Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner
This study investigates the characteristics of shaped charge jet formed with a high-polymer (PTFE) liner, as well as its penetration capabilities, by theoretical, experimental, and numerical methods. This work presents a viscoplastic model and equation of compressible fluid to describe the jet cohes...
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Yi, J.Y. Wang, Z.J. Yin, J.P. Chang, B.H. 2020-12-12T13:45:34Z 2020-12-12T13:45:34Z 2017 Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner / J.Y. Yi, Z.J. Wang, J.P. Yin, B.H. Chang // Проблемы прочности. — 2017. — № 1. — С. 34-44. — Бібліогр.: 12 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173580 539.4 This study investigates the characteristics of shaped charge jet formed with a high-polymer (PTFE) liner, as well as its penetration capabilities, by theoretical, experimental, and numerical methods. This work presents a viscoplastic model and equation of compressible fluid to describe the jet cohesive condition. It also shows that the high-polymer jet is inevitably distended. Two types of liner materials were studied: a high-polymer PTFE liner and a pure copper one. The corresponding numerical simulations of the two jet formations are presented. The pulse X-ray photographic technology was employed to observe the distended jet of the PTFE liner and the particulate jet of the copper one. The simulation and jet radiography results show that the two types of jet behavior with particulate and radial dispersion are ductile and related to the liner material. The distended jet formation result from the liner material was crushed at the high-pressure region because a sudden pressure jump induces the radial velocity rise, which results in lateral expansion. As compared with a typical copper penetration performance, the polymer distended jet had a larger aperture and lower penetration depth. Due to polymer liner lower density, this jet will have limited penetration as compared to that of a copper liner. The simulated results strongly agree with the experimental ones. The polymer material can be modified to obtain much better performance, which will greatly enhance the penetration capacity of polymer jets. The authors would like to acknowledge the financial support from the Project supported by the National Natural Science Foundation of China under Grant No. 11572291. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner Численное моделирование проникновения размытой реактивной струи кумулятивного заряда с высокополимерной облицовкой в стальную мишень Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner |
| spellingShingle |
Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner Yi, J.Y. Wang, Z.J. Yin, J.P. Chang, B.H. Научно-технический раздел |
| title_short |
Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner |
| title_full |
Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner |
| title_fullStr |
Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner |
| title_full_unstemmed |
Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner |
| title_sort |
numerical simulation of steel target penetration by shaped charge distended jet with a high-polymer liner |
| author |
Yi, J.Y. Wang, Z.J. Yin, J.P. Chang, B.H. |
| author_facet |
Yi, J.Y. Wang, Z.J. Yin, J.P. Chang, B.H. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2017 |
| language |
English |
| container_title |
Проблемы прочности |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Численное моделирование проникновения размытой реактивной струи кумулятивного заряда с высокополимерной облицовкой в стальную мишень |
| description |
This study investigates the characteristics of shaped charge jet formed with a high-polymer (PTFE) liner, as well as its penetration capabilities, by theoretical, experimental, and numerical methods. This work presents a viscoplastic model and equation of compressible fluid to describe the jet cohesive condition. It also shows that the high-polymer jet is inevitably distended. Two types of liner materials were studied: a high-polymer PTFE liner and a pure copper one. The corresponding numerical simulations of the two jet formations are presented. The pulse X-ray photographic technology was employed to observe the distended jet of the PTFE liner and the particulate jet of the copper one. The simulation and jet radiography results show that the two types of jet behavior with particulate and radial dispersion are ductile and related to the liner material. The distended jet formation result from the liner material was crushed at the high-pressure region because a sudden pressure jump induces the radial velocity rise, which results in lateral expansion. As compared with a typical copper penetration performance, the polymer distended jet had a larger aperture and lower penetration depth. Due to polymer liner lower density, this jet will have limited penetration as compared to that of a copper liner. The simulated results strongly agree with the experimental ones. The polymer material can be modified to obtain much better performance, which will greatly enhance the penetration capacity of polymer jets.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173580 |
| citation_txt |
Numerical Simulation of Steel Target Penetration by Shaped Charge Distended Jet with a High-Polymer Liner / J.Y. Yi, Z.J. Wang, J.P. Yin, B.H. Chang // Проблемы прочности. — 2017. — № 1. — С. 34-44. — Бібліогр.: 12 назв. — англ. |
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| first_indexed |
2025-11-27T08:47:35Z |
| last_indexed |
2025-11-27T08:47:35Z |
| _version_ |
1850806720233734144 |
| fulltext |
UDC 539.4
Numerical Simulation of Steel Target Penetration by Shaped Charge
Distended Jet with a High-Polymer Liner
J . Y. Y i,1 Z . J . W ang , J . P . Y in , an d B. H . C hang
School of Mechatronic Engineering, North University of China, Taiyuan, China
1 yijianya513@126.com
This study investigates the characteristics o f shaped charge je t formed with a high-polymer (PTFE)
liner, as well as its penetration capabilities, by theoretical, experimental, and numerical methods.
