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TECHNICAL PAPERS

The Mode III Interface Crack in Piezo-Electro-Magneto-Elastic Dissimilar Bimaterials

[+] Author and Article Information
R. Li, G. A. Kardomateas

School of Aerospace Engineering,  Georgia Institute of Technology, Atlanta, GA 30332-0150

J. Appl. Mech 73(2), 220-227 (Jun 01, 2005) (8 pages) doi:10.1115/1.2073328 History: Received February 19, 2005; Revised June 01, 2005

The mode III interface crack problem is investigated for dissimilar piezo-electro-magneto-elastic bimaterial media, taking the electro-magnetic field inside the crack into account. Closed form solutions are derived for impermeable and permeable cracks. The conventional singularity of r12 is found for the fields at the distance r ahead of the interface crack tip. Expressions for extended crack tip stress fields and crack opening displacements (ECODs) are derived explicitly, and so are some fracture parameters, such as extended stress intensity factors (ESIFs) and energy release rate (G) for dissimilar bimaterials. An approach called the “energy method,” finding the stationary point of the saddle surface of energy release rate with respect to the electro-magnetic field inside the crack, is proposed. By this method, the components of the induced electro-magnetic field inside the crack are determined, and the results are in exact agreement with those in the literature if the two constituents of the bimaterial media are identical. The effects from mechanical and electro-magnetic property mismatches, such as differences in the stiffness, electric permittivity and magnetic permeability, between the two constituents of the bimedia on the mode III interface crack propagation are illustrated by numerical simulations. The results show that the applied electric and magnetic loading usually retard the growth of the interface crack and the directions of the combined mechanical, electric, and magnetic loading have a significant influence on the mode III interface crack propagation.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

An interface crack between dissimilar anisotropic bimedia

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Figure 2

ΔD20 versus the bimaterial properties

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Figure 3

ΔB20 versus the bimaterial properties

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Figure 4

Energy release rate, G, versus the stiffness ratio c44II∕c44I, for an interface crack under pure mechanical loading

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Figure 5

The effect of the direction of the applied D2 on the energy release rate, G, for an impermeable interface crack

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Figure 6

The effect of the direction of the applied B2 on the energy release rate, G, for an impermeable interface crack

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Figure 7

The effect of the directions of the combined applied B2 and D2 on the energy release rate, G, for an impermeable interface crack

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Figure 8

Energy release rate, G, versus the electric permittivity ratio, ε11II∕ε11I, for an impermeable interface crack under pure D0∞ loading

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Figure 9

Energy release rate, G, versus the magnetic permeability ratio, μ11II∕μ11I, for an impermeable interface crack under pure B0∞ loading

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Figure 10

Energy release rate, G, versus the stiffness ratio, c44II∕c44I, for an impermeable interface crack under combined applied loading

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Figure 11

Energy release rate, G, versus the electric permittivity ratio, ε11II∕ε11I, for an impermeable interface crack under combined applied loading

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Figure 12

Energy release rate, G, versus the magnetic permeability ratio, μ11II∕μ11I, for an impermeable interface crack under combined applied loading

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