This paper deals with the formulation and development of fracture criteria for high-strength structural members containing surface damage in the form of notches (i.e., blunt defects). The important role of the yield strength of the material and its strain hardening capacity (evaluated by means of the constitutive law or stress-strain curve) is analysed in depth by considering the fracture performance of notched samples taken from high-strength steels with different levels of cold drawing (the most heavily drawn steel being commercial prestressing steel used in prestressed concrete). The final aim of the paper is to establish fracture-based design criteria for structural members made of steels with distinct yield strength and containing very different kinds of notch-shape surface damage.