Arbitrary number of electrically permeable cracks on the interface between two one-dimensional piezoelectric quasicrystals with piezoelectric effect

A set of finite number collinear cracks along the interface of two 1D piezoelectric hexagonal quasicrystals is considered. The cracks can have arbitrary lengths and distances between their tips and they are considered as electrically permeable. Remote phonon and phason loading, which results in plane strain state, are applied at infinity and the cracks are assumed to be open. By using the presentations of phonon and phason characteristics through sectionally-analytic functions, the problem of linear relationship is formulated and solved in an analytical form. Phonon and phason stresses outside cracks and also correspondent crack faces displacement jumps are presented in the closed forms. It is found out that all fields have an oscillating singularity at the crack tips, therefore, the energy release rate (ERR) is the most appropriate fracture parameter in this case. Using the asymptotic presentations of the phonon and phason fields at the crack tips and the crack closure integral approach, the analytical formula for the ERR have been obtained. The variations of the phonon and phason crack faces displacement jumps, stresses along the interface and the ERR are presented in graph and table forms for different crack tips, loading, crack lengths and their locations. New valuable conclusions have been made concerning the influence of the cracks interaction, their number and locations on the ERR, phonon and phason fields.