Interaction of Two Collinear Interface Cracks with Different Electrical Conditions at Their Faces in a One-Dimensional Piezoelectric Quasicrystal

An interaction of electrically conductive and electrically permeable cracks at the interface between two semi-infinite 1D piezoelectric quasicrystalline (QC) spaces is considered. The half-spaces are subjected to uniformly distributed shear phonon and phason stresses and also by an electric field parallel to the crack faces at infinity that produce the out-of-plane mechanical and in-plane electrical state for QC materials. Using the presentations of phonon, phason and electric quantities via the sectionally-holomorphic functions, the Hilbert problem and combined Dirichlet–Riemann boundary value problem are formulated. The solution of these problems satisfying the condition at infinity as well as the condition of the displacement uniqueness and the absence of an electric charge in the crack’s region are found in an analytical form. The formulas for the phonon, phason stresses and the electric field along the bonded parts of the material interface, their intensity factors and also phonon and phason derivatives of displacement jumps in the crack region are found. Numerical illustrations of the obtained analytical solutions are given in table and graph forms.