Oblique Impact
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Proceedings of ICTACEM 2010 International Conference on Theoretical, Applied, Computational and Experimental Mechanics
December 27-29, 2010, IIT Kharagpur, India
ICTACEM-2010/XXXX(144)
Oblique Impact of Cylindro-conical Projectile
on Thin Aluminium Plates
R. Ansaria *, Sanaan H. Khan
a and Arshad H. Khan
a
a Mech. Engg. Department, A.M.U., Aligarh-202002, India
ABSTRACT
In the present experimental program an attempt has been made to study the response of thin aluminium plates in
oblique and normal impact of cylidro-conoical projectile in sub-ordnance velocity range. Hardened steel
projectile of 12.8 mm diameter and 30o half cone angle were impacted on to the plates at different obliquities
through a pneumatic gun at varying impact velocities to study the response of the plates. Impact and residual
velocities of the projectile were measured before and after perforation and profile of the perforated plate is drwn
for further calculation. The mode of failure, ballistic limit and energy absorption charecteristics of the plate have
been presented. The experimental results found to be in good agreement with computed results.
Keywords: Oblique impact, Conical projectile, Aluminium plate
1. INTRODUCTION
The study of the impact of projectiles on structural elements has long been of interest in
many engineering application like crashworthiness of vehicles, defense application and
several production processes. The perforation of a target plate due to the impact of a
projectile may occur through various mode of deformation, like petal formation, ductile hole
enlargement, plug formation, and the fragmentation of the target material. Several studies
related to normal impact of projectile have appeared in literature [1-7] however the oblique
impact has not been studied much. Forrestal and Rosenberg [2] developed an engineering
model based partially on the dynamic, elastic-plastic expansion of a cylindrical cavity by a
rigid penetrator. The cylindrical cavity approximation idealizes the target as thin, independent
normal to the penetration direction. Thus, the analysis is simplified to one dimensional
motion in the radial direction. The perforation model of this study was derived from kinetic
energy-work balance and used this cavity expansion as one ingredient. The studies on
projectile perforation of metal plates usually focus on the measurement and prediction of
residual velocity and ballistic limit.
Gupta et al. [6] carried out the experiments on thin aluminium plates by ogive nosed
projectile at normal impact. They carried out the experiments on the aluminium plates of
* Further author information: (Send correspondence to R. Ansari)
R.Ansari.: E-mail: [email protected], Telephone: +91-9456404433
Sanaan H. Khan.: E-mail: [email protected], Telephone: +91-9045043698
Arshad H. Khan: Email: [email protected], Telephone: +91-9412049206
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thicknesses (0.5, 0.74, 1.0, 1.5 and 2 mm) impacted by the ogive nosed projectile with 2.0
calibar radius head (CRH) and 10 and 15 mm diameter and d/h ratio varies from 7.5 to 30.
Gupta and Madhu [9] carried out an experimental investigation on normal and oblique impact
on single and layered targets for jacketed hard-core projectile at an impact velocity of about
820 m/sec. Relations are developed to determine the residual velocity for a plate of thickness
less then „h‟ and to relate h* with the hardness of the material, where h* is the plate for which
820 m/s is the ballistic limit. The oblique impact of a projectile on single plate is an important
aspect of the projectile impact on targets, because most cases of the impact is other than
normal impact in real life situations. The studies related to the oblique impact are quite less
[8-11].
2. EXPERIMENTAL SETUP & PROCEDURE
The aim of this work is to study experimentally the normal and oblique impact of projectile
on thin aluminium plates at sub-ordnance velocity range up to about 100 m/s. The
experimental setup shown in figure 1 is used for carrying out the experiments. It essentially
consist of,
A pneumatic gun for propelling the projectile through the barrel.
An arrangement for measuring the impact velocity of the projectile.
An arrangement for measuring the residual velocity of projectile.
Clamping fixture for holding target plate at different obliquity.
Fig. 1 Overview of the experimental setup.
