Analytical and numerical simulations of ballistic impact on composite lightweight armours

12 Pages·2014·2.07 MB·English

by  Sunrise Settings

Projectile Impacts: modelling techniques and target performance assessment 191
Analytical and numerical simulations
of ballistic impact on composite
lightweight armours
V. Sánchez-Gálvez & L. Sanchez Paradela
Universidad Politécnica de Madrid, UPM, Spain
Abstract
This paper summarizes the utilization of analytical and numerical computation as
valuable tools for lightweight armour design optimisation. Several analytical
models for ballistic impact simulation onto composites and ceramic faced targets
have been developed at our department. This paper shows a few examples of the
utilization of those models as well as numerical computations using commercial
hydrocodes.
Keywords: ballistic impact, lightweight armours, analytical simulation,
numerical simulation.
1 Introduction
The deployment of peacekeeping forces in conflict areas (Afghanistan, Iraq) has
dramatically increased the danger of casualties caused by terrorist attacks [1].
The use of Improvised Explosive Devices (IEDs) by insurgents has produced a
very high number of injuries among the soldiers in the area. Protection systems
of both vehicles and personnel designed to defeat less effective threats such as
low calibre ammunition appear often ineffective against the more efficient
threats used by terrorists, such as shrapnel or debris produced by heavy weight
explosive loads.
The utilization of advanced materials such as ceramics or composites appears
as a promising solution to improve protection capability of armours keeping their
weight under acceptable levels.
Advanced ceramics (such as alumina, silicon carbide, silicon nitride) and
composites (Aramid, polyethylene fibres) have been used to manufacture
lightweight bulletproof vests and helmets since several decades ago.
WIT Transactions on State of the Art in Science and Eng ineering, Vol 75,©2014 WIT Press
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192 Projectile Impacts: modelling techniques and target performance assessment
Also, advanced materials begin to be included in the armour structure of
lightweight military vehicles, either to retrofit traditional armours or to produce
liners aimed to protect occupants. Several Infantry Fighting Vehicles (IFV) are
now including advanced ceramics as a mean to improve their protection
capability.
Although ballistic impact behaviour of ceramics and composites has been
widely studied, published information is scarce, probably due to classification
reasons. Hence, designing lightweight armours using advanced materials either
as a main armour or to improve protection of an existing armour usually requires
launching a research programme aiming to find out the behaviour of the optimal
combination of materials among a very high number of possible solutions.
The exclusive use of experimental procedures (firing tests) to achieve an
optimal design of composite armour to defeat a definite threat is expensive, due
to the high number of parameters (materials, thicknesses) involved. The
utilization of analytical or numerical simulation of penetration phenomena
appears advantageous as these valuable tools reduce the experimental effort.
The numerical simulation of ballistic impact is carried out using finite
element method (FEM) or finite difference method (FDM) codes (hydrocodes) to
discretize both target and penetrator and solve the equations governing the
penetration process. Several commercial hydrocodes, for instance LS-DYNA
and AUTODYN, are available.
The numerical simulation of phenomena involving ballistic impact into
composite armours provides a great amount of information (such as stress, strain,
velocity histories, damage extension, erosion, crater dimensions). However, a
numerical simulation is a difficult task especially when advanced materials are
involved, due to the lack of reliable models of materials behaviour, particularly
in the context of fracture criteria and post-failure behaviour [2].
On the other hand, an analytical simulation is based on the integration of laws
of mechanics of continuous media, to which several simplifying hypotheses are
introduced leading to equations governing the penetration process. Although
analytical models are less accurate in predicting actual ballistic behaviour than
numerical simulations, they permit the investigation of a large number of
parameters, due to their simplicity, leading to a high reduction of time and cost
of armour designing.
This paper presents a methodology for lightweight armour design
optimisation based on a combination of all three approaches mentioned.
2 Lightweight armour design
The methodology proposed for lightweight armour design when advanced
materials (ceramics, composites) are used is a combination of the three
approaches mentioned, empirical, analytical and numerical and it is sketched in
figure 1.
After defining the threat (specifying, among others, geometry, material,
striking velocity, impact obliquity) and the requirements of the protection
(maximum weight, thickness, cost), analytical models may be used for rough
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Projectile Impacts: modelling techniques and target performance assessment 193
computations to make a clear distinction among the preliminary solutions.
Subsequent to that, numerical simulation is a valuable tool to tune the solution
and to validate the analytical model. Finally, firing tests are always required to
check the performance of the solution.

Figure 1: Flow chart of the proposed methodology of armour design.
3 Analytical simulation
As previously mentioned, an analytical simulation is based on the development
of expressions, derived from the equations of continuum mechanics and able to
describe the penetration process and to yield valid data concerning, among
others, perforation, crater dimensions, residual velocity and mass of projectile
after perforation. Often, equations governing the process are quite involved
requiring the use of the computer to solve for the unknowns [3] but computations
may be carried out in a few seconds, thus a very high number of parameters can
be analysed very rapidly.
The degree of accuracy achieved by analytical models depends on the
simplifying hypotheses adopted. Ballistic impact is a very complex phenomenon,
thus its analytical modelling requires the making of several assumptions,
neglecting some effects considered less important as compared to those
considered as the controlling ones.
In recent years, several analytical models for high-speed impact onto
composite targets have been developed at the authors’ department. In the
following, the main features of such models are summarized as well as some
relevant results achieved are presented.
3.1 Modelling ballistic impact onto composites
Composite materials are currently being used to produce body armours and
helmets to provide protection to personnel (soldiers and police officers) against
impact from fragments and low calibre ammunition, as well as to produce liners
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194 Projectile Impacts: modelling techniques and target performance assessment
that improve protection to occupants of military vehicles when subjected to blast
or projectile impact [4].
Body armours and liners are soft materials in the form of cross-stitched
multilayer fabrics; helmets are produced by pressed lamination multilayer fabrics
into a polymeric matrix to achieve a rigid composite material that reduces trauma
to the head.
Analytical modelling of high-speed impact onto composites is a very difficult
task. The target is inhomogeneous and anisotropic and usually manufactured by
lamination of several layers. Hence, the mechanical behaviour of the laminate is
not easily derived from data obtained by testing fibres or even fabrics. Hence, a
set of hypotheses should be adopted to make the analysis of the phenomenon
tractable.
Based on the ideas firstly introduced by Roylance [5] and Smith, [6] several
analytical models aiming to simulate high-speed penetration into composite
targets have been developed at the authors’ department.
The basic hypotheses are the following (see fig. 2).

Figure 2: Sketch of yarns impacted transversely.
– When the target is impacted, an elastic longitudinal wave propagates along
the yarns, spreading the impacted surface.
– The matrix is immediately fractured, and thus it is assumed that only the
fibres are responsible for decelerating the penetrator. Nevertheless, the
matrix mass is taken into account in computing the reduction of linear
momentum of the penetrator as well as in calculating the stress wave speed.
– The process continues until either the projectile comes to rest or fibre
breakage (full perforation of the target) occurs.
The differences among those models are found in the additional hypotheses
adopted. Parga’s model [7] assumes that friction between yarns at cross-overs is
the parameter controlling the stress decay along the yarns. It is able to predict the
ballistic limit V (striking velocity for 50% probability of full perforation) but it
50
requires adjusting arbitrarily the friction coefficient to match experimental data.
Chocron’s model [8] uses an energy balance equation to to derive an expression
for the residual velocity of the projectile after perforation. Fig. 3 shows a good
agreement between analytical results and experimental data obtained by Cunniff
[9] firing FSP (fragment simulating projectiles) onto Kevlar 29 fabric. However,
Chocron’s model assumes that fibre failure takes place when a parameter R
reaches a critical value that is also chosen to match experimental data. Finally,
the newest Sanchez Paradela’s model [10] does not require utilisation of any
parametric quantity to derive equations that predict residual velocity, ballistic
limit as well as target shape and energy absorption and, at the same time, is in
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Projectile Impacts: modelling techniques and target performance assessment 195
good agreement with experimental results. See for instance fig. 4 that illustrates
ballistic limit V vs. areal density for the impact of a 16 grain (1.1 g) FSP onto
50
UD 66 Dyneema target (High performance polyethylene fibre). Dots are
experimental results obtained by van Gorp [11] and the solid line is the analytical
model prediction.

Figure 3: Experimental [9] and analytical results [8] for FSP impact onto
Kevlar 29 fabric.

Figure 4: Experimental results [11] and analytical predictions [10]. Ballistic
limit against areal density for 1.1 g FSP impact onto UD 66
Dyneema fabric.
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196 Projectile Impacts: modelling techniques and target performance assessment
3.2 Modelling ballistic impact onto ceramic faced targets
Advanced ceramics (such as alumina, silicon carbide, silicon nitride, boron
carbide, titanium diboride) are being increasingly used to achieve more efficient
armours against kinetic energy projectiles, shape charges, explosive forming
projectiles (EFP) while keeping armour weight under acceptable levels.
Advanced ceramics have been proven to exhibit a much higher ballistic
efficiency compared to that of traditional materials (steel, aluminium). Ceramics
however are quite brittle, being fractured a few microseconds after high-speed
impact. The utilisation of ceramics for armour production requires therefore the
inclusion of a ductile backing plate, either a metallic alloy or a composite to
withstand the effects of the fractured ceramic. Such structures are known as
composite armours, which can be employed as the main armour (for instance,
rigid body vests, helicopter seats) or attached to the main armour of the vehicle
(add-on armour).
The penetration process into ceramic faced composite armours is sketched in
fig. 5. A few microseconds after the initial contact, a cone of comminuted
ceramic is produced, distributing the pressure on the ductile backing plate. The
penetrator is decelerated and eroded while penetrating the ceramic and the
backing plate is bulged. The process ends either by projectile arrest or by
backing plate fracture in tension along a spread surface.

Figure 5: Sketch of ceramic faced armour impacted by high-speed penetrator.
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Projectile Impacts: modelling techniques and target performance assessment 197
In recent years, several analytical models have been developed at the authors’
department able to simulate ballistic impact on ceramic/metal [12] as well as on
ceramic/composite [13] targets. As pointed out already, analytical models
validated by experiments may be very useful tools as a first step towards armour
designing.
For instance, figs 6 and 7 illustrate some results obtained with the SCARE
analytical programme, developed to simulate ballistic impact onto ceramic/metal
targets [12]. Fig. 6 depicts optimum results of areal density vs. ceramic
thickness/metal thickness ratio for impact of 25 APDS (armour piercing
discarding sabot) projectiles onto alumina/aluminium alloy at different
obliquities while fig. 7 shows the residual velocity after perforation against
ceramic thickness for the same projectile and target materials.
Similarly, figs 8 and 9 illustrate analytical results obtained with the model
developed to simulate penetration into ceramic/composite targets [13]. Fig. 8
summarizes the analytical predictions of residual velocity vs. striking velocity
for alumina/Kevlar 29 targets of different areal densities and three different
armour piercing (AP) projectiles: 7.62 AP, 12.70 AP and 14.5 AP. From fig. 8 it
is easy to derive the results shown in fig. 9, which depicts the ballistic limit vs.
areal density for the three mentioned projectiles. This figure includes also
numerical results as will be described in the next section and experimental data,
showing a good agreement between the results obtained by the three approaches
used.

Figure 6: Analytical predictions [12] of optimal design of alumina/aluminium
armour to defeat 25 APDS projectiles.

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198 Projectile Impacts: modelling techniques and target performance assessment

Figure 7: Residual velocity vs. ceramic thickness for alumina/aluminium
armour perforated by 25 APDS projectiles.
4 Numerical simulation
As already pointed out, numerical simulations are carried out by discretizing
projectile and target and using either the finite element method or the finite
difference method and computing the penetration process step by step with the
use of a numerical computation code. The whole process may last from a few
minutes up to several hours. The main difficulty in numerical simulations of
high-speed impact onto composite targets arises from dearth of material
behaviour data. Although the dynamic behaviour of metal alloys is usually well
known, the necessary data for advanced ceramics and composites are much
scarcer, probably due to classification reasons. Especially, the data needed to
feed the failure criterion and the mechanical behaviour of damaged materials are
not easily available. Hence, the predictive capability of numerical simulations is
limited and often parametric data must be used to match experimental results.
On the other hand, numerical simulation, after validation by comparison with
experimental results, provides a great amount of information, such as stress and
strain distributions, damage extension, penetrator mass and velocity.
For instance, fig. 10 shows the perforation of a 20 mm AD 95 alumina +
10 mm 5083 aluminium alloy add-on armour by a 20 mm APDS projectile and
30˚ obliquity. The figure shows both the numerical simulation with AUTODYN
2D hydrocode as well as experimental results with X-ray shadowgraph for the
same time. The comparison between experimental observations and numerical
simulation proves that this approach provides reliable results with much less
expensive effort. The figure gives also very interesting results; both methods
show a high erosion of the projectile, which is destabilized after perforation,
being unable to perforate the main armour.
Another example of numerical simulation is shown in fig. 11. It illustrates the
penetration process into an add-on armour alumina/aluminium by a tungsten
APFSDS (armour piercing fin stabilized discarded sabot) projectile. The figure
shows the phenomenon several times. The projectile perforates the add-on
armour, but suffers a severe deformation and erosion being unable to perforate
the steel main armour.
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Projectile Impacts: modelling techniques and target performance assessment 199

Figure 8: Analytical predictions [13] of residual velocity vs. striking velocity
for three armour piercing (AP) projectiles after perforation of
alumina/Kevlar 29 armours.
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200 Projectile Impacts: modelling techniques and target performance assessment

Figure 9: Analytical, numerical and experimental results of ballistic limit
against areal density for optimal design of alumina/Kevlar 29
armour to defeat three AP projectiles.

Figure 10: Numerical simulation with AUTODYN 2D and shadowgraph of
perforation of alumina/aluminium add-on armour by 20 APDS
projectile.

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