Hydrocode numerical modeling of projectile impact on moving aluminum targets

This paper deals with the investigation of high velocity normal impacts of a rigid cylindrical projectile on moving aluminum plates. The targets are supported with mixed boundary conditions which permit their rigid body motion in the plane perpendicular to the initial striker’s trajectory with a predetermined initial velocity. A 3D numerical modeling procedure based on the finite difference method is implemented for this problem with the ANSYS AUTODYN hydrocode. The Johnson-Cook plasticity and damage models are used for the aluminum target. The numerical modeling is validated through suitable comparisons with experimental data concerning stationary targets. The effect of striker’s and target’s initial velocities is studied on the projectile’s trajectory and the striker’s energy loss after the full perforation of the target. It is found that the energy loss of the striker’s kinetic energy is higher for relatively higher values of the projectile’s velocity. The striker’s energy loss decreases as the velocity of the target increases. Diagrams of the energy time-histories of the striker-target system are constructed for different initial velocities of the plate and the projectile. It is observed from these diagrams that the internal energy of the plate depends mainly on the plastic work.


Introduction
The outer surface of aerospace structures, which consists of various integrated thin-walled panels, is usually made from metal alloys with several desirable properties such as low density, high specific strength and stiffness, and high fatigue resistance.However, these structures are often subjected to unwanted though unavoidable impact incidents, which cover a wide range of shapes and velocities of the involved objects, due to various uncontrollable reasons like maintenance damage from dropped tools, bird impact or hail.Therefore, sufficient impact resistance is another criterion that needs to be satisfied for these structures and the study of their impact behaviour is a major research area [1][2][3].
Ballistic impact experiments are generally expensive, time consuming and restricted by the practical test conditions [4].The motion of the target increases the complexity of the experimental arrangement and makes the experimental investigation even more expensive and difficult.Furthermore, although the scientific research for the impact performance of aerospace materials with stationary target specimens is extensive, the theoretical research for impacts on moving targets is rather limited and relevant published experimental research is rare.Representative studies concerning high velocity impact on moving targets are cited in the next paragraph.
Wu and Goldsmith [5] performed an experimental investigation to study projectile impacts on circular metallic targets moving at right angles to the striker's trajectory with a velocity of 40 m/s.The same authors developed an analytical model [6] for the normal impact of cylindrical projectiles on thin circular metallic targets moving normally to the projectile's trajectory.It is noted that in references [5,6] the targets rotate so that their centers exhibit a constant translational velocity.Hou and Goldsmith [7] investigated experimentally the normal impact and perforation of blunt and conically tipped cylindrical projectiles on rotating annular plates moving orthogonal to their initial trajectory with three different velocities.In reference [8] the effect of target condition (static and dynamic) and number of bullet impacts on the ballistic performance of aluminum and FML plates has been investigated experimentally and numerically.The authors showed that the motion of the target affects the exit velocity of the bullet and alters its penetration behaviour.A numerical investigation of the impact of an ogive projectile on a helicopter shaft has been carried out by Colombo and Giglio [9] in order to identify the effect on the residual strength of the component.Resnyansky et al. [10] studied numerically and experimentally the ballistic impacts of 0.5ʺ calibre bullets against simulated moving targets that were pre-stressed.
The aforementioned rarity of published research concerning impact on moving targets indicates the necessity and increases the value of carrying out a relevant theoretical study.This paper deals with high velocity normal impacts of a rigid projectile on moving aluminum plates supported with mixed boundary conditions (bc) which permit their rigid body motion in the plane perpendicular to the striker's trajectory with a predetermined initial velocity.A numerical modeling procedure is implemented for this problem with the ANSYS AUTODYN hydrocode.The modeling procedure is validated through comparison of the numerical results with published experimental data [11] concerning ballistic impacts on stationary aluminum targets.The results of the present investigation will help engineers and researchers to understand the impact behavior of aluminum plates subjected to high velocity impact by a rigid projectile taking into account the motion of the target, which is the most likely scenario in real impact events of aerospace structures.

