Numerical Simulations of Ballistic Impact of ss109 on Alumina/Steel Armor
Tarin Vanichayangkuranont1, Nuwong Chollacoop2 and Kuntinee Maneeratana1
1
Department of Mechanical Engineering, Chulalongkorn University, Bangkok 10330, Thailand
*
Tel: 0-2218-6639, Fax: 0-2252E-mail: tarinv@yahoo.com and kuntinee.m@chula.ac.th
2
National Metal and Materials Technology Center (MTEC), Pathumthani 12120, Thailand
Tel: 0-2564-6500 ext 4700, Fax: 0-2564-6403, E-mail: nuwongc@mtec.or.th
Abstract
This article concerns with the ABAQUS simulation
of ss109 bullet impacts with initial velocities about 936
m/s on alumina/steel armor plates, which is rated between
the level 3A and 4 of the National Institute of Justice
(NIJ) standard. The current model setup was extended
from the prior investigation [1] of the 9-mm bullet impact
with the initial velocity of about 420 m/s (level 3A of NIJ
standard), with the implementation of frictional effect
between impacting bullet and armor plate. Despite the
seemingly simple computational model, the simulation
result showed qualitatively agreement with the
experimental observations of the armor testing.
Keywords: Ballistic impact, ss109, alumina, steel,
ABAQUS
1. Introduction
The National Metal and Materials Technology Center
(MTEC) has initiated a project to develop the light
weight hard armor, aiming to improve materials, design
and produce hard armor prototypes with local materials
[2]. As hard armors comprise of layers of alumina, steel
and polymer composite plates, the design involves the
parameter specification on alumina tile shape/sizes,
thicknesses and arrangements of material layers. Thus,
the numerical simulation is used to analyze ballistic
impacts on the armors in order to obtain rough guidelines,
particularly parameter adjustments for the prototype
configuration.
The prior studies on various aspects of ABAQUS
finite element simulation were the effects of stress wave
propagation from dynamic loads, involving elastic and
elastic plastic armor plate [3], the impact of elastic bullet
on an alumina plate which fails by brittle failure criterion
[4], and the preliminary development of the
computational model for NIJ level 3A ballistic testing
[1].
This study aims to extend the previously developed
computational model for the greater damage ballistic
testing with the sharper bullet (ss109) and faster speed of
936 m/s. At this high impacting velocity (almost 3x
speed of sound in the air), the effect of frictional
interaction is significant. Such implementation enables
the qualitative prediction of the experimental results.
2. Experimental Observations
The shooting experiments on alumina/steel plates are
used for comparison with the simulation [2]. They were
conducted at the certification firing range (Fig. 1) in an
arsenal on 25-26 August 2005. A single ss109 bullet was
fired upon each specimen. The impact was classified
between the 3A and 4 threat-level of the NIJ standard [5],
which is also adopted into an equivalent code for the
Royal Thai Military.
Among many cases, 2 armor specimens, each made
up of a layer of alumina on top of a steel back layer, were
chosen for numerical study. The alumina layers were
constructed from hexagonal ceramic tiles of 8cm2 area,
which were bonded together with epoxy and wrapped up
by a dynema cloth (shown white in Table 2) before being
bonded to the back steel plate with the same epoxy. The
thickness of the ceramic tile was 8mm for both samples
with the steel plate of 1.5mm thick. The velocity of the
bullets V0, measured by the sensors after the bullets left
from the barrel (Fig. 1, left), were 924 and 936m/s for
sample I and II, respectively. Post firing test revealed
that the bullet hit sample I (925m/s) at the edge of the
alumina tile while it hit sample II at the center of the
alumina tile.
Figure 1. Standard firing tests
The images of the plate damages after impact are
shown in Table 1. Both specimens showed some
localized damages on a single tile while the back steel
plates showed full penetration by petal damage in sample
I and large bulge on sample II, due to the differences in
the locations of the alumina tiles impact. The edges of
the alumina tiles were weaker due to the epoxy bond.
Table 1. Plate damages after impacts
ceramic
metal
side
front
case
back
I
front
Figure 2. Mesh design for the bullet and central layers of
alumina and steel (red).
back
II
3. Numerical Simulations
All finite element simulations in the present study
were performed using ABAQUS/Explicit solver [6] due
to the high speed, non-linear transient responses in the
solutions. An axisymmetric model was chosen for
simulations of a spear-shape bullet penetrating layers of
alumina and steel plates, as shown in Figure.
A real ss109 Full Metal Jacketed (FMJ) bullet is
made of an outer copper alloy jacket covering a softer
lead core and has the nominal mass of 3.95-5.18 g. In the
modeling, the bullet was assumed to be a single piece
with a sharp tip and a total length of 18 mm, estimating
the commercial bullets in terms of diameter and mass.
