Rigorous bounds, model predictions and mixture rule for the effective thermal conductivity of multiphase and porous ceramics – from theory to practice

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22310%2F21%3A43923153" target="_blank" >RIV/60461373:22310/21:43923153 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Rigorous bounds, model predictions and mixture rule for the effective thermal conductivity of multiphase and porous ceramics – from theory to practice

Popis výsledku v původním jazyce

Thermal conductivity is a fundamental property of ceramic materials. It is in general represented by a second-order tensor and defined via Fourier’s law, which is a linear constitutive equation. It plays a major role during drying and sintering of ceramics and determines the performance of ceramics in many practical applications, ranging from electronic substrates to high-temperature thermal insulation. Together with the density, specific heat and mechanical properties it is also an important parameter for the assessment of thermal shock resistance. In heterogeneous materials, either single-phase polycrystalline or multiphase (composites), the effective thermal conductivity has to be calculated for engineering purposes via appropriate averaging or homogenization procedures. The first step in these calculations is usually the determination of the effective conductivity of the individual crystalline phases, which is performed via orientational averaging of the conductivity tensor components. Depending on the degree of orientation, the effective conductivity tensor can range from the monocrystal tensor to an isotropic tensor that represents the scalar conductivity for random orientation of crystallites. For multiphase (and porous) materials the second (and third) step is the calculation of the effective conductivity via volume averaging of the phase conductivities for given volume fractions (for statistically isotropic microstructures) and texture parameters (orientation tensors). An additional complication may arise when the phase domains (grains, inclusions, pores) are so small that the finite thickness of the interface (grain boundary or phase boundary) and the interface resistivity has to be taken into account. This chapter gives a profound and detailed summary of the rigorous bounds (Molyneux bounds for orientational averaging, multiphase Wiener and Hashin-Shtrikman bounds for volume averaging), model predictions (linear approximations and nonlinear effective medium approximations) and mixture rules (volume-weighted arithmetic, geometric, harmonic and other averages, as well as fixed- and floating-parameter weighted means) that can be used for estimating the effective thermal conductivity of single-phase, two-phase, three-phase and porous ceramics. It is emphasized that apart from the volume fraction the shape of the phase domains, mainly their surface curvature (and the aspect ratio in matrix-inclusion microstructures), is a key parameter even in statistically isotropic materials. In particular, for porous ceramics the difference between convex and concave porosity is a key point that deserves special focus in this chapter, because it is the most extreme example of a two-phase composite material and is practically important for assessing the possibilities of tailoring the thermal conductivity via microstructure control and processing (e.g. by partial sintering, pore-forming agent or foaming techniques). Interface effects and correlations to other properties, mainly elastic constants, are discussed as well, mainly because of their importance for assessing the grain size dependence of thermal conductivity. Practical examples include the comparison of analytical predictions with experimental data for real-world materials and numerical effective conductivity calculations for computer-generated model materials.

Název v anglickém jazyce

Rigorous bounds, model predictions and mixture rule for the effective thermal conductivity of multiphase and porous ceramics – from theory to practice

Popis výsledku anglicky

Thermal conductivity is a fundamental property of ceramic materials. It is in general represented by a second-order tensor and defined via Fourier’s law, which is a linear constitutive equation. It plays a major role during drying and sintering of ceramics and determines the performance of ceramics in many practical applications, ranging from electronic substrates to high-temperature thermal insulation. Together with the density, specific heat and mechanical properties it is also an important parameter for the assessment of thermal shock resistance. In heterogeneous materials, either single-phase polycrystalline or multiphase (composites), the effective thermal conductivity has to be calculated for engineering purposes via appropriate averaging or homogenization procedures. The first step in these calculations is usually the determination of the effective conductivity of the individual crystalline phases, which is performed via orientational averaging of the conductivity tensor components. Depending on the degree of orientation, the effective conductivity tensor can range from the monocrystal tensor to an isotropic tensor that represents the scalar conductivity for random orientation of crystallites. For multiphase (and porous) materials the second (and third) step is the calculation of the effective conductivity via volume averaging of the phase conductivities for given volume fractions (for statistically isotropic microstructures) and texture parameters (orientation tensors). An additional complication may arise when the phase domains (grains, inclusions, pores) are so small that the finite thickness of the interface (grain boundary or phase boundary) and the interface resistivity has to be taken into account. This chapter gives a profound and detailed summary of the rigorous bounds (Molyneux bounds for orientational averaging, multiphase Wiener and Hashin-Shtrikman bounds for volume averaging), model predictions (linear approximations and nonlinear effective medium approximations) and mixture rules (volume-weighted arithmetic, geometric, harmonic and other averages, as well as fixed- and floating-parameter weighted means) that can be used for estimating the effective thermal conductivity of single-phase, two-phase, three-phase and porous ceramics. It is emphasized that apart from the volume fraction the shape of the phase domains, mainly their surface curvature (and the aspect ratio in matrix-inclusion microstructures), is a key parameter even in statistically isotropic materials. In particular, for porous ceramics the difference between convex and concave porosity is a key point that deserves special focus in this chapter, because it is the most extreme example of a two-phase composite material and is practically important for assessing the possibilities of tailoring the thermal conductivity via microstructure control and processing (e.g. by partial sintering, pore-forming agent or foaming techniques). Interface effects and correlations to other properties, mainly elastic constants, are discussed as well, mainly because of their importance for assessing the grain size dependence of thermal conductivity. Practical examples include the comparison of analytical predictions with experimental data for real-world materials and numerical effective conductivity calculations for computer-generated model materials.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

20504 - Ceramics

Projekt

<a href="/cs/project/GA18-17899S" target="_blank" >GA18-17899S: Částečně a plně slinutá keramika - příprava, mikrostruktura, vlastnosti, modelování a teorie slinování</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

An Essential Guide to Thermal Conductivity

ISBN

978-1-68507-196-7

Počet stran výsledku

137

Strana od-do

1-137

Počet stran knihy

376

Název nakladatele

Nova Science Publishers, Inc.

Místo vydání

New York

Kód UT WoS kapitoly

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