# Experimental Evidence of Specimen-Size Effects on EN-AW6082 Aluminum Alloy in VHCF Regime
## 2 Materials and Methods
### Ultrasonic Fatigue Testing Machine  
The ultrasonic fatigue testing machine used in this work was developed by Italsigma(@) (UFTM MU90) and it is shown in Figure 1. The UFTM MU90 is equipped with an ultrasonic generator (Branson(@) DCX Series S 4 kW), which provides an electric signal at the piezoelectric transducer at 20 kHz (Branson CR-20). Therefore, thanks to the converse piezoelectric effect, the latter converts the electric signal in a sinusoidal mechanical vibration with the same frequency of 20 kHz. In addition, it is possible to vary the amplitude of the mechanical vibration of the piezoelectric converter in the 5.3-21.7 \(\upmu\)m range, by changing the output voltage setting of the ultrasonic generator. The piezoelectric converter is rigidly connected to a booster ([PERSON](@) 2000X Series Gold) through a screw connection, which provides fixed support to the whole mechanical system and amplification of the mechanical vibration equal to 1.5. Finally, a catenoidal horn (Branson(@) 126-192), characterized by an amplification factor of 2.0, is assembled in line with the booster with the aim of magnifying the displacement provided to the specimen, which is connected with an M6 screw. Therefore, the mechanical vibration is transmitted from the piezoelectric transducer to the specimen using the two mechanical amplifiers, so that an amplitude variable from 16 \(\upmu\)m up to 50 \(\upmu\)m is guaranteed at the free end of the specimen, where the maximum allowed value is evaluated in order to prevent unwanted failures of the horn. Furthermore, the mechanical vibration amplitude at the bottom of the specimen is monitored through an eddy current sensor (Micro-Epsilon(@) eddyNCDT 3300/3301) to keep the strain amplitude in the middle section of the specimen constant by adjusting the power setting of the ultrasonic generator. Notice that, since the piezoelectric transducer works in the 19.5-20.5 kHz range, all the components of the resonant system, as well as the specimen, must be designed in order to have an axial fundamental frequency included within the same interval. It is also worth noting that, when the fatigue crack propagates inside of the specimen up to a critical amount, the fundamental frequency falls below the lower limit of 19.5 kHz. Consequently, the test is automatically interrupted, since the piezoelectric transducer is no longer able to excite the mechanical components. Furthermore, an air-cooling system is used to control the temperature increment in the sample which could occur due to internal heat arising from high-speed deformations in ultrasonic fatigue tests [27]. At the same time, the temperature is monitored during the test with a pyrometer (Optris(@) CT LT22 CF), which is characterized by an accuracy of \(\pm\)1 \({}^{\circ}\)C, a resolution of 0.1 \({}^{\circ}\)C, and a measurable temperature range comprised between \(-\)50 \({}^{\circ}\)C and 975 \({}^{\circ}\)C. Besides, the ultrasonic fatigue testing machine (MU90) can operate discontinuously, in a pulse-pause mode, in order to  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Diameter** & \(\rho\) **(kg/m\({}^{3}\))** & \(E_{d}\) **(GPa)** & \(\sigma_{y}\) **(MPa)** & \(\sigma_{u}\) **(MPa)** & \(e_{u}\) **(\%)** & **Brinnel** \\
**of Bar** & \(\rho\) **(kg/m\({}^{3}\))** & \(E_{d}\) **(GPa)** & \(\sigma_{y}\) **(MPa)** & \(\sigma_{u}\) **(MPa)** & \(e_{u}\) **(\%)** & **Hardness** \\  & & & & & & **(HB)** \\ \hline
20 mm & 2713 & 72.3 & – & – & – & \(91\pm 1.4\) \\
30 mm & 2700 & 70.1 & \(357\pm 1.3\) & \(375\pm 0.2\) & \(11\pm 1.0\) & \(91\pm 1.7\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical and mechanical properties of the investigated EN-AW6082 aluminum alloy.  
avoid excessive heating of the specimen. Finally, the UFTM is equipped with a load cell able to provide a maximum constant preload of 1.5 kN, so that it is possible to carry out tests with non-zero mean stresses (\(R>-1\)).