Propagation of cracks and dislocations in 2D quasicrystals

A closed-form solution is provided for the stress, strain and velocity fields due to a planar crack steadily propagating in an elastic quasicrystal with fivefold symmetry at speed lower than the bulk wave-speeds. The cases of a semi-infinite rectilinear crack and a Griffith crack which propagates maintaining a constant length, according to the Yoffe model, are considered. Crack face loading and remote loading conditions are taken into consideration. The dynamic theory of quasicrystal with inertia forces, but neglecting dissipative phonon activity, is assumed to govern the motion of the medium. The phonon and phason stress fields turn out to be square-root singular at crack tip. The energy release rate is positive for subsonic and subRayleigh crack propagation.