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Abstract

We use the correspondence principle of linear viscoelasticity and the Mori-Tanaka averaging method to determine the effective electroviscoelastic moduli of a piezocomposite made of piezoceramic (PZT) inclusions and a viscoelastic matrix whose dielectric constants also vary with time t. For elliptic cylindrical PZT inclusions, closed form expressions for the electroviscoelastic moduli are derived. It is found that for the 1-3 piezocomposite, the relaxation of the dielectric constants of the matrix affects only the dielectric moduli and the shear components of the piezoelectric and the viscoelastic moduli of the piezocomposite. However, the viscoelasticity of the matrix influences every effective electroelastic modulus of the piezocomposite. The relaxation times of any two effective moduli are different, and the piezocomposite is an orthotropic material. For time-harmonic loading of the piezocomposite studied, only frequencies in the range of 10 ²- 10² Hz strongly influence the effective storage and the effective loss moduli. Whereas thin PZT ribbons provide the most mechanical strength to the piezocomposite, they give the least piezoelectric effect.

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References

Aboudi, J. 2000. “Micromechanical Modeling of Finite Viscoelastic Multiphase Composites,” Zeitschrift Für Angewandte Mathematik und Physik, 51(1): 114-134.

Agbossou, A. , Viet, H.N. and Pastor, J. 1999. “Homogenization Techniques and Application to Piezoelectric Composite Materials,” Int. J. Appl. Electromagn. Mech., 10(5): 391-403.

Alberola, N.D. and Benzarti, K. 1998. “Modeling of the Relationship Between Morphology and Viscoelastic Behavior of Unidirectional Fiber-Reinforced Polymers,” Polymer Engg. Sci., 38(3): 429-439.

Avellaneda, M. and Swart, P.J. 1998. “Calculating the Performance of 1-3 Piezoelectric Composite for Hydrophone Application: A Effective Approach,” J. Acoustical Society America, 103(3): 1449-1467.

Chan, H.L.W. and Unsworth, J. 1989. Simple Model for Piezoelectric Ceramic/Polymer 1-3 Composites Used in Ultrasonic Transducer Applications,” IEEE Trans. On Ultrasonic Ferroelectric and Frequency Control, 36: 434-441.

Christensen, R.M. 1982. Theory of Viscoelasticity, An Introduction, Academic Press, New York.

Dias, C.J. and Das-Gupta, D.K. 1996. “Inorganic Ceramic/Polymer Ferroelectric Composite Electrets,” IEEE Trans. on Dielectrics and Electrical Inclusions, 3(5): 706-733.

Dunn, M.L. and Taya, M. 1993. “Micromechanics Predictions of the Effective Electroelastic Moduli of Piezoelectric Composites,” Int. J. Solids Structures, 30: 161-175.

Ferry, J.D. 1970. Viscoelastic Properties of Polymers, John Wiley and Sons, Inc., New York.

10.

Hashin, Z. 1965. “Viscoelastic Behavior of Heterogeneous Media,” Journal of Applied Mechanics, 28(11): 1111-1120.

11.

Hashin, Z. 1966. “Viscoelastic Fiber Reinforced Materials,” AIAA Journal, 4: 1411-1417.

12.

Hedvig, P. 1977. Dielectric Spectroscopy of Polymer, Akademiai, Budapest.

13.

Hornsby, J.S. and Das-Gupta, D.K. 2000. “Finite-Difference Modeling of Piezoelectric Composite Transducers,” J. Appl. Phys., 87(1): 467-473.

14.

Jiang, B. , Fang, D.N. and Hwang, K.C. 1999a. “A Unified Model for the Multiphase Piezocomposites with Ellipsoidal Inclusions,” Int. J. Solids and Structures, 36(18): 2707-2733.

15.

Jiang, B. , Fang, D.N. and Hwang, K.C. 1999b. “Constitutive Models of Ferroelectric Composites with a Viscoelastic and Dielectric Relaxation Matrix I: Theory,” Sci. in. China Series A, 42(11): 1193-1200.

16.

Jiang, B. , Fang, D.N. and Hwang, K.C. 2000. “Constitutive Models of Ferroelectric Composites with a Viscoelastic and Dielectric Relaxation Matrix II: Experimenting and Calculating,” Sci. in China Series A, 43(6): 647-654.

17.

Jiang, B. and Batra, R.C. 2001. “Effective Electroelastic Moduli of Piezocomposite with Elliptic Cylinder Piezoelectric Inclusion,” submitted for publication.

18.

Kaliske, M. 2000. “A Formulation of Elasticity and Viscoelasticity For Fiber-Reinforced Material at Small and Finite Strains,” Computer Methods in Applied Mechanics and Engineering, 185(2-4): 225-243.

19.

Li, J. and Weng, G.J. 1994. “Effective Creep Behavior and Complex Moduli of Fiber- and Ribbon-Reinforced Polymer-Matrix Composites,” Composites Science and Technology, 52: 615-629.

20.

Lovinger, A. 1983. “Ferroelectric Polymers,” Science, 220: 1115-1121.

21.

Mori, T. and Tanaka, K. 1973. “Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusion,” Acta Metallurgica, 21: 571-574.

22.

Papanicolaou, G.C. , Zaoutsos, S.P. and Cardon, A.H. 1999. “Prediction of the Non-linear Viscoelastic Response of Unidirection Fiber Composite,” Composites Science and Technology, 59(9): 1311-1319.

23.

Shapery, R.A. 1967. “Stress Analysis of Composite Materials,” Journal of Composite Materials, 1: 228-267.

24.

Shapery, R.A. 1969. “On the Characterization of Non-linear Viscoelastic Materials,” Polymer Engineering and Science, 9(4): 295-310.

25.

Skurda, A.M. and Auzukalns, Ya V. 1970. “Creep and Long-Term Strength of Unidirectional Reinforced Plastics in Compression,” Polymer Mech., 6: 718-722.

26.

Tressler, J.F. , Alkoy, S. and Newnham, E.E. 1998. “Piezoelectric Sensors and Sensor Materials,” J. Electroceramics, 2(2): 257-272.

Effective Electroelastic Properties of a Piezocomposite with Viscoelastic and Dielectric Relaxing Matrix

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