Stress Analysis Of The Line Crack In The Functionally Graded Materials

Functional graded material is non-uniform composite material, which has the nature of continuous graded that changes gradually in the microscopic details. The functional graded material with special purposes in the respect of engineering always shows satisfactory effect. The functional graded material has important application value in aeronautics, astronautics field and other fields. Therefore, we require that must have a strong understanding of the material, especially we shall further study its nature in the respect of fracture. So, the research of fracture mechanics of the functional graded material has critical support effect to the safe application of the functional graded material.This paper introduces the reasons of the widespread application of the functional graded material and the reasons of its specificity firstly; and at the same time, also simply introduces several advantages of the functional graded material while comparing with the common material; then, makes a brief introduction of the development history of the functional graded material; next, simply introduces the research that all scholars conducted to the fracture of the functional graded material in the last 30 years. Chapter Ⅱ introduces some basic knowledge to be used for the fracture analysis of the functional graded material in detail, and gives some basic equations of the functional graded material.In Chapter Ⅲ, the model commonly used in engineering is chosen, and we establish its mathematical) model according to this model, and gives the boundary conditions of this model. In the case that the geometric equation and balance equation of this model are known, we obtain its governing equation which is a complex system of partial differential equations.In Chapter IV, we will solve the equation and obtain its solution. In the process of solving the equation, this paper firstly creates the potential function to divide the original equation into several parts, each part of which is independent partial differential equation. We use the integral transformation and other comprehensive methods in the process of solving these partial differential equations. This method not only makes the solving process of equation simplify, but also avoids solving the system of high order partial differential equation, and can reflect the elasticity characteristic and the property characteristics of the functional graded material, which will lay the foundation for the research of blunt crack.In Chapter V, draw stress image, so as to intuitively reflect the stress of crack and the stress around it. At the end of this paper, we summarize the conclusions of this paper and look far ahead into the future work.