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ISB ’10 05-020 Experimental and Numerical Investigations on the
Origins of the Bodywork Effect (K-Effect)
F. Coghe1,*, N. Nsiampa1, L. Rabet2, G. Dyckmans1
1 Dept. Weapon Systems & Ballistics, Royal Military Academy, Renaissance Avenue 30, 1000 Brussels, Belgium,
2 Dept. Civil Engineering & Materials, Royal Military Academy, Renaissance Avenue 30, 1000 Brussels, Belgium
Abstract
This work presents experimental and numerical results, giving qualitative and quantitative
knowledge about the so-called bodywork effect or K-effect (from its German designation
“Karroserie-effekt”). This effect is encountered in applications where an existing vehicle is
armoured by integrating a ballistic kit composed of high hardness steel plates, inside the
existing bodywork of the vehicle. It manifests itself as a lowering of the ballistic limit velocity
of the total armour configuration compared to the single armour plate against common
military rifle ammunition, when a thin metallic plate (the bodywork of the vehicle) is added at
a small distance in front of the armour plate. Ballistic tests were used to quantify the change
in ballistic resistance by using different target configurations and different projectiles. It was
observed that the origins of the bodywork lay in the change of the projectile geometry
(flattening of the projectile tip) after the passage through the thin bodywork sheet, leading to a
change in the stress triaxiality in the armour plate. This gives rise to a higher sensitivity of the
high hardness steel armour plate to shear failure (leading to plugging from a ballistic point of
view). This was confirmed by using an adapted projectile (truncated nose) against the armour
plate, which failed by plugging. This sensitivity to the projectile geometry and hence stress
* Corresponding author. Tel :+3227426475; Fax: +3227426320 – E-mail: frederik.coghe@rma.ac.be
triaxiality was also illustrated by the relative vulnerability of these high hardness steel plates
against the impact of soft lead-cored ammunitions, while they protect effectively against
semi-armour piercing ammunitions. Dynamic material tests were used to characterize the
armour plate (strength and failure) and to obtain material models that afterwards were used in
an explicit finite element code. The finite element simulations show that the influence of the
changed projectile geometry can be captured by such a code, and help clarify certain
phenomena encountered during the ballistic testing. The results of this work could have great
repercussions for everyone working in the field of up-armouring vehicles and/or working in
the field of testing, evaluation and validation of vehicle armour systems. It could also help
steel manufacturers in assessing new high hardness ballistic steels.
INTRODUCTION
For the up-armouring of light non-protected vehicles, as in the case of VIP limousines or
military logistic vehicles to be used in conflict zones, typically an armour kit is fixed to the
original structure of the vehicle. In order to keep a low profile, these armour kits are typically
integrated into the existing bodywork, which makes the extra armour practically invisible
from the outside of the vehicle. Different solutions can be found for this application, ranging
from the integration of soft armour blankets to the use of ceramic tile inserts. To achieve
protection against military rifle ammunition (e.g. the omnipresent 7.62 x 39 M1943 Soviet
ammunition, used for the AK-47 Kalashnikov rifle) a weight (and cost) efficient approach is
the use of high hardness steel plates [1]. Several manufacturers are producing this kind of
ballistic steel plate. The plates are produced by alloying the base steel and by giving them an
adapted thermal (quenching and tempering) or thermo-mechanical (rolling at intermediate
temperatures, possibly followed by a thermal cycle) treatment, which typically gives them a
hardness in the range of 400 to 600 (and higher) on the Brinell Hardness Scale (HBN). The
higher hardness gives improved ballistic protection (by breaking up and shattering an
incoming projectile), while the lower hardness gives combined ballistic and explosive
protection due to the increased impact toughness of the metal [2].
In order to ensure quality and give proof of their ballistic protection level, ballistic steel plates
are afterwards tested following a ballistic testing norm or a client testing protocol. One of the
most common used norms is the STANAG 4569 [4], in which the resistance against standard
(as opposed to armour-piercing) rifle rounds is checked by proof firing of 7.62 x 51 NATO
Ball, 5.56 x 45 NATO Ball (SS109) and 5.56 x 45 M193 ammunition, corresponding to the
so-called Level I protection level, a typical protection level for up-armoured standard
vehicles.
Undisclosed reports have mentioned on several occasions (during testing or in operations) the
perforation of up-armoured vehicles by impacts that were perceived as a lower threat to the
armour, than the one it was proof tested for. In some of these instances origins of the failing
of the armour system could be traced back to be due to the so-called bodywork effect. As the
name implies this effect is due to the integration of the armour kit in an existing bodywork,
and means that the ballistic limit of the combined bodywork plate and armour plate is lower
than the ballistic limit of the armour plate on itself. At least one report [5] suggests that this is
due to the flattening of the nose of the projectile while passing first through the thin plate of
the bodywork, facilitating deformation localization and hence the plugging perforation
mechanism when impacting afterwards on the armour plate. This suggestion was based solely
on numerical simulation results, without any experimental validation (except for the lowered
ballistic limit).
Previous experimental research [6] validated this assumption and dismissed an alternative
explanation that the higher energy density that would be reached during the impact on the
armour plate by the loss of the projectile envelope (jacket) during the perforation of the first
thin bodywork plate, would enhance the performance of the remaining projectile core when
impacting on the armour plate afterwards.
