PSI - Issue 68

494 Lucia Morales-Rivas et al. / Procedia Structural Integrity 68 (2025) 493–499 Lucia Morales-Rivas, Eberhard Kerscher / Structural Integrity Procedia 00 (2025) 000–000 range, ∆σ g,th , vs. the crack or defect size, . Two asymptotic limits are distinguishable: the theoretical fatigue limit of the smooth specimen, ∆σ 0 ; and the limit defined by the propagation/non-propagation threshold of the stress intensity range for long cracks, ΔK !"_$%&' . El Haddad, et al. (1979) proposed the following expression (eq. 1) to describe the evolution of ∆σ g,th as a function of the crack or defect size, . Correspondingly, the grey area in the diagram of Fig. 1.a defines the conditions under which cracks can neither nucleate nor propagate leading to the failure of the specimen. !,#$ = %& !"_$%&' '((*+* ( ) (1) where ( , the El-Haddad-Smith-Topper (EHST) parameter, is defined as the crack length at which the asymptotes intersect each other (eq 2). - = / . ( %& !"_$%&' %1 ( ) 2 (2) Considering the behaviour of short cracks, the successive microstructural barriers that they encounter are represented by the green line in Fig. 1.a, inducing crack arrestment, as proposed by Miller and O’donnell (1999). The major microstructural barrier would define the ∆σ 0 value, according to that hypothesis. 2

Fig. 1. Schematic illustrations of Kitagawa-Takahashi-like diagrams, where is (a) the size of the crack/defect for the smooth specimen or (b) the defect/notch for the notched specimen. In (a), the green line corresponds to Miller’s interpretation of microstructural barriers.

For notched specimens, the Kitagawa-Takahashi diagram can be modified in order to incorporate the notch effect (schematic illustration in Fig. 1.b, where now stands for the size of the defect or notch). In this sense, for a notch factor ) (i.e., the theoretical stress concentration factor), Δσ *,), approaches -. ! 0 " as the blunt character of the notch intensifies; while its sharpness makes it progressively deviate from -. ! 0 " and to behave more similarly as a crack, as explained by Atzori and Lazzarin (2002). Different equations have been proposed in order to describe the transition from sharp notches to pure blunt notches -Atzori and Lazzarin (2002), Atzori, et al. (2003), Ciavarella and Meneghetti (2004), Atzori et al. (2005)-. One of the best known empirical approaches on this topic was developed by Neuber, as reported in ref. Heywood (1962). According to his rule (eq. 3), the parameter 1 , which is defined as -. ! -. #,"% is a function of: ) ; the radius of the notch tip, ; and a parameter, 2 . , which was proposed to be a function of the ultimate tensile strength (UTS). 4 = 1 + ( # −1) .+ . 5 ) + * (3) The main objection to this empirical equation is that it does not express the effect of fracture-related properties of the material. As opposed to it, other authors have pursued the description of 1 as a function of the size of the notch. A modified Neuber´s equation -eq. 2, Ciavarella and Meneghetti (2004)- has been suggested to be applicable to any notch geometry, where now the material features are represented in a more complete way.