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Electric field intensity factors for conducting paths in anisotropic dielectric bimaterials

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Abstract

Conducting paths in an anisotropic dielectric bimaterial as well as in a homogeneous anisotropic material subjected to electric loading are investigated. The conducting path problems are formulated by using a linear transformation method. Electric field intensity factors are obtained for conducting paths emanating from a surface electrode in an orthotropic material. The asymptotic problem of a kinked conducting path in dissimilar anisotropic dielectric materials is considered. The electric field intensity factor for the asymptotic problem is obtained in the infinite product form. To ascertain validity of the solution obtained from the linear transform method, numerical computations are carried out by using finite element method. The electric field intensity factor for a conducting path emanating from the vertex of a bimaterial wedge with a tilt boundary is also obtained in the closed form.

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Abbreviations

D (m) i :

electric displacement

E (m) i :

electric field

f(z):

analytic function

F (m) :

linear transformation matrix

J :

J integral

J 0 :

energy release rate for an interfacial crack without kink

k 0 :

interfacial electric field intensity factor of wedge without the conducting path

K E :

electric field intensity factor

K t E :

electric field intensity factor for kinked conducting path

L*(m) :

real matrix

p (m) :

complex constant

z (m) :

complex variable

α m :

apex angle

γ :

Dundurs parameter for the dielectric bimaterial

ɛ :

equivalent dielectric constant for the anisotropic solid

\(\hat \varepsilon \) :

dielectric constant for the isotropic material

ɛ (m) ij :

anisotropic dielectric constant

ɛ p(m) ij :

dielectric constants in the principal material coordinate system

η (m) :

anisotropic parameter

λ (m) :

anisotropic parameter

λ p(m) :

anisotropic parameter in the principal material coordinate system

Λ*:

real matrix

θ (m) p :

inclination angle of principal material direction

ϕ (m) :

electric potential

ω :

kink angle

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, Inha University, 253 Yonghyun-dong, Incheon, Republic of Korea, 402-751

    Song Lin, Hyeon Gyu Beom & Cheng Bin Cui

Authors
  1. Song Lin
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  2. Hyeon Gyu Beom
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  3. Cheng Bin Cui
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Correspondence to Hyeon Gyu Beom.

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Lin, S., Beom, H.G. & Cui, C.B. Electric field intensity factors for conducting paths in anisotropic dielectric bimaterials. Int. J. Precis. Eng. Manuf. 14, 439–449 (2013). https://doi.org/10.1007/s12541-013-0060-8

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  • DOI: https://doi.org/10.1007/s12541-013-0060-8

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