Interfacial Defects Of Circular Inclusion In Quasicrystal Materials

Quasicrystals are a kind of interesting materials.As a new intelligent material,they form a series of special structures with peculiar physical and mechanical properties compared with metal alloys.Quasicrystal material is a kind of coating material.In the process of use and preparation,the working environment is more harsh conditions such as high temperature and high pressure.It is inevitable that there will be cracks,holes,inclusions and dislocations and other defects,which will greatly reduce the performance of the material.In this paper,the problem of a circular elastic inclusion with multiple interfacial cracks in an infinite dodecagonal two-dimensional symmetric quasicrystal matrix under the action of a point heat source is studied.The concentrated heat source is located at any point in the matrix.Based on the zonal holomorphic theory of complex function,the general complex potential solutions of the temperature field and the phonon field of the interface with multiple cracks are obtained.The special case of only one crack,the closed form solution of the thermal stress intensity factor at the crack tip is given.The change of the thermal stress intensity factor at the crack tip with the change of the crack geometry is also given.The results show that the stress at the crack tip reaches the peak value and the stress field presents oscillatory singularity.Secondly,Riemann-Schwarz analytical continuation technique and singularity principal part analysis method of complex potential function are used to study the plane problem of two-dimensional decagonal quasicrystal with rigid circular inclusion under infinite tension and concentrated force.The general solutions of the problem of interface rigid line with circular inclusion under infinite tension and concentrated force are obtained The analytical solutions of the stress singularity factor at the tip of the rigid line inclusion are obtained,and the variations of the stress intensity factor at the tip of the rigid line inclusion with the size of the inclusion and the material of the inclusion are plotted.Finally,based on the complex function method,the plane problem of three-dimensional icosahedral quasicrystal with circular rigid line inclusion under the action of plane concentrated force and infinite uniform tensile stress is studied.According to the boundary conditions of continuous displacement and stress on the interface,the general solutions of stress and displacement components in several typical cases are obtained,and the singular factors of stress field at the tip of rigid line are given.The numerical results show that the influence of the inclusion radius on the stress singularity factor is greater than that of the coupling coefficient.