PSI - Issue 39

Daniela Scorza et al. / Procedia Structural Integrity 39 (2022) 503–508 Author name / Structural Integrity Procedia 00 (2019) 000–000

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the typical fatigue fracture origins, since cracks nucleate at the interface between the inclusion and the matrix and/or through the inclusion itself (Yakura et al., 2016; Khameneh and Azadi,2018). Consequently, non-metallic inclusions affect both short and long lifetimes of high strength steels. Moreover, it is worth noting that, usually, the sizes of inclusions in such steels are greater than a critical value, allowing to treat such inclusions as small defects. During an extensive experimental campaign performed on two types of steels, Murakami (2002) observed that fatigue problems involving small defects (such as NMIs) may be studied as those involving short cracks. As a consequence, the fatigue limits could be related to the square root area ( area ) of such small defects projected into the plane perpendicular to the maximum principal stress direction. By taking full advantage from the observations made by Murakami, Machado et al. (2020) have recently proposed to use a classical critical plane-based criterion in conjunction with the concept of the area -parameter to perform the fatigue assessment of a high strength steel under multiaxial loading. In the present work, the area concept is implemented in the Carpinteri et al. criterion (Carpinteri et al., 2015; Vantadori et al., 2020; Vantadori et al., 2022) to estimate the fatigue lifetime of naturally defective high strength steels under multiaxial loading. The effectiveness of the criterion is evaluated by analysing the experimental data, available in the literature, related to specimens made of AISI 4140 subjected to multiaxial fatigue loadings (Machado et al., 2020).

Nomenclature a C , a N

amplitude of the shear and normal stress components on the critical plane, respectively

eq,a N

equivalent normal stress amplitude on the critical plane control volume and standard inspection volume, respectively

V , 0 V

1 af , σ − ,

1 af , τ −

material fatigue strengths under fully reversed normal and shear stresses, respectively

eq,a σ

equivalent uniaxial stress amplitude

wl σ , wl τ x ,a σ , xy ,a τ

lower bound of the fatigue limits under normal loading and torsion, respectively

amplitude of the applied normal and shear stresses, respectively

2. Uniaxial fatigue strength affected by non-metallic inclusions: the area -parameter model In low/medium strength steels, the fatigue fracture origin is characterised by slip bands and/or grain boundary cracks and the fatigue strength under normal loading, w σ , may be defined by exploiting its linear relationship with the material Vickers Hardness, HV , i.e. 1 6 w . HV σ = . In presence of non-metallic inclusions, such as in the case of high strength steels, instead, such a relationship is no longer valid. By considering NMIs as small defects and by observing that, usually, such inclusions are more than a single one, Murakami (2002) proposed an upper and a lower bound for the normal fatigue strength, where the upper bound is given by the above-mentioned relationship valid for low/medium strength steels, and the lower one by: ( ) ( ) 1 6 1 44 120 wl max . HV area σ + = (1) where area is the square root of the “area” of an inclusion into a plane perpendicular to the maximum principal stress direction. Eq. (1) had been written by assuming that: (i) the inclusion with the maximum area, max area , contained in the selected specimen cross-section, is expected to become the fatigue fracture origin, and (ii) such an inclusion is just below the cross-section surface.