This work presents a viscoplastic model and equation o f compressible fluid to describe the je t
cohesive condition. It also shows that the high-polymer je t is inevitably distended. Two types o f liner
materials were studied: a high-polymer PTFE liner and a pure copper one. The corresponding
numerical simulations o f the two je t formations are presented. The pulse X-ray photographic
technology was employed to observe the distended je t o f the PTFE liner and the particulate je t o f the
copper one. The simulation and je t radiography results show that the two types o f je t behavior with
particulate and radial dispersion are ductile and related to the liner material. The distended je t
formation result from the liner material was crushed at the high-pressure region because a sudden
pressure jump induces the radial velocity rise, which results in lateral expansion. As compared with
a typical copper penetration performance, the polymer distended je t had a larger aperture and lower
penetration depth. Due to polymer liner lower density, this je t will have limited penetration as
compared to that o f a copper liner. The simulated results strongly agree with the experimental ones.
The polymer material can be modified to obtain much better performance, which will greatly enhance
the penetration capacity o f polymer jets.
K eyw ords: explosive m echanics, shaped charge, high-polym er, jet.
In tro d u c tio n . To produce longer and m ore stable jets, designers have used m etal liner
m aterials because m etals have h igh density, high sound speed, good therm al conductivity,
high dynam ic fracture elongation properties, low viscosity, and low com pression properties.
These are necessary conditions for the form ation of cohesive and stable jets. M ost research
about m etal je ts describe hom ogeneous dense m etal m aterials that form the jet, and the
penetration process through the constant ideal incom pressible fluid theory and quasi ideal
incom pressible theory; this research is relatively mature. However, w ith the developm ent o f
new materials, techniques, designs, and protective devices (composite, reactive, electro
m agnetic, and intelligent armors), there is a need for additional research. M oreover, the
superior protection ability o f the new protective devices challenges the traditional anti
arm or weapons. Considering these factors, the im provem ent o f dam age perform ance o f
armor-piercing w eapons has becom e a research focus in recent years.
Currently, research on liner m aterial is divided into three categories: pure metal,
m ultiphase com posite material, and non-m etal material. Pure m etal liners are m ainly
produced from Cu, Ni, Mo, W, and Ta [1], while m ultiphase com posite ones involve
W -C u, R e-C u, and T a-C u [2]. Cowan and Bourne [3] studied oxide glasses as shaped
charge liner m aterials due to their ability to stretch w ithout the form ation o f necks that
characterize je ts produced from pure m etal liners. Keeskes and W alters [4] studied the
Zr-based bulk m etallic glasses as shaped charge liner materials. The results showed that the
liner behaved sim ilar to particulate je ts m ade from pressed pow der liner materials. Jet
form ation w as asymmetric and the particles in the je t were not uniform in size and
dispersion. Baker et al. [5] used traditional silica-based glasses as shaped charge liner
materials. The je t radiography results show the distinct regions w ith extrem ely particulate,
ductile, or radically dispersed behavior. The resulting je t behavior appears to be both
© J. Y. YI, Z. J. WANG, J. P. YIN, B. H. CHANG, 2017
34 ISSN 0556-171X. Проблемы прочности, 2017, N2 1
mailto:yijianya513@126.com
Numerical Simulation o f Steel Target Penetration
m aterial- and design-dependent. The extreme particulate je t behavior appears to be related
to the brittle nature o f glasses observed at low er tem peratures and pressures. Helte and
Lundgren [6] empirically tested the penetration capability o f precursors o f tandem warheads
against ERA (Explosive Reactive A rm or), and found out that precursors w ith liners made
o f alum ina powder, alum inum powder, and glass could penetrate but not detonate the ERA
panels. In addition to the inorganic non-m etallic materials, the current application of
organic non-m etallic m aterials (nylon, PTFE, and other polym er) has also been studied.
