# Probabilistic Analysis of Fatigue Behavior of Single Lap Riveted Joints
## 2 Materials and Methods  
Figure 1 shows the geometry of the specimen subjected to fatigue tests. It consists of two plates (260 mm \(\times\) 20 mm \(\times\) 1.2 mm sized), made of Alclad Aluminum 2024-T3 and overlapped for 60 mm. ASNA 2050 DCJ 032-04 rivets were used. They are made of 2117-T4 Aluminum with a diameter of 3.2 mm, a length of 7 mm and without countersink. The specimens were cut out from the 1.2 mm thick sheet in such a way that the applied axial load direction was perpendicular to the rolling direction of the sheet. This is consistent with the most common sheet orientations in a pressurized fuselage, considering that the hoop stresses affect axially the riveted joints. The rivet holes were drilled according to the diameters (d) and tolerances reported in the MIL-HDBK-5J (US Department of Defense Handbook, Metallic Materials and Elements for Aerospace Vehicle Structures, 2003) [21]. The riveting was carried out under load control, to achieve a rivet driven head diameter to the rivet shank diameter (_D/d_) ratio ranging between 1.3 and 1.6, which is a typical range for aerospace applications.  
The chemical composition of Al 2024 T3 aluminum is reported in Table 1 while the mechanical properties obtained by tensile tests are reported in Table 2 in terms of yield stress \(\sigma_{s}\), ultimate tensile stress \(\sigma_{r}\), Young's modulus \(E\) and percentage elongation \(Z\) with standard deviation (\(S\)).  
The fatigue tests were carried out at the University of Naples Federico II by using an Instron 8502 servo-hydraulic test machine (Figure 2a). Two hundred specimens were tested under tensile fatigue loads with stress ratio \(R\) = 0.05 and a frequency of 10 Hz. The load was applied perpendicularly to the rolling direction of the plate and three different levels of stress were considered for the tests: 90 MPa, 120 MPa and 160 MPa. 100 specimens were tested at a stress level of 90 MPa, while 50 specimens were tested for each of 120 MPa and 160 MPa stress levels. Figure 2b shows the testing machine grip system that ensures the perfect alignment of the specimens in all directions. Since life depends strongly on the riveting force, few preliminary fatigue tests were carried out in order to establish the global position of the _S-N_ curve. Successively, a low intermediate and high stress level was chosen for the tests. Life was defined as the number of cycles leading to the failure, assuming that life consumption by crack growth is short compared to the crack initiation period.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Material** & **Cu** & **Mg** & **Mn** & **Fe** & **Cr** & **Si** & **Ti** & **Zn** & **Al** \\ \hline Al 2024-T3 & 3.8–4.9 & 1.2–1.8 & 0.3–0.9 & \(\leq\)0.5 & \(\leq\)0.1 & \(\leq\)0.5 & \(\leq\)0.15 & \(\leq\)0.25 & Balance \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical composition of Al 2024 T3 (wt%).  
Figure 1: Test article geometry.  
In order to analyze the surface of fracture, some specimens were cut by using a low speed, water-cooled, sectioning machine REMET MT60 and submitted to microscopic analysis. The fracture surfaces were inspected with stereo-microscope LEICA MZ12 with a magnification of 5x.