Effect of target span and configuration on the ballistic limit

International Journal of Impact Engineering 42 (2012) 11e24

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Effect of target span and configuration on the ballistic limit M.A. Iqbal a, *, P.K. Gupta a, V.S. Deore a, S.K. Tak a, G. Tiwari a, N.K. Gupta b a b

Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 July 2010 Received in revised form 10 October 2011 Accepted 25 October 2011 Available online 15 November 2011

Three-dimensional numerical simulations were carried out with ABAQUS/Explicit finite element code to study the influence of target span and configuration on its ballistic limit. 1 mm thick 1100-H12 aluminum targets of varying span diameter and configuration were impacted by blunt and ogive nosed projectiles of 19 mm diameter and 52.5 g mass. The effect of target span was studied by varying the span diameter of 1 mm thick monolithic target as 50 mm, 100 mm, 204 mm, 255 mm and 500 mm. The effect of configuration was studied by taking the monolithic, double layered in-contact and double layered spaced targets of 1 mm equivalent thickness and 255 mm span diameter. The spacing between the layers was varied as 2 mm, 5 mm, 10 mm, 20 mm and 30 mm. In each case the target was impacted normally by blunt and ogive nosed projectile to obtain the ballistic limit. The highest ballistic limit was observed for monolithic target followed by layered in-contact and spaced targets respectively. The variation of spacing between the layers did not have significant influence on the ballistic limit in the case of ogive projectile but some effect was seen in the case of blunt projectile. The ballistic limit was found to increase with increase in target span diameter for both the projectiles and it was found to be higher for blunt nosed projectile as compared to that of ogive nosed projectile for all the spans considered excepting in the case of 50 mm span for which it was higher for ogive nosed projectile. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Span diameter Layered target Spaced target Projectile nose shape ABAQUS

1. Introduction Ballistic resistance of metallic targets such as armored vehicle, military bunker and shields to arms and explosive is influenced by various parameters such as target thickness, its configuration, effective span, angle of incidence and projectile nose shape. The influence of some of these parameters such as projectile nose shape, angle of incidence and target thickness has been significantly studied in the literature. The configuration of target is another important parameter influence of which has also been studied in the literature. It has been observed that a layered target may offer greater resistance than equivalent monolithic target when the deformation mode changes from bending to membrane stretching of individual layer. Marom and Bonder [1] carried out analytical and experimental studies on the ballistic resistance of thin flat aluminum beams arranged in various layers in-contact as well as spaced, impacted by 0.22 in. caliber projectiles. The multi-layered beams in-contact showed greater resistance to penetration than the equivalent monolithic beams. Corran et al. [2] investigated the performance of

* Corresponding author. Tel.: þ91 1332 285866. E-mail addresses: [email protected], [email protected] (M.A. Iqbal). 0734-743X/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2011.10.004

multi-layered steel plates under projectile impact. Layers placed incontact were found superior to equivalent monolithic plate when the response of individual layer changed from petalling and shearing to membrane stretching. Radin and Goldsmith [3] studied the ballistic resistance of monolithic and layered targets of 20240 aluminum and polycarbonate with blunt and 60
conically-nosed projectiles. Ballistic resistance of adjacent layers was found lesser than that of the equivalent monolithic target. Spaced targets were found less effective than layered in-contact targets. Nurick and Walter [4] studied the penetration resistance of layered and spaced steel plates using conical and blunt projectiles. Ballistic limit of monolithic plate was 4e8% higher than that of in-contact layered plate of equivalent thickness. The layered spaced targets were found less efficient when compared to the layered in-contact targets of equivalent thickness. Ballistic limit decreased when the spacing between the targets was increased. The decrease in the ballistic limit was more significant in the case of blunt projectile. Almohandes et al. [5] investigated experimentally the ballistic resistance of single and layered steel plates impacted by 7.62 mm standard bullets. The effect of number, thickness and arrangement of layer was explored. Single steel plates were found to be more effective than layered plate of equal thickness. The resistance of layered plate increased as the number of layers decreased and the thickness of back plate increased. Gupta et al. [6,7] studied

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M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

Fig. 1. Finite element model; (a) ogive nosed projectile case; (b) blunt nosed projectile case.

