PSI - Issue 37

Jesús Toribio et al. / Procedia Structural Integrity 37 (2022) 989–994 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000 – 000

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On the other hand, certain disadvantages also arise in this kind of specimens such as the frequent appearance of fatigue non-symmetric crack advance (Stark and Ibrahim, 1986), thus producing eccentricity of the circular ligament in relation to the bar axis. This phenomenon may be caused by slight non-symmetries regarding the sample, the grips or the testing machine, as well as non-uniform material properties (Ibrahim and Kotousov, 1999), residual stress effects, etc. Diverse stress intensity factor (SIF) solutions have been published in the scientific literature in the matter of a circumferentially-cracked round bar (CCRB) subjected to tensile loading, for both symmetric (Bueckner, 1965; Zahn, 1965; Benthem and Koiter, 1973; Gray, 1977; Lefort, 1978; Nisitani and Noda, 1984; Dieter, 1988) and non symmetric cracks (Mattheck et al ., 1985; Ibrahim and Stark, 1990; Ibrahim and Kotousov, 1999) where the ligament eccentricity produces additional bending stresses. The SIF at the points of maximum and minimum crack depth have been calculated using the superposition of known solutions for symmetric problems (Ibrahim and Kotousov, 1999). The maximum SIF has also been obtained using three dimensional (3D) finite element analyses and the direct stress method for small cylindrical circumferentially notched and cracked bars (Ibrahim and Stark, 1990), and using weight functions obtained by the finite element method for geometries of maximum eccentricity, i.e., for sickle-shaped cracks (Mattheck et al ., 1985). CCRB have been successfully employed to measure the fracture toughness of different materials (Stark and Ibrahim, 1986; Ibrahim and Stark, 1990; Ibrahim and Kotousov, 1999; Neelakantha et al. , 2015). They have also been used to evaluate fatigue crack propagation (Pinter et al ., 2007 Neelakantha et al ., 2015) and stress corrosion cracking (SCC) phenomena in general (Rihan et al ., 2006), or hydrogen assisted cracking (HAC) in particular (Raykar et al ., 2012). In the matter of fatigue crack propagation, the eccentricity reduces the time to reach the critical situation (Zhao et al ., 2011; Kim et al ., 2013) and also increases the instability of the fracture process itself, as pointed out by Yngvesson (2000). In spite of the afore-said references, there is a lack of information in the scientific literature regarding SIF values in points of the crack front different from the maximum crack depth. This paper tries to fill this gap by providing solutions along the crack front and analyzing the problem of contact between the crack faces. 2. Numerical modelling The finite element method (FEM) together with the MSC.Marc code was employed to obtain the SIF in cylindrical bars with a non-symmetric external annular crack under tensile loading. The resistant ligament, characterized as a circle, is not centred in relation to the bar axis, so a quarter of the solid was modelled (Fig. 1) with the adequate boundary conditions.

Fig. 1. 3D mesh of the bar with a non-symmetric annular crack.