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The pneumatic gun shown in figure 1 consists of a high-pressure cylinder of 190 mm
internal diameter 215 mm outer diameter and 690 mm in length covered with 30 mm thick
mild steel plates held with eight tie rods of 19 mm diameter and 800 mm length. The
projectile is placed in the barrel through the charging window consisting of a cylindrical
sleeve and a cover with a rectangular ventilated slot of 75 mm x 19 mm. Thick aluminium
tube of 12.8 mm internal diameter and 1.25 m in length is used as barrel. The impact velocity
of projectile is measured before impact with the help of three sets of infrared emitter and
photo-diodes at the exit point of the barrel. A rigid fixture shown in figure 2 is used to clamp
the target plate in such a way that it can rotate the target plate from 0 deg to 90 deg with
respect to axis of the barrel without displacing the center of the target plate. The fixture
consists of 23 mm thick 300 mm x 330 mm plate with eight-tapped hole on 230 mm p.c.d and
a 100 mm through hole at the center. The arrangement is made in such a way that rigidity of
the target plate is maintained.
A number of experiments on aluminium plates of thickness 0.81 and 1.52 mm were carried
out to study the response of the plates subjected to impact of the projectile. Circular plates of
255 mm diameter were cut out of the commercially pure aluminium sheets. Eight holes of
12.7 mm diameter were made at the circumference of each plate to maintain the fixed end
condition. Two sets of aluminium foil screens were placed behind the target at a fixed
distance apart. This distance was kept 104 mm for normal as well as oblique
impact. Each screen was made of two aluminium foils fixed in front and back of a mica sheet
Figure 2. Target holder and arrangement for measuring residual velocity.
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of 3.3 mm thickness to cover a circular hole of diameter 100 mm cut in it. Two of these
screens were placed behind the target for measuring the residual velocity in each experiment,
as shown in figure 2. Impact and residual velocities were recorded in each run with the help
of 4-channel digital storage oscilloscope with a voltage amplifier circuit.
To study the effect of obliquity of the projectile impact on plates, three different angles viz.
30°, 45°, and 60° from normal were selected along with the normal impact of the projectile.
Aluminium plates of 255 mm diameter, similar to one tested in normal impact were rigidly
held on holding fixture at 30° obliquity. The plate then impacted by hardened steel conical
nosed projectile of 12.8 mm diameter, 40.8 mm length, and weighing 31.44 gm at different
impact velocities between 25m/s to 105 m. The hardness of projectile was measured to be Rc
56-57.
Figure 3. Photographs showing 1.52 mm thick aluminium plate and 12.8 mm diameter conical steel projectiles.
3. EXPERIMENTAL RESULTS AND DISCUSSION
3.1 Mechanism of deformation in oblique impact
In case of oblique impact the deformation of the target plate is in the form of unsymmetrical
petalling along with dishing of the plate. It was observed, during experiments, that a single
uniform petal is initially formed in the direction of motion of the projectile and two non-
uniform petals were formed on the sides of the first petal (see figure 4 and 5). The first petal
was normally bent and rolled completely along the movement of the projectile. As the impact
angle decreases, the mode of deformation tends to be symmetrical, wherein 3 or 4 petals were
formed. The mechanism of deformation of single plates in an oblique impact is quite different
than that of a normal impact.
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Figure 4. Impacted plates showing partial penetration at the center of 1.52mm and perforation of 0.81mm thick
aluminium plate at 30 and 45 degree obliquity respectively.
Figure 5. Photographs of the impacted plate showing indent and petal formation of the 1.52 mm thick
aluminium plate at 60 degree obliquity.
3.2 Effect of plate thickness and obliquity
The overall response of aluminium plates of two thicknesses at normal projectile
impact and at 45 degree obliquity are given in Table 1 and 2. The residual velocity increases
and velocity drop decreases with increase in impact velocity of the projectile for normal as
well as oblique impact. The velocity drop and energy absorbed increases with increase in
plate thickness. The overall velocity drop and energy absorbed for a particular plate thickness
increases with increase in obliquity. Ricochet of the projectile has been observed at 54 m/s
for 1.52 mm thick plate at 45 degree obliquity whereas the same plate is perforated at a lower
impact velocity (40 m/s) in case of normal impact.
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Table 1. Response of aluminum plates at normal impact
S.
No.
