Finite element analysis of the effective properties of corundum-containing piezoceramics with multiscale pores
DOI:
https://doi.org/10.7242/1999-6691/2020.13.1.4Keywords:
piezoelectricity, three-phase piezocomposite, granular inclusion, porosity, effective modulus, representative volume, finite element methodAbstract
The homogenization problems for determining the effective material modules of ceramicmatrix piezocomposites with respect to multiscale porosity are considered. The piezocomposite consists of a piezoceramic matrix, more rigid elastic corundum inclusions and pores. Two porosity models for micropores and for mesopores are used. Here the pores, distributed in piezoceramics with sizes much smaller than the sizes of inclusions, are called micropores, and the pores, comparable in size to inclusions, are called mesopores. Mesopores are considered as a separate phase of a piezocomposite. In the presence of microporosity, the homogenization problem is solved at two scale levels. First, we calculate the effective modules for microporous piezoceramics, where micropores are considered as a separate phase of a two-phase piezocomposite without inclusions, and then we solve the homogenization problem in the general case, i.e. for a three-phase composite consisting of microporous piezoceramics, inclusions and, possibly, mesopores. To solve the homogenization problems, the method of effective modules in the standard formulation, the finite element method and the ANSYS computational package are used. The finite element models of representative volumes of 3-0 connectivity for two-phase composites and 3-0-0 connectivity are developed for three-phase composites with isolated inclusions and pores. A complete set of effective modules was determined from the solutions of five boundary value problems with different linear essential boundary conditions. The results of computational experiments showed that effective modules quite significantly depend not only on the volume fractions of inclusions and pores, but also on the structure and size of the pores. Moreover, the structure of porosity affects to a greater extent the effective stiffness modules than the piezoelectric modules and dielectric constants.
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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
Yang B., Chen X.M. Alumina ceramics toughened by a piezoelectric secondary phase. J. Eur. Ceram. Soc., 2000, vol. 20, pp. 1687-1690. https://doi.org/10.1016/S0955-2219(00)00049-2">https://doi.org/10.1016/S0955-2219(00)00049-2
Borzov P.A., Filippov S.E., Topolov V.Yu., Brill O.E., Panich A.E. Elastic properties and frequency characteristics of a piezo-active 3–0-type corundum-containing composite. Adv. Compos. Hybrid Mater., 2018, vol. 1, pp. 558-566. https://doi.org/10.1007/s42114-018-0039-0">https://doi.org/10.1007/s42114-018-0039-0
Borzov P.A., Filippov S.E., Topolov V.Yu., Brill O.E., Panich A.E. Piezoelectric properties and related parameters of a novel 3–0-type composite. Funct. Mater. Lett., 2018, vol. 11, 1850082. https://doi.org/10.1142/S1793604718500820">https://doi.org/10.1142/S1793604718500820
Borzov P.A., Topolov V.Yu., Bowen C.R. Relations between the piezoelectric performance and quality factors in a corundum-containing composite. Mater. Chem. Phys., 2019, vol. 233, pp. 194-202. https://doi.org/10.1016/j.matchemphys.2019.05.019">https://doi.org/10.1016/j.matchemphys.2019.05.019
Hwang H.J., Sekino T., Ota K., Niihara K. Perovskite type BaTiO3 ceramics containing particulate SiC: Part I. Structure variation and phase transformation. J. Mater. Sci., 1996, vol. 31, pp. 4617-4624. https://doi.org/10.1007/BF00366360">https://doi.org/10.1007/BF00366360
Hwang H.J., Niihara K. Perovskite type BaTiO3 ceramics containing particulate SiC: Part II Microstructure and mechanical properties. J. Mater. Sci., 1998, vol. 33, pp. 549-558. https://doi.org/10.1023/A:1004365006839">https://doi.org/10.1023/A:1004365006839
