PSI - Issue 82

L. Mata et al. / Procedia Structural Integrity 82 (2026) 16–23

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Mata et al. / Structural Integrity Procedia 00 (2026) 000–000

Experimental crack initiation angle, b (°)

Numerical crack initiation angle, b (°)

Fig. 4. Fatigue crack initiation angles for bending-torsion loading with σ⁄τ = 4⁄3: experimental observations versus numerical predictions (β 1 represents the angle at the top, and β 2 represents the angle at the bottom; the definition of the b angles can be seen in Fig. 3(a)). Experimental results obtained from Cunha (2024). The fatigue life prediction (N f ) was estimated by combining the Smith-Watson-Topper (SWT) model and the Theory of Critical Distances (TCD) using the methodology proposed by Mata (2024). Briefly, the Line Method of the TCD was used to account for the notch effect based on a SWT-distance function, extracted from the numerical models described in Section 2, over a straight line emanating from the point of the maximum value of the first principal stress, i.e., from the initiation site of the first crack in a direction normal to the hole surface. Plasticity effects were accounted for through the Equivalent Strain Energy Density (ESED) concept, considering the cyclic stress-strain curves of both the untreated and stress-relieved material conditions. Fig. 5 presents the fatigue life predictions obtained with the proposed methodology under bending-torsion and tension-torsion loading for the untreated and stress-relieved material conditions. Plotting the nominal normal stress amplitude (σ a ) as a function of the predicted number of cycles to failure (N f ), it is possible to obtain representative stress-life curves for different loading scenarios (bending-torsion and tension-torsion), material conditions (as-built and stress-relived), and normal-to-shear stress ratios ( s ⁄ t = 4/3 and s ⁄ t = 2) . It is evident from Fig. 5 that, in both loading scenarios, an increase in the σ⁄τ ratio led to a less steep S-N fatigue curve for both material conditions (i.e., a slope with lower absolute value). Therefore, for s ⁄ t = 2, the same reduction in nominal stress amplitude led to a larger difference in fatigue life. Moreover, the slopes of the stress-relieved material (blue series) tended to be quite similar when comparing simulations with the same σ⁄τ ratio, regardless of the loading scenario. The same trend was observed for the untreated material (black series). Furthermore, an increase in the level of shear stress amplitude relative to the normal stress amplitude resulted in reduced fatigue life under both loading scenarios, agreeing with the trends discussed above. A reduction in fatigue life was also observed in the simulations of the stress-relieved material (blue series) compared to those without heat treatment (black series). Based on these results, the influence of the heat treatment was more pronounced under lower σ⁄τ ratios.