Abstract
In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.
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References
Aboudi J.: Mechanics of Composite Materials: A Unified Micromechanical Approach. Elsevier, Amsterdam (1991)
Averill R.C., Yip Y.C.: Development of simple, robust, finite elements based on refined theories for thick laminated beam. Comput. Struct. 59(3), 529–546 (1996)
Benveniste Y., Chen T., Dvorak G.J.: The effective thermal conductivity of composite reinforced by coated cyllindrically orthotropic fibers. J. Appl. Phys. 67, 2878–2884 (1990)
Cho Y.B, Averill R.C.: First order zig-zag sublaminate plate theory and finite element model for laminated composite and sandwich panels. Composite Struct. 50(1), 1–15 (2000)
Chung P.W., Tamma K.K., Namburu R.R.: Homogenization of temperature-dependent thermal conductivity in composite materials. J. Thermophys. Heat Transf. 15, 10–17 (2001)
Drugan W.J., Willis J.R.: A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J. Mech. Phys. Solids 44, 497–524 (1996)
Farmer J.D., Covert E.E.: Thermal conductivity of a thermosetting advanced composite during its cure. J. Thermophys. Heat Transf. 10, 467–475 (1996)
Fish J., Shek K.: Multiscale analysis of composite materials and structures. Composite Sci. Technol. 60, 2547–2556 (2000)
Ganapathysubramanian B., Zabaras N.: Modeling multiscale diffusion processes in random heterogeneous media. Comput. Methods Appl. Mech. Eng. 197, 3560–3573 (2008)
Goyheneche J.M., Cosculluela A.: A multiscale model for the effective thermal conductivity tensor of a stratified composite material. Int. J. Thermophys. 26, 191–202 (2005)
Haj-Ali R.M., Muliana A.H.: A multi-scale constitutive framework for the nonlinear analysis of laminated composite materials and structures. Int. J. Solids Struct. 41(13), 3461–3490 (2004)
Haj-Ali, R.: Nested nonlinear multiscale framework for the analysis of thick-section composite materials and structures. In Kwon, Y. W., Allen, D.H., Talreja, R. (eds.) Multiscale Modeling and Simulation of Composite Materials and Structures, pp. 332–371. Springer Pub., ISBN 978-0-387-36318-938 (2007)
Haj-Ali R., Muliana A.H.: A micro-to-meso sublaminate model for the viscoelastic analysis of thick-section multi-layered frp composite structures. Mech. Time-dependent Mater. 12(1), 69–93 (2008)
Hashin Z.: Assessment of the self consistent scheme approximation: conductivity of particulate composites. J. Composite Mater. 2, 284–300 (1968)
Hill R.: Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phyis. Solids 13, 213–222 (1963)
Jiang M., Jasiuk I., Ostoja-Starzewski M.O.: Apparent elastic and elastoplastic behavior of periodic composites. Int. J. Solids Struct. 39, 199–212 (2002)
Jiang M., Jasiuk I., Ostoja-Starzewski M.O.: Apparent thermal conductivity of periodic two-dimensional composites. Comput. Mater. Sci. 25, 329–338 (2002)
Kaminski M.: Homogenization based finite element analysis of unidirectional composites by classical and multiresolutional techniques. Computer. Method Appl. Mech. Eng. 194, 2147–2173 (2005)
Khan K.A., Muliana A.H.: Effective thermal properties of viscoelastic composites with field dependent constituent properties. Acta Mech. 209, 153–178 (2010)
Kolodziej J.A., Konczak Z.: Determination of effective thermal conductivity for a laminated composite slab in a nonlinear case. Int. Commun. Heat Mass Transf. 21, 403–410 (1994)
Kouznetsova V., Brekelmans W.A.M., Baaijens F.P.T.: An approach to micro-macro modeling of heterogeneous materials. Comput. Mech. 27, 37–48 (2001)
Kulkarni M.R., Brady R.P.: A model of global thermal conductivity in laminated carbon/carbon composites. Composite Sci. Technol. 57, 277–285 (1997)
Lee Y.M., Yung R.B., Gao S.S: A generalized self consistent method for calulation of effective thermal conductivity of composites with interfacial contact conductance. Int. Commun. Heat Mass Transf. 33, 142–150 (2006)
Lewis T., Nielsen L.: Dynamic mechanical properties of particulate-filled polymers. J Appl. Polym. Sci. 14, 1449–1471 (1970)
McIvor S.D., Darby M.I., Wostenholm G.H., Yates B.: Thermal conductivity measurements of some glass and carbon fiber reinforced plastics. J. Mater. Sci. 25, 3127–3132 (1990)
Monteiro E., Yvonnet J., He Q.C.: Computational homogenization for nonlinear conduction in heterogeneous materials using model reduction. Comput. Mater. Sci. 42, 704–712 (2008)
Muliana A.H., Sawant S.: Viscoelastic responses of polymer composites with temperature and time dependent constituents. Acta Mech. 204, 155–173 (2009)
Noor A.K., Shah R.S.: Effective thermoelastic and thermal properties of unidirectional fiber reinforced composites and their sensitivity coefficients. Composite Struct. 26, 7–23 (1993)
Ozdemir I., Brekelmans W.A.M., Geers M.G.D.: Computational homogenization for heat conduction in heterogeneous solids. In.t J. Numer. Methods Eng. 73, 185–204 (2008)
Pilling M.W., Yates B., Black M.A.: The thermal conductivity of carbon fibre-reinforced composites. J. Mater. Sci. 14, 1326–1338 (1979)
Rolfes R., Hammerschmidt U.: Transverse thermal conductivity of CFRP laminates: a numerical and experimental validation of approximation formula. Composite Sci. Technol. 54, 45–54 (1995)
Springer G.S., Tsai S.W.: Thermal conductivities of unidirectional materials. J. Composite Mater. 1, 166–173 (1967)
Yu Q., Fish J.: Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales: a coupled thermo-viscoealstic example problem. Int. J. Solids Struct. 39, 6429–6452 (2002)
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Muliana, A.H., Kim, J.S. A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites. Acta Mech 212, 319–347 (2010). https://doi.org/10.1007/s00707-009-0264-2
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DOI: https://doi.org/10.1007/s00707-009-0264-2