Thickness effects for a penny-shaped dielectric crack in a magnetoelectroelastic layer

Abstract

The problem of a penny-shaped dielectric crack in a magnetoelectroelastic layer is considered within the theory of linear magnetoelectroelasticity. Under the assumption of mode-I magnetoelectromechanical loadings, the semipermeable crack-face electromagnetic boundary conditions are applied to describe the case of an opening penny-shaped crack. In order to solve the boundary-value problem, the Hankel transform technique is utilized and three coupled Fredholm integral equations are further derived. The intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) are further determined by the composite Simpson's rule. Thickness effects of a magnetoelectroelastic layer on the electric displacement and magnetic induction of the crack interior, and the field intensity factors are illustrated through numerical computations for a BaTiO₃-CoFe₂O₄ composite. The obtained results reveal that an increase of the ratio of the layer thickness and the crack radius h/a increases the electric displacement and magnetic induction of a dielectric crack interior, and decreases the field intensity factors regardless of the permeability of the crack interior. Based on the COD intensity factor, the influences of applied electric and magnetic fields on the growth of a dielectric crack are further investigated and presented graphically.

Keywords:

• magnetoelectroelastic layer
• penny-shaped crack
• semipermeable conditions
• thickness effects
• field intensity factors

Acknowledgements

The work was supported by the Scientific Research Foundation of Guangxi University (X081088) and the Scientific Research Fund of Guangxi Provincial Education Department. Valuable comments and suggestions from two anonymous reviewers that improved the paper are acknowledged.