CIRCULAR RIGID PUNCH ON A SEMI-INFINITE PLANE WITH AN OBLIQUE EDGE CRACK SUBJECTED TO CONCENTRATED FORCES OR POINT DISLOCATIONS

A circular rigid punch is located on a semi-infinite plane with an oblique edge crack. The punch is acted by an eccentric load to keep the punch vertical, and frictional force is assumed to exist on the contact region. A pair of concentrated forces or point dislocations is assumed to act at arbitrary points in the semi-infinite plane. The analytical solution (Green function) is obtained by a rational mapping function and a complex variable method. To solve the problem, the complex stress functions are divided into two parts; one is the principal part, which corresponds to the fundamental solution of the semi-infinite plane with an oblique edge crack; the other is the holomorphic part of the problem, which can be derived explicitly. The stress intensity factors and resultant moment on the contact region to decide the position of the vertical load on the punch are shown.