## 3 Results
### Fatigue Properties
\[\frac{\Delta\gamma_{\text{max}}}{2}\bigg{(}1+\text{k}\frac{\sigma_{\text{n}}^{ \text{max}}}{\sigma\ y}\bigg{)}=\gamma^{\prime}_{\text{f}}(2\text{N}_{\text{f}}) ^{\text{c}_{0}}+\frac{\tau^{\prime}_{\text{f}}}{\text{G}}(2\text{N}_{\text{f}}) ^{\text{b}_{0}}. \tag{1}\]  
\(2\text{N}_{\text{f}}\) fatigue life cycle. Figure 8.0  
\(\sigma_{\text{f}},\ \dot{\varepsilon}_{\text{f}}\) are the fatigue strength, and fatigue ductility, and, (b, c) are the exponents. This model is suitable for materials or circumstances that exhibit mode I fatigue failure mode. The connection between fatigue life and elastic strain range can be calculated by [PERSON]'s equation given by Equation (3). Figure 8.1  
\(\varepsilon_{e}^{a},\ \text{is the elastic strain amplitude, fatigue strength coefficient, and fatigue strength exponent. Figure 13 shows the fatigue life data for specimens with and without notches (b). Estimates from the FS and SWT models are shown as blue squares and green triangles, respectively. The SWT findings were not conservative and diverged even more with increasing fatigue life. A similar tendency was seen with the FS model, but with a considerably smaller divergence towards the nonconservative side. By increasing the size of the hole to 1 mm, the SWT findings become more conservative than those of the FS model. Using the critical plane approach, the fatigue life and fracture development angles were computed. The fatigue life of the specimens with stress concentrators was more conservative. Compared to the FS model results, the SWT model's behavior at lower load levels was less conservative. However, the modified FS model obtained better approximations than the SWT model, even when the critical plane on which fatigue damage had been obtained did not coincide with the appearance of cracks at high cycles. Compared to the FS model, the critical planes of the highest primary strain from the SWT model were closer to the experimental ones. The SWT model seems to have a longer fatigue life. In contrast, the FS model showed the material is more suitable for the material at both low and high-cycle fatigue. According to the S-N data shown in Figure 14, the specimen with the greater yield stress (horizontal orientation) demonstrated a shorter fatigue life. The vertical yield stress is 16% less than  
Figure 8.2 Parameter k in a Fatemi–Socie model for 18 Ni300 managing steel. Reprinted with permission from ref. [71]. 2022, Elsevier. the uniaxial fatigue strength [72]. The fatigue life and elastic strain also can be calculated by Basquin's Equation (4). Figure 8.3  
Figure 8.4 Fatigue test data for ER70S-6 specimens under (**a–c**) uniaxial, (**d–f**) torsion, and (**g–i**) multiaxial loading conditions. Reprinted with permission from ref. [73]. 2022, Elsevier. Figure 8.5 Fatigue life estimation of Fatemi-Socie and Smith–Watson–Topper and critical plane models contrasted with the experimental life found for 18 Ni300 steel. (**a**) Unnotched specimen, (**b**) notched specimen. Reprinted with permission from ref. [71]. 2022, Elsevier. As shown in Figure 15 for AM Ti6 Al4V, using this critical length while applying the TCD method [74] yields very excellent correlations between the notched and unnotched data within the scatter band of \(\pm 3\). Figure 15 shows correlations between multiaxial notched and unnotched data for as-fabricated, surface-annealed Ti6 Al4V specimens (c). While the data for other loadings are strongly linked within scatter bands of \(\pm 3\), the torsion data deviate from the other data as life increases. This is due to the stair-stepping effect along the perimeter of the hole, which results in larger stress concentrations on the upper half of the notch's perimeter, which may lead to a shorter lifespan under torsional loading. The total strain energy is expressed by the Coffin Manson Equation (5).