## 3 Experimental Results  
Fifty-five specimens were tested under the stress range from 10-19 MPa. Fatigue experiments were performed at 20 kHz using the UFTM and at 5, 25, and 50 Hz using the Instron(r) 8801 servo-hydraulic testing machine. A standard procedure suggested by the adhesive manufacturer was followed to obtain the highest adhesive strength. In particular, abrasive sandpapers were used to prepare the substrate surface to increase the surficial roughness, followed by a cleaning phase with acetone for removing the aluminum powder and impurities. The thin layer of adhesive was thus applied between the substrates and spread to reach a uniform bonding area. Suitable alignment devices were designed to guarantee the substrate co-axiality. The joint curing required one day under a constant load at room temperature and, once the adhesive was fully dried, the surplus was removed from the substrate edges with a cutter. In this way, it was possible to maintain the 0.3 mm adhesive layer without resin concentration effects on the experimental results. In Figure 9, the testing configurations are reported. Figure 9a depicts the UFTM testing conditions whereas Figure 9b shows the low-frequency testing configuration. Specifically, fatigue tests at conventional frequencies were performed by joining the two long non-singular bars and clamping them in the Instron(r) grips. Experimental tests were carried out up to failure or to a run-out threshold equal to \(10^{9}\) cycles in ultrasonic VHCF tests and to \(2\times 10^{6}\) cycles in servo-hydraulic low-frequency tests. This difference is mainly attributable to the testing time required by the hydraulic machine working below 100 Hz, which is unable to test specimens in VHCF within a reasonable timeframe. Both cohesive and mixed adhesive-cohesive failures were observed at the end of the testing campaign; nonetheless, only fully cohesive failures were accepted as valid failures in the S-N diagram shown in Figure 10. Indeed, adhesive-cohesive failures in both the VHCF and HCF ranges were associated with a very short fatigue life compared to the fully cohesive failures. In general, a specimen is considered failed when there is a complete separation between the two bars for both ultrasonic and low frequency configurations. However, specifically for VHCF tests, failure is also considered when the longitudinal frequency of the mechanical system falls below 19.5 kHz, which is outside of the UFTM operative range. In this circumstance, the internal crack nucleates and propagates without a complete splitting between adherends, and an extra load (manual or automatic) is applied to separate the elements. According to Figure 10, the frequency rate effect is clear. Indeed, the fatigue response is significantly different depending on the testing frequency. Specimens obtained through ultrasonic fatigue tests are characterized by significantly longer fatigue lives compared to those of specimens tested at lower frequencies. Experimental run-outs from (13-15) MPa were found for five samples in ultrasonic VHCF tests, whereas only one, at 10 MPa, was observed for 25 and 50 Hz frequencies. These experiments highlight an important frequency effect for the whole fatigue data distribution and, in general, a high sensitivity to excitation frequency for the SikaPPower(r)-1277 adhesive. VHCF tests were carried out under temperature-controlled conditions, as mentioned in Section 2. Accordingly, possible self-excited temperature effects were excluded, as well as significant changes in the adhesive joint properties that could have influenced the test outcomes. Indeed, it was numerically demonstrated in [50] that for the investigated stress  
Figure 10: S–N data from VHCF and HCF experiments. Figure 9: (a) VHCF test configuration [43]; (b) HCF test configuration. range the thermal increment within the adhesive layer was limited and remained in an acceptable range for testing adhesive joints.