Table 1 Material parameters for 1100-H12 aluminum target. Modulus of Elasticity, E (N/mm2) Poison’s Ratio, n Density, r (kg/m3) Yield Stress, A (N/mm2) B (N/mm2) n Reference Strain Rate, έ0 (s1) C m Tmelt (K) T0 (K) Specific Heat, Cp (J/kg K) Inelastic heat fraction, a D1 D2 D3 D4 D5

65762 0.3 2700 148.361 345.513 0.183 1.0 0.001 0.859 893 293 920 0.9 0.071 1.248 1.142 0.0097 0.0

experimental and numerical behavior of single and layered 1100H12 aluminum plates impacted by blunt, ogive and hemispherical nosed projectiles. For two layered plate the residual velocity of projectile was comparable to that of the single plate of equivalent

thickness, however, when the number of layers was increased the velocity drop in equivalent monolithic plate was found to be higher. Dey et al. [8] studied the ballistic response of Weldox 700 E steel plates impacted by blunt and ogive nosed projectiles through experiments and numerical simulations. For blunt nosed projectile two layered plate of 6 mm thickness showed better resistance as compared to 12 mm thick monolithic plate. When two layers were separated by 24 mm air gap the resistance was greater than monolithic plate but lesser than layered in-contact plate. For ogive nosed projectile however, monolithic plate showed highest resistance followed by layered in-contact and spaced plates respectively. Teng and Wierzbicki [9] performed numerical simulations wherein monolithic and double layered steel plates of 12 mm thickness having different ductility were impacted by blunt and conical nosed projectiles of different masses. The configuration with front layer of high ductility and low strength material and the rear layer of low ductility and high strength material gave highest ballistic resistance. The subject of target configuration has been studied in literature by varying the number of in-contact as well as spaced layers. The order of layering of the plates with different thicknesses and material has also been studied. However, available studies have

Table 2 Experimental and numerical results for varying configuration of 1 mm thick target impacted by ogive nosed projectile. Total Target Thickness ¼ 1 mm, Span Diameter ¼ 255 mm Ogive Nosed Projectile (Mass ¼ 52.5 g, Diameter ¼ 19 mm) Experimental Results Gupta et al. [7]

Axi-symmetric Numerical Results Gupta et al. [7]

Double Layered Target

3D Numerical Results of Present Study

Monolithic Target

Double Layered Target

Spaced Target 10 mm

20 mm

30 mm

Impact Velocity Vi (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

116.19 110.44 103.52 95.26 89.55 85.61 77.4 64.46 60.0 54.77 53.0 50.0 46.0 45.0 44.0 41.3 39.18

104.96 96.91 85.87 73.99 64.49 56.89 43.26 25.35 e 12.0 e e e e e e 0

109.48 99.89 88.82 75.9 67.01 58.49 46.13 29.72 e 14.85 e e e e e 0 e

102.27 96.21 88.19 74.52 66.33 62.87 53.1 32.19 14.31 e 0 e e e e e e

104.83 98.85 91.0 81.7 74.56 68.26 59.54 40.76 e 22.39 e 12.58 0 e e e e

107.6 101.3 93.5 84.3 77.6 73.2 62.8 45.5 e 31.0 e e 6.36 1.5 0 e e

107.7 101.4 93.6 84.4 77.7 73.18 62.71 45.6 e 31.0 e e 6.73 1.9 0 e e

107.6 101.3 93.5 84.4 77.7 73.2 62.8 45.7 e 30.7 e e 7.19 2.1 0 e e

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Table 3 Experimental and numerical results for varying configuration of 1 mm thick target impacted by blunt nosed projectile. Total Target Thickness ¼ 1 mm, Span Diameter ¼ 255 mm Blunt Nosed Projectile (Mass ¼ 52.5 g, Diameter ¼ 19 mm) Experimental Results Gupta et al. [7]

Axi-symmetric Numerical Results Gupta et al. [7]

Double Layered Target

3D Numerical Results of Present Study

Monolithic Target

Double Layered Target

Spaced Target 10 mm

20 mm

30 mm

Impact Velocity Vi (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

120.64 116.13 113.92 107.73 98.15 92.33 88.47 81.32 76.0 75.0 73.8 72.0 69.34 66.93 66.0 64.0 58.63 51.22

