Ballistic protection performance of curved armor systems with or without debondingsdelaminations

Materials and Design 64 (2014) 25–34

Contents lists available at ScienceDirect

Materials and Design
journal homepage: www.elsevier.com/locate/matdes

Ballistic protection performance of curved armor systems
with or without debondings/delaminations
Ping Tan ⇑
Land Division, Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend, Melbourne, Victoria 3207, Australia

a r t i c l e

i n f o

Article history:
Received 14 February 2014
Accepted 14 July 2014
Available online 24 July 2014
Keywords:
Finite element
Projectile impact
Ballistic protection
Curved armor
Debonding/delamination

a b s t r a c t
In order to discern how pre-existing defects such as single or multiple debondings/delaminations in a
curved armor system may affect its ballistic protection performance, two-dimensional axial finite element models were generated using the commercial software ANSYS/Autodyn. The armor systems considered in this investigation are composed of boron carbide front component and Kevlar/epoxy backing
component. They are assumed to be perfectly bonded at the interface without defects. The parametric

study shows that for the cases considered, the maximum back face deformation of a curved armor system
with or without defects is more sensitive to its curvature, material properties of the ceramic front component, and pre-existing defect size and location than the ballistic limit velocity. Additionally, both the
ballistic limit velocity and maximum back face deformation are significantly affected by the backing component thickness, front/backing component thickness ratio and the number of delaminations.
Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.

1. Introduction
Boron carbide (B4C) is one of the most attractive ceramics for
lightweight armor systems against ballistic/projectile threats. It
has become more commonly used in military body armors over
the past decades. This is due to its attractive characteristics including low density, high hardness and high compressive strength
[1–7]. However, owing to its brittleness, which makes it susceptible to tensile failure, ceramic armor systems such as B4C generally
contain some sort of backing materials such as composite materials. This will prevent the ceramic strike face from suffering large
deflection which can cause tensile failures. Also, the composite
backing layer absorbs the kinetic energy of the decelerated
bullet/projectile and catches the ceramic and bullet/projectile fragments, preventing them from doing further harm.
To better understand the responses of B4C and its composite
armor systems subjected to high velocity projectile/bullet impacts,
various numerical and experimental studies have been conducted.
For example, Brantley [8] conducted microstructural and fractographic studies of the response of hot-pressed boron carbide
ceramic subjected to projectile impact. Shockey et al. [9] experimentally investigated the failure phenomenology of various
ceramics, including B4C, struck by a long rod penetrator. Orphal
et al. [10] carried out ballistic tests for measuring the penetration
⇑ Tel.: +61 3 96268500; fax: +61 3 96267820.
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of confined boron carbide targets subjected to long tungsten rod
impact. Westerling et al. [11] performed an experiment to investigate the influence of impact velocity and confinement on the
resistance of boron carbide targets to the penetration of tungsten
long-rod projectiles. Also, finite element (FE) simulations were

conducted using the commercial finite element software ANSYS/
Autodyn, in which the Johnson–Holmquist model (JH-2) [12] was
used for modeling the response of boron carbide subjected to
dynamic impacts. It was reported that the simulated results for
penetration velocity vs. impact velocity agreed fairly well with
the experimental results provided damage evolution was suspended below the transition region. Holmquist and Johnson [13]
carried out an investigation for the responses of boron carbide
subjected to plate or projectile impact, in which the Johnson–
Holmquist–Beissel (JHB) constitutive model developed previously
by Johnson et al. [14] was used. Shokrieh and Javadpour [4]
developed FE model using ANSYS/Lsdyna software for investigating the response of ceramic composite armor system subjected to
a projectile impact, in which the ceramic composite armor was
composed of boron carbide ceramic-faced panel and Kevlar 49
fiber composite backup panel. It was shown that when the ratio
of the plate thicknesses is different from the optimum magnitude
evaluated according to Hetherington method [15], the armor performance is lower than the optimum case. Chocron-Benloulo and
Sánchez-Gálvez [16] developed an analytical model for simulating
projectile impact onto ceramic/composite armors. A good agreement between the numerical and analytical results was noted,


26

P. Tan / Materials and Design 64 (2014) 25–34

especially for the high velocity cases. Savio et al. [5] conducted an
experimental study for the ballistic performance of boron carbide
tiles subjected to 7.62 mm armor piercing projectile impact. It
was reported that an insignificant or marginal increase in efficiency was observed for an increase in tile thickness from
5.2 mm up to 7.3 mm. Zhang et al. [17] developed a FE model using
MSC.DYTRAN software for optimum design of a flat panel made of

boron carbide ceramic strike face and Kevlar/epoxy backing plate
under the impact of a projectile. Fountzoulas and LaSalvia [6,7]
developed two-dimensional (2D) and three-dimensional (3D) FE
models using ANSYS/Autodyn for simulating the responses of the
confined hot-pressed boron carbide targets subjected to tungsten-based penetrator impact, in which the boron carbide was
modeled using the Polynomial equation of state (EOS) and Johnson–Holmquist strength and failure models (JH-2) available in
Autodyn material library [18].
It was noted from literature that the majority of research on
ballistic performance of B4C and its composite armor systems has
been conducted on flat panels, and investigation of the performance of curved B4C composite armor systems is very limited.
The ballistic protection behavior of curved armor system can be
different from that of flat body armor, due to the curvature given
to the curved body armor during its manufacturing from flat laminates. This leads to stretching and shortening of fibers [19].
Recently, optimal design of curved body armor systems is attracting military’s attention. This is because body armor designed for
men does not fit female soldiers well, and thus the armor is
uncomfortable for female soldiers. Also, if modern body armor is
to become more ergonomic, it should be designed with a curvature
for a comfortable body fit without undue bulk [20]. It is a concern
that undesirable pre-existing defects such as debondings/delaminations, which can occur in the armor system during the manufacturing process and/or in service, may significantly degrade the
ballistic protection performance of a curved armor system. It is
therefore essential to understand the effect of pre-existing debondings/delaminations on the ballistic protection performance of
curved armor systems to improve their defect/damage-survivability and defect/damage-tolerance.
In order to investigate the ballistic protection performance of
various curved B4C/Kevlar armor systems subjected to flat-faced
cylindrical projectile impact, 2D axial FE models with or without
single or multiple pre-existing debondings/delaminations were
developed using the commercial FE software ANSYS/Autodyn and
following the similar procedure used previously [21,22]. Subsequently, a parametric study was conducted to investigate the
effects of key parameters such as the shape and thickness of the
armor system components, the size, location and number of the

pre-existing debondings/delaminations on the ballistic protection
performance of the armor systems, including the ballistic limit
velocity (Vbl) and maximum back face deformation (MAXBFD).
Also, the influences of erosion strain of B4C and Kevlar/epoxy composite on the ballistic protection performance of the curved armor
system were discussed, respectively.
2. Development of the finite element models
To simulate the ballistic protection performances of curved B4C/
Kevlar armor systems with or without pre-existing debondings/
delaminations, corresponding 2D axial FE models were generated
using the commercial FE software ANSYS/Autodyn, which is a
special hydrocode for non-linear transient dynamic events such
as ballistic impact, penetration and blast problems [23]. Fig. 1(a)
and (b) illustrates two typical curved B4C/Kevlar armor systems
with a pre-existing debonding or delamination, in which only half
of the panel above the central line is shown due to the symmetry of
the FE model. In Fig. 1, Rv and Lv stand for the size of the

debonding/delamination and the distance between the debonding/delamination and the front surface of the Kevlar/epoxy component. Gauge 1 located at the center of the projectile is used for
predicting the value of Vbl while gauge 2 located at the back face
of the Kevlar/epoxy composite component is used for obtaining
the value of MAXBFD.
The baseline case considered in this investigation was composed of 2 mm thick B4C front layer, 0.5 mm thick epoxy resin middle layer (i.e., adhesive layer), and 20 mm thick Kevlar/epoxy
composite backing layer. The thicknesses of the B4C and Kevlar/
epoxy composites were selected based on those of generic ballistic
hard armor plates. The armor system components were assumed
to be perfectly bonded together at the interface without defects.
The length and diameter of the flat-faced cylindrical projectile
were chosen to be 13.8 mm and 12.58 mm, which were determined based on those of a fragment-simulating caliber 50 [24].
The Lagrange solver [25] was used for all armor material components and projectiles. The interaction between each component
in the present FE model was achieved using the Lagrange/Lagrange

interaction logic. An erosion algorithm was used for enhancing the
ability of the Lagrange processor to simulate impact problems
involving large deformation [11,21,25,26]. This erosion option
allows removal of elements when the local element geometric
strain exceeds the specified value. The geometric strain is calculated from the principal strain components (ei, eij, i = 1–3, j = 1–3)
as [23]:

eeff ¼

Ã1=2
2Â 2
jðe1 þ e22 þ e23 Þ À ðe1 e2 þ e2 e3 þ e3 e1 Þ þ 3ðe212 þ e223 þ e231 Þj
3
ð1Þ

In this investigation, the geometric strain for erosion was selected
to be 2.0. The type of geometric strain was chosen to be instantaneous. The inertia of the eroded nodes was not retained. Zero
x-velocity and y-velocity boundary conditions were applied to the
top surfaces of all composite components. Gravity and friction from
air resistance were ignored [22].
2.1. Material models
The ability of a numerical model to realistically predict the
response of an armor system to the projectile impact depends
largely on the selection of appropriate material models and
availability of associated input data. In this investigation, the B4C
was modeled by the Polynomial equation of state (EOS) and
Johnson–Holmquist strength and failure model (JH-2) [12]. The
Polynomial EOS is expressed as:

P ¼ A1 l þ A2 l2 þ A3 l3 þ ðB0 þ B1 lÞq0 e

q
q0

ð2Þ

where P is pressure, l ¼ À 1; q and q0 stand for the density and
zero pressure density, and e is the internal energy per unit mass
(or specific internal energy). A1, A2, A3, B0 and B1 are material constants, and their corresponding data are listed in Table A-1 in
Appendix A [23,27].
The Johnson–Holmquist strength model (JH-2) for boron carbide was described in Fig. 1 [12]. This model has been commonly
used to simulate the dynamic response of boron carbide subjected
to high velocity impact [6,11,28]. The required input data for the
JH-2 strength model, including shear modulus (G), Hugoniot elastic
limit (HEL), intact strength constant (A), intact strength exponent
(N), strain rate constant (C), fracture strength constant (B), maximum fracture strength ratio, fracture strength exponent (M), and
those for Johnson–Holmquist failure model, including damage
constant (D1), Damage constant (D2), Hydro tensile limit, Bulking
constant (b), are listed in Table A-1 in Appendix A [23,27]. In this
investigation, the BORONCARBI material model available in the


27

P. Tan / Materials and Design 64 (2014) 25–34

Kevlar/epoxy
composite

B4C

R=170mm

Epoxy resin
Gauges

85mm
Steel 4340
projectile

Rv
Central
line

Lv
(a) Curved armor with
debonding

(b) Curved armor with
delamination

(c) Flat armor with
debonding

Fig. 1. Schematics of typical curved and flat B4C/Kevlar armor systems with pre-existing debonding/delamination.

ANSYS/Autodyn material library was used to model the B4C armor
component subjected to projectile impact.
The epoxy resin was modeled using the Mie–Gruneisen EOS and
Von Mises strength model. The Mie–Gruneisen EOS [29] is generally written as:

P ¼ PH þ Cq½e À eH Š

ð3Þ

Y ¼ ½A þ Benp Š½1 þ C ln eÃp Š½1 À T m
HŠ

ð9Þ

where ep is the effective plastic strain, eÃp is the normalized effective
plastic strain rate, A is the basic yield stress at low strains, B is the
hardening constant, C is the strain rate constant, n is the hardening
exponent, m is the thermal softening exponent and TH is the homologous temperature, which can be obtained by:

where P is pressure and C is the Gruneisen coefficient. The functions PH and eH are expressed as [30]:

T H ¼ ðT À T room Þ=ðT melt À T room Þ

q c2 lð1 þ lÞ
PH ¼ 0 1
½1 þ ðs1 À 1ÞlŠ2

in which T stands for temperature of a material, Troom is the room
temperature and Tmelt is the melting temperature. The required
material properties for epoxy resin, Kevlar/epoxy composite and
steel 4340 are listed in Table A-1 in Appendix A [23,27].

EH ¼

ð4Þ



PH
l
2q0 1 þ l

ð5Þ

in which the parameters c1 and s1 for epoxy resin were obtained
from the corresponding shock Hugoniot curve in the shock particle
velocity plane.
The Von Mises strength model is given by:

ðr1 À r2 Þ2 þ ðr2 À r3 Þ2 þ ðr3 À r1 Þ2 ¼ 2Y 21

ð6Þ

where r1, r2 and r3 are the principal stresses and Y1 is the yield
strength in simple tension.
The Kevlar/epoxy composite was modeled using the orthotropic
EOS (also known as the AMMHIS material model in [31]) and elastic strength model. The incremental constitutive relation for this
orthotropic material can be expressed as

3 2
Dr11
C 11
6 Dr 7 6 C
22 7
6

6 12
7 6
6
6 Dr33 7 6 C 13
7 6
6
6 Dr 7 ¼ 6 0
23 7
6
6
7 6
6
4 Dr31 5 4 0
0
Dr12
2

C 12
C 22

C 13
C 23

0
0

0
0

C 23

C 33

0

0

0

0

C 44

0

0

0

0

C 55

0

0

0

0

3
32 d
De11 þ 13 Dev ol
6
76 Ded þ 1 De 7
76 22 3 v ol 7
7
7
7
0 76
Ded33 þ 13 Dev ol 7
76
7
6
7
7
0 76
De23
7
76
7
6
0 54 De31
5
C 66
De12
0
0

ð7Þ
d
ij

where Cij, Drij, De and Devol stand for the stiffness constant, deviatoric stress component, deviatoric strain component, and volumetric strain increment, respectively. The volumetric strain increment
can be evaluated by Eq. (8) as follows [32]:

Dev ol % e11 þ e22 þ e33

ð8Þ

The above material model has been used by other authors for
simulating the non-linear stress–strain relationships for Kevlar/
epoxy composites [33–35].
The steel 4340 material used for the projectile was modeled
using linear EOS and the Johnson–Cook strength model. In the
Johnson–Cook strength model [30], the yield stress Y is defined as:

ð10Þ

2.2. Convergence and validation of the present finite element model
For assessing the convergence of the present FE model, a mesh
sensitivity analysis was conducted by varying the mesh size of the
components, such as the mesh size for the Kevlar/epoxy was chosen to be 0.2, 0.5, 1 and 1.5 mm, respectively. The differences of the
ballistic limit velocity between the models having mesh size of
0.2 mm and 0.5 mm, 0.2 mm and 1 mm, 0.2 mm and 1.5 mm are
0.9%, 1.7% and 12.1% respectively, thus demonstrating convergence
of the FE model. All subsequent investigations used the mesh size
equal to or less than 1 mm. Validations of the modeling approach,
which was used for developing the previous and present FE models, were conducted in [21–22].

Fig. 2 shows the dynamic response of a curved B4C/Kevlar armor
system with a pre-existing debonding (Fig. 1(a)) and subjected to a
projectile impact at t = 0, 0.01, 0.03 and 0.05 ms, respectively. As
the projectile moves forwards, the projectile length is diminished
and the armor system plug occurs. These findings are similar to
those shown in Fig. 25 in [36] for demonstrating blunt ballistic
penetrator erosion and plate plugging when a ballistic plate is subjected to a blunt ballistic penetrator impact. This suggests that the
FE model used here has the capability to simulate the dynamic
response of a curved B4C/Kevlar armor system subjected to a projectile impact.
3. Results and discussion
The effects of key parameters on the predicted values of Vbl and
MAXBFD for a curved B4C/Kevlar composite armor system, which
was subjected to a flat-faced cylindrical projectile impact, were
evaluated using the present FE model. These key parameters
include: erosion strain; curvature of the armor system; ceramic
material properties; size, location and number of the pre-existing
or artificially introduced debondings/delaminations; ratio of B4C
to Kevlar/epoxy backing plate thickness (Rcd = hc/hb); Kevlar/epoxy


28

P. Tan / Materials and Design 64 (2014) 25–34

Epoxy
resin

Kevlar/Epoxy
composite

B4C

Projectile

(a) t = 0

(b) t = 0.01 ms

(c) t = 0.03 ms

(d) t = 0.05 ms

Fig. 2. Dynamic response of a curved B4C/Kevlar armor system having pre-existing debonding of Rv = 5 mm and subjected to a projectile impact.

backing plate thickness (hb). They are varied in individual simulation: erosion strain of 0.5, 1, 1.5, and 2 [23]; radius of curved armor
of 120, 170 and 220 mm; ceramic material properties of B4C in
Table A-1 and SiC in Table 1 in [22]; size of the pre-existing
debonding/delamination of 0, 5 and 15 mm; location of the preexisting debonding/delamination of 0, 11 and 18 mm; the B4C
and Kevlar/epoxy component thickness ratio of 1/9, 0.2, 1/3, 0.5,
0.7 and 1; Kevlar/epoxy thickness of 10, 20 and 30 mm and delamination number of 1, 3 and 5 were used. The predicted value of Vbl
was obtained by averaging the initial velocity V p0 that led to a partial penetration and the velocity V c0 that led a complete penetration. The difference between V p0 and V c0 was chosen to be 10 m/s.
To evaluate the MAXBFD, an initial velocity of 700 m/s was applied
to the projectile, which was determined based on the results from
a preliminary study to avoid removal of the element on which the
gauge 2 is located.
The predicted values of Vbl and MAXBFD as a function of the
erosion strain are presented in Fig. 3 for the B4C component and
Fig. 4 for the Kevlar/epoxy component. For the cases considered,
the predicted values of Vbl and MAXBFD are not sensitive to variation of the erosion strain except for the case in Fig. 4(b), in which
the predicted value of MAXBFD reduces significantly when the erosion strain of the Kevlar/epoxy component increases from 0.5 to 1,