It is known that the shape of the projectile greatly influences the penetration process [7,8],
although depending upon the relative strength of the projectile to the armour plate and the
sensitivity of the armour plate to adiabatic shear localization, the geometry of the projectile
seems to have an opposite effect. In the case where the strength of the projectile is such that
the penetration mechanism approaches a rigid body penetration, a conical or ogival shape will
enhance the penetration performance of the projectile (assuming that it is an oblique impact
and that the projectile has enough ductility not to shatter upon impact). When the strength of
the target although overmatches the strength of the projectile material, a blunted projectile
will enhance a plugging penetration mechanism and lower the ballistic limit velocity of the
armour plate, especially since in most practical cases the high-strength armour plate will have
limited ductility and be sensitive to adiabatic shear localization. An ogival or conical
projectile will be blunted and/or shattered and due to this show a much lowered penetration
performance. In the case of standard military projectiles with different configurations and
different materials and composite armour configurations, the above analysis is no longer as
straightforward.
In this work the susceptibility of the Secure 500 ballistic steel to the bodywork effect will be
investigated by adapted ballistic testing. By determining the ballistic limit velocity with and
without a bodywork sheet, the importance of the bodywork effect will be illustrated and
quantified. In order to confirm that the changed projectile geometry after perforation of the
thin sheet of bodywork and the hence changed triaxiality of the stress state are the main
origins of the bodywork effect, the ballistic limit velocity for flat-tipped and soft-cored
projectiles has also been determined. In order to afterwards correctly simulate the perforation
of the armour plate by the use of a finite element code, the Secure 500 steel was characterized
dynamically by the use of the Split Hopkinson Pressure Bars technique (also called Kolsky
bars). The constitutive strength and failure behaviour of the material was modelled with
respectively the Johnson-Cook strength model and the Johnson-Cook failure model. In this
way the effect of the temperature and the triaxiality, both primary factors influencing
localization of deformation and hence adiabatic shear localization, can be taken into account
in the material behaviour. These material models will afterwards be used in a finite element
model, to see, in a first step, if the model is able to capture this complex phenomenon, since
finite element models are more and more frequently used in the optimization of an armour
configuration. The model will be compared to the results obtained during the ballistic testing,
both quantitatively by comparing the ballistic limit velocities and residual velocities for the
different projectiles, and qualitatively by comparing the plugging phenomenon in the
simulations with the ballistic tests by the use of light-optical microscopy (LOM). Secondly,
the validated finite element model will be used to clarify some special features observed
during the initial ballistic testing.
EXPERIMENTS
Projectile and target configurations
Ballistic tests were used to quantify the ballistic resistance of different target configurations
against different projectiles. In this work the ThyssenKrupp Secure 500 high-hardness
ballistic steel was used [3] as the armour material. This quenched and tempered steel has a full
fine martensitic microstructure which gives it a hardness in the range of 480 to 530 HBN.
This leads to a yield strength of 1300 MPa and a failure strength in tension of 1600 MPa (for a
minimal elongation of 9%). Its chemical composition is given in Table 1.
Table 1: Chemical composition of the ThyssenKrupp Secure 500 ballistic steel.
Element
C
Si
Mn
P
S
Cr
Mo
Ni
Al
Fe
Mass fraction wt%
< 0,32
< 0,50
< 1,00
< 0,020
< 0,008
< 1,50
< 0,50
< 0,70
< 0,110
Balanced
Three different projectiles were used for the ballistic testing, of which two were standard
projectiles [10], corresponding to the NATO protection level I for light armoured vehicles,
and one was an adapted projectile to simulate a projectile with a flattened tip.
The first projectile used is the 5.56x45 mm NATO Ball bullet (SS109, M855). This bullet is
composed of a high-hardness steel penetrator followed by a lead core, enveloped in a brass
jacket (Fig. 1 (a)). Concerning the bodywork effect it is important to mention that just in front
of the flat steel penetrator there is a small cavity between the penetrator and the brass jacket.
The bullet weight is 4 grams and its typical muzzle velocity when fired with a common
assault rifle, ranges from 900 m/s to 960 m/s. This type of ammunition is known to frequently
lead to a bodywork effect.
The second projectile used for ballistic testing is the 5.56x45 mm M193 Ball bullet (also
known as FN SS92), which was the bullet originally developed for the AR-15 and M16
family of weapons. Contrary to the 5.56x45 mm NATO Ball bullet, it is composed of a fully
lead core enveloped in a brass jacket (Fig. 1 (b)). The bullet weight is 3.6 grams while its
typical muzzle velocity is a little higher compared to the 5.56x45 mm NATO Ball bullet and
ranges from 940 m/s to 980 m/s. This projectile was used to validate the reported lower
ballistic resistance of the Secure 500 armour steel against this threat, even if this projectile
does not have a steel penetrator and a lower mass. This can also be attributed like in the case
of the bodywork effect to the rapid blunting of the projectile tip upon impact and the
following plugging failure of the armour plate due to adiabatic shear localization, as will be
shown further on.
In order to avoid the ballistic variance of the perforation process of the thin bodywork plate
and to enhance the shear localization effect, an adapted 5.56x45 mm NATO Ball bullet was
also used. To simulate the 5.56x45 mm NATO Ball bullet with a flattened tip due to
perforation of the thin bodywork sheet, a version with a truncated nose was produced (Fig. 1
(c)). The projectiles were made out of original 5.56x45 mm NATO Ball bullets by sawing of
the nose of the projectiles along the flat-sided front of the steel penetrator with a low-speed
diamond saw. Due to this, the bullet weight was 3.96 grams on average, while the typical
muzzle velocity remained quasi unaffected.
An overview of the different projectile and target combinations is given in Table 2.
(a)
(b)
(c)
Figure 1: Different projectile geometries used for ballistic testing with (a) standard SS109 projectile, (b)
standard M193 projectile and (c) adapted flat-tipped SS109 projectile.
