Study On The Anti-plane Central Crack Problem Of Quasicrystals

QCs are both a new structure of solids and a kind of novel materials,which were discovered in recent two decades.Compared with the classical problem of an elastic crystal,the quasicrystal elasticity problem is much more complicated.It not only has the phonon field,but also increases the phase field of the quasi-periodic arrangement of atoms and the coupling of the phonon field and phase field.On the study of the quasicrystal and defect problems,predecessors have given some solutions,such as Green function method,Fourier transform method,perturbation method and the finite difference method,etc.Compared with the quasicrystal dynamics,the study of its static problem is much simpler.One-dimensional hexagonal quasicrystal structure is relatively simple,naturally become the first choice.Westergaard stress function method and Muskhelishvili method are very practical and effective as two kinds of complex function methods to solve the linear elastic fracture mechanics problem.In the second chapter,we use the complex function method to study the anti-plane problem of Dugdale model of one-dimensional hexagonal quasicrystals by conformal transformation.The analytic solution of the size of the crack tip and the tearing displacement of crack tip are obtained.The results are consistent with the results given by Fan.This provides the basis for themetamorphic material engineering to measure the plastic deformation of the crack tip.In the third chapter,the finite element method is used to study the dynamic response of three-dimensional quaternary quasicrystals with central crack by means of quasicrystal fluid dynamics model.The theoretical and numerical analysis of the crack in the phonon field,the phase field and the phonon-phase sub-coupling effect are given.Finally,the numerical solution of stress,displacement and normalized dynamic stress intensity factor is obtained.By contrasting with the crystal results,the influence of the fundamental field of phonon and phase elasticity is highlighted,which reveals their important position in quasicrystal dynamic deformation.