Micromechanical theories of effective properties (elastic constants, thermal and electric conductivity, permittivity) are summarized for isotropic and transversely isotropic ceramic matrix composites (with isometric particulate fillers, aligned continuous fibers, platelets or short fibers, either randomly or preferentially oriented). In particular, the one-point (Wiener-Paul) and two-point (Hashin-Shtrikman) bounds for isotropic composites are given and compared with published literature data (with oxide and non-oxide ceramic matrices). It is shown that for small phase contrast (ratio of the phase properties) the Hashin-Shtrikman bounds give a good estimate of the effective property, while for large phase contrasts the effective properties typically exhibit an S-shaped curve in dependence of the second-phase volume fraction, being close to the upper Hashin-Shtrikman bound when the phase with the higher property value is the matrix phase and vice versa. In the extreme case of porous ceramics (where the inclusion phase are vacuous voids) the transition between the two regimes degenerates to a percolation threshold, while the non-linear self-consistent effective medium approximation (Bruggeman model) reduces to the linear approximation (dilute or non-interaction approximation) in this case. Literature data are shown for alumina-zirconia composites and fiber- or platelet-reinforced ceramics.

Acknowledgement: This study was part of the project “Porous ceramics, ceramic composites and nanoceramics“ (Grant No. IAA401250703), supported by the Grant Agency of the Academy of Sciences of the Czech Republic.

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1. The effective Poisson ratio of two-phase composites