Problem Of Width Crack In The Semi-infinite Plane

Fracture Mechanics theory is the core theory of Solid mechanics. It is helpful to ensure the service life of materials, if we make a pre-judgment of unstable crack with Fracture Mechanics theory. This dissertation is composed by five parts. Among those the third part and the forth part are the main parts. It solves the partial problem in engineering. The model which we discuss is semi-infinite crack in the semi-infinite plane.The first part is exordium. It summarizes the advance of the Fracture Mechanics and the main job of this dissertation. The second part gives the basic theory and equations which we will use in this dissertation. The third part discusses this model with singularity theory. This chapter gets the analytical solutions of stress intensity factor by introducing two types of conformal mapping functions. It discusses the influencing factors of the stress intensity factor. The analytical solution which we obtain is helpful to solve the partial problem in engineering. Because the result we get is under considering stress intensity factor as the parameter. The method is wrong. So the forth part discusses this model with non-singularity theory (considering width crack). This chapter introduces theory of singular integral equation. Then the problem is reduced to solve the boundary value problem. By introducing a Sherman transformation, the boundary value problem is transformed into singular integral equation. And by a series of calculation, this equation is reversed singular integral equation which is only on crack. In the end this singular integral equation is solved by employing quadrate formulas. It proves the existence and uniqueness of solution. The result we obtained doesn't show stress singularity. Because the time is limited, we only obtained the singular integral equation. The last part summarizes this dissertation briefly, and gives some work we will go on doing in future.