## 3 Numerical Results and Discussions
Figure 7: Crack growth trajectory of CTS04: (**a**) present study, (**b**) experimental [54], (**c**) Quebra2D [32], and (**d**) artificial neural networks [31]. Figure 10 presents a comparison between the simulated fatigue life results obtained in the present study and the experimental results reported by [PERSON] and [PERSON] (2018) for the four different MCTS geometries, namely CTS02, CTS03, CTS04, and CTS05. It is worth noting that the simulated fatigue crack growth (FCG) life, obtained using ANSYS, demonstrates an impressive level of agreement with the experimental results obtained by [PERSON] and [PERSON] in their study. This remarkable agreement can be observed in Figure 10, further validating the accuracy and reliability of the simulated FCG life predictions. The observed trend in the fatigue life cycles, as shown in Figure 10, provides further insights into the theoretical and experimental results. Figure 8: Crack growth trajectory of CTS05: (**a**) present study, (**b**) experimental ([PERSON] et al., 2018), (**c**) Quebra2D (2018), and (**d**) artificial neural networks ([PERSON] et al., 2018). Figure 9: Results for normalized SIFs for different configurations of the MCTS. the effects of hole position and crack growth behavior on the overall fatigue performance of the specimens. CTS05 exhibits the lowest number of cycles, indicating a significantly reduced fatigue life. The crack growth trajectory in CTS05 brings it in closer proximity to the hole, leading to accelerated crack propagation. As a result, the specimen experiences a higher stress concentration and is more prone to crack initiation and subsequent failure. The relatively shorter crack length of CTS05 further contributes to its lower fatigue life cycle, as the crack quickly propagates into the hole zone. With approximately 137,869 cycles, CTS05 demonstrates the most limited resistance to fatigue failure among the tested specimens. On the other hand, CTS04 performs better in terms of fatigue life compared to CTS05. It exhibits a higher number of cycles, approximately 240,000 cycles, before failure. While still influenced by the proximity to the hole, the crack growth trajectory for CTS04 allows for a slightly longer fatigue life. This suggests that the crack growth behavior and proximity to the hole have a less severe impact on fatigue life compared to CTS05. These findings highlight the critical role of hole position and crack growth behavior in determining the fatigue performance of the specimens. The results emphasize the need for careful consideration of geometric factors and crack propagation paths in structural designs to mitigate fatigue-related failures and ensure longer service life. The fatigue life cycle for CTS02 and CTS03 are approximately 342,000 and 345,000 cycles, respectively. This highlights the influence of hole position and crack growth behavior on the fatigue life cycle, with closer proximity to the hole resulting in a more rapid decrease in the number of cycles until failure. Figures 11 and 12 depict the constant amplitude equivalent stress intensity factor ranges obtained numerically using ANSYS for two configurations of the MCTS: CTS02 and CTS05. The stress ratios considered range from 0.1 to 1, with a total of ten simulations conducted. The stress ratios chosen for the present study ranged from 0.1 to 0.9 to intentionally avoid extensive crack closure. By utilizing stress ratios within this range, the study aimed to examine fatigue crack propagation under conditions where crack closure is still possible but expected to be less significant compared to a stress ratio of 1. This approach was adopted to obtain more precise insights into the crack behavior and fatigue life of the  
Figure 10: Fatigue life cycle for different configurations of the MCTS, Experimental for CTS02–CTS05, [PERSON] and Miranda [32]. materials being studied, free from the predominant influence of crack closure observed at a stress ratio of 1.