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Ballistic impact performance of ultra-high molecular weightpolyethylene (UHMWPE) composite armour
NAYAN PUNDHIR, HIMANSHU PATHAK* and SUNNY ZAFAR
School of Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh 175075, India
e-mail: [email protected]
MS received 6 March 2020; revised 6 June 2020; accepted 23 August 2021
Abstract. Present work deals with the nonlinear finite element analyses of ultra-high molecular weight
polyethylene (UHMWPE). UHMWPE has been presented for ballistic design investigation of lightweight body
armour using ANSYS-Workbench. The ballistic performance of UHMWPE has been compared with Kevlar/
epoxy composite and alumina. The study is presented in terms of the ballistic limit of UHMWPE, Kevlar/epoxy,
and alumina plate, the implication of obliquity (at 30�, 45�, and 60�), projectile shape (elliptical, conical, and
spherical shape). The sequencing order of material layup for a bi-layer composite and ballistic performance of
single-layered UHMWPE has been compared with the multi-layered plate. The parametric studies have been
presented in the form of residual velocity, the ratio of energy transferred to impact velocity of the ballistic plate,
and perforation rate for the single and multi-layered UHMWPE. The results of the numerical analyses of
UHMWPE have been compared with the Kevlar/epoxy composite. It has been found that the armour system
made of UHMWPE laminate composite resulted in a 40.6% weight reduction compared to Kevlar/epoxy
configuration with a 17.3% higher ballistic limit.
Keywords. AUTODYN; ballistic; impact mechanics; UHMWPE; body armour; kevlar.
1. Introduction
Throughout human civilization, humans have used dis-
parate armour materials to protect themselves in the bat-
tlefield. The demand for lighter protection systems with
good ballistic performance has led to the use of composite
materials in armour due to its good protection/weight
relation. The present emphasis on greater survivability lies
in the reduction in weight and consequently an increase in
mobility.
With the expansion in human society, wooden and
metals were gradually considered for use as armour mate-
rials. In the fifteenth century, Italian and Roman sovereigns
came up with the idea of bulletproof vests. They designed
armour shield made from multiple metallic layers to deflect
the fired bullets. The jackets/armour made of metallic
(steel) layers were heavy and uncomfortable; mobility with
such material configuration was quite challenging [1–3].
Further, the material bulkiness and discomfort must be
resolved, and the need for lightweight armour was felt. The
currently available body armour materials include tough
metals, ceramics, laminated composite structures, and para-
aramid ballistic fabrics.
Aramid fibers (Kevlar�) emerged as potential armour
materials due to their high energy absorbing capacity and
lightweight [4]. Kevlar has a long chain of cross-linked
molecules, making it stiff enough to absorb impact load,
but it is effective up to a limit. The further thickness of the
material has to be increased. It escalates the discomfort [5].
Therefore, multi-layered composites were the alternative
for armour applications. In a multi-layered composite, skin
layer does not contribute much to the ballistic performance
[6–8]. It has been seen that the striking plate blunts the
projectile and absorbs a large fraction of the kinetic energy
[9, 10]. Impact of the projectile can be observed at the back
face of plate/armour. Projectile velocity, shape, weave
architecture are some of the parameters which govern the
rear face deflection [11, 12].
Recently, UHMWPE has emerged as a novel material for
ballistic protection applications. In consequence,
UHMWPE fibers are ballooning acceptance in the field of
survival technology against the impact of projectiles or
explosive blasts. UHMWPE composites have been used to
produce armour materials for personnel protection (vests
and helmets), and in military and civil armoured vehicles.
Weave structure of the UHMWPE have loosely bonded
fibers, which outweighs its energy-absorbing capacity
[13–19]. Hence, the material is best suitable for a ballistic
performance application.
Sapozhnikov et al [20] compared the ballistic perfor-
mance of multi-layered UHMWPE with the aramid fibers
and found out that, UHMWPE outweighs 10% of the*For correspondence
Sådhanå (2021) 46:194 � Indian Academy of Sciences
https://doi.org/10.1007/s12046-021-01730-0Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)
ballistic limit and 25% of absorbed energy. Chen and Chu
[21] found that increasing the bonding of UHMWPE fibers
after certain point fallouts to be a slump in the energy
absorption. Liu et al [9] found that UHMWPE bolsters the
ballistic limit and energy absorption of Ti6Al4V sandwich
composite by using UHMWPE as a middle layer. Zhang
et al [15] explored the weave architecture of the UHMWPE
and found that unidirectional UHMWPE has the highest
energy-absorbing capacity.
