# Experimental Evidence of Specimen-Size Effects on EN-AW6082 Aluminum Alloy in VHCF Regime  
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[PERSON]  
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resistance in the ultralong life regime. In fact, VHCF tests are commonly performed on specimens with a standard diameter of 3 mm, so that the fatigue resistance of full-scale components has to be extrapolated through theoretical models, which nevertheless have not yet been fully validated experimentally by using ultrasonic fatigue testing machines. To this aim, [PERSON] [9] performed VHCF tests on high-strength steel specimens with a diameter in the middle cross-section ranging from 3 mm up to 8 mm. From these experimental campaigns, he found that the larger the risk volume, the lower the fatigue limit, where the risk volume is usually defined as the region where the stress is higher than the 90% of the peak value [10; 11]. Moreover, [PERSON] et al. [12; 13] found that the internal fatigue cracks origin is the largest defect within the risk-volume. In addition, the probability to find defects with larger sizes increases with the risk-volume, so that a decrease in the fatigue resistance in the VHCF region can be expected. A few years ago, [PERSON] et al. [14; 15; 16] designed an innovative specimen shape with a Gaussian profile, which can be used to enlarge the risk volume of the specimen. Therefore, they were able to test a high-strength steel, AISI H13 steel, and to analyze results from a wide range of different risk volumes from 194 mm\({}^{3}\) up to 2300 mm\({}^{3}\)[17; 18]. More recently, in order to increase the range of tested risk volume, the same authors carried out VHCF experiments on AISI H13 steel hourglass and gaussian samples with risk volumes of 55 mm\({}^{3}\) and 5000 mm\({}^{3}\), respectively [19]. [PERSON] et al. [20; 21] also investigated the VHCF response of SLM AlSi10 Mg and SLM Ti6 Al4V gaussian specimens with a large loaded volume, pointing out that specimen-size effects on the VHCF region are observed in non-ferrous metallic materials, like aluminum alloy, as well. [PERSON] et al. [22] performed fatigue tests on Al-Si-Cu cast alloy specimens of different sizes beyond \(10^{9}\) cycles with an ultrasonic fatigue testing machine operating at 20 kHz and \(R=-1\). Firstly, they observed that pores within the material act as a preferential site for the fatigue crack initiation. Secondly, they observed experimentally that, for a certain number of cycles, the larger the risk volume of the specimen, the lower the fatigue life. In the present investigation, fully reversed ultrasonic fatigue tests up to \(10^{9}\) cycles were performed on hourglass specimens made of EN-AW6082-To aluminum alloy, which is characterized by good tensile strength, weldability, and an excellent corrosion resistance. Furthermore, in order to investigate the specimen-size effects on this material, three different dimensions of specimens were considered, with diameter ranging between 3 mm and 12 mm. Firstly, the optimal geometry of the specimens was designed based on numerical finite element simulations. Secondly, strain gauge calibrations were carried out before the tests to validate the assumed stress distribution in the designed hourglass specimens. Furthermore, the experimental results were analyzed, and P-S-N curves were obtained for the three different specimens. Finally, by exploiting lacunar fractality concepts [23], the specimen-size effect on fatigue resistance was theoretically assessed, and scale invariant generalized P-S\({}^{*}\)-N curves provided.