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Proceedings Paper

Macroscopic description of nonlinear electromechanical coupling in ferroelectrics
Author(s): Marc Kamlah; Ulrich Boehle; Dietrich Munz; Ch. Tsakmakis
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Paper Abstract

As in many cases piezoelectric devices are made of PZT, it is our objective to incorporate the nonlinearly coupled electro-mechanical behavior of ferroelectric PZT-ceramics into a finite element tool for reliability analyses. In this paper, we will present a phenomenological model for ferroelectrics which is conceived to be valid for complex electro-mechanical loading histories and simple enough to be implemented with acceptable effort in an FE-code. This has been achieved by introducing irreversible polarization and irreversible strain as internal variables besides stress, strain, electric field and polarization. The internal variables represent the loading history and are governed by ordinary differential equations. Each of these evolution equations is subjected to two loading conditions differing in nature. The first indicates the onset of irreversible change by domain switching, while the second characterizes the maximum amount of possible irreversible change corresponding to a totally switched domain structure. Polarization induced anisotropy is taken into account to the extent deemed necessary. For sake of simplicity, no rate effects are included. The model response to uniaxial electro-mechanical loading histories will be discussed and compared to known experimental results. By bilinear approximation the following characteristic macroscopic phenomena of PZT-ceramics can be represented: dielectric hysteresis, polarization induced piezoelectricity, butterfly hysteresis, ferroelastic hysteresis, mechanical depolarization, field dependent coercitive stress.

Paper Details

Date Published: 13 June 1997
PDF: 12 pages
Proc. SPIE 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, (13 June 1997); doi: 10.1117/12.276533
Show Author Affiliations
Marc Kamlah, Forschungszentrum Karlsruhe GmbH (Germany)
Ulrich Boehle, Forschungszentrum Karlsruhe GmbH (Germany)
Dietrich Munz, Forschungszentrum Karlsruhe GmbH (Germany)
Ch. Tsakmakis, Forschungszentrum Karlsruhe GmbH (Germany)

Published in SPIE Proceedings Vol. 3039:
Smart Structures and Materials 1997: Mathematics and Control in Smart Structures
Vasundara V. Varadan; Jagdish Chandra, Editor(s)

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