Research Papers

Modeling Surface Electrodes on a Piezoelectric Layer

[+] Author and Article Information
B.-L. Wang, Y.-W. Mai

Centre for Advanced Materials Technology (CAMT), School of Aerospace, Mechanical and Mechatronic Engineering, Mechanical Engineering Building J07, The University of Sydney, Sydney, New South Wales 2006, Australia

J. Appl. Mech 75(2), 021007 (Feb 20, 2008) (8 pages) doi:10.1115/1.2775504 History: Received March 12, 2007; Revised June 11, 2007; Published February 20, 2008

This paper considers a piezoelectric ceramic layer with a surface electrode. It focuses on the effect of the layer thickness on the electrode tip fields. A closed-form solution for the electromechanical fields at the electrode tip is obtained and is expressed in terms of the applied electric field intensity factor, which can be obtained exactly for infinite layer thickness and numerically for finite layer thickness. The stress, electric displacement, and electric field are plotted to show the effect of layer thickness. It is found that the stresses and field intensities at the electrode tip can be reduced considerably by decreasing the thickness of the piezoelectric layer, confirming the previous finding. The paper also gives a solution for two identical and collinear surface electrodes. The relative distance between the electrodes is observed to have significant influence on the electromechanical field in the piezoelectric layer.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Various electrode configurations of reference papers (the bold lines represent electrodes). (A) Two external electrodes attached to a piezoelectric layer (Refs. 9-10 for antiplane problem). (B) Two internal electrodes between two piezoelectric layers poled in opposite directions (Ref. 11 for anti-plane problem; Ref. 12 for in-plane problem). (C) Circular surface electrode of radius a on a piezoelectric layer (Ref. 13 for finite h; Ref. 14 for infinite h). (D) An internal electrode between two piezoelectric half-planes (Refs. 15-17). (E) Two external electrodes attached to the surfaces of a piezoelectric layer (Ref. 18 gave the results for infinite h). (F) An internal semi-infinite electrode between two infinite piezoelectric layers poled in opposite directions (Ref. 19).

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Figure 2

A surface electrode on a piezoelectric layer

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Figure 3

Two symmetric surface electrodes; electrode length 2a=c−b; electrode center of the right electrode is at d=(c+b)∕2

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Figure 4

Electric displacement Dy(x,0) on the electrode plane above the electrode, Dy is zero for x>a; D0=Q0∕a

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Figure 5

Electric field Ex(x,0) on the electrode plane ahead of the electrode; Ex is zero for x<a; E0=Q0∕(a∊33)

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Figure 6

Electric field intensity factor at the electrode tip as a function of layer thickness; K0=2G0Q0∕πa is the intensity factor for infinite layer thickness

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Figure 7

Distributions of cleavage stress σθθ with angle; σ0=e33Q0∕∊33a

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Figure 8

Electric displacement Dy(x,0) above the right electrode for the collinear electrode problem shown in Fig. 3. Out of the electrode region on the y=0 plane, Dy is zero. D0=Q0∕a and h=a.

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Figure 9

Electric field intensity factor at the electrode tips as functions of the layer thickness for the collinear electrodes shown in Fig. 3; K0=2G0Q0∕πa




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