1283.PDF

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
LONG-ROD MOVING-PLATE INTERACTION
Y. Partom
Rafael, P.O. Box 2250, Haifa 31021 Israel
Understanding the mechanics of interaction of a long rod projectile with a forward moving plate at
an angle is essential to understanding long rod interaction with an explosive reactive armor cassette.
To investigate the mechanics of such an interaction we use AUTODIN2D/EULER in plane
geometry, although the problem is 3D. We assume that this is a satisfactory approximation, as we're
only interested in the main features, and are not comparing fine details to experimental results. From
the simulations we learn that the interaction never reaches steady state. Initially each material splits
into two streams, and the interaction plane is perpendicular to the rod. But with time the interaction
plane rotates slowly, until it becomes parallel to the rod, which is then able to continue moving
forward without interruption. During this process interacting rod material of length AL is diverted at
an angle and becomes ineffective for penetrating the main target. We made many such runs to
determine the dependence of AL on the parameters of the problem. This dependence makes it
possible to predict AL for a variety of rod-plate situations.
We use AUTODYN2D/EULER in plane
geometry.
The
problem
is
3D,
but
AUTODYN3D/EULER was not fully debugged
when we did this work. WE know that plane
geometry is sometimes only a crude approximation
to a 3D problem, but we believe that it can
reproduce the correct physical picture. Using an
Euler grid, it is more efficient to apply to the
problem a Galilean velocity transformation, so that
the interaction region is almost stationary and
doesn't move out of the grid. Referring to Fig. 1,
Vp is the rod velocity, Vt the plate velocity, and 6 is
the angle between the rod and its projection on the
plate.
INTRODUCTION
The outcome of the interaction of a long rod
projectile with an explosive reactive armor cassette
depends mainly on its interaction with the forward
moving plate (FMP) of the cassette. The outcome
of this interaction depends on many parameters
such as: rod velocity, diameter, density and
strength; obliquity angle; plate velocity, thickness,
density and strength.
In what follows we use computer simulations to
study the physical picture of the interaction, and to
perform an extensive parameter study of the
problem. From the results we formulate a
procedure to predict the performance of the FMP
on degrading the penetration capacity of the rod.
V
P.
Rod
Plate
SIMULATIONS
FIGURE 1. Velocity transformation.
* Work done while on sabbatical leave at SwRI, San Antonio, TX.
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We first decompose Vt into Vt and Vt and then
apply to the system the velocity -V t . The
transformed velocities Vp and Vt are shown in Fig.
2 and given in (1).
FIGURE 2. Transformed velocities.
Vt' = V t /tan9 ; V t "=V t /sin0
v;=v p -v t f f =v p -v t /sine
(1)
We see that the transformed problem is that of two
interacting streams.
In Fig. 3 we show material location plots every
100 jus from an AUTODYN run. The grid cells are
1x1 mmxmm throughout. The initial projectile is
Hp=10 mm thick tungsten alloy with pp=17.0
g/cm3, Yp(flow stress)=1.2 GPa, Gp(shear
modulus)=140 GPa? STFp(strain to failure)=0.1 and
Vp =0.75 km/s. More projectile material is fed in
from the boundary at the same velocity up to a total
length of 300 mm (L/H=30). The plate is at an
angle of 30°, is Ht=10 mm thick, is made of steel
with pt=7.83 g/cm3, Yt=1.0 GPa, Gt=80 GPa?
STFt=0.5 and Vt'=0.75 km/s. More plate material is
fed in from the boundary at the same angle and
velocity.
From Fig. 3 we see that both rod and plate split
into two streams of unequal thickness. For the rod
the upper branch is thicker, while for the plate the
lower branch is thicker. The interaction surface
rotates slowly clockwise until it finally breaks up,
and the two flows slide past each other. In this run
the length of the rod that stays approximately
straight and aligned with the x direction is 34 mm,
so that AL=266 mm of the length is diverted and
becomes ineffective for penetrating the main target.
We repeated the run with different values of V p ,
and in Fig. 4 we show results for AL as a function
of Vp for runs with Vt=0.5 km/s. We see from Fig.
4 that for Vp <0.73 km/s, the entire rod (300 mm)
is diverted away from its original direction, most of
it upwards. For Vp >0.73 km/s only part of the rod
is diverted. We also see that AL is quite sensitive to
FIGURE 3. Material location plots for a run with Vp'=Vt'=0.75
km/s.
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g/cm3, pp=17.0 g/cm3. Around the nominal set we
evaluate the partial derivatives dajdxj by giving
each parameter a displacement Ax,- and running the
simulation. We then evaluate the derivatives by:
projectile velocity. For the above plate velocity (0.5
km/s at 30°), the range 0.5<VP<0.8 km/s is
equivalent to 1.5<VP<1.8 km/s (also shown in Fig.
4), which is the ordnance range for long rod
projectiles. We see that for the high end of this
range the FMP is only partly effective in diverting
the rod. Beyond Vp=2 km/s only a small part of the
rod would be diverted.
