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

In this thesis, fracture problems for some complex defect of classic and piezoelectric materials are investigated by using complex variable function method and integral equation theory on the basis of linear macroscopic theory. The main job and conclusions in this thesis include the following three parts.First, using the complex variable function method and the technique of conformal mapping, the plane problem of the semi-infinite plane with a semi-elliptical notch are studied, the analytical solution of the stress function and the stress distribution are obtained, then the stress distribution for the boundary of the notch are analyzed. By means of complex variable function method, the plane problem for an infinite plane with a circular hole and a straight crack is discussed by introducing the Sherman transformation. The problem is finally reduced to a singular integral equation on the crack by using the integral equation theory. And the stress distribution near the crack tip and the formula of stress intensity factor by the solution of the singular integral equation are derived.Second, by using the complex variable function method, the anti-plane problem of the piezoelectric strip with an infinite crack is solved through introducing a conformal mapping, the analytical solutions of the field intensity factors and the mechanical strain energy release rate are obtained with the impermeable boundary condition. The anti-plane problem of infinite piezoelectric material with three asymmetrical straight edge cracks emanating from a circular hole is studied in the two cases of permeable and impermeable boundary conditions, the explicit and exact solutions of the field intensity factors and energy release rate are derived, then the solutions of the two electric boundary conditions are compared and the solutions of two perpendicular edge cracks originating from a circular hole and L-shaped crack are obtained. Moreover, numerical examples are conducted to analyze the results obtained in this section and some important conclusions are derived.Third, using the complex variable function method, the plane problems of an infinite crack, two collinear semi-infinite cracks in a piezoelectric strip and a power function crack in an infinite piezoelectric material with the crack penetrating across the material perpendicular to the poling direction are investigated by proposing new generalized conformal mappings, the analytical solutions of the field intensity factors are presented with the impermeable boundary condition, and the analytical solutions of plane electroelastic problems for some new defects are also derived under limiting conditions. Numerical examples are conducted to analyze the analytic solutions and some conclusions are obtained.