A simplified Navarro-Rios model to predict fatigue limits in notched components.

Many methods have been proposed to predict fatigue failure in the presence of notches, among which is the Navarro-Rios model. This 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 crack growth from a notch under cyclic loading and has been successfully used for many years to predict the fatigue limit in some notched geometries, as shown in several published works. However, the application of this model is not easy, mainly for two reasons: the first is that to build the equations of the model, it is necessary to know the stress field generated by a dislocation in the vicinity of the specific notch, which is a complicated elasticity problem except for very simple notch geometries. The second is related to the resolution of the equations of the model, which are singular integral equations that are difficult to solve except for very simple cases. This work shows a simplified version of the Navarro-Rios model, which allows us to overcome these two difficulties. First, the elastic problem of a dislocation near a notch is simplified to that of a dislocation in an infinite medium, which has a known analytical solution. Second, the study of the equilibrium at the crack line is simplified by using the elastic stress at the midpoint of the crack line instead of using the full stress gradient. After this simplification, the singular integral equation has a known and simple solution. This simplified Navarro-Rios model is applied to some notched geometries and provides similar fatigue limit predictions to those of the classic Navarro-Rios model. It is also compared with results in the literature, where it provides similar predictions to the experimental fatigue limits. The simplified Navarro-Rios model can be a relatively simple alternative to critical distance models for predicting the fatigue limit in notched solids.

Automated summary

The Navarro-Rios model is one of the methods proposed to predict fatigue failure in the presence of notches. However, due to the difficulties in its application, a simplified version has been developed which provides similar fatigue limit predictions.