H irsch and Sadwin [7] showed that the firing o f shaped charge liners m ade from a m aterial
o f high compressibility, such as therm oplastic, produced cavities that expanded in diam eter
near the base o f the cavity. This w ould have the potential to induce failure in brittle
m aterials such as concrete. They showed that this effect was associated w ith short
stand-offs o f 1.5 cone diam eters (CD) but no details were given o f the liner m aterial or
cone angle. H aney and W esson [8] described the use o f polym er liners as an intermediate
layer betw een a conventional m etallic shaped charge liner and the explosive. The polym er
w ould be forced into the cavity created by the m etallic jet, where it w ould burn and
decom pose; the increased volum e o f com bustion products w ould induce failure in the
surrounding target material. Chang et al. [9, 10] studied the m odified PTFE je t penetrating
shell charge, w hich showed good efficiency at destroying shell charges. The perforation
efficiency was enhanced by about 70% for the panel, and 30% for the back plate.
Clearly, because o f the specific features o f the above polymer, it has good penetration
potential as the shaped charge liner material. The aim o f the present w ork is to investigate
the behavior o f shaped je t charges that use high-polym er liners.
1. G overn ing E q u a tio n s fo r M e ta l J e t F o rm a tio n Processes. In the studies o f m etal
je ts, B irkhoff et al. proposed the classical steady je t theory. Later, Pugh et al. further
developed the theory, proposing quasi-steady je t theory. The m ost im portant assum ption of
the initial je t form ation theory is that the liner m aterial is a non-viscous and incompressible
fluid. This theory accurately describes the conical copper je t form ation process. However,
w ith the developm ent and innovation o f liner materials, these theories cannot accurately
describe the je t form ation o f com posite pow der m etal liners and non-m etallic liners. The
developm ent o f com posite pow der m etal liner prom otes the form ation o f shaped charge je t
theory, and gives the effect o f the liner m aterial viscosity and com pressibility to the je t
formation.
So far, the viscoplastic m odel [11] basically does not include the non-steady state
(non-constant) effect. The assum ption is that the je t is regarded as an incom pressible fluid,
the other is regarded as a com pressible fluid, and the m aterial constitutive relation is based
on the fully elastic-plastic strain hardening model. Godunov [12] studied the pressure
m odel o f the shaped charge liner, including the effect o f the liner m aterial viscosity on the
je t formation. The je t form ation standard basically does not consider the effects o f the
shock wave and the critical M ach number, but rather the m etal liner viscoplastic properties.
However, the standard shows that the je t is agglom erative rather than scattered or
distended. That is to say that it has no radial velocity. Obviously, this m odel cannot
accurately explain w hy the polym er je t is distended.
The com pressibility effect can be ignored in the collapse process o f the polym er liner.
A pplying the viscoplastic m odel, m aterial viscosity can be expressed in the following form:
о 0е V s in 2 ß
Re = (1 • ß ) , ( і)p (1 — sin ß )
where p 0 and £ represent density and thickness, respectively, g is the dynam ic viscosity
coefficient, f is the pressed angle, and V is the flow velocity. W hen g increases, R e will
decrease. M eanwhile, the coefficient o f the kinetic viscosity o f polym er m aterials is m uch
ISSN Ü556-171X. Проблемыг прочности, 2Ü17, Ne 1 35
J. Y. Yi, Z. J. Wang, J. P. Yin, and B. H. Chang
higher than that o f m etal m aterials, and the initial density is low er than that o f m etal
materials. The Reynolds num ber relation o f the two m aterials is given by
where R ep and R em are the Reynolds num bers o f the polym er m aterial and metal,
respectively. The fluid velocity associated w ith the Reynolds num ber is expressed as
A ccording to the m aterial viscosity coefficient, the velocity relationship is expressed as
In the cohesive collapse process o f the liner initial stage, the polym er fluid velocity is
low er than that o f the m etal because o f the introduction o f the dynam ic viscosity
coefficient. G iven the conditions that the m etal je t cohesive is R e > 2 and R ep < R em, the
polym er je t cannot form a coherent je t because it is m ore easily dispersed than the m etal
one w hen considering only the viscosity effect. As pressure increases, the liner elem ent will
produce the radial velocity, w hich leads to lateral expansion after they converge into the
high-pressure region. Hence, the liner m aterial com pressibility cannot be ignored.