Setup and methods
All ballistic testing was done following the guidelines of STANAG 2920 [9]. While for the
configurations that incorporated the armour plate the ballistic limit velocity V50 (for a 50%
chance on complete perforation) was used to characterize the ballistic resistance, the average
deceleration (based on residual velocity measurements) was used to quantify the ballistic
resistance of the single mild steel sheet, simulating the bodywork of a vehicle, due to the
inability to determine a ballistic limit velocity for very low impact speeds. All projectiles were
fired from a rifled bore weapon with a 7 in (0.178 m) rifling. Stability and yaw angle of all
projectiles (see next paragraph) was checked by the use of yaw cards approximately 5 m after
exiting the muzzle. The velocity before impact was measured using a double infrared optical
velocity measurement base (2 m base) with a less than 1 m/s error margin. The exit velocity
of the plug/projectile in case of complete perforation was measured using a single short
optical velocity measurement base (0.5 m base) and a continuous wave (CW) Doppler radar.
The measurements were done as close to the back face of the armour plate as practically
possible. The exit velocity could only be estimated since the different fragments originating
from either the armour plate or the projectile gave multiple triggers in the case of complete
perforation. In the applicable cases the ballistic limit velocity V50 was calculated according to
the method described in STANAG 2920.
Results and discussion
The ballistic limit velocities for the different projectiles and target configurations are given in
Table 2. In all cases the final perforation of the armour plate was a plugging penetration
mechanism [11], which was confirmed by high speed photography and soft recovery of the
plugs. There was almost no ductile hole formation observed and the transition zone of partial
to complete perforation showed an abrupt change from only minor indentation of the plate at
velocities close to the ballistic limit velocity to an almost complete plugging penetration
process (see Fig. 2) with the height of the plugs corresponding to almost 90% of the original
plate thickness. In case of non-perforation the projectile is completely shattered on the front
face of the armour plate without any remaining projectile debris with significant mass lodged
in the plate. This shows that the penetration process and the ballistic resistance of the armour
plate are almost completely determined by the shear resistance and the failure behaviour
under shear loading of the armour plate.
The 6.5 mm armour plate as expected has a ballistic limit velocity against the SS109 above its
regular muzzle velocity. If a thin (1 mm) steel sheet is put in front of the armour plate, the
ballistic limit although drops by almost 4% and the armour plate can be perforated at
velocities commonly encountered with current assault rifles. This leads to the paradox that
more material in front of the projectile not necessarily increases the protection level and has
led to the use of the term “bodywork effect”. Not withstanding its soft core and lower mass,
the M193 round perforates the single armour plate even more easily and the V50 is almost 9%
lower than for the original semi-armour piercing SS109 round. Conversely, the M193
projectile deforms heavily or fragments on impact on the thin steel sheet and as such does not
lead to a bodywork effect.
By measuring the residual velocity after complete perforation of the 1 mm mild steel
bodywork plate, it was shown that the normal SS109 projectile (Fig. 3 (a)) lost around 40 m/s
of its initial velocity for a nominal impact velocity. High speed photography and soft recovery
of the projectile after perforation showed that the tip of the projectile was severely blunted
(see Fig. 3 (c): in this particular case a ring of mild steel was punched out of the bodywork
sheet and stayed attached to the projectile tip) or even completely flattened (due to the relative
motion of the penetrator inside the jacket, which brings the flat front surface of the penetrator
at the height of the projectile tip; Fig. 3 (b)). Both the blunted and flattened projectile tip lead
to a bodywork effect and no significant difference in residual velocity was observed.
In order to check that the flattening of the projectile is the cause for the lowered ballistic
resistance, the same SS109 projectile but with a truncated nose (Fig. 3 (d)) was fired against
the single armour plate. The V50 is lowered by 7% when the tip of the projectile has been sawn
off prior to the ballistic testing. Another proof of the fact that the change in projectile
geometry is the cause for the bodywork effect, is that the ballistic resistance of the combined
bodywork sheet and armour plate is close to the sum of the velocity deceleration of the
regular SS109 projectile due to the perforation of the 1 mm of mild steel, and the ballistic
limit velocity of the single armour plate against the adapted SS109 projectile with the
truncated tip:
(1)
Table 2: Overview of the different target configurations and their experimental and simulated ballistic
limit velocities (*: deceleration instead of ballistic limit velocity for the 1 mm bodywork sheet).
1 mm bodywork
10 mm air gap
6.5 mm armour plate
6.5 mm armour plate
1 mm bodywork
Standard
Flat-tipped
Full lead core
Standard
Standard
Target
(SS109)
(SS109)
(M193)
(SS109)
(SS109)
Experimental V50
(m/s)
1002.5
932.3
913.5
963.9
40.2*
Simulated V50 (m/s)
995
935
885
-
-
Relative difference
(%)
-0.7
+0.3
-3.1
-
-
(a)
(a’)
(b)
(b’)
Figure 2: front (a) and back face (a') of a non-perforating impact (impact velocity 911 m/s) and front (b)
and back face (b') for a completely perforating impact (impact velocity 911 m/s).
(a)
(b)
(c)
(d)
Figure 3: Different original and recovered projectiles with (a) the original SS109 projectile, (b) an SS109
projectile after perforation of the 1mm bodywork sheet, showing a flattened projectile tip, (c) an SS109
projectile after perforation of the 1 mm bodywork sheet, showing blunting of the projectile tip with
detached ring of the bodywork sheet attached to the projectile tip, and (d) the adapted flat-tipped SS109
projectile.
MATERIAL MODELLING
This work focusses only on the armour material characterization as for the projectile materials
model parameters were found in the literature.
