Analysis Of Surface Crack Semi-infinite Solid In Rolling Load

The investigation of crack problems is very important in fracture mechanics. In the last thirty years, A boundary element method for three-dimensional crack problems have been developed. Due to the advantage of the boundary element method for reducing the dimension of the problems and calculation time, this method is very effective for dealing with three-dimensional crack problems. From the character of the boundary element method and that of contact problems, the boundary element method is more appropriate than other numerical methods for the contact problems. Now the contact problems have been important aspect in the application of the boundary element method. In the paper, the surface crack problems of semi-infinite solids in rolling load are discussed.On the basis of the stress formula of interfacial crack on the biomaterial solids, the paper derive hyper-singular integral equations with the unknown displacement discontinuities of a three-dimensional flat crack under arbitrary loads in semi-infinite elastic solids. If the crack is far from the free surface, the equations reduce to hyper-singular integral equations in infinite elastic solids.According to the above theory, the finite-part integral combined with boundary element method and linear models of the displacements (displacements discontinuities) are used to discretize the hyper-singular integral equations as a set of linear algebraic equations, where the singular integrals of various types are specially treated and the specific calculating formula are given. So far, the numerical techniques solving the hyper-singular integral equations are established, and these are called finite-part integral—boundary element method. To test the reliability of this method, rectangular crack elliptical crack and semi-elliptical crack in infinite space and in semi-infinite space are calculated.The result of stress intensity factor is very correct. Thus the problems of semi-elliptical surface crack and rectangular surface crack of semi-infinite solid in rolling load are discussed, including the fluid pressure case and no fluid pressure case. For the numerical result of semi-elliptical surface crack which a/b is equal to two and rectangular surface crack are inexistent in the literatures.