## 4 Conclusions  
The VHCF response of SLM AlSi10 Mg specimens built in a vertical direction was experimentally assessed in the present paper. Ultrasonic tension-compression tests (stress ratio of -1) were carried on as-built (mechanically polished) Gaussian specimens with large risk volume (2300 mm\({}^{3}\)). The main results can be summarized as follows:  
1. The quasi-static mechanical properties were larger than those of the cast parts and close to those reported in the literature.
2. VHCF failures originated from defects (defects due to an incomplete fusion and defects due to an improper layer bonding) concentrated in a region of material close to the specimen surface (1.1 mm distance from the specimen surface). Since the VHCF response is driven by the defect size, a significant enhancement of the VHCF behavior could be achieved by optimizing the process parameters that permit to minimize the defect size.
3. The 0.1% P-S-N curve was shown to be below all the experimental failures and proved to be a possible reliable choice for designing AM parts. On the other hand, for horizontally as-built AlSi10 Mg specimens, the 1% P-S-N was below all the experimental failures. Therefore, the large VHCF scatter of vertically built specimens implies a more conservative choice for the design curve to avoid unexpected failures due to rare critical defects.
4. The scatter associated to the VHCF response, significantly larger than that of tests carried out on machined hourglass specimens, was mainly related to the specimen conditions. The tested Gaussian specimens were not machined and, therefore, surface defects due to incomplete fusion or improper layer bonding, whose size was characterized by a large dispersion, were not removed and contributed to increase the experimental scatter of the VHCF response.  
The tested risk volume, significantly larger than the largest risk volume tested in the literature, also contributed to increase the scatter of the experimental results. According to the size effect, in larger risk volumes, the probability of finding large and rare defects at the origin of the fatigue failures increases, with a consequent increment of the defect size range and, accordingly, of the scatter of the experimental failures.
* The surface region is critical for the VHCF response of vertically built AlSi10 Mg parts. The removal of a layer of surface material does not significantly affect the average VHCF strength, but it permits us to reduce the experimental scatter and, therefore, to increase the VHCF strength for the same required reliability.  
[PERSON] supervised the research, suggested the adopted models, and reviewed the manuscript; [PERSON] carried out the VHCF tests at PoliTO, analyzed the VHCF test results, and wrote the paper; [PERSON] performed the static mechanical tests, the microstructural and fractographic analysis at CNR, and made additions to parts of the manuscript; [PERSON] supervised the preparation of SLM prints and made additions to parts of the manuscript; [PERSON] supervised the work and reviewed the full manuscript; [PERSON] reviewed the full manuscript; [PERSON] supervised the work and made additions to parts of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.