, L., Gu, B., Sun, B.: Multi-scale finite element analyses on the thermal conductive behaviors of 3D braided composites. Compos. Struct. 143, 9–22 (2016)

    Article  Google Scholar 

  14. Zhao, Y., Song, L., Li, J., Jiao, Y.: Multi-scale finite element analyses of thermal conductivities of three dimensional woven composites. Appl. Compos. Mater. 24, 1525–1542 (2017)

    Article  CAS  Google Scholar 

  15. Bensoussan, A.: Asymptotic Analysis for Periodic Structures. North-Holland Pub. Co (1978)

  16. Sanchez-Palencia, E.: Non-homogeneous Media and Vibration Theory. Springer, Berlin, Heidelberg (1980)

    Google Scholar 

  17. Yongcun, Z.H.A.N.G., Shipeng, S.H.A.N.G., Yujing, L.I.A.N.G.: A new algorithm of asymptotic homogenization method for predicting the effective thermal conductivity and its implementation of periodic composite materials. Acta Meteriae compositae Sinica. 35, 208–217 (2018)

    Google Scholar 

  18. Hassani, B., Hinton, E.: A review of homogenization and topology optimization I—homogenization theory for media with periodic structures. Comput. Struct. 69, 707–717 (1998)

    Article  Google Scholar 

  19. Hassani, B., Hinton, E.: A review of homogenization and topology optimization II—analytical and numerical solution of homogenization equations. Comput. Struct. 69, 719–738 (1998)

    Article  Google Scholar 

  20. Geng-dong, C., Shu-tian, L.: Prediction of thermal conductivity of unidirectional fiber reinforced composites. Acta Meteriae compositae Sinica. 13, 78–85 (1996)

    Google Scholar 

  21. Shabana, Y.M., Noda, N.: Numerical evaluation of the thermomechanical effective properties of a functionally graded material using the homogenization method. Int. J. Solids Struct. 45, 3494–3506 (2008)

    Article  Google Scholar 

  22. Dasgupta, A., Agarwal, R.K.: Orthotropic thermal conductivity of plain-weave fabric composites using a homogenization technique. J. Compos. Mater. 26, 2736–2758 (1992)

    Article  CAS  Google Scholar 

  23. Nasution, M.R.E., Watanabe, N., Kondo, A., Yudhanto, A.: Thermomechanical properties and stress analysis of 3D textile composites by asymptotic expansion homogenization method. Compos. Part B. 60, 378–391 (2014)

    Article  CAS  Google Scholar 

  24. Zhai, J., Cheng, S., Zeng, T., Wang, Z.H., Jiang, L.L.: Thermo-mechanical behavior analysis of 3D braided composites by multiscale finite element method. Compos. Struct. 176, 664–672 (2017)

    Article  Google Scholar 

  25. Songhe, M.E.N.G., Jin, K.A.N., Chenghai, X.U., Liming, W.E.I.: Relations between Microstructure and Mechanical Properties of Fiber-Matrix Interfaces in C/C Composite. Acta Materiae Compositae Sinica. 27, 129–132 (2010)

    Google Scholar 

  26. Yongzhong, S., Junshan, W.: Pore structure of 3D carbon/carbon composites. Carbon techniques. 35, 32–35 (2016)

    Google Scholar 

  27. Wang, X., Li, J., Zhang, Y., Wang, Y.: Improvement of interfacial bonding and mechanical properties of cu-Al2O3 composite by Cr-nanoparticle-induced interfacial modification. J. Alloys Compd. 695, 2121–2130 (2017)

    Google Scholar 

  28. Wang, X., Wang, Y., Su, Y., Qu, Z.: Synergetic strengthening effects on copper matrix induced by Al2O3 particle revealed from micro-scale mechanical deformation and microstructure evolutions. Ceram. Int. 45, 14889–14895 (2019)