Malič B., Kosec M., Kosmač T. Mechanical and electrical properties of PZT-ZrO2 composites. Ferroelectrics, 1992, vol. 129, pp. 147-155. https://doi.org/10.1080/00150199208016985">https://doi.org/10.1080/00150199208016985
Rybyanets A.N., Rybyanets A.A. Ceramic piezocomposites: Modeling, technology, and characterization. IEEE Trans. Ultrason. Ferroelectr. Freq. Control., 2011, vol. 58, pp. 1757-1773. https://doi.org/10.1109/TUFFC.2011.2013">https://doi.org/10.1109/TUFFC.2011.2013
Rybyanets A.N., Konstantinov G.M., Naumenko A.A., Shvetsova N.A., Makar’ev D.I., Lugovaya M.A. Elastic, dielectric, and piezoelectric properties of ceramic lead zirconate titanate/α-Al2O3 composites. Phys. Solid. State, 2015, vol. 57, pp. 527-530. https://doi.org/10.1134/S1063783415030270">https://doi.org/10.1134/S1063783415030270
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
Banno H. Effects of porosity on dielectric, elastic, and electromechanical properties of Pb(Zr,Ti)O3 ceramics with open pores: A theoretical approach. Jpn. J. Appl. Phys., 1993, vol. 32, pp. 4214-4217. https://doi.org/10.1143/JJAP.32.4214">https://doi.org/10.1143/JJAP.32.4214
Bowen C.R., Kara H. Pore anisotropy in 3–3 piezoelectric composites. Mater. Chem. Phys., 2002, vol. 75, pp. 45-49. https://doi.org/10.1016/S0254-0584(02)00028-7">https://doi.org/10.1016/S0254-0584(02)00028-7
Dunn M.L., Taya M. Electromechanical properties of porous piezoelectric ceramics. J. Am. Ceram. Soc., 1993, vol. 76, pp. 1697-1706. https://doi.org/10.1111/j.1151-2916.1993.tb06637.x">https://doi.org/10.1111/j.1151-2916.1993.tb06637.x
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
Kudimova A.B., Nadolin D.K., Nasedkin A.V., Oganesyan P.A., Soloviev A.N. Finite element homogenization models of bulk mixed piezocomposites with granular elastic inclusions in ACELAN package. Mater. Phys. Mech., 2018, vol. 37, pp. 25-33. https://doi.org/10.18720/MPM.3712018_4">https://doi.org/10.18720/MPM.3712018_4
Levassort F., Lethiecq M., Desmare R., Tran-Huu-Hue L.P. Effective electroelastic moduli of 3-3(3-0) piezocomposites. IEEE Trans. Ultrason. Ferroelectr. Freq. Control., 1999, vol. 46, pp. 1028-1034. https://doi.org/10.1109/58.775670">https://doi.org/10.1109/58.775670
Martinez-Ayuso G., Friswell M.I., Adhikari S., Khodaparast H.H., Berger H. Homogenization of porous piezoelectric materials. Int. J. Solid. Struct., 2017, vol. 113-114, pp. 218-229. https://doi.org/10.1016/j.ijsolstr.2017.03.003">https://doi.org/10.1016/j.ijsolstr.2017.03.003
Nasedkin A.V., Shevtsova M.S. Improved finite element approaches for modeling of porous piezocomposite materials with different connectivity. Ferroelectrics and superconductors: Properties and applications, ed. I.A. Parinov. New York: Nova Science Publ., 2011. P. 231-254.
Nguyen B.V., Challagulla K.S., Venkatesh T.A., Hadjiloizi D.A., Georgiades A.V. Effects of porosity distribution and porosity volume fraction on the electromechanical properties of 3–3 piezoelectric foams. Smart Mater. Struct., 2016, vol. 25, 125028. https://doi.org/10.1088/0964-1726/25/12/125028">https://doi.org/10.1088/0964-1726/25/12/125028
Odegard G.M. Constitutive modeling of piezoelectric polymer composites. Acta Mater., 2004, vol. 52, pp. 5315–5330. https://doi.org/10.1016/j.actamat.2004.07.037">https://doi.org/10.1016/j.actamat.2004.07.037
Pan’kov A.A. Statisticheskaya mekhanika p’yezokompozitov [Statistical mechanics of piezocomposites]. Perm, Izd-vo Perm. gos. tekhn. un-ta, 2009. 480 p.
Perry A., Bowen C.R., Mahon S.W. Finite element modelling of 3-3 piezocomposites. Scripta Materialia, 1999, vol. 41, pp. 1001-1007. https://doi.org/10.1016/S1359-6462(99)00249-3">https://doi.org/10.1016/S1359-6462(99)00249-3
Khoroshchn L.P., Maslov B.P., Leshchenko P.V. Prognozirovaniye effektivnykh svoystv p’yezoaktivnykh kompozitnykh materialov [Prediction of the effective properties of piezoelectric composite materials]. Kiev, Naukova Dumka, 1989. 208 p.
