## 4 Results and Discussion
### Modified Compact Tension Specim (MCTS)
#### 4.1.6 G7 Specimen  
The previous five specimens have only one hole, whereas the G7 specimen has two identical 5 mm diameter holes symmetrically distributed along the axis of the specimen. The predicted crack growth path in both software compared to the experimental path obtained by [32], the numerical path predicted by [29], and incomplete crack growth path predicted by [28] using FRANC3D [28] are shown in Figure 16. The fatigue crack growth path in this specimen is almost straight, just like that for the G1 specimen due to the effect of the symmetrical holes. The predicted values of K\({}_{1}\) from FRANC2D/L program were in the range from 650 to 900 MPa.mm\({}^{0.5}\) compared to the range from 530 to 897 MPa.mm\({}^{0.5}\) calculated by ANSYS, as shown in Figure 17, in which comparable results with the numerical values predicted by [29] are also shown in Figure 17a. Furthermore, Figure 17b shows the predicted values of \(K_{II}\), which have lower values, indicating that this factor had no impact on the crack growth direction and that the crack will propagate in a straight line. The predicted fatigue life cycles for all specimens resulting from ANSYS and FRANC2D/L were compared to those values obtained numerically by [32] using FRANC3D software with good agreement, whereas the predicted values obtained by [29] did not have any comparable results with other data as shown in Table 3. As seen in this table, because there are no holes in the G1 specimen, it has the highest value of fatigue life cycles. Figure 16: Predicted crack growth path for G7 specimen (**a**) ANSYS Workbench, (**b**) FRANC2D/L and (**c**) Experimental [32], (**d**) numerical [33], (**e**) FRANC3D [32]. Similar studies were carried out for these geometries by [33], who used ANSYS software and his own source code, which is not available to use by any researchers, unlike Franc2D/1, which is free distributed software. According to the following points, there were many differences between the findings of this investigation and the numerical study performed by [33]:  
1. For several geometries such as G1, G5, G6, and G7, the author of [29] did shown the completed crack growth path to be comparable to the experimental path in his computational results. 2. The values of the second mode of stress intensity component, KII, which have a significant influence on the crack growth path according to Equation (1), have not been represented accurately by the author [29]. If the KII values were close to zero, the crack would propagate in a straight line, but as the values are increased, the crack began to grow in a curvature trajectory as many crack growth paths were achieved for the studied geometries. 3. The author [29] used the J-integral method to evaluate the stress intensity factors, which were also used in the present study in both software, resulting in a comparable result for SIFs, whereas there were no comparable results for the fatigue life cycles number for the ANSYS results computed by [29] compared to the FRANC3D results [32], which were achieved in the present study with comparable results as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{\begin{tabular}{c} **Number of Cycles** \\ **(ANSYS)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Number of Cycles** \\ **(FRANC2D)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Number of Cycles** \\ **(FRANC3D)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Number of Cycles** \\ **[**29**]** \\ \end{tabular} } \\ \hline G1 & 11923 & 11848 & 11765 & 44803 \\ \hline G2 & 6243 & 6325 & 6018 & 52116 \\ \hline G3 & 4021 & 4125 & 3818 & 70751 \\ \hline G4 & 4685 & 4712 & 4716 & 46314 \\ \hline G5 & 6219 & 6189 & 6018 & 52116 \\ \hline G6 & 5618 & 5587 & 5519 & 44968 \\ \hline G7 & 7425 & 7385 & 7211 & 57762 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison for the fatigue life cycles for all specimens.