# Nonlinear Impact Force Reduction of Layered Polymers with the Damage-Trap Interface
## 5 Discussion  
According to Equation (2), we find that the maximum impact force is a nonlinear function of impact energy. Figures 5 and 6 exactly show this trend of experimental data (mainly the first 70% impact energy ranges). Due to the contact stiffness difference between two kinds of polymers with and without the 5083 bonding, their maximum impact force is quite different as we expected. However, we lack enough material properties to provide a rough prediction using Equation (2). Usually, the adhesive manufacturers only provide very limited material data, because measuring the properties of pure adhesives in the form of thin and soft layers is always difficult [27; 28]. In Figure 5, we notice that the maximum impact force increases very slowly after impact energy exceeds 15 J. Therefore, for specific materials/structural designs such as impact resistance designs of new cell phones or cell phone cases, if their performance against low-speed or low-energy impact is satisfied, their further performance against high-energy impact would require much fewer efforts after a critical impact energy (15 J in this case). Of course, the above estimation needs detailed stress and deformation analysis of all potential impact energy ranges for the service requirements (i.e., cell phones' drop locations and heights). Figure 7 shows the baseline PMMA specimen after the impact of 12 J energy, and the specimen cracked throughout its thickness. On the other hand, at the same impact energy level, cracks were observed only on the top layer of the layered specimen as shown in Figure 8. Debonding was found on the adhesive layer of the layered specimen. By comparing Figures 7 and 8, it is noticed that for the baseline specimen, impact energy dissipation was polymer damage only, while for the layered specimen, impact energy dissipation included polymer damage and adhesion damage. To support this statement, we have also conducted impact experiments on the specimens without the adhesive layer, i.e., two PMMA layers were simply stacked together at the test section of the drop-weight impact machine. The clamping force applied by the clamp during testing keeps both the layers in place as mentioned in Section 2.3. Figure 9 shows the layered specimen without adhesion after impact, and we observed that both the top and bottom layers cracked after impact. Therefore, based on the three polymer designs as seen in Figures 7-9, we conclude that the adhesive layer dissipated some impact energy, reduced the maximum impact force, and saved the bottom layer from being damaged. Figures 10 and 11 show photos of the baseline and layered Polycarbonate specimens at the same impact energy of 120 J. No crack was noticed on the Polycarbonate specimens, but permanent plastic deformation was observed, and this was expected because Polycarbonate is much more ductile than PMMA. Figure 11 shows that debonding occurred around the impact site as additional energy dissipation. Figure 8: Layered PMMA specimen at 12 J impact energy (**a**) top layer and (**b**) bottom layer. Figure 7: Top view of a damaged baseline specimen at 12 J energy. Obviously, the reduction of the maximum impact force leads to less damage to the target [29,30]. On the other hand, it also causes less damage to the projectile. For some applications, this feature would be a win-win case. For example, failure of composite turbine blades is often caused by bird/bat strikes, and debris/hail impact [31]. Replacing or repairing these large wind blades is a very expensive and time-consuming task. The bird strike is becoming a key issue for major wind energy companies, because they not only have to repair or replace the damaged components sooner than economically feasible, but they  
Figure 10: Plastic deformation on a baseline PC specimen after impact (**a**) top view and (**b**) bottom view. Figure 9: PMMA Specim without adhesion at 12 J impact energy, (**a**) top layer and (**b**) bottom layer. are also being pursued to pay heavy fines for causing wildlife fatalities to the government.