The Complex Defects Problems Of One-dimensional Hexagonal Piezoelectric Quasicrystals

As a kind of new material, quasicrystals are immensely applied in different fields because of the special nature, such as aeronautics, optics, phonics. Quasicrystal is easily brittle at room temperature, so quasicrystal material is sensitive to defects. In the practical application, we often find some quasicrystal materials with crack under electric load. The crack will rapidly expand until fracture if effective measure is not taken. So, research on such problem is necessary for the preparation and application of quasicrystal material.So far, research on dislocation, holes, cracks, contact of quasicrystal material has made some progress. There have been some research on one-dimensional hexagonal quasicrystals piezoelectric properties, too. But mostly devoted to no thickness crack surface or linear-like cracks. As we known, defect is not always on a regular basis, we often see some curved polygonal crack in nature and engineering application, but we almost never see about research on the anti-plane problem of this kind of crack. Therefore, this paper focuses on the research curved polygonal crack containing cusps only.There are six chapters in this paper. Under two kinds of boundary conditions for impermeable and permeable case, the antiplane problem for a one-dimensional hexagonal piezoelectric quasicrystals with a lip-shape crack, airfoil crack, an circular hole with four cracks are analyzed by using the conformal mapping technique and the complex variable function method, the solutions of static and dynamics of the stress intensity factor and electric displacement intensity factor for the Ⅲ crack is given in analytical form. The solutions will provide theoretical basis for the engineering application.