An electrically conducting interface crack with a contact zone in a piezoelectric bimaterial

• An electrically conducting interface crack under electromechanical loading is considered.
• A frictionless contact zone at the crack tip is taken into consideration.
• The problem is reduced to combined Dirichlet–Riemann problem which is solved exactly.
• Equations for the determination of the contact zone length and intensity factors are obtained.
• A significant influence of the electric field on the contact zone length is observed.

A plane problem for an electrically conducting interface crack in a piezoelectric bimaterial is studied. The bimaterial is polarized in the direction orthogonal to the crack faces and loaded by remote tension and shear forces and an electrical field parallel to the crack faces. All fields are assumed to be independent of the coordinate co-directed with the crack front. Using special presentations of electromechanical quantities via sectionally-analytic functions, a combined Dirichlet–Riemann and Hilbert boundary value problem is formulated and solved analytically. Explicit analytical expressions for the characteristic mechanical and electrical parameters are derived. Also, a contact zone solution is obtained as a particular case. For the determination of the contact zone length, a simple transcendental equation is derived. Stress and electric field intensity factors and, also, the contact zone length are found for various material combinations and different loadings. A significant influence of the electric field on the contact zone length, stress and electric field intensity factors is observed. Electrically permeable conditions in the crack region are considered as well and matching of different crack models has been performed.