Abstract：The type III fracture mechanics problem of a nanoscale cracked elliptical hole in one-dimensional hexagonal quasicrystals is investigated. Based on the complex elastic theory and the surface elasticity theory, analytical s of stress fields, stress intensity factors and energy release rate of an elliptical hole with edge crack considering surface effects are presented, and the degraded results are consistent with the existing literatures. The influences of defect size, crack/hole ratio, coupling coefficient and applied loads on the stress intensity factors and the energy release rate are discussed. The results show that the dimensionless stress intensity factors of the phonon field and the phase field and the dimensionless energy release rate are significantly size-dependent when considering the surface effects of the defects and the size of the defects are at the nanoscale. When the relative size of the crack is very small, the surface effect has little effect on the dimensionless stress intensity factors of the phonon field and the phase field; on the contrary, the effect on above is greater. The dimensionless energy release rate increases with the increase of the coupling coefficient at the nanoscale. When the coupling coefficient is constant, the dimensionless energy release rate is affected by the size of elliptical hole; and the larger the defect size, the higher the dimensionless energy release rate. With the increase of the phonon field loads, the dimensionless energy release rate decreases first, then increases and finally stabilizes. The dimensionless energy release rate monotonously decreases with the increase of the phase field loads, that is, very small and very large phonon field loads (or phase field loads) shield the effects of phase field loads (or phonon field loads). This work shows that the Gurtin-Murdoch surface elasticity theory can be theoretically extended to the quasicrystal material, which is helpful to the development of quasicrystal fracture mechanics.
2020, Vol. 41 