beyond that the MAXBFD decreases slightly up to erosion
strain = 2. In the following discussion, the erosion strain is chosen
to be 2 for both B4C and Kevlar/epoxy composite.
The variations of the predicted Vbl and MAXBFD with the radii of
curved armor systems (Rp) with and without debonding were plotted in Fig. 5(a) and (b), respectively. Fig. 5(a) illustrates that for
both cases with and without debonding, an increase in the panel’s
radius results in a slight reduction in Vbl. This is consistent with the
experimental results shown in Figure 4.3 in [37] (i.e., the ballistic
limit for graphite epoxy composite panels increased monotonically
as the curvature of the panel was increased). Fig. 5(b) shows that
the predicted value of the MAXBFD increases with the radius of
the panel with or without debonding. It is consistent with the finding in [38] (i.e., for the same indentation force, the indentation
depth increases with increasing radii of curvature).
A comparison of the ballistic protection performance between
the curved and flat panels is illustrated in Fig. 6 for the cases with
and without debonding of Rv = 5 mm. As expected, the predicted
value of Vbl for the curved panel is higher than the flat panel. This
is consistent with the findings in [33] (i.e., the helmet has a higher
Table 1
The selected values of Rcb, hc, hb and hcb for the case of AD = 4.0357 g/cm2.
Rcb (=hc/hb)

1/9

1/5

1/3

1/2

7/10

1

hc (mm)
hb (mm)
hcb (=hc + hb) (mm)

2.3
21
23.3

3.7
18.5
22.2

5.3
16
21.3

6.84
13.67
20.51

8.16
11.66
19.82

9.5
9.5

19

ballistic resistance than that of a Kevlar laminate), [39] (i.e., the
convex panel has higher ballistic resistance than the corresponding
flat panel made of the same material), and [40] (i.e., normalized
ballistic limits for the KevlarÒ KM2 helmets are higher than those
for the KevlarÒ KM2 flat panels). In contrast, the predicted value of
MAXBFD for the curved panel is significantly lower than the flat
panel. Also, it is noted from Fig. 6 that a pre-existing debonding
of Rv = 5 mm results in slight reduction in the predicted Vbl, which
is similar to the finding in [22]. However, it is interesting to note
that for both curved and flat panels, the predicted value of MAXBFD for the case with debonding of Rv = 5 mm is the same as that
without debonding, which is different from that reported in [22]
(i.e., a pre-existing debonding of Rv = 5 mm within a SiC/Kevlar
composite flat panel results in significant increase in the predicted
value of MAXBFD). This implies that the B4C/Kevlar flat panel
considered in this investigation could be less sensitive to the preexisting debonding than the SiC/Kevlar composite panel in [22],
and thus have better defect/damage-survivability and defect/damage-tolerance.
Fig. 7 shows a comparison of the predicted Vbl and MAXBFD
between the B4C/Kevlar and SiC/Kevlar curved armor systems having a radius of 170 mm and debonding of Rv = 5 mm. It indicates
that for the cases considered, replacing the B4C with SiC slightly
reduces the predicted value of Vbl, but significantly increases the
predicted value of the MAXBFD for both cases with and without
debonding. Also, it is interesting to note that a pre-existing debonding of Rv = 5 mm results in slight reduction in predicted Vbl
for both SiC/Kevlar and B4C/Kevlar curved armors. However, it does
not affect the predicted MAXBFD for the B4C/Kevlar armor system
but results in a slight increase in the MAXBFD for the SiC/Kevlar
armor system. This implies that for the cases considered, the
B4C/Kevlar armor system has better ballistic performance than
the SiC/Kevlar armor system, which is consistent with the outcome