The studied literature has explored that UHMWPE holds
the potential for a lightweight body armour application. But
there is no literature scrambling UHMWPE and Kevlar
composites as a bulk material. Therefore, present work
investigates the numerical design of the UHMWPE using
the commercial finite element method (FEM) package,
namely ANSYS-AUTODYN 16.0. In this work, different
design parameters have been investigated to measure the
ballistic limit, residual velocity and ratio of energy trans-
ferred to impact energy. The salient features of this work
are as follows:
• A computational algorithm has been proposed for
numerical design analysis of UHMWPE composite
under a ballistic loading environment.
• A comparative study has been presented for UHMWPE
composite and Kevlar/epoxy with different design
parameters.
• Residual velocity and energy transfer to the ballistic
composite plate have been analyzed with different
design parameters.
• The implication of obliquity, projectile shape, multi-
layering and order of the material layup has been
studied.
• Von-Mises stress distribution for single-layered and
multi-layered UHMWPE has been studied.
2. Problem formulation
The projectile’s kinetic energy is not only a function of the
mass of the projectile; it also depends on the type of gun
from which it is fired. Short barrel gun gives low-velocity
impact compared to long barrel guns. In the high-velocity
impact situation, there is complete penetration of the pro-
jectile. Whereas, low-velocity impact condition has partial
perforation. In fact, the projectile is either embedded in the
specimen or rebounds back depending on the impact
velocity. The projectile will not pierce the given target if
the impact velocity is lower than the ballistic limit.
The kinetic energy of the projectile, upon impact, is
converted to increase the internal energy of the specimen.
At the instant of impact, the transverse waves are gener-
ated. These waves travel to the back face of the specimen as
compressive waves and get reflected as the tensile waves.
These two opposite-nature waves collide while traveling
against each other and liberate some energy. This liberated
energy is responsible for the failure of the armour. The
intensity of the generated waves depends on the velocity of
impact [22]. Friction between projectile and plate, com-
pression and elongation of the material, delamination of
plies occur, which reduces the projectile’s initial kinetic
energy and causes the material’s failure [23]. Energy-ab-
sorbing criteria would be applied for failure analysis if the
impact velocity is below the material ballistic limit [24]. In
the presented condition, the energy transferred to the bal-
listic plate can be estimated by equation (1) [25]:
Et ¼ 1
2mp V2
i �V2r
� � ð1Þ
Then the ratio of energy transferred to the impact energy
of the projectile is calculated by equation (2) [25]:
Et
Ek¼ 0:5mp V2
i �V2r
� �0:5mp V
2i
where Ek ¼ 0:5mp V2i
� � ð2Þ
The residual velocity of perforation can be estimated by
the Recht-Ipson model (equation (3)) [10]:
Vr ¼ FffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVci �Vc
50
� �c
qwhereF ¼ mp
�mp þmf
� �� � ð3Þ
Lambert and Jonas have modified equation (3) for bal-
listic application by assuming constant energy transferred
(c = 2), for residual velocity prediction and proposed
equation (4) [15]:
Vr ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2i �V2
50
� �qð4Þ
This model is valid Vi [ V50. Therefore, for the present
work, impact velocity is considered more significant than
the ballistic limit. The value of A is taken unity, as it has
been assumed that the projectile is non-deformable. In this
way, the projectile is chosen as of structural steel material.
The difference between the Recht-Ipson model and Lam-
bert-Jonas model was analytically found by G. Ben-Dor,
and it was reported that the accuracy of both the model is
nearly the same [26].
2.1 Constitutive equations
The constitutive equation provides the relation between
different variables using material constants. The orthotropic
equation of state requires young’s modulus in X, Y, and Z
direction. Poison’s ratio and shear modulus in XY, YZ, and
XZ planes. In the present work, the UHMWPE plate (as a
bulk polymer) and Kevlar/epoxy composite have been
modeled as an orthotropic material (E1, E2, E3,t12, t23, t31,G12, G23, G31). Alumina (99.5%) and structural steel have
been modeled with polynomial and linear equations of
state, respectively. Linear equation of state only requires
bulk modulus to satiate the criteria. A polynomial equation
194 Page 2 of 15 Sådhanå (2021) 46:194
of state is presented by the Mie-Gruneisen model (equa-
tions (5) and (6)) for compressive and tensile behavior,
respectively) [27].
P ¼ A1 þA2 l2 þA3 l
3 þ Bo þBo lð Þ qo x ð5Þ
P ¼ T1 þ T2 l2 þBo qo x where l ¼ q
qo� 1
� �ð6Þ
The strength and failure model used to govern the failure
of the materials are orthotropic yield in nature, Johnson-
Holmquist, elastic and material stress/strain for the
UHMWPE, alumina (99.5%), Kevlar/epoxy composite and
structural steel, respectively. Orthotropic yield has yielded
in the XY, YZ, and XZ planes. Similarly for the elastic
model, shear modulus must be specified. The material
stress/strain model requires maximum tensile stress and
strain in the XY, YZ and XZ planes to satiate the failure
criteria [6, 28, 29].