Kudimova A., Nasedkin A. Analysis of porosity influence on the effective moduli of ceramic matrix PZT composite using the simplified finite element model. J. Adv. Dielectr., 2019, vol. 9, 1950043. https://doi.org/10.1142/S2010135X19500437">https://doi.org/10.1142/S2010135X19500437
Iovane G., Nasedkin A.V. Finite element study of ceramic matrix piezocomposites with mechanical interface properties by the effective moduli method with different types of boundary conditions. Wave dynamics, mechanics and physics of microstructured metamaterials, ed. M. Sumbatyan. Springer, 2019. P. 163-179. https://doi.org/10.1007/978-3-030-17470-5_12">https://doi.org/10.1007/978-3-030-17470-5_12
Iovane G., Nasedkin A.V. Numerical modelling of two-phase piezocomposites with interface mechanical anisotropic effects. Dynamical processes in generalized continua and structures, eds. H. Altenbach, A. Belyaev, V. Eremeyev, A. Krivtsov, A. Porubov. Springer, 2019. P. 293-304. https://doi.org/10.1007/978-3-030-11665-1_16">https://doi.org/10.1007/978-3-030-11665-1_16
Nasedkin A.V., Kornievsky A.S. Finite element modeling of effective properties of elastic materials with random nanosized porosities. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2017, vol. 10, no. 4, pp. 375-387. https://doi.org/10.7242/1999-6691/2017.10.4.29">https://doi.org/10.7242/1999-6691/2017.10.4.29
Eichhorn F., Biggemann J., Kellermann S., Kawai A., Kato K., Kakimoto K., Fey T. Influence of cell size on mechanical and piezoelectric properties of PZT and LNKN ceramic foams. Adv. Eng. Mater., 2017, vol. 19, 1700420. https://doi.org/doi/10.1002/adem.201700420">https://doi.org/doi/10.1002/adem.201700420
Kumar B.P., Rawal B., Rajan K.M. Characterization of high porous PZT piezoelectric ceramics by different techniques. Def. Sci. J., 2018, vol. 68, pp. 500-504. https://doi.org/10.14429/dsj.68.12315">https://doi.org/10.14429/dsj.68.12315
Tajima K.-I., Hwang H.J., Sando M., Niihara K. Electric-field-induced crack growth behavior in PZT/Al2O3 composites. J. Am. Ceram. Soc., 2000, vol. 83, pp. 651-653. https://doi.org/10.1111/j.1151-2916.2000.tb01248.x">https://doi.org/10.1111/j.1151-2916.2000.tb01248.x
Gerasimenko T.E., Kurbatova N.V., Nadolin D.K., Nasedkin A.V., Nasedkina A.A., Oganesyan P.A., Skaliukh A.S., Soloviev A.N. Homogenization of piezoelectric composites with internal structure and inhomogeneous polarization in ACELAN-COMPOS finite element package. Wave dynamics, mechanics and physics of microstructured metamaterials, ed. M. Sumbatyan. Springer, 2019. P. 13-131. https://doi.org/10.1007/978-3-030-17470-5_8">https://doi.org/10.1007/978-3-030-17470-5_8
Lewis R.W.C., Dent A.C.E., Stevens R., Bowen C.R. Microstructural modelling of the polarization and properties of porous ferroelectrics. Smart Mater. Struct., 2011, vol. 20, 085002. https://doi.org/10.1088/0964-1726/20/8/085002">https://doi.org/10.1088/0964-1726/20/8/085002
Martínez-Ayuso G., Friswell M.I., Khodaparast H.H., Roscow J.I., Bowen C.R. Electric field distribution in porous piezoelectric materials during polarization. Acta Mater., 2019, vol. 173, pp. 332-341. https://doi.org/10.1016/j.actamat.2019.04.021">https://doi.org/10.1016/j.actamat.2019.04.021
Nan C.-W., Weng G.J. Influence of polarization orientation on the effective properties of piezoelectric composites. J. Appl. Phys., 2000, vol. 88, pp. 416-423. https://doi.org/10.1063/1.373675">https://doi.org/10.1063/1.373675
Zhang Y., Roscow J., Lewis R., Khanbareh H., Topolov V.Yu., Xie M., Bowen C.R. Understanding the effect of porosity on the polarisation-field response of ferroelectric materials. Acta Mater., 2018, vol. 154, pp. 100-112. https://doi.org/doi:10.1016/j.actamat.2018.05.007">https://doi.org/doi:10.1016/j.actamat.2018.05.007
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