## 3 Numerical Results and Discussions
It selectively refines the mesh in critical areas, such as the crack front and vicinity of the crack tip, based on predefined criteria like stress intensity factors. These ANSYS techniques improve the accuracy of stress and displacement calculations, capturing the effects of stress concentration and deformation near the crack. \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Value in Metric Unit** \\ \hline Modulus of elasticity, \(E\) & 205 GPa \\ [PERSON]’s ratio, \(v\) & 0.29 \\ Yield strength, \(\sigma_{y}\) & 285 MPa \\ Ultimate strength, \(\sigma_{u}\) & 491 MPa \\ Paris’ law coefficient, \(C\) & \(8.59\times 10^{-14}\) \\ Paris law exponent, \(m\) & 4.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of specimens. Figure 2: Finite element generated meshes for CTS01 and CTS02. Figure 3 shows the trajectory of crack propagation as determined through the numerical analysis conducted with ANSYS. The figure distinctly displays a straight crack trajectory, which is characteristic of pure mode I fracture mode. Moreover, the symmetric distribution of stresses and strains observed in the figure further confirms the consistent behavior of the crack growth in this mode. Figure 4 shows a comparison between the computed results of the first mode of SIF and the analytical solution determined using Equation (2). The results demonstrate a substantial agreement between the two, indicating a high level of consistency. Figure 4: First mode of SIF for CTS01. Figure 3: Crack growth path for the standard CTS, CTS01. Figures 5-8 provide a comparative analysis of the current study's results with experimental and numerical data obtained by other researchers. The present study results in Figures 5, 7 and 8 were compared to numerical data obtained from [54], numerical crack paths simulated using Dual boundary element software (Quebra2D) by [PERSON] and [PERSON] [32], and artificial neural network results obtained by [PERSON] et al. [31]. These figures illustrate the comparison between the different approaches for CT02, CT04, and CT05 cases; additionally, Figure 6 provides a comparative analysis of the estimated crack growth path in the present study, along with the experimental and numerical results using the extended finite element method by [PERSON] et al. [55], and numerical results along with artificial neural network results obtained by [PERSON] et al. [31]. The depicted figures demonstrate the effectiveness of the modified CTS holes, which were intentionally designed to influence the direction of crack propagation. The predicted crack growth paths depicted in these figures demonstrate a close alignment with the experimental and numerical predictions. These findings indicate a strong correlation between the predicted crack growth paths and the observed behavior in both experimental and numerical analyses. The results presented in Figure 9 depict the normalized stress intensity factor for specimens CTS02-CTS05. The data reveals that up to a crack length of 5 mm, specimens CTS02 and CTS04 exhibit similar values of the normalized SIF; however, beyond this threshold, CTS02 demonstrates a slightly higher value compared to CTS04. This discrepancy is evident in the observed shift in the crack growth direction behavior for these specific specimens. Furthermore, it is worth noting that the normalized stress intensity factor values for CTS05 are higher than those for CTS03. This disparity can be attributed to the fact that CTS05 is situated in closer proximity to the main hole. As a result, CTS05 experiences more significant stress concentrations, leading to elevated stress intensity factors compared to CTS03. Figure 5: Crack growth trajectory of CTS02: (**a**) present study, (**b**) experimental [54], (**c**) Quebra2D [32], and (**d**) artificial neural networks [31]. Figure 6: Crack growth trajectory of CTS03: (**a**) present study, (**b**) experimental [54], (**c**) experimental [55], (**d**) XFEM [5], and (**e**) artificial neural networks [31].