# A Sensitivity Analysis of the Damage Behavior of a Leading-Edge Subject to Bird Strike
## 4 Sensitivity Analysis
Figure 10: Ductile criteria envelope for starting, best and worst configuration at different time steps. Figure 11 reports the time history of displacement at the skin apex (impact point) and the distance between the external ribs, for starting, worst and best configuration. The starting configuration is subject to the maximum deformation that it is achieved at about 9 ms. After this time step the structure is able to recover, partially, the deformation by elastic spring back. The data related to the worst case are not realistic, since the bird penetrate the skin thus their evolution stop at penetration time step. The best configuration allows to obtain a clear reduction in maximum apex displacement, about 50%, and a more relevant reduction in tip web displacement. In order to compare the three reported configurations, the time-history of the energy balances are reported, calculated globally and for each part. In particular, in the following, the internal energy (internal energy = energy of elastic deformation + energy of plastic deformation + energy of damage + other minor contributions), the plastic deformation energy, and the damage energy are reported. The evaluation of these results helps to better understand how the configuration change contributes to modify the dissipative forms of energy. Figure 12 shows the internal energy for the two components of the test article, which are the skin and the two ribs. It is clear that the two ribs contribute in a minimal way to the energy dissipation; therefore, the maximum value is about 0.8% of the total energy (about 30 kJ). As the configuration changes, this value decreases and, in particular, assumes the minimum values for the worst configuration. In this case, having a sudden failure and a complete perforation of the projectile, the remaining parts have no capability to withstand large deformations and therefore to dissipate a considerable amount of energy. This highlights that the remaining parts of the test article structure have a negligible influence on overall performance. Comparing the internal energy of the three configurations, it is clear that the starting configuration shows a higher capability to absorb impact energy; therefore, the internal energy is greater than the other two configurations. The best configuration has an internal energy level smaller than the starting configuration, mainly due to the bigger stiffness related to the thicker face. Thus, the plasticized area is smaller than the ones related to the starting configuration, as reported in Figures 13 and 14, too (the plastic energy represents about 90% of the internal energy). This aspect is confirmed in Figure 10, which shows a larger plasticized area in the starting configuration. Moreover, the amount of dissipated energy can be verified by looking at the projectile rebound at the end of the simulation: the smaller is this, the higher is the structure dissipated energy. Obviously, in the worst configuration, no rebound occurs since the projectile totally penetrates the skin. Figure 11: (**A**) Time-history of the displacement along impact direction of the skin central point; (**B**) tip web distance time-history. Figure 13 shows the dissipated/absorbed energy of the entire test rig (mainframe, interface fame and upper and lower beam), classified by plastic energy, elastic energy and internal energy. The plastic energy represents the energy dissipated by plasticization, which starts at the yield point and finishes at the strength limit (it is possible to define it as stress or strain value, and it depends on the adopted criteria). After this point, the software starts to calculate the energy dissipated by damage phenomena that are not instantaneous. The damage starts by the strength limit and finishes at the maximum allowed strain (that can be calculated, setting the total strain energy up to total failure) [26; 27]. In this case, since no other dissipative phenomena occur, the internal energy of the test rig should be equal to the sum of the plastic and elastic energy.