Sound speed relates to the com pression perform ance o f the medium. Sound speed will
be low er w hen the com pressibility o f the m edium is higher. The sound speed o f the
polym er m aterial is m uch low er than that o f the m etal material, so the polym er m aterial
com pressibility is better than that o f the m etal material. The Bernoulli equation o f
com pressible fluid is expressed as
where e represents the fluid energy per unit mass. The above form ula shows that, in the
one-dim ensional case o f entropic com pressible fluid, the sum o f pressure potential energy,
kinetic energy, and internal energy in each section o f fluid per unit m ass is constant.
A ccording to the continuity equation o f com pressible fluid,
where p denotes fluid density, u denotes fluid velocity, and A denotes fluid width. The
introduction o f a streamline is nam ed /, w hich is not close to the outer surface (Fig. 1). The
relationship betw een the initial and flow states is given by
Here p 0 and u0 denote the initial fluid density and velocity, respectively; p 1 and u 1 are
the outflow fluid density and velocity, respectively; whereas A 0 and A 1 are the initial and
outflow fluid w idth values, respectively.
(2)
(3)
*
where V is the flow velocity related to the correlation coefficient o f dynam ic viscosity.
(4)
P u 2
— H eH------ = const,
P 2 ’
(5)
p uA = const, (6)
p 0 u 0 A 0 = p 1 u 1 A 1' (7)
36 ISSN 0556-171X. npoôëeubi 2017, N2 1
Numerical Simulation o f Steel Target Penetration
The com pressible fluid energy equation is expressed as
2 2
u o , , p 0 u i , , p i— + eo + - — = — + e i + — .
2 P 0 2 P i
(8)
A ccording to the viscous com pressible fluid m odel, the streamline entropy is constant,
Tds = d h dp = 0,
p
(9)
where s denotes entropy and h denotes enthalpy. In addition, the m om entum equation
along the streamline is sim plified as
udu H— dp = 0.
p
(10)
Since the density is higher than zero, the enthalpy and pressure are the same, so the
form ula is given by
dp
— = —p u < 0.
du ( ї ї )
The above form ula can be expressed as
dp Эр j dp p u <
du I dp I du c 2 (12)
where c denotes the speed o f sound. A long the streamline by m ass flux density per unit
area on the cross section o f P u , then
d (p u ) = udp + pdu.
The above equation can be expressed as
d (p u )
du = p
2 j
і—Yc 2 J
(13)
(14)
ISSN Q556-Î7ÎX. Проблемы! прочности, 2QÎ7, N І 37
J. Y. Yi, Z. J. Wang, J. P. Yin, and B. H. Chang
This shows that the m ass flux density increases w ith fluid velocity in the subsonic
speed, but in supersonic speeds, it exhibits the reverse trend.
In addition, the relationship betw een sound speed and fluid velocity can be expressed
as
dc 1 d c 2 1 (dc 2 ^ dp p u 'd 2 p '
du 2c du 2c ! dp y du 2c 3s l dp2 J
< 0. (15)
This shows that the sound speed decreases w ith fluid velocity. The relationship
betw een the M ach num ber and fluid velocity is given by
d M _ d ( u 1 + p M
du d u \ c
d 2 p
dp 2
> 0. (16)
This implies that the M ach num ber increases w ith fluid velocity
The initial state o f the flow end is equal to the unloading pressure in the high-pressure
region, and p 0 _ p 1 _ 0, because the dynam ic viscosity coefficient o f the polym er is very
large, so the term e cannot be ignored. The m olecular theory o f viscosity is very complex;
it is seen as the viscosity o f the m olecular interaction m ovem ent o f the friction resistant, so
the end w ork flow overcom es viscosity resistance. The relationship betw een the initial state
and the energy o f the flow state is expressed as
In view o f Eq. (8), we get
Equation (7) yields
e 0 > e1.
u 0 < U1.
p 0 A 0 > p 1 A 1.
