In order to simulate mechanical fatigue phenomena under macroscopically elastic condition, the plastic stretching within a yield surface has to be described, whilst the plastic strain is induced remarkably as the stress approaches the dominant yielding state. In this study, a phenomenological plasticity model, proposed for the description of the cyclic loading behavior observed for typical carbon steels during the high-cycle fatigue subjected to stresses lower than the yield stress, is applied for the prediction of fatigue initiation life. The model is formulated based on the unconventional plasticity model and is applied for materials obeying isotropic and kinematic hardening law. The mechanical responses under cyclic loading conditions are examined briefly. Finally, the initiation life of fatigue cracking is discussed based on the proposed model with the damage counting parameter.

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