Abstract --The problem of reducing the jet penetration capability upon its interaction with the finite-thickness target, due to the erosion of the front region of the jet having perforated through the target, is considered. The experimental examination and the mathematical modeling of the process were performed; semi-empirical formulas were obtained. The calculation techniques are shown to allow the description of interaction processes with satisfactory accuracy

Boris A Klopov

Nicolai P Kovalev

Oleg V Svirsky

Vadim V Bashurov

Victor A Krutyakov

CiteSeerX

PERGAMON 
INTERNATIONAL 
JOURNAL OF 
IMPACT 
ENGINEERING 
International Journal of Impact Engineering 26 (2001) 735-744 
www.elsevier.com/locate/ijimpeng 
THE SHAPED CHARGE JET INTERACTION WITH FINITE 
THICKNESS TARGETS 
OLEG V. SVIRSKY, NICOLAI P. KOVALEV, BORIS A. KLOPOV, 
VADIM V. BASHUROV, and VICTOR A. KRUTYAKOV 
Russian Federal Nuclear Center-VNIIEF, Sarov, Nizhnii Novgorod Region, 607190, RUSSIA 
Abstract - -  The problem of reducing the jet penetration capability upon its interaction 
with the finite-thickness target, due to the erosion of the front region of the jet having 
perforated through the target, is considered. The experimental examination and the 
mathematical modeling of the process were performed; semi-empirical formulas were 
obtained. The calculation techniques are shown to allow the description of interaction 
processes with satisfactory accuracy. © 2001 Elsevier Science Ltd. All rights reserved. 
Keywords: shaped charge, jet, target, foreshortening, erosion, perforating, penetration, tip 
velocity, standoff distance. 
AI 
V 
Vt 
B 
A 
S 
P 
P 
u 
FS 
RHA 
HE 
NOTATION 
jet diameter 
additional jet length erosion 
jet tip velocity 
jet tail velocity 
virtual origin 
target thickness 
standoff distance 
penetration 
density 
penetration velocity 
foreshortening (jet shortening due to radial erosion of  its front region) 
rolled homogenous armor 
high-energy explosives 
INTRODUCTION 
Notwithstanding considerable efforts made by many researchers and in spite of  its great 
practical importance, the problem of calculation description of the shaped charge jet interaction 
with the target, still remains not studied enough. The sophistication of  calculations considerably 
increases, for instance, in the problems of  gas-oil well perforating, where the geometry of the 
target and the heterogeneity of  its materials play a significant role. It is essential that the 
interaction is not strictly axisymmetric, and direct numerical modeling requires the application of 
three-dimensional and probabilistic algorithms. 
0734-743X/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. 
PII" S 0 7 3 4 - 7 4 3 X ( 0  1)001 23-3  
736 O.V. Svirsky et al. / International Journal of Impact Engineering 26 (2001) 735-744 
The existence of the said difficulties does not allow the obtaining of the direct problem 
solution. In this case, it is worthwhile solving the problem stage-by-stage splitting it into 
separate sub-problems, which can be resolved in one or another way. 
In the given paper, the problem concerning the interaction of the shaped charge jet with the 
target whose thickness does not exceed several jet diameters as well as with a set of such targets, 
spaced at some distance apart from each other, is considered. The existence of air gaps between 
such targets lead to additional losses of the jet length due to the erosion of its tip region upon the 
target perforation, which was first noticed by Brown and Finch [1] and was termed 
"foreshortening" (forefront shortening). 
The aim of the present work is to investigate this problem both computably and 
experimentally, and to derive semi-empirical formulas enabling the calculation of losses of the 
jet penetration capability upon separate and spaced-apart targets perforation. 
DESCRIPTION AND EXPERIMENTAL CONFIRMATION OF THE JET TIP 
EROSION EFFECT UPON FINITE THICKNESS TARGET PERFORATION 
Upon penetration of the shaped charge jet into the target, jet "wear" takes place, i.e. its 
energy, mass and length are spent for target perforating. The process of jet 'wear" considerably 
