PSI - Issue 57

Kimmo Kärkkäinen et al. / Procedia Structural Integrity 57 (2024) 271–279

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K. Ka¨rkka¨inen et al. / Structural Integrity Procedia 00 (2023) 000–000

3

Fig. 1: Model geometry, finite element mesh and repeating loading sequence.

growing crack in its entirety at all times but for the overload step, where a single breach into the unstructured mesh was necessary due to the relatively massive overload plastic zone size. In literature, it is often recommended to base the element size in the theoretical reversed plastic zone size (Roy chowdhury and Dodds, 2003; Solanki et al., 2003), or forward plastic zone size (Camas et al., 2018; Oplt et al., 2019; McClung and Sehitoglu, 1989). The most common recommendation is that the element size equals at most one tenth of the theoretical forward plastic zone size r p , which according to the Irwin estimation is given by Eq. 1 (Rice, 1967; Oplt et al., 2019),

K 2 max απσ 2 y

r p =

(1)

,

where α = 1 corresponds to plane stress condition and α = 3 to plane strain condition. In a short crack propagation analysis this recommendation is di ffi cult to fulfill as the plastic zone size increases with increasing crack length. If crack propagation begins at zero length without an initial crack, as is the case with the present analysis, the plastic zone is initially very small which results in an overly strict element size requirement. In the base model, element size is chosen to be l e = 0 . 5 µ m, which corresponds to approximately l e / r p = 0 . 1 at the end of crack propagation if the smaller, plane strain plastic zone estimation is used. This provides continuous and reasonable results.

2.3. Material model

The material model is not fitted to a specific material, but resembles a conventional high-strength steel. For com patibility with the Murakami-Endo fatigue model, the strength property is defined in terms of Vickers hardness, which is chosen to be 300 HV. An empirical relationship between hardness and yield strength, Eq. 2 (Pavlina and Vantyne, 2008), is used in order to link the Murakami–Endo fatigue limit to the material model used in simulations. Thus, the hardness of 300 HV corresponds to a yield strength of 772.10 MPa. σ y = − 90 . 7 + 2 . 876 HV (2) It is known that generally better correlation is achieved between ultimate tensile strength and hardness than between yield strength and hardness. In the regime of the hardness value chosen for this study, 300 HV, yield strength also