Ballistic impact response of 2024-T 3 monolithic aluminum plates : prediction and comparison with GLARE 4 A fiber-metal laminates

This article deals with the evaluation of the ballistic resistance of aluminum plates subjected to high velocity impact by a rigid cylindrical projectile. Important impact variables such as the ballistic limit, the ballistic energy and the impact load time history are predicted using the ANSYS LS-DYNA software. A comparison with the ballistic resistance of GLARE 4A fiber-metal laminated plates is also implemented. The time history of the transient impact load of the collision on the aluminum targets is analyzed and useful conclusions are drawn. It is found that the ballistic limit and the ballistic energy of aluminum and GLARE 4A panels increase as their thickness and their areal weight become higher. It is also found that 2024-T3 aluminum plates offer comparable ballistic limit velocities with the GLARE 4A fiber-metal laminates of the same thickness or the same


Introduction
The 2024-T3 aluminum alloy is widely used in the aerospace industry.It is also the metal constituent for the majority of commercially available material grades of GLARE fibermetal laminates, including GLARE 4A.GLARE is the most successful fiber-metal laminate up to now and is currently being used for the construction of primary aerospace structures, such as the fuselage of the Airbus A380 air plane.Impact properties are very important in aerospace structures, since impact damage is caused by various sources, such as maintenance damage from dropped tools, collision between service cars or cargo and the structure, bird strikes, and hail.For this reason, many researchers have studied the response of aerospace materials to impact loading.In pertinent impact studies, the static indentation, the low and high velocity impact, and the ballistic impact response of the materials are treated using analytical, numerical, and experimental methods.
This article deals with the response of square clamped 2024-T3 aluminum plates subjected to central normal ballistic impact by a rigid free-flying cylindrical projectile.The principal objective of the article is to assess the ballistic resistance of 2024-T3 monolithic aluminum.A comparison with the ballistic resistance of GLARE 4A fiber-metal laminated plates is also implemented.
In order to simulate the ballistic impacts, ANSYS LS-DYNA software is employed.Important impact variables such as the ballistic limit, the ballistic energy and the transient impact load are predicted.The presented results will help engineers and researchers, occupied with similar theoretical or experimental impact studies of aluminum and GLARE hybrid laminates, to understand the physical phenomenon and to compare the considered materials as far as their ballistic resistance is concerned.To the authors' knowledge, a comparison of the high velocity ballistic resistance of aluminum and GLARE 4A material grade has not been presented previously in other scientific publications.