Meanwhile, the armor plates were assumed to be
homogeneous in each layer spanning the total length of
30mm in diameter to minimize the effect from the far
field condition. Complication from the finite alumina
tiles were not yet taken into account for the present
investigation.
Due to the anticipated severe deformation at contact, a
finer mesh was used at the region directly beneath the
bullet tip for both alumina and steel layers while a coarser
mesh was used in the region further away to reduce
computational expense, as shown in Fig. 2. All regions
were modeled with axisymmetric 4-node elements with
enhanced hour-glass control. There were 95, 9,00 and
1,800 elements for the bullet, alumina and steel sections,
respectively.
The fully restrained boundary condition was applied
to the outer edge (right side) of the armor plates while the
center (left side) of the plate assumed axisymmetric
boundary condition. In addition, the interaction between
the bullet and alumina layer were governed by the
surface-to-surface contact model with friction coefficient
of 0.3. Using the kinematic contact method, the bullet
nose was assigned to be the master surface while the
armor plate was the slave node region. The impact was
simulated by assigning the initial downward velocity to
the bullet. To ensure numerical accuracy and stable
computation, the time step size δt = 3.2 ns.
The elastic bullet was modeled after the gliding
copper [7] with the Young’s modulus E of 115 GPa and
the Poisson’s ratio ν of 0.307. However, the density ρ
was modified to approximate the commercial ss109 bullet
mass. The alumina layer was modeled with elasticperfectly plastic constitutive relation having ρ = 3,900
kg/m3, E = 350 GPa, ν = 0.22, the compressive yield
stress σyc = 2400 MPa [8] and the tensile strength σts =
600 MPa [1]. During the impact, the elements were
removed when any component of the stress exceeded 600
MPa in tension.
The Johnson-Cook model was used for the steel plate
as it has been well suited to model metals that are
subjected to high strain rate loadings [9]. The yield stress
at non zero strain rate  depends on the strain hardening,
strain rate hardening and temperature softening such that
   A  B( pl )n  1  C ln( pl  0 )  (1  ˆm ) ,
(1)
where  pl is the equivalent plastic strain,  0 is the
reference strain rate. The parameters A, B, C, n and m are
material parameters measured at or below the transition
temperature tran .
The ˆ is the nondimensional
temperature which is equal to 1 when the current
temperature  is greater than the melting temperature
melt , 0 when   tran , and linearly proportional inbetween. The Johnson-Cook shear failure is based on the
damage parameter 
    
pl
 fpl  ,
(2)
where 
is an increment of the equivalent plastic
strain and  fpl is the strain at failure.
pl

p 
q 
 fpl   d1  d 2 exp(d3 )  1  d 4 ln(

 pl 
)  (1  d5ˆ) ,
0 
(3)
where p is the pressure or mean stress, q is the Mises
stress, d1 – d5 are failure parameters. Failure occurs when
the value of  exceeds a unity.
The parameters values of the steel were adjusted
from [9] and [10] such that ρ = 7,870 kg/m3, E = 200 GPa
and ν = 0.33. The yield stress and strain hardening
parameters were A = 532 MPa, B = 229 MPa and n =
0.3024. It is noted that the values of A and B were
reduced from [9] as the normal graded steels, with
weaker properties, were used in the experiments. The
strain rate hardening constants were C = 0.0114 and
 0  5  104 s 1 . The temperature softening parameters
were specific heat capacity Cp = 452 J/kgK, inelastic heat
fraction α = 0.9, coefficient of thermal expansion
  1.1105 K1 , m = 1, tran = 283 K and melt = 1793
K. The fracture strain constants d1 = 0.0705, d2 = 1.732,
d3 = 0.54, d4 = 0.015 and d5 = 0.
4. Results and Discussions
The contour plots of von Mises stress on the
deformed mesh at various times after initial impact are
shown in Fig. 3. Failed elements predicted from the
constitutive relations of each layers were deleted from the
simulation results for visualization purpose.
They
exhibits high stresses during the first period after the
initial impact at the center of the ceramic plates. The
stress values decrease afterwards as elements in the high
stress regions fail and are deleted from the grids.
Damages at the back sides of the alumina layer,
producing many broken pieces, are more extensive than
the front sides that receive the direct impact. These
damages clearly affect the metal plates in the next layer,
causing large deformations in the form of bulging and
subsequent the petal damage characteristics.
Both
damage characteristics of steel plates concur with the
photos from experiments in Table 1.
The velocity (V2) and depth (U2) of the bullet tip are
also shown in Fig. 4. Note that the negative value of U2
implies the bullet penetrating into the armor layers. The
velocity V2 of the bullet is reduced from the initial value
of 936 m/s to almost zero at t = 0.2 ms, implying that the
bullet has come to a complete stop. Further confirmation
on the bullet arresting event is shown by the upcoming
energy plots.
