Revisiting the generalized self-consistent scheme in composites: Clarification of some aspects and a new formulation

The determination of an effective property in composite materials necessitates the knowledge of some averaged field quantities in the constituents (like the average heat intensity or average strain) of a composite sample, which is subjected to homogeneous boundary conditions. In the generalized self-consistent scheme (GSCS) which is today a classical micromechanics model suited for the determination of the effective properties of matrix-based composites, those average quantities are estimated by using an auxiliary configuration in which a particulate phase is first surrounded by some matrix material and then embedded in the effective medium. In the present study, we revisit the GSCS both for two- and multi-phase matrix-based composites containing spherical particles, and clarify aspects related to the volume fractions of the particle core and matrix shell within the composite element which is embedded in the effective medium. The contribution of this study is believed to be mainly on the conceptual side and resides in a new formulation of the method in which the embedding volume fractions are determined in the course of the analysis by means of some fundamental relations on the averaged fields. The study is carried out in thermal conduction and elasticity and contains new results on the effective shear modulus of multi-phase composites.

[1]  T. Miloh,et al.  A generalized self‐consistent method for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies , 1988 .

[2]  Y. Benveniste,et al.  A micromechanics model for the effective thermomechanical behaviour of multiphase composite media , 1991 .

[3]  Zvi Hashin,et al.  Thermoelastic properties and conductivity of carbon/carbon fiber composites , 1990 .

[4]  A. Kelly,et al.  Maxwell's far-field methodology applied to the prediction of properties of multi-phase isotropic particulate composites , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[5]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[6]  F. Montheillet,et al.  A generalized self-consistent method for solids containing randomly oriented spheroidal inclusions , 1999 .

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

[8]  R. Christensen.  Two Theoretical Elasticity Micromechanics Models , 1998 .

[9]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[10]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[11]  R. Roscoe.  The viscosity of suspensions of rigid spheres , 1952 .

[12]  Yonggang Huang,et al.  A Generalized Self-Consistent Mechanics Method for Solids Containing Elliptical Inclusions , 1995 .

[13]  Richard M. Christensen,et al.  A critical evaluation for a class of micro-mechanics models , 1990 .

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

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

[16]  Y. Benveniste,et al.  The effective mechanical behaviour of composite materials with imperfect contact between the constituents , 1985 .

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

[18]  L. Walpole.  On bounds for the overall elastic moduli of inhomogeneous systems—I , 1966 .

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

[20]  Zvi Hashin,et al.  The Elastic Moduli of Heterogeneous Materials , 1962 .

[21]  S. Shtrikman,et al.  A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials , 1962 .

[22]  J. Mackenzie,et al.  The Elastic Constants of a Solid containing Spherical Holes , 1950 .

[23]  R. Christensen,et al.  Solutions for effective shear properties in three phase sphere and cylinder models , 1979 .

[24]  E. H. Kerner.  The Elastic and Thermo-elastic Properties of Composite Media , 1956 .

[25]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .

[26]  Y. Cheung,et al.  A generalized self-consistent method accounting for fiber section shape , 2003 .

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

[28]  G. Weng.  THE THEORETICAL CONNECTION BETWEEN MORI-TANAKA'S THEORY AND THE HASHIN-SHTRIKMAN-WALPOLE BOUNDS , 1990 .

[29]  G. Weng,et al.  A generalized self-consistent polycrystal model for the yield strength of nanocrystalline materials , 2004 .