Anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain

On condition that any perfectly plastic stress component at a crack tip is nothing but the function of by making use of equilibrium equations, unisotropii plastic stress-strain-rale relations, compatibility equations and Hill anisotropic plastic vivid condition, in the present paper, we derive the generally analytical expressions of the anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain. Applying these generally analytical expressions to the mixed-mode cracks, we can obtain the analytical expressions of anisotropic plastic stress fields at the tips of mixed-mode I-III,II-III and I-II-III cracks.