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.