Mode-III fracture of a nanoscale cracked hole in one-dimensional hexagonal piezoelectric quasicrystals

Based on the surface elasticity theory and the boundary value problem theory, the Mode-III fracture problem of a nanoscale cracked elliptical hole edge cracks in one-dimensional hexagonal piezoelectric quasicrystals is studied. The analytical expressions of the stress fields, the field intensity factors and the energy release rate are obtained. The effects of the defect size, the coupling coefficient and the applied loads on the fracture characteristics of the one-dimensional hexagonal piezoelectric quasicrystals with nanoscale defects are discussed. The research shows that the dimensionless stress intensity factors of the phonon field and phason field, the electric displacement field intensity factor and the dimensionless energy release rate have significant size-dependent effects with the change of defect size. The smaller the shape ratio of the elliptical hole is, the greater the influence of surface effects on the dimensionless field intensity factors. Too large elliptical hole shape ratio shields the influence of the surface effect. The coupling coefficient has different effects on the dimensionless stress intensity factor of the phonon field, the phason field and the electric displacement field intensity factors. With the increase of the phonon field loading and the phason field loading, the dimensionless energy release rate both first increases and then decreases, and finally tends to stable value.