According to the previous report, low cycle fatigue strength of the pipe bend specimens subjected to in-plane cyclic bending displacement is beneath the best fit fatigue curve and its reason can be explained by the cumulative damage rule considering reduction of fracture ductility under multi-axial stress state. Further discussion of the proposed cumulated damage rule considering reduction of fracture ductility induced by multi-axial stress degree is shown in this paper. First, physical meaning of the proposed cumulative damage rule is clarified using equivalent plastic strain range. Secondly, estimated low cycle fatigue lives based on the proposed cumulative damage rule are compared with the experimentally obtained fatigue lives. Also, similar comparison is carried out on the equivalent strain range. The equivalent strain ranges for fatigue analyses have good coincidences with the estimated values by the proposed cumulative damage rule. Thus, applicability of the proposed cumulative damage rule considering multi-axial stress degree is again confirmed for elbow piping subjected to in-plane cyclic bending displacement. Finally, low cycle fatigue equation including ductility exhaustion considering multi-axial stress state is proposed and is compared with the advanced revised universal slope method which is an empirical fatigue equation proposed by the author. These two equations have a good coincidence each other and also with experimental data. Thus, adequacy of these equations is confirmed.
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