A Unified Notch S–N Framework for Fatigue Life Prediction of Metallic Components Across Low and High Cycle Regimes

Fatigue failure is still persistent and practically consequential challenges in the structural integrity assessment of metallic components. Although the classical separation between low-cycle fatigue and high-cycle fatigue has provided a useful conceptual framework for decades, it has also fostered a fragmented methodological landscape. In practice, engineers are often required to navigate between stress-based formulations rooted in linear elasticity and strain-based descriptions that explicitly invoke plastic deformation, depending on the nominal fatigue regime under consideration. This division becomes particularly problematic when dealing with notched components, where strong stress gradients coexist with localized plasticity and where the conventional boundaries between fatigue regimes lose their clarity. Historically, the S–N curve, originating from Wöhler’s pioneering work, has been regarded as the natural tool for high-cycle fatigue, whereas the Coffin–Manson relation has been reserved for low-cycle fatigue. The implicit assumption underlying this dichotomy is that elastic stress measures are insufficient to describe damage accumulation when cyclic plasticity becomes significant. However, an increasing body of experimental evidence suggests that this assumption may be overly restrictive, especially when fatigue life is evaluated from a global structural perspective rather than from local cyclic strain amplitudes alone. The question, therefore, is not whether plasticity exists, but whether it must always be explicitly modeled to achieve reliable life predictions. The difficulty is amplified in notched metallic components, where stress concentrations dominate fatigue behavior and where traditional approaches often require the introduction of multiple correction factors, local strain estimations, or geometry-specific calibration procedures. Such methods, while theoretically appealing, tend to sacrifice simplicity and robustness when applied across different notch geometries, loading modes, and fatigue regimes. From an engineering standpoint, there is a strong incentive to seek unified approaches that can accommodate both low- and high-cycle fatigue without continuously switching conceptual frameworks. To this end, new research paper published in Engineering Fracture Mechanics and led by Professor Xiangqiao Yan from the Center for Composite Materials and Structure at Harbin Institute of Technology, the author developed a unified notch-specific S–N curve methodology for predicting the fatigue life of metallic components across low- and high-cycle regimes using linear-elastic stress analysis. By integrating local stress field descriptions with critical distance concepts, the approach captures notch effects without explicit elastic–plastic modeling. Extensive validation against literature data confirms its accuracy under uniaxial and multi-axial loading.

Professor Xiangqiao Yan adopted a comparative and integrative strategy, re-analyzing existing datasets that span low-cycle, high-cycle, and transitional fatigue regimes. The method allowed the proposed framework to be tested against diverse materials, notch geometries, and loading conditions without tailoring the model to a single experimental configuration. In each case, fatigue life is correlated with a stress-based intensity parameter derived from linear-elastic analysis. For notched components, this parameter is not taken directly at the notch root, but evaluated through a local stress field formulation that accounts for the spatial decay of stress ahead of the notch. The analysis incorporates the concept of a critical distance, interpreted as a material- and life-dependent characteristic length over which fatigue damage is effectively governed. Importantly, this distance is not assumed to be universal or fixed; instead, it emerges implicitly through calibration using reference fatigue curves for smooth and notched specimens.

The author’s finding showed across multiple materials including structural steels, piping steels, cast iron, and titanium alloys the fatigue data for notched specimens collapse onto well-defined notch-specific S–N curves when expressed in terms of the proposed stress parameter. This holds not only in the high-cycle regime, where elastic assumptions are traditionally justified, but also in low-cycle and even extremely low-cycle fatigue, where plastic deformation is undoubtedly present. The implication is not that plasticity is absent, but that its cumulative effect on fatigue life may be adequately captured by an effective stress representation within an S–N framework. He also investigated multi-axial loading cases, including combined tension–torsion and non-proportional loading paths and by embedding the notch S–N formulation within a generalized stress-invariant fatigue model, the investigator demonstrates that multi-axial fatigue lives can be predicted with error ranges comparable to those reported for established elastic–plastic approaches. Mean prediction errors remain within acceptable engineering bounds, and no systematic bias toward over- or under-prediction is observed. A particularly instructive finding is that different notch geometries naturally give rise to different S–N curves, rather than requiring ad hoc notch sensitivity factors. This observation reinforces the physical interpretation of the notch S–N curve as an inherent property of the notch–material system.

 In conclusion, the work of Professor Xiangqiao Yan establishes notch S–N curves as inherent properties of notch–material systems rather than empirical corrections. He successfully demonstrated that notch-specific S–N curves can accurately describe fatigue behavior across low- and high-cycle regimes using linear-elastic stress analysis, and by this the new study challenges a deeply ingrained methodological divide within fatigue mechanics. The implications of the work are substantial and the unified notch S–N framework simplifies fatigue assessment workflows, reduces reliance on complex elastic–plastic simulations, and facilitates the use of existing fatigue databases. We believe this is especially valuable in industry where rapid design iteration, limited material data, or multi-axial loading conditions make detailed plasticity modeling impractical. The new approach also offers a transparent pathway for incorporating notch effects without resorting to empirical notch sensitivity factors that often lack clear physical interpretation.

Moreover, the findings demonstrates that although plastic deformation influences crack initiation and growth, its net effect on fatigue life may be captured indirectly through stress-based measures that reflect the averaged mechanical environment ahead of stress concentrators. Additionally, the study also strengthens the role of local approaches, such as the theory of critical distances, by embedding them within a practical life-prediction framework rather than treating them as isolated failure criteria. The new methodology   remains adaptable to different notch geometries and loading modes. Looking forward, the notch S–N curve method provides a promising foundation for further extensions, including probabilistic fatigue assessment, variable-amplitude loading, and integration with fracture-mechanics-based crack growth models. Its compatibility with multi-axial stress invariants also suggests potential applications in complex structural systems where traditional fatigue classifications are limited.