Post-mortem observations of the failed armour plate showed an extreme sensitivity to
adiabatic shear localization which are thermo-viscoplastic instabilities. As such the effect of
temperature and triaxiality, both primary factors influencing localization of deformation and
hence adiabatic shear localization, has to be taken into account in the constitutive models. The
constitutive strength and failure behaviour of the material was modelled with respectively the
Johnson-Cook strength model and the Johnson-Cook failure model. Since the simulated
impact problem considers mainly limited material velocities compared to explosive shock
loadings, the equation of state (Mie-Grüneisen [12]) and its parameters were taken from
literature [13] for a comparable steel type. The parameters are given in Table 3.
Armour material characterization
To determine the different dynamic material parameters of the different models, use was
made of a Split Hopkinson Pressure Bars setup (SHPB) [14,15]. The setup used for this
research was a SHPB setup with 2 m long input and output bars with a 30 mm diameter and
made out of high strength maraging steel (quasi-static yield strength above 1800 MPa). The
setup also comprised a robotized heater system [16] that can heat the sample in an external
furnace (to avoid heating of the bars) up to temperatures of 500 °C depending on the material
tested. In order to minimize possible problems with microstructural evolution during heating,
the heating cycle is limited to 30 s. After the heating cycle the temperature of the sample is
measured with a thermocouple and a robot arm puts the heated sample in between the two
SHPB bars. The dynamic testing is then initiated automatically after a 1 s delay. Due to this
delay and the fact that the heated sample is in contact with the cold bars (who act like heat
sinks), an important temperature drop is observed in the sample. This temperature drop can be
estimated by the use of a one-dimensional heat flux model that has been implemented in a
numerical model [16,17]. It has also been shown [18] that the heat loss during the movement
of the sample from the furnace to the SHPB bars is negligible compared to the heat loss when
in contact with the bars, due to the rapid positioning of the robot system.
The cylindrical samples used for the material characterization, had a diameter of 5 mm and a
length of 6 mm (length over diameter ratio of 1.2) and were cut out of the original armour
plate by spark erosion cutting. In order to protect the SHPB bars from indentation by the
specimen, protective disks with 4 mm thickness and the same diameter as the SHPB bars, also
made out of Secure 500 were attached to the bars (magnetically and/or by the use of a
lubrificative film). Since the disks made out of Secure 500 had an acoustic impedance
(with E the elastic modulus and
!
the density of the material) closely matching the
acoustic impedance of the maraging steel of the bars, the wave propagation in the SHPB setup
was not altered and no special signal processing was necessary. This was checked
experimentally by performing an SHPB test with only the disks inserted in between the input
and output bar (no sample, see Fig. 4). Due to the fact that the disks are loaded in a uniaxial
strain state, while the samples are loaded in a uniaxial stress state, the disks remained in the
elastic regime, even if the samples made out of the same material deformed plastically while
in contact with the protective disks. Minor damage did occur in the cases where the sample
fractured dynamically and the sharp edges of the remaining sample fragments impacted the
surface of the protective disks. In these cases the surface of the protective disks was
repolished after the test by the use of sand grid paper. A commercial lubrificant was applied
on the surfaces of the protective disks in order to minimize the barrelling of the samples.
(a)
(b)
(c)
Figure 4: Protective disks (one attached to the input bar of the SHPB on the left, second placed above the
output bar on the right) used to protect the SHPB (a) from damage (b). The presence of the protective
disks did not alter the wave propagation in the SHPB setup (c).
(a)
(b)
Figure 5: (a) Typical fracture for specimens tested at a strain rate of 1500 /s; (b) initial and final
temperatures of the specimens after being placed in the SHPB setup.
Constitutive strength model
The empirical Johnson-Cook strength model [19] was used to model the flow stress of the
Secure 500 armour steel. The Johnson-Cook model gives the equivalent flow stress of the
material as a function of equivalent plastic strain , equivalent plastic strain rate and
temperature T, where the influences of all three variables are treated as being independent one
from the other:
(2)
with A, B, C, n and m the material parameters to be determined, a reference equivalent
plastic strain rate (in this case 1 /s), Tref the reference temperature (in this case a room
temperature of 20 °C) and Tm the melt temperature of the material. The Secure 500 material
was tested for two different strain rates (nominally 1000 /s and 1500 /s) and four different
temperatures (room temperature, 100 °C, 200 °C and 300 °C). The temperature rise due to
adiabatic heating was taken into account according to Eq. (3) [20], with an assumed Taylor-
Quinney coefficient
"
of 0.9, typical for metals [21]:
(3)
where Cp is the heat capacity of the considered material. The initial nominal temperatures of
the samples were corrected for the heat loss due to the contact between the sample and the
bars (Fig. 5 (b)). The model parameters were fitted simultaneously by applying a least-squares
method on the measured stress-strain curves, after removal of the pseudo-elastic regime by
use of the 0.2% offset criterion, normally used for static tensile testing. The results for both
strain rates can be seen in Fig. 6, while the optimized parameters for the Johnson-Cook model
can be found in Table 3. In Fig. 6 it can also be seen that the Johnson-Cook model
overestimates the influence of the temperature for the lower initial temperatures (room
temperature RT, 78 °C/100 °C nominally and 150 °C/200 °C nominally), while for the higher
initial temperature (222 °C/300 °C nominally) the influence is underestimated. This can
probably be attributed to a softening in the temperature range of 150 °C to 200 °C (martensite
tempering) with a consequent loss of strength and hardness, although no information is
currently available on the kinetics of the tempering. It seems although possible that the Secure
500 steel has at least been partially tempered after 30 s at temperatures above 200 °C [3,22].