varies if the target is not semi-infinite, i.e. if its thickness is limited or if the target consists of 
several layers separated with air gaps. The point is that during the process of the target 
perforating, the compression of the jet material occurs. Upon leaving the target, the relief of  the 
compressed material takes place leading to considerable expansion of the jet tip having left the 
target. It is evident that the jet region, expanded radially, has the reduced penetration capability. 
Brown and Finch [ 1 ] noticed the additional loss of the jet length due to the erosion of  its tip upon 
the target perforation. They suggested its accounting by introducing a certain arbitrary shim on 
the jet way, having no thickness but interacting with the jet in the same manner as does a 10-mm 
steel plate. In the next papers, Chanteret [2,3] presented a semi-empirical formula to calculate 
the loss of the jet length due to the foreshortening effect: 
A I  _ 2 . 9 .  1 -  e dj 
dj (1) 
The accounting of the foreshortening effect with the use of this empirical formula allowed 
Chanteret to essentially improve the calculation results for the finite-thickness-target perforation 
by a jet. 
Figure 1 show the X-ray radiograph of copper jet with the radially expanded tip. Upon 
perforating the 8-mm-thick steel plate at the angle of 90 degrees, the 100-mm-caliber shaped 
charge jet has the tip velocity of - 8.8 km/s. The dimensions of the jet's blurred tip are the 
following: the length is - 9 jet 's diameters, the mean diameter is -5.5 jet 's diameters. 
Fig. 1. The jet upon perforating the 8-mm-thick steel plate (reconstruction of X-ray radiograph). 
O.V. Svirsky et al. /International Journal of Impact Engineering 26 (2001) 735-744 737 
The presented X-ray radiograph is the direct experimental evidence of the foreshortening 
effect existence, though it does not offer enough information for qualitative description. The 
process's in-depth study can be performed using the multi-frame flash radiography, which 
requires a great number of experiments with shaped charges. The application of numerical 
simulations followed by the experimental results calibration, with the limited number of 
experiments, is a less expensive though a highly effective technique as well. The said 
investigation technique is employed in the present paper. 
H Y D R O C O D E  MODELING OF JET INTERACTION WITH THE FINITE- 
THICKNESS TARGET 
To study the effect of various factors (of the jet velocity, of the target material and thickness) 
on the loss value AI of the jet length in detail, the numerical simulation of the physical model 
"target-jet", using the EGAK [4] and SPH [5] 2D-hydrocodes, was carried out. An Eulerian 
(stationary) computational grid and a concentration method for visualizing of different 
components are used in EGAK. An irregular moving computational grid and a smoothed 
particle method [6] are used in SPH. Equations of state, of the Mie-Gruneisen form, and 
constitutive relations were taken from the material library of the EGAK and SPH codes. 
Although these two methods are very different, they produced results coinciding with 5% 
accuracy. 
Two bodies represent the <~target-jet>> model. The 50-mm-diameter and A-thick (1; 2; 6; 10 
mm) immovable metal (steel or aluminum) "A" plate represents a target. The 4 mm-diameter 
and/-long flat-faced copper "B" rod, moving with the velocity V (4; 6; 8; 10 km/s), represents a 
jet. The zone size in the computational grid was chosen so that there were 64 zones across the 
diameter of the jet. The flow pattern obtained in the EGAK computation for several instants of 
time are given in Fig.2. 
Upon perforating the target and after the arrival of the tip (front end) of the "B" rod at the free 
surface of the "A" plate, the process of relief of the front region of the "B" rod, compressed in 
the process of perforation, and of material particles' flying apart begins. This process leads to 
further reduction of the rod length to the finite value l .  Subtractmg the equwalent (an 
hydrodynamic approximation) thickness of the perforated target from the length difference (l-l*), 
we will obtain the rod length loss Ales due to the foreshortening effect: 
Alrs = I - I * - A .  e ~  (2) 
The results are given in Tables 1-2, where the rod length losses, due to foreshortening, are 
given for different target materials and thickness as well as on the jet velocity V. 
Table 1. Calculated copper rod length losses for steel targets 
V, km/s u, km/s Code 
Losses for steel, mm 
A=I A=2 A=6 A=IO 
4 2.08 
6 3.11 
8 4.13 
8 4.13 
10 5.15 
* Values not calculated 
EGAK * 5.2 7.8 8.6 
EGAK * 6.4 8.9 10.0 
EGAK 5.7 7.3 9.8 10.7 
SPH 5.0 6.9 10.1 11.3 
EGAK * 7.9 10.3 10.8 
738 O.V. Svirsky et al. /International Journal of Impact Engineering 26 (2001) 735-744 
T=0 mks T=6 mks 
T=2 mks T=8 mks 
T=4 mks 
S. 
T =10 mks 
°$ .  
Fig. 2. EGAK hydrocode computation illustrating the additional jet erosion effect on finite 
thickness plate perforation. 
O.V. Svirsky et al. /International Journal of Impact Engineering 26 (2001) 735-744 739 
Table 2. Calculated copper rod length losses for aluminum targets 
Losses for aluminum, mm 
V, kngs u, km/s Code 
d=2 A=6 A=IO 
4 2.72 EGAK 3.5 4.6 5.1 
6 4.05 EGAK 4.6 5.8 6.3 
8 5.37 EGAK 5.5 6.6 7.2 
8 5.37 SPH 5.3 7.0 7.6 
10 6.70 EGAK 6.2 7.0 7.5 
With the further processing of the calculation results the attempt was made to derive the semi- 
empirical formula, including parameters, easily measured in the experiments, namely the target 
thickness, the jet velocity and diameter, for calculating the jet length losses AlEs. Of course, this 
processing is only formal mathematical procedure for searching of better functional form than 
Chanteret formula. 
The dependence of loss on the target thickness A was sought in functional form flA/(A+dj)). 
The AIFs results, obtained from the calculations performed using EGAK, were described by the 
power function, whose base slightly varied depending on the jet velocity, and the exponent 
variations linearly depended on V (Fig. 3, 4 for specific target materials). Averaging the base 
value, one can write it as a constant coefficient of the parameter A/(A+dj). The coefficients of 
the linear function from V, describing the exponent k (V), can be easily found from the curve of 
this linear function (Fig. 3, 4). 
The final formula is written as: 
B-C.V 
(3) 
where: for steel A=3, B=0.8, C=0.04 
for aluminum A=2, B=0.65, C=0.04 
Let us see how values ALES. derived by using the Svirsky and Chanteret formulas, agree with 
the calculated data, derived by the two-dimensional EGAK and SPH codes. Since the Chanteret 
formula was derived only for a steel target and is illustrated by the data for the jet velocity V=8 
km/s, then, for comparison, the same initial data should be taken both in the Svirsky formula and 
in the EGAK and SPH calculations. Fig.5 represents curves AIFs=f(A) obtained in various ways. 
It is seen that in the range A~.3-10 mm, all the curves are in satisfactory agreement with each 
other, in addition, the calculations by the Chanteret formula exhibit the greatest discrepancy with 
EGAK and SPH. 
THE EXPERIMENTAL VERIFICATION OF THE SEMI- 
EMPIRICAL FORMULA 
Let us consider the capabilities of the computation techniques for calculating the perforation 
losses in the problems of the jet penetration through the spaced targets. Fig.6 represents the 
layout of the experiments involving the interaction of the 120 mm-caliber shaped charge with the 
spaced targets. 
740 O.V. Svirsky et al. / International Journal of lmpact Engineering 26 (2001) 735-744 
12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  
Al(v.m ) = 12,5945 °,42°7 
10 R 2 = 0,9938 
8 A/Iv'sI = 12'6658" ~°ls 
R -~= 1 
6 12 0761~'5793 A/(v..*) = , 
4 R 2 = 0,9988 
2 AI(v'4) = 10'8555°'6677 
R 2 = 0,9987 
0 
0.2 0.4 0,6 0,8 
6=dd(A+dj) 
{eV-~lkm/s AV=6km/s llV=Skm/s eV=10kmls] 
~ tmnr ~ ~eqm=t on the~tity ktV) 
0 , 8  t ..................................................................................................................................... 
0,7 ~ k=-O, C409V+0,8289 
0,5 
a4 
o31 
2 4 6 8 10 I2 
V, lefts  
Fig. 3. The computation results approximation for steel targets. 