105.28 99.53 95.51 86.43 75.2 66.92 60.44 49.61 e e e e e 29.63 e e e 0

109.0 102.99 98.24 89.16 74.96 65.67 58.8 44.6 e e e e e 25.99 e e 0 e

105.2 99.52 96.76 88.82 74.3 65.37 58.72 44.03 27.66 e 0 e e e e e e e

101.5 95.7 92.8 84.2 69.8 59.6 52.3 36.0 e 17.08 5.19 0 e e e e e e

102.59 97.13 94.6 87.38 74.3 66.0 59.5 45.8 e e e e 1.94 0 e e e e

104.14 99.2 96.7 89.2 76.9 68.8 62.8 51.1 e e e e e 12.0 6.31 0 e e

104.3 99.3 96.7 89.4 77.3 69.2 63.2 51.0 e e e e e 11.8 7.14 0 e e

disagreement regarding the efficiency of monolithic, layered and spaced targets. The influence of projectile nose shape on target configuration is also not clear and requires more investigation. On the other hand there is hardly any study wherein the span of the target has been varied to understand its effect on the ballistic limit. The present numerical study describes the effect of target span diameter and configuration on the ballistic limit. 1 mm thick monolithic 1100-H12 aluminum targets of span diameters 50 mm,

100 mm, 204 mm, 255 mm and 500 mm were impacted by blunt and ogive nosed projectiles to obtain ballistic limit. The configuration of 255 mm span diameter target was also varied as monolithic, double layered in-contact and double layered spaced of equivalent thickness 1 mm. Spacing between the layers was varied as 2 mm, 5 mm, 10 mm, 20 mm and 30 mm. The target with varying configuration was also impacted by blunt and ogive nosed projectile in order to obtain ballistic limit. To study the influence of target

Table 4 Experimental and numerical results for 1 mm thick monolithic target with varying span diameter impacted by ogive nosed projectile. Target Thickness ¼ 1 mm Ogive Nosed Projectile (Mass ¼ 52.5 g, Diameter ¼ 19 mm) Experimental Results Gupta et al. [7]

Axi-Symmetric Numerical Results Gupta et al. [7]

3D Numerical Results of Present Study

Span Diameter 255 mm

Span Diameter 255 mm

Span Diameter 50 mm

Span Diameter 100 mm

Span Diameter 204 mm

Span Diameter 255 mm

Span Diameter 500 mm

Impact Velocity Vi (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

112.72 97.23 82.97 81.91 73.30 65.80 59.00 58.85 57.28 55.50 52.50 52.10 51.60 51.27 50.0 48.0 46.5 45.3

99.11 78.26 61.62 58.19 44.38 29.68 e e 17.86 e e e e 8.72 e e e 0

95.64 73.25 55.71 53.27 38.67 26.04 e e 15.93 e e 0 e e e e e e

99.2 83.05 66.89 65.3 52.33 40.41 32.64 32.54 29.73 27.73 21.32 20.01 19.16 18.2 14.25 5.2 0 e

96.85 80.91 65.09 64.17 50.66 37.3 30.83 29.78 27.64 24.55 18.4 16.19 15.13 12.7 9.2 0 e e

95.49 80.01 61.66 60.20 43.08 27.24 21.34 20.72 19.68 14.62 7.15 4.35 0 e e e e e

95.14 79.69 61.54 60.45 45.40 27.03 13.96 13.13 12.12 6.62 0 e e e e e e e

94.97 79.57 61.02 62.03 39.33 26.67 6.24 0 e e e e e e e e e e

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Table 5 Experimental and numerical results for 1 mm thick monolithic target with varying span diameter impacted by blunt nosed projectile. Target Thickness ¼ 1 mm Blunt Nosed Projectile (Mass ¼ 52.5 g, Diameter ¼ 19 mm) Experimental Results Gupta et al. [7]

Axi-symmetric Numerical Results Gupta et al. [7]

3D Numerical Results of Present Study

Span Diameter 255 mm

Span Diameter 255 mm

Span Diameter 50 mm

Span Diameter 100 mm

Span Diameter 204 mm

Span Diameter 255 mm

Span Diameter 500 mm

Impact Velocity Vi (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

Residual Velocity Vr (m/s)

115.6 104.03 102.5 92.45 87.45 78.45 77.50 77.20 75.0 74.70 73.98 73.0 72.70 66.70 61.3 55.23 52.0 48.23 45.0 42.5

92.98 80.17 79.16 67.45 58.26 e e e e e 43.84 e e e 0 e e e e e

98.66 83.91 82.51 63.30 53.15 e e e e e 40.64 e e 0 e e e e e e

102.47 90.21 88.46 78.015 72.61 62.61 61.53 61.21 58.68 58.27 57.45 56.27 55.95 48.48 e 32.57 e 19.72 11.21 0

97.49 81.77 79.91 65.54 58.41 46.34 45.16 44.71 42.1 41.68 40.82 39.66 39.26 32.5 26.08 e 9.35 0 e e

97.09 80.70 78.75 63.59 54.73 34.02 30.28 29.36 e 18.91 13.06 3.8 0 e e e e e e e