(17)
(18)
(19)
Due to high com pression perform ance o f polym er materials, the relationship between
the initial state and the density o f the flow state is expressed as
P 0 * P 1 . (20)
The pressure and density decreases w ith fluid velocity, but if pressure is constant, the
density decreases. The relationship betw een the initial state density and the flow state one is
expressed as
p 0 > p 1. (21)
From Eqs. (18) and (21), w e get
A 0 < A 1 (22)
Therefore, the high-polym er je t is inevitably distended due to the effects o f viscosity
and compressibility.
2. N um erica l S im u la tion o f J e t F o rm a tio n . The com putational geom etric m odel for
the num erical sim ulation is shown in Fig. 2. Figure 2a is the schematic diagram o f a shaped
charge structure and Fig. 2b is the finite elem ent model. The initialization param eters are as
follows: the liner cone angle is 60°, the diam eter is 50 mm, and the charge height is 65 mm.
5
s
38 ISSN 0556-171X. npo6n.eubi 2017, N2 1
Numerical Simulation o f Steel Target Penetration
The m odel consists o f three com ponents: the liner, explosive, and airflow. LS-DYNA-3D
finite elem ent software w as used to num erically sim ulate the process w hen the jet was
form ed from high-polym er liner under the influence o f blast loading. M eanwhile, the ALE
algorithm, a representative o f the unit algorithm, w as used to sim ulate the detonation
process o f the explosives, the collapse o f the liner, and the form ation o f the high-polym er
jet. The A LE grid w as sufficient to cover the detonation products and the form ation space
o f the high-polym er jet. The 1/4 m odel w as established according to the symm etrical
structure o f the charge to save com puting time.
The m aterials used in the num erical sim ulation are copper and PTFE, the m aterial
m odel is the elastic plastic fluid model, and the m ain m aterial constitutive param eters are
shown in Tables 1 and 2.
T a b l e 1
Simulation Param eters of W arhead Explosive
p , D , A, B, R1 R2 o E , Pc- J ,
g/cm3 m/s GPa GPa kJ/m3 GPa
1.83 8480 748.6 13.38 4.5 1.2 0.38 9.0 36
T a b l e 2
Simulation Param eters of Liner Materials
Material P , G , aY , Eh Grüneisen c 1, S1
g/cm3 GPa GPa coefficient m/s
PTFE 2.16 2.33 0.05 0.0364 0.90 1340 1.930
Cu 8.96 50.90 0.12 0 1.99 3940 1.497
65
X Explosive
8
'S
L iner Aii*
a b
Fig. 2. Computational model: (a) schematic diagram of a shaped charge structure; (b) the finite
element model.
To study the properties o f polym er liner forming jets, tw o kinds o f materials, PTFE
(polym er) and copper (metal), w ere selected as the shaped charge liners, w ith a single point
detonating charge at the center. Figure 3 shows the je t form ation process o f the PTFE and
copper liner. As can be seen from Fig. 3a, the PTFE liner also can form an excellent ductile
o f the shaped charge jet. As com pared w ith the typical copper je t patterns, the difference is
m ore significant, w ith je t diam eter as the m ost significant difference. The result o f this
distinction is that the radial velocity o f the PTFE je t is too large, causing the je t radial
distension in the tensile process.
ISSN Ü556-171X. Проблемыг прочности, 2Ü17, № І 39
J. Y. Yi, Z. J. Wang, J. P. Yin, and B. H. Chang
0 10 ps 20 ps 30 ps 40 ps 50 ps
b
Fig. 3. The jet formation process of PTFE (a) and copper (b) liner shaped charges.
