| Quasicrystal structure often exists defects (cracks, inclusions, holes, etc.),which will have an impact on the performance of solid materials. When the crack quickly spreads, the performance of the material will also be affected.Therefore, it is of great significance to study the fracture mechanics problem of quasicrystal materials. The following is the main work of this article.In the second chapter, first of all, the anti-plane problem of a parabolic crack embedded in piezoelectricity of one-dimensional hexagonal quasicrystals is studied. The analytical expressions for the crack tip stressintensity factor and the mechanical strain energy release rate are presented.Without considering the phase field or the electric field, the present results are reduced to the conclusions of ordinary piezoelectric materials or quasicrystals,respectively. Secondly, by using the conformal mapping method and the perturbation technique, the model of the wedge-shaped crack in classical elasticity and quasicrystal mechanics is introduced into the quasicrystal piezoelectric materials. Explicit analytical solutions are obtained for the crack tip stress intensity factor, as well as the force on dislocation. In addition, the effect of dislocation position and wedge angle on the forces acting on dislocation is discussed by numerical examples. In the special case, the results are reduced to the previous ones or give new ones.For quasicrystal piezoelectric materials, research on curve propagating cracks is rarely reported. In the third chapter, the methods of the complex variable function are applied to dynamics. The anti-plane problem of one-dimensional hexagonal piezoelectric quasicrystals with a circular hole in collinear asymmetry rapid propagating cracks is investigated. The analytic solutions of the problem are given in certain boundary conditions. In special conditions, it can be reduced to problems of complex defects in the static problems. |
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