Конечно-элементный анализ эффективных свойств корундосодержащей пьезокерамики c разномасштабными порами
DOI:
https://doi.org/10.7242/1999-6691/2020.13.1.4Ключевые слова:
пьезоэлектричество, трехфазный пьезокомпозит, гранулированное включение, пористость, эффективный модуль, представительный объемАннотация
Рассматриваются задачи гомогенизации для определения эффективных модулей керамоматричных пьезокомпозитов с учетом разномасштабной пористости. Полагается, что пьезокомпозит состоит из пьезокерамической матрицы, более жестких упругих корундовых включений и пор. Применяются две модели пористости: для микропор и для мезопор. Микропорами называются распределенные в пьезокерамике поры с размерами, много меньшими размеров включений, а мезопорами - поры, сравнимые по размерам с включениями. Мезопоры в совокупности считаются отдельной фазой пьезокомпозита. При наличии микропористости задача гомогенизации решается на двух масштабных уровнях. Вначале вычисляются эффективные модули для микропористой пьезокерамики, в которой микропоры выступают как отдельная фаза двухфазного пьезокомпозита без включений, а затем реализуется задача гомогенизации для общего случая, то есть для трехфазного композита из микропористой пьезокерамики, включений и, возможно, мезопор. Для решения задач гомогенизации использован метод эффективных модулей в стандартной формулировке, метод конечных элементов и вычислительный комплекс ANSYS. Разработаны конечно-элементные модели представительных объемов 3-0 связности (для двухфазных композитов) и 3-0-0 связности (для трехфазных композитов) с изолированными включениями и порами. Полный набор эффективных модулей находился из решений пяти краевых задач с различными линейными главными граничными условиями. Результаты вычислительных экспериментов показали, что эффективные модули существенно зависят не только от объемных долей включений и пор, но и от размеров пор и их конфигурации. При этом наличие пористости в структуре пьезокомпозитов в большей степени влияет на их эффективные модули упругости, чем на пьезомодули и диэлектрические проницаемости.
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Библиографические ссылки
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Liu Y.G., Jia D.C., Zhou Y. Microstructure and mechanical properties of a lithium tantalate-dispersed-alumina ceramic composite. Ceram. Int., 2002, vol. 28, pp. 111-114. https://doi.org/10.1016/S0272-8842(01)00065-7">https://doi.org/10.1016/S0272-8842(01)00065-7
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Thommerel E., Madigou V., Villain S., Musso J., Valmalette J.-C., Gavarri J.-R. Microstructure modifications and modulated piezoelectric responses in PLZT/Al2O3 composites. Mat. Sci. Eng. B, 2003, vol. 97. pp. 74-82. https://doi.org/10.1016/S0921-5107(02)00407-5">https://doi.org/10.1016/S0921-5107(02)00407-5
Xiang P.-H., Dong X.-L., Chen H., Zhang Z., Guo J.-K. Mechanical and electrical properties of small amount of oxides reinforced PZT ceramics. Ceram. Int., 2003, vol. 29, pp. 499-503. https://doi.org/10.1016/S0272-8842(02)00193-1">https://doi.org/10.1016/S0272-8842(02)00193-1
IEEE Standard on piezoelectricity. ANSI-IEEE Std. 176–1987. New York: IEEE, 1988. https://doi.org/10.1109/IEEESTD.1988.79638">https://doi.org/10.1109/IEEESTD.1988.79638
Newnham R.E., Skinner D.P., Cross L.E. Connectivity and piezoelectric-pyroelectric composites. Mater. Res. Bull., 1978, vol. 13, pp. 525-536. https://doi.org/10.1016/0025-5408(78)90161-7">https://doi.org/10.1016/0025-5408(78)90161-7
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Dunn M.L., Taya M. Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites. Int. J. Solid. Struct., 1993, vol. 30, pp. 161-175. https://doi.org/10.1016/0020-7683(93)90058-F">https://doi.org/10.1016/0020-7683(93)90058-F
Iovane G., Nasedkin A.V. Finite element modelling of ceramomatrix piezocomposites by using effective moduli method with different variants of boundary conditions. Mater. Phys. Mech., 2019, vol. 42, pp. 1-13. https://doi.org/10.18720/MPM.4212019_1">https://doi.org/10.18720/MPM.4212019_1
Iyer S., Alkhader M., Venkatesh T.A. On the relationships between cellular structure, deformation modes and electromechanical properties of piezoelectric cellular solids. Int. J. Solid. Struct., 2016, vol. 80, pp. 73-83. https://doi.org/10.1016/j.ijsolstr.2015.10.024">https://doi.org/10.1016/j.ijsolstr.2015.10.024
Iyer S., Venkatesh T.A. Electromechanical response of (3–0) porous piezoelectric materials: Effects of porosity shape. J. Appl. Phys., 2011, vol. 110, 034109. https://doi.org/10.1063/1.3622509">https://doi.org/10.1063/1.3622509
Iyer S., Venkatesh T.A. Electromechanical response of (3–0, 3–1) particulate, fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method. Int. J. Solid. Struct., 2014, vol. 51, pp. 1221‑1234. https://doi.org/10.1016/j.ijsolstr.2013.12.008">https://doi.org/10.1016/j.ijsolstr.2013.12.008
Kudimova A., Mikhayluts I., Nadolin D., Nasedkin A., Nasedkina A., Oganesyan P., Soloviev A. Computer design of porous and ceramic piezocomposites in the finite element package ACELAN. Procedia Structural Integrity, 2017, vol. 6, pp. 301‑308. https://doi.org/10.1016/j.prostr.2017.11.046">https://doi.org/10.1016/j.prostr.2017.11.046
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