96.96 80.31 78.11 62.90 53.76 31.22 26.79 25.66 5.91 0 e e e e e e e e e e

96.58 80.01 77.62 62.10 52.33 23.74 15.24 0 e e e e e e e e e e e e

span, impact velocities of projectiles were kept identical to those obtained during experiments carried out by Gupta et al. [7] on 1 mm thick monolithic target. To study the influence of target configuration, impact velocities of projectiles were kept identical to those obtained during experiments carried out by Gupta et al. [7] on 0.5 mm thick double layered in-contact target. In general the ballistic limit was found to increase with an increase in target span diameter. Monolithic targets were found to offer highest ballistic limit followed by layered in-contact and layered spaced targets of equivalent thickness. Spacing between the layers was found to have some influence on the ballistic limit for blunt nosed projectile. Moreover, blunt nosed projectile experienced higher ballistic limit velocity at each configuration and span diameter except for 50 mm span diameter for which ogive nosed projectile experienced higher ballistic limit velocity.

120

The present study is based on the numerical investigation of ballistic resistance of monolithic and layered, both in-contact and spaced, targets. 1100-H12 aluminum targets of 1 mm equivalent thickness were impacted by blunt and ogive nosed projectiles of 19 mm diameter and 52.5 g mass. Three-dimensional finite element model of the projectile and target was made using ABAQUS/CAE. Fig. 1 shows a typical finite element model of the projectile and target. Projectile was modeled as rigid and the target as a deformable body. To model the spaced target a predefined spacing was given between both the layers. The contact between the projectile and target was modeled using kinematic contact algorithm of ABAQUS-6.7-3 [10]. Outer surface of the projectile was modeled as the master surface and the contact region of the target as node

120

Experimental results (Gupta et al.) Axi-symmentric numerical results (Gupta et al.) 3D numerical results (present study)

100 Residual Velocity (ms)

100 Residual Velocity (m/s)

2. Numerical investigation

80 60 40

Experimental results (Gupta et al.) Axi-symmetric numerical results (Gupta et al.) 3D numerical results (present study)

80 60 40 20

20

a

0 35

55 75 95 Impact Velocity (m/s)

115

b

0 35

55

75

95

115

Impact Velocity (m/s)

Fig. 2. Comparison of present three-dimensional numerical results with the previous experimental and axi-symmetric numerical studies for 0.5 mm thick double layered 1100-H12 aluminum target impacted by (a) ogive nosed projectile; (b) blunt nosed projectile.

M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

120

100 Residual Velocity (ms)

100 Residual Velocity (m/s)

120

Experimental results (Gupta et al.) Axi-symmentric numerical results (Gupta et al.) 3D numerical results (present study)

80 60 40

15

Experimental results (Gupta et al.) Axi-symmetric numerical results (Gupta et al.) 3D numerical results (present study)

80 60 40 20

20

a

0

35

55 75 95 Impact Velocity (m/s)

115

b

0

50

70

90

110

130

Impact Velocity (m/s)

Fig. 3. Comparison of present three-dimensional numerical results with the previous experimental and axi-symmetric numerical studies for 1 mm thick monolithic 1100-H12 aluminum target impacted by (a) ogive nosed projectile; (b) blunt nosed projectile.

based slave surface. Frictional effects were not considered between the target and projectile due to small target thickness. The contact between the contacting surfaces of layered in-contact as well as spaced target was modeled using general contact algorithm of ABAQUS-6.7-3 [10]. The rear surface of front layer was considered as master surface and front surface of rear layer was considered as the slave surface. A coefficient of friction of 0.5 was assigned between the contacting surfaces of layered in-contact target. The value of coefficient of friction was obtained from inclined plane experiments, Gupta et al. [7]. Effect of friction was considered negligible between the contacting surfaces of spaced target. In the case of layered in-contact as well as spaced target the contact of projectile with both the layers was assigned. The geometry, length (50.8 mm), mass (52.5 g) and diameter (19 mm) of blunt and ogive nosed projectiles was kept identical to those of the projectiles used by Gupta et al. [7]. The target was restrained at its periphery with respect to all degrees of freedom. Eight node brick elements (C3D8R) were used in all the simulations carried out in this study.

