PSI - Issue 76

Mirco Daniel Chapetti et al. / Procedia Structural Integrity 76 (2026) 89–98

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Figure 3 illustrates the contribution of different crack growth stages to the total fatigue life at a nominal stress range of Ds = 550 MPa. The results highlight the potential scatter in fatigue life arising from the statistical distribution of defect sizes. This scatter can be estimated by combining the fracture mechanics-based approach with a statistical analysis (the latter not performed here).

Fig. 3. Estimated Ds - N curves for different initial defect sizes, a i . 2.25Cr1Mo steel

4. The Shiosawa and Lu proposal, D K vs. N/ a For materials exhibiting crack propagation-dominated fatigue behavior (where the total fatigue life can be approximated by the crack growth life ( N ≈ N P )), a modified representation and interpretation of defect-influenced fatigue results can be employed, following the approach proposed by Shiozawa et al. (2008). In this method, the Paris Erdogan law, da/dN = C D K m , is integrated from the initial defect size a i to the final (failure) crack length a f , leading to the following transformed expression: ∆ - =7 . (, 0 &0) 8 &12, . : ) + ! ; &12, (4) The Paris-Erdogan coefficient C and exponent m in Eq. (4) can be determined by fitting a power law to experimental data, plotting the stress intensity factor range at the failure-initiating defect, D K i , against the defect related number of cycles to failure, defined as N / a i , where ai is the initial defect size. Using a log-log plot, the fatigue behavior can be represented by a given curve ( D K- N / a ), analogous to the conventional Wöhler Ds - N curve. However, this approach has clear limitations. It does not account for propagation thresholds, which are necessary for defining fatigue or endurance limits. Additionally, it considers only long cracks, and thus cannot capture the distinct behavior of small cracks during the early stages of crack propagation from defects. 5. The Murakami et al. proposal, Ds / Ds th vs. N Murakami et al. (2020) proposed that the driving force for fatigue failure is not the absolute applied stress range, Ds , but rather the ratio of the local stress range to the threshold stress, Ds th , as defined by the Murakami-Endo threshold model (see Eq. 6). Accordingly, it was suggested that the relative parameter Ds / Ds th , particularly when Ds / Ds th > 1, governs the fatigue life to failure, N . Under these conditions, the fatigue life can be expressed as: = : ∆ ∆ 4 4 "# ; 5 (5) for Ds > Ds th , and A and B are constants that depend on the material and the loading ratio R . That proposal estimates