An analytic solution of an arbitrary location through-crack emanating from a nano-circular hole in one-dimensional hexagonal piezoelectric quasicrystals

Abstract

The mode III fracture performance of an arbitrary location through-crack at the edge of a nano-circular hole in one-dimensional hexagonal quasicrystals is studied. Based on the G-M elasticity theory, the piezoelectric quasicrystal theory and the boundary value problems theory, the phonon, phason and electric fields of the nano-defects (nano-hole and nano-cracks) are obtained, and the analytic expressions of the field intensity factors at both ends of through-crack are present. The present solution can be degenerated into the existing results. The relationship between the field intensity factors with the nano-defects related parameters, far-field loads and piezoelectric quasicrystal coupling coefficient are discussed. The field intensity factors have obvious size effects when the defects size is at nanoscale and the surface effect is considered. The field intensity factors tend to be classical theory with the increase in defect size. The field intensity factors show different changes with the increase in crack location angle and relative size between cracks. The size effect of the field intensity factors is significantly affected by the crack location. The far-field mechanical-electric loads and the piezoelectric quasicrystal coupling coefficient have obvious influence on the field intensity factors.