In this article,elastic-plastic curved crack tip opening displacement in hardened material under quasi-static loads has been mainly studied,and curved crack tip opening displacement has been calculated as a practical application of a second order perturbation method and theorem of surname KA,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. Diagrams have been constructed to analyse the transformation relationships between curved crack tip opening displacement size and hardening exponents. Curved crack tip opening displacement will decrease when hardening exponents increase in hardened material. The decrease extent of curved crack tip opening displacement will be more and more severe when hardening exponents increase evenly. Curved crack tip opening displacement will decrease when external loads decrease with the same hardening exponents. A brand new domain of theoretical model where CTOD was calculated has been reclaimed in hardened material.