Perfectly plastic stress field at a stationary crack tip

Under the hypothesis that all the perfectly plastic stress components at a crack tip are the functions of only, making use of yield conditions and equilibrium equations, we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode I. Mode II, Mode III and Mixed Mode I–II cracks are obtained.