Fracture Mechanics Analysis Of One-dimensional Hexagonal Quasicrystal Nano-scale Cracked Elliptical Hole

It is very important to study the fracture mechanics problems of composite materials in the actual production and use process.With the emergence of the Gurtin-Murdoch surface elasticity theory,people gradually turn their attention to the fracture problem of nano defects in materials.When the size of defects reaches the nanometer scale,the surface stress should be considered on the surface of defects,and the microstructure fracture performance of materials will change significantly due to the increase of specific surface area of atoms constituting the surface of materials.Therefore,the study of nano-scale fracture mechanical properties of materials is helpful to promote the development of nano-composite mechanics,and the reliability analysis and prediction of materials can also put forward the corresponding toughening mechanism,which has important reference value.In this paper,the Gurtin-Murdoch surface elasticity theory is extended to quasicrystal materials,and the boundary conditions for displacement and stress of nanoscale defect surfaces are established.The type III fracture performance of nanoscale defects in one-dimensional hexagonal quasicrystals is analyzed:(1)The anti-plane shear problem of the combination of cracks and nano-scale elliptical holes in one-dimensional hexagonal quasicrystal elastomers is studied mainly.The displacement and stress boundary conditions under surface effect of the nanoscale elliptical hole and the crack surface are established,the analytical expressions of the stress intensity factor and energy release rate of the nano-scale crack tip were obtained by using complex variable function theory and conformal mapping theory,the influence of defect size,coupling coefficient,and applied stress loads on the stress intensity factor and energy release rate were analyzed.(2)The anti-plane shear problems of double-asymmetric cracks on the nano-scale elliptical holes and four cracks on the nano-scale elliptical holes in the one-dimensional hexagonal quasicrystal under the piezoelectric effect are studied in depth.Based on the complex variable function theory and conformal mapping method,the analytical expressions of the crack tip stress intensity factor,electric displacement field strength factor,and energy release rate at the crack tip caused by the applied loads are obtained.The basic rule of the influence of the geometrical size of the defect,the quasicrystal coupling coefficient,the applied stress,electrical loads on the stress intensity factor and electric displacement field strength factor and energy release rate of the crack tip was discussed,especially the influence of multi-crack interaction on fracture performance of elliptical hole with cracks.