# Ultrasonic VMCF Tests on Very Large Specimens with Risk-Volume Up to 5000 mm+
## 4 Conclusions  
In this paper, ultrasonic Very-High-Cycle Fatigue (VHCF) tests at a loading frequency of 20 kHz were carried out on Gaussian specimens with very large risk-volumes, above 5000 mm\({}^{3}\). The geometry of the specimens made of a H13 steel subjected to an ElectroSlag Remelting (ESR) process was analytically defined, verified through Finite Element Analyses (FEA) and validated through a strain-gage calibration. Fully reversed tension-compression tests were carried out up to 10\({}^{9}\) cycles on Gaussian specimens and also on small hourglass specimens characterized by a risk-volume of 55 mm\({}^{3}\), to highlight and discuss size-effects in VHCF. The main results can be summarized as follows:  
1. Ultrasonic VHCF tests on Gaussian specimens with very large risk-volumes above 5000 mm\({}^{3}\) are feasible. The strain-gage calibration validated the stress distribution assessed through FEA  
Figure 9: Gumbel plot of the defect size for hourglass specimens (blue points are experimental values; the solid blue curve is the estimated LEVD) and Gaussian specimens (green points are experimental values; the dashed blue curve is the estimated LEVD from hourglass data).  
and confirmed that no spurious bending loads are present, even by significantly enlarging the risk-volume.
2. Fatigue failures were uniformly distributed within the risk-volume in Gaussians specimens, whereas they were more concentrated close to the surface for small hourglass specimens, mainly due to the different stress gradients and stress distributions within the risk-volumes of the two specimen types.
3. The median P-S-N curve for a risk-volume of 5000 mm\({}^{3}\) was predicted by considering the experimental results on hourglass specimens with a statistical model proposed by the authors. The predicted median curve was found to be above the experimental P-S-N curve. The main reason was that the distribution of defects size, assumed to follow a Largest Extreme Value Distribution (LEVD), was not capable of accurately predicting the largest defect for the risk-volume of Gaussian specimens. The prediction error was mainly due to the fact that the estimated LEVD did not take into account the stress gradient within the specimen risk-volume. A statistical distribution of defect size capable of considering the stress gradient would permit us to more properly predict the defect size within the component volume and, accordingly, the VHCF response.
4. Experimental results pointed out that larger tested risk-volumes lead to a more reliable design against VHCF failures. Very large tested risk-volumes allow for a more proper assessment of the critical defect size and of the P-S-N curves for components in service conditions.  
[PERSON] designed the specimens, performed the calibration and the experimental tests, analyzed the data and wrote the paper. [PERSON] supervised the research, suggested the adopted models and reviewed the full manuscript. [PERSON] reviewed the full manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.