Finite element modeling
In order to simulate the normal ballistic impacts of free-flying projectiles on aluminum targets, we use the structural arrangement of the ballistic impact experiments of reference [1].In our finite element modeling procedure we employ SOLID164 elements for the meshing of the projectile and the targets.Two solid elements are used along the thickness of the plates.In order to simulate the contact between the projectile and the plate we use the surface-to-surface contact type with the eroding contact option.
In order to reduce the computational cost, the projectile is considered rigid.For this reason, a rigid material model is used for the projectile.The simplified Johnson-Cook plasticity material model [2] is employed for modeling the material behavior of aluminum.
For the simulation of the perforation of the panels, the panels' finite elements in way of the projectile must be eroded.In order to achieve this goal, a strain-based erosion criterion is added to the aluminum material model.
In order to further reduce the high computational cost of the considered problem, we take advantage of the symmetry of the problem by modeling a quarter of the structure and by applying suitable symmetry boundary conditions to all nodes of the symmetry planes.
Given that the projectile is considered rigid, instead of meshing a solid cylinder, only the exterior surface with 0.8 mm thickness was meshed.The density of the projectile's material was modified so that the full projectile's mass remains constant.A fine mesh is used for the projectile in order to represent its geometry accurately, including the radius of the impacting face.With this meshing approach the number of the finite elements needed to model the projectile is minimized and the computational cost is further reduced.In order to verify the accuracy of the hollow projectile model FEM results, complete projectile models were also implemented and solved yielding practically identical results.
The one-point integration has been selected for the SOLID164 elements.For each ballistic impact case we analyze, we verify that the hourglass energy and the sliding energy are small relative to the internal energy, as recommended for an explicit analysis with LS-DYNA [3].
An explicit transient dynamic analysis is employed with geometric and material nonlinearities.The initial velocity of the projectile is predetermined.The duration of our analysis is controlled with a predetermined termination time which allows for complete panel perforation, provided that the initial velocity of the projectile is greater than or equal to the ballistic limit.It is noted that in order to determine the unknown ballistic limit of a specific panel, several trial analyses have to be executed with different initial projectile velocity.
In order to verify the convergence of FEM results, the ballistic limit of the panel, we built two models with increasing in-plane mesh density for each specific analyzed case of square panel.The projectile's mesh density remains the same for all models.For each MATEC Web of Conferences 188, 02010 (2018) https://doi.org/10.1051/matecconf/201818802010ICEAF-V 2018 model we obtain the ballistic limit and compare them in order to verify that satisfactory convergence has been achieved.
It is noted that the implemented finite element modeling procedure has also been used in reference [4] in order to predict the ballistic impact response of fiber-metal laminates and monolithic metal plates consisting of different aluminum alloys, and by comparison with published experimental data the validity of the procedure was demonstrated there.
With reference to the GLARE laminates, each 2024-T3 aluminum layer of these grades has a thickness of 0.5 mm.Each prepreg ply has a thickness of 0.125 mm and consists of S2-glass UD fiber prepregs.The material properties of 2024-T3 aluminum and S2-glass fiber reinforced epoxy layers can be found in references [1,5].Each intermediate composite laminate has thickness equal to 0.375 mm and layup: 0 0 glass / 90 0 glass / 0 0 glass.
In Figure 1 the calculated 4 ballistic limits are compared.It can be seen from Figure 1 that the ballistic limit of aluminum plates is increased as their thickness increases, but with a variable rate.In Figures 2 and 3 the variation of the ballistic limit of the considered GLARE 4A and 2024-T3 aluminum panels is depicted versus the panel's thickness and the panel's areal weight, respectively.It can be observed from these figures that the calculated ballistic limits of aluminum panels are very close to their experimental values from reference [1], in all examined cases.Furthermore, the experimental and numerical ballistic limit curves of aluminum in Figures 2 and 3 have a similar trend versus the thickness and the areal weight.These observations further demonstrate the validity of the implemented finite element analysis.It can be verified from Figures 2 and 3 that the ballistic limits of the GLARE 4A panels can be approximated satisfactorily using the depicted cubic equation trendlines of ballistic limits as a function of the panel's thickness or the panel's areal weight, respectively.This finding is also confirmed by the depicted values of the coefficients of determination, R 2 , which are close to unity in both cases.This fact indicates that the cubic polynomials are reliable trendlines.mean that it is preferable to construct thin GLARE 4A structures in order to achieve optimized impact resistance.
It is seen from Figure 3 that for any specific panel areal weight value w: 35 N/m 2 ≤ w ≤ 120 N/m 2 , 2024-T3 aluminum and GLARE 4A offer comparable ballistic limits.GLARE 4A demonstrates slightly higher ballistic resistance than 2024-T3 aluminum when the panel is very light.For heavier panels, with an areal weight greater than 60 N/m 2 , 2024-T3 aluminum has higher ballistic resistance than GLARE 4A.It is noted that approximately the same threshold limit of 60 N/m 2 concerning the transition from higher to lower ballistic resistance of GLARE in comparison with 2024-T3 aluminum has been reported in the experiments of reference [1].From a designer's point of view, these observations mean that it is preferable to avoid GLARE 4A structures with relatively high areal weight in order to achieve optimized impact resistance.
The prediction of the energy required to perforate target plates is very important for the impact engineer [6].For this reason, in Figures 4 and 5 the variation of the ballistic energy of the considered GLARE 4A and 2024-T3 aluminum panels is depicted versus the panel's thickness and the panel's areal weight, respectively.It can be observed from these figures that the calculated ballistic energies of aluminum panels are close to their experimental values from reference [1].Furthermore, the experimental and numerical ballistic energy curves of aluminum in Figures 4 and 5 have a similar trend versus the thickness and the areal weight.However, there is increased deviation between experimental and numerical results in comparison with Figures 2 and 3, since the squared value of velocity magnifies the difference between two data points.
It can be verified from Figures 4 and 5 that the ballistic energies of the GLARE 4A panels can be approximated satisfactorily using the depicted cubic equation trendlines of ballistic energies as a function of the panel's thickness or the panel's areal weight, respectively.This finding is also confirmed by the depicted values of R 2 , which are close to unity in both cases.This fact indicates that the cubic polynomials are reliable trendlines in this case as well.The approximation equation trendlines given in Figures 2-5 are applicable for GLARE 4A panels with t and w within the aforementioned limits.They can be used when experimental or theoretically calculated ballistic limits are not available for a specific t or w value.It is seen from Figure 4 that for panel thickness up to about 2.5 mm, 2024-T3 aluminum and GLARE 4A offer comparable ballistic energy values.With the exception of very thin panels, 2024-T3 aluminum has higher ballistic energy limits.According to Figure 4, the 2024-T3 aluminum panels with a thickness greater than 2.5 mm are clearly advantageous in comparison with GLARE 4A panels of the same thickness as far as their ability to absorb higher impact energy levels before the full panel perforation occurs, is concerned.
It can be observed from Figure 5 that for any specific panel areal weight value w: 35 N/m 2 ≤ w ≤ 60 N/m 2 , 2024-T3 aluminum and GLARE 4A offer comparable ballistic energies.GLARE 4A demonstrates slightly higher ballistic energy than 2024-T3 aluminum when the panel is very light.For heavier panels, 2024-T3 aluminum has higher ballistic energy values than GLARE 4A.According to Figure 5, the 2024-T3 aluminum panels with areal weight greater than 70 N/m 2 are advantageous in comparison with GLARE 4A panels of the same areal weight as far as their ability to absorb higher impact energy levels before the full panel perforation occurs, is concerned.
In Figure 6 the impact load time histories of the examined aluminum plates are depicted for duration from the beginning of the projectile's motion equal to 0.15 ms.At time t ≈ 0.15 ms, all aluminum targets have been perforated.This means that according to our pertinent calculations concerning the GLARE 4A laminates, the duration of ballistic impact of the 2024-T3 plates is about one half of the ballistic impact duration of the GLARE 4A panels.As in the case of fiber-metal laminates, the maximum impact load is applied at the beginning of ballistic impact on aluminum targets.Significant sudden contact forces at the beginning of ballistic impact events, concerning target plates perforated by free-flying projectiles have also been found in the numerical simulations of references [5,7,8].It is seen from Figure 6 that the impulse at the beginning of impact increases for increasing thickness of the aluminum plates.The initial impact load time history always has a unique peak and the maximum impact load is an increasing function of the plate's thickness, as shown in Figure 6.The absence of internal damage mechanisms during the local indentation of the aluminum targets, similar to those we have observed in GLARE 4A fiber-metal laminates, yields higher maximum impact load in the case of relatively thick aluminum panels in comparison with the GLARE 4A panels, since in this case there is not any impact load reduction due to damages with the presence of characteristic multiple  6 that after the beginning of impact, the time histories follow a similar but less noisy trend in comparison with the calculated time histories of the GLARE 4A panels.Fig. 6.Impact load time history curves of 2024-T3 aluminum plates subjected to ballistic impact by a cylindrical projectile.
The observed higher maximum impact load in the case of aluminum target is also applied to the supporting structure, which has to be further reinforced in order to sustain the maximum impact loading.This finding reveals an important advantage of the fiber-metal laminated structures in comparison with monolithic aluminum structures, which is related with the need for increased strength and stiffness of the aluminum skin's supporting structure in order to achieve comparable ballistic resistance.This need may increase the structural weight as well, a parameter which is critical in aerospace engineering.
In Figure 7 the impact load versus the projectile's displacement curves of the considered panels are depicted.It is noted that the projectile is initially located at a distance of 1 mm from the panels.As illustrated from Figure 7, the aluminum panels have been perforated for a displacement equal to 13 mm.Consequently, according to our pertinent calculations the GLARE 4A panels demonstrate a more flexible response to ballistic impacts in comparison with the 2024-T3 aluminum panels.The area under the impact load-displacement curve is equal to the work done by the contact force during the collision of the two bodies.It can be observed from Figure 7 that the work done at the beginning of impact increases for increasing plate thickness.This finding is reasonable since the observed suddenly absorbed impact energy at the beginning of impact becomes higher as the plate thickness increases.Thus, the associated reduction of the projectile's kinetic energy becomes higher as well.But according to the work-kinetic energy theorem, the variation of the striker's kinetic energy is equal to the work done by the impact load.This is why this work increases for increasing thickness, as shown in Figure 7.It is interesting to note that the impact loaddisplacement curves of the aluminum plates at the beginning of impact form approximately similar triangles with the lower vertex located at point (1, 0) and a lower edge that makes an angle with the horizontal axis.

