Analysis of an inclined elliptic crack in one-dimensional hexagonal quasicrystals: Shear mode

This paper investigates an inclined elliptic crack in one-dimensional (1D) hexagonal quasicrystals (QCs), where the crack lies in a plane perpendicular to the transversely isotropic plane and is oriented at an arbitrary angle to the quasi-periodic axis. A pair of uniform shear loadings is applied antisymmetrically on the crack surface. The governing equations are established and the complete solutions are obtained in terms of simple integrals using the potential theory method. Explicit expressions are obtained for the crack slip displacement (CSD) and stress intensity factors (SIF). Numerical results validate the present solution and elucidate the effects of the phason field, inclination angle, and eccentricity on the fracture parameters. This study provides insight into the fracture mechanisms of 1D hexagonal QCs, and offers fundamental theoretical guidance for the design and application of QCs as advanced materials.