Abstract: Based on Yu Maohang’s unified strength theory, the unified analytical solutions to the shapes and sizes of Ⅰ,Ⅱ mixed mode crack tip plastic zone under small scale yielding are derived. Then a set of loci for crack tip plastic zone under different material parameters：The ratio of tensile strength to compressive strength a, poisson’s ratio v and material constant b are obtained. Furthermore the influences of the material pa-rameters to the shapes and sizes of crack tip plastic zone are discussed essentially. Amongst them the a parameter effects much more than other parameters, it causes discontinuity in crack’s up and down surface as a 11, meanwhile upper bound and lower bound of the loci for the plastic zone are corre-sponded to parameters using b=0 and b=1. The new solutions are compared with the former solutions to the problem by using Tresca criterion and Von Mises criterion, the former solutions are only the special cases or linear proximity to this problem. The new solutions have unification in the strength theory and universality for the different materials.

Key words: Crack tip plastic zone, Mixed mode crack, Small scale yielding, Unified strength theory