Fatigue limit reliability of axisymmetric complex surface

In this paper, a method to predict fatigue limit reliability of specimens with 2D complex rough surface is proposed. First, a effective surface profile on fatigue limit is proposed. This is obtained from the ineffective crack length against the fatigue limit. Next, an equivalent notch depth is proposed to replace a rough profile to a smooth profile with a notch. To calculate the stress concentration of the notch and to determine the equivalent notch depth, an exact solution is given for a problem of an infinite plate with a complex profile under tension. The solution is obtained with the complex variable method. Finally, a method to predict the fatigue limit reliability is discussed. The Linear Notch Mechanics and \(\sqrt{area}\) parameter model is used to predict the fatigue limit of a smooth profile with a notch, and then the fatigue limit reliability is estimated with the fatigue limit of many simulated surfaces. Moreover, rotating bending fatigue tests of 0.1% carbon steel with a complex surface are carried out. The experimental fatigue limit data is compared with the present estimated value. As results, the validity of the present method is examined.