## 3 Numerical Results and Discussions  
_Modified Compact Tension Specim (MCTS)_  
A comprehensive analysis was conducted on a set of five compact tension specimens subjected to constant amplitude fatigue loading. The primary research objective was to investigate the influence of altering the position of the third hole on the crack growth path and the fatigue performance of the specimens. The first specimen was designated as the standard reference, providing a baseline for comparison. Meanwhile, the remaining four specimens were meticulously modified to systematically vary the position of the third hole to simulate mixed-mode FCG, as shown in Figure 1. These modifications were carried out with the aim of elucidating the intricate relationship between hole position and the specimens' fatigue characteristics. By carefully manipulating the position of the third hole, the researchers sought to uncover any discernible effects on crack initiation, propagation, and ultimately, the overall fatigue life of the specimens. This rigorous examination of hole positioning aimed to provide valuable insights into the structural integrity and durability of compact tension specimens under constant amplitude fatigue loading conditions. A compact tension specimen (CTS) typically exhibits pure mode I fatigue crack growth (FCG) conditions; however, introducing a hole can result in crack deflection and the emergence of mixed-mode conditions. The center coordinates of the third hole in Figure 1 were adjusted, thereby altering the dimensions of this specimen. The adjustment was made based on the vertical distance, denoted as C, and the horizontal distance, denoted as k, as indicated on the right side of Figure 1. The presence of a hole in the specimen can have two different effects on the crack path. It can either attract the crack path, acting as a sink hole, or deflect the crack path, acting as a miss hole. The specific properties of the material can be found in Table 1 for SAE 1020 steel. The specimen was subjected to a maximum load of 10 kN, and a stress ratio (R) of 0.1 was applied individually to each hole. Figure 1: Geometrical representation of the MCTS. The analytical solution for the standard compact tension specimen, as provided by [2; 3], allows for the determination of the first mode stress intensity factor (SIF) for this particular geometry. The expression provided in the reference can be used to calculate the first mode of SIF, which can be expressed as follows:  
\[K_{I}=\frac{P\overline{\Delta K}}{B\sqrt{W}} \tag{7}\]  
where \(P\) is the load, \(B\) is the geometric thickness, \(W\) denotes the width, and \(\overline{\Delta K}\) is the normalized stress intensity factor, which is dependent on the ratio of crack length to specimen width (\(a/W\)). It is expressed as follows:  
\[\overline{\Delta K}=\Big{(}2+\frac{a}{W}\Big{)}\bigg{(}0.886+4.64\Big{(}\frac{ a}{W}\Big{)}-13.32\Big{(}\frac{a}{W}\Big{)}^{2}+14.72\Big{(}\frac{a}{W}\Big{)}^{3}-5.6 \Big{(}\frac{a}{W}\Big{)}^{4}\bigg{)}/\Big{(}1-\frac{a}{W}\Big{)}^{3/2} \tag{8}\]  
where \(a\) represents the crack length. The mesh generated for CTS01 and CTS02 is depicted in Figure 2, with an element size of 0.5 mm. It is important to mention that the same element size of 0.5 mm was used for the mesh generation of the other three specimens as well. In the case of CTS01, the total number of elements was 189,235, and the total number of nodes was 292,639. As for CTS02-CTS05, the total number of elements increased to 212,514, and the total number of nodes reached 320,154. Before crack growth occurs, the concept of the sphere of influence is often used in ANSYS simulations to determine the region around the crack tip that requires mesh refinement. The sphere of influence represents the zone where the stress field is significantly affected by the presence of the crack. ANSYS Smart Crack Growth further enhances the simulation by automatically adapting the mesh during crack growth.