Problem definition
The investigation of the impact performance of moving aluminum targets impacted by a cylindrical projectile is carried out considering similar structural arrangement to the one employed for the ballistic impact experiments of reference [11].As it is illustrated in figure 1, square aluminum panels 3.2 mm thick are considered with in-plane dimensions 152.4 mm x 152.4 mm.The projectile is flat-faced cylinder, 25.4 mm long with 12.7 mm diameter and its initial velocity vector is normal to the panel and intersects the center of the panel.The mass of the projectile is 14.125 g and and its impacting face has a small radius of 0.8 mm.Before the impact, the plate and the projectile have only X-and Zcomponent of velocity, respectively, according to the coordinate system of figure 1.The considered mixed bc of the panel are described in section 3 and permit its rigid body motion in the X-direction.The bc have been selected in order to simulate the support of an aluminum panel οn a moving aerospace structure.The evaluation of the high velocity impact behavior of moving metal targets is implemented with the numerical modeling of several impact cases.Specifically, apart from the cases with stationary targets, two projectile velocities in combination with three velocities of the plate are considered.The examined impact phenomenon is a transient nonlinear problem involving geometric and material nonlinearities with contact interaction.The ANSYS AUTODYN hydrocode is used for its study.

Numerical modeling procedure
In this study a three-dimensional (3D) numerical modeling procedure based on the finite difference method is implemented with the ANSYS AUTODYN hydrocode, in order to study the impact event of moving square panels impacted normally by a cylindrical free-flying projectile.The panels consist of monolithic aluminum alloy and their stiffness behavior is modeled as deformable.On the contrary, the stiffness behavior of the projectile is modeled as rigid, since its material has adequate strength and hardness.This assumption of the rigid projectile has been employed in other theoretical studies as well [6,9,11] and lowers the computational cost of the problem.
The target and the striker are discretized with Lagrangian grids consisting of hexahedral eightnoded volume elements (cells) as it is illustrated in figure 2. The fine numerical grid is depicted in this figure for the aluminum plate along with the projectile, consisting of 45,000 and 29,044 cells, respectively.It is shown that two cells are employed along the thickness of the target.Two elements along the thickness are also employed in the study of Bikakis et al. [12] for the finite element simulation of monolithic plates consisting of different aluminum alloys and subjected to ballistic projectile impact.Taking into account the fact that the grid density of the rigid projectile does not affect considerably the computational cost, a very dense grid is constructed for the striker in order to represent accurately its geometry, including the 0.8 mm radius of its impacting face.The aluminum plate in the coarse model consists of 22,472 cells.The grid of the projectile is the same for all models.The ballistic limit is defined as the lowest initial projectile velocity for complete penetration of the panel [11].Furthermore, since the initial projectile velocity is greater than the ballistic limit of the moving target, the convergence check has been extended to include the kinetic energy of the projectile after the target's perforation.It is always verified that the convergence of the final kinetic energy of the projectile corresponding to the coarse and the fine grid of the target is satisfactory for each examined impact case.The mixed bc of the panel are applied by setting the Z-component of velocity of the grid points located at the four boundary faces of the target equal to zero.Additionally, the Y-component of velocity of the grid points located at the two boundary faces of the target which have constant Y ordinate (Y = 7.62 mm, Y = -7.62 mm) is also set equal to zero.It is reminded that the coordinate system is depicted in figure 1. Referring to figure 1.b, the top and bottom boundary faces are clamped and the left and right boundary faces are simply supported but the applied bc permit the motion of the plate in the X-direction.
The contact interaction between the projectile and the aluminum plate is simulated with Lagrange/Lagrange frictional body interaction [13].The value of the friction coefficient between the target and the striker is set equal to 0.4.The simulation of the penetration of the panels is accomplished through the numerical mechanism of erosion.Namely, cells are automatically eroded (deleted during the solution) when the failure criterion defined below for the material of the plates is satisfied.
The aluminum alloy of the targets is modeled as an elasto-plastic material with rate-dependent behavior employing the simplified Johnson-Cook plasticity material model [13,14]: where σ y is the flow stress, A, B, C and n are material parameters, ε pl is the equivalent plastic strain and ̇  * is the dimensionless plastic strain rate.This simplified model does not take into account temperature effects or damage and it has been used in references [12,15,16] as well.
Additionally, the damage of aluminum is considered with the Johnson-Cook failure model given by the following cumulative damage law [13,14]: where Δε pl is the increment of the equivalent plastic strain during an increment in loading,    is the fracture strain and σ * is the mean stress normalized by the equivalent stress.D i (i = 1-4) are material damage constants.Failure of the material is assumed to occur when D = 1 [13,16].
The volume cells are used with single point integration to reduce the computational cost of the simulation.However, the combination of this type of integration with hexahedral volume cells can lead to hourglass modes of deformation which may cause degradation of the numerical results [13].For this reason, it is always verified that the hourglass energy of each solution is low compared with the internal energy of the system.

