A novel mode-I elliptic crack problem in one-dimensional hexagonal quasicrystals with the crack plane parallel to the quasi-periodic direction

This article studies a non-traditional elliptic crack problem in one-dimensional (1-D) hexagonal quasicrystals (QCs). The crack surface is parallel to the quasi-periodic axis of QCs and is subjected to a pair of uniform normal loadings. A unit point dislocation problem is considered first to derive the governing equation for the crack problem with an arbitrarily shaped planar crack, based on the potential theory method. The phonon-phason coupling field of the crack problem is expressed by simple integrals. The key fracture parameters, including the crack surface displacement (CSD) and stress intensity factor (SIF) are obtained. The analytical solutions are validated and the effects of eccentricity, phason field, crack orientation and material constants on the CSD and SIF are investigated. The results presented in this paper offer insights into the fracture mechanism of 1-D hexagonal QCs, while also providing a theoretical foundation for the design, optimization, and manufacture of QCs.