The Johnson-Holmquist damage material model is used
to model the mechanical behavior of brittle materials under
the ballistic impact loading. The normalized equivalent
stress can be written as a power-law function. The gener-
alized equivalent stress used for alumina has been presented
by equation (7) [30].
r� ¼ r�u �D r�u � r�f�
ð7Þ
where r� ¼ rrh
r�u ¼ GP
Phþ S
Sh
� �N
1þ H ln _eð Þ and r�f
¼ BP
Ph
� �M
1þ H ln _eð Þ
2.2 Comparative weight
UHMWPE is lighter in weight as compared to Kevlar/
epoxy and alumina. The density of UHMWPE is 980 kg/
m3, whereas the densities of Kevlar/epoxy and alumina are
1650 kg/m3 and 3890 kg/m3, respectively. In the present
work, the dimension of the plates is taken as 200920096
mm3. Hence we can quantify the mobility of UHMWPE
armour in terms of the percent reduction in weight of
armour by equation (8). It can be calculated that UHMWPE
is 40.61% and 74.81 % lighter than Kevlar/epoxy and
alumina, respectively
% reduction inweight ¼ Mm �MU
Mm
� �� 100 ð8Þ
2.3 Meshing of the geometric model
For the numerical analysis, erosion of the damaged ele-
ments ensures the time step’s stability by automatically
deleting damaged elements [31]. For the present work, the
geometric strain has been used as erosion criteria. By
default, the geometric strain of 1.5 has been selected.
Default meshing facilitates to optimize the process solution
time; therefore, present work utilizes default meshing to
have the minimum process time with minimum error in
numerical results.
It can be observed from table 1, that the default mesh
with an average element size took 34.32 min of solution
with a 0.53 % difference in experimental velocity.
Whereas, when the mesh size was decreased, it caused an
increase of the solution time with not much difference in
the residual velocity. And on increasing the mesh size, the
percent difference with the residual velocity increased.
Therefore, default mesh had been used for the study, as it
shows an optimal solution in an optimal time interval. The
mesh topology has been generated with four-node tetrahe-
dral elements with 3 degrees of freedom for each node and
eight-node brick elements with 3 degrees of freedom for
each node for the projectile and striking plate.
2.4 Percent increase in the ballistic limit
The effectiveness of UHMWPE is seen by calculating the
percent increase in its ballistic limit compared to the bal-
listic limit of Kevlar/epoxy composite. The percent increase
in the ballistic limit of UHMWPE is calculated by equation
(9):
% increase in ballistic limit ¼ VU �VK
VK
� �� 100 ð9Þ
Table 1. Convergence study for residual velocity.
Average element size
(mm)
Solution time
(min)
Experimental residual velocity
(m/s)
Simulated residual velocity
(m/s)
Difference with
experimental (%)
1 174.2 939 934.1 0.52
2 64.7 939 934.65 0.46
3 (Default mesh) 34.32 939 944 0.53
4 34.96 939 901.5 3.99
5 36.8 939 897.26 4.44
Sådhanå (2021) 46:194 Page 3 of 15 194
2.5 Cases studied for numerical modeling
For case 1, the individual ballistic limit for the UHMWPE,
Kevlar/epoxy, and alumina plate have been acquired and
further compared with each other to find out the lower
residual velocity by the Lambert-Jonas equation. A ballistic
plate of dimension 200920096 mm3, where 200 mm is the
length and breadth of the plate, and 6 mm is the thickness
of the plate, has been considered for numerical modeling.
For case 2, the bi-layer composite plate of UHMWPE/
alumina and Kevlar/epoxy-alumina plates are simulated.
The thickness of the bi-layer is 12 mm (6 mm of each plate
in the bi-plate case). The composite bi-plates of UHMWPE/
alumina (UHMWPE as a bulk polymer) and Kevlar/epoxy-
alumina are geometrically modeled in such a way that the
back face of one is in contact with the front face of the
other, and they are glued to each other by add frozen option
in ANSYS workbench. This glue operation will facilitate
the elemental connectivity between the material interfaces.
For a multi-layered composite, the tensile stress is gener-
ated at the interface of the composites, which tries to sep-
arate the two connected layers. Therefore, to maintain the
continuity at the interface of the layers, equation (10) must
be satisfied. Lagrange multiplier (equation 11) has been
introduced to impose equation (10) [32, 33].