^foj __ \ i /displaced
——-— — -f
r
J
V J''displaced
\ i /nominal
7
\————
,~^
(:))
V JAiominal
Two examples of the displaced and nominal
hyperbolas are shown in Figs. 5 and 6.
—»— Nominal, (y-71.6Xx-0.7)=10.37
--»—Yp=2.0 GPa, (y-72.3Xx-0.75)=6.58
300
260
S1 200
b.
100
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Transformed projectile velocity (km/s)
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Transformed projectile velocity (km/s)
FIGURE 4. Diverted projectile length versus transfbrmed
projectile velocity for Hp/Ht=l, Vt=0.5 km/s and 0=30°.
FIGURE 5. AL versus V p . Nominal runs (circles) and runs with
displaced Yt (squares). Curves are the fitted hyperbolas.
PARAMETER STUDY
Nominal, (y-71.6Xx-0.7)= 10.37
Vt prime =1.386 km/s, (y-81.4Xx-1.25)=9.84
Performing many runs like that described in the
previous section, but with different values of the
parameters, we find that for all the cases that we
checked, the AL(VP ) relation is always a
hyperbola-like curve that can be fitted with:
(AL-a 1 )(v;-a 2 ) = a 3
(2)
where ai (i=l,3) depend on the material and
kinematics parameters. Denoting the parameters by
Xj we have:
a^a^xj i = l,3 ; j = l,10
(3)
To first order approximation we can express ai(Xj)
by:
*i
=
(ai)nom 1 nal + Z^-( X J-( X j)nominJ
Transformed prqectile velocity (km/s)
FIGURE 6. Same as Fig. 5 but with Vt' displaced to 1.386 km/s.
The partial derivatives extracted in this way are
shown in Table 1.
To check our prediction procedure using these
partial derivatives we performed additional
simulation runs in which we used the nominal set
of parameters, but with the rod and plate materials
interchanged. In Fig. 7 we compare the results
<4>
relative to a nominal set of parameters Xj.
The nominal set of parameters we use is
Vt =0.866 km/s, 9=30°, Hp=Ht=10 mm, Yt=1.0
GPa, Yp=1.2 GPa, STFt=0.5, STFP=0.1, pt=7.83
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obtained from the runs to those predicted from the
partial derivatives.
We see from Fig. 7 that the prediction is not
ideal, but in view of the large change in density
relative to the nominal case, it is satisfactory.
In subsequent work use this approach in a model
to predict the performance of explosive reactive
cassettes against long rod projectiles.
TABLE 1. Partial derivatives of parameters ai in (2)
with respect to material parameters
i=2
i=l
i=3
Xj
displace
ment
0.7
Nominal
71.6
10.37
mm
km/s mm2/|is
8i
67.4
0.75
0.5 GPa
Displ. ai
8.13
-8.40
0.10
-4.48
dai/dYt
72.3
0.75
Displ. ai
0.8 GPa
8.58
0.875 0.0625
-2.24
dai/dYp
-0.4
0.4
5 g/cc
- 5 g/cc
5 mm
0.52 km/s
5 mm
5 degrees
Displ. ai
dai/dSTFt
Displ. ai
dai/dSTFt
Displ. ai
daj/dpt
Displ. ai
da/dpp
Displ. ai
dai/dHp
Displ. ai
daJdVt
70.8
2.0
64.1
-18.75
111.8
8.04
88.7
-3.42
74.1
-0.5
81.4
18.85
0.75
-0.125
0.7
0
0.90
0.04
0.85
-0.03
0.7
0
1.25
1.058
7.80
6.425
10.14
- 0.575
11.86
0.298
11.97
-0.32
14.02
0.73
9.84
-1.019
Displ. ai
dai/dHt
Displ. ^
dai/dO
65.7
-1.18
56.0
-3.12
0.75
0.01
0.65
-0.01
22.51
2.428
10.12
-0.05
SUMMARY
We use AUTODYN2D/EULER in plane
geometry to study the phenomenology of long rod
interaction with a forward moving plate. The
essence of the phenomenology is that part or the
entire projectile is diverted from the original
direction, and thereby becomes less effective in
penetrating the main target. In reality, the diverted
projectile is bound to break into several fragments.
Performing many simulation runs with different
sets of parameters we conclude that, the relation
AL(Vt ) can always be fitted by an hyperbola with
three parameters en that depend on the problem
parameters Xj. We evaluate the partial derivatives
da/dxj numerically, and are able to predict ai(Xj)
using a first order approximation.
Applying this approach to realistic situations of
long rod interaction with an explosive reactive
cassette (not reported here), we find that potential
benefit of such cassettes against long rods cannot
be fully exploited because of practical geometrical
constrains.
600
-. 500
REFERENCES
— Nominal
— — Simulation, interchanged materials
— Predicted from partial derivatives
This reference list is empty, as we couldn't find
anything relevant to the subject in the open
literature.
£ 400
I
= 300
K 200
I 100
Q
0.6
0.8
1
1.2
1.4
1.6
1.8
2.2
Transformed projectile velocity (km/s)
FIGURE 7. Results of check runs.
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