Elastic-plastic analysis near the crack surface region on a mode III crack under a pair of point forces

The crack line analysis method is used to obtain the near-crack-surface stress field of a mode III crack loaded by a pair of anti-plane point forces in an elastic-perfectly plastic material, which expands the research method from the crack line region to the crack surface region. The stresses in the plastic region, the length of the plastic region, and the geometry of the elastic-plastic boundary near the surface area of the crack are obtained analytically. Further, the maximum value of size of the plastic region along the surface of the crack is obtained. The results are sufficiently precise near the surface area of the crack, as the usual small-scale yielding condition has been given up in the analysis.