## 3 Results
### Analysis of the Critical Defects  
The location of the defects originating the fatigue failure is analyzed. Figure 4 shows the distribution of the critical defect size along the axial and radial directions. The effect of defects on the VHCF response and a detailed comparison of the VHCF life found in the present paper and in [22] will be carried out in Figure 8.  
According to Figure 4, all the experimental failures are concentrated near the specimen surface, in a region with radial distance, with respect to the surface below 1.1 mm. The external region in as-built specimens is the most critical region, with respect to VHCF failures for vertically built specimens. Figure 3: S-N plot of the experimental results: (a) \(s_{center}\) with respect to \(N_{f}\); (b) \(s_{local}\) with respect to \(N_{f}\). The same occurs in horizontally built specimens, for which the most critical region is near the region where the supports are removed [20]. As for the axial distribution, defects are randomly distributed within the risk volume \(V_{90}\) (volume of material subjected to a stress amplitude larger than the 90% of the largest applied stress). This analysis highlights the importance of testing large risk volumes, which permit a more reliable assessment of the critical defects and VHCF behavior. It is worth noting that surface or subsurface defects are characterized by a larger stress intensity factor (SIF) than internal defects, according to [29], thus confirming that an external surface free of large defects would enhance the VHCF response. Thereafter, the type of defects originating the fatigue failures are investigated. Three types of defects, described in [38; 39; 40], were mainly observed in bulk SLMed aluminum products: Metallurgical pores, originating from gas entrapment, defects caused by an incomplete fusion of powder, and defects induced by insufficient adhesion between successive layers. Two types of defects were found at the origin of the fatigue failures: Defects due to an incomplete fusion and defects due to an improper layer bonding, as shown in Figure 5a,b, respectively. In contrast to [22], no pores originating failure were found. However, non-critical spherical pores with a smaller size, shown in Figure 5c, were observed at a larger distance from the specimen surface. The different type of defects at the origin of the fatigue failures could be explained by considering the specimen post-process machining. Defects due to an incomplete fusion and due to an improper layer bonding is mainly concentrated in a region close to the specimen surface, but in [22] this critical region of material was removed through machining. After machining, internal pores become critical surface defects, which induce VHCF failures. Moreover, a larger building platform temperature was considered for specimen production in [22] (50 \({}^{\circ}\)C higher than in the present investigation), which yielded an expansion of the gas within the pores and increased their size. The pore population therefore was not analyzed in detail, since the main objective of this work is to investigate the critical defects, i.e., the defects which originate the fatigue crack and which control, therefore, the VHCF response. It is worth noting that, if the testing conditions change and pores become the critical defects, their effect on the VHCF response should be analyzed in detail. Figure 4: Distribution of defects along the longitudinal and radial directions. Figure 5: _Cont._  
The effect of the defect size was then investigated. In order to compare defects characterized by different morphology and chemical composition, the equivalent defect size \(\sqrt{a_{c}}\), was considered. Figure 6 plots \(\sqrt{a_{c}}\), measured according to [16; 29], with respect to \(N_{f}\). According to Figure 6, \(\sqrt{a_{c}}\) decreases with the \(N_{f}\).