The meshing of the target was done in such a manner that accurate results can be obtained within the available computational facility. Mesh was highly refined and the element aspect ratio was kept unity in the central influenced region. A mesh convergence study was carried out wherein the size of element in 1 mm thick monolithic target was varied by varying the number of elements over thickness from 3 to 7, and the target was impacted at each mesh configuration by ogive nosed projectile at a constant velocity of 64.46 m/s. Hence the target was meshed with five different configurations taking element size 0.33  0.33  0.33 mm3, 0.25  0.25  0.25 mm3, 0.20  0.20  0.20 mm3,0.16  0.16  0.16 mm3 and 0.14  0.14  0.14 mm3 corresponding to 3, 4, 5, 6 and 7 elements respectively. The residual velocity of projectile was found to be 17.92 m/s, 28.14 m/s, 29.4 m/s, 32.19 m/s and 32.41 m/s corresponding to 3, 4, 5, 6 and 7 elements respectively. The velocity drop of projectile decreased up to 5 elements and thereafter it became almost constant. It was therefore decided to mesh the monolithic target with 6 elements over thickness. Another mesh

Fig. 4. Fracture modes of 1 mm thick monolithic and 0.5 mm thick double layered target impacted by (a) ogive nosed projectile; (b) blunt nosed projectile.

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Fig. 5. Perforation of 1 mm thick monolithic target by ogive and blunt nosed projectiles.

Fig. 6. Perforation of 0.5 mm thick double layered in-contact targets by ogive and blunt nosed projectiles.

Fig. 7. Perforation of 0.5 mm thick double layered target with 10 mm spacing by ogive and blunt nosed projectiles.

M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

120

Monolithic Layered incontact 10mm spaced 20mm spaced 30mm spaced

100 80 60 40 20

80 60 40

20

a

0

40

60 80 100 Impact Velocity (m/s)

Monolithic Layered incontact 10 mm spaced 20 mm spaced 30mm spaced

100

Residual Velocity (m/s)

Residual Velocity (m/s)

120

17

b

0 60

120

80 100 Impact Velocity (m/s)

120

Fig. 8. Impact and residual velocity curves for 1 mm thick monolithic, 0.5 mm thick double layered in-contact and 0.5 mm thick double layered spaced targets impacted by (a) ogive nosed projectile; (b) blunt nosed projectile.

Table 6 Ballistic limit of different configurations of 1 mm thick target. Target Configuration

Monolithic Double layered in-contact 2 mm Spacing 5 mm Spacing 10 mm Spacing 20 mm Spacing 30 mm Spacing

Ballistic Limit (V50 m/s) Ogive Nosed Projectile

Blunt Nosed Projectile

56.5 48.0 44.9 44.6 44.5 44.5 44.5

74.9 72.9 69.3 68.7 68.1 65.0 65.0

3. Constitutive model

convergence study was carried out for layered and spaced target wherein each layer of layered in-contact and 10 mm spaced target was meshed with 3, 4 and 5 elements at the thickness. The corresponding size of element was 0.16  0.16  0.16 mm3, 0.125  0.125  0.125 mm3 and 0.1  0.1  0.1 mm3 and the total number of elements was 199,178, 208,482 and 388,882 in the whole model respectively. The layered in-contact and 10 mm spaced target with the above mesh configurations was hit by ogive nosed projectile at 64.46 m/s velocity. The residual velocity was found to be 40.8 m/s, 41.4 m/s and 41.4 m/s for layered in-contact and 45.5 m/s, 45.61 m/s and 45.67 m/s for spaced target corresponding to 3, 4 and 5 elements respectively. A typical simulation for layered in-contact and spaced target with 3, 4 and 5 elements took about 36, 73 and 144 CPU hours respectively on HP xW 4600 Xeon Workstation. As the time taken for each simulation was very

60

The material behavior of 1100-H12 aluminum target was incorporated in the numerical simulations using JohnsoneCook elasto-viscoplastic material model [11,12]. It includes the effect of linear thermo-elasticity, yielding, plastic flow, isotropic strain hardening, strain rate hardening, softening due to adiabatic heating and damage. The equivalent von-Mises stress s of the JohnsoneCook model is expressed as;




s

54 52 50 48 46





"

 pl n

¼ A þ Bð3 Þ

1 þ Cln

3_

pl

3_ 0

!# h

i bm ; 1T

(1)

(2)

where T is the current temperature, Tmelt is the melting temperature and T0 is the room temperature. The fracture model proposed by JohnsoneCook [11] takes into account the effect of stress

76

b

74 72 70 68 66

44

64

42

62

Target Configuration

pl b ; 3_ ; T

b ¼ ðT  T0 Þ=ðTmelt  T0 Þ T0  T  Tmelt T

Ballistic limit (m/s)

56

3

p1

where A, B, n, C and m are material parameters. 3 pl is equivalent pl plastic strain, 3_ is equivalent plastic strain rate, 3_ 0 is a reference b is non dimensional temperature defined as; strain rate and T

a

58 Ballistic limit (m/s)

high and the residual velocity obtained for each of the three mesh configurations was almost identical therefore all the simulations of layered in-contact and spaced target were run with 3 elements over thickness.