Further thermodynamic and microstructural research would be required to analyze the kinetics
of the tempering further. Although this phenomenon will certainly enhance adiabatic shear
localization, it is for this research considered to be of secondary order compared to the local
triaxiality of the stress state.
(a)
(b)
Figure 6: Stress-strain curves obtained with the SHPB for different temperatures and nominal strain rates
of 1000 /s (a) and 1500 /s (b), and the fitted constitutive strength model (JC: Johnson-Cook).
Table 3: Material models and parameters used to model the Secure 500 steel.
Model
Type
Parameters
Strength
Johnson-Cook
A = 1299 MPa, B = 2230 MPa, C = 0.044, n = 0.56, m = 0.95
Failure
Johnson-Cook
D1 = 0.168, D2 = 0.035, D3 = -2.44, D4 = -0.0450, D5 = 0.92
Equation of state
Shock
C0 = 4569 m/s, S = 1.490,
#
= 2.17
Constitutive failure model
Although different failure models can be used to model failure in the case of a dynamic event
[23,24], the Johnson-Cook failure model [25] was used for this research. Since adiabatic shear
localization, associated with the macroscopic plugging penetration mechanism encountered
during the ballistic testing, is sensitive to the stress triaxiality, the failure model had to include
the stress triaxiality. Compared to other models the Johnson-Cook model does although have
the advantage of taking into account the influence of the strain rate and the temperature as
well, two effects that are considered to be primary factors for adiabatic shear localization.
Nevertheless, it has the drawback of only being able to capture part of the real fracture curve.
Since the high-hardness steel armour plate considered in this work fails primarily by plugging
macroscopically, and hence by shear failure on a microscopic level, in the case of a ballistic
event, this was not considered to be of a problem as long as the failure model was rightly
fitted for the lower triaxiality regimes (compressive state, corresponding to a stress triaxiality
of -1/3, to pure shear state, corresponding to a stress triaxiality of 0).
According to the Johnson-Cook failure model, the equivalent failure strain is calculated
as:
(4)
where D1, D2, D3, D4 and D5 are the model parameters to identify, and
$
* is the stress
triaxiality ratio, given by Eq. (5):
(5)
with
$
H the hydrostatic pressure component. The fracture criterion is finally used in a damage
evolution law where the damage D of a material element is expressed as:
(6)
where is the increment of the accumulated (equivalent) plastic strain that occurs during
an elemental deformation step (corresponding to an integration cycle in an FEM code).
Failure is assumed to occur instantaneously when D equals unity, as no coupling between the
damage and the constitutive strength model is considered in this study.
The optimised parameter set can be found in Table 3. The model parameters were optimised
by a least square method using the loading and fracture data from the SHPB tests. Since no
samples tested at a strain rate of 1000 /s fractured during the SHPB testing, only the test data
for an average strain rate of 1500 /s could be used. A high speed camera was used to check
that fracture occurred during the first passage of the loading wave through the specimen. As a
first approximation the evolution of the triaxiality ratio was not taken into account and a
constant value of -1/3 was supposed. Although fracture is not supposed to occur under these
triaxiality conditions [26], the real fracture locus is considered to be only minorly shifted
away [27] due to the limited ductility and hence localization for this kind of high-hardness
steel. This does although mean that the determined fracture locus is a lower-bound estimation
of the real fracture locus, since locally the material can still accommodate an important
amount of deformation after localization of the deformation. As in upsetting tests, the
specimens failed along a single diagonal (45°) fracture plane (Fig. 5 (a)). The average (at least
3 tests for every temperature) experimental fracture points and the approximative (i.e. for
constant strain rate and adiabatic heating conditions, while for the parameter optimization the
complete loading data was used) Johnson-Cook fracture curves are given in Fig. 7 (a). As a
way to quickly check the validity of the model for the higher triaxiality regimes, the fracture
point for a classical quasi-static tensile test (as given by the supplier) is also shown. As
expected it lies below the model curves, since the tensile test was performed at a much lower
strain rate and since no correction for necking of the specimen was made, which can be
considerable for a tensile stress state.
Figure 7 (b) gives a comparison between the experimental fracture data points and the failure
model as a function of temperature. The temperature for the experimental data was chosen to
be the average temperature of the sample during the compression testing (adiabatic heating
taken into account according to Eq. (3)). It shows that for the higher temperatures the
experimental data points tend to show a lowering of the fracture strain, a tendency that can not
be captured by the Johnson-Cook failure model. The fracture curve lies although within the
experimental scatter interval. This lowered failure strain is probably again due to a
microstructural change in the material in the 200 °C-300 °C temperature range, as one would
expect the failure strain to increase with increasing temperature. The phenomenon could be
related to the temper embrittlement problem encountered in alloy steels [28]. As for the
constitutive strength model, this effect is considered to be a secondary effect compared to the
influence of the local triaxiality, but might enhance localization even further.
(a)
(b)
Figure 7: Comparison of the fracture loci given by the failure model (JC: Johnson-Cook) and the average
experimental data points (a); and statistical evaluation of the failure model for different temperatures by
use of the experimental fracture data (b).
NUMERICAL MODELLING
Model setup
To get more insight into the bodywork effect, numerical simulations were carried out using
the ANSYS Autodyn explicit code. Since the experimental part of this work showed that the
bodywork effect could be attributed to the flattening of the projectile, and in order to avoid an
elaborate characterization of the bodywork steel, the simulation of the full experimental
configuration of the bodywork effect has been omitted. As shown before, the effect is very
comparable to the impact of the flat-tipped SS109 projectile and as such the encountered
phenomena are highly comparable.
