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

Abstract

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.