Electroelasticity Relations and Fracture Mechanics of Piezoelectric Structures

[+] Author and Article Information
V. M. Bogomol’nyi

 Moscow State University of Service, 141220, Glavnaya 99, Pushkinsky raion, Cherkizovo, Moscow region, Russia

Appl. Mech. Rev 60(1), 21-36 (Jan 01, 2007) (16 pages) doi:10.1115/1.2375142 History:

Three-dimensional (3D) constitutive equations of piezoelectric (PZ) plates and shells are considered for inverse linear and electrostrictive (quadratic) piezoeffects. Prestressed multilayer PZ shells reinforced with metal including the case of uneven thickness polarization are studied. Asymptotic and variational methods to solve the governing differential equations of PZ shells are considered. Concentrations of electrical and mechanical fields near structure imperfections and external local loading are investigated. The electrothermoviscoelastic heating of PZ shells is considered at harmonic excitation. From numerical analysis and the experimental data of energy dissipation and the temperature behavior of PZ shell the conditions of optimal transformation of electric energy into mechanical deformations are defined. Thus, the geometrical parameters and working frequencies are determined with due account of dielectric relaxation processes. The following nonlinear phenomena are studied: acoustoelectronic wave amplification; electron injection into metalized polar dielectric; resonance growth by 5–20 times of internal electrical field strength in the PZ shells and plates; and autothermostabilization of ferroelectric resonators. For a better understanding of R.D. Mindlin’s gradient theory of polarization in view of electron processes in thin metal-dielectric-metal structures, use was made of solid state physics interpretations as well as experimental data. High concentration of mechanical stresses and temperature and electrical fields near structure defects (first of all, near boundary between various materials) defines the main properties of polar dielectrics. An unknown domain of electrode rough surface influence was estimated, and as result an uneven polarization distribution was found. A theory of nonlinear autowave systems with energy dissipation was used in a physical model of the electrothermal fracture of dielectrics (contacting with metal electrodes), and as a result a nondestructive testing method to study the microstructure defect formation has been suggested.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Electric field near the electroded surface vs ratio of the driving frequency to the antiresonance frequency for Q=50 value, (a)ωc∕ωa=10; (b)ωc∕ωa=1; (c)ωc∕ωa=0.1; (d)ωc∕ωa=0

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Figure 2

Distribution of electrical potential V(x) and polarization P(x) in dielectric layer of MDM structure: (a) classical theory (b) gradient theory of polarization PM(x), VM(x)

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Figure 3

Distribution in MDM structure of qualitative space-charge potential for both “blocking” electrodes (252)

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Figure 4

Distribution of the electrical potential in crystal quartz plate (Ioffe’s experiment (36)), (h is the crystal thickness)




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