Study On Crack And Dislocation In New Materials

Quasi-crystals and magneto-electro-elastic materials belong to new materials, and their theoretical research and application are not perfect yet. Fracture mechanics of the new materials plays an important role in enhancing the mechanical performance of the these materials and it has a great significance for the practicability and reliability in the process of the developing, manufacturing and use. Due to their brittleness, new materials will contain many defects such as cracks, dislocation and inclusion, etc.First of all, by using the complex function method and the technique of conformal mapping, the nonlinear behavior of a semi-infinite crack propagation was studied in an infinite two-dimension dodecahedron quasi-crystals. Utilizing the Galilean transformation and the Cauchy integral, the analytical solution of the dynamic intensity factors were obtained. By analyzing the elastic-plastic of the crack tip, the dynamic crack opening displacement and the size of plastic zone for a semi-infinite crack were derived. Numerical examples showed the impacts of the speed of crack propagation and the size of plastic zone on the stress intensity factors.Secondly, based on the complex function method and the superposition principle,the interaction between a screw dislocation and an oblique crack in one-dimensional hexagonal piezoelectric quasi-crystals were investigated. By using the technique of conformal mapping and Cauchy integral, the closed-form solution of the field intensity factors, the energy release rates and image force at the crack-tip interacting with the screw dislocation were derived. Numerical examples showed that the influences of distance between the dislocation and oblique crack on the field intensity factors and the influences of the included angle between the dislocation position and oblique crack on the energy release rates were discussed in the numerical analysis.Thirdly, by using the Stroh-type formalism and conformal mapping technique, the anti-plane problems of a lip-shaped crack were considered in magneto-electro-elastic materials. By means of the Residue theorem and Cauchy integral formula, the analytical expressions of the field intensity factors and the energy release rate were obtained with the assumption that the crack surfaces were electrically and magnetically impermeable and permeable. Numerical examples were provided to show the influences of the geometrical parameters and applied loads on the field intensity factors and the energy release rate.Finally, by introducing the Schwartz-Christopher conformal mapping and using superposition principle and Cauchy integral, the analytical solution of the field intensity factors and the energy release rates at the crack-tip interacting with the screw dislocation were derived. Numerical examples were conducted to show the influences of distance between the dislocation and oblique crack on the field intensity factors and image forces.Furthermore, the effects of the included angle between the dislocation position and oblique crack on the energy release rates were discussed.