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TECHNICAL PAPERS

Multiaxial Constitutive Behavior of Ferroelectric Materials

[+] Author and Article Information
Wei Chen, Christopher S. Lynch

The Woodruff School of Mechanical Engineering, The Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Eng. Mater. Technol 123(2), 169-175 (Sep 09, 2000) (7 pages) doi:10.1115/1.1329874 History: Received September 14, 1999; Revised September 09, 2000
Copyright © 2001 by ASME
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References

Jaffe, B., Cook, W. R., and Jaffe, H., 1971, Piezoelectric Ceramics, Academic Press, London and New York, pp. 135–137.
Stratton, J. A., 1941, Electromagnetic Theory, McGraw-Hill, New York and London.
Lines, M. E., and Glass, A. M., 1977, Principles and Applications of Ferroelectrics and Related Materials, Oxford University Press.
Cao,  H., and Evans,  A. G., 1993, “Nonlinear deformation of ferroelectric ceramics,” J. Am. Ceram. Soc., 76, pp. 890–896.
Lynch,  C. S., 1998, “The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT,” Acta Metall. Mater., 44, pp. 4137–4148.
Lubliner, J., 1990, Plasticity Theory, Macmillan, New York, pp. 102–110.
Schaufele,  A., and Hardtl,  K., 1996, “Ferroelastic properties of lead zirconate titanate ceramics,” J. Am. Ceram. Soc., 79, pp. 2637–2640.
Huber, J., 2000, “Multiaxial Models and Experiments with Ferroelectric Ceramics,” SPIE Conference on Smart Structures and Materials, Active Materials: Behavior and Mechanics, Vol. 3992.
Huber,  J. E., Fleck,  N. A., Landis,  C. M., and McMeeking,  R. M., 2000, “A constitutive model for ferroelectric polycrystals,” JMPS, 47, pp. 1663–1697.
Haertling,  G. H., 1987, “PLZT electro-optic materials and applications—A review,” Ferroelectrics, 75, pp. 25–55.
Chen,  W., and Lynch,  C. S., 1998, “A micro-electro-mechanical model for polarization switching of ferroelectric materials,” Acta Mater., 46, pp. 5303–5353.
Hwang,  S. C., Huber,  J. E., McMeeking,  R. M., and Fleck,  N. A., 1998, “The simulation of switching in polycrystalline ferroelectric ceramics,” J. Appl. Phys., 84, No. 3, pp. 1530–1540.

Figures

Grahic Jump Location
Stresses on the specimen in the axial, radial, and tangential directions
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(a) Measured axial stress/axial strain for unpoled PLZT and (b) axial stress/transverse strain for various compressive hoop stress levels
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(a) Measured axial stress/axial strain for unpoled PLZT and (b) axial stress/transverse strain for various transverse tensile stresses
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(a) Measured axial stress/axial strain curves for poled PLZT and (b) axial stress/transverse strain for various compressive transverse stress levels
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(a) Measured axial stress/axial strain curves for poled PLZT and (b) axial stress/transverse strain for various tensile transverse stress levels
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(a), (b), (c) show the polarization and strain change for several possible unit cell orientations. The elongation represents the spontaneous strain. The arrow represents the polarization direction.
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The offset method was used to determine the switching stress. Two offset strains are shown, one for the onset of switching and one for the onset of polarization saturation.
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Yield and saturation stresses for unpoled and poled materials are shown together with the Tresca and Mises criteria
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Projections of predicted yield surface of poled material in (a) (σ1−σ3)(σ1−σ3) plane and (b) π-plane. The Tresca yield surface is shown for comparison.
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The perovskite type crystal structure of lead titanate is cubic above the Curie temperature and tetragonal and polar below the Curie temperature
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Schematic of the multiaxial loading system. A load frame is used to apply the axial force to the tubular specimen. Inner and outer pressure are used to apply the radial and tangential stresses.

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