A semi-inverse method of a Griffith crack in one-dimensional hexagonal quasicrystals

A semi-inverse method of a Griffith crack in a one-dimensional hexagonal quasicrystal is proposed in this work. By introducing Westerggaard’s stress functions, the expressions for stress, strains, displacements and field intensity factors of the phonon and the phason fields in the vicinity of a crack tip are obtained in closed-form. The path-independent integral derived by a conservation law equals the energy release rate for a mode III fracture problem in a one-dimensional hexagonal quasicrystal. It is found that the energy release rate is dependent on the phonon fields as well as the phason fields, which can be used as a fracture criterion. In the absence of the phason fields, the obtainable results in this paper match with the classical ones.