X1s1 ¼ X2
s2 and T1s1 þT
2
s2 ¼ 0 ð10Þ
P ¼ZC
kt x1 � x2� �
dC ð11Þ
Where : k ¼ T1 ¼ � T2
Case 3 examines the implication of obliquity on
UHMWPE and Kevlar/epoxy plate. The projectile is
directed to strike at the center of the plate at 30�, 45�, and60�. Case 4 shows the implication of different projectile
shapes on residual velocity and energy transferred on
UHMWPE and Kevlar/epoxy plate. The three different
projectile shapes are elliptical, conical, and spherical faces,
as shown in figures 1(a–c). Figure 1d shows the meshed
model of the plate and the projectile for ballistic simulation.
Case 5 shows the implication of multi-layering on the
UHMWPE plate. A single-layered plate of UHMWPE plate
Figure 1. Types of projectiles used in the simulation work
(a) elliptical, (b) conical, (c) spherical face projectile and
(d) meshed model of the projectile and plate.
Table 2. Mechanical properties of UHMWPE used in the bal-
listic simulation [31].
Property/Parameter Value
Density 980 kg/m3
Young’s modulus (E1) 3.62 GPa
Young’s modulus (E2) 26.90 GPa
Young’s modulus (E3) 26.90 GPa
Poisson’s ratio (t12) 0.0013
Poisson’s ratio (t31) 0.5
Shear modulus (G12) 30.70 MPa
Shear modulus (G23) 42.30 MPa
Shear modulus (G31) 30.70 MPa
A1 0.03
A2 0.5
A3 0.5
Tensile Failure Stress 11 1.010009 1014 (GPa)
Tensile Failure Stress 22 753.0 MPa
Tensile Failure Stress 33 753.0 MPa
Table 3. Mechanical properties of alumina used in the ballistic
simulation [34].
Property/Parameter Value
Density 3890 kg/m3
Young’s modulus (E1) –
Bulk Modulus A1 23.10 GPa
Shear Modulus 15.20 GPa
Damage Constant, D1 0.01
Damage Constant, D2 0.7
194 Page 4 of 15 Sådhanå (2021) 46:194
has a 6 mm thickness, and the multi-layered plate (5 layers
of UHMWPE) has a 1.2 9 5 mm thickness (total thickness
of the multi-layered plate is 6 mm). Case 6 studies armour
composed of four layers of different materials. The thick-
ness of each material layer is 5 mm (the total thickness of
the modeled armour is 20 mm).
Case 6, this section simulates four square plates of
dimensions 200920095 mm3 and further glued with each
other, taking the ’add frozen’ option in the ANSYS.
Therefore, the total thickness is 20 mm. Here two cases
have been studied. Case-A with stacking sequence of
Rubber1-Alumina-Kevlar/epoxy-UHMWPE (R/A/K/U)
and case-B with stacking sequence of Rubber1-Alumina-
UHMWPE-Kevlar/epoxy (R/A/U/K).
3. Results and discussions
In this work, a simulation algorithm for the ballistic study
has been presented using finite element software ANSYS-
AUTODYN 16.0. AUTODYN is a commercial hydrocode
that relates the stress and strain relation and other param-
eters while giving the optimal solution. The projectile is
directed to strike at the center of the front plate. The
shortest distance between the projectile and the striking
face of the plate is taken at 30 mm (the distance between
the projectile and plate is to provide evidence that the
projectile and plate were not initially in contact. Residual
velocity has been recorded when the velocity profile is
parallel to the X-axis of the graph. Therefore, the numerical
analysis results are unaffected by the distance between the
projectile and the plate).
The full geometrical model is simulated to see the best
effect of the designed parameters. In the present work, the
properties of UHMWPE are taken from the literature [31].
Here author used the UHMWPE as the bulk polymer and
performed mechanical testing to get the desired properties
of UHMWPE. Material properties of the UHMWPE, alu-
mina and Kevlar/epoxy used for the numerical analysis at
ambient temperature (228C) are listed in tables 2, 3 and 4
respectively (properties listed in tables are according to the
ANSYS-AUTODYN 16.0 co-ordinate system, where
directions 1, 2 and 3 are the orthogonal Cartesian co-ordi-
nate directions along X, Y and Z respectively. The
Table 4. Mechanical properties of Kevlar/epoxy used in the
ballistic simulation [34].
