Micromechanics of Nano-Defects in One-Dimensional Hexagonal Piezoelectric Quasicrystals

The Gurtin-Murdoch surface model is extended to theoretically study the fracture characteristics of the one-dimensional hexagonal piezoelectric quasicrystals with nano-defects. The complex electrostatic theory and the conformal mapping method are used to study the type III fracture problem of the one-dimensional hexagonal piezoelectric quasicrystals containing cracked nano-elliptical hole. An analytical expression of the electrostatic field intensity factors is obtained. The influences of defect size, relative crack length and coupling coefficient on the dimensionless stress intensity factor and the electric displacement field intensity factor are discussed. The results show that the dimensionless stress intensity factor and the electric displacement field intensity factor are obviously size dependent when the defect is at the nanometer scale. Geometric parameters of the defects and material parameters have a significant impact on the dimensionless electrostatic field intensity factors.