Plate
Thickness
(mm)
Impact
Velocity
(m/s)
Residual
Velocity
(m/s)
Velocity
Drop
(m/s)
Impact
Energy
(N-m)
Energy
Absorbed
(N-m)
*Remark
1. 0.81 25 …….. 25 14.15 …….. NP
2. 34.72 18.3 16.42 18.95 13.69 P
3. 44.64 30.32 14.41 31.32 16.99 P
4. 54.34 44.78 9.56 46.42 14.9 P
5. 62.5 61 1.5 61.4 2.91 P
6. 78.3 71.5 6.8 95.95 15.59 P
7. 83.33 74.2 9.13 109.07 22.52 P
8. 104.16 98.7 5.4 170.55 17.47 P
1. 1.52 40 5.6 34.4 25.15 24.64 P
2. 49 18.5 30.5 37.74 32.36 P
3. 62.5 42.5 20 61.4 33.01 P
4. 69.44 58 11.44 75.8 22.92 P
5. 78.13 60 18.13 95.95 15.59 P
6. 83.33 73.4 9.93 109.15 24.46 P
7. 96.15 82 14.15 145.32 39.62 P
Table 2. Response of aluminum plates at 45 degree oblique impact
S.
No.
Plate
Thickness
(mm)
Impact
Velocity
(m/s)
Residual
Velocity
(m/s)
Velocity
Drop
(m/s)
Impact
Energy
(N-m)
Energy
Absorbed
(N-m)
*Remark
1. 0.81 36 5.7 30.3 20.37 19.86 P
2. 44.64 34.21 10.43 31.27 12.87 P
3. 62.8 53.61 8.98 61.99 16.81 P
4. 78.13 74.9 3.23 95.95 7.77 P
5. 96.15 84.7 11.45 145.32 32.55 P
1. 1.52 53.7 …….. 53.7 45.33 …….. Ri
2. 65.79 48.6 17.19 68.04 30.91 P
3. 78.13 53.4 24.73 95.95 51.73 P
4. 89.29 80.0 9.29 125.33 24.72 P
5. 104.16 83.7 20.46 170.55 60.42 P
*P -Perforated
NP-Not Perforated
Ri -Ricochet
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The variation of the different output parameters of the plate at different obliquities with
respect to impact velocity and impact energy are shown in figure 6, 7 and 8. It is found that
the residual velocity increases with increase in impact velocity. This increase is more rapid
initially and later the curve of residual velocity versus impact velocity tends to become linear.
This trend is similar for each angle of obliquity as shown in figures 6.
Figure 6. Comparison of experimental residual velocity with results obtained from Eq 1and 2.
Figure 7. Comparison of experimental Velocity drop with results obtained from Eq. 2 and 3.
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The velocity drop for 0.81 mm thick plate at different obliquity is shown in figure 7. The
velocity drop decreases steeply near the ballistic limit and it tends to be constant afterwards
for each plate thickness. The trend is similar for each angle of obliquity. The energy of the
projectile absorbed by the plate of 1.52 mm at different impact energies and obliquities are
shown in figure 8. It is found that the absorbed energy increases with increase of obliquity.
Figure 8. Comparison of experimental absorbed energy with results obtained from Eq 4and 8.
3.3 Effect of obliquity on plate profile
The deformation of the perforated plate near and away from the impact region was measured
with the help of a dial gauge setup. It was found from experiments that the deformation is
approximately symmetrical about the horizontal diameter of the plate in normal impact,
whereas in case of oblique impact the deformation about the horizontal diameter is
unsymmetrical. The deformation of the perforated plates in case of normal impact for
different thicknesses is shown in the figure 9 and it is observed that the deformation of the
plate, in general increases with increase in thickness of the target plate. The deflection is
large near the point of impact and gets reduced towards the circumference. In the case of
oblique impact, it is found that the deformation of the perforated target plate decreases with
increase in angle of obliquity (refer Fig. 10).
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Figure 9. Plate profiles of 0.81 and 1.52mm thickness at 0 and 30 degree obliquity.
Figure 10. Plate profile of 1.52 mm thick plate impacted at different angles of obliquity.
4. ANALYSIS
It is found on the basis of the experimental observation that the primary modes of failure in
plates of ductile materials are petalling along with dishing of the plate when impacted by
conical nose projectile. Thus the total mode of deformation is divided into two types;
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1. Deformation of the plate in the contact region of the plate and projectile (petalling).
2. Deformation in rest part of the plate (dishing).
Total work done for petalling in case of normal impact is given by [11]
(a)
and for dishing
(b) thus total work done in case of normal impact W=W1+W2
(c)
Now, total work done in case of oblique impact Wob has been calculated by introducing
effective thickness heff in place of h0 in equation (c)
(d)
Where R is the radius of projectile, h0 is the thickness of the plate, Y is yield strength of the
plate material (95 MPa), ρt is density of the target (2690 kg/m3), Vi is impact velocity, ln is the
nose length, wc is the deflection of the plate at centre, a is a constant obtained from plate
profile, lcr is the crack length and ν is the Poisson‟s ratio of the plate material (0.3).
Using energy balance before and after impact in normal as well as oblique impact, the
residual velocity Vr, velocity drop Vd and energy of the projectile absorbed by the plate Eab is
given by
(1)
(2)
Vd = Vi - Vr or Vdo = Vi – Vro (3)
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Eab = W (4)
Eabo = Wob (5)
The firm lines in figures 6, 7 and 8 are representing the above equations.
4.1 Comparison with existing model
The experimental results obtained in normal as well as oblique impact are also compared with
existing model [2] in the literature in which residual velocity is given as
(6)
Where Vbl is the ballistic limit of the plate, σr and σs are dynamic radial stress and quasi-static
radial stress respectively. The ratio of the two is taken in this case as unity because the
increase in σr/ σs has small effect on Vr whereas (Vi/ Vbl )2
has larger effect on Vr
The dash lines in figure 6, 7 and 8 are drawn with help of equation (6).
It is evident from these figures that the model proposed shows better correlation with
experimental values than the existing model in the employed range of velocity.
5. CONCLUSION
It is found experimentally that the thin aluminium plates fail by petalling in the
contact region and dishing in rest part of the plate. Generally 3 to 5 petals were
formed in case of normal impact and 3 petals in oblique impact; on in the direction of
motion of projectile and one each in either side.
Dishing increases with increases in thickness of the plate and decreases with increase
in impact angle and the impact velocity of the projectile.
The residual velocity of the projectile increases with increase in impact velocity and
decreases with increase of plate thickness and angle of obliquity. The increase in
residual velocity is rapid near the ballistic limit and then their curve tends to be linear.
Ballistic limit of the target plate increases with increase in plate thickness and angle of
obliquity.
The absorbed energy for a particular plate thickness is almost constant at varying
impact energy and this energy increases with increase in the plate thickness and angle
of obliquity.
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The velocity drop decreases steeply near the ballistic limit and then on their curve
tends to be constant, for a particular plate thickness, with increase in impact velocity.
The velocity drop increases with the increase in plate thickness and angle of obliquity.
REFERENCES
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Review”, Int. J. Impact Engg. 18, pp. 141 —230, 1995.
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rods”, Transactions of ASME, 54, pp. 230 —232, 1987.
3. Backman M.E. and Goldsmith W., “The mechanics ofpenetration of projectiles into targets”, Int. J. Engg.
Sci. 16, pp. 1-94, 1978.
4. Colder C.A. and Goldsmith, “Plastic Deformation and preforation of thin plates resulting from projectile
impact”, Int. J. Impact Engg., pp. 863-879, 1971.
5. Thomson, W.T. “An approximate theory of arms penetration”, J.Appi. Phys. 26, pp. 80-82, 1955.
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Impact Engg., 25, pp. 64 1-660, 2001.
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impact”, Int. J. Impact Engg., pp. 863-879, 1971.
8. Goldsmith W. and Finnegan “Normal and oblique impact of cylindro condal and cylindrical projectiles on
metallic plates”, Int. J. Impact Engg., 4, pp. 83-105, 1986.
9. Gupta N.K and Modhu V. “An Experimental study of normal and oblique impact of hard core projectile on
single and layered plates “, Int. J. Impact Engg., 19, pp. 395 -414, 1997.
10. Goldsmith W. and Finnegan “Normal and oblique impact of cylindro conical and cylindrical projectiles on
metallic plates”, Tnt. J. Impact Engg., Vol-4, pp. 83-105, 1986.
11. Afzal M.,”Normal and Oblique Impact of Conical Projectiles on Thin Plates” M.Tech. Theses, Mech.
Engg. Dept., A.M.U., Aligarh, 2004.