## 3 Results and Discussion
### Self-Piercing Riveted Joint of Vibration-Damping Aluminum and GA590 DP  
In this section, the quality of the self-piercing riveted joint formed between vibration-damping Al and GA590 DP is investigated. The cross-sectional views of the joints between the two materials are shown in Figure 9. Similarly to the previous section, three different types of die profiles (types A, B, and C), as shown in Figure 3, and two different panel configurations (vibration-damping Al on top and GA590 DP on the bottom, and vice versa), were used to form the joints. The figure shows that when the vibration-damping Al panel is on top ((a), (b), and (c)), good top panel penetration of the rivet is observed with minimal gaps between the two sheets comprising the vibration-damping Al. The figure also shows that marginal gaps are present within the top seal regardless of the die type  
Figure 8: Failure modes of self-piercing riveted joints formed between vibration-damping Al and Al5052-H32 with respect to the die types and the panel configuration: (**a,d**) die type **A**, (**b,e**) die type **B**, and (**c,f**) die type **C**. Figure 7: (**a**) The interlock width and the bottom thickness, and (**b**) tensile shear loads for the self-piercing riveted joint between vibration-damping Al and Al5052-H32 with respect to die types. used. When the vibration-damping Al panel is on the bottom ((d), (e), and (f)), the results show cavity formations between the rivet and the top GA590 DP panel. The formation of a cavity is a common phenomenon when the top steel panel is riveted with a bottom aluminum panel, since higher-strength steel undergoes an inadequate amount of plastic deformation during the riveeting process to completely fill the rivet head. The results show that the cavity can be reduced by using a protruded die; for example, a larger cavity is formed for the flat die type (d) while the size of the cavity is successively reduced as the protrusions become larger, as seen from (e) and (f). Nevertheless, the presence of cavities, as shown in the next paragraph, does not affect the strength of the joint. The cross-sections also reveal relatively large gaps within the top and bottom seals, which are especially evident in (d) and (f). The geometrical indexes (\(w_{l}\) and \(t_{B}\)) were measured for the joints, and the results are shown in Figure 10a. The figure shows that when the vibration-damping Al panel was positioned on top, \(w_{l}\) and \(t_{B}\) were 0.16\(\sim\)0.24 mm and 0.35\(\sim\)0.60 mm, respectively. For the case when the vibration-damping Al panel was on the bottom, \(w_{l}\) and \(t_{B}\) were 0.42\(\sim\)0.58 mm and 0.40\(\sim\)0.55, respectively. Figure 10: (**a**) The interlock width and the bottom thickness, and (**b**) the tensile shear loads of the self-piercing riveted joint formed between vibration-damping Al and GA590 DP with respect to the die type and the panel configuration. Figure 9: Cross-sectional images for the self-piercing riveted joint formed between the vibration-damping Al and GA590 DP with respect to SPR die type and panel configuration: (**a,d**) die type **A**, (**b,e**) die type **B**, and (**c,f**) die type **C**. To investigate the strength of the joints, tensile shear tests were performed, and the results are shown in Figure 10b. The figure shows that when the vibration-damping Al was positioned on top, the tensile shear load was approximately 2.6 kN for all three types of dies, indicating that there are no significant differences in joint strengths within the margin of error. When the vibration-damping Al panel was positioned on the bottom, the tensile shear load increased to approximately 3.6 kN for all three types of dies. Again, this shows that there are no significant differences in the strengths between the joints formed using different die types, yet the joint strength consistently increases by approximately 1 kN when the steel plate is on top. Such results can be attributed to the fact that the latter joints have larger interlock widths, as shown in Figure 10a.