PSI - Issue 76

Kimmo Kärkkäinen et al. / Procedia Structural Integrity 76 (2026) 11–18

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It is evident from Table 2 that the predicted fatigue limits are conservative in comparison to the Murakami–Endo fatigue limit of Eq. 1. This could be expected given the omission of other crack growth resistance mechanisms in the simulated cyclic R-curves. However, plasticity-induced crack closure is the fastest to saturate (Maierhofer et al., 2018a), and thus dominant in the initial part of the cyclic R-curve most relevant in terms of the fatigue limit. It is worth noting that for small cracks, microstructural barriers also provide a significant resistive element (Vaara et al., 2025), which may also contribute to the di ff erence. Alternatively, the mean stress sensitivity in the reference value is expected to be underestimated, providing another explanation to the conservative prediction (see, e.g., Endo and Murakami, 2025). Related to this issue, as the aspect of crack initiation becomes important especially with increased mean stresses (Scho¨nbauer et al., 2017), the experimen tally obtained reference values may be masked by higher crack initiation resistance and not serve as a valid reference for the fracture-mechanical fatigue limit. This aspect provides a concrete example of why it is important to know the mechanism behind the fatigue limit observation to better understand and predict the quantity. Finally, it is worth noting that the cyclic R-curve results in part from the development of crack closure, and assum ing it universal is therefore unjustified. Rather, it is a multivariate function of quantities such as crack length, constraint conditions, material, crack surface morphology, environment, and even load level, for example (Suresh and Ritchie, 1983; McClung and Sehitoglu, 1989; Maierhofer et al., 2018b; Pokorny´ et al., 2025). Especially the lattermost depen dence is interesting; it is widely understood that crack closure is predominantly a near-threshold phenomenon (Pippan and Hohenwarter, 2017). This means that the cyclic R-curve would not manifest to the same degree for higher loads, complicating its use in finite life fatigue design, for example. However, assuming a fixed, material-specific curve is more convenient and may be justified particularly in near-threshold conditions. Note that if significant stress ampli tude dependence were to manifest, this would need to be considered in the fatigue limit prediction outlined in Section 4, iteratively for instance. In conclusion, although the model is still incomplete, the methods demonstrated in this article allow for the case specific, physics-based prediction of the fracture-mechanical fatigue limit. Once all the relevant mechanisms are in cluded and the model is validated with experimental data, it may be relied on for fatigue design. Incorporating explicit descriptions of other crack closure mechanisms, microstructural barriers, and crack initiation resistance are seen as the necessary steps towards a general fatigue limit prediction toolkit. The present article demonstrated a simple method for estimating the fatigue limit via simulated cyclic resistance curves. Conclusions of the study are as follows. • The cyclic R-curve is not unique, but rather a multivariate function governed by crack closure behavior. Fatigue limits can be estimated case-specifically by simulating the crack closure response and deriving the cyclic R curve from the result with respect to the intrinsic threshold. • Long crack thresholds inferred from the simulated cyclic R-curves are considerably lower than what is usually reported in literature for similar steels. It can be inferred that roughness- and oxide-induced crack closure should often account for the majority of the total crack closure influence of long cracks. • Due to its fast saturation, plasticity-induced crack closure may be the most important form of crack closure in terms of the fracture-mechanical fatigue limit. While other closure mechanisms are needed to explain long crack behavior, they may be insignificant for the fatigue limit determined by short crack arrest. 6. Conclusions

Acknowledgements

The authors would like to acknowledge the financial support of Business Finland in the form of the research project Fadefuel 7818 / 31 / 2024. The authors wish to acknowledge CSC – IT Center for Science, Finland, for computational resources.