THERMAL SCIENCE

International Scientific Journal

External Links

A NOVEL DETERMINATION OF THE MINIMAL SIZE OF A PROBABILISTIC REPRESENTATIVE VOLUME ELEMENT FOR FIBER-REINFORCED COMPOSITES’ THERMAL ANALYSIS

ABSTRACT
In order to provide an accurate thermal analysis method of fiber-reinforced composites, a novel model based on a probabilistic representative volume element (RVE) is presented in this paper. Monte Carlo methods, probability analysis and finite element analysis have been applied together. The effective transverse thermal conductivity, heat flux field and thermal gradient field of typical fiber-reinforced composites are examined. The criteria of RVEs have been determined, and the minimal size for thermal analysis is obtained using the main statistics and the cross-entropy theory. At the same time, the fiber-to-matrix ratio of thermal conductivity and volume fraction have been changed to determine the influence on heat transfer inside fiber-reinforced composites. It is shown that different purposes of simulations lead to different minimal RVE sizes. The numerical results indicate that the non-dimensional minimal RVE sizes for calculating the effective thermal conductivity, heat flux and thermal gradient are 30, 80 and 80, respectively. Compared with the volume fraction, the fiber-to-matrix ratio of the thermal conductivity has a more significant effect on minimal RVE size. When the thermal conductivity ratio increases, the minimal size of the RVE increases at first, then it remains almost unchanged.
KEYWORDS
PAPER SUBMITTED: 2016-04-30
PAPER REVISED: 2016-07-27
PAPER ACCEPTED: 2016-07-29
PUBLISHED ONLINE: 2016-09-05
DOI REFERENCE: https://doi.org/10.2298/TSCI160430222T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 6, PAGES [2551 - 2564]
REFERENCES
  1. Rabearison, N., Jochum, C., Grandidier, J., A FEM coupling model for properties prediction during the curing of an epoxy matrix, Comput. Mater. Sci., 45 (2009), 3, pp. 715-724
  2. Corden, T.J., Jones, I.A., Jones, D.T., Middleton, V., The mechanisms of interlaminar cracking in thick resin transfer moulded composite cylinders, Compos. A. Appl. Sci. Manuf., 29 (1998), 4, pp.455-464
  3. Plepys, A., Farris, R., Evolution of residual stresses in three-dimensionally constrained epoxy resins, Polymer, 31 (1990), 10, pp.1932-1936
  4. Rayleigh, L., LVI on the influence of obstacles arranged in rectangular order upon the properties of a medium, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 34 (1892), 211, pp.481-502
  5. Hasselman, D.P., Johnson, L.F., Effective thermal conductivity of composites with interfacial thermal barrier resistance, Journal of Composite Materials, 21(1987), 6, pp.508-515
  6. Zou, M., Yu, B., Zhang, D., Study on optimization of transverse thermal conductivities of unidirectional composites, Journal of heat transfer, 125 (2003), 6, pp.980-987
  7. Hill, R., Elastic properties of reinforced solids: some theoretical principles, J Mech Phys Solid, 11 (1963), 5, pp.357-372
  8. Islam, M.R., Pramila, A., Thermal conductivity of fiber reinforced composites by FEM, Journal of Composite Materials, 33 (1999), 18, pp.1699-1715
  9. Klett, J.W., Ervin, V.J., Edie, D.D., Finite-element modeling of heat transfer in carbon/carbon composites, Composites Science and technology, 59 (1999), 4, pp.593-607
  10. Car, E., Zalamea, F., Oller, S., Miquel, J., Qnate, E., Numerical simulation of fiber reinforced composite materials: two procedures, Inter J Solid Struct, 39 (2002), 39, pp.1967-1986
  11. Buryachenko, V.A., Pagano, N.J., Kim, R.Y., Spowart, J.E., Quantitative description and numerical simulation of random microstructure of composites and their effective elastic moduli, Int. J. Solids Struct, 40 (2003), 1, pp.47-72
  12. Trias, D., Analysis and simulation of transverse random fracture of long fiber reinforced composite. Ph.D. Thesis, Department d'Enginyeria Mecanica I de la Construccio Industrial, Universitat de Girona, 2005
  13. Ganapathy, D., Singh, K., Phelan, P.E., Prasher, R., An effective unit cell approach to compute the thermal conductivity of composites with cylindrical particles, Journal of heat transfer. 127 (2005), 6, pp.553-559
  14. Swaminathan, S., Ghosh, S., Pagano, N.J., Statistically equivalent representative volume elements for unidirectional microstructures: Ⅰ. Without damage, J. Compos. Mater, 40 (2006), 7, pp.583-604
  15. Rakow, J.F., Waas, A.M., Size effects in metal foam cores for sandwich structure, AIAA J, 42 (2004), 7, 1331-7
  16. Heinrich, C., Aldridge, M., Wineman, A.S., Kieffer, J., Waas, A.M., The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites, Modelling and simulation in materials science and engineering, 20 (2012), 7, 075007
  17. Trias, D., Costa, J., Turon, A., Hurtado, J.E., Determination of the critical size of a statistical representative volume element (SRVE) for carbon reinforced polymers, Acta Materialia, 54 (2006), 13, pp.3471-3484
  18. Kanit, T., Forest, S., Galliet, I., Mounoury, V., Jeulin, D., Determination of the size of the representative volume element for random compistes: statistical and numerical approach, International Journal of Solids and Structures, 40 (2003), 13-14, pp.3647-3679
  19. Zadeh, L.A., Probability measures of fuzzy events, Journal of Mathematical Analysis and Applications, 23 (1968), 2, pp.4212-427
  20. Mao, J.J., Yao, D.B., Wang, C.C., A novel cross-entropy and entropy measures of IFSs and their applications, Knowledge- Based Systems, 48 (2013), 2, pp.37-45
  21. Qin, Z.F., Li, X., Ji, X.Y., Portfolio selection based on fuzzy cross-entropy, Journal of Computational and Applied Mathematics, 228 (2009), 1, pp.139-149
  22. Wang, Y., Power system short-term reliability evaluations based on cross-entropy theory, Ph.D. Zhejiang, College of electrical engineering, Zhejiang University, 2014
  23. He, F., Carbon Fiber & Graphite Fiber, Chemical Industry Press, Beijing, China, 2010
  24. Brockenborough, J.R., Suresh, S., Wienecke, H.A., Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape, Acta Metall Mater, 39 (1991), 5, pp.735-752
  25. Ohser, J., Mucklich, F., Statistical analysis of microstructures in materials science Statistics in practice. (New York: Wiley), 2000

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence