CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
ON THE ENTRANCE PHASE IN LONG ROD PENETRATION
Z. Rosenberg and E. Dekel
RAFAEL, P.O. Box 2250, Haifa, Israel
Abstract. The penetration of long rods into semi-infinite targets is a three-stage process, in which the
first (entrance) and last are very short, and transient, while the second phase (primary penetration) is
a long and quasi-steady process. The present paper summarizes our recent work on the entrance phase
using 2D numerical simulations of strengthless steel rods (L/D=5-20) impacting aluminum targets at
l-4km/s. We look for the significance of this phase as impact velocity, target strength, and
penetrator's length are increased. We also show that the target free surface (impact face) is not the
cause for the entrance phase. Rather, it is the passage from a cylindrically-shaped to a mushroomshaped penetrator nose which is responsible for this phase.
INTRODUCTION
recently that, the characteristics of the entrance
phase are not due to the free surface of the target.
He performed 2D numerical simulations in which
he supported the area around the impact area with
a rigid wall, and monitored the penetration depths
of an L/D^IO tungsten alloy rod impacting a steel
target.
The penetration of long rods into semi-infinite
targets, is considered as a three-stage process (see
Orphal [1], for example). The transient first and
third stages are very short compared with the
relatively long middle stage which has steady-state
characteristics. The one-dimensional model of
Tate [2] and Alekseevskii [3] accounts for the
main features of the steady state, using a modified
Bernoulli
equation
and considering the
deceleration of the rod during penetration. Orphal
summarizes much of the work performed on the
third stage considering the extra penetration in the
target right after the completion of rod
consumption. This stage has also been investigated
by us recently [4] in a numerical study of the
secondary penetration process. The first stage in
the penetration process (termed the entrance
phase) has received relatively less attention,
because it is considered as very short, and thus,
less important. Ravid et al. [5] analyzed the
transient passage from a 1-D planar shock-wave
model, which results at the impact of a cylindrical
rod on a flat target, to the 2D penetration mode
several microseconds later. Partom [6] has argued
The purpose of the work presented here is to
highlight some of the typical aspects of the
entrance phase by using 2D simulations for long
steel rods impacting semi-infinite aluminum
targets.
NUMERICAL SIMULATIONS
The 2D simulations were performed with the
Eulerian processor of the PISCES 2DELK code.
As always, our meshing has 11 cells on the
penetrator radius and a similar meshing for the
central region of the target (about 5 penetrators
diameters). Farther, zones have coarser meshing
by a factor of 1.05. The target side and back
surfaces are supported by FLOW conditions, thus,
guaranteeing its semi-infinite nature.
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Our simulations follow the time histories of the
penetration velocity, penetration depth, rod length,
and the pressure at the penetrator-target interface.
From all these, we chose the penetration velocity
for our examinations of the entrance phase since it
is much more sensitive to subtle changes in the
relevant parameters. The penetration process is a
good example, since penetration depth histories are
much less sensitive than either interface pressures
or penetration velocities. We also found that it is
much better to simulate penetrations of zero
strength rods since these attain a true steady-state
penetration right after the entrance phase, which
simplifies the distinction between the two phases.
Thus, in all simulations presented the steel rods
are strengthless, while the aluminum targets have
a strength in the 0.4-1.6GPa range. We used a
simple von-Mises strength criterion with no
hardening or failure mechanisms. Since we are
mainly interested in the first stage of penetration,
while interface pressures are very high, fine details
in constitutive relations, such as strain to failure
have negligible influence.
As expected, the relative importance of the
entrance phase diminishes as L/D increases. This
is the reason for the choice of L/D=5 rods for our
next set of simulations with different impact
velocities. Figure 2 shows the results of this set for
velocities in the range of 1-2.5 km/s. It is clear
that the relative importance of the entrance phase
decreases with increased velocity, as expected.
2.0
1.51.0-
I
•5
0.0
-0.5
0
60
80
100
Thus, as far as the entrance phase is concerned,
its contribution diminishes with higher velocities
and longer rods. This is the reason for the success
of the ID penetration models for fast long rods and
shaped charge jets, for which the penetration is
mostly a steady-state process.
The first simulations with different L/D rods
150
40
FIGURE 2. Increasing impact velocities.
demonstrate the fact that the entrance phase is not
dependent on rod length and is over in a very short
time. Figure 1 shows the time histories of the
penetration velocities for L/D=5, 10 and 20 steel
rods impacting a semi-infinite aluminum target at
3 km/s.
