In Elastic-Plastic Fracture Mechanics, several J-estimation schemes are based on the reference stress approach. This approach has been developed initially for creep analyses and later on for elasto-plastic fracture assessments in 1984, then included in the R6 rule. Much later, other methods, based on the reference stress concept, were derived for 3D applications like the Js method introduced in the French RSE-M code in 1997 and the Enhanced Reference Stress (ERS) method in Korea around 2001. However, these developments are based on the J2 deformation plasticity theory and well established for a pure power hardening law. Js and ERS schemes propose some corrections for recorded behavior laws which cannot be fitted by a power law. Nevertheless, their application to materials governed by a bilinear hardening law has been called into question by several studies. One of these, carried out by M. T. Kirk and R. H. Dodds [1, 2] is of great interest since addressing the practical case of a surface cracked plate.

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