Property/Parameter Value
Density 1650 kg/m3
Equation of State Ortho
Young’s modulus (E1) 3.24 GPa
Young’s modulus (E2) 13.07 GPa
Young’s modulus (E3) 13.07 GPa
Poisson’s ratio (t12) 0.077
Poisson’s ratio (t31) 0.312
Poisson’s ratio (t23) 0.062
Bulk Modulus A1 4.15 GPa
Shear Modulus 1 GPa
Volumetric response Polynomial
Parameter A2 40 GPa
Parameter T1 4.15 GPa
Reference Temperature 300 K
Specific Heat 1420 J/kgK
Strength Elastic
Shear Modulus 1 GPa
Post Failure Option Orthotropic
Residual Shear Stiffness Fraction 0.2
Decomposition Temperature 700 K
Failed in 11, Failure Mode 11 only
Failed in 22, Failure Mode 22 only
Failed in 33, Failure Mode 33 only
Failed in 12, Failure Mode 12 & 11 only
Failed in 23, Failure Mode 23 & 11 only
Failed in 31, Failure Mode 31 & 11 only
Melt Matrix Failure Mode Bulk
Stochastic failure No
Material Cutoffs -
Maximum Expansion 0.1
Minimum Density Factor 0.00001
Minimum Density Factor (SPH) 0.2
Maximum Density Factor (SPH) 3
Minimum Soundspeed 0.000006 (m/s )
Figure 2. Simulation algorithm for residual velocity.
Sådhanå (2021) 46:194 Page 5 of 15 194
projectile moves along direction-1, and direction-2 repre-
sents the vertical dimension of the plate, and direction-3 is
orthogonal to directions 1 and 2. Figure 2 shows the
complete simulation algorithm, where the algorithm starts
with CAD geometry generation and meshing of the plate
and projectile. Then from the next step, the algorithm
shows the numerical modelling of the present work, with
the variable assignment and decision making in respect of
perforation.
3.1 Validation of the numerical model
Galvez et al (2009) had proposed an experimental tech-
nique for impact analysis of alumina/aluminum armour by
a tungsten projectile. The presented computational
approach has been validated with the experimental results
of Galvez et al (2009) [35]. From table 5, it can be
observed that the proposed approach is in good agreement
with the experimental results of Galvez et al (2009) [35]having an average deviation of 2% in the presented sim-
ulation results.
3.2 The implication of material on the ballisticlimit
To reveal the ballistic characteristics of considered com-
posite materials, the ballistic limit velocity has been found
for the UHMWPE, Kevlar/epoxy, and alumina (99.5%)
individually. When impacted by an elliptical projectile, the
ballistic limit velocity for UHMWPE, Kevlar/epoxy, and
alumina plate are obtained as 461.5 m/s, 393.5 m/s, and 248
m/s, respectively.
It is evident from the analysis that UHMWPE has better
ballistic limit characteristics than Kevlar/epoxy and alu-
mina. Further, residual velocity has been calculated by the
Lambert-Jonas equation (EQUATION (6)) using the bal-
listic limit velocity. From figure 3(a), it can be seen that
the residual velocity of the UHMWPE plate is less as
compared to Kevlar/epoxy and alumina plate. Thus, the
UHMWPE plate shows good stress distribution
characteristics.
Figure 3(b) shows the ratio of energy transferred to
impact energy, which indicates that the energy absorbed by
UHMWPE is 78.8% of total energy at 520 m/s impact
Table 5. Validation of numerical results.
Thickness alumina/aluminium
(mm)
Galvez et al (2009)Present work
Experimental data (residual
velocity) (m/s)
Simulation data (residual velocity)
(m/s)
% error with experimental
data
20/15 930–960 966 3.87
25/10 960 985 2.60
25/15 939 944 0.53
Figure 3. (a) Residual velocity and (b) ratio of energy transferred to impact energy of projectile impacted on UHMWPE, Kevlar/epoxy
and Alumina plate.
194 Page 6 of 15 Sådhanå (2021) 46:194
velocity and Kevlar/epoxy takes 52.3% of the impact
energy. Still, alumina plate takes only 27.8% of total energy
at the same impact velocity. Hence, UHMWPE is more
prominent in energy-absorbing than Kevlar/epoxy com-
posite and alumina due to its ductility, which facilitates
absorbing higher impact energy.
Figure 4. Geometrical combination of bi-layer composite plates for projectile impact.
Figure 5. (a) Residual velocity and (b) ratio of energy transferred to impact energy for a composite bi-layer of UHMWPE/alumina and
Kevlar/epoxy-alumina.
Sådhanå (2021) 46:194 Page 7 of 15 194
As impact energy increases with the increase of impact
velocity, the energy absorption capacities of ballistic plates
diminished, due to the increased velocity of generated
tensile and compressive waves within the plates. The slope
of energy absorption capacity of UHMWPE is higher than
the Kevlar/epoxy and alumina because alumina and Kevlar/
epoxy are harder than UHMWPE can absorb more energy,
but the stress distribution is more favorable in UHMWPE
plate.
