Table of Contents
ISRN Materials Science
Volume 2012 (2012), Article ID 659352, 19 pages
http://dx.doi.org/10.5402/2012/659352
Research Article

Antiplane Shear Crack Normal to and Terminating at the Interface of Two Bonded Piezo-Electro-Magneto-Elastic Materials

Department of Mechanics of Materials, Technical University of Lodz, Al. Politechniki 6, 93-590 Lodz, Poland

Received 15 December 2011; Accepted 13 February 2012

Academic Editor: V. Sglavo

Copyright © 2012 Bogdan Rogowski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The magnetoelectroelastic analysis of two bonded dissimilar piezo-electro-magneto-elastic ceramics with a crack perpendicular to and terminating at the interface is made. By using the Fourier integral transform (in perpendicular directions in each materials), the mixed boundary conditions and continuity conditions are transformed to a singular integral equation with generalized Cauchy kernel, the solution of which has been well studied, and classical methods are directly applicable here to obtain the closed form solution. The results are presented for a permeable crack under anti-plane shear loading and in-plane electric and magnetic loadings, as prescribed electric displacement and magnetic inductions or electric and magnetic fields. Obtained results indicate that the magnetoelectroelastic field near the crack tip in the homogeneous PEMO-elastic ceramic is dominated by a traditional inverse square-root singularity, while the coupled field near the crack tip at the interface exhibits the singularity of power law π‘Ÿ βˆ’ 𝛼 , π‘Ÿ being distant from the interface crack tip and 𝛼 depending on the material constants of a bimaterial. In particular, electric and magnetic fields have no singularity at the crack tip in a homogeneous solid, whereas they are singular around the interface crack tip. Numerical results are given graphically to show the effects of the material properties on the singularity order, field intensity factors and energy release rates. Results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures.