Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect

In this paper, an interface crack between dissimilar one-dimensional (1D) hexagonal quasicrystals with piezoelectric effect under anti-plane shear and in-plane electric loadings is studied. By using integral transform techniques, the mixed boundary value problem for the interface crack is reduced to the solution of singular integral equations, which can be further reduced to solving Riemann-Hilbert problems with an exact solution. An analytical full-field solution for phonon and phason stresses, electric fields and electric displacement in the cracked bi-materials is given, and of particular interest, the analytical expression of the phonon and phason stresses and electric displacements along the interface is obtained. The crack sliding displacements of the interface crack are provided, and it is found that the phonon and phason stress distributions inside the dissimilar quasicrystal material are independent of the material properties under the anti-plane shear and in-plane electric loadings. The results of the stress intensity factors energy release rate indicate that the crack propagation can either be enhanced or retarded depending on the magnitude and direction of the electric loadings.