Orthotropically textured elastic aggregates of cubic crystals |
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| Institution: | 1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt;1. China State Key Lab of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;2. Department of Mathematics, Institute of Natural Sciences, and Ministry of Education Key Laboratory of Scientific and Engineering Computing (MOE-LSC), Shanghai Jiao Tong University, Shanghai 200240, China;3. Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA;4. General Motors Global Research & Development, China Science Laboratory, Shanghai 201206, China;1. Arts et Métiers ParisTech, PIMM - UMR CNRS 8006, 151 Bd de l''Hôpital, 75013 Paris, France;2. Univ Lille Nord de France, Unité Matériaux et Transformations, USTLille - CNRS UMR 8207, Cité Scientifique, Batiment C6, 59655 Villeneuve d''Ascq, France;3. Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle MSME UMR 8208 CNRS, 5 bd Descartes, F-77545 Marne-la-Vallée, France;1. College of Electronic Information and Electrical Engineering, Shangluo University, Shangluo 726000, China;2. Shaanxi Key Laboratory of Comprehensive Utilization of Tailing Resources, Shangluo University, Shangluo 726000, China;3. State Key Laboratory of Gansu Advanced Nonferrous Metal Materials, Lanzhou University of Technology, Lanzhou 730050, China |
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| Abstract: | The linear orthotropic relations between stress and infinitesimal strain require only seven, instead of the usual nine, independent elastic moduli, and one of them can be identified as a bulk modulus coincident with that common to all the grains. Each of the remaining six overall moduli is placed between upper and lower, “Voigt-Reuss-Hill”, and also “Hashin- Shtrikman”, bounds, in terms of the grain moduli and of three measurable parameters that take account of the particular mix of lattice orientations. One or more of them can be determined at once in exceptional cases where the grains all have a particular fixed or somewhat variable lattice orientation: the upper and lower bounds come to the appropriate coincidence then. Generally the vagaries of the configuration have an influence in keeping each pair of bounds apart, but effective estimates of the overall elastic moduli can be offered, except perhaps when the grains have a very pronounced cubic anisotropy. We shall refer in particular to the more symmetrical, tetragonal and transversely isotropic, textures for which correspondingly fewer overall moduli and orientation parameters are required. |
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