Numerical simulation of the tumbling of kinetic energy projectiles after impact on ceramic/metal armours

Transcription

1 Computational Ballistics II 21 Numerical simulation of the tumbling of kinetic energy projectiles after impact on ceramic/metal armours F. Gálvez 1, S. Chocron 2, D. Cendón 1 & V. Sánchez-Gálvez 1 1 Department of Materials Science, Polytechnic University of Madrid, Spain 2 SouthWest Research Institute, San Antonio, Texas, U.S.A. Abstract Ceramic metal armours are widely accepted as a very efficient solution for protection of lightweight armoured vehicles against kinetic energy projectiles. The high hardness of ceramics is responsible for eroding the projectiles while failure of the ceramic is progressing, while the backing material is supporting the ceramic. When the impact is oblique, failure of the ceramic is completely asymmetrical, and therefore the forces applied to the projectile are distributed non-symmetricaly making the projectile tumble after the impact. This behaviour is very efficient for add-on armours because a side impact on the main armour penetrates much less than a front impact. In this paper a numerical simulation of this effect is studied. The simulations have been performed using Autodyn 3D. A tungsten projectile impacting onto alumina backed with aluminium has been simulated. Different impact angles have been studied. The influence of the spinning of the projectile is also considered. The results show that the tumbling of the projectile only appears on ceramic faced armours, while in the case of impact onto a monolithic metallic material such as steel it does not appear. The results show also that tumbling increases with the impact angle. Keywords: ballistic impact, kinetic energy projectiles tumbling, ceramic armours, numerical simulation. 1 Introduction In this paper the influence of the spin velocity of a projectile impacting onto ceramic-metal armour is studied numerically. The variables studied are residual

2 22 Computational Ballistics II mass and the residual velocity after impact, as well as the destabilization of the projectile after perforation. This last aspect is extremely important for the design of add-on armours, because is the main factor to compute the gap between the main armour and the add-on. Figure 1: Lateral view of the materials location for a 40º impact angle. 2 Problem simulated The problem analysed was the oblique impact of a kinetic energy projectile against onto a composite armour (see figure 1). The projectile used was the 20APDS impacting a range of different angles. This projectile is a bi material projectile, with a tungsten alloy core and a nose made of aluminium. The first material gives the projectile the penetrating capabilities and the aluminium is just to stabilize its flight. The selected target was an 99.5% alumina tile backed with 7075T6 aluminium. The thickness was 20 mm for the alumina and 15 mm for the aluminium. In addition an alternate target of steel was also used for comparison. The mesh used for the calculations is shown in figure 2. A range of different angles were studied, from normal impact up to 50º. The experimental results on the author s database reports perforation for all those angles, while larger impact angles stops the projectile. The calculations were performed using Autodyn3D. To introduce the spin of the projectile, a user subroutine was needed and implemented into the code. The base spin velocity selected for the projectile was rpm (13000 rad/s), which is called 1x in this paper. For comparison also twice and four times the base spin (called 2x and 4x respectively) was studied. In addition the case without spin velocity was also studied and is called the 0x spin. The material properties selected for the ceramic tile was the Johnson- Holmquist equation of state and failure model [1]. The calculations were performed using an erosion based on a geometric strain. The metallic materials were modelled using the Shock equation of state with a strength model based on the Steinberg et al model [2]. It applies for the aluminium and the tungsten alloy

3 Computational Ballistics II 23 with its corresponding parameters. All the values of the parameters used are included in the Autodyn3D material model library [3]. Figure 2: Full view of the mesh used in calculations for a 40º impact angle. 3 Numerical results The results of the numerical study show that the spin of the projectile has not any influence when the target is a metallic material. The residual path of the projectile after penetration is independent of the spin of the projectile, as well as the residual mass and velocity. When the ceramic target is simulated, the results show that at low impact angles (from normal impact up to 20º) the residual mass and velocity are not significantly influenced by the projectile spin rate. However at larger impact angles the differences are more marked. The projectile mass and velocity histories for the 30º impact angle are presented in Figure 3. The results show that the residual mass is clearly affected by the spin rate of the projectile. The residual mass decreases with the spin of the projectile. The velocity history of the projectile also looks to decrease with the spin velocity, but its influence is not as marked as in the mass.

