On perfect stress field at a mixed-mode crack tip under plane and anti-plane strain (Q1115682)

In the work of \textit{Lin Baisong} [(*) ibid. 6, 915--922 (1985; Zbl 0588.73172)], under the condition that all the perfectly plastic stress components at a crack tip are functions of \(\theta\) only, making use of equilibrium equations, stress-strain rate relations, compatibility equations and yield conditions, and the general analytical expressions of the perfectly plastic stress field at a mixed-mode crack tip under plane and anti-plane strain were derived. But in (*) several restrictions on the proportionality factor \(\lambda\) in the stress-strain rate relations were given, such as supposing that \(\lambda\) is independent of \(\theta\) and that \(\lambda =c\) or \(cr^{-1}\). In this paper, we abolish these restrictions. The cases in (*), \(\lambda =cr^ n(n=0\) or -1) are the special cases of this paper.