Abstract: For metal materials with yielding plateau, the authors established piece-wise Ramberg-Osgood Relation and corresponding Failure Assessment Curve. The new established curve is based on piece-wise computed J-integral and stable equilibrium expression K_r=(J_e/J)^1/2. It can be used to carry out the fracture assessments of finite extension amount and tearing instability with higher precision. The newly plotted Failure Assessment Curve lays the foundation for the improvement of reliability of fracture assessment of materials with yielding plateau.