8 
7 
6 
5 
~ 4  
3 
2 
I 
0 
0.2 0,4 0.6 
~eV-~km/s AV=6km/s mV=8km/s *V=lOkm/sJ 
A/~v.tol = 8.03118 °~u 
R 2 = 0.9788 
A/tv.Bi = 7,983750-~24 
R 2 = 0,9896 
A/tv.~l = 7,19085 °'4°~ 
R ~ = 0,9987 
A/iv.41 = 5.9595~ °.4~6 
R 2 = 0,9977 
0,8 
~ r m r  ~ a r ~ m = t  ~ t  ~o~ty ~ 
0,6 ............................................................................................ 
0,5 ~ k = "0,0405V + 0, 6521 
0,4 = 
0,3 
0,2 
0,t 
4 6 8 10 
V, lan's 
Fig. 4. The computation results approximation for aluminum targets. 
12 ] ,, a 
10 ~ 8 
8 
6 
4 
2 
0 
| 
0 1 2 3 4 5 6 7 8 9 10 I1 
A 9 real 
I O E G A K  ~ Chantaret  + Svirsky t~ SPH [ i J 
Fig. 5. The comparison of dependencies Alvs=f(A) obtained in various ways 
(A-thickness steel target, V=8 km/s, dj=4 mm.) 
O.V. Svirsky et al. / International Journal of Impact Engineering 26 (2001) 735-744 741 
Two experiments were performed in the same setup. The jet velocities in different regions 
and the residual penetration in the last steel target were calculated using the ATOS [4] technique 
both with accounting of foreshortening effect and without it. The results of calculations and 
experiments are presented in Table 3, where the indices Vi0 indicate the jet velocities in front of 
the target and Vii - are the jet velocities behind the target. 
Table 3. Calculated and experimental data for 120-mm shaped charge 
V, km/s 
Calculations Calculations Experiment 
without with 
foreshortenin~ foreshortening, "V-° I N_o2 
Vl0 8.8 8.8 8.77 8.8 
V2o 8.3 8.17 8.15 8.25 
V21 7.77 7.64 7.65 7.7 
V30 7.77 7.55 7.59 7.62 
V31 7.34 7.12 7.16 7.11 
V40 7.34 7.04 7.0 7.03 
pC*) 0,832 0,782 0,802 0,775 
(*) - the part from the mean penetration value with the charge affecting the target 4, with no 
additional targets 1-3 being installed. 
As it is seen from Table 3, the calculation values V and P with the accounting of the 
foreshortening effect are in much better agreement with the experiment than without accounting 
of this effect. 
100 mm-caliber shaped charge results appear more convincing. The layouts of the 
experiments are represented in Fig.7. 
The experimental data on the tip velocity of the shaped charge jet, on residual penetration in 
the last steel target as well as the calculation data with the accounting of the foreshortening effect 
and without it are presented in Tables 4,5. 
Table 4. Calculated and experimental data for 100-mm shaped charge 
(First layout) 
Calculations 
Calculations with 
V, km/s without Experiment 
foreshortenin~g foreshortening 
Vt0 9.3 9.3 9.3 
V20 9.09 8.82 8.73 
V3o 8.83 8.41 8.44 
P(*) 0,900 0,841 0,812 
742 O.V. Svirsky et al. /International Journal of lrapact Engineering 26 (2001) 735-744 
5 2 
I 
6 1 
400 
600 
800 
1 
900 
1,2,3,4 - Steel targets 
5 - Shaped charge 
6 - Contact guides 
3 
i nfinite 
4 
Fig. 6. The layout of the experiments with 120-mm-caliber shaped charge. 
5 4 
\ 
1 2 
Semi - infinite 
3 
S2 ~ > 
$3 
1, 2 - Additional targets 
3 - Main steel target 
4 - Contact guides 
5 - Shaped charge 
Sl 
Exper. 1 195 
Exper. 2 160 
AI 
8" 
12"" 
$2 A 2 
475 30" 
475 50- 
* - Aluminum 
**- Steel 
$3 
580 
675 
Fig. 7. The layout of the experiments with 100-mm-caliber shaped charge. 
O.V. Svirsky et aL /International Journal of Impact Engineering 26 (2001) 735-744 743 
Table 5. Calculated and experimental data for 100-mm shaped charge (Second layout) 
Calculations 
Calculations with 
V, km/s without Experiment 
foreshortening foreshortening 
Vl0 9.3 9.3 9.3 
V20 8.96 8.64 8.64 
V30 8.22 7.8 7.42 
P(*) 0,782 0,718 0,708 
(*) - the part from the mean penetration value with the charge affecting the target 3, with no 
additional targets 1-2 being installed. 
Here, as well as in the previous experiments, one can note the satisfactory agreement of the 
calculations with the experimental data. 
Because the proposed formula (3) differs from Chanteret's model primarily in prediction of 
foreshortening through thin plates (A/dj<l) some additional experiments were made to validate 
it's significance. Experiments have been performed using 46-mm caliber point initiated shaped 