Target Configuration

Fig. 9. Variation of ballistic limit with target configuration of 1 mm equivalent thickness (a) for ogive nosed projectile; (b) for blunt nosed projectile.

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M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

120 120 Residual Velocity (m/s)

100

Residual Velocity (m/s)

Span 50 mm Span 100 mm Span 204 mm Span 255 mm Span 500 mm

80 60 40

Span 50 mm Span 100 mm Span 204 mm Span 255 mm Span 500 mm

100 80 60 40 20

20

a 0

b

0 40

50

60 70 80 90 100 110 Impact Velocity (m/s)

40

50

60

70

80

90 100 110 120

Impact Velocity (m/s)

Fig. 10. Comparison of impact and residual velocities for varying span diameter of 1 mm thick monolithic target impacted by (a) ogive nosed projectile and (b) blunt nosed projectile.

Table 7 Ballistic limit of 1 mm thick monolithic target with varying span diameter. Target Span Diameter (mm)

50 100 204 255 500

model as well as the identification procedure of the material parameters is mentioned in our earlier study, Gupta et al. [13].

Ballistic Limit (V50 m/s) Ogive Nosed Projectile

Blunt Nosed Projectile

47.25 49.0 51.8 54.0 58.9

43.75 51.0 72.8 74.8 77.3

triaxiality, strain rate and temperature on the equivalent fracture pl strain. The equivalent fracture strain 3 f is expressed as; 3

pl f


s

m

s

b ; 3_ ; T pl



" h
s i m 1 þ D4 ln ¼ D1 þ D2 exp D3 h

i b ;  1 þ D5 T

s

3_

pl

!#

3_ 0

(3)

where D1eD5 are material parameters, sm =s is the stress triaxiality ratio and sm is the mean stress. The material parameters used in the present investigation are given in Table 1. The detail of the material

4. Results and discussion The results of the present numerical study for varying target configuration are shown in Tables 2 and 3 in the form of impact and residual velocities of ogive and blunt nosed projectiles respectively. Each projectile was impacted normally on 1 mm thick targets which were monolithic, double layered in-contact and double layered with different spacings. Monolithic target offered highest ballistic limit followed by layered in-contact and layered spaced targets respectively for both the projectiles. The spacing between the layers also affected the ballistic limit. However, this effect was prominent against blunt nosed projectile only. The results for varying span diameter are presented in Tables 4 and 5 in the form of impact and residual velocities of ogive and blunt nosed projectiles respectively. It was observed that the ballistic limit of target increases with an increase in span diameter. Again, the increase in the ballistic limit with span diameter was more significant for blunt nosed projectile. Fig. 2 130

Energy absorbed in bending (Joule)

Ogive Blunt

80 Ballistic limit (m/s)

50 mm span 100 mm span 204 mm span 255 mm span 500 mm span

120

90

70

60

50

110 100 90 80 70 60 50 40 30 20 10 130

40 0

50 100 150 200 250 300 350 400 450 500

160

190

220

250

280

310

340

Impact energy (Joule)

Span diameter (mm) Fig. 11. Variation of ballistic limit with the target span diameter.

Fig. 12. Energy absorbed in bending for 1 mm thick monolithic target impacted by blunt nosed projectile.

M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

120

ogive Blunt

100 80 60 40 20

70 90 110 Impact velocity (m/s)

60 40

130

120

b

Blunt

80 60 40

40

60 80 100 Impact velocity (m/s)

Blunt

100 80 60 40

c

0 40

Blunt

80

60 40 20

d

0 40

60 80 100 120 Impact Velocity (m/s)

Ogive

100

20

20

120

120

Ogive Residual Velocity (m/s)

Ogive Residual Velocity (m/s)

Residual Velocity (m/s)

80

0 50

100

Blunt

20

a

0

120

Ogive

100 Residual velocity (m/s)

Residual Velocity (m/s)

120

19

e

0 40

60 80 100 120 Impact Velocity (m/s)

60 80 100 120 Impact Velocity (m/s)

Fig. 13. Comparison of impact and residual velocities of blunt and ogive nosed projectiles impacted on targets (a) 1 mm thick monolithic; (b) 0.5 mm thick double layered incontact; (c) 0.5 mm thick double layered with 10 mm spacing; (d) 0.5 mm thick double layered with 20 mm spacing; (e) 0.5 mm thick double layered with 30 mm spacing.

