An interface crack with partially electrically conductive crack faces under antiplane mechanical and in-plane electric loadings

An interface crack in a bimaterial piezoelectric space under the action of antiplane mechanical and in-plane electric loadings is analyzed. One zone of the crack faces is electrically conductive while the other part is electrically permeable. All electro-mechanical values are presented using sectionally-analytic vector-functions and a combined Dirichlet-Riemann boundary value problem is formulated. An exact analytical solution of this problem is obtained. Simple analytical expressions for the shear stress, electric field and also for mechanical displacement jump of the crack faces are derived. These values are also presented graphically along the corresponding parts of the material interface. Singular points of the shear stress, electric field and electric displacement jump are found. Their intensity factors are determined as well. Intensity factors variations with respect to the external electric field and different ratios between the electrically conductive and electrically permeable crack face zones are also demonstrated.