A Lagrangian solver was used for the different parts of the simulation. As the target plate fails
by plugging, as a consequence of shear localization, a fine meshing is necessary to capture
these complex failure mechanisms. In order to reduce the computation time and because of
the nature of the problem, an axisymmetric model was used. A typical mesh size of 0.05 mm
was used. The number of nodes of the projectile (value is for the standard SS109 projectile;
other projectiles had a comparable number of nodes) and the armour plate are 16554 and
26462 respectively.
Since the main focus of this research was on the behaviour of the armour material, the
material parameters for the different projectile components were taken from the material
library available in the ANSYS Autodyn FEM code (jacket and core) or from literature (steel
penetrator [29]). The different models and their parameters can be found in Tables 4-6.
Table 4: Strength models used for the projectile materials.
Part
Material
Strength model
Parameters
Penetrator
Steel
Johnson-Cook
A = 1600 MPa, B = 807 MPa, C = 0.008, n = 0.10, m = 1.00
Jacket
Brass
Von Mises
YS = 300 Mpa
Core
Lead
Von Mises
YS = 30 Mpa
Table 5: Failure models used for the projectile materials.
Part
Material
Failure model
Parameters
Penetrator
Steel
Johnson-Cook
D1 = 0.051, D2 = 0.018, D3 = -3.00, D4 = 0.0002, D5 = 0.55
Jacket
Brass
Plastic strain
= 0.3
Core
Lead
Plastic strain
= 0.3
Table 6: Equations of state (EOS) used for the projectile materials.
Part
Material
Equation of state
Parameters
Penetrator
Steel 4340
Shock
C0 = 4569 m/s, S = 1.490,
#
= 2.17
Jacket
Brass
Linear
!
0 = 8450 kg/m3, K = 100 Gpa
Core
Lead
Shock
C0 = 2006 m/s, S = 1.429,
#
= 2.74
Results, comparison and discussion
The ballistic limit velocities determined by numerical modelling and a comparison with the
experimentally determined ballistic limit velocities are shown in Table 2. The agreement
between the experimental and the simulated results is extremely well. Nonetheless no iterative
scheme to change the material models to improve the output of the finite element modelling
was used: all simulations were ab initio calculations based on the initially determined material
models. The relative difference between experimental and simulated ballistic limit velocities
falls within 5% for every simulated case.
A comparison between the residual velocities for complete perforations (for the single armour
plate) of the experimental and numerical results in Fig. 8, shows that the simulated values are
always above the experimental values, even if the ballistic limit velocities showed a very good
correspondence. This shows that the localization of the plugging penetration mechanism has
been accurately modelled (which depends upon the interaction of the strength model and the
failure model), but that the actual failure mechanism of the material and its associated energy
absorption is not captured completely. This can mainly be attributed to the inaccuracy in the
determination of the failure model parameters, more precisely the abstention of the influence
of localization during the compression testing when determining the model parameters of the
Johnson-Cook failure model. As mentioned earlier, the fracture loci given by the material
parameters determined in the previous paragraph are a lower bound value of the real fracture
curves. As such the simulations will systematically overestimate the residual velocities, since
in the real penetration process more energy will be absorbed.
In some cases residual velocity testing is used to estimate the ballistic limit velocity of an
armour configuration. The work of Recht and Ipson [30] showed that for metallic materials
there is a semi-empirical relation between the impact velocity Vin, the ballistic limit velocity
V50 and the residual velocity Vr:
(7)
with Mp the mass of the projectile and Mt the material driven from the target. When Eq. (7) is
used to estimate the ballistic limit velocity, the equation is typically altered to Eq. (8) in order
to increase the fit with the empirical data:
(8)
where V50, a and p are used as fitting parameters. Although Eq. (8) introduces large errors in
the estimated V50 for small errors in the measured Vr, it still is a very convenient way to
rapidly make ballistic limit velocity estimations (at least for metallic materials; for composites
the V50 in Eq. (7) and (8) must be replaced by the minimum perforation velocity Vx which can
be very different from the actual ballistic limit velocity), since it is much easier to obtain a set
of completely perforating shots, than have a mixed set of perforating and non-perforating
shots as typically used to calculate the ballistic limit velocity.
Equation (8) is only valid in the case the mass of the projectile is not significantly altered
during the perforation process. If although the projectile mass is altered considerably, Eq. (8)
should be adapted into:
(9)
with Mp,r the residual mass of the projectile after complete perforation of the target.
Although in both the ballistic test results and the simulation results an effort was done to
estimate the different variables in Eq. (9), with relative good agreement between both, the
equation proved to be unuseful to estimate the ballistic limit velocity. In the case of the
ballistic tests, the soft recovery of the fragments proved to be difficult and showed a large
scatter in mass and velocity. It was also impossible to know the different velocities of the
different fragments since typically only one velocity (the highest) was recorded. In the case of
the simulations the mass and velocity of the different fragments could be estimated quite
accurately, but since the different fragments (plug, lead core and steel penetrator) all have
different velocities, an averaging routine is necessary to calculate a mean velocity, for
example by using conservation of energy or momentum. The mass and the velocity of the
different projectiles is also a function of the arbitrarily chosen numerical erosion strain [31],
the strain at which the elements in the simulation are removed from the mesh in order to avoid
that cells that become extremely distorted, block the simulation.
To circumvent these problems, Eq. (8) instead of Eq. (9) was used to fit the experimental and
simulated residual velocity data. The conservation of energy was used to calculate a mean
fragment velocity for the simulated results. The parameter estimations for the different
projectiles is given in Table 7, while Eq. (8) is graphically shown in the Fig. 8. All ballistic
data points are an average of at least three experiments with comparable impact velocity.
Table 7 shows that the residual velocity approach to estimate the ballistic limit velocity works
well for the experimental and the simulated data, even if the actual values of the residual
velocities differs considerably. The relative difference, compared to the experimentally
determined ballistic limit velocities (Table 2), is small, as can be seen in Table 7.
Although at first sight the simulations seem to be valid to make estimations of ballistic limit
velocities, the good estimation was only achieved by using at least one data point in the
rapidly descending branch of the analytical model. If these data points are not used in the
fitting procedure, very large errors can be introduced. This problem did not occur with the
experimental data where even when a data point in the first part of the model (before the
‘elbow’) is not available, a good estimation is obtained by using Eq. (8) (see for example Fig.
8 (b)). This can again be attributed to the imprecise failure model that is unable to capture the
energy absorption after localization of the deformation due to adiabatic shear banding. This
leads to a very abrupt change from non-perforation to complete perforation, even more abrupt
than the narrow transition zone observed experimentally. From a practical point of view this
means that the residual velocity approach in this case will not limit the total number of
simulations necessary to estimate the ballistic limit velocity: the simulations spend on finding
a point in the first rapidly descending branch of the analytical model, could be used more
efficiently to narrow down the interval between the highest non-perforating impact velocity
and the lowest completely perforating velocity.
In the case of the simulated data points it was also necessary to evaluate the obtained data
points, since numerical instabilities (see for example Fig. 8 (a) the simulation point for an
impact velocity of 1000 m/s, very close to the experimentally determined V50), the numerical
erosion strain and the averaging scheme (see for example Fig. 8 (b) where for impact
velocities of 1050 m/s and 1100 m/s the residual velocities deviate considerably of the rest of
the data set) all can lead to large scatter in the obtained residual velocities. For the
determination of the parameters for the Recht and Ipson analytical model, these data points
were consequently omitted from the fitting procedure.
Table 7: Parameters for the Recht and Ipson analytical model and comparison between experimental and
simulated results.
Projectile
Experiment
Simulation
V50 (m/s)
a (/)
p (/)
Relative
difference
(%)
V50 (m/s)
a (/)
p (/)
Relative
difference
(%)
SS109
1020,9
0,525
0,054
1,8
1010,0
0,688
0,103
0,7
SS109 flat-tipped
918,3
0,624
0,210
-1,5
938,0
0,744
0,026
0,6
M193
926,7
0,529
0,024
1,4
897,3
0,922
0,302
-1,8
(a)
(b)
(c)
Figure 8: Comparison of the analytical Recht and Ipson model for the simulated and experimental results
for the different projectile geometries; (a) regular SS109 projectile, (b) flat-tipped SS109 projectile, and
(c) regular M193 projectile.
A comparison of some typical penetration channels as a function of the impact velocity is
given in Fig. 9 for the M193 projectile (other projectiles showed similar features). Again there
is a good agreement between the experimental and numerical results. A marked feature that
was overlooked during the first initial ballistic experiments was revealed by the numerical
modelling: as can be seen in Fig. 9 (c’) there is a double plug formation in the numerical
model for the higher impact velocities. Additional ballistic testing revealed that this double
plugging phenomenon is not a numerical artefact, but that it was also present in the
experimental results. Figure 10 shows the two types of different plugs obtained by soft
recovery ballistic experiments: for low velocity completely perforating shots a single plug
was formed, while for the higher velocity completely perforating shots a central plug with a
partially circumferential second plug was recovered. Investigation of the perforation channels
shows that for the experimental shots, perforating at higher velocity, typically only part of the
circumferential second plug is formed before rupture from the plate due to variance in the
ballistic and mechanical characteristics of the test conditions and the materials (see Fig. 12
(c)).
(a)
(b)
(c)
(a’)
(b’)
(c’)
Figure 9: Penetration channel as a function of impact speed for the M193 projectile.; experimental results
for respective impact velocities of 911 m/s (a), 911 m/s (b) and 1062 m/s (c); numerical results for
respective impact velocities of 880 m/s (a’), 900 m/s (b’) and 1100 m/s (c’).
(a)
(b)
(c)
Figure 10: Plugging mechanisms; (a) single plug for low impact velocities; (b) double plug for higher
impact velocties; (c) front face of armour plate for higher impact velocity showing dual diameter.
CONCLUSION
The bodywork effect is an important phenomenon for people working in the field of armour
development, testing and/or evaluation of high-hardness ballistic steels, since it is a counter-
intuitive phenomenon in which the addition of extra material does not lead to a higher level of
protection, but even to a lowered level of protection. Due to this contradictory nature, its
influence might be overlooked during the development and/or application of armour
configurations based on high-hardness ballistic steel plates.
High-hardness ballistic steels are sensitive to deformation localization in the case of ballistic
impact, leading to a typical plugging failure of these kinds of steel armour plates. The local
stress triaxiality ratio and the adiabatic heating of the material play a very important role in
this. The influence of these two factors is also a key parameter to the bodywork effect, where
the addition of a thin mild steel sheet (like the sheet used for a vehicle bodywork) in front of
the armour plate, lowers the ballistic resistance of the total armour configuration significantly
from the level offered by the single armour plate.
The experimental part of this work has shown that for the 5.56x45 mm NATO Ball bullet this
can be attributed to the change in projectile geometry (flattening or blunting of the projectile
tip) after perforation of the bodywork sheet. The main origin for the bodywork effect, the
changed stress triaxiality, also explains the low ballistic resistance of high-hardness steel
armour plates against soft-cored projectiles, like the M193, compared to the higher ballistic
resistance offered against semi-armour piercing ammunitions like the SS109.
By the use of adapted dynamic characterization techniques for the armour material, the
bodywork effect can be captured with an explicit finite element model. The Johnson-Cook
strength model and the Johnson-Cook failure model, introduced in the numerical finite
element model, resulted in very good predictions of the experimentally determined ballistic
limit velocities. The numerical model correctly predicted the experimental plug morphology
as a function of impact velocity.
Nevertheless, the residual velocities for the different projectiles were systematically
overestimated in the numerical results. This could be attributed to the fact that the parameters
used for the failure model, were determined without taking into account neither the evolution
of the stress triaxiality nor the localization of the deformation during the compression testing.
Adapted material testing techniques (for example by the use of notched specimens and tests
for different triaxiality ratios) could be used to refine the failure model.
The residual velocity approach, based on the analytical model of Recht and Ipson, showed to
be able to give good estimations of the ballistic limit velocity for both the experimental and
the numerical results. It was although shown that due to the overestimation of the residual
velocities, the approach seemed not to be time-reducing in the case of the numerical
modelling.
Future work will include the numerical modelling of the complete experimental bodywork
configuration, which will necessitate the dynamic characterization and modelling of the thin
mild steel sheet used for the bodywork. In order to improve the residual velocity estimations,
improvement of the parameters of the Johnson-Cook model, or the use of a different failure
model, will be necessary.
Nomenclature
A
Reference yield strength Johnson-Cook strength model
a
Mass parameter Recht and Ipson model
B
Strain hardening constant Johnson-Cook strength model
C
Strain rate hardening constant Johnson-Cook strength model
C0
Bulk sound velocity
Cp
Heat capacity
D
Accumulated damage
D1,D2,D3,D4,D5
Parameters Johnson-Cook failure model
E
Young modulus or elastic modulus
K
Bulk modulus
m
Softening exponent Johnson-Cook strength model
Mp
Projectile mass
Mp,r
Residual projectile mass after complete perforation
Mt
Material mass driven from the target
n
Hardening exponent Johnson-Cook strength model
p
Exponent Recht and Ipson model
S
Linear term in shock velocity relation
T
Temperature
Tm
Melt temperature
Tref
Reference temperature
V50
Ballistic limit velocity
Vin
Impact velocity
Vr
Residual velocity
Vx
Minimum perforation velocity
YS
Yield strength
Z
Acoustic impedance
#
Grüneisen parameter
Equivalent failure strain
Equivalent plastic strain
Equivalent plastic strain rate
Reference equivalent plastic strain rate
!
Density
!
0
Reference/initial density
Equivalent flow stress
$
*
Stress triaxiality ratio
$
H
Hydrostatic stress
"
Taylor-Quinney coefficient
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Figure 1: Different projectile geometries used for ballistic testing with (a) standard SS109 projectile, (b)
standard M193 projectile and (c) adapted flat-tipped SS109 projectile.
Figure 2: front (a) and back face (a') of a non-perforating impact (impact velocity 911 m/s) and front (b)
and back face (b') for a completely perforating impact (impact velocity 911 m/s).
Figure 3: Different original and recovered projectiles with (a) the original SS109 projectile, (b) an SS109
projectile after perforation of the 1mm bodywork sheet, showing a flattened projectile tip, (c) an SS109
projectile after perforation of the 1 mm bodywork sheet, showing blunting of the projectile tip with
detached ring of the bodywork sheet attached to the projectile tip, and (d) the adapted flat-tipped SS109
projectile.
Figure 4: Protective disks (one attached to the input bar of the SHPB on the left, second placed above the
output bar on the right) used to protect the SHPB (a) from damage (b). The presence of the protective
disks did not alter the wave propagation in the SHPB setup (c).
Figure 5: (a) Typical fracture for specimens tested at a strain rate of 1500 /s; (b) initial and final
temperatures of the specimens after being placed in the SHPB setup.
Figure 6: Stress-strain curves obtained with the SHPB for different temperatures and nominal strain rates
of 1000 /s (a) and 1500 /s (b), and the fitted constitutive strength model (JC: Johnson-Cook).
Figure 7: Comparison of the fracture loci given by the failure model (JC: Johnson-Cook) and the average
experimental data points (a); and statistical evaluation of the failure model for different temperatures by
use of the experimental fracture data (b).
Figure 8: Comparison of the analytical Recht and Ipson model for the simulated and experimental results
for the different projectile geometries; (a) regular SS109 projectile, (b) flat-tipped SS109 projectile, and
(c) regular M193 projectile.
Figure 9: Penetration channel as a function of impact speed for the M193 projectile.; experimental results
for respective impact velocities of 911 m/s (a), 911 m/s (b) and 1062 m/s (c); numerical results for
respective impact velocities of 880 m/s (a’), 900 m/s (b’) and 1100 m/s (c’).
Figure 10: Plugging mechanisms; (a) single plug for low impact velocities; (b) double plug for higher
impact velocties; (c) front face of armour plate for higher impact velocity showing dual diameter.
Table 1: Chemical composition of the ThyssenKrupp Secure 500 ballistic steel.
Table 2: Overview of the different target configurations and their experimental and simulated ballistic
limit velocities (*: deceleration instead of ballistic limit velocity for the 1 mm bodywork sheet).
Table 3: Material models and parameters used to model the Secure 500 steel.
Table 4: Strength models used for the projectile materials.
Table 5: Failure models used for the projectile materials.
Table 6: Equations of state (EOS) used for the projectile materials.
Table 7: Parameters for the Recht and Ipson analytical model and comparison between experimental and
simulated results.