Conclusions
This article deals with the transient response of square clamped 2024-T3 aluminum plates subjected to central normal ballistic impact by a rigid flat-faced cylindrical projectile.ANSYS LS-DYNA software is employed in order to simulate and study the ballistic impact phenomenon.A comparison with the ballistic resistance of GLARE 4A fiber-metal laminated plates is also implemented.
It is found that the ballistic limit and the ballistic energy of the GLARE 4A and monolithic aluminum panels increase as their thickness and their areal weight become higher.With reference to the considered GLARE 4A panels, the variation of ballistic limit and ballistic energy as a function of the thickness and the areal weight can be approximated with cubic polynomials.
The GLARE 4A fiber-metal laminates offer comparable ballistic limit velocities with 2024-T3 aluminum plates of the same thickness or the same areal weight.

Fig. 3 .
Fig. 3. Ballistic limits of GLARE 4A fiber-metal laminates and 2024-T3 aluminum plates versus the panel areal weight.It is seen from Figure2that for any specific panel thickness value t: 1.5 mm ≤ t ≤ 5 mm, 2024-T3 aluminum and GLARE 4A offer comparable ballistic limits.GLARE 4A demonstrates slightly higher ballistic resistance than 2024-T3 aluminum when the panel is very thin.For panel thickness values greater than 2 mm, 2024-T3 aluminum has higher ballistic resistance than GLARE 4A.From a designer's point of view, these observations

Fig. 7 .
Fig. 7. Impact load versus striker's displacement curves of 2024-T3 aluminum plates subjected to ballistic impact by a cylindrical projectile.