Analysis of One-Dimensional Hexagonal Piezoelectric Quasicrystal with a Periodic Distribution of Slant Mode-III Cracks

The electroelastic problems of one-dimensional hexagonal piezoelectric quasicrystal materials with a periodic distribution of slant mode-III cracks under anti-plane shear and electromechanical loading are analyzed in this paper. Based on the three electrical boundary conditions at the crack surfaces, electrically permeable, electrically semi-permeable and electrically impermeable condition, the problems are classified as solving singular integral equations by using screw dislocation solutions. For two special cases of coplanar and parallel periodic crack arrays, the closed form solutions for the electroelastic fields, including stress fields, electric fields and tearing displacements, have been determined. The solutions of the singular integral equations for slant cracks can be transformed into the solutions of algebraic equations, the field intensity factors and mechanical strain energy release rates have been determined. The numerical solutions show that the normalized mechanical strain energy release rates increase under the influence of phonon field stress, phason field stress as well as electric fields, indicating that cracks are more likely to propagate in piezoelectric quasicrystal materials. In addition, it is found that the stress fields at the crack tips exhibited singularity, and the variation law of the total energy release rates with the applied electrical loading are also obtained.