Path-independent integral in fracture mechanics of quasicrystals

•Coupled governing equations for phonon and phason displacements for quasicrystal.•Conservation laws for quasicrystals to derive path-independent integrals for cracks.•Path-independent integrals for evaluation of fracture parameters in quasicrystals.•The Bak’s model for dynamic fracture study.

Path-independent integrals are successfully utilized for accurate evaluation of fracture parameters in crystalic materials, where atomic arrangement is periodic. In quasicrystals (QC) the atomic arrangement is quasiperiodic in one-, two- or three-directions. The 2-d elastic problem for quasicrystal is described by coupled governing equations for phonon and phason displacements. Conservation laws for quasicrystals are utilized to derive path-independent integrals for cracks. The relation between the energy release and stress intensity factor for a crack under the mode I is given for decagonal QCs. The path-independent integral formulation is valid also for cracks in QCs with continuously varying material properties.