Research On Fracture Mechanics Of Anti-plane Problems In One-dimensional Orthorhombic And Hexagonal Quasicrystals

Compared with traditional materials,quasicrystal based on special atomic structure have excellent properties.Since its discovery,it has become hotspot research in material science of different countries and has broad application prospects in many fields of science and technology.However,defects(such as holes,dislocations and cracks)exist widely in kinds of materials.It is easy to form stress concentration at the crack tip,which will destroy the material structure and cause fracture.There are huge hidden dangers for the engineering practice of modern industry.The introduction of stress intensity factor can be used as a gauge for judging material fracture.Therefore,the key to the study of material fracture mechanics is to solve the stress field of various complex defects under stress and the stress intensity factor at the crack tip.In this paper,some fracture problems of 1D orthorhombic quasicrystals and 1D hexagonal quasicrystals are analyzed and studied.Some useful theoretical results are obtained as follows:The first chapter is introduction,which introduces discovery of quasicrystals and performances with potential research value,then thedevelopment and research status of fracture mechanics are briefly introduced,finally,it extends to the development of fracture dynamics.In the second chapter,the generalized complex function method is applied to the fracture study of elliptic hole defects with four asymmetric cracks in 1D orthorhombic quasicrystals.The basic equation of plane elasticity problem is simplified to a fourth-order partial differential equation,and the complex representation of each stress component and the analytical solution of stress intensity factor are given.In the third chapter,the analytical solution of the problem under piezoelectric effect is studied on the basis of second chapter.By using the method of complex variable function,the final governing equation of the problem is transformed into an eighth-order partial differential equation.Finally,the analytical solutions of stress intensity factor and electricdisplacement intensity factor are obtained.In the four chapter,the classical complex function method is applied to dynamics,the anti-plane shear problem of fast propagation cracks near triangular holes in 1D hexagonal piezoelectric quasicrystals is studied.Under the boundary conditions of electrically unpassable and passable,the analytic solutions of dynamic stress intensity factors and electric displacement intensity factors of moving crackare obtained.The fifth chapter is summary and outlook.It summarizes the work done by the original and makes a prospect for the future research directions.