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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 107

Finite Element Modelling of Effective Moduli of Porous and Polycrystalline Composite Piezoceramics

S.V. Bobrov1, A.V. Nasedkin1 and A.N. Rybjanets2

1Research Institute of Mechanics and Applied Mathematics, Rostov State University, Rostov-on-Don, Russia
2Ultrashape Ltd, Tel Aviv, Israel

Full Bibliographic Reference for this paper
S.V. Bobrov, A.V. Nasedkin, A.N. Rybjanets, "Finite Element Modelling of Effective Moduli of Porous and Polycrystalline Composite Piezoceramics", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 107, 2006. doi:10.4203/ccp.83.107
Keywords: piezocomposite, porous piezoceramic, polycrystalline piezocomposite, effective moduli, finite element method.

Summary
Porous piezoceramic materials have received considerable attention due to their application in ultrasonic transducers, hydrophones, pressure sensors and other piezoelectric devices. The classification of piezoelectric composites was initiated by Newnham's connectivity theory. In compliance with this theory porous piezoceramic can be classified as two phase composite. As is well known, the 3-0 and 3-3 piezocomposites in the form of porous PZT materials show considerably improved transducer characteristics. Porous piezocomposites have great potential for low acoustic impedance and higher efficiency compared to conventional dense PZT piezoceramic materials. However, their depth-handling capability and the stability to hydrostatic pressure have yet to be proved, particularly for 3-3 porous structures. The mechanical strength of the devices can be improved by filling with polymer material as the second phase. Note, that the original concept of microstructural designing of polymer-free polycrystalline composite materials is suggested in [1].

Porous or polycrystalline composite piezoceramic having pore or inclusion sizes, lesser that may be accepted as a quasi homogeneous medium with some effective moduli for most applications. At present, there are many publications in which the effective properties of 3-0, 3-3 piezocomposite media have been analyzed. The approximate formulas of engineering character for piezocomposites with various types of connectivity have been received. However, the strict mathematical approaches of the mechanics of composites were used only in a small number of papers.

In present work we have developed the effective moduli method and finite element technique in accordance with [2,3,4]. Theoretical aspects of the effective moduli method for inhomogeneous piezoelectric media were examined. Four static piezoelectric problems for a representative volume that allow the determination of the effective moduli of an inhomogeneous body were specified. These problems differ by the boundary conditions which were set on a representative volume surfaces: a) mechanical displacements and electric potential, b) mechanical displacements and normal component of electric displacement vector, c) mechanical stress vector and electric potential, and d) mechanical stress vector and normal component of the electric displacement vector. Respective equations for calculation of effective moduli of piezoelectric media with arbitrary anisotropy were derived.

Based on these equations the full set of effective moduli for porous and polycrystalline composite piezoceramics having wide porosity and, or injection range was calculated with help of the finite element method (FEM). Different models of representative volume were considered: piezoelectric cubes with one cubic and one spherical pore inside, cubic volume evenly divided on partial cubic volumes a part of which randomly declared as pores for 3-0 and 3-0 - 3-3 connectivety. For the modeling of porous and polycrystalline piezoceramics with 3-3 connectivity the representative volume having skeleton structure was considered. For taking into consideration inhomogeneous or incomplete ceramics polarization the preliminary modeling of the polarization process was performed. To determine the zones that have different polarization, the FEM calculations for the electrostatic problem were executed [5].

For polycrystalline piezoceramics the crystallites of sapphire (-corundum) were considered as the material of the inclusions. The effective moduli for inclusions were calculated as the average moduli of monophase polycrystallite of a trigonal system.

The results of the FEM modeling were compared with the experimental data for different porous ceramics in the relative porosity range of 0-70 %.

References
1
A.N. Rybianets, A.V. Nasedkin, A.V. Turik, "New microstructural design concept for polycrystalline composite material", Integrated Ferroelectrics, 63, 179-182, 2004. doi:10.1080/10584580490459404
2
I. Getman, S. Lopatin, "Theoretical and experimental investigation of the porous PZT ceramics", Ferroelectrics, 186, 301-304, 1996. doi:10.1080/00150199608218088
3
A.V. Nasedkin, "On some methods of calculation the inhomogeneous piezoelectric materials effective properties", Modern Problems of Continuum Mechanics, Proc.. VII Int. Conf., Rostov on Don, 22-24 Oct. 2001, Rostov on Don, Novaja Kniga, Vol. 1, 182-188, 2002. (in Russian)
4
A. Nasedkin, A. Rybjanets, L. Kushkuley, Y. Eshel, R. Tasker, "Different approaches to finite element modelling of effective moduli of porous piezoceramics with 3-3 (3-0) connectivity", Proc. 2005 IEEE Ultrason. Symp., Rotterdam, Sept. 18 -21, 2005. 1648-1651, 2005. doi:10.1109/ULTSYM.2005.1603179
5
A.V. Nasedkin, A.N. Rybjanets, "The simulation for representative volumes of porous piezocomposite structure and the calculation of their effective properties", Russian Izvestiya, North-Caucas. Region. Ser. Techn Sciences, Spec. Issue, 91-95, 2004. (in Russian)

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