the use of 3d numerical simulations for the interaction of ... · velocity and obliquity are...

The use of 3D numerical simulations for the interaction of long rods with moving plates

Z. Rosenberg & E. Dekel RAFAEL, Israel

Abstract

The use of 3D numerical simulations for terminal ballistics has been very fruitful during the past decade, with the advancements of 3D codes, as far as accuracy and computational times are concerned. These simulations enable us to look more carefully at the interaction of projectiles with targets in real situations which include oblique impacts, with or without yaw, at stationary and moving plates. The purpose of the present paper is to demonstrate the usefulness of these codes for long rods impacting metallic targets for the purpose of designing reactive armor systems against these rods. Here, we demonstrate how one can answer several questions regarding this interaction without the need for costly and complicated experiments. In particular, the issues of rod disruption, erosion and deflection are highlighted in 3D simulations by changing rod and plate obliquities and velocities, as well as plate thickness and strength. Several experimental results are also presented to demonstrate the validity of code predictions. Keywords: terminal ballistics, long rods, reactive armor.

1 Introduction

One of the most important issues in the area of armor technologies concerns the interaction of shaped charge jets and long-rod penetrators with moving plates (reactive armor). The efficiency of relatively thin steel plates, propelled by an explosive layer which is detonated by the impacting jet, has been demonstrated by many workers (see [1-3], for example). Relatively few works have been published on the interaction of long rods and moving plates, probably because this is a much less understood phenomenon, (see [4, 5]). We recently published [6] some of our results on the interaction between a tungsten-alloy rod impacting

© 2005 WIT Press WIT Transactions on Modelling and Simulation, Vol 40, www.witpress.com, ISSN 1743-355X (on-line)

Computational Ballistics II 53

a receding steel plate, at obliquities in the range of 25°-40°. We found experimentally that this interaction can result in a severely distorted and shattered penetrator, if certain conditions are maintained as far as the impact velocity and obliquity are concerned. Outside this range of parameters the rod suffered a relatively slight disruption and its penetration efficiency did not diminish by much. Using 3D numerical simulations of the interaction enabled us to understand the mechanism for this severe disruption and to construct a simple engineering model, which accounts for the different situations obtained when varying the impact velocity or obliquity angle, [see [6]). The aim of the present paper is to demonstrate the usefulness of these simulations in studying the mechanism of rod disruption by varying other parameters such as plate thickness, its hardness and velocity. Such simulations are very convenient for sensitivity studies and they can save a lot of expensive experiments. Nonetheless, their predictions have to be examined by relevant experiments, as we shall demonstrate here.

Figure 1: Results from two typical experiments.

2 A short summary of the disruption mechanism

Fig. 1 shows the results of two experiments in which tungsten alloy rods (L/D=20, D=8 mm) impacted 4.3 mm RHA plates at 1400 m/s. The plates were moving at 430 m/s in the direction normal to their plane, receding from the rods. Each picture consists of three shadowgraphs at different times (30, 170 and 310 µs after impact) and one can clearly see the difference between rod disruption for the two cases. The impact at an obliquity of 35° (between rod and plate) resulted in a severe disruption to the rod while that with 40° broke the rod to several pieces, which were only slightly diverted from its original direction. One should note that these very different results for rod disruption were obtained with two

α=35o

α=40o


54 Computational Ballistics II

similar experiments differing only by 5° in the obliquity of the plates. Further experiments showed that the severe disruption can be obtained for a range of impact velocities and obliquities (see [6]). In order to understand this phenomenon we performed 3D simulations with the Lagrangian processor of the Antodyn 3D code. Material properties were taken from tables supplied by the code for steel and the tungsten-alloy. A simple von-Mises yield criterion was used for both materials with 1.2 GPa for the rod and 1.8 GPa for the plate. This value is higher than the regular 1.0–1.2 GPa yield strength of RHA plates, but we found that such enhanced values are needed in these codes in order to achieve a better agreement with the experiments. Since the main aim of the numerical simulation, as we see it, is to understand the physics of the interaction, rather than to fully account for it, we feel that such discrepancies are allowable.

Figure 2: Simulation results for the two experiments shown in fig. 1.

Fig. 2 shows the results of two simulations with obliquities of 30° and 40° which closely follow the experimental results shown in fig. 1. Moreover one can clearly see that the difference between the two interactions is due to the different orientation of the strip which is cut from the target by the rod. For the 30° impact the strip is pushed backwards and the rod is actually ricocheting from it as it

t=50µs

t=125µs

t=175µs

α=40o α=30o



continues the interaction. On the other hand, for the 40° impact, this strip is pushed towards the rod as it penetrates the moving plate. Once we realized the different directions of the strips torn from the target by the rod we were able to construct the engineering model which accounts for the disruption of the rod (see [6]).

Figure 3: The two different strip directions.

In order to highlight this issue we show in fig. 3 these different strip directions in both experiments and simulations presented above. As is clearly evident the target strips follow the same behavior in the experiments as in the numerical simulation. Our model treats the interaction of the rod at the acute obliquities as a nonpenetrating case while for the larger angles (40° and above) the rod is penetrating the plate. The borderline between these two cases is determined by the relation between the relative velocity, between rod and plate, and the critical velocity for penetration (Vc), as defined by the 1D hydrodynamic theory of penetration of Alekseevskii [7] and Tate [8]. In terms of the relevant parameters we found that the condition for strong disruption is given by the following inequality (see [6]):

α=40o α=35o



αSinVV

VV

p

C

p

t )1( −> (1)

where Vt and Vp are plate and rod velocities, respectively, and α is the obliquity as measured between rod and plate.

3 Sensitivity studies

3.1 The influence of plate thickness

The experimental study and the 3D simulations described above were performed with 8mm in diameter tungsten alloy rods (L/D=20) and 4.3mm thick steel plates. We constructed an analytical model (see [6]) which does not consider the thickness of the moving plate and, in effect, treats it as thick enough, so that back surface effects do not play a role during the interaction. It is obvious that reducing the thickness of the plate will result in, at a certain point, a change in the disruption mode. In order to investigate this issue we performed a large number of simulations in which we varied both the plate thickness and its velocity in order to look for the thickness effect. Fig. 4 shows the results for a simulation with a 3mm steel plate moving at 450 m/s. The impact angle is 32.5°, which for the thicker plate resulted in the strong disruption for the rod, as seen in fig. 1. In contrast we see that with the thin plate the interaction starts as a ricochet but continues as complete penetration with minor disruption to the rod. This intermediate behaviour evidently is the consequence of the lower thickness of the plate and in order to recover the strong disruption of the rod, the velocity of the plate had to be increased.

Figure 4: Simulation results for an intermediate case.

t=50µs

t=100µs t=150µs

t=75µs



Fig. 5 summarizes all our results for 30° impacts of the tungsten alloy rods, at 1400 m/s on 3-5 mm thick steel plates moving at 385-520 m/s. One can clearly see the borderline between strong disruption and total penetration, and the intermediate situations along this line. The slope of this line is -35 m/s per 1 mm of plate thickness as is clearly seen in the figure. This is the most important result of our set of simulations since it can guide the armor designer as to what change in plate velocity should be accompanied with a change in plate thickness, in order to maintain the effectiveness of rod disruption.

380 400 420 440 460 480 500 520

3.0

3.5

4.0

4.5

5.0

H (m

m)

V (m/sec)

Figure 5: Simulation results for 30° impact. Circle – disruption, triangle – penetration and crosses – intermediate situation.

380 400 420 440 460 480 500 520

3.0

3.5

4.0

4.5

5.0

H (m

m)

V (m/sec)

Figure 6: Simulation results for 35° impact. Circle – disruption, triangle – penetration and crosses – intermediate situation.

A similar set of data for an impact angle of 35° is shown in fig. 6 and it is clearly seen that the pattern repeats itself. The slope of the borderline is the same with a shift towards higher velocities, as expected.



Thus, by using such 3D simulations instead of experiments one can clearly save a lot of effort and time, at least as far as sensitivity studies are concerned. In order to check the validity of these results we performed an additional experiment with a thin plate (3.2 mm) moving at 560 m/s impacted by the L/D=20 (D=8 mm) tungsten alloy rod at an angle of 35°. Fig. 7 shows the three consecutive shadowgraphs (at 30, 170 and 310 µs after impact) from this experiment. It is clearly evident that this experimental result belongs to the intermediate case in which the rod is strongly disrupted during the first part of the interaction, where it is shattered and deflected, while later on it is only slightly bent and deflected without shattering.

Figure 7: An experiment with the intermediate case.

380 400 420 440 460 480 500 520

3.0

3.5

4.0

4.5

5.0

H (m

m)

V (m/sec)

Figure 8: Results for a stronger steel plate. Nomenclature as in figs. 5, 6.

3.2 Increasing plate strength

An additional set of simulations was performed for stronger steel plates (by 50%) without changing any of the other relevant parameters. Fig. 8 shows the results of these simulations for the same velocity range and plate thicknesses. One can clearly see that the same slope is obtained for the dividing line between strong disruption and no disruption, with a shift towards higher velocities. This shift amounts to 20 m/s for the 50% change in plate strength. Thus, by these



relatively simple simulations we are able to determine the sensitivity of this disruption mechanism to the strength of the plate and save a lot of effort in determining this sensitivity empirically.

4 Conclusions

The interaction of long rods with moving plates has been studied in a series of 3D numerical simulations in order to obtain its sensitivity to various parameters. We focused, in this study, on the strong disruption mechanism which was observed experimentally [6] with tungsten alloy rods and steel plates. We followed this disruption as we change the thickness of the plate and its strength and found the changes needed in its velocity in order to keep the disruption effectively. These 3D simulations are relatively simple to perform and they are very useful for the armor designer as a complement to the experimental work which is needed. Several experiments are also described here to demonstrate the validity of the numerical predictions and their usefulness.

References

[1] Mayseless, M., Ehrlich, Y., Falcovitz, J., Weiss, D. & Rosenberg, G., Interaction of shaped-charge jets with reactive armor. Proc. 8th Int. Symp. on Ballistics, Orlando, FL, pp. VII-15-VII-20, 1984.

[2] Held, M., Effectiveness factors for explosive reactive armors. Prop. Explos. Pyrotech, 24, p. 70, 1999.

[3] Koch, A. & Haller F., Sensitivity of ERA boxes initiated by shaped charge jets. Proc. 19th Int. Symp. on Ballistics, Interlaken, Switzerland, pp. 1077-1082, May 2001.

[4] Linden, E., Ottoson, J., & Holmberg, L., WHA long rods penetrating stationary and moving oblique steel plates. Proc. 16th Int. Symp. On Ballistics, San Francisco, CA, p. 703, September 1996.

[5] Li, K., A new approach to study impact on moving targets. Proc. 15th Int. Symp. on Ballistics, Jerusalem, Israel, p. 267, May 1995.

[6] Rosenberg, Z. & Dekel, E., On the role of material properties in the terminal ballistics of long rods. Int. J. Impact Eng., 30, p. 83, 2004.

[7] Alekseevskii, V.P., Penetration of a rod into a target at high velocity, Combust. Explos. and Shock Waves, 2, p. 3, 1966.

[8] Tate, A., A theory for the deceleration of long rods after impact, Mech. Phys. Solids, 15, p. 387, 1967.



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