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TECHNICAL PAPERS

The Mixed Mode I and II Interface Crack in Piezoelectromagneto–Elastic Anisotropic Bimaterials

[+] Author and Article Information
R. Li

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

G. A. Kardomateas

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150george.kardomateas@aerospace.gatech.edu

J. Appl. Mech 74(4), 614-627 (Jun 02, 2006) (14 pages) doi:10.1115/1.2424468 History: Received November 16, 2005; Revised June 02, 2006

Abstract

Taking the electric–magnetic field inside the interface crack into account, the interface crack problem of dissimilar piezoelectromagneto (PEMO)–elastic anisotropic bimaterials under in-plane deformation is investigated. The conditions to decouple the in-plane and anti-plane deformation is presented for PEMO–elastic biaterials with a symmetry plane. Using the extended Stroh’s dislocation theory of two-dimensional space and the analytic continuition principle of complex analysis, the interface crack problem is turned into a nonhomogeneous Hilbert equation in matrix notation. Four possible eigenvalues as well as four eigenvectors for the fundamental solution to the corresponding homogeneous Hilbert equation are found, so are four modes of singularities for the fields around the interface crack tip. These singularities are shown to have forms of $r−(1∕2)±iϵ1$ and $r−(1∕2)±iϵ2$, in which the bimaterial constants $ϵ1$ and $ϵ2$ are proven to be real numbers for practical dissimilar PEMO–elastic bimaterials. Compared with the solution for the interface crack of dissimilar elastic bimaterials without electro–magnetic properties, two new additional singularities are discovered for the interface crack in the PEMO–elastic bimaterial media. The electric–magnetic field inside the crack is solved by employing the “energy method,” which is based on finding the stationary point of the saddle surface of the energy release rate with respect to the electro–magnetic field inside the crack. Closed form expressions for the extended crack tip stress fields and crack open displacements are formulated, so are some other fracture characteristic parameters, such as the extended stress intensity factors and energy release rate $(G)$ for dissimilar PEMO–elastic bimaterial solids. Finally, fundamental results and some conclusions are presented, which could have applications in the failure of piezoelectro/magneto–elastic devices.

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Figures

Figure 1

An interface delamination between dissimilar piezoelectromagneto–elastic anisotropic bimedia and the associated contour integral path

Figure 2

Energy release rate versus bimaterial constant c2 under pure mechanical loading σ33

Figure 3

Energy release rate versus bimaterial constant c2 under pure mechanical loading σ13

Figure 4

Figure 5

Energy release rate versus σ33 for a given σ13

Figure 6

Energy release rate versus σ13 for a given σ33

Figure 7

Figure 8

Energy release rate versus σ33 for a given D3

Figure 9

Figure 10

Energy release rate versus σ33 for a given B3

Figure 11

Figure 12

Figure 13

Figure 14

Variation of energy release rate versus σ13: top for a given D3 only; bottom for a given pair (D3,σ33)

Figure 15

Variation of energy release rate versus σ13: top for a given B3 only; bottom for a given pair (B3,σ33)

Figure 16

Variation of energy release rate versus (σ33,σ13) for a given (D3,B3)

Figure 17

Variation of energy release rate versus σ33 for a given (σ13,D3,B3)

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