Effective thermal conductivity of composites with a thermal contact resistance between the constituents: Nondilute case

The effective thermal conductivity of a particulate composite exhibiting a thermal contact resistance at interphase boundaries is considered. Two micromechanical models, the generalized self‐consistent scheme, and the Mori–Tanaka theory [Acta Metall. 21, 571 (1973)] previously used in composite media with perfect interfaces, are generalized to allow for the phenomenon of thermal contact resistance between the constituents. Spherical inclusions are considered and their interaction is approximately taken into account, so that the presented treatment is valid at nondilute concentrations. Both methods, distinctly different in their approach, result in the same closed‐form simple expression for the effective thermal conductivity.

[1]  David J. Bergman,et al.  The dielectric constant of a simple cubic array of identical spheres , 1979 .

[2]  Graeme W. Milton,et al.  Bounds on the transport and optical properties of a two‐component composite material , 1981 .

[3]  Touvia Miloh,et al.  The effective conductivity of composites with imperfect thermal contact at constituent interfaces , 1986 .

[4]  G. Milton.  Concerning bounds on the transport and mechanical properties of multicomponent composite materials , 1981 .

[5]  George J. Weng,et al.  Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions , 1984 .

[6]  M. Taya,et al.  Void growth in a viscous metal , 1981 .

[7]  G. Milton.  The coherent potential approximation is a realizable effective medium scheme , 1985 .

[8]  Ping Sheng,et al.  A generalized differential effective medium theory , 1985 .

[9]  Ping Sheng,et al.  Effective-medium theories for two-phase dielectric media , 1985 .

[10]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  Zvi Hashin,et al.  Assessment of the Self Consistent Scheme Approximation: Conductivity of Particulate Composites , 1968 .

[12]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[13]  David J. Bergman,et al.  Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material , 1980 .

[14]  Tsu-Wei Chou,et al.  On two kinds of ellipsoidal inhomogeneities in an infinite elastic body: An application to a hybrid composite☆ , 1981 .

[15]  S. Torquato,et al.  Effective properties of fiber-reinforced materials: I—Bounds on the effective thermal conductivity of dispersions of fully penetrable cylinders , 1986 .

[16]  E. H. Kerner,et al.  The Electrical Conductivity of Composite Media , 1956 .

[17]  David J. Bergman,et al.  The dielectric constant of a composite material—A problem in classical physics , 1978 .

[18]  Concerning the effective transverse conductivity of a two-dimensional two-phase material , 1977 .

[19]  M. Taya,et al.  On Stiffness and Strength of an Aligned Short-Fiber Reinforced Composite Containing Fiber-End Cracks Under Uniaxial Applied Stress , 1981 .

[20]  H. M. Rosenberg,et al.  The thermal conductivity of epoxy-resin / powder composite materials , 1974 .

[21]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .