PSI - Issue 19

Jan Papuga et al. / Procedia Structural Integrity 19 (2019) 405–414 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Both approaches are today used in commercial fatigue solvers (RSG approach can be found e.g. in Femfat or MSC.Fatigue, TCD approach in Fe-Safe), but they were not directly compared according to the authors. This paper presents such a comparison performed on five notch types (U-notch, V-notch, fillet, hole and bi-notch).

2. The three computational concepts 2.1. Nominal stress approach (NOM)

This straightforward approach is used traditionally, see e.g. Schijve (2009). The fatigue limit of the notched specimen is decreased compared with the fatigue limit of the unnotched material, if described by the nominal stress. The relevant factor is called notch factor K f : � = � ��,��� � ��,����� (1) It is retrieved from the stress concentration factor K t set at the notch root as a measure of the notch acuity: � = � ��� � ��� (2) The relation between both is usually described by the notch sensitivity factor q : = � � � �� � �� (3) Various formulas and functions to compute it based on some material value and the notch root radius  were developed, and the proposal by Peterson (1974) belongs to the most often used ones: = �� � � � . (4) For aluminum alloys treated in this paper, Schijve (2009) notes the value of the material constant a =0.51. Less known is a later proposal by Buch (1984), who tried to prove that only one material parameter is not sufficient for describing the relation and proposed the formula: � � � � = � � �1 − � � � .� � � � � (5) This complicated formula contains already three parameters to be set. It can be noted that for blunt notches with high notch radius, the effect of the notch root acuity diminishes and K t = K f ·A. Questionable remains the problem how to define the slope of the nominal S-N curve of the notched specimen. Schijve (2009) proposes to diminish the notch effect while moving to lower lifetimes and to use the tensile strength as the limit stress at the quasi-static domain. In some cases, this approach is expected to be valid only for ductile materials, and the limit state in this condition can be also set to tensile strength divided by K t for brittle materials.

2.2. Stress gradient approach (RSG) The RSG approach assumes that the magnitude of the maximum relative stress gradient: ′ = � � ��� � � � �

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