Interface fracture phenomena in quasicrystals.

The two-dimensional setting selected here allows the use of Stroh formalism, leading to a complex variable representation of generalized stress and displacement fields in terms of four complex potentials. We adapt it to the mechanics of QCs by following the path used to describe the steady-state crack propagation of straight cracks in bodies constituted by a single type of QCs. When applied directly to the mechanics of QCs, the procedure based on the standard Stroh formalism involves a degenerate eigenvalue problem, so appropriate modifications have to be considered. The bi-material nature of the body under scrutiny here is accounted for by generalizing the approach used for classical elastic bimaterial. The results shows that macroscopic and substructural stresses display oscillatory behaviour or classical square root singularity at the crack tip, depending on the constitutive parameters of both QCs. Finally, the energy release rate is evaluated for subsonic sub-Rayleigh crack propagation.