4 24 Computational Ballistics II The projectile mass and velocity histories for the 40º impact angle are presented in figure 4, and for 50º angle in figure 5. As in the 30º impact results, the residual mass decreases with the spin rate of the projectile. This decrease of the mass looks to be linear with the spin increase. The velocity history of the projectile at 40º has the same behaviour than in 30º, but at 50º angle the influence of the spin is more relevant. Figure 3: Histories of projectile mass (left) and the projectile tail velocity (right) for a 30º impact angle. Figure 4: Histories of projectile mass (left) and tail velocity (right) for a 40º impact angle.

5 Computational Ballistics II 25 Figure 5: Histories of projectile mass (left) and tail velocity (right) for a 50º impact angle. The destabilization and the tumbling of the projectile are shown in figure 6. This figure shows the images of the 30º impact angle for the four different spin velocities studied. The images reveal that when no spin is used (the first row of images) the projectile penetrates following the plane of symmetry and symmetrically in it. Because the spin is zero, there are no forces that could break the symmetry. However, as spin velocity increases (second to fourth row of images from figure 6) the deviation from the plane of symmetry is more relevant. As spin increases the projectile tumbles more. All the images show the position of the projectile at 200 µs after impact. As can be seen, the tumbling of the projectile (the angle of the projectile axis with the initial plane of symmetry) is 60º for the 4x spin velocity, 45º for the 2x, 15º for the 1x and null for the 0x (which is no spin). The same behaviour for the 40º impact angle can be observed in figure 7. In this case, the time shown is 175 µs after impact. Now the destabilization and the tumbling of the projectile are greater than in the 30º impact angle. However on the images shown it looks to be smaller, but it is because of the lower time showed and the lees space travelled by the projectile after penetration due to the lower residual velocity. The 50º impact angle results (figure 8) show the behaviour near the ballistic limit. The simulation show that the projectile penetrates better at lower spin rates, while the projectiles of higher spin rates are near to be defeated. This is because the tumbling is higher at high spin rates and the armour is acting over a larger area of the projectile. As can be seen in figure 5, residual velocities are very low and near zero for the 4x spin rate.

6 26 Computational Ballistics II Figure 6: Images of the 30º angle impact after 200ms of four different spin velocities. First row is without spin velocity. Second to fourth rows are spins of 1x, 2x and 4x respectively. Left column is the front view and right column is the side view.

7 Computational Ballistics II 27 Figure 7: Images of the 40º angle impact after 175ms of four different spin velocities. First row is without spin velocity. Second to fourth rows are spins of 1x, 2x and 4x respectively. Left column is the front view and right column is the side view.

8 28 Computational Ballistics II Figure 8: Images of the 50º angle impact after 350ms of four different spin velocities. First row is without spin velocity. Second to fourth rows are spins of 1x, 2x and 4x respectively. Left column is the front view and right column is the side view.

9 Computational Ballistics II 29 4 Conclusions For the monolithic metallic targets studied the destabilization of the projectile does not appear in the range of spin rates studied. The results show that the tumbling of the projectile only happens when a ceramic material is used on the target. The destabilization has been found to be greater at higher spin rates. Thus for non spinning projectiles the tumbling disappears. The destabilization can be neglected below impact angles of 10º but rapidly increases with the impact angle, being relevant at 30º and over The effect of the spin rate on the residual velocity is not relevant, but in the vicinity of the ballistic limits it founds its own importance. The effect of the spin rate on the residual mass of the projectile is important. Higher spin velocities produces less residual mass. Acknowledgements The authors wish to express their gratitude to the Ministerio de Ciencia y Tecnología for the funds awarded through the project MAT and to the Comunidad de Madrid for the financial support through the project 07/0120/2002 References [1] Johnson G. R., Holmquist T. J., An improved computational constitutive model for brittle materials., Joint AIRAP/APS Conference, Colorado Springs, Colorado, June [2] Steinberg, D.J., Cochran, S.G. and Guinan, M.W. Constitutive model for metals applicable at high strain rate, J. Appl. Phys., 51, 3, March [3] Autodyn3D v5 User Manual. Century Dynamics Inc. 2004