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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: ruansari@rediffmail.com, Telephone: +91-9456404433

Sanaan H. Khan.: E-mail: er.sanan@yahoo.com, Telephone: +91-9045043698

Arshad H. Khan: Email: arshad1976@rediffmail.com, 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.

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