Quasi-crystalline Materials Fracture Study

The discovery of quasicrystal around 1984 is a significant breakthrough for condensed matter physics in recent years. It's focused on fracture mechanism and lacuna propagation research among ology field. The paper makes study of mechanical analysis about several kinds of cracks inside of quasicrystal materials, which includes infinity crack in cubic quasicrystal and co-linear double cracks in it at the same time with a load at the edge of the material. Finally it gives discussions of an infinity crack in a 10mm decagonal quasicrystal.Firstly, it's started from anti-plane problem of cubic quasicrystal. Take the basic equation into account, use equilibrium equation and syncretic function to solve the stress, strain and displacement. In the case of cubic quasicrystal with a infinity crack because of the solution before-mentioned. It's used the Williams formula, so all complex variables can be transferred into the form of angle and radius. When the boundary conditions are satisfied, it gives out the characteristic value problem for determining the stress singularity factors A over the crack tips. And it also solve the stress and displacement distribution.Secondly, for the antiplane problem of cubic quasicrystal with co-linear double cracks, when the load σ₃₁^∞, σ₃₂^∞, H₃₁^∞ , H₃₂^∞ are applied at infinity, it must be produced stress and strain inside. By using holomorphic function, boundary conditions at the cracks and displacement single valued condition, the general solution of stress and strain are obtained, which are dependent on σ₃₁^∞, σ₃₂^∞, H₃₁^∞ , H₃₂^∞ and are related to the shape and dimension of cracks. The phonon field and phason field stress intensity factors and stress distribution at the crack tips are also given.The results show that though phason field is coupling with phonon field by constitutive equations, the stress intensity factors are not coupling with any other factors. If there's no phason stress acted at infinity, then singularity of the phason field doesn't exist at crack tips.Finally, to discuss the plane stress problem of a group of 10mm decagonal quasicrystal, which gives out stress and strain equations and it transforms classicalelasticity problem into a single higher-order partial differential equations. By using complex variable method, the higher-order partial differential equations are expressed by holomorphic functions, from which the phonon field and phason field stress, strain and displacement are expressed in terms of complex variable. The infinity crack produced inside the group of 10mm decagonal quasicrystal is considered. When the boundary conditions are satisfied, it gives out an equation of stress singularity factors near the crack tips.This dissertation is divided into seven chapters. The research actuality of the related quasicrystal field is briefly introduced in the first section. And the work to be done, the research methods and its significance are also explained in this section; Then it's briefly presented linear elasticity theory and some related physic functions in chapter 2; It gives out stress singularity factors and stress field .strain field, stress and strain distribution, stress intensity factors near the crack tips from two types of cracks, one is infinity crack, the other is co-linear double cracks inside cubic quasicrystal in chapter 3 and 4; It's taken a group of 10mm decagonal quasicrystal as an example to introduce how to solve plane stress problem in chapter 5; It's analysed and researched that a group of 10mm decagonal quasicrystal stress singularity factors over the crack tips in chapter 6; The last chapter includes the summary and prospect.