A nalyzing the je t form ation process o f the two liner materials, the collapse o f the
PTFE liner cohere at 10 p s w hen the copper liner experiences the same variation. However,
because o f the different nature o f liner materials, the PTFE belongs to the polym er liner
m aterials and the copper belongs to the m etal liner materials; the difference o f the two jets
in the patterns occurs at this moment. The PTFE je t had a distinctly larger diam eter than the
copper je t, w hich shows that the states o f the two liners are the same in the collapse
process, w hich can be collapsed w ith axial im pact at certain speeds. The PTFE je t obtained
a greater radial expansion velocity, w hich increases the je t diam eter after the high-pressure
disturbance region.
Fringe Levels
■ 2.120e-06_
1319e-0S_|
1.710e-O6 J
1.517e-06_
1.3168-06 m w 1.115e-06_
9.139e-07_
7.129e-07_
5.11Se-07j
3.1106-07 J
1.100e-07
4i I
r>
I
a b
Fig. 4. The density distribution map of jets from charges with liners of (a) PTFE (a) and copper (b).
A t 20 p s, the copper je t w as continually stretched w ith the tip becom ing m ore pointed.
The PTFE je t had a continued radial expansion; it w as also continually stretched because
the polym er is ductile. A t 30 ps, the head diam eter o f the PTFE je t becam e smaller, while
the head o f the copper je t broke into particles, and the rest o f the cohesive je t still moved.
As show n by the density distribution m ap (Fig. 4), the part o f the intact (defect-free) copper
je t w as still a coherent jet, the je t density rem ained the same, the fracture je t particles had a
low er density, and the PTFE je t had a m uch greater density near the axis. As the radial
density distribution becom e smaller, the PTFE je t did not form the typical coherent je t
40 ISSN 0556-171X. npo6n.eubi 2017, N2 1
Numerical Simulation o f Steel Target Penetration
under the influence o f the radial velocity, but the expansion je t w hich was form ed by
uniform particle distribution. O ver time, the copper je t head form ed particles after
continuous fractures, w hile the diam eter o f the PTFE je t rem ained unchanged, but the head
o f the PTFE je t becam e smaller. This distrubution map also shows that the slug o f PTFE je t
is sim ilar to that o f the copper one, w hich implies that the difference in the liner m aterials is
related only to the je t shape, but not the slug shape if both charges have the same structure.
N evertheless, as shown by the je t density distribution chart, the copper je t slug m aintained
a full state while that o f the PTFE je t dispersed into a particle state; nonetheless, the two
parts were sim ilar in shape. As a consequence o f the non-negligible viscidity and
com pressibility o f polymer, there were two different states.
Figure 5 shows radiographs o f the observed jets, and the shaped charge structure used
in the experim ent is the same as the num erical simulations. The figure shows that the head
diam eter o f the PTFE je t had a larger diameter, w hich show ed the radial expansion state.
However, the head diam eter o f the copper je t w as very small, and the head o f the copper je t
form ed a granular je t in the tensile process.
b
Fig. 5. Radiographs of jets from charges with liners of PTFE (a) and copper (b).
Figure 6 shows the state param eter graph o f the je t w hen two different m aterials were
used. Figure 6a is the graph o f the head velocity curve o f the jet, and Fig. 6b is the graph o f
the radial velocity curve o f the jet. Figure 6c is the graph o f the length curve o f the jet, and
Fig. 6d is the graph o f the diam eter curve o f the jet.
Figure 6a illustrates that the velocity o f the copper je t is slowly decreased due to air
resistance in the tension process. The velocity o f the PTFE je t is identical to that o f the
copper je t in the form ation stage je t collapse process. However, the velocity sharply
declines in the tensile phase, due to high-speed particles o f the distended je t consum ing the
form ation energy by air resistance, and to continuous collision as a result o f h igher energy
consumption.
Figure 6b shows that the radial velocity o f the PTFE je t reaches the m axim um value
w hen the je t flows in the process o f the je t collapse, and is continually reduced during the
stretching process. However, the radial velocity o f the copper je t is very low, as com pared
to the PTFE one, and is gradually reduced, w hich affects the distended je t form ation
process.
Figure 6c shows that the je t length is the same at the initial stage, but the unstable
fracture o f the copper je t head in the tensile process results in a low er length growth rate for
the copper je t as com pared to that o f the PTFE one. N evertheless, the length o f PTFE je t
slowly decreases after a sharp increase due to je t velocity reduction.
