# Computational Simulation of 3D Fatigue Crack Growth under Mixed-Mode Loading
## 3 Numerical Results and Discussion  
### Single Edge Cracked Plate with a Three-Hole  
A rectangular plate with a dimension of 120 mm \(\times\) 65 mm \(\times\) 16 mm contains two holes with a diameter of 13 mm near both ends of the plate and a 20-mm hole near the center of the plate, as depicted in Figure 1a. An initial crack of 10 mm is located at the center edge of the plate. The plate is made from Aluminum 7075-T6 with a Young's Modulus of 71.7 GPa, yield strength of 469 MPa, the ultimate strength of 538 MPa, Paris' law coefficient, C = 5.27 \(\times\) 10\({}^{-10}\), Paris law exponent, m = 2.947, fracture toughness of 938.25 MPa mm 0.5, and a Poisson's ratio of 0.33. A 100 N load was applied at the top and bottom holes. The applied force is P = 20 kN with a stress ratio R = 0.1, and the behavior of the material is assumed to linear elastic. The initial mesh generated by Ansys is shown in Figure 1b, with an element size of 1 mm, generating 495,354 nodes and 348,892 elements. As seen in Figure 2, a straightforward comparison is made of the crack path simulated with ANSYS software on the present study, one from experiment [36], the other three from XFEM [36], XFEM with ABAQUS software [37], and by using XFEM with a controllable crack propagation strategy [38] as displayed in Figure 2a-d. It can be shown that the numerically obtained crack path agrees well with the predicted experimental path. Figure 1: (a) 2D and 3D geometric Details of the single edge cracked plate with a three-hole, (b) Initial mesh. The effect of thickness on fatigue crack growth parameters was investigated for this geometry using three different thicknesses, 4, 8, and 16. It is noticeable that there no influence of the geometry thickness on the crack extension trajectory. In contrast, there is a more significant influence on the stress and strain distribution as the thickness increased or decreased. Therefore, as thickness increases, the stress-strain field in the crack tip tends to change from the plane-stress state to the plane-strain state, meaning that the crack tip is in the tension state in all three directions and small scope the plastic zone will be limited. As the geometry thickness increases in a plane strain state, critical fracture toughness decreases, and brittle fracture is more likely to occur, which is much more dangerous than ductile fracture. Consequently, as the geometry thickness is increased, the equivalent Von-Mises stress and the maximum principal stress were decreased with approximately the same ratio  
Figure 2: Comparison of crack growth trajectory, (**a**) present study, (**b**) experimental observation [36], (**c**) numerical [36], (**d**) numerical [37], and (**e**) numerical [38]. as shown in Figure 3. Figure 4 illustrates the equivalent elastic strain distribution for the three different thicknesses and gives additional insight into the effect of thickness on mechanical properties. The equivalent elastic strains decreased as the thickness increased, approximately in the same proportion as the equivalent Von-Mises and maximum principal stresses, as seen in this figure. The stress concentration is greater at the crack tip on the right top of the hole, as shown in Figure 3. The other stress value, which is somewhat lower than the previous value, is concentrated on the mid-right of the hole, providing the continuity of the crack to grow until the right end of the specimen, similar to the experimental study. Figure 3: Equivalent Von-Mises stress and maximum principal stress distribution with different geometry thickness. Figure 4: Equivalent elastic strain distribution with different geometry thicknesses of 4 mm, 8 mm, and 16 mm, respectively. Figures 5 and 6 display the estimated values of the two SIFs modes, \(K_{I}\) and \(K_{II}\), respectively.