charges with 70 ° opening conical 1-mm thickness copper liner. The main jet parameters are 
presented in Table 6. 
Table 6. Jet parameters 
Parameter Value 
Virtual origin, B 20 mm 
Tip velocity, V 6.6 km/s 
Tail velocity, Vt 3.0 km/s 
Jet diameter, dj 3.0 mm 
(at 20-mm standoff) 
Breakup distance, Xb 350 mm 
The first three experiments were made to determine the penetration value in RHA target at 
100-mm standoff. Then an additional 1-mm thickness steel plate was installed at 20-mm 
standoff (Sp) and three recurrent experiments were made. The experimental data on residual 
penetration in the last RHA target are presented in Table 7. 
Table 7. RHA penetration data 
Exp. Additional Penetration, Average 
No plate mm value 
1 N o  160 
2 No 161 
3 No 150 
4 Yes 120 
5 Yes 129 
6 Yes 123 
157 
124 
The jet penetrates continuously because the sum of target standoff and penetration value is no 
greater than the breakup distance. Thus the penetration value is given by Allison-Vitali formula 
[7,8]. 
744 O. V. Svirsky et al. /International Journal of lmpact Engineering 26 (2001) 735-744 
P = ( S  + B ) .  - 1  
(4) 
Using Eq. (4), jet parameters (Table 6) and penetration value P=124 mm (Table 7) allows to 
calculate the residual jet x~elocity Vr =5.84 km/s after 1-mm plate perforating and foreshortening. 
The calculated jet velocity after 1-mm plate perforating only is equal Vp=6.45 km/s. The 
experimental value for the loss of the j et length due to the foreshortening can be calculate as AIFs 
= (Sp+B+A).(Vp-Vr)/Vp. Table 8 represents values AIFs obtained in various ways. 
Table 8. Jet length losses AlEs 
Calculation 
Experiment Chanteret (1) Svirsky (3) 
2.67 mm 4.22 mm 
3.88 mm 
(-31°/o / (+9% / 
CONCLUSION 
The numerical modeling of the interaction process between the jet and the finite-thickness 
target was performed. The empirical formula, enabling the calculation of  losses AIFs, using the 
known initial data, namely the thickness and the target material, the velocity and the diameter of  
the jet region, interacting with the target, was derived. The results of calculation performed 
using this formula are in satisfactory agreement with the results of 2-D hydrocode computation 
and with the Chanteret calculations [3]. 
The algorithm of additional loss accounting, based on the derived empirical formula, was 
introduced into the ATOS program for the penetration computation. Its application allowed the 
calculation of  the residue jet penetration after passing through the additional targets, spaced 
apart, with the deviation of not more than 4% from the values obtained in the experiments. 
REFERENCES 
[1] J. Brown and D. Finch. The Shaped Charge Jet Attack of Confined and Unconfined Sheet Explosive at 
Normal Incidence. Proc. llth Int. Syrup. Ballistics, Brussels, 9-11 May 1989. 
[2] P.Y. Chanteret. On Modelling of Shaped Charges Jet Interaction with Spaced Plates. Proc. 6th Int. Syrup. on 
Interaction of Nonnuclear Munitions with Structures. Panama City Beach, 3-7 May 1993. 
[3] P.Y. Chanteret. Considerations about the Analytical Modeling of Shaped Charges. Propellants, Explosives, 
Pyrotechnics, 1993; 18: 337-344. 
[4] I.D. Sofronov, R.I. Ilkaev, N.P. Kovalev and O.V. Svirsky. Calculation of shaped charge performance. Proc. 
Int. Seminar on Fundamental Problems of Cumulation. St. Petersburg, July 7-12,1997. 
[5] V.V. Bashurov, G.V. Bebenin, A.G. Ioilev. Numerical simulation of rod particles hypervelocity impact 
effectivity at various attack angles. Space Forum. 1996; 1(1-4): 255-262. 
[6] L.D. Cloutman. Basic of Smoothed Particle Hydrodynamics. LLNL Report. 1990; UCRL-ID-103698. 
[7] F.E. Allison and R. Vitali. A New Method of Computing Penetration Variables for Shaped-Charge Jets. BRL 
Report., January 1963, No 1184. 
[8] W. Schwartz, Modified SDM Model for the Calculation of Shaped Charge Hole Profiles. Propellants, 
Explosives, Pyrotechnics. 1994; 19: 192-201. 


THE SHAPED CHARGE JET INTERACTION WITH FINITE THICKNESS TARGETS

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THE SHAPED CHARGE JET INTERACTION WITH FINITE THICKNESS TARGETS

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