Elliptic crack problem under shear mode in one-dimensional hexagonal quasicrystals with crack surface parallel to the quasiperiodic axis

In this work we are concerned with a special elliptic crack problem in one-dimensional hexagonal quasicrystals. The crack surface is assumed to be parallel to the quasiperiodic axis. A couple of anti-symmetrical uniform shear loadings is applied on the crack surfaces. Taking advantage of the potential theory method, we develop the governing integral equation and obtain the phonon–phason field in terms of simple integrals. The crack slip displacement and the stress intensity factor are derived explicitly. Based on the analytical solution, we investigate the effects of phason field, crack orientation and the eccentricity of elliptic crack on the important fracture parameters. The solutions obtained in this work are helpful to understand the fracture behavior of one-dimensional hexagonal quasicrystals, especially for the situations in which the cracks are not located on the isotropic planes.