Abstract: In this paper,the propagation process of a crack in the power-law hardeningmaterials is accurately calculated by the elastic- plastic finite element method under planestrain and Mode I conditions. The elaistic-plastic fields near the growing crack tip are givenin detail.A unified three term solutions of stress fields ahead of the growing crack tip are firstpresented. The firs t term is t he H RR singularity solut io n. T he second t erm describes thetriaxiality The third term includes a linear term of t...