INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
ISSN 2277-8616
Ballistic Penetration Response Of Glass Fibre
Reinforced Polyester (Gfrp) Composites: Body
Amour
P.C. Onyechi, S.O. Edelugo, E.O.Chukwumuanya, S.P.N. Obuka
Abstract: This work is aimed primarily at the development of armour protecting bodies for armoured vehicle technology, automobile, ship and
aerospace industries. Samples of Glass Fibre-Reinforced Plastics (GFRP) composites were subjected to ballistic deformation. Detailed
parametric studies considering conical and ogival nosed projectiles and the targeted laminate variables were carried out to find their effect on the
response of the plate and the ballistic parameters such as ballistic limit and absorbed energy. This work shows that one of the governing factors in
the damage resistance is the nose shape of the impacting projectile. The ballistic penetration test indicates that the conical nosed projectile has a
higher penetration effect on the GFRP samples than the ogival nosed projectile, with Sample E showing the best penetration resistance. The
ballistic limits, residual velocities, and ballistic energy were predicted for over a range of thicknesses of the armour protecting body.
Keywords: Ballistic Deformation, Composite Laminate, Absorbed Energy, Residual Velocity, Ballistic Limit, Projectiles
————————————————————
The impact resistance and subsequent load-bearing
capacity of composite depend on many factors such as
The advanced composites materials are being looked upon
fibre and matrix properties, fibre-matrix lay-up, number of
as the key materials for applications in armoured vehicle
layers or ply, thickness, and impact velocity. Cantwell et al
technology, automobile, ship, aerospace industries and
[1] and Prewo [2] stated that the impact, resulting in
ballistic protection. The design of composite armour is a
complete penetration of laminate due to the high velocity is
very complex task as compared to conventional single-layer
called ballistic impact and is of major concern to the armour
metallic armour, due to the exhibition of coupling among
designers. Further, the damage caused to the armour under
membrane, torsion and bending strains, weak transverse
high velocity impact is quite significant and has major
shear strength and discontinuity of the mechanical
effects on the dynamic properties of the laminates.
properties along the thickness of the composite laminates.
Evaluation of ballistic parameters, such as ballistic limit and
This has drawn attention of several researchers to study the
absorbed energy, residual velocity etc of the GFRP is very
penetration phenomenon in composite amours. Fibre
important in this study.
reinforced composite laminates are now widely used in
application due to their superiority over metals such as high
2. LITERATURE REVIEW
stiffness and strength as well as low weight, better
The glass-fibre reinforcement comes in a number of forms
corrosion resistance, acoustic and vibrating properties, a
including roving woven glass cloth and Glass mats [3].
high fatigue, crack resistance, impact and explosive shock
Glass-fibre is the most common reinforcement used in
resistance. However, a major concern about the use of the
polymeric composite formulation use in aerospace, aircraft,
composite is their low resistance to out-of-plane localized
military and ballistic protection. Reinforcement plays a
impact loading. The damage resistance and damage
dominant role determining mechanical strength properties
tolerance under impact loading are of the most importance
of composite. The glass content of Glass Reinforced
of composite material characteristics because they are
Polymer (GRP) composites effects strength properties and
often susceptible to impact and subsequent penetration
durability (the higher the glass-fibre content, the stronger
and/or perforation.
the material). However, too high a glass content may result
to insufficient impregnation, and therefore poorer bonding.
The glass content of GRP reinforced with chopped strand
mat generally varies between 25 to 35 ℅; for GRP
reinforced with cloth, the glass content ranges from 50 to 63
_______________________
℅. Sheet material manufactured by hand lay-up process
will have lower strength properties than those fabricated by
 P.C. Onyechi, S.O. Edelugo, E.O. Chukwumuanya
a press-molding process [4]. Ballistic type of impact tests
S.P.N. Obuka
were studied in an attempt to study speed effects of a
 Department
of
Industrial
and
Production
projectile that would maximize the damage. The study of
Engineering, Nnamdi Azikiwe University, Awka
foreign objects became critical for speed and shape of
Nigeria
indenters relationship. The first ballistic impact resistance
 Department of Mechanical Engineering, University of
test was conducted on the GRP in 1940. In their study it
Nigeria, Nsukka, Nigeria
was found that the maximum de-lamination damaged area
was a linear function of the force of impact whether the
 Department of Mechanical Engineering, Enugu State
force was introduced by falling weight or static indentation
University of Science and Technology, Enugu,
tests. The analysis of high velocity impact problems has
Nigeria
been of interest for many years. Solution to these problems
 Corresponding Author’s
often require the inclusion of large strains and
Email: silvermeks7777@yahoo.com
displacement, as well as the materials strength and
1 INTRODUCTION
226
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
compressibility effects, the analysis techniques are
complicated and large computer codes are necessary to
obtain these solutions. The earlier solutions of high velocity
impact problems were often obtained with two-dimensional
Lagrangian codes such as HEMP of [5] and TOODY II by
[6]. Two-dimensional Eulerian codes such as HELP
program by [7] were later applied to these problems. A
three-dimensional version of HEMP has also been
developed [8]. The finite-element method has recently been
applied to two-dimensional impact problems involving
severe distortion [9]. Various theories proposed for
predicting the characteristics of penetration of composite
laminates by different projectiles have been reviewed by
[10, 11]. Ductile composite materials, such as laminates
reinforced by aramids or polyethylene fibres, have been
studied by [12, 13, and 14]. They proposed both
experimental and analytical models to predict the
perforation and the ballistic limit for Kevlar/epoxy laminated
composite by conical projectiles, considering local and
global deformations. Vinoson and Walker [15] developed a
conical shell model and solve the perforation problem using
the finite-difference technique. Sun and Potti [16] developed
a simple ring model for a cylindrical im16pactor which was
then solved numerically to predict residual velocities. These
models tend to be specific to the composite configurations
tested. Abrate [10] reviewed a large number of papers on
ballistic impact and he focused his discussion on predictive
models for the ballistic limits. High velocity projectiles owe
their destructive penetrating ability to the kinetic energy
they carry with them. Conversely, the efficacy of any
material resisting such kinetic energy projectiles depends
on its ability to absorb the kinetic energy. The energy
absorption capacity in turn depends on target material
properties. For a given set of properties of laminate targets,
the absorption capability also depends on the anisotropic
nature of the target material, the thickness of the target, the
angle of attack and the type of projectile. Kumar and Bhart
[17] studied the effect of thickness of the laminates and the
angle of attack on the energy absorption by the composite
laminates and the area of damage caused by impact. Lee
and Sun [18] used quasi-static finite element analysis to
simulate the penetration process in the graphite/epoxylaminate composites, where-in the penetration criterion is
based on statistic punch test. Wen et-al [19] proposed an
empirical formula for predicting the ballistic limit based on
experimental observations, while Wen [20] predicted
penetration and perforation of the Fibre-Reinforced Plastic
(FRP) laminates based on mean pressure offered by the
laminated target to resist the penetrator. Wen et al. [19],
Reddy et al. [21] and Reid et al. [22] carried out a
comprehensive study on the penetration and perforation of
FRP laminates and sandwich panels with such laminates as
skin and with foam cases in the context of offshore
applications as part of the UK collaborative research
programme on the cost effective use of fibre-Reinforced
composites offshore. The results of penetration and
perforation test performed on composite laminates and
sandwich panels using flat–faced, hemispherical ended and
conical-nosed indenters/missiles under quasi-static, dropweight and ballistic impact conditions with impact velocities
up to 305m/s were reposted. Ballistic limits and perforation
energies were determined and classifications of the
responses were deduced from the test data. Experimental
ISSN 2277-8616
evidence shows that projectile/ballistic impact of FRP
laminates and sandwich panels with such laminates as
skins and with foam cases can be categorized into low
velocity impact (global) and wave-dominated (localized)
responses. Wen et al [23] and He et al. [24] presented
analytical equation for the prediction of the penetration and
perforation of thick FRP laminates struck normally by
missiles over a range of impact velocities. Gupta and
Davids [25] studied the penetration resistance of fibre
glass-reinforced plastics against small caliber projectiles.
Their experimental results indicated that the energy
absorbed increases linearly with the areal density or
thickness of the laminate. Abdullah and Cantwell [26] have
performed ballistic impact tests showing that the ballistic
limit increases almost linearly with the thickness of the
laminate. Cantwell and Morton [27] have predicted the
ballistic limit for Carbon Fibre-Reinforced Plastics (CFRP)
accounting for the energy dissipation in delaminating
deformation and shear. These models can predict the
energy absorption for thin laminates with reasonable
success but underestimate the same for thick laminates,
due to the absence of a well-defined conical damaged
zone. The models described above are primarily based on
conservation of the energy and no progressive damage
propagation was considered except by [14]. To study the
influence of various parameters affecting the penetration
process in high velocity impact, the model should be able to
describe the physical events, such as indentation, fibre
breakage, de-lamination, bulging occurring during
penetration.
3. METHODOLOGY
3.1 Experimental Procedure
Mixed methods of experimental and numerical methods
were used. The class of glass fibres used in this work is the
matted woven roving E-glass procured from NYCIL
Chemical Industries Nkpor, Idemili North L.G.A., Anambra
State, Nigeria. E-glass class, which is a low alkali
Borosilicate was initially, developed for electrical
application, hence the designation E. The diameter of each
E-glass fibre is about 0.01 mm with an average length of
50mm. It has a density of 2550kg/m3; Young’s Modulus of
72 GN/m3; and a strength of roughly 3.4 GN/m2. The
Polyester Resin used for this work was also procured from
NYCIL. It services as the polymer matrix (greatest in
percentage of the reagents) for the sample preparation. The
speed at which the resin sets can be controlled by the
quantity of catalyst and accelerator used. Methyl Ethyl
Ketone Peroxide (MEKP), served as catalyst to the reaction
process. Cobalt II Ethyl Hexanoate acted as an accelerator
for the release of the free of radical that enhances curing by
the catalyst. Paraffin Wax was applied on the surface of
mould to enhance the ease removal of the prepared sample
from the mould untampered. This is also called a releasing
agent. The hand lay-up method was used in formation of
the composite materials. Here the polyester resin was
applied on the mould evenly with the help of a hand brush
to a thickness of about 1mm, then the woven roving fibres
were lay-up in the mould and properly wetted out in a
process known as fibre impregnation. More fibre plies were
lay-up in the mould and compressed according to the
required laminate thickness. For the thickness of 28 mm, 24
227
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
ISSN 2277-8616
mm, 20 mm, 16 mm, 12mm and 8mm, the number of plies
were 22, 18, 15, 12, 9, and 6 respectively. The fibre content
by volume fraction varies from 0.48 to 0.50.
3.2 Principle of Ballistic Penetration and Perforation
It is assumed that the mean pressure () applied normally
to the surface of the projectile provided by a Glass Fibre
Reinforced Plastics (GFRP) laminate material to resist
penetration and perforation by the projectile can be
decomposed into two parts, one part is resistive pressure
(s) due to the elastic-plastic deformations of the laminate
material and the other is the dynamic resistive pressure
(d) arising from velocity effects. Thus;
ς = ςs + ςd
(1)
If it is further assumed that resistive pressure is equal to
static linear elastic limit (e) in through-thickness
compression of the GFRP laminates [8, 9], that is s = e
and that the dynamic resistive pressure (d) which is a
0.5
ρ
function of the parameter t ςe
Vi , and is taken to be,
ςd = β
ρt
0.5
ςe
Vi ςe
(2)
Then equation (3.1) can be written as
ς = 1+β
ρt
ςe
0.5
Vi ςe
(3)
Where ρt and Vi are the density of the GFRP laminate and
the initial impact velocity of the projectile respectively. The
values of the term β were easily determined
experimentally for simple geometries. For a unidirectional
laminate β=1, while for a (0/90) cross-piled laminate with
equal proportions of the fibre in the two direction β= 0.5. For
a (±45, 90) composite with one quarter of the fibres in each
direction β= 0.375. For a three dimensional random array
β= 0.2 [28]. Also, the values of the parameter β in the
equations have been empirically determined and are taken
to be equal to 2 Sin θ 2 and 3 4ψ for conical-nosed and
ogival-nosed projectiles respectively [20]. For fibrereinforced plastic it has been observed in the static
indentation tests [14] that the first term in equation (3) is
related to the static strength of FRP laminates in
compression in the two principal directions, through the
thickness and in-plane. Abdulla and Cantwell [26] used eqn.
(3) to predict the ballistic limit of fibre-metal laminates. The
same assumption (eqn. 3) was used by Ben-Dor et al [29]
in their study of the penetration of fibre-reinforced plastic.
3.2.1. Penetration of Semi-Infinite GFRP Laminates
The types of projectiles (life bullets) that were used are the
rigid projectile with ogival and conical nosed.
228
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
D
D
L
L
𝛗 S
ISSN 2277-8616
LN
LN
(a)
(b)
Fig. 1: Projectile geometries (a) Ogival nose and (b) Conical nose
The projectiles are assumed to have density ρp and mass
M with diameter D (or radius r), L and LN are the lengths of
the shank and nose of ogival and conical projectile as
shown in Fig. 1. Fig. 1(a) shows the ogive profile as the arc
of the circle(s) that is tangent to the shank. It is also
FRP
dp
common to define the ogive in terms of caliber – radius –
head (CRH);
S
CRH = = ψ
(4)
2r
Fig. 2: Schematic diagrams of a conical-nosed projectile
impacting on semi-infinite FRP laminate targets (i) dp < LN;
(ii) dp > LN.
Fig. 2 shows the impact of a rigid projectile with conical
nose on an FRP laminates target at normal incident with an
initial impact velocity Vi. Two situations may arise
depending upon the initial kinetic energy of the projectile as
shown in Fig. 2. One situation is that the final depth of
penetration has not reached the shoulder of the projectile
when its kinetic energy has been dissipated and the other is
that the final depth of penetration is greater than the nose
length. Similar situations may occur for a rigid ogival-nosed
projectile transversely impacting an FRP laminate target.
3.2.2 Conical-Nosed Projectiles
For a rigid conical-nosed projectile, the motion and the final
depth of penetration can be calculated if the resistive forces
are known.
Case (i), dp ≤ LN
The resistive force of a conical-nosed projectile penetrating
an FRP laminate target at normal incidence can be written
as;
F = σA
(5)
Where F is the resistive force and  is the mean resistive
pressure provided by the target material and A, is instant
cross-sectional area.
θ
A = πdp 2 tan2
(6)
2
dp
FRP
T
T
 and dp is the cone angle and the depth of penetration
respectively. Substituting equations (3) and (5) in (6) gives;
F = πdp 2 tan2
ρ
θ
1+β t
2
σe
0.5
V i σe
(7)
For energy conservation, one obtains;
dp
Ek =
(8)
Fd dp
0
Where Ek; is the initial kinetic energy of the projectile.
Substituting equation (7) in (8) will yield.
Ek =
dp 3 A 0
3LN
2
1+β
ρt
σe
0.5
Vi σe
(9)
Using tan (/2) = r/LN and Ao = r2. Here Ao is the crosssectional area of the projectile shank. Substituting Ek =
1
mVi 2 into equation (9) and rearranging gives that, [20].
2
ρp ρt V i 2
dp
1
=
LN
ρt σ e 2
ρ 0.5
L+
1+β t
Vi
3
σe
3
And m = A0 L +
LN
3
dp
LN
2
(10)
ρp
Case (ii) dp > LN
The resistive force F can be written as;
229
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
𝐹 = 𝐴0 𝜎 = 𝐴0 𝜎𝑒 1 + 𝛽
𝜌𝑡
𝜎𝑒
ρp ρt V i 2
ρt σ e
0.5
𝑉𝑖
dp = L + 8ψ3 ηγ
(11)
According to energy balance, one obtains,
LN
Ek =
+
p
Fd dp +
0
0.5
Vi
(13)
Substituting Ek = 1 2 GVi 2 into (11) and using G =
A0 L + LN 3 ρp gives the final depth of penetration as;
ρp ρt V i 2
ρt σ e
1
ρ
1+β t
σe
Vi
4ψ − 1 0.5 − 8ψ3 η γ
L + 8ψ3 ηγ
(19)
3.3 Ballistic Limit Condition of GFRP Laminates.
The ballistic limit condition for a GFRP laminate with finite
thickness T, struck transversely by a rigid projectile with
conical or ogival noses can be estimated by the energy
balance method. There are three phases of penetration for
a rigid projectile with conical or ogival nose impacting on a
finite plate. First the nose enters the plate, second, the nose
is fully embedded and finally, the nose exits the plate. From
energy consideration, it is easy to show that;
Eb = πr2 Tσe 1 + β
0.5
Vi
1
2
+
L
3
+1
LN
Substituting Ek = mVb 2
2
rearranging yields.
(14)
dp= (4Ψ − 1)0.5 − 2Ψ cos φ r
(16)
In which φ is the tip angle, r is the radius of the projectile,
and the mean resistive pressure � is determined by Eq. (3)
φo and η are evaluated as follows;
2ψ − 1
2ψ
+
(20)
Vb
into the above equation and
0.5
(21)
t
ρp L + 8Ψ 3 ηr Vi2 =
− cos φ + 1 3 cos 3 φ − Ψ − 1 2 sin 2φ sin φ0
16Ψ³rςe
(15)
− sin² φ0 cos φ + π 2 sin φ0 + η
(17)
1
ρ
2 1+β t
σe
0.5
0.5
Case (i) dp < LN
Case (ii) dp > LN
ρp ρt V i 2
dp
=
L + 8ψ3 ηγ
ρt σ e
ρt
σe
πβ ρt σe D2 T
8m
Vb =
1+ 1+ 2
4m
πβ ρ D2 T
3.2.3 Ogival-Nosed Projectiles
−1
0.5
(12)
Fd dp
ρ
2
E k = dp − L N A 0 σ e 1 + β t
3
σe
φ0 = Sin
1
ρ
2 1+β t
σe
LN
Substituting (7) and (11) in (12) yields;
LN
dp = L +
3
ISSN 2277-8616
Where Vb is the critical impact velocity or ballistic limit and
m is the mass of the projectile. The residual velocity can
also be determined as;
Vr = Vi − Vb
(22)
4. BALLISTIC TEST
The Ballistic or resistance to penetration tests were
successfully done at the Nigerian Police Force (NPF)
weapon divisional shooting ground at Uwani, Enugu,
Nigeria. Six composite laminate armour sample plates of
size 300mm by 400mm and thicknesses of 8mm, 12mm,
16mm, 20mm, 24mm and 28mm were targeted using two
types of life bullets (Ogival and Conical nosed) of equal
diameter and mass. The rifle used was the Beretta Cal 9 x
19 parabellum models 951 of muzzle velocity of 355m/s
and the angle of attack was 00(normal). Figs. 3 to 8 show
the ballistic impact, perforation and penetration on the six
GFRP composite laminate samples.
0.5
Vi
4ψ − 1 0.5 − 8ψ3 η γ
L + 8ψ3 ηγ
(18)
230
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
Fig. 3: Sample E, showing complete
absorption of impact.
Fig. 5: Sample C, showing some
shattering and penetration, but no
perforation.
Fig. 7: Sample A, showing heavy shattering
but no perforation
ISSN 2277-8616
Fig 4: Sample D, showing minimal
shattering by impact.
Fig. 6: Sample B, showing sign of penetration
but no perforation.
Fig. 8: Sample F, showing failure with
complete perforation.
231
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
It was observed that five samples resisted or arrested the
assault of the projectiles while the sixth sample failed (the
bullets went through). The distance between the target and
the gun was measured to be 50meters. After the ballistic
experiment, the samples were examined. The Ultrasonic
thickness measurement/Penetration and inspection was
carried out on the six GFRP composite samples at BVL
SAMPLE
E
D
C
B
A
F
ISSN 2277-8616
Nigeria Limited Port Harcourt, Rivers State, with Calibration
Sensitivity Compression-Wave and Share-Wave Scanner.
For composite analyzer probe of procedure ASTM E258007, the calibration was set at 200mm screen, while the
sensitivity was set at 80% full screen height for 1.5mm hole
from the calibration block. Scanning and transfer loss
reduction values are as indicated in Table 1.
Table 1: Ultrasonic Thickness Measurement/Penetration Inspection Result.
PENETRATION
TYPE
OF ORIGINAL
MEASURED OR
PROJECTILE THICKNESS
THICKNESS REDUCTION
TYPE
USED
(mm)
(mm)
(mm)
TEST
OF
Conical
28
10
18
PEN. TEST
Ogival
Conical
Ogival
Conical
Ogival
Conical
Ogival
Conical
Ogival
Conical
Ogival
28
24
24
20
20
16
16
12
12
8
8
12
7
8.5
4
6
2.5
4
1
2
0
0
16
17
15.5
16
14
13.5
12
11
10
8
8
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
PEN. TEST
4.1 Ballistic Test Results
Equations (5) to (19) were compared with the experimental
data for indentation, penetration and perforation of GRP
laminate target samples by the rigid conical and ogival
nosed projectiles. The values of the parameter (β) in the
equation have been empirically determined and are taken
to be 2sinθ/2 and 3/(4Ψ) for conical-nosed and ogivalnosed projectiles respectively. Wen(2000).
(i)
(ii)
The values of ballistic limit or critical impact
velocity Vb, ballistic or critical impact energy
Eb and residual velocity VR are obtained with
equations (20),(21) and (22) and are shown in
Table 3.
The values of thickness T, from zero(0) to 7,
gave the theoretical values of Vb, Eb and VR.
4.1.1 Conical Nose Projectile
For the condition dp ≤ LN
(i)
The values of the resistive force and kinetic
energy were determined with equations (7), (9)
and (10) using the material properties of the
composite sample and projectile properties in
Tables 2 and 3.
(ii)
Resistive force, Fi = 4.285N
(iii)
Kinetic energy, EKi = 107.12Joules and the
depth of penetration, dp = 0. These values are
in good agreement with the theoretical values
of initial condition obtained from literature.
Wen( 2000).
For the condition dp ≥ LN
(i)
The values of resistive force, kinetic energy
and depth of penetration were determined with
equation (11), (13) and (14) considering
projectile and sample properties in tables of
initial condition (Table 2).
(ii)
The values of resistive force F, the absorbed
energy Ek, and depth of penetration dp are
shown in Table 3. The values of thickness T
from zero (0) to 7 gave the theoretical values
of F, Ek and dp.
For the ballistic limit condition (perforation)
232
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
ISSN 2277-8616
Table 2: Initial Conditions in Conical Projectile Analysis
D
[mm]
A
[mm2]
Ѳ
[deg]
LN
[mm]
L
[mm]
ρp
[Kg/m3]
ρt
[Kg/m3]
σe
[N/mm2]
β
σ
[N/mm2]
5.7
25.52
45
6.8
10.7
11400
1650
145.83
0.7654
133426.7
Table 2 Cont’d: Initial Conditions in Conical Projectile Analysis
m [g]
1.7
Vi [m/s]
355
x [m/s]
50
t [m/s]
0.14
a [m/s2]
2520.50
Fi [N]
4.28
Ei [J]
107.12
Table 3: Results Obtained in Conical Projectile Analysis
T [mm]
0
1
2
3
4
5
6
7
8
9
10
12
16
20
24
28
dp
[mm]
0
1
2
3
4
5
6
7
8
9
10
11
13.5
16
17
18
T/D
0
0.175439
0.350877
0.526316
0.701754
0.877193
1.052632
1.22807
1.403509
1.578947
1.754386
2.105263
2.807018
3.508772
4.210526
4.912281
Ek [J]
0
0.012225163
0.391205221
2.970714647
12.51856707
38.20363487
95.06286872
82.1558888
116.2031682
150.2504476
184.297727
218.3450064
303.4632049
388.5814034
422.6286828
456.6759622
Vb [m/s]
0
32.57527
65.14829
97.72131
130.2943
162.8674
195.4404
228.0134
260.5864
293.1594
325.7325
390.8785
521.1706
651.4627
781.7548
912.0468
600
900.00
800.00
700.00
V b [m/s]
200
Vr [m/s]
Vr
355
322.4247
289.8517
257.2787
224.7057
192.1326
159.5596
126.9866
94.41358
61.84056
29.26754
-35.8785
-166.171
-296.463
-426.755
-557.047
1000.00
Theoretical
Plot
Experimental
Plot
400
0
-200 0
Eb [J]
0
4.033387
8.690893
13.97252
19.87826
26.40812
33.5621
41.3402
49.74242
58.76875
68.41921
89.59248
139.4284
199.2503
269.058
348.8517
10
20
30
600.00
500.00
Experimental plot
400.00
Theoretical plot
300.00
Predicted plot
200.00
-400
100.00
-600
-800
0.00
0
T [mm]
5
10
15
20
25
30
T [mm]
Fig. 9: Effect of Thickness on Residual Velocity
Fig. 10: Effect of Thickness on Ballistic Limit
233
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
ISSN 2277-8616
500.00
y = -0.462x2 + 32.68x - 93.64
R² = 0.996
450.00
400.00
350.00
Ek [J]
300.00
250.00
Experimental plot
200.00
Theoretical plot
150.00
Predicted plot
100.00
50.00
0.00
0
5
10
15
20
25
30
T [mm]
Fig. 11: Effect of Depth of Penetration on Ballistic Limit
Fig. 12: Effect of Thickness on Absorbed Energy
600
400
Theoretical Plot
y = -x + 355
R² = 1
Experimental Plot
Vr [m/s]
200
0
-200 0
200
400
600
800
1000
-400
-600
Vb [m/s]
-800
Fig. 13: Effect of Ballistic Limit on Ballistic Energy
Fig. 14: Effect of Ballistic Limit on Residual Velocity
4.1.2 Ogival-Nosed Projectile
Similarly,
For conditions dp ≤ LN
(i)
The values of resistive force, kinetic energy and depth of penetration were determined with equations (7), (9) and
(16) using the material and projectile properties in Tables 4 and 5. The resistive force Fi = 4.165N and EKi =
107.165Joules and dp = 0.
The condition dp ≥ LN
(i)
The values of resistive force, F absorbed energy EK and depth of penetration dp using equations (11), (13) and (19)
with material and projectile properties in the Table 4, are shown in Table 5.
For Ballistic limit condition
(a) The ballistic or critical velocity Vb, critical energy Eb and residual velocity VR are obtained with equations (20), (21) and
(22) and are shown in Table 5. For values of the thickness from zero (0) to 7, Vb, Eb and Vr values obtained were the
theoretical values.
Table 4 : Initial Conditions in Ogival Projectile Analysis
Do
[mm]
A
[mm2]
LN [mm]
L
[mm]
m
[g]
Vi
[m/s]
x
[m/s]
t [s]
a [m/s2]
Fi
[N]
Ei [J]
5.7
0.00
6.9
10.7
1.7
355
50
0.141
2520.50
4.28
107.12
Ѳ
[deg]
S
45
5.588
Table 4 cont’d : Initial Conditions in Ogival Projectile Analysis
Φ
φo
ρp
ρt
σe
Ψ
Η
β
[deg]
[deg]
[Kg/m3]
[Kg/m3]
[N/mm2]
σ
[N/mm2]
0.9851
133368.4
29.34
37.68
22.70
11400
1650
145.833
0.7650
234
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
ISSN 2277-8616
Table 5: Results obtained in Ogival Projectile Analysis
dp
[mm]
0
T
[mm]
0
T/D
F
Ek [J]
Vb [m/s]
Eb [J]
Vr
0
0
0
0
0
355
1
1
0.175439
0.071887
0.901187
32.56103
4.033114
322.439
2
2
0.350877
0.287549
3.604501
65.1198
8.689801
289.8802
3
3
0.526316
0.646985
8.10994
97.67858
13.97006
257.3214
4
4
0.701754
1.150195
14.4175
130.2374
19.87389
224.7626
5
5
0.877193
1.79718
22.5272
162.7961
26.4013
192.2039
6
6
1.052632
2.587939
32.44901
195.3549
33.55228
159.6451
7
7
1.22807
3.403241
49.7436
227.9137
41.32683
127.0863
8
8
1.403509
3.403241
68.4203
260.4725
49.72496
94.52752
10
12
2.105263
3.403241
89.59133
390.7076
89.55319
-35.7076
12
16
2.807018
3.403241
139.4320
520.9427
139.3586
-165.943
14
20
3.508772
3.403241
199.2544
651.1778
199.1412
-296.178
15.5
24
4.210526
3.403241
269.0629
781.4129
268.9009
-426.413
16
28
4.912281
3.403241
348.8513
911.6481
348.6378
-556.648
1000
Theoretical Plot
Experimental Plot
Predicted Plot
Vr (m/s)
200
500
0
-200
0
10
20
y = 3E-14x2 + 32.55x + 0.002
R² = 1
Vb (m/s)
400
30
Theoretical Plot
Experimental Plot
Predicted Plot
0
-400
0
-600
10
20
30
T (mm)
T (mm)
Fig. 15: Effect of Thickness on Residual Velocity
Fig. 16: Effect of Thickness on Ballistic Limit
1000
y = 0.762x3 - 22.53x2 + 274.3x - 862.6
R² = 0.992
400
500
y = 0.000x2 + 0.114x - 0.000
R² = 1
Theoretical Plot
Experimental Plot
Predicted Plot
Theoretical Plot
Experimenta Plot
Predicted Plot
0
0
5
10
15
20
Eb (J)
Vb(m/s)
200
0
0
400
600
800
1000
Vb(m/s)
dp(mm)
Fig. 17: Effect of Depth of Penetration on Ballistic Limit
200
Fig. 18: Effect of Ballistic Limit on Ballistic Energy
235
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
400
400
y = -1.044x + 365
R² = 0.999
Theoretical Plot
Experimental Plot
Vr [m/s]
200
200
0
-200 0
y = -0.004x3 + 0.617x2 - 2.976x + 47.29
R² = 0.998
Theoretical Plot
Experimental Plot
Predicted Plot
Ek (J)
600
ISSN 2277-8616
200
400
600
800
1000
-400
0
-600
-800
0
10
20
30
T (mm)
Vb [m/s]
Fig. 20: Effect of Thickness on Absorbed Energy
Fig. 19: Effect of Ballistic Limit on Residual Velocity
Experimental and analytical investigation have been
performed concerning the static and ballistic resistance of
woven roving GFRP laminate plates of thicknesses 8mm up
to 28mm penetrated and perforated by ogival and conical
projectiles. From the plots of the theoretical, experimental,
and predictive data (Figs. 9 to 20), it is deduced that; (i)
Ballistic impact is characterized by three phases namely;
indentation, penetration and perforation. (ii) Ballistic limit is
linearly related to the thickness of the GFRP laminate
composite investigated. (iii) The ballistic limit or critical
velocity increases linearly over the range of thickness of the
plate investigated in correspondence with predicted values
which are uniformly satisfactory. (iv)The residual velocity
decreases with the increase in ballistic limit or critical
velocity. (v) The ballistic limit and the peak resistive force of
the plate were closely equal for conical and ogival nosed
projectile.
[4] Wood, R. (1980). Car Body in Glass Reinforced
Plastic. Pentech Press Limited, London, pp 43 - 45.
[5] Wilkins, M.L. (1964). ―Calculation of Elastic-Plastic
Flow‖ Methods in Computational Physics, Vol. 3,
eds., Alder, B., Furbish, S., and Rotenberg, M.,
Academic Press, New York , pp. 211 – 263.
[6] Berholf, L.D., and Benzley, S.E. (1968). ―TOODY II, A
Computer Program for Two-Dimensional Wave
Propagation,‖ SC-RR-68-41, Sandia Laboratories,
Alburquerque, New Mexico, November .
[7] Hageman, L.J., and Walsh, J.M. (1971). ―HELP, A
Multi-Material Eulerian Program for Compressible
Fluid & Elastic-Plastic Flows in Two Space
Dimensions and Time,‖ Vol. 1, BRL CR 39, Systems,
Science, and Software, LA Jolla, Calif.
5. Conclusion
This work shows that one of the governing factors in the
damage resistance is the nose shape of the impacting
projectile. Here the performance of the laminates could be
properly tailored by controlling the strength parameters for
the design against failure. It has also shown that great
strides can be achieved in the production and testing (static
and ballistic) of the armour protecting hand lay-up GFRP
composite laminate plates. Finally for a range of thickness
of the armour protecting body, the ballistic limit, residual
velocities and depth of penetration were predicted for this
novel GFRP composite laminates produced.
[8] Wilkins, M.L., French, M.L., French, S.J., & Sorem,
M. (1970). ―Finite-Difference Scheme for Calculating
Problems in Three Space Dimensions & Time,‖
Proceedings of International Conference on
Numerical Methods in Fluid Dimensions – II,
Berkeley, California, pp. 30 – 33.
REFERENCES
[10] Abrate, S. (1994). Impact on Laminated Composites:
Recent Advances. Applied Mech. Rev., 4711 pp.
517-544.
[1] Cantwell, W.J. & Morton, J. (1989). Comparison of
Low Velocity & High Velocity Impact Response of
CERP Composites, 20, 545–51.
[2] Prewo, K.M. (1980). The Importance of Fibres in
Achieving Impact Tolerant Composites. Phil. Trans.
R. Soc. London, A 294, 551 – 58.
[3] Babaniyi, B. (2000). Self-reinforcing Polymeric
Composite Materials in Ballistic Protection. Technical
Conference of the Polymer Institute of Nigeria.
November 22 and 25.
[9] Johnson, G.R. (1976). ―Analysis of Elastic-Plastic
Impact Involving Severe Distortions‖, Journal Of
Applied Mechanics, Vol. 43, No. 3, TRANS. ASME,
Vol. 98, Series E, Sept. pp. 439 – 444.
[11] Cantwell, W.J. & Morton, J. (1991). The Impact
Resistance of Composite Materials: A Review
Composites, 22, 347 – 362.
[12] Navarro, C. (1998). Simplified Modelling of the
Ballistic Behaviour of Fabrics and Fibre-Reinforced
Polymeric Matrix Composites. Key Eng. Mat., Vol.
141-143. 383- 403.
236
IJSTR©2014
www.ijstr.org
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 8, AUGUST 2014
[13] Zhu, G., Goldsmith, W., and Dharan, C.K.H. (1992).
Penetration of Laminated Kevlar by Projectiles – II
Analytical Model Int. J. Solids Structure, Vol. 29,
421-436.
[14] Zhu, G., Goldsmith, W., and Dharan, C.K.H. (1991).
Penetration of Laminated Kevlar by Projectiles – I
Experimental Investigation. Int. J. Solids Structure,
Vol. 29, pp 399-420.
[15] Vinoson J.R. and Walker J.M. (1995) Ballistic Impact
into Composite Material Structures. American Society
of Aero and Astrophysics. Paper no AIAA-95-1388CP.
[16] Sun,C.T. and Potti,S.V. (1995) A Simple Model to
Predict Residual Velocities of Thick Composite
Laminate Subjected to High Velocity Impact.
International Journal of Impact Engineering. Vol. 16,
No 6, Pp 1-15.
[17] Kumar, K. Siva and Bhat, T. Blakrishna. (1998)
Response of Composite Laminates on Impact of High
Velocity. Key Engineering Materials. Vol. 141-143, Pp
337-348.
ISSN 2277-8616
[25] Gupta, B.P. and Davids, N. (1966) ―Penetration
Experiments
with
Fibre-reinforced
Plastics.’’
Experimental Mechanics. Pp 445-450.
[26] Abdullah, M.R; Cantwell, W.J. (2006) The impact
resistance of fibre-metal laminates based on glass
fibre reinforced polypropylene. Polymer Composites.
Vol. 27, no. 6, Pp 700 – 708.
[27] Cantwell, W.J., and Morton, J. (1990). Impact
Perforation of Carbon Fibre-Reinforced Plastic.
Comp. Sci. Tech., 38, 119-41.
[28] Edelugo, S. O. (2000). Damage Evaluation &
Reinforcements, Combination in the Development
of GRP Automobile body Work. Ph.D. Thesis,
University of Nigeria, Nsukka. pp 1-300.
[29] Ben-Dor, G., Dubinsky, A. and Elperin, T., (2002)
―Optimization of the nose shape of an impactor
against a semi-infinite FRP laminates‖, Composites
Science and Technology, Vol. 62, No. 5, Pp. 663 –
667.
[18] Lee, S.W.R. & Sun, C.T. (1993) Dynamic Penetration
of Graphite Epoxy Laminates Impacted by a BluntEnded Projectile. Comp. Sci. Tech., Vol. 49, 369-80.
[19] Wen, H.M; Reddy, T.Y., Reid, S.R and Soden, P.D.
(1998). Indentation, Penetration, & Perforation of
Composite Laminates & Sandwich Panels under
quasi-static & projectile loading. Key Engineering
Material, 141-143, 501-52.
[20] Wen, H.M. (2000). Predicting the Penetration &
Perforation of FRP Laminates Struct Normally by
Projectiles with Different Nose Shapes. Composite
Structures, Vol. 49, pp 321 –329.
[21] Reddy, T.Y., Wen, H.M., Reid,S.R. and Soden
P.D.(1998) Penetration and Perforation of Composite
Sandwich Panels by Hemispherical and Conical
Projectiles. Trans. ASME. Journal Press Ves. Tech
Vol. 120, Pp 186-194.
[22] Reid,S.R., Wen, H.M., Seden P.D. and Reddy T.Y.
(1999) Response of Single Skin Laminates and
Sandwich Panels to Projectile Impact. In: Wang S.S.,
Willians J.J. and Lo, K.H. Editors. Composite
Materials for Offshore Operation-2. Amer Bur Shipp,
Pp 593-617.
[23] Wen, H.M. (2001) Penetration and Perforation of
Thick FRP Laminate. Composites Science and
Technology, Elsevier, Vol. 61, Pp. 1163 – 1172.
[24] He, T., Wen, H.M., and Qin, Y, (2007) Penetration
and Perforation of FRP Laminates Structure
Transversely
by
Conical-nosed
Projectiles.
Composite Structures, Elsevier, Vol. 81, Pp. 243-252.
237
IJSTR©2014
www.ijstr.org