Research For Some Fracture Problems Of Piezoelectric And Quasicrystals Materials With Complicated Defects

The development of linear elastic fracture mechanics is the most perfect and earliest,as one branch of Fracture Mechanics. Solving the complex stress intensity factors of the crack tip and studying the stress fields of all kinds of complicated defects under loading conditions is the key to the study of the fracture mechanics. The problems of this paper are studied by using the Muskhelishvili method.The main idea of the Muskhelishvili is mapping the area in physics plane onto the interior(or exterior) of unit disk in phase plane by using the technique of conformal mapping.With the Cauchy integral theory of complex variable function, the exact analytic solutions of stress intensity factors are determined.The anti-plane problem of complicated defects in piezoelectric materials,quasicrystal materials, piezoelectricity of quasicrystals materials is studied by this idea. Linear crack is extended to curved polygon,the curved polygon crack always occur in engineering application,such as wing-shape crack and lip-shape crack.The main job and conclusions in this paper include the following three parts.First, Based on the technique of conformal mapping and the complexvariable function method, the anti-plane problem of a wing-shape in a piezoelectric composite material was studied. By using Cauchy integral formula and the Residue theorem, the analytical expressions of the field intensity factors and the mechanical strain energy release rate were presented with the assumption that the surfaces of the crack were electrically impermeable and electrically permeable.Second, by using the complex variable function method and a conformal mapping, the fracture problem of a lip-shape crack in a point group 6 of one-dimensional hexagonal quasicrystals strip is studied under anti-plane shear stress load in the crack surface. And I have got the analytic solution of the stress intensity factors at the crack tip.Third, Based on the fundamental equations of peizoelasticity of quasicrystal materials, by using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional hexagonal quasicrystals is investigated, the control equations of anti-plane problems are derived,variable function method and the technique of conformal mapping in the anti-plane problem of a lip shape cracks of piezoelectricity of one-dimensional hexagonal quasicrystals is adopted. By using Cauchy integral formula, the analytical expressions of the field intensity factors and the mechanical strain energy release rate were presented with the assumption that the crack were electrically impermeable.