3.3 The implication of material layupon the ballistic limit
In this section, the bi-layered armour plate has been sim-
ulated to investigate the implication of material layup on
ballistic performance regarding residual velocity and
energy transferred. Four different material layup combina-
tions have been formed to accomplish the objective, as
shown in figure 4. UHMWPE and Kevlar/epoxy composite
induces ductile hole formation upon impact. In such failure
mode due to plastic deformation of the material, impact the
material absorbs energy. Therefore, in this section effect of
material on the residual velocity with alumina as backing
material has been compared with alumina as striking
material.
In figure 4, case 1(a) and 1(b) depict the impact on the
UHMWPE side and alumina side, respectively for the
UHMWPE/alumina combination. Case 2(a) and 2(b) illus-
trate the impact on Kevlar/epoxy side and alumina side,
respectively, for the Kevlar/epoxy-alumina combination.
Figure 6. (a) Schematic of Oblique impact, (b) residual velocity and (c) ratio of energy transferred to impact energy for oblique impact
on UHMWPE and Kevlar/epoxy plate.
Table 6. Variation of the ballistic limit with the impact angle.
Impact angle (h)
Ballistic limit (V50) (m/s)
UHMWPE Kevlar/epoxy
30� 403.5 381.5
45� 444 451
60� 535.5 580
194 Page 8 of 15 Sådhanå (2021) 46:194
In the case of the UHMWPE/alumina bi-layer, when the
projectile hits the alumina plate side, the ballistic limit is
found to be 680 m/s, and the ballistic limit for the impact on
UHMWPE side is obtained as 815 m/s. Whereas for the
Kevlar/epoxy-alumina bi-layer, when the projectile hits the
Kevlar/epoxy layer, the ballistic limit is found to be 783.5
m/s, and it is predicted as 745.5 m/s for the alumina side.
Thereby it can be avowed that a soft material as the
striking face facilitates absorbing more energy from the
projectile. When the perforation percolates in the plate,
there is the loss of kinetic energy by the striking plate. After
reaching the backing plate, the (alumina) further loses
kinetic energy as it shows higher energy absorption
capacity. Simultaneously the ballistic limit of a bi-layered
plate is increased.
If the rigid material (alumina) is used as the striking
material, transverse waves enable to travel much faster,
which reduces the dwell time for the projectile.
Therefore, the obtained residual velocity is more for
the cases when the projectile hits the alumina layer for
both the configurations. Figure 5(a) depicts the residual
velocity plot, showing the comparatively lesser residual
velocity for striking on UHMWPE and Kevlar/epoxy
face side.
Figure 5(b) shows the ratio of energy transferred to the
impact energy for the striking on different layers of the bi-
layer. The plot shows that the rate of change of the energy
transferred to the alumina side face is lesser than the
UHMWPE side impact. When the impact velocity is
increased from 840 m/s to 880 m/s, there is approximately a
10% drop in the energy-absorbing capacity when the pro-
jectile impacts on the UHMWPE and Kevlar layers. But
there is approximately 8% drop in the energy-absorbing
capacity when the projectile impacts the alumina layer. As
the impact velocity is increased, the energy absorbing
capacity of UHMWPE and Kevlar decrease at a higher rate
than when compared to alumina.
3.4 The implication of obliquity on the ballisticlimit
In actual impact situation, the impact may not always be
perpendicular to the plate. Therefore, this section examines
the implication of impact angle on the plates. Fig-
ure 6(a) shows the schematic of the computational model
for oblique impact. In the schematic, h represents the
impact angle of the projectile.
Table 7. Effect of projectile shape on the ballistic limit.
Projectile shape
Ballistic limit(V50) (m/s)
% increase in the ballistic limit of UHMWPEUHMWPE Kevlar/epoxy
Elliptical 461.5 393.5 17.28
Conical 471.5 412 14.44
Spherical 506 386 31.09
Figure 7. (a) Residual velocity and (b) ratio of energy transferred to impact energy of the projectile upon impact on UHMWPE and
Kevlar/epoxy plate by different projectiles.
Sådhanå (2021) 46:194 Page 9 of 15 194
Figure 8. Simulation evolutions of the projectile penetrating process for UHMWPE single-layered plate at (a) 30 ls, (b) 60 ls, (c) 90ls, (d) 120 ls and for multi-layered plate at (e) 30 ls, (f) 60 ls, (g) 90 ls and (h) 120 ls.
