## 3 Results
### Numerical Simulations
The value of the stress concentration factor for four distinct pore geometries was determined using an elastic FE model under uniaxial loading conditions and a Poisson's ratio of 0.324. It demonstrates that Poisson's ratio influences the stress concentration factor in three-dimensional geometry. As shown in Figure 22a, the stress concentration factor increases as the distance between the pore and the free surface decrease below the pore diameter. Figure 22b,c illustrates the stress distribution for subsurface pores under unit stress application. Lastly, the stress concentration factor was also high for an internal oblate spherical pore. This shows that the shape of the pore also has a big effect on the local stress concentration factor. Figure 20: The distribution of maximum principal stresses around the 0.4 mm notch for the loading case B2. Reprinted with permission from ref. [71]. 2022, Elsevier. The distribution of the Crossland fatigue indicator parameter (FIP) for three geometries is shown in Figure 23. In terms of FIP localization, it is evident that Schwartz cells substantially localize FIP in their central zone, but gyroids do not. In the latter instance, the FIP localizes to a single cell branch. In contrast, the diamond cell provides for a more uniform distribution of the stress field over the whole volume of the cell. It is surprising to see that the two cells with the highest FIP localization have the lowest fatigue resistance. Figure 21: Fatigue failure surface of **(a)** diamond structure, **(b)** rhombic dodecahedron, and **(c)** truncated cuboctahedron structure. Reprinted with permission from ref. [57]. 2015, Elsevier. Figure 22: Subsurface pore of diameter d: (**a**) stress concentration factor, Kt vs. distance, x to free surface (point A, marked as dot), (**b,c**) overall model (top left corner) and enlarged view of local stress distribution under applied unit stress in the Z-X plane; x = 0.2 d, Kt = 2.52 in (**b**), x = 0.5 d, Kt = 2.18 in (**c**). Reprinted with permission from ref. [77]. 2018, Elsevier. During the computational area of numerical simulations, initial material conditions are considered to be loaded for elastic and plastic deformation. As seen in Figure 13, a Von-Mises stress contour map has been constructed to comprehend the stress distribution throughout the specimen. A sectional view (Figure 24b) gives a better understanding of the essential stress fluctuation near the fracture tip along the direction of the crack's thickness. The critical zone (Figure 24b) in the fracture area of the CT specimen indicates that crack growth started near the crack tip. When it exceeds the fracture toughness value, it becomes unstable. So, it seems likely that the results of the simulation and the experiment are similar. The XFEM is an efficient approach for resolving fracture mechanics issues, namely the elastic-plastic crack development behavior for a wide range of engineering materials. Figure 25a depicts the results of a simulated tensile test, with a magnified view showing the crack initiation, propagation, and ductile fracture at the alloy gauge section. At the commencement of necking, clusters of micro-voids and interfacial non-connected cracks collect towards the secondary phase, resulting in the production of small-sized cracks. Furthermore, as plastic straining increases, these fractures spread and are primarily responsible for the specimen's central weakening at the necking regime. This phenomenon is well modeled by the XFEM simulation seen in Figure 25a. It is obvious from the data that the plasticity is accommodated by plastic straining in the tensile curve, and this phenomenon of ductile tearing is also visible in the magnified image of the tensile failed specimen. The stress-strain curve is compared to the graph in Figure 25b. Excellent agreement exists between the simulated and empirically determined curves. Figure 23: Crossland FIP distribution on the three different lattices. (**a**) Gyroid, (**b**) Diamond, (**c**) Schwartz. Reprinted with permission from ref. [83]. 2020, Elsevier.