Analysis Of Interface Fracture Problem Of Two-dimensional Decagonal Quasicrystal-crystal Composites

Compared with traditional materials,quasicrystal materials possess unique and superior properties,and have been used in engine blades,aircraft wings and fuselage surfaces,and solar industrial films.In the process of preparing quasicrystal-crystal composites,it is inevitable that there are various defects such as inclusion and crack at the interface,the existence of interfacial cracks affects the reliability of quasicrystal-crystal composites.In this paper,discontinuous displacement boundary element method(BEM)is used to study the interface crack fracture of two-dimensional decagonal quasicrystal-crystal composites.This thesis consists of following main parts:1.Analysis of planar interfacial cracks of two-dimensional decagonal quasicrystal-crystal composites: Based on the general solution of two-dimensional decagonal quasicrystals and crystals,the discontinuous displacement boundary element method is extended to planar interfacial cracks of two-dimensional decagonal quasicrystal-crystal composites.The fundamental solution of discontinuous displacements of unit points in x direction and y direction is obtained by using Fourier transform method.According to the superposition principle,the discontinuous displacement boundary integro-differential equation of two-dimensional decagonal quasicrystal-crystal interface crack is constructed,the stress expression expressed by the discontinuous displacement on the interface crack surface at any point in the space is obtained.The oscillatory singularities of the stress field near the interface crack tip are eliminated by using the Gaussian distribution function to replace the Delta function approximately,the expression of stress field intensity factor at crack tip expressed by discontinuous displacement is obtained.By using the boundary element method,the discontinuous displacements and stress intensity factors of different material combinations under tensile and shear loads are discussed.2.Analysis of antiplane interfacial cracks of two-dimensional decagonal quasicrystal-crystal coatings: The fracture behavior of the interfacial cracks of two-dimensional decagonal quasicrystal-crystal coatings under antiplane loading is studied by using the extended discontinuous displacement method.By using the Fourier transform method,the fundamental solutions of discontinuous displacement of unit point on the anti-plane interfacial crack of infinite strip,finite strip with free boundary and finite strip with simply supported boundary are obtained.Fredholm integral equation of antiplane interfacial crack is established according to the basic solution and superposition principle,the stress singularity near the crack tip is analyzed,the Chebyshev polynomials of the second kind are used to numerically solve the Fredholm integral equation of the first kind.Based on the coefficients of chebyshev polynomial,the discontinuous displacement,stress intensity factor and energy release rate on the crack surface are calculated.