Calculation of fatigue limits in notches with a micro-mechanical model in a simple way

Abstract

Many methods have been proposed to predict fatigue failure in the presence of notches, among which is the N-R model. The N-R model is based on short-crack fracture mechanics. Specifically, the model analyses the capacity of the crack, which is formed at the notch root by cyclic loading, to overcome successive microstructural barriers such as grain boundaries. This model provides a fairly reasonable explanation of the crack growth from a notch under cyclic loading. The N-R model has been successfully used for many years to predict the fatigue limit in some notched geometries, as shown in several published works, but this model has a certain mathematical complexity. This work shows a simplified version of the N-R model. The elastic problem of a dislocation near a notch is simplified to that of a dislocation in an infinite medium and the study of the equilibrium at the crack line is simplified by using the elastic stress at the midpoint of the crack line. This simplified N-R model has been applied to a circular hole of variable root radius and provides similar fatigue limit predictions to those of the classic N-R model. It has also been compared with results in the literature, where it provides similar predictions to the experimental fatigue limits.