Validation of numerical modeling
The validation of the numerical modeling procedure is implemented through comparisons of the ballistic limits of the present study with published experimental data [11] concerning stationary targets.The square clamped aluminum plates with thickness 1.6 mm and 3.2 mm are modeled for this purpose.Το the authors' knowledge, there are no published experimental results concerning the ballistic impact of flat-faced cylindrical projectiles on moving with purely translational motion aluminum plates.
The material and Johnson-Cook model parameters of the 2024-T3 aluminum are given in table 1 [15,16].The density of the projectile's material is defined 4390 kg/m 3 so that its mass calculated using its exact volume is equal to 14.125 g.The geometry of the projectile has been modeled accurately since its mass calculated from the volume of its cells is equal to 14.08 g.

Results and discussion
Figure 3 illustrates representative absolute velocity contours of the striker-target system before and during the impact.It is noted that, initially, the Z-velocity component of the projectile is -230 m/s and the X-velocity component of the plate is 100 m/s.It is found that the projectile's trajectory changes during the impact, because of the motion of the plate.The change of the projectile's trajectory is depicted with the trajectory angle, which is defined as the angle between the longitudinal axis of the striker and the axis normal to the target (Z-axis) [7].It is shown clearly from figure 3.b that this angle is no longer equal to zero, as it was before the impact.Although this change is observed in all examined cases concerning moving targets, it is more noticeable for relatively lower values of the projectile's velocity.In the impact cases with stationary targets, the failure mechanism of plugging principally due to shear is observed with symmetric plug separation.A circular hole is formed on the plate after its perforation and the striker continues to move normally to the target with reduced velocity.But in the impact cases with moving targets, the aforementioned change of the trajectory angle of the projectile causes additional damage of the plate and the formation of a crater.At the beginning of the impact an asymmetric plug is observed, the formation of which is attributed to the contact of the impacting face of the projectile with the target.It is observed that this plug is separated from the plate partially or fully, depending on the velocity of the projectile and the target's velocity.Full separation (plug ejection) is observed for higher values of projectile's and lower values of plate's velocity.
Subsequently, as the plate moves the striker gradually gets X-component of velocity apart from the initial Z-component and rotates (figure 3.b).The gradual rotation of the cylindrical projectile causes the contact of its side surface with the target.This contact interaction of the involved bodies leads to further damage of the target due to the impact of the side surface of the cylindrical projectile.In figure 4 the aforementioned crater is depicted for a plate moving, initially, with velocity 200 m/s and subjected to impact by a rigid projectile with initial velocity 300 m/s.It is observed that the crater is approximately elliptical in this impact case.It is found that the area of the crater is increased as the plate's velocity increases.The impact phenomenon causes the loss of a certain amount of the initial striker's kinetic energy, which is mainly absorbed by various damage mechanisms such as global panel deformation, plastic work, fracture and by the work of friction.Figure 5 illustrates the striker's energy loss as a function of the initial plate's velocity for both examined cases of initial projectile's velocity.The striker's energy loss equals to its initial kinetic energy minus its final kinetic energy after the full perforation of the target.It is observed from this figure that the energy loss values corresponding to the higher initial projectile's velocity (300 m/s) are greater than the values corresponding to the lower initial projectile's velocity (230 m/s), for each specific initial velocity of the plate.Furthermore, it is observed from figure 5 that the aforementioned deviation of the energy loss values between the two initial projectile's velocities is systematically increased as the velocity of the plate increases.For example, when the target is stationary, the energy loss of the projectile with initial velocity 300 m/s is 10.1% greater than the energy loss corresponding to striker's velocity 230 m/s, whereas it becomes 164.4% greater when the velocity of the plate is 200 m/s.It is also observed from figure 5 that, with respect to the moving aluminum plates, the striker's energy loss is decreased as the velocity of the plate increases, for both cases of the projectile's velocity.Figures 6 and 7 illustrate the energy time histories of the striker target system for a stationary plate and a plate moving initially at 200 m/s, respectively.Both figures correspond to the initial projectile's velocity of 300 m/s.It is always verified in accordance with the physics of the problem and AUTODYN recommendations that the numerical results of the present study satisfy the momentum and energy conservation laws.It is also verified, as in Figures 6 and 7, that the hourglass energy level is low.The hourglass energy is due to nonphysical hourglassing deformation modes because of the single point integration of the volume cells.According to AUTODYN energy conventions, the total current energy of the system decreases due to the external work done and the contact energy [13].The presence of contact energy is due to the defined frictional interaction between the colliding bodies.The kinetic energy of the system is equal to the sum of the striker's and the plate's kinetic energy.The plastic work is equal to the work done in permanent (plastic) deformations.The internal energy includes elastic strain energy and work done in permanent deformations.It is observed from figures 6 and 7 that the total and the kinetic energy time histories of the strikertarget system are significantly affected by the target's motion since the moving target's initial kinetic energy is added to the system's initial total and kinetic energy.Furthermore, it is observed that the kinetic and total energy time histories of the system are reduced more abruptly for the case of the stationary target in comparison with the case of the moving target.The plastic work and the internal energy time histories are increased more abruptly for the case of Figure 6 in comparison with the case of figure 7. Since the projectile is rigid and has zero internal energy, it is observed from figures 6 and 7 that the internal energy of the plate depends mainly on the plastic work.Furthermore, it is found that as the plate's velocity increases the distance between the curves of plastic work and internal energy timehistories is reduced despite the variation of the initial total energy of the system.These findings from figures 6 and 7 are valid for all examined impact cases of this study.