194 Page 10 of 15 Sådhanå (2021) 46:194
From table 6, it can be observed that the ballistic limit of
the projectile is escalating with the increase of the impact
angle. But the ballistic limit of Kevlar is more than that of
UHMWPE beyond 45� of impact angle. It can be observed
that at 45�, the ballistic limit of Kevlar outweighs by
1.58%, and at 60� outweighs by 8.31% than UHMWPE.
Therefore, UHMWPE is effective up to 45� of impact angle
in preventing the perforation.
Figure 6(b) depicts that the residual velocity of the
projectile dwindles as the impact angle increases. It might
be because the effective distance between the projectile tip
and the back face of the plate is increased. As a result, the
dwell time of the projectile is increased. Consequently,
there is a drop in the residual velocity of the projectile.
Thereby, it can be avowed that the ballistic limit of the
material is a function of the impact angle.
Figure 6(c) shows the ratio of energy transferred to
impact energy with respect to impact velocity by changing
the impact angle. It can be observed that there is approx.
41.67% decrease in the ratio of energy transferred to impact
energy at 30� for Kevlar/epoxy when the impact velocity
increases from 760 m/s to 1000 m/s. But for UHMWPE, it
is only 37.5%. Similarly, for Kevlar/epoxy, the percent
change of ratio is approx. 43.1% at 60�, and for UHMWPE,
it is approx. 40.82%. Therefore, it can be avowed that in the
case of obliquity, Kevlar/epoxy is more prominent in
energy absorption.
3.5 The implication of projectile shapeon the ballistic limit
Projectiles fired from different guns are disparate. It can be
observed from figure 1 that the diameter of the projectiles is
13 mm or 12 mm. Such diameter is classified under the
category of Class1 armor-piercing projectiles. The maxi-
mum diameter of class1 projectile is 12.7 mm at halfway of
its length. Ryan et al [36] studied the effect of Class1
armor-piercing projectile on ultra-high hardness armour
steel in support of the U.S. Army Research Laboratory data.
Borvik et al [37] used blunt, hemispherical, and conical
nose tips to study their sensitivity on a steel plate. To
simplify the geometry and to maintain the same weight as
that of the steel core of 12.7 mm projectile, the diameter of
the projectile used in the present work is 12 mm and 13
mm, and conical, spherical, and elliptical projectiles had
been used. Table 7 shows the comparative ballistic limit of
UHMWPE and Kevlar/epoxy for different projectile
shapes.
Figure 7(a) shows that the residual velocity of the
elliptical projectile is approximately twice that of the
spherical projectile for the UHMWPE. But no significant
difference can be observed in the residual velocity of the
elliptical and conical projectile at 520 m/s. It is due to
their face tips which are near of the same shape. The
projectile with a pointed tip induces localized stress at
the point of impact. Therefore, a significant difference
can be observed for pointed projectiles with respect to
other projectiles.
On juxtaposing the residual velocity for Kevlar/epoxy
composite, there is a difference of only 40 m/s for different
projectiles at 520 m/s. It might be due to the less sensitivity
of Kevlar/epoxy for different projectile shapes. A similar
trend can be observed from figure 7(b). The graphs of
Kevlar/epoxy composite for the three projectiles are very
near to each other. But UHMWPE shows a different trend.
It can be observed that UHMWPE has a higher energy
absorbing capacity due to its ductile nature.
Figure 9. (a) Cross-section and (b) residual velocity for composite armour system.
Sådhanå (2021) 46:194 Page 11 of 15 194
3.6 The implication of plate number
This section expounds on the implication of multi-lay-
ering of the composite plate on von Mises stress. Von-
Mises stress is an essential property to predict the
yielding of the ductile material. More the ductility of
material more will be its energy absorbing capacity.
Consequently, it will lead to a higher ballistic limit.
UHMWPE is a ductile material; therefore, stress values
for a single and multi-layered plate have been compared
in this section. Figures 8(a, b, c and d) and 8(e, f, g, and
h) show the simulation evolutions of the projectile
penetrating process for a single-layered plate and the
multi-layered armour plate, respectively.
Figures 8(d) and 8(h) show that the maximum stress
value for multi-layered UHMWPE outweighs single-lay-
ered plate. It states that a multi-layered plate has a higher-
yielding capacity with respect to a single plate. Moreover,
the ballistic limit for the multi-layered UHMWPE plate is
542.65 m/s, which is higher than the single-layered plate of
490.33 m/s. It might be because the intensity of the trans-
mitted wave decreased in the case of the multi-layered
palate. Which leads to lower stress generation; conse-
quently the ballistic limit for the multi-layered plate
outweighs.
Figure 10. Perforation of elliptical projectile on R/A/K/U composite layer at (a) 10 ls, (b) 20 ls, (c) 30 ls and (d) 40 ls.
