Anti-plane analysis on a finite crack in a one-dimensional hexagonal quasicrystal strip

• Fourier transform is used for a finite mode-III crack in a 1D hexagonal QC strip.
• Exact solution of the dual integral equations is given by the elliptic integral.
• The J-integral derived by a conservation law equals the energy release rate.
• The energy release rate greatly depends on the phonon and the phason fields.
• An increase of the height of the strip can retard the propagation of the crack.

The anti-plane fracture problem for a finite crack in a one-dimensional hexagonal quasicrystal strip is analyzed. By using Fourier transforms, the mixed boundary value problems are reduced to the dual integral equations. The solution of the dual integral equations is then expressed by the complete elliptic integrals of the first and the third kinds. The expressions for stress, strains, displacements and field intensity factors of the phonon and phason fields near the crack tip are obtained exactly. The path-independent integral derived by a conservation law equals the energy release rate, which can be used as a fracture criterion for a mode III fracture problem.