THE NEW AND ANALYTICAL SOLUTIONS FOR MODE III CRACKS IN AN ELASTIC-PERFECTLY PLASTIC MATERIAL

The analysis of this paper is suitable not only for small scale yielding but also for large scale yielding. In this paper, the usual suggestion of small scale yielding has not been adopted. The accurate elastic stress and displacement fields (i.e. Westergaard's fields) for a mode III crack in an infinite plate have been expanded in a power series of the angle-theta to the crack line. By matching the elastic stresses and displacement with the plastic fields at the elastic-plastic boundary near the crack line, accurate solutions of the plastic fields near the crack line and the length of the plastic zone ahead of the crack tip and the unit normal vector of the elastic-plastic boundary near the crack line have been obtained for a mode III static crack in an elastic-perfectly plastic material. The elastic-plastic nature of an antiplane crack in a finite body has also been investigated. As an interesting example, the near crack line analysis method has been applied to a problem of Linear Elastic Fracture Mechanics (LEFM).