194 Page 12 of 15 Sådhanå (2021) 46:194
3.7 Residual velocity for composite armour system
Rationally there are multiple plates of different materials.
Hence, this section shows the computational analysis of a
complete lightweight armour system. Figure 9(a), plate 3,
and plate 4 are filled with UHMWPE and Kevlar/epoxy
material properties and vice-versa. Plate 2 has been con-
sidered alumina. The ballistic cover plate, i.e., plate 1 is of
a rubber1 material (properties of rubber1 have been taken
for AUTODYN material library). The configurations are
made to strike by an elliptical projectile, and the corre-
sponding ballistic limit is found for the configuration.
It has been observed that the ballistic limit for stacking
sequence R/A/K/U is 970 m/s and for R/A/U/K is 820 m/s.
The residual velocity plots for both configurations have
been shown in figure 9(b). The result shows that the
material sequence of R/A/K/U is much more effective than
a material combination of R/A/U/K. It is due to UHMW-
PE’s higher energy absorbing capacity, which facilitates the
armour to absorb higher energy as projectile had undergone
a large loss of energy before reaching the UHMWPE layer.
Further, UHMWPE facilitates energy absorption by ductile
hole formation.
Figure 10 shows the perforation evaluation at 10 ls, 20ls, 30 ls, and at 40 ls. An illustration of the projectile
perforation has been presented by modeling the half model.
It can be observed from figure 10 (a), that the projectile
penetrates 25% of the armor width. As the perforation
evolves to 20 ls, there is a brittle fracture demonstrated by
the alumina layer, and there is almost 50% of the perfora-
tion. But when the projectile reaches the third layer of
Kevlar/epoxy composite, the projectile is arrested in the
layer due to the ductile nature of the plate. The third layer is
supported by the UHMWPE plate, which is also a ductile
material. Thus the combined effect of the third and fourth
layer facilitates to oppose the movement of the projectile.
4. Conclusions
In the present work, a comparative numerical study has
been presented for UHMWPE composite with Kevlar/
epoxy with different design parameters. The implication of
obliquity, projectile shape, and order of the material layup
have been considered for the comparison. Analyses have
been based on residual velocity and a ratio of energy
transferred to impact energy. The following conclusions
can be drawn based on the presented work:
• The ballistic limit velocity of the UHMWPE plate is
higher among the Kevlar/epoxy composite and alu-
mina plate with lighter weight.
• The energy-absorbing capacity of the UHMWPE is
superior to the other considered materials.
• It has been found that using alumina as a backing layer
of UHMWPE or Kevlar/epoxy composite facilities to
enhance the ballistic performance of the bi-layer
composite armor.
• Obliquity amends the ballistic performance of the
material. UHMWPE has superior ballistic performance
up to 45� of impact angle than Kevlar/epoxy composite
plate.
• The ballistic limit is sensitive to the projectile nose.
However, Kevlar/epoxy composite is significantly less
sensitive to the different projectiles. It was found that
spherical face projectile shows the highest ballistic
limit for both the materials.
• It has been found that a material sequence of R/A/K/U
is much more effective than a material combination of
R/A/U/K. It is due to the higher energy absorbing
capacity of UHMWPE.
• Based on the findings of the presented work,
UHMWPE composite may be preferred over Kevlar/
epoxy composite for ballistic protection purposes.
List of symbolsV50 Ballistic limit velocity
Et Energy transferred to plate by a
projectile
Ek Impact energy of the projectile
Vi The impact velocity of the
projectile
Vr The residual velocity of the
projectile
mp Mass of the projectile
mf Mass of the fractured part
P The pressure at the impact point
A1, A2, A3, Bo, T1, T2 Material constant for Mie-
Gruneisen model
q Density
qo Zero pressure density
x Internal energy per unit mass
r�u Normalize intact strength
r�f Normalized fractured strength
_e Normalized strain rate
S=Sh Normalized strength at Hogonoit
Elastic Limit
P=Ph Normalized pressure at Hogonoit
Elastic Limit
D Scalar damage parameter
(0�D� 1)
G, B, H, N, M Material constants
Mm Mass of Kevlar/epoxy or alumina
plate
MU Mass of UHMWPE plate
VK The ballistic limit for Kevlar/
epoxy plate
VU Ballistic limit of UHMWPE plate
Sådhanå (2021) 46:194 Page 13 of 15 194
X1s1 and X2
s2Xi is the deformed position at the
end of 1st surface and at the
starting of 2nd surface,
respectively
T1s1 and T2
s2Ti is the traction force at the end of
1st surface and at the starting of
2nd surface respectively
k Lagrange multiplier
C Domain of integral
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