    Article  CAS  Google Scholar 

  29. Klett, J.W., Ervin, V.J., Edie, D.D.: Finite-element modeling of heat transfer in carbon/carbon composites. Compos. Sci. Technol. 59, 593–607 (1999)

    Article  CAS  Google Scholar 

  30. ZH Feng, J.Y., ZHi, Z.F., Sun, D., et al.: An Analytical Model of Thermal Conductivity for Carbon/Carbon Composites with Pitch-Based Matrix. Advances in Mechanical Engineering. (2015). https://doi.org/10.1155/2014/242586

  31. Liu, Y., Qu, Z.G., Guo, J., Zhao, X.M.: Numerical study on effective thermal conductivities of plain woven C/SiC composites with considering pores in interlaced woven yarns. Int. J. Heat Mass Transf. 140, 410–419 (2019)

    Article  CAS  Google Scholar 

  32. Vorel, J., Sejnoha, M.: Evaluation of homogenized thermal conductivities of imperfect carbon-carbon textile composites using the mori-tanaka method. Struct. Eng. Mech. 33, 429–446 (2009)

    Article  Google Scholar 

  33. Shigang, A., Rujie, H., Yongmao, P.: A numerical study on the thermal conductivity of 3D woven C/C composites at high temperature. Appl. Compos. Mater. 22, 823–835 (2015)

    Article  Google Scholar 

  34. Fitzer, E., Manocha Lalit, M.: Thermal Properties of Carbon/Carbon Composites. In: Thermal Properties of Carbon/Carbon. In: Fitzer E, M Manocha Lalit. Carbon Reinforcements and Carbon/Carbon Composites, pp. 237–262. Springer, Berlin, Heidelberg (1998)

    Chapter  Google Scholar 

  35. Lian-xing, W., Feng-xian, L., Xiao-long, Z.: Comparison of C/C composites thermal conductivity. Coal conversion. 62-71, 34 (2011)

    Google Scholar 

  36. Yan, D., Wen, J., Xu, G.: A Monte Carlo simulation and effective thermal conductivity calculation for unidirectional fiber reinforced CMC. Appl. Therm. Eng. 94, 827–835 (2015)

    Article  Google Scholar 

  37. Li, C.Z., Sun, X.H., Chen, M.W., Baozhu, Y.: Multiscale modeling and theoretical prediction for the thermal conductivity of porous plain-woven carbonized silica/phenolic composites. Compos. Struct. 215, 278–288 (2019)

    Article  Google Scholar 

  38. Pilling, M.W., Yates, B., Black, M.A., Tattersall, P.: The thermal conductivity of carbon fibre-reinforced composites. J. Mater. Sci. 14, 1326–1338 (1979)

    Article  CAS  Google Scholar 

  39. Clayton, W.: Constituent and composite thermal conductivities of phenolic-carbon and phenolic-graphite ablators. Am Inst Aeronaut Astronaut. (2012). https://doi.org/10.2514/6.1971-380

  40. Wang, X., Wang, X., Liu, M., Crimp, M.A., Wang, Y., Qu, Z.: Anisotropic thermal expansion coefficient of multilayer graphene reinforced copper matrix composites. J. Alloys Compd. 755, 114–122 (2018)

    Article  CAS  Google Scholar 

  41. Song, J., Zhang, Y.: Effect of an interface layer on thermal conductivity of polymer composites studied by the design of double-layered and triple-layered composites. Int. J. Heat Mass Transf. 141, 1049–1055 (2019)

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work is e financially supported by the National Basic Research Program (973) of China (No. 61391).

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Correspondence to Kun-long Wei.

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Wei, Kl., Li, J., Shi, Hb. et al. Two-Scale Prediction of Effective Thermal Conductivity of 3D Braided C/C Composites Considering Void Defects by Asymptotic Homogenization Method. Appl Compos Mater 26, 1367–1387 (2019). https://doi.org/10.1007/s10443-019-09785-3

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