## 4 Results and Discussion
### Modified Compact Tension Specim (MCTS)
#### 4.1.1 G1 and G2 Specimens  
Two specimens are included in the first group of Table 1. G1 is a specimen without a hole, while G2 is a specimen with a hole. The hole diameter d1 for specimen G2 is 8 mm. It has a horizontal distance of 6.5 mm and a vertical distance of 3 mm. A constant amplitude loading of 3 kN with cyclic load ratio \(R=0\) is applied to the top 12.3 mm hole of each geometry, while the structure is clamped at the bottom 12.3 mm hole and the displacements and rotations of all nodes along its boundaries are completely constrained. Figure 4 shows the fatigue crack growth path predicted by ANSYS Workbench and the FRANC2D/L program for G1, which is almost similar to the experimental finding obtained by [32] and numerical findings obtained by [33] and more accurate than the incomplete crack growth path using Franc3D software by [32].  
The predicted values of stress intensity factors for mode I and mode II (\(K_{I}\) and \(K_{II}\)) with respect to crack length are shown in Figure 5. The range of K\({}_{I}\) in FRANC2D/L program is 635 to 1081 MPa.mm\({}^{0.5}\), while in ANSYS, it ranges between 590 to 1065 MPa.mm\({}^{0.5}\). The predicted values for both programs vary by approximately 2.8%. There were also comparable results for \(K_{I}\) to the numerical data obtained by [33], whereas for the \(K_{II}\), there were ambiguous data obtained by [33] to make a comparison with it.  
The predicted crack growth path in both software for the G2 specimen is shown in Figure 6 compared to the experimental crack growth path predicted by [32] with an identical crack path. There were another two comparisons with the numerical data obtained by [29] and FRANC3D results, which have incomplete crack growth path compared to the present study results. Due to the presence of the small hole near the crack growth direction, the crack changes its direction toward the hole, which illustrates the influence of the hole position on the direction of the crack growth. The stress intensity factors computed by the ANSYS program and the FRANC2D/L program vary by 0.57 percent in the simulation of specimen G2. There were also comparable results for \(K_{I}\) with the numerical results obtained by [29] as seen in Figure 7. Furthermore, for the second mode of stress intensity factors \(K_{II}\), which affected the crack growth path to grow toward the hole, there are higher values for this specimen compared to the previous one, as shown in Figure 7b.  
Due to the large scale of the curves as a consequence of combining \(K_{I}\) and \(K_{II}\) in the same curve, these values of KII were also found ambiguously by [29].  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**MCTS**} & \multicolumn{2}{c}{**FRANC2D/L**} & \multicolumn{2}{c}{**ANSYS Workbench**} \\ \cline{2-5}  & **Nodes** & **Elements** & **Nodes** & **Elements** \\ \hline G1 & 4722 & 2314 & 166835 & 121915 \\ \hline G2 & 4576 & 2352 & 160678 & 112195 \\ \hline G3 & 4684 & 2367 & 176831 & 121916 \\ \hline G4 & 4687 & 2477 & 156815 & 107646 \\ \hline G5 & 4635 & 2295 & 167885 & 114429 \\ \hline G6 & 464 Figure 4: Predicted crack growth path for G1 specimen (**a**) ANSYS Workbench, (**b**) FRANC2D/L and (**c**) Experimental [32], (**d**) numerical [33], (**e**) FRANC3D [32].  
Figure 5: Stress intensity factors with corresponding crack length for specimen G1, (**a**) \(K_{l}\), and (**b**) \(K_{ll}\).