PSI - Issue 82

L. Mata et al. / Procedia Structural Integrity 82 (2026) 16–23 Mata et al./ Structural Integrity Procedia 00 (2026) 000–000

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3. Results and discussion The predicted crack initiation sites were located at two diagonally opposite points on the notch surface, as denoted by the white arrows in Fig. 3. These locations correspond to the regions where the maximum values of the first principal stress were observed. These two points appear under bending-torsion loading or tension-torsion loading, regardless of the s ⁄ t ratio. However, their positions around the hole surface vary with the s ⁄ t ratio, either under bending-torsion or tension-torsion. It can be concluded that these points tend to approach the vertical dashed white line, as the s ⁄ t ratio increases. This may be explained by the variation in the induced shear stress relative to the normal stress, clearly showing that the locations of these points depend on the s ⁄ t ratio. Table 2 presents the numerical predictions of the crack initiation locations ( b 1 and b 2 ) and the early-stage crack growth directions ( a 1 and a 2 ) for the bending-torsion and tension-torsion loading simulations, considering both the untreated (UT) and stress-relieved (SR) material conditions. The subscripts 1 and 2 refer to the crack observed at the top and at the bottom of the notch, respectively. The definitions of b and a are represented in Fig. 3(a). These angles were measured relative to the vertical dashed white line, which corresponds to the x-axis direction in Fig. 1. From the obtained results, it can be stated that the predicted crack initiation angle (β) decreases noticeably as the σ⁄τ ratio increases, as expected, also agreeing with conclusions reported by Branco et al. (Branco, 2021). The same statement can be made regarding the predicted crack propagation angle (α) which also tends to decrease with an increasing σ⁄τ ratio. This behaviour is consistent across both loading scenarios. Concerning the loading type, the analysis of results suggests minor influence of this variable in the crack initiation angle ( b ) and the early-stage crack growth direction ( a ) . Nevertheless, in general, it seems that the two angles tend to be slightly lower under bending torsion compared to tension-torsion. This can be explained by the different local stress gradients resulting from the two types of normal stress (axial or bending) applied in the simulations. Regarding the material condition, it is also clear from Table 2 that the numerical predictions are relatively close, suggesting a minor influence of the residual stress relief treatment compared to the untreated material. Table 2. Numerically predicted initiation and early-stage crack growth angles for bending-torsion and tension-torsion loading. Loading type s ⁄ t ratio Condition (°) (°) (°) (°) B-T 4/3 UT 21.2 32.5 22.5 29.2 B-T 4/3 SR 22.8 32.7 22.4 32.1 B-T 2 UT 19.3 24.2 17.3 24.4 B-T 2 SR 19.2 27.7 17.5 24.2 T-T 4/3 UT 20.3 29.8 21.1 29.0 T-T 4/3 SR 20.2 29.8 21.3 28.6 T-T 2 UT 19.3 28.1 17.3 24.4 T-T 2 SR 16.3 21.7 17.7 24.8 (B-T: bending-torsion; T-T: tension-torsion; UT: untreated condition: SR: stress-relieved condition) Fig. 4 compares the predicted b angles for the two material conditions (untreated and stress-relieved) under bending-torsion loading ( s ⁄ t = 4/3) with the experimental results reported by Cunha (2024) for the same conditions. Overall, the predicted values align well with the experimental observations, regardless of the material condition, with most data points within scatter bands of ±10°, which validates the proposed approach for the tested material under these loading scenarios. The scatter observed in the experiments under similar loading levels can be attributed to the characteristic defects associated with the SLM process, such as porosities and unmolten particles located near the notch surface, which act as local stress concentrators and serve as preferential sites for fatigue crack initiation.