PSI - Issue 76

Luca Esposito et al. / Procedia Structural Integrity 76 (2026) 50–58

52

( S u − S e ) N β + 1

S = S e +

(1)

where S is the applied stress (maximum value or amplitude), N is the number of cycles to failure, S e is the fatigue limit (endurance limit), S u is the ultimate tensile strength, and β is a fitting parameter controlling the transition between the low-cycle and high-cycle fatigue regimes. In this work, S refers to the maximum value of the applied stress range, although the stress amplitude could alternatively be used. The value of the ultimate tensile strength S u was determined from monotonic tensile tests and found to be 435 MPa; this value was adopted as a fixed input parameter in the fatigue model calibration. The main advantage of using this formulation is that the fatigue limit S e can be directly identified through model calibration, rather than being assumed at a predefined number of cycles (e.g., 10 6 or 10 7 cycles) as is often done in traditional engineering practice. Assuming that the nature of the critical defect influences the fatigue life, it is proposed to adopt two distinct S–N curves: one for failures initiated by porosity-type defects and another for failures originating from LoF defects. This approach allows a more accurate representation of the fatigue behavior by accounting for the di ff erent morphologies and stress concentrations associated with each defect type. The following asymptotic formulations are used to describe the median S–N curves for the two defect populations:

( S u − S eP ) N β P + 1 ( S u − S eL ) N β L + 1

(Porosity-induced)

S = S eP +

(2)

S = S eL +

(LoF-induced)

where S eP , S eL , β P , and β L are defect-specific fitting parameters representing the asymptotic fatigue limit and the curvature of the curve for Porosity- and LoF-induced failures, respectively. It should be noted that performing a direct non-linear fit of Eq. (1) or (2) in the form S = f ( N ) is not statistically rigorous, since in fatigue experiments the number of cycles to failure N is the stochastic variable, while the applied stress S is experimentally controlled. A statistically consistent approach requires modeling N as a function of S , or adopting likelihood-based estimation techniques that explicitly treat N as the dependent random variable.

2.4. Statistical Modeling and Fatigue Life Estimation

The experimental scatter in fatigue life can be statistically represented by associating a failure probability to each lifetime and stress level. In this work, the adopted statistical model is based on the log-Weibull distribution, which defines the cumulative probability of failure P f as: P f ( N , S ) = 1 − exp − log( N ) ˜ N m (3)