# Ultrasonic VMCF Tests on Very Large Specimens with Risk-Volume Up to 5000 mm+
## 3 Results
### Fracture Surfaces and Defect Analysis  
At first, the distribution of defects within the risk-volume was analyzed. The location of defects in the radial direction was measured through digital image processing of the fracture surface images obtained by using the optical microscope (Leica Z16 APO A) and the SEM; meanwhile, the location of the defect along the longitudinal direction was measured by using a digital caliber with a nominal resolution of 0.01 mm. Figure 5 shows the distribution of defects within the risk-volume of hourglass specimens (Figure 5a) and Gaussian specimen (Figure 5b). In the following, the defect at the origin of the fatigue failure is called \"critical defect\". According to Figure 5, critical defects in hourglass and Gaussian specimens were randomly distributed within the risk-volume, but in hourglass specimens, they were mainly concentrated near the specimen surface, with all but one of the defects at a distance from the surface smaller than 0.8 mm. On the other hand, critical defects in Gaussian specimens were more internal and more uniformly  
Figure 4: S–N plot of the experimental dataset. Figure 5: Critical defect distribution: (**a**) hourglass specimens; (**b**) Gaussian specimens. distributed within the risk-volume. This can be explained by considering, for the two specimen types, the different stress gradients and stress distributions within the risk-volume. Moreover, one failure in hourglass specimen and one failure in Gaussian specimens originated from a defect outside the \(V_{90}\) region, for stress amplitudes equal to the 83% and the 88% of the maximum stress amplitude. Figure 6a shows an example of a typical fracture surface found both in hourglass and in Gaussian specimens and observed with the optical microscope (Leica Z16 APO A): in particular, it is shown the fracture surface of a Gaussian specimen. All but one fracture surfaces showed a fish-eye morphology, with the initial defect surrounded by a Fine Granular Area (FGA). Figure 6b shows an example of the initial defect (spherical inclusion) originating the fatigue failure, observed with the SEM. In almost all the fatigue failures with a fish-eye morphology (22 out of 28), the initial defect was a spherical inclusion with regular shape, whereas in 6 out of 28 failures, the initial defect showed a more irregular morphology. EDX (EDAX Genesis) analysis was also performed and confirmed that all the initial defects were oxide inclusions with high percentage of Al, Ca, Si and, in some cases, S. Figure 6c shows an example of a typical EDX spectrum taken at the center of an inclusion originating the fatigue failure. Further detailed analyses on the chemical composition of the inclusions originating the fatigue failures were not carried out, since, according to [3], the defect size mainly controls the VHCF response, with the chemical composition having a limited influence. Therefore, since one of the main objectives of the paper was to validate the methodologies proposed to deal with size-effects in VHCF (Section 3.5), the EDX was carried out to qualitatively verify if the critical inclusions in hourglass and in Gaussian specimens were similar, without focusing on their origin and chemical composition, which is out of the scope of the present paper. Figure 6: Fracture surfaces and analysis of defects: (**a**) fish-eye fracture in Gaussian specimen (optical microscope); (**b**) example of a spherical inclusion originating failure (SEM image); (**c**) typical EDX spectrum taken at the center of an inclusion originating the fatigue failure. The sizes of the critical defects were also compared. According to [3], the defect size, \(\sqrt{a_{d,0}}\), mainly affects the VHCF response, provided that an \"equivalent defect size\" is considered when dealing with defects with irregular morphology and shape. Accordingly, the equivalent defect size for non-spherical inclusions was assessed by following the indications in [3; 14]. Table 2 reports the defect sizes in hourglass and Gaussian specimens.