100
20
Time (jisec)
RESULTS AND DISCUSSION
50
0.5-
We should note here that the time scales for the
entrance phase are 10-25 microseconds (see Figure
2). These are much longer than the time scales
that Ravid et al. [5] relate to this phase, assuming
it lasts as long as rarefactions from penetrator sides
reach its center (a few microseconds).
In order to examine the influence of target
strength on the entrance phase, we performed
several simulations with target strengths in the
range of 0.4-1.6 GPa. Figure 3 shows results of
these simulations at an impact velocity of 2 km/s.
It is evident that with increasing target strength the
relative importance of the entrance phase
increases. It is interesting to note the effect of
target strength on the steady-state penetration
velocity which decrease from 1 km/s (for a 0.4 GPa
200
Time (Msec)
FIGURE 1. Penetration velocity for three L/D rods.
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target) to 0.7km/s, for the strongest target (1.6
GPa).
0
50
Since both simulations resulted in very similar
time histories for the penetration velocity, one can
conclude that the effect of the free surface of the
target is indeed negligible. This result strongly
supports the conclusion of Partom [6] who
followed the penetration depths of tungsten alloy
rods into steel targets, with similar simulations.
The main conclusion from this set of
simulations, is that the entrance phase is due to the
non-steady nature of the penetration at its first
stage. This is the result of the process by which
the rod nose is changing from a cylindrical shape
to the well-known mushroom shape during the
steady-state stage. In order to demonstrate this
issue, we performed an extra simulation in which
the rod is penetrating first a thin target, 40mm
thick. After the rod nose becomes mushroomshaped, as it leaves the thin target, it then impact a
semi-infinite target positioned 40mm away. Figure
5 shows the result of this simulation where zero
time for the split target coincides with the
mushroom-shaped projectile impacting the semiinfinite target
100
Time (usec)
FIGURE 3. The effect of target strength.
The issue we explored next concerns the
question that was dealt with by Partom [6]. It is
known that penetration is easier at the first stage,
where the penetrator is close to the target free
surface. The question Partom raised is whether this
fact is the cause of the entrance phase. In order to
answer this question, we performed a simulation
with a target having a deep circular hole in its
middle. This way the penetrator hits the target in
an area, which is deep inside (33 mm) and the
effect of the free surface is diminished. The hole
diameter is just slightly larger than that of the rod
(9 mm vs. 8.0 mm). Figure 4 shows the results of
this simulation, together with the reference
simulation for a regular target. In both cases, the
strength of the target is 1.2 GPa and the impact
velocity is 2 km/s.
——Reference Target
——SpKTarget
10
—Reference Target
Holed Target
20
30
Time (jisec)
FIGURE 5. A mushroom-shaped rod compared with a
cylindrical one.
0
10
Time(fisec)
We can see from the figure that the entrance phase
is greatly influenced by the nose shape of the
projectile. The mushroom-shaped rod, in the split
target, penetrates with a higher velocity during the
entrance phase. Thus, it is more effective than the
cylindrical rod. Moreover, the penetration velocity
history of this rod looks like the ideal two-step
20
FIGURE 4. Comparison between a regular target and one
with a deep circular hole.
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history, in which the first (higher) step
corresponds to the impact shock, and the second
(lower) step to steady-state value.
CONCLUSIONS
The 2D numerical simulations presented here,
highlight some of the relevant aspects of the
entrance phase in the penetration process of long
rods into semi-infinite targets. In particular, it is
shown that with increasing impact velocity and rod
length, the significance of this phase diminishes,
while the opposite is true for increasing target
strength. Moreover, we strengthen the claim that
the origin of this phase is in the passage from a
cylindrical-shaped rod to a mushroom shape.
REFERENCES
1. D. L Orphal, Int. J. ImpactEng. 20,601 (1997).
2. A. Tate, J. Mech. Phys. Solids, 15,387 (1967).
3. V.P. Alekseevskii, Comb. Explos. and Shock Waves,
2,63(1966).
4. Z. Rosenberg and E. Dekel, Int. J. Impact Eng., to
be published.
5. M. Ravid, S.R. Bodner and I. Holcman, Int. J. Eng.
ScL, 25,473 (1987).
6. Y. Partom, Proc. APS Conf. On Shock Waves in
Condensed Matter, eds. S.C. Schmidt and W.C. Tao
(New York, 1995), p. 1123.
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