120

Blunt

80 60

40 20

80 60

40

b 0

40

60 80 100 Impact velocity (m/s)

120

Ogive Blunt

100

120

40

60 80 100 Impact velocity (m/s)

120

ogive Blunt

100

80 60 40 20

80 60 40 20

c

0 40

60 80 100 Impact velocity (m/s)

120

120

ogive Blunt

100

Residual Velocity (m/s)

Residual Velocity (m/s)

Residual Velocity (m/s)

Blunt

20

a

0

120

ogive

100 Residual Velocity (m/s)

100

Residual Velocity (m/s)

120

ogive

80 60 40 20

d

0 50

70 90 110 Impact velocity (m/s)

130

e

0 50

70 90 110 Impact velocity (m/s)

130

Fig. 14. Comparison of impact and residual velocities of blunt and ogive nosed projectiles impacted on 1 mm thick monolithic target with span diameter: (a) 50 mm, (b) 100 mm; (c) 204 mm; (d) 255 mm; (e) 500 mm.

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M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

Plate deformation (mm)

compares the results of present three-dimensional numerical study with the experimental and axi-symmetric numerical studies carried out by Gupta et al. [7] on double layered 0.5 mm thick plates in-contact. For ogive nosed projectile the ballistic limit of this target was found to be 48.0 m/s from the present numerical simulation and 46.9 m/s from the experiments. While for blunt nosed projectile it was found to be 72.9 m/s from the present numerical simulation and 59 m/s from the experiments. Fig. 3 compares the results of present numerical study with experiments and axisymmetric numerical simulations carried out by Gupta et al. [7] for 1 mm thick monolithic target of 255 mm span diameter. For ogive nosed projectile the ballistic limit of target was found to be 54 m/s from the present numerical study and 48.2 m/s from the experiments. For blunt nosed projectile the same was found to be 74.8 m/s from the present numerical study and 67.6 m/s from the experiments. Fig. 4(a) shows the failure mode of 1 mm thick monolithic and 0.5 mm thick double layered in-contact targets impacted by ogive nosed projectile. The projectile caused failure through ductile hole enlargement and petal formation. This is a typical failure mode of thin ductile targets impacted by sharp nosed projectiles. Four equal petals were formed in single, layered as well as spaced targets of equivalent thickness. Petals were bent at 90
from the surface of

Plate deformation (mm)

-102

target for each configuration. Petals were found to be highly sharp and thin at their tip, thickness increased from the tip to the root of petals. Experiments [6,7] also revealed that four equal petals were formed in 1 mm thick monolithic and 0.5 mm thick double layered in-contact targets when impacted by ogive nosed projectiles. Fig. 4(b) shows the failure modes of 1 mm thick monolithic and 0.5 mm thick double layered in-contact targets impacted by blunt nosed projectile. The projectile failed monolithic, layered and spaced targets through shear plugging. A clean cut circular hole was formed in the target. There was no sign of thinning of target material. A circular plug of diameter equal to that of the projectile was also removed from the target. Thickness of plug was equivalent to that of the target, confirming the experimental finding [6,7]. Fig. 5 shows the perforation phenomenon of 1 mm thick monolithic targets impacted by ogive and blunt nosed projectiles. The nose of the projectile has played a critical role in the deformation as well as fracture mode of target. The phenomena of ductile hole enlargement and petal formation by ogive nosed projectile can be seen. While the shearing of target and removal of a clear circular plug by the blunt nosed projectile is also visible. Fig. 6 shows the perforation behavior of layered in-contact targets impacted by ogive and blunt nosed projectiles. The deformation as well as fracture mode of layered targets was identical to

12

112.725 m/s 97.236 m/s 82.973 m/s 81.913 m/s 65.801 m/s 57.28 m/s 51.6 m/s

10 8 6 4

a

2 -85

-68

-51

0 -34 -17 0 17 34 51 Radial distance from the centre of plate (mm)

68

85

102

16

112.72 m/s 97.23 m/s 82.97 m/s 81.91 m/s 65.80 m/s 59.0 m/s 57.28 m/s 55.5 m/s 52.5 m/s

14 12 10 8 6 4

b

2

0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5

7.5

22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5

Plate deformation(mm)

Radial distance from centre of plate (mm) 20

112.725 m/s 97.236 m/s 82.973 m/s 81.913 m/s 73.307 m/s 65.801 m/s 58.85 m/s

15 10

c

5 0

-250

-200

-150

-100

-50

0

50

100

150

200

250

Radial distance from the centre of plate (mm) Fig. 15. Variation of the plastic deformation with impact velocity for 1 mm thick monolithic target impacted by ogive nosed projectile (a) 204 mm span diameter; (b) 255 mm span diameter; and (c) 500 mm span diameter.

