# Ultrasonic VMCF Tests on Very Large Specimens with Risk-Volume Up to 5000 mm+
## 1 Introduction  
Design methodologies for structures and components subjected to static or cyclic loads have the main objective of preventing failures or minimizing the risk of failures. According to International Standards, the material strength against static or fatigue failures is generally assessed through laboratory tests on small specimens with standard geometries. The size of components is, however, significantly larger than that of specimens commonly tested, and the material strength, as well as the stress gradient [1], in the most stressed region is size-dependent. This is known as size-effect, and it must be properly considered for the structural integrity of components [2], particularly when components are subjected to fatigue loads in service. Size-effects have been extensively investigated in the literature, in the case of High-Cycle Fatigue (HCF) response of metallic materials. It is mainly caused by the variation of the stress gradient within the so-called process-zone from specimens, with small volumes, to components, characterized by larger volumes. Secondly, the probability of weak sites (e.g., microstructural discontinuities) increases with larger process-zones, thus inducing a reduction of the HCF strength [3]. International Standards prescribe how to deal with size-effects when components subjected to HCF loads are to be designed. On the other hand, size-effects in the Very-High-Cycle Fatigue (VMCF) region (i.e., the region below the conventional fatigue limit and above \(10^{7}\) cycles) represent an almost unexplored research field. It is well-known that the fatigue crack in the VMCF region generally originates from the largest defectpresent within the volume of stressed material (risk-volume). Size-effects in VHCF are associated to the random distribution of the defect size within the risk-volume, denoted as V\({}_{90}\) and defined [3] as the volume of material subjected to a stress amplitude above the 90% of the maximum applied stress. According to [3], the probability of defects with larger size increases with the risk-volume, thus inducing a reduction of the VHCF strength. [PERSON] [3] proposed a methodology for predicting the most critical defect in the component volume based on inclusion inspections on polished metallographic samples. In [4], the size-effect was investigated by performing ultrasonic VHCF tests (load frequency of 20 kHz) on hourglass specimens with small V\({}_{90}\) (33 mm\({}^{3}\)) and on dog-bone specimens with larger V\({}_{90}\) (912 mm\({}^{3}\)). Experimental results showed that a significant decrement of the VHCF response occurs when increasing the tested V\({}_{90}\). The non-uniform distribution of the stress amplitude in dog-bone specimens [5] prevented from a more extended investigation of size-effects on larger risk-volumes in [4]. For this reason, the authors [6] proposed a new specimen geometry, the so-called Gaussian specimen, which permitted them to significantly increase the maximum testable V\({}_{90}\) with ultrasonic machines. In [7], the authors carried out tests on hourglass and Gaussian specimens with V\({}_{90}\) of 294 and 2300 mm\({}^{3}\), respectively. The investigation was made on specimens made of an AISI H13 steel before and after the ElectroSlag Remelting (ESR) process. Both materials evidenced a significant size-effect, which was more relevant in the case of the unrefined H13 steel. In [8], ultrasonic VHCF tests were carried out up to 10\({}^{10}\) cycles on Al-Si-Cu hourglass specimens with increasing diameter, from 3 to 6 mm. In the present research, ultrasonic VHCF tests up to 10\({}^{9}\) cycles were carried out on Gaussian specimens made of an AISI H13 steel. The tested risk-volume, about 5000 mm\({}^{3}\), was two times larger than the largest tested in the literature. Fully reversed tension-compression tests were carried out with the ultrasonic testing machines developed at Politecnico di Torino.