Abstract
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.
Highlights
In elastic-plastic fracture mechanics, traditional analyses are confined by the small-scale yielding condition
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 small-scale yielding condition includes two basic assumptions: the first assumption is that the plastic region is sufficiently small that the elastic field outside the plastic region is the singular field K in the crack tip region; the second one is that the elastic singular field K virtually extends by a distance along the crack extension direction
Summary
In elastic-plastic fracture mechanics, traditional analyses are confined by the small-scale yielding condition. The method was applicable for many practical crack problems.[8,9,10,11,12,13] By using this analysis method, Yi14 revisited the Hult-McClintock closed form solution[15] in elastic-plastic fracture mechanics, thoroughly analyzed the inappropriateness of the two assumptions of the traditional small-scale yielding condition, and illustrated that no singularity exists in the plastic strain fields. By substituting Equation (7) into Equation (3), the general solutions of the near-crack-surface stress field in the plastic region are obtained as follows: τxz = −k,. It is clear that τxz and τyz in the plastic region near the area of crack surface are the same in form as those obtained in Reference 16.
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