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Phase mixture modeling of the grain size dependence of Young’s modulus and thermal conductivity of alumina and zirconia ceramics |
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| Affiliation: | 1. Instituto de Cerámica y Vidrio (ICV-CSIC), C/ Kelsen 5, 28049, Madrid, Spain;2. Grupo de Investigación en Aplicaciones del Láser y Fotónica (ALF-USAL), Universidad de Salamanca, Plaza de la Merced s/n, 37008, Salamanca, Spain;3. Université de Lyon, INSA-Lyon, MATEIS UMR CNRS 5510, 7 Avenue Jean Capelle, 69621, Villeurbanne Cedex, France;1. Université François Rabelais de Tours, CNRS, CEA, ENIVL, GREMAN UMR 7347, IUT de BLOIS 15 rue de la chocolaterie, CS 2903, 41029 Blois Cedex, France;2. Laboratoire des Sciences des Procédés et des Matériaux, CNRS, LSPM – UPR 3407, Université Paris 13, Sorbonne Paris Cité, 99 Avenue J.B. Clément, 93430 Villetaneuse, France;3. Université de Montpellier 2, IES, UMR 5214, Place E. Bataillon, 34095 Montpellier, France;1. School of Materials Science and Engineering, Zhengzhou University of Aeronautics, Zhengzhou, 450046, China;2. State Key Laboratory of Green Building in Western China, Xi′an University of Architecture and Technology, Xi′an, 710055, China;1. Art & Architecture Faculty, Yadegar-e Imam Khomeini (RAH), Shahre-Rey Branch, Islamic Azad University, Tehran, Iran;2. Faculty of Materials & Manufacturing Processes, Malek-Ashtar University of Technology, Tehran, Iran |
| Abstract: | The grain size dependence of Young’s modulus and thermal conductivity of alumina and zirconia ceramics is predicted via phase mixture modeling, using both analytical and numerical approaches. Using typical values for the thickness and properties of the grain boundaries, the equivalent volume fraction of “grain boundary phase” is calculated for a given grain shape. Based on this volume fraction estimate and a rough estimate of the grain boundary properties, the effective properties of the polycrystalline materials are calculated and compared in terms of volume-equivalent sphere diameters. For grains of cubic and tetrakaidecahedral shape excellent agreement is found between numerical calculations and analytical predictions based on the lower Hashin-Shtrikman bound. The grain size dependence is extremely weak for Young’s modulus, but can be more significant for thermal conductivity, especially when the intrinsic conductivity of the material is high. The predictions are compared to literature data. |
| Keywords: | Grain size (crystallite size volume-equivalent sphere diameter mean chord / mean intercept length Jeffries grain size) Grain shape (cube / cubic tetrakaidecahedron / tetrakaidecahedral / Kelvin cell randomly polyhedral) Young’s modulus (elastic modulus tensile modulus) Thermal conductivity (heat conductivity) Phase mixture modeling |
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