Analysis of a dielectric crack in a magnetoelectroelastic layer

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto-electrically dielectric Griffith crack embedded in a magnetoelectroelastic layer is investigated under in-plane magneto-electro-mechanical loadings. The semi-permeable crack-face magnetoelectric boundary conditions are utilized to simulate the case of an opening dielectric crack. Applying the Fourier transform technique, the boundary-value problem is reduced to solving three coupling singular integral equations. Field intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) are further determined by the Lobatto-Chebyshev collocation method. The electric displacement and magnetic induction of crack interior are discussed in detail. The obtained results reveal that the magnetoelectric field inside the crack is dependent on the material properties, applied loadings, the dielectric permeability of crack interior, and the ratio of the crack length and the layer width. Numerical computations are carried out to present that the volume fraction of piezoelectric phase in BaTiO 3 – CoFe 2 O 4 composites has great influences on the magnetoelectric field inside the dielectric crack. Based on the COD intensity factor, the analysis for the growth of a dielectric crack in a magnetoelectroelastic layer is examined. The proposed procedure can be reduced to dealing with the case of a dielectric crack in a piezoelectric layer and the obtained results can be verified by the experimental observations.