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Ballistic resistance capacity of carbon nanotubes

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  • Southern University of Science and Technology (SUSTech)

Abstract and Figures

Carbon nanotubes have high strength, light weight and excellent energy absorption capacity and therefore have great potential applications in making antiballistic materials. By examining the ballistic impact and bouncing-back processes on carbon nanotubes, this investigation shows that nanotubes with large radii withstand higher bullet speeds and the ballistic resistance is the highest when the bullet hits the centre of the CNT; the ballistic resistance of CNTs will remain the same on subsequent bullet strikes if the impact is after a small time interval.
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IOP PUBLISHING NANOTECHNOLOGY
Nanotechnology 18 (2007) 475701 (4pp) doi:10.1088/0957-4484/18/47/475701
Ballistic resistance capacity of carbon
nanotubes
Kausala Mylvaganam and L C Zhang
1
Centre for Advanced Materials Technology, University of Sydney, Sydney, NSW 2006,
Australia
E-mail: k.mylvaganam@usyd.edu.au and l.zhang@usyd.edu.au
Received 15 June 2007, in final form 28 August 2007
Published 17 October 2007
Online at stacks.iop.org/Nano/18/475701
Abstract
Carbon nanotubes have high strength, light weight and excellent energy
absorption capacity and therefore have great potential applications in making
antiballistic materials. By examining the ballistic impact and bouncing-back
processes on carbon nanotubes, this investigation shows that nanotubes with
large radii withstand higher bullet speeds and the ballistic resistance is the
highest when the bullet hits the centre of the CNT; the ballistic resistance of
CNTs will remain the same on subsequent bullet strikes if the impact is after
a small time interval.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Diverse applications of carbon nanotubes (CNTs) have been
envisioned due to their remarkable chemical, mechanical, elec-
tronic and magnetic properties [1]. They are being considered
to make useful articles such as artificial muscles, reinforced
materials, bulletproof vests, explosion-proof blankets, etc. In
the past, various types of materials such as wooden and metal
shields were used as body armour to protect humans from in-
jury in combat. With the invention of firearms, they became
ineffective. New ballistic-resistant body armour has been de-
veloped using, for instance, multiple layers of Kevlar, Twaron
and Dyneema fibres [2]. When a bullet strikes body armour,
the fibres of these materials absorb and disperse the impact en-
ergy to successive layers to prevent the bullet from penetrating.
However, the dissipating forces can still cause non-penetrating
injuries which is known as blunt force trauma. Even when the
bullet is stopped by the fabric, the impact and the resulting
trauma would leave a severe bruise and, at worst, damage crit-
ical organs. Hence the best material for body armour should
have a high level of elastic storage energy that will cause the
bullet to bounce off or be deflected.
The energy absorption capacity of different radii CNTs
under ballistic impact has been reported in two extreme cases
in which the bullet moved with constant speed [3]. For a
nanotube with one end fixed, the maximum load bearing bullet
speed of the nanotube increases and the energy absorption
1
Author to whom any correspondence should be addressed.
efficiency decreases with the increase in relative heights at
which the bullet strikes; these values have been found to be
independent of the nanotube radii when the bullet hits at a
particular relative height. For a nanotube with both ends fixed,
the energy absorption efficiency reaches the minimum when
the bullet hits around a relative height of 0.5. The challenge in
exploring the ballistic resistance capacity of carbon nanotubes
lies in the understanding of the bullet impact mechanism
involving how the force, energy, momentum and velocity vary
in the time domain at ballistic striking. The present research
aims to resolve this problem.
2. Computational methodology
Single-walled carbon nanotubes (27, 0), (22, 0) and (18, 0) of
radii 10.576
˚
A, 8.608
˚
A and 7.051
˚
A having a length,
L,of
about 75
˚
Awere used in this investigation. The nanotubes were
fixed at both ends to represent roughly its condition within a
composite. A piece of diamond
(35.6×35.6×7.1
˚
A
3
) was used
as a bullet, with its tip width being several orders of magnitude
larger than that of a flattened nanotube. This, in a sense,
mimics the real situation since the width of a real bullet is
always larger than that of the biggest nanotube after flattening.
The bullet was released from a position about 15
˚
A from
the centre axis of the nanotube at different heights,
h, with
a speed varying between 1000 and 3500 m s
1
,asshownin
figure 1. The initial bullet speeds for which the nanotubes
could bear without any bond breakage or detachment were
0957-4484/07/475701+04$30.00 1 © 2007 IOP Publishing Ltd Printed in the UK
Nanotechnology 18 (2007) 475701 K Mylvaganam and L C Zhang
Figure 1. The molecular dynamics model of a carbon nanotube
subjected to ballistic impact. (a) Initial model, (b) a deformed (18, 0)
nanotube at its maximum energy absorption.
estimated from the maximum absorption energy of the CNT
that was determined in a separate simulation by shooting the
bullet with an arbitrarily selected constant speed of 400 m s
1
.
A range of values, around this estimated speed, were used
as the initial speeds of the bullet and, since its release, the
speed was recalculated after every time step of 0.5 fs using
the principle of energy conservation, i.e. after every time step,
the kinetic energy of the bullet was calculated by subtracting
the energy absorbed by the nanotube in the previous time step,
assuming there was no other energy loss. Hence, to avoid
the heat dissipation, only two rows of atoms that are next to
the fixed rows of atoms at each ends were taken as thermostat
atoms. As the impact deformation takes place in a very short
duration, the heat dissipation via the thermostat atoms at the
ends of the CNT would be minimal. The ballistic performance
of a nanotube was examined using the classical molecular
dynamics analysis for bullets released at various positions with
speeds that would only elastically deform the nanotubes.
In this work the atomic interactions within the nan-
otube were described by a three-body Tersoff–Brenner poten-
tial [4, 5] that has been used to simulate various deforma-
tion processes [6–10] of carbon nanotubes. The non-bonded
interaction between the bullet and nanotube were described
by a two-body Morse potential,
V (r
ij
) = D[e
2α(r
ij
r
0
)
2e
α(r
ij
r
0
)
], which has been successfully used for a large
number of machining and indentation processes involving
substrate–tool interactions [11–13]. The parameters used in the
Morse potential are:
α = 5.110
˚
A
1
, D = 139.71 kcal mol
1
and r
0
= 2.522
˚
A.
3. Results and discussion
3.1. Understanding the dynamic properties
A bullet moving with a constant speed towards a nanotube
that is fixed at both its ends will deform the nanotube which
absorbs the energy of the bullet. Eventually, the nanotube will
be broken regardless of the magnitude of the bullet speed. Thus
the energy difference of the CNT before its interaction with the
bullet and just before the onset of fracture gives the maximum
absorption energy of the CNT. In reality, from the moment of
impact, the speed of a bullet would begin to decrease as it hits
Figure 2. Variation of relative absorption energy with the relative
positions
) of the nanotubes at which the bullet strikes.
any object and eventually either the bullet would bounce back
as the speed became zero or the bullet would penetrate the
object if the initial speed is high enough. Thus the initial bullet
speed for a bouncing-back process is estimated by equating
the maximum absorption energy of the nanotube as calculated
above to the kinetic energy of the bullet, i.e.
E
abs
= E
f
E
i
=
1
2
mV
2
ini
, (1)
where
E
f
is the energy of the nanotube just before breakage
and
E
i
is that before the CNT–bullet interaction, m is the
mass of the bullet and
V
ini
is the initial bullet velocity. In
our simulation, the decrease of the bullet speed at every time
step is determined by the law of energy conservation, i.e. by
equating the energy absorbed by the nanotube to the decrease
in kinetic energy of the bullet. The bullet is then bounced back
as the nanotube releases its energy elastically stored and
V
bb
is
determined when the bullet bounces off the CNT and attains a
constant value.
It was found that the highest bullet speed which a nanotube
can bear is a function of the nanotube radius,
R, and the relative
impinging location of a bullet on the nanotube defined by
ρ
h/L
,whereL is the length of the nanotube and h is the distance
between the bullet impinging point and an end of the nanotube
asshowninfigure1(a). A bigger tube, as it can absorb more
energy, withstands a greater bullet speed,
V
ini
and the energy
absorbed increases as
ρ increases and reaches its maximum
at
ρ = 0.5. However, as shown in figure 2, the variation of
relative absorption energy with
ρ (i.e. the maximum energy
absorbed normalized by the total energy of the nanotube before
impact) or the variation of energy absorbed per unit area with
ρ
is very similar when R changes, showing that these quantities
are not really dependent on the nanotube radius. On the other
hand, the maximum absorption energy varies almost linearly
with nanotube length, as shown in figure 3.
Figure 4 shows the variation of the bullet speed with time
t
during its impacting–bouncing process when the bullet struck
at different positions on a (18, 0) nanotube. This shows that
the bullet started to bounce back almost at the same time
irrespective of its initial speed and the position of striking.
However, the deceleration and the acceleration of the bullet are
different. This is because the nanotube deformation depends
on
ρ. The variation of bullet speed (curve 1), bullet–nanotube
2
Nanotechnology 18 (2007) 475701 K Mylvaganam and L C Zhang
Figure 3. Variation of the maximum energy absorbed with nanotube
length.
Figure 4. Variation of the bullet speed with time during its impact
and bouncing-back processes. Note also the variation with the bullet
impact location,
ρ. The nanotube used for this analysis is an (18, 0)
nanotube.
distance (curve 2) and the bullet travelling distance (curve 3)
with time are shown in figure 5 when the bullet impacts at the
centre of a (18, 0) CNT. Part PQ of curve 1 represents the speed
variation during the impact and part QR of the curve stands for
that during the bouncing back. We can see that the bullet attains
a constant bouncing-back speed
V
bb
when t = 7850 fs, which
is lower compared to the initial impact speed of the bullet
V
ini
,
indicating that a certain amount of energy is retained by the
nanotube when the bullet bounces off. The impact process is
represented by AB in curve 3. When the bullet speed becomes
zero at point B, it starts to bounce back. Thus BCD represents
the bouncing-back process. At C (
t = 7300 fs) the bullet has
returned to its initial impact position, but curve 2 shows clearly
that it is still in contact with the nanotube. The bullet departs
from the nanotube at a much later time,
t = 7850 fs, due to
the reverse elastic deformation of the nanotube in releasing its
stored energy.
If a subsequent impact takes place immediately after the
first bullet’s bouncing off, the nanotube cannot withstand the
same speed although its microstructure was not damaged under
the first impact. For instance, for an (18, 0) nanotube, the
maximum load bearing speed and the maximum absorption
energy on the second impact are 2200 m s
1
and 572.8 eV,
Figure 5. Variation of different properties of a bullet with time
during its impact and bouncing-back processes when impacting the
middle of a (18, 0) nanotube.
Figure 6. A schematic showing a layer of woven carbon nanotube
yarn material.
compared to 2560 m s
1
and 775.6 eV, respectively, for the
first impact. This is because immediately after the first impact,
the nanotube has not completely released the elastic energy
retained from the first impact which reduces its capacity for
absorbing further energy. On the third impact these values
become 2050 m s
1
and 497.3 eV, respectively. However, the
above changes do not influence the bouncing-back speed of the
bullet.
If a subsequent ballistic impact occurs not immediately
after the first, e.g. only after 12.5 ps, the nanotube’s
performance remains the same, because this short duration is
long enough to allow full release of the elastic energy stored
in the nanotube. This means that nanotubes have an excellent
resistance to repeated ballistic impacts, which is essential for
body armour and explosion-proof blankets.
3.2. A case study
Based on the properties of CNTs obtained above, we can carry
out a case study as a potential application example. We may
very roughly estimate the thickness of a possible CNT body
armour material composed of several layers of woven carbon
nanotube yarns illustrated schematically in figure 6, if we can
assume that the above nanoscale property can be extended
simply to a macroscale case. One may argue that, as in the
mechanical property characterization of metals, a nanoscale
property cannot be extended to the macroscopic scale directly
because of the scale-effect. This is true because a metal is a
single crystal on the nanoscale, but possesses a polycrystalline
3
Nanotechnology 18 (2007) 475701 K Mylvaganam and L C Zhang
structure on the macroscale which contains numerous grain
boundaries and makes the metal significantly weaker compared
with its single-crystalline state. However, the situation with a
CNT is rather different. When a CNT is grown, its diameter
is in nanometres but its atomic structure along its length, in
micrometres, does not change. In other words, it is completely
different to the metal case of the microstructural change
from monocrystalline to polycrystalline. Hence, as a first
approximation, it is reasonable to make the above assumption
because the length change of CNTs does not involve atomic
structure change.
Baughman [14] has demonstrated that carbon nanotube
fibres can be easily woven into textiles. Carbon nanotube
yarns of various diameters
(3.2–100 μm) have been made by
spinning [15–17] and the carbon nanotubes in a yarn will have
much better mechanical strength than loose individuals [18].
Let us take yarns of diameter 100
μm and, for simplicity,
assume that a yarn is only a bundle of loose carbon nanotubes.
Such a yarn can have about 5
× 10
9
(18, 0) nanotubes of
14.1
˚
A in diameter. Supposing this yarn is used to make
potential armour material, the thickness of the material that
may protect the wearer from a revolver bullet can be estimated
as follows. According to John Schaefer [19], a popular police
revolver bullet of 0.358 inches (9.1 mm) in diameter would
damage an area of 0
.101 inch
2
(0.652 cm
2
). Hence, to cover
this area, about 180 nanotube yarns of about 0.9 cm in length
will be needed to form a woven fabric. Since the maximum
absorption energy is approximately a linear function of the
nanotube length, as discussed before, a single nanotube yarn of
the above dimension will absorb 0.344 J. Thus the nanotubes
in the impact area will absorb 62 J/layer. To prevent damage to
the wearer, the body armour in the impact area should be able
to elastically absorb all the muzzle energy of the bullet [20],
320 J. This means that six layers of woven nanotube yarn
material are sufficient. If the thickness of a layer equals the
diameter of a yarn, the thickness of the body armour material
to absorb all the muzzle energy of the bullet will be 600
μm.
4. Conclusion
This study shows that the ballistic resistance capacity of a
carbon nanotube is highest when the bullet hits its centre and a
larger tube withstands a higher bullet speed. On a subsequent
impact after a small time interval, a nanotube could withstand
almost the same speed as in the first impact, indicating that
carbon nanotube body armour can have a constant ballistic
resistance even when bullets strike at the same spot. This study
estimates, though based on a very strong assumption, that body
armour of 600
μm in thickness made from six layers of 100 μm
carbon nanotube yarns could bounce off a bullet with a muzzle
energy of 320 J.
Acknowledgments
The authors thank the Australian Research Council for its
continuous financial support. This work was also supported
by the Australian Partnership for Advanced Computing.
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4
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Војска Србије је једна од институција друштвеног система Републике Србије која поседује и наменски користи експлозивна средства . Рад је заснован на сагледавању утицаја експлозива, превасходно на живот и здравље људи који са средствима рукују, али и утицаја на целокупну животну средину. У раду је дата кратка историјска ретроспектива развоја употребе експлозива. Рад је настао на основу комбинације искустава аутора у раду са ескплозивима, као и на основу елементарних теоретских одредби везаних за експлозиве. Кроз рад је приказано колико и на какав начин нестручна употреба само једног типа средстава које тренутно Војска користи, може да има негативних последица по човека, али и на животну средину. У раду су дате превентивне мере, које су се преко система научених лекција (који већ неко време егзистира у Војсци Србије) показале као веома поуздане у погледу смањења ризика од настанка било које врсте повреда и/или професионалног обољења при раду са експлозивима. Овде треба узети у обзир чињеницу да кроз рад нису обухваћени сви штетни ефекти рада са експлозивима, већ се рад бави искључиво негативним утицајима на људе који су непосредни руковаоци при раду са овом врстом средстава.
Chapter
In the greater part of nanotubes materials, a combination of structure, topology, and dimension makes a large group of physical properties such as mechanical, magnetic, thermal, and electrochemical that is resembled by barely any known materials. A short rundown will be given of the astonishing structural and electronic properties of carbon nanotubes (CNTs), which are nanoscopic configurational of subatomic measurements as cylinders with approximately 20 carbon molecules around the edge of the cylinders and microns long. Carbon nanotubes can demonstrate remarkable electrical and thermal conductivity, exceptional tensile strength, chemical inertness, also low density, low dimensionality, and briefly, all these and other properties make it outstanding material for many potential applications especially technology industries, for example, in electronics, optics, medicine, gene and drug delivery, composite materials, nanotechnology, and other application of material science. In addition, parameters of CNTs like structure, surface area, charge distribution, surface chemistry, and agglomeration state have a significant effect on these materials. Besides this, other remarkable and unique properties, as observed in their vibrational spectra and in their strength and stiffness. Since the discovery of carbon nanotubes, have motivated researches and are already finding practical applications in various fields based on their unique properties. Herein, we will talk about morphology, topology, different production methods, chemical modification and characterization, and some potential applications of nanotubes in recent future.
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