In this article,elastic-plastic curved crack tip plasticity area in hardened material under quasi-static loads has been mainly studied,and curved crack tip plasticity area has been calculated as a practical application of a second order perturbation method, where the effects of quasi-static applied stresses and quasi-static normal and shear stresses on the boundaries of plasticity area are synthetically taken into considerations. Projected length of elastic-plastic curved crack tip hardened plasticity area on straight crack extension line portion has been calculated by numerical solutions,diagrams have been constructed to analyse the transformation relationships between curved crack tip plasticity area size and hardening exponents.Curved crack tip plasticity area size will decrease when hardening exponents increase in hardened material. The decrease extent of curved crack tip plasticity area size will be more and more severe when hardening exponents increase evenly. Curved crack tip plasticity area size will decrease when external loads decrease with the same hardening exponents. A new theoretical model where curved crack tip plasticity area size was calculated has been established in hardened material.