M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

Plate deformation (mm)

those of the monolithic targets impacted by respective projectiles. The layers were in-contact before the commencement of fracture, however, as the fracture started both the layers separated with each other. The separation of layers was more prominent in the case of blunt nosed projectile impact. Fig. 7 shows the perforation of double layered target with 10 mm spacing between the layers. In this case also the failure mode of target remained identical to that of the monolithic and layered in-contact target for respective projectiles. It can be seen that there is a contact established between the front and rear layer as the projectile deforms the front layer. This phenomenon occurred for 2 mm, 5 mm and 10 mm spaced target. In case of 20 mm and 30 mm spaced target the layers did not come in-contact with each other. However, the contact between layers was defined for all the cases of spaced targets. Fig. 8(a) and (b) show the impact and residual velocity curves of ogive and blunt nosed projectiles respectively as a result of impact on monolithic, layered in-contact and layered spaced targets of 1 mm equivalent thickness. For both the projectiles the ballistic limit of monolithic target was found to be the highest followed by layered in-contact and layered spaced target respectively. It was also observed that at higher velocities of blunt nosed projectile, the

21

layered in-contact target offered better resistance than monolithic target. The spaced targets were found to be least effective in both the cases. The spacing between the layers also affected the resistance of the target. However, it was not significant at 10 mm, 20 mm and 30 mm spacing against either of the projectile probably due to the lesser interaction between layers. Therefore in order to closely examine this effect, the spacing between the layers was further reduced to 2 mm and 5 mm and ballistic limit was obtained, Table 6. The reduced spacing affected the ballistic limit however it was noticeable only for blunt nosed projectile. The variation of ballistic limit with target configuration is plotted in Fig. 9(a) and (b) for ogive and blunt nosed projectile respectively. Both the projectiles experienced highest ballistic limit velocity against monolithic target followed by layered in-contact and layered spaced target respectively. For ogive nosed projectile the ballistic limit of monolithic target was found to be 17.7% and 25.8% higher than that of the double layered in-contact and 2 mm spaced target respectively. The ballistic limit of layered in-contact target was found to be 7% higher than that of the 2 mm spaced target. While the ballistic limit of spaced target remained almost identical at varying spacing, Fig. 9(a). For blunt nosed projectile, the ballistic limit of monolithic target was found to be 2.7% and 8% higher than double layered in-

14

115.6 m/s 104.03 m/s 102.5 m/s 92.45 m/s 87.45 m/s 73.98 m/s 72.7 m/s

12 10 8 6

a

4 2

0 -102

-85

-68

-51

-34

-17

0

17

34

51

68

85

102

Radial distance from centre of plate (mm)

Plate deformation(mm)

16

115.6 m/s 104.036 m/s 102.5 m/s 92.455 m/s 87.455 m/s 74.7 m/s

14 12 10 8

b

6 4 2

Plate deformation (mm)

0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 Radial distance from the centre of plate(mm)

-250

115.6 m/s 104.036 m/s 102.5 m/s 92.455 m/s 87.455 m/s 78.45 m/s 77.5 m/s 77.2 m/s

-200

-150

20 15 10

c

5 0 -100 -50 0 50 100 Radial distance from centre of the plate (mm)

150

200

250

Fig. 16. Variation of the plastic deformation with impact velocity for 1 mm thick monolithic target impacted by blunt nosed projectile (a) 204 mm span diameter; (b) 255 mm span diameter; and (c) 500 mm span diameter.

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M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

contact and 2 mm spaced target respectively. The ballistic limit of layered in-contact target was found to be 5.2% higher than that of the 2 mm spaced target. While, the ballistic limit of 2 mm spaced target was found to be 0.9%, 1.2%, 6.6% and 6.6% higher than 5 mm, 10 mm, 20 mm and 30 mm spaced target respectively. Fig. 10 (a) and (b) show impact and residual velocity curves of ogive and blunt nosed projectiles respectively for 50 mm, 100 mm, 204 mm, 255 mm and 500 mm span diameters. Results reveal that at higher impact velocities the increase in the resistance offered by target of larger span is not significant. However, with decrease in the impact velocity, targets with larger span diameter were found to offer significant increase in resistance. This behavior was seen to be more prominent at the ballistic limit, Table 7, which consistently increased with increase in span diameter for both projectiles. