An Interface Crack with Mixed Electro-Magnetic Conditions at it Faces in a Piezoelectric / Piezomagnetic Bimaterial under Anti-Plane Mechanical and In-Plane Electric Loadings

Abstract

Abstract An interface crack between two semi-infinite piezoelectric/piezomagnetic spaces under out-of-plane mechanical load and in-plane electrical and magnetic fields parallel to the crack faces is considered. Some part of the crack faces is assumed to be electrically conductive and having uniform distribution of magnetic potential whilst the remaining part of the crack faces is electrically and magnetically permeable. The mechanical, electrical, and magnetic factors are presented via functions which are analytic in the whole plane except the crack region. Due to these representations the combined Dirichlet-Riemann and Hilbert boundary value problems are formulated and solved in rather simple analytical form for any relation between conductive and permeable zone lengths. Resulting from this solution the analytical expressions for stress, electric and magnetic fields as well as for the crack faces displacement jump are presented. The singularities of the obtained solution at the crack tips and at the separation point of the mention zones are investigated and the formulas for the corresponding intensity factors are presented. The influence of external electric and magnetic fields upon the mechanic, electric and magnetic quantities at the crack region are illustrated in graph and table forms.