Interaction between a semi-infinite crack and a straight dislocation in a decagonal quasicrystal

The interaction between a semi-infinite crack and a line dislocation in a decagonal quasicrystalline solid is investigated in detail by employing the complex variable method. The local stress intensity factors and energy release rate at the crack tip as well as the Peach-Koehler force acting on the line dislocation are presented. The crack tip shielding effect due to the line dislocation can be easily observed from the expressions of the local stress intensity factors. It is found that all the four components of the Burgers vector of the line dislocation can affect the local phonon and phason stress intensity factors. Besides, the problem of a line dislocation in a decagonal quasicrystalline half-space in which the boundary of the half-space is traction-free is also investigated and the Peach-Koehler force on the dislocation due to the presence of the free surface is derived.