A non-linear model for the fatigue assessment of notched components under fatigue loadings

This paper presents a general theory for the estimations of an entire fatigue curve in ductile materials based on the implicit gradient approach. In order to modify the slope of the Woehler curves, the material was considered non-linear. The average stress of the hysteresis loop was taken into account by means of Walker's model. Subsequently, the implicit gradient method was adopted for the numerical evaluation of the effective stress and strain at low- and medium-cycle fatigue life and was then related to the fatigue strength of the material. The characteristic length, relating to the fatigue behaviour of the material, was considered constant for the fatigue lifetime. In order to confirm the proposed method, new experimental data were obtained, relating to axisymmetric notched specimens loaded with nominal stress ratio R = −1 and R = 0. In terms of the effective strain amplitude, evaluated by means of the implicit gradient approach, the different Woehler curves of notched specimens were summarised in a unique fatigue curve as a function of Walker's cycle parameter.