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

2006 ◽  
Vol 74 (4) ◽  
pp. 614-627 ◽  
Author(s):  
R. Li ◽  
G. A. Kardomateas
Keyword(s):  
Magnetic Field ◽  
Energy Release Rate ◽  
Energy Release ◽  
Interface Crack ◽  
Release Rate ◽  
Plane Deformation ◽  
Crack Problem ◽  
Crack Tip ◽  
Electro Magnetic ◽  
Anisotropic Bimaterials

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.

An Energy Harvester With Bistable Compliance Characteristics

2010 ◽  
Author(s):  
Andrea Cammarano ◽  
Stephen G. Burrow ◽  
David A. W. Barton
Keyword(s):  
Experimental Approach ◽  
Permanent Magnets ◽  
Energy Harvester ◽  
Bistable System ◽  
Complex Dynamic ◽  
Trade Off ◽  
Magnetic Loading ◽  
Electro Magnetic ◽  
Simplified Mathematical Model ◽  
Comparison With Experimental Data

In this paper we present a bistable energy harvesting device. The bi-stability is produced by the particular arrangement of the permanent magnets which form the electro-magnetic transduction mechanism, in conjunction with an iron-cored stator. The harvester features a high magnetic loading but the resulting bistable compliance introduces complex dynamic behaviors. An experimental approach is first used to characterize the device, from which a simplified mathematical model has been developed. The model is then validated by comparison with experimental data. It has been shown that both chaotic and periodic responses are possible. The paper explores the dynamic behavior of the bistable system and attempts to understand the trade-off between the complex mechanical behavior and the benefits of increased magnetic loading.

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

2005 ◽  
Vol 73 (2) ◽  
pp. 220-227 ◽  
Author(s):  
R. Li ◽  
G. A. Kardomateas
Keyword(s):  
Magnetic Field ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Interface Crack ◽  
Release Rate ◽  
Mode Iii ◽  
Electro Magnetic Field ◽  
Magnetic Loading ◽  
Electro Magnetic

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 r−1∕2 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.

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

The Procedure and Device of Pulse-Magnetic Loading Parameters Measuring

1997 ◽  
Vol 07 (C3) ◽  
pp. C3-217-C3-221
Author(s):  
R. J. Jusupov ◽  
V. A. Glouschenkov ◽  
S. A. Igolkin
Keyword(s):  
Magnetic Loading

Radiated Electro-Magnetic Waves Caused by Electrical Tree Development in Epoxy Resin

2009 ◽  
Vol 129 (12) ◽  
pp. 915-921 ◽  
Author(s):  
Hideki Ueno ◽  
Takashi Nagamachi ◽  
Masaki Nakamura ◽  
Hiroshi Nakayama ◽  
Kunihiko Kakihana
Keyword(s):  
Epoxy Resin ◽  
Electrical Tree ◽  
Electro Magnetic ◽  
Tree Development ◽  
Magnetic Waves
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