Study On Plane Fracture Problem Of One-dimensional Hexagonal Quasicrystal Bi-material

Quasicrystal(QC),which is a new smart material,possesses many desirable properties like high hardness,low friction coefficient,heat proof,wear proof and so on.So QC can be used as the coating material of the engine to improve the hot components and decrease the strength of friction between cylinder and cylinder block.The fracture failure may occur on the interface between coating and matrix and this will affect its work stability and service life.This paper mainly discuss the plane fracture failure of the QC.The main works are as follows:1.Using the Stroh formalism,Green's functions are obtained for phonon and phason dislocation and opening displacements on the interface of a one-dimensional(1D)hexagonal QC bi-material.The integro-differential equations governing the interfacial crack are then established,and the singularities of the phonon and phason displacement at the crack tip on the interface are analyzed.To eliminate the oscillating singularities,we represent the delta function in terms of the Gaussian distribution function in the Green's functions and the integro-differential equations,which helps reduce these equations to the standard integral equations.Finally,a boundary element numerical approach is also proposed to solve the integral equation for the crack opening displacements.In numerical examples,the effect of the Gaussian parameter on the numerical results is discussed,COMSOL software is used to validate the analytical solution,and the influence of the different phonon and phason loadings on the interfacial crack behaviors is further investigated.2.Utilizing the Stroh formalism,the fundamental solutions of the extended dislocation,the distributed crack opening displacement and the concentrated displacement on the interface of the QC-crystal bi-material are obtained.We establish the integro-differential equations of the interfacial crack and discuss the singularities at the crack tip.Based on the integro-differential equations,the extended intensity factors and the energy release rate are also obtained.We obtain the crack opening displacement along the interface by using the boundary element method and investigate the effect of phonon field loads on the energy release rate.3.We derive a fundamental solution for extended dislocations(phonon dislocation,phason dislocation,electric dislocation)of 1D hexagonal piezoelectric QCs by extending the Stroh formalism.Based on the dislocation theory,we derive the crack opening displacement,intensity factor,and energy release rate in terms of the extended dislocation.By considering the continuously distributed dislocations to be a crack,we establish an impermeable crack model under applied loadings and derive the related solutions.Numerical calculations are used to confirm the validity of the theory and to investigate the effect of different parameters on the energy release rate.