Conclusions
The present article deals with high velocity normal impacts of a rigid cylindrical flat-faced projectile on moving aluminum plates.The targets are supported with mixed boundary conditions which permit their rigid body motion in the plane perpendicular to the initial striker's trajectory.Eight impact cases with different initial velocities of the colliding bodies are analyzed by implementing hydrocode simulations with ANSYS AUTODYN.
It is found that the projectile's trajectory changes during the impact due to the motion of the plate and this change is more noticeable for the lower value of the projectile's velocity.A greater energy loss of the striker's kinetic energy is observed for the impact cases corresponding to the higher value of the projectile's velocity, when a specific value of the plate's velocity is considered.It is also found that, with respect to moving targets, the striker's energy loss decreases as the velocity of the plate increases.The plastic work time-history governs the internal energy of the target during the impact.

Figure 1 .
Figure 1.(a) Side and (b) top view of the striker-target system before the impact.

Figure 2 .
Figure 2. Isometric view of the target-striker fine Lagrangian grid.The convergence of the numerical results is verified by comparison of the ballistic limits of stationary targets calculated from models with increasing in-plane grid density of the square panel.

7th
International Conference of Engineering Against Failure Journal of Physics: Conference Series 2692 (2024) 012050

Figure 3 .
Figure 3. Absolute velocity contours of the aluminum plate impacted by the projectile before (a) and during (b) the impact.

Figure 4 .
Figure 4. Crater of a perforated aluminum plate moving initially at 200 m/s and impacted by a projectile with initial velocity 300 m/s.

Figure 5 .
Figure 5. Energy loss of the striker after the full perforation of the target as a function of the initial plate's velocity.

Figure 6 .
Figure 6.Striker-target system energy time history curves of a stationary aluminum plate impacted by a projectile with initial velocity 300 m/s.

7th
International Conference of Engineering Against Failure Journal of Physics: Conference Series 2692 (2024) 012050

Figure 7 .
Figure 7. Striker-target system energy time history curves of a moving aluminum plate (200 m/s) impacted by a projectile with initial velocity 300 m/s.6.ConclusionsThe present article deals with high velocity normal impacts of a rigid cylindrical flat-faced projectile on moving aluminum plates.The targets are supported with mixed boundary conditions which permit their rigid body motion in the plane perpendicular to the initial striker's trajectory.Eight impact cases with different initial velocities of the colliding bodies are analyzed by implementing hydrocode simulations with ANSYS AUTODYN.It is found that the projectile's trajectory changes during the impact due to the motion of the plate and this change is more noticeable for the lower value of the projectile's velocity.A greater energy loss of the striker's kinetic energy is observed for the impact cases corresponding to the higher value of the projectile's velocity, when a specific value of the plate's velocity is considered.It is also found that, with respect to moving targets, the striker's energy loss decreases as the velocity of the plate increases.The plastic work time-history governs the internal energy of the target during the impact.

Table 1 .
[15,16]l and Johnson-Cook model parameters[15,16]of 2024-T3 aluminum.The comparison between the numerical and the experimental results is presented in table 2.An excellent agreement is observed from this comparison, since the deviation of the numerical ballistic limits from their experimental values is lower than 4%.