The 180 sweep of the axisymmetric deformed plot
at t = 0.2 ms with the steel plate profile at various time
are shown in Fig. 5 for comparison with the experimental
observation in Table 1. The bulge area with diameter of
50 mm predicted by the simulation in Fig. 5 is in a good
agreement with the value of 50-55 mm observed in the
post-firing samples in Table 1.
.
5 s
10 s
15 s
35 s
95 s
200 s
Figure 3. The deformation and von Mises stress at time
instant t = 5, 10, 15, 35, 95 and 200 s after the impact.
AE/IE
Bullet tip
-5
800
-10
600
-15
400
-20
200
-25
0
4%
V2
U2
AE/IE
1000
5%
U2 (mm)
0
V2 (m/s)
1200
0.05
0.1
0.15
2%
1%
0%
-30
0
3%
0
0.2
0.05
time (ms)
IE
200 s
Steel Displacement
U2 (mm)
-1
-2
-3
-4
900
800
700
600
500
400
300
200
100
0
Cera
Steel
Armor
Bullet
0
20 x (mm) 30
0.05
0.1
0.15
0.2
time (ms)
0 us
5 us
10 us
15 us
20 us
25 us
30 us
35 us
35 us
200 us
KE
1400
1200
1000
KE (J)
0
0.2
Figure 6. The ratio of the artificial strain energy to the
internal energy (AE/IE) during the simulation run.
IE (J)
~25 mm
10
0.15
time (ms)
Figure 4. The velocity and depth of bullet penetrating into
the armor plate.
0
0.1
Cera
Steel
Armor
Bullet
800
600
400
-5
200
Figure 5. The deformed plot at t = 0.2 ms for bulge area
measurement (top) with the steel layer profile at various
time (bottom)
0
0.05
0.1
0.15
0.2
time (ms)
TE
1400
1200
Cera
Steel
Armor
Bullet
Fric
1000
TE (J)
In the explicit runs, the amount of artificial strain
energy, AE, which are generated by the programs in order
to prevent unduly high deformation and distortion of
elements, has to be considered. This artificial energy
should be low compared to the total internal energy, IE,
of the system for reliable results [6]. Figure 6 shows that
the ratio of artificial energy over internal energy (AE/IE)
for the present simulation never exceeds of 5%, the
recommended value from ABAQUS [6]
The energy of the systems, namely the internal strain
energy (IE), the kinetic energy (KE) and total energy
(TE), during impacts are plotted in Fig. 7, along with the
frictional work from the interaction between penetrating
bullet and armor plate.
0
800
600
400
200
0
0
0.05
0.1
0.15
0.2
time (ms)
Figure 7. The energy distribution plots for all parts (top:
IE = Internal Strain Energy, middle: KE = Kinetic
Energy, and bottom: TE = Total Energy, Fric = Frictional
work)
From the kinetic energy graphs in Fig. 7, the KE of
bullet decreases rapidly for the first 0.015 ms, which
corresponds to the duration where the bullet is being
stopped in the alumina layer, as shown in Fig. 3. This is
consistent with the much larger energy absorption in the
alumina layer, as shown by the IE plot. Between t =
0.015-0.05 ms, the KE decreases further but with a
slower rate till it almost vanishes about 0.075 ms,
corresponding to when the bullet is completely stopped
by the steel layer shown in Fig. 3. Note that the shape of
the bullet KE plot is consistent with the bullet velocity in
Fig. 4.
From strain and total energy plots, it can be seen that
the armor plate can effectively dissipate the impact
energy of the bullet into the internal strain energy in each
layer and the frictional work due to the contacting
interactions. Note that the friction during the bullet
impact is significant, which is about half the internal
strain energy absorbed in the participating armor layers.
5. Conclusions
The computational model from the previous studies
[1, 3-4] was extended and modified to simulate the
ballistic impact of ss109 bullet traveling with the speed of
over 900 m/s upon the armor plate, consisting of alumina
and steel layers. The results show that alumina layer
absorbs about two-thirds of the impact energy from the
bullets with the remaining one-thirds dissipating into
frictional work from the contacting interaction. The most
severe damages to the armor occur at the back side of the
alumina layer due to the superposition of reflecting stress
waves [1]. The Johnson-Cook material model can
effectively simulates the damages characteristics of the
steel layer, with the bulge area qualitatively consistent
with the experimental observation.
Acknowledgments
This research is supported by the National Metal
and Materials Technology Center (MTEC), contract no.
MT-B-48-CER-07-188-I. Special thanks are due to Dr. K.
Sujirote, Dr. D. Atong, Dr. K. Prapakorn, Dr. A.
Manonukul, Assc. Prof. Dr. T. Amornsakchai, Asst. Prof.
Dr. S. Rimdusit and Maj. Gen. Dr. W. Phlawadana.
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