## 2 Materials and Methods  
### Material and Testing Devices  
Experimental tests were carried out on an adhesively bonded cylindrical butt joint that was 14.6 mm in diameter. Aluminum 7075 T6 composed the cylindrical substrates that were bonded together with a thin 0.3 mm layer of bi-component SikaPower(r)-1277 epoxy resin. This adhesive is adopted for bonding structural components in transportation and general industry. Its characteristics make it a good choice for repair purposes in combination with spot welding or riveeting. Glass spheres were pre-mixed by the producer in the resin tube, and these are responsible for maintaining the 0.3 mm thickness. In Table 1, the mechanical properties of the adopted material for both design and testing purposes are collected. These properties were extracted through specific preliminary tests or extracted from published scientific works [50; 52]. Six specimens of aluminum 7075 T6 and six specimens of SikaPower(r)-1277 epoxy resin were tested in compliance with [53; 54], respectively, whereas values for Ti-6 Al-4V were already known from a past study [50]. The viscosity value was assumed to be valid based on the datasheet [55] and no additional tests were performed regarding the variation in the quantity with respect to the temperature. Extracted values for SikaPower(r)-1277 refer to a hardening period of 24 h at 23 \({}^{\circ}\)C, as suggested by the adhesive supplier. The capability of sustaining and transmitting loads between Aluminum 7075 T6 and SikaPower(r)-1277 epoxy resin was assessed in [43], where dedicated tensile tests were performed at 2.5 mm/min. The load-displacement curves were comparable, and processed stress data were in line with those extracted from the bulk adhesive in Table 1. Moreover, specimens failed fully cohesively without the macroscopic presence of adhesive detachments, further validating the test results. The adopted experimental equipment for performing VHCF tests was an ultrasonic fatigue testing machine (UFTM). The UFTM is shown in Figure 1 and was developed at Politecnico di Torino for testing components in the chosen fatigue range. The UFTM can perform tests at 20 \(\pm\) 0.5 kHz under fully reversed tension-compression stress (\(R=-1\)), which significantly reduces the testing time compared to conventional testing apparatuses. To perform fatigue tests, the UFTM adopts the following devices: (i) an electric generator (Branson DCX 4 kW, not visible in Figure 1) which generates an electrical sinusoidal wave at 20 kHz; (ii) a piezoelectric transducer, responsible for converting the electrical wave into a mechanical vibration; (iii) a booster and a horn made of Ti-6 Al-4V that amplify and convey the vibration to the specimen under testing; (iv) the specimen under investigation, which was designed for the UFTM resonance conditions; (v) a laser displacement sensor that measures the displacement at the specimen free end; (vi) vortex tubes to keep the temperature controlled in the range (20-24) \({}^{\circ}\)C; and (vii) a temperature sensor to observe the temperature evolution during the test execution. Performing fatigue tests with the UFTM consists of the application of alternated stress in specimens that are designed to work in resonance conditions. The specimen and the vibration components are thus designed to have a resonance frequency corresponding to a longitudinal mode of vibration close to 20 kHz. Moreover, the UFTM adopts a closed-loop proportional-integrative-derivative (PID) control logic where the displacement measured