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  • The sigmoidal average between the upper and lower Hashin-Shtrikman bounds is shown to be the appropriate average relation for isotropic two-phase composites consisting of geometrically equivalent grains. This average ensures that the prediction is close the upper bound for low volume fractions of the low-conductivity phase (corresponding to low-conductivity inclusions in a high-conductivity matrix) and vice versa. In the intermediate concentration range the sigmoidal average reflects the fact that the microstructure is bicontinuous and can undergo a percolation-type transition. It is shown that the sigmoidal average of the Hashin-Shtrikman bounds lies automatically within the three-point bounds (Miller bounds) for a practically important class of microstructures (symmetric-cell materials with spherical cells) and that in the infinite-phase-contrast case (porous media) it is close to the exponential relation, which has been very successful in describing the porosity dependence of properties. Theoretical predictions are compared with experimentally measured values for alumina-zirconia composites in the whole range of volume fractions, from pure alumina to pure zirconia. Even after appropriate correction for porosity, essentially all experimental data are below the sigmoidal average. The fact that some values are even below the lower Hashin-Shtrikman bound is indicative of microcracking and / or grain size (interface) effects.
  • The sigmoidal average between the upper and lower Hashin-Shtrikman bounds is shown to be the appropriate average relation for isotropic two-phase composites consisting of geometrically equivalent grains. This average ensures that the prediction is close the upper bound for low volume fractions of the low-conductivity phase (corresponding to low-conductivity inclusions in a high-conductivity matrix) and vice versa. In the intermediate concentration range the sigmoidal average reflects the fact that the microstructure is bicontinuous and can undergo a percolation-type transition. It is shown that the sigmoidal average of the Hashin-Shtrikman bounds lies automatically within the three-point bounds (Miller bounds) for a practically important class of microstructures (symmetric-cell materials with spherical cells) and that in the infinite-phase-contrast case (porous media) it is close to the exponential relation, which has been very successful in describing the porosity dependence of properties. Theoretical predictions are compared with experimentally measured values for alumina-zirconia composites in the whole range of volume fractions, from pure alumina to pure zirconia. Even after appropriate correction for porosity, essentially all experimental data are below the sigmoidal average. The fact that some values are even below the lower Hashin-Shtrikman bound is indicative of microcracking and / or grain size (interface) effects. (en)
Title
  • The sigmoidal average - a powerful tool for predicting the thermal conductivity of composite ceramics
  • The sigmoidal average - a powerful tool for predicting the thermal conductivity of composite ceramics (en)
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  • The sigmoidal average - a powerful tool for predicting the thermal conductivity of composite ceramics
  • The sigmoidal average - a powerful tool for predicting the thermal conductivity of composite ceramics (en)
skos:notation
  • RIV/60461373:22310/12:43894496!RIV13-GA0-22310___
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  • P(GAP108/12/1170)
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  • 167806
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  • RIV/60461373:22310/12:43894496
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  • alumina-zirconia composites; micromechanical bounds; , composite ceramics; thermal conductivit; Sigmoidal average (en)
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [0EC6815AAE1E]
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  • Journal of Physics: Conference Series
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  • 395
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  • Gregorová, Eva
  • Pabst, Willi
issn
  • 1742-6596
number of pages
http://bibframe.org/vocab/doi
  • 10.1088/1742-6596/395/1/012021
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  • 22310
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