Figure 6d shows that the PTFE je t diam eter is larger than that o f copper one at the
initial stage. W ith the increased the gap in stretching process, the diam eters o f the tw o jets
reach their m axim um values at the same tim e, and then are slowly reduced.
ISSN Ü556-171X. Проблемыг прочности, 2Ü17, № І 41
J. Y. Yi, Z J. Wang, J. P. Yin, and B. H. Chang
Fig. 6. State parameter graph of the jet: (a) the two jet tip velocity curves; (b) the two jet radial
velocity curves; (c) the two jet length curves; (d) the two jet diameter curves.
In summary, the PTFE showed the greatest density o f plastic m aterials in the polymer.
A s a line r m aterial, PTFE can form distended je ts, w hich is d ifferent from traditional
coherent je ts. The above research studied the shape particularity o f distended je ts by
com paring their perform ance param eters to those o f typical copper jets. The penetration
perform ance o f the polym er je t w as studied by num erical sim ulation and experim ental
m ethod, as follows.
3. C o m p ariso n o f N um erica l an d E x p erim en ta l R esults. The shape o f the polym er
liner je t is different than that o f a typical jet. In further study, the penetration perform ance
o f the polym er liner distended jet, the penetration experim ent was designed and com pared
w ith the num erical sim ulation results.
Figure 7 shows the shaped charge used in the experiments. The distended je t
properties m ust be know n to determ ine the penetration depth and crater diam eter o f the
shaped charge je ts at 3 CD standoffs.
The results obtained show that penetrations (crater depths) were higher for copper
than for PTFE (Fig. 8). The penetration o f the PTFE je t into the steel target w as 14 m m and
created a 20.9 m m diam eter entry hole. The num erical sim ulation results gave a 11.8 mm
penetration depth, and 18.61 m m crater diameter. In contrast, a copper liner w ith the same
cone angle and standoff gave 30 m m penetration w ith a tapering hole and a 14.6 mm
diameter entry hole. Numerical simulation gave a 24.87 m m penetration depth and an 8.4 mm
crater diameter.
42 ISSN 0556-171X. npo6n.eubi 2017, N2 1
Numerical Simulation o f Steel Target Penetration
a b
Fig. 7. The experimental arrangement of jet penetrating steel target: (a) copper; (b) PTFE.
The dam age effect o f the two je ts in a steel target is different. The copper je t
penetration depth is large, and the crater diam eter is small. However, the PTFE je t
penetration depth is small, and the crater diam eter is large. However, its rem arkable ability
to produce large penetration holes is an advantage.
Conclusions. This study presents theoretical, numerical, and experimental examinations
on the characteristics o f je t form ation w ith polym er liners, and their ability to penetrate
steel targets. Two different liner m aterials (PTFE and copper) were studied.
1. Considering the liner m aterial viscosity and compressibility, the application o f the
viscoplastic m odel fluid equations o f the liner state and through the research on the liner
into the crushed high pressure region, com parative analysis o f outflow o f m etal je t and
polym er jet. The cohesive condition o f the polym er je t w as obtained, w hich indicates that
the charge structure is the same as that o f the m etal charge structure.
2. The sim ulated results o f the je t form ation w ith two different liner m aterials show
that the PTFE liner produces a distended jet, while the copper one produces a particle jet.
The num erical results agree w ith the radiography data.
3. This study presents the results o f the num erical sim ulation and param eter analysis
o f the head velocity, radial velocity, length, and diam eter evolutions o f both jets. The initial
stage o f the PTFE je t exhibits a higher radial velocity, w hich causes a larger je t diameter.
ISSN Ü556-171X. Проблемыг прочности, 2Ü17, № І 43
J. Y. Yi, Z. J. Wang, J. P. Yin, and B. H. Chang
4. N um erical and experim ental results show that the PTFE je t penetration into steel
target displays a low er penetration depth and higher crater diam eter than those o f copper
one. This suggests that the penetration capacity o f the PTFE je t is influenced by the radial
velocity, resulting in the enhanced radial expansion and deteriorated axial penetration
abilities.
A cknow ledgm ents. The authors w ould like to acknowledge the financial support from
the Project supported by the N ational N atural Science Foundation o f China under Grant
No. 11572291.
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Received 30. 08. 2016
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