ABSTRACT
This chapter reviews some boundary problems for dislocations. It shows that the stress components of a dislocation loop in a finite body can be expressed by line integrals of known functions along the dislocation line. Most of elasticity solutions for dislocations are those for infinitely extended media. The elastic stress field of a dislocation loop L must be independent on location of S, where S is a slip surface bounded by L. Keer, Lee and Mura have considered a quarter plane containing a dislocation. The solution is a sum of two solutions. One is the known solution for the two dislocations in a half-plane and the other is the solution for the boundary value problem in the quarter plane. The chapter shows the geometry and coordinate system for the quarter plane containing a crack. The crack is simulated by a continuous distribution of dislocations such that the dislocation stress traction equals to that prescribed value.