for the flat panel mentioned previously.
The variations of the predicted Vbl and MAXBFD with Rv and Lv
are plotted in Figs. 8 and 9, respectively. Fig. 8 shows an increase in
Rv results in an increase in the predicted MAXBFD but slight reduction in the predicted Vbl. These are similar to the findings for the
SiC/Kevlar flat panel in [22], and the testing results in [41] (i.e.,
for hard armor plates made of B4C strike plates backed with
ultra-high-molecular-weight polyethylene (UHMWPE) backing
plates and subjected to 7.62 Â 39 M43 FMJ projectile impact, the
size of an artificially introduced debonding/delamination does
not significantly affect the ballistic limit of the hard armor plates).
Also, it is similar to that reported in [42] (i.e., the existence of
deliberately introduced delamination did not significantly
influence impact resistance. This may be caused by the fact that
delamination did not seem to dissipate a major amount of energy).
Fig. 9 illustrates that effect of Lv on the predicted Vbl or MAXBFD is
insignificant. This is similar to the finding in [41] (i.e., the location


29

1500

20

1200

16

MAXBFD (mm)

Vbl (m/s)

P. Tan / Materials and Design 64 (2014) 25–34

900

600

12

8

300

4

0

0
0

0.5

1

1.5

2

2.5

0

1

2

3

Erosion strain

Erosion strain

(b) Variation of MAXBFD vs. erosion strain

(a) Variation of Vbl vs. erosion strain

1500

20

1200

16

MAXBFD (mm)

Vbl (m/s)

Fig. 3. Variations of the predicted Vbl and MAXBFD vs. erosion strain for B4C.

900

600

12

300

8
4
0

0
0

0.5

1

1.5

2

0

2.5

0.5

1

1.5

2

2.5

Erosion strain

Erosion strain

(a) Variation of Vbl vs. erosion strain

(b) Variation of MAXBFD vs. erosion strain

2000

20

1600

16

MAXBFD (mm)

V bl (m/s)

Fig. 4. Variations of the predicted Vbl and MAXBFD vs. erosion strain for Kevlar/epoxy composite.

1200

800
perfect panel

400

perfect panel
panel having Rv = 5 mm

12
8

4

panel having Rv = 5 mm
0

0

0

50

100

150

200

250

Rp (mm)

(a) Variation of Vbl vs. Rp

0

50

100

150

200

250

Rp (mm)

(b) Variation of MAXBFD vs. Rp

Fig. 5. Effect of Rp on the predicted Vbl and MAXBFD for the cases with and without debonding of Rv = 5 mm.

of an artificially introduced debonding/delamination does not significantly affect the ballistic limit of the hard armor plates).
Fig. 10 shows the schematics of six armor system having the
same areal density (AD) of 4.0357 g/cm2 but different value of
the B4C and Kevlar/epoxy component thickness ratio (Rcb). The
thicknesses for these armor systems (hcb) and their corresponding
components (hb, hc) were listed in Table 1.

The variations of the predicted Vbl and MAXBFD vs. Rcb are
plotted in Fig. 11. It indicates that the predicted Vbl increases
significantly with Rcb. This finding is similar to that shown in
Fig. 3 in [15] for the armor systems without any defect (i.e., for
the case of Rcb 6 1, the theoretical and experimental results of
the Vbl for ceramic/aluminum armor systems increases significantly as the Rcb increases). Also, the figure shows the predicted


30

P. Tan / Materials and Design 64 (2014) 25–34

20

2000
perfect

having Rv = 5 mm

perfect

16

MAXBFD (mm)

1600

Vbl (m/s)

having Rv = 5 mm

1200

800

400

12

8

4

0
Flat panel

0

Curved panel

Flat panel

Curved panel

Type of panel

Type of panel

(a) Effect of panel type on Vbl

(b) Effect of panel type on MAXBFD

Fig. 6. Comparisons of the predicted Vbl and MAXBFD between the curved and flat armor systems.

20

1500
perfect

perfect

having Rv = 5 mm

16

MAXBFD (mm)

1200

V bl (m/s)

having Rv = 5 mm

900

600

12

8

4

300

0

0
B4C/Kevlar

B4C/Ke vlar

SiC/Kevlar

Type of ceramic

SiC/Kevlar

Type of ceramic

(a) Effect of ceramic type on Vbl

(b) Effect of ceramic type on MAXBFD

2000

20

1600

16

MAXBFD (mm)

Vbl (m/s)

Fig. 7. Comparison of the predicted Vbl and MAXBFD between the SiC/Kevlar and B4C/Kevlar curved armor systems with and without debonding of Rv = 5 mm.

1200

800

400

12

8

4

0

0
0

4

8

12

16

20

0

5

10

15

Rv (mm)

Rv (mm)

(a) Effect of Rv on Vbl

(b) Effect of Rv on MAXBFD

20

Fig. 8. Effect of Rv on the predicted Vbl and MAXBFD for the curved armor system having radius of 170 mm (for the case of Lv = 0).

MAXBFD significantly decreases with an increase in Rcb until
Rcb = 1/3, up to Rcb = 1 the predicted MAXBFD changes slightly.
Fig. 12 shows the variations of the predicted Vbl and MAXBFD
with the thickness of Kevlar/epoxy backing component (hb). It is

noted that for the curved armor systems with and without debonding of Rv = 5 mm, an increase in hb results in an obvious decrease in
the predicted MAXBFD and a significant increase in the predicted
Vbl. This is due to that for the panel having higher value of hb, more


31

P. Tan / Materials and Design 64 (2014) 25–34

20

1600

16

MAXBFD (mm)

2000

Vbl (m/s)

1200

800

12

400

8

4

0

0
0

5

10

15

20

0

5

10

Lv (mm)

15

20

Lv (mm)

(b) Effect of Lv on MAXBFD

(a) Effect of Lv on Vbl

Fig. 9. Effect of Lv on the predicted Vbl and MAXBFD for the curved armor system having radius of 170 mm (for the case of Rv = 5 mm).

Epoxy
resin

B4C

Kevlar/epoxy
composite

Projectile

(a) Rcb = 1/9

(b) Rcb = 1/5

(c) Rcb = 1/3

(d) Rcb = 1/2

(e) Rcb = 7/10

(f) Rcb = 1

Fig. 10. Schematics of the B4C/Kevlar curved armor systems having different value of Rcb (for the case of having Rv = 5 mm and AD = 4.0357 g/cm2).

4000

10

8

MAXBFD (mm)

Vbl (m/s)

3000

2000

1000

6

4

2

0

0

0

0.2

0.4

0.6

0.8

Rcb

(a) Effect of Rcb on Vbl

1

0

0.2

0.4

0.6

0.8

1

Rcb

(b) Effect of R cb on MAXBFD

Fig. 11. Variations of the predicted Vbl and MAXBFD vs. Rcb for the case of R = 5 mm and AD = 4.0357 g/cm2.

work is done to cause failure of the panel and more energy is spent
in overcoming the friction between the panel and projectile, and
thus result in that the Vbl for a panel having higher value of hb is
greater than that having a smaller value of hb.
The schematics of the curved armor systems having different
number of pre-existing or artificially introduced delamination
(Ndel) are shown in Fig. 13. The variations of the predicted Vbl
and MAXBFD with Ndel are plotted in Fig. 14. It indicates that an
increase in Ndel results in a reduction in the predicted Vbl. This is

expected since the Vbl decreases with a reduction of the areal mass
of the armor system around the projectile impact point [15], which
is reduced as Ndel increases. However, it is interesting that for the
cases considered, the predicted MAXBFD for the case of Ndel = 3 is
less than that for Ndel = 1 or Ndel = 5. It is hard to interpret the predicted MAXBFD results since the dynamic fracture mechanics for
the composite armor system is extremely complex as mentioned
in [43]. The inertia effects, vibrations and stress wave interactions
can all be present and can cause unexpected results.


P. Tan / Materials and Design 64 (2014) 25–34

2000

20

1600

16

MAXBFD (mm)

Vbl (m/s)

32

1200
800

12
8

Debond with Rv=5

400

4

Perfect

Debond with Rv=5
Perfect

0

0
0

10

20

30

0

40

10

20

30

40

hb (mm)

hb (mm)

(b) Effect of hb on MAXBFD

(a) Effect of hb on Vbl

Fig. 12. Effect of hb on the predicted Vbl and MAXBFD for the curved B4C/Kevlar armor systems with and without debonding of Rv = 5 mm.

B4C

Kevlar/epoxy

composite

Epoxy
resin

Projectile

(a) Ndel = 1

(b) Ndel = 3

(c) Ndel = 5

Fig. 13. Schematics of the B4C/Kevlar curved armor systems having Ndel = 1, 3, 5,
respectively (for the case of Rv = 15 mm).

4. Conclusions

1500

12

1200

10

MAXBFD (mm)

Vbl (m/s)

Optimal design of curved body armor systems is attracting the
attention of military users. This work aims at investigating the ballistic protection performance of curved B4C/Kevlar composite
armor systems with or without debondings/delaminations, including the maximum back face deformation and ballistic limit velocity. A parametric study has been conducted using the present 2D
axial FE model, which was developed using the commercial finite
element analysis software ANSYS/Autodyn and following a procedure similar to that used previously for investigating the protection behaviors of selected flat panels against projectile impacts.

The parametric study shows that for the considered curved armors
subjected to flat-faced cylindrical projectile impact, the predicted
maximum back face deformation is more sensitive to its curvature
and the material properties of the ceramic front component than
the predicted ballistic limit velocity. The effects of the size and
location for a single pre-existing debonding/delamination on the
predicted maximum back face deformations are more significant
than those on the predicted ballistic limit velocity. For considered
curved body armors having the same areal density but different
front/backing component thickness radio, an increase in the ratio
results in a significant increase in the predicted ballistic limit
velocity. However, it is interesting to note that the predicted maximum back face deformation significantly decreases with an
increase in front/backing component thickness ratio Rcb until
Rcb = 1/3, up to 1 the predicted maximum back face deformation
changes slightly. As expected, an increase in the backing component thickness causes an increase in the predicted ballistic limit
velocity and a reduction in the predicted maximum back face
deformation. An increase in the number of pre-existing delaminations within the Kevlar/epoxy backing component results in a
reduction in the predicted ballistic limit velocity, whereas the predicted maximum back face deformation for the case having three
pre-existing delaminations is less than that having one or five
pre-existing delaminations. Replacing SiC with B4C for the front
component does not result in a significant increase in the predicted
ballistic limit velocity but significant reduction in the predicted
maximum back face deformation. Also, the predicted maximum
back face deformation for the case having B4C front face is less

900

600

300

8
6
4
2
0

0
0

1

2

3

Ndel

4

5

6

0

1

2

3

4

5

6

Ndel

Fig. 14. Effect of Ndel on the predicted Vbl and MAXBFD for the curved armor systems with delamination of Rv = 15 mm.


33

P. Tan / Materials and Design 64 (2014) 25–34
Table A-1
Material properties [23,27].
Epoxy resin

C0

q0 (kg/m3)

1.13

1186

c1 (m/s)
2730

s1
1.493

Shear modulus (kPa)
1.45 Â 106

Steel 4340
q0 (kg/m3)
7830
Hardening exponent
0.26

Bulk modulus (kPa)
1.59 Â 108
Strain rate constant
0.014

Shear modulus G (kPa)
7.7 Â 107
Thermal softening exponent
1.03

Yield stress (kPa)

7.92 Â 105
Melting temperature (K)
1.793 Â 103

Hardening constant (kPa)
5.1 Â 105
Ref. strain rate
1

Bulk modulus A1 (kPa)
2.33 Â 108
G (kPa)
1.99 Â 108
B
0.5
D2
1

A2 (kPa)
5 Â 107
HEL (kPa)
1.25 Â 107
Max. fracture strength ratio
0.15
Hydro tensile limit (kPa)
À7.3 Â 106

A3 (kPa)
0
A

0.987
M
1
b
1

B0
0
N
0.77

C22 (kPa)
1.35 Â 107
G12 (kPa)
1 Â 106
Tensile failure strain 22
0.08

C33 (kPa)
1.35 Â 107
G13 (kPa)
1 Â 106

C12
1.14 Â 106
G23 (kPa)
1 Â 106
Tensile failure strain 33
0.08

Yield stress (kPa)
2.76 Â 104

Boron carbide

q0 (kg/m3)
2516
B1
0
C
0.027
D1
0.1
Kevlar/epoxy

q0 (kg/m3)

C11 (kPa)
1650
3.425 Â 106
C23
C13
1.2 Â 106
1.14 Â 106
Tensile failure strain 11
0.01

sensitive to pre-existing debonding than that having SiC front face.
This implies that the B4C/Kevlar armor systems may have better
defect/damage-survivability and defect/damage-tolerance.

Acknowledgements
This research work was motivated by the Defence Materials
Technology Centre Personnel Survivability program, Project 7.1.2
on Life of Type of Armor materials. The author would like to thank
Dr. M. Ling, Dr. B. Dixon, Dr. R. Gailis and Dr C. Woodruff for assistance during the preparation of the manuscript.
Appendix A.
See Table A-1.
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