PSI - Issue 72

José A.F.O. Correia / Procedia Structural Integrity 72 (2025) 547–556

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2. Probabilistic local fatigue models In engineering practice, S-N curves are generated through a linear regression analysis of fatigue data, given by and , presented on a logarithmic scale. This approach typically employs a probabilistic method based on the normal distribution, as recommended in design codes. Several approaches and methodologies have been proposed to generate the probabilistic fatigue field for materials and structural components. Researchers have employed various statistical distributions, including the Log Normal distribution (Zhao et al., 2009; Schijve, 2005) 3-parameter Weibull distribution (Schijve, 2005), and 3 parameter log( − 0 ) -Normal distribution (Schijve, 2005), among others.

Fig. 2. Conventional S-N field (adapted from Correia & De Jesus, 2025).

In 2001, the research conducted by Castillo and Fernández-Canteli revitalised analytical probabilistic models for characterising the complete Wohler field through physical and statistical conditions (see Figure 3). The probabilistic S – N field for a fixed stress level is represented by the equation ( ; ∆ ) = = 1 − {− [ ( − )( ∆ − )− ] } (10) ( − )( ∆ − ) ≥ (11) In this equation, represents the probability of failure, denotes the lifetime in cycles, indicates the applied stress range, and signifies the threshold value of the lifetime, is the endurance limit (or fatigue limit, for → ∞ ). Additionally, , , and correspond to the shape, scale, and location parameters of the Weibull distribution, respectively.

B

p=0

p=0.05

Log Δσ

p=0.5

p=0.95

Fig. 3. Probabilistic S-N fields based on Castillo & Fernández-Canteli fatigue model (adapted from Correia & De Jesus, 2025). Log N f C