On the estimation of notch fatigue limits by using the Theory of Critical Distances: L, a0 and open notches

This paper investigates some theoretical aspects related to the use of the Theory of Critical Distances (TCD) when employed to estimate notch fatigue limits. The linear-elastic TCD takes as a starting point the hypothesis that notched components are in their fatigue limit condition when an effective stress, whose value depends on a characteristic length, equals the material plain fatigue limit. Such an idea can be formalised by following different strategies: either assuming that the effective stress depends only on the profile of the stress field damaging the fatigue process zone and the reference distance is a material property or assuming that, for a given material, the values of both critical stress and critical distance change as the geometrical feature weakening the component to be assessed changes. The accuracy of the above different formalisations of the TCD was systematically checked by using experimental data taken from the literature and generated by testing metallic samples containing different types of notches. This systematic validation allowed us to confirm that the simplest formalisation of the TCD, in which both critical distance and critical stress are material constants, is also the most accurate one, giving predictions falling within an error interval of about $\pm $20{\%}. Subsequently, in order to better explore the peculiarities of the above formalisation of the TCD, its accuracy was also checked considering notches having large values of the opening angle. This type of notch represents an interesting testing ground for our theory because, when the opening angle becomes larger than about 90\textdegree , the profile of the linear elastic-stress in the fatigue process zone is strongly influenced by such an angle. The comparison with the experimental data proved that the TCD formalisation based on the assumption that both critical distance and critical stress are material constants is successful also in assessing these particular geometrical features. The exercises summarised in the present paper allowed us to further confirm that the simplest formalisation of the TCD is a powerful engineering tool, allowing real components to be assessed with an adequate degree of safety by simply post-processing linear-elastic Finite Element (FE) models.