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Describing the Effective Conductivity of Two-Phase and Multiphase Materials via Weighted Means of Bounds and General Power Means

  • Modeling and Simulation of Composite Materials
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Abstract

The theoretical status of empirical means (based on the heuristic Wyllie–Southwick and Krischer models) of the upper and lower Wiener bounds (i.e., the parallel and series model) for describing the effective thermal conductivity of multiphase materials is clarified, and other useful fit relations are recalled (geometric weighted mean) or newly proposed (generalized sigmoidal mean). All these relations, as well as the general power mean, are compared with the Hashin–Shtrikman bounds, and the admissible fit parameter ranges are determined for materials with isotropic microstructures. It is shown that weighted means result in curves with inflection points, but with different changes in curvature, whereas the curves of general power means do not exhibit inflection points at all. For materials with isotropic microstructure it is recommended to apply the fixed-parameter weighted means and sigmoidal means to Hashin–Shtrikman bounds instead of the Wiener bounds, as is common practice so far.

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Acknowledgements

This work is part of the project “Partially and fully sintered ceramics—processing, microstructure, properties, modeling and sintering theory” (GA18-17899S), supported by the Czech Science Foundation (GAČR).

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  1. Department of Glass and Ceramics, University of Chemistry and Technology, Prague (UCT Prague), Technická 5, 166 28, Prague 6, Czech Republic

    Willi Pabst & Soňa Hříbalová

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  1. Willi Pabst
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  2. Soňa Hříbalová
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Correspondence to Willi Pabst.

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Pabst, W., Hříbalová, S. Describing the Effective Conductivity of Two-Phase and Multiphase Materials via Weighted Means of Bounds and General Power Means. JOM 71, 4005–4014 (2019). https://doi.org/10.1007/s11837-019-03693-4

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  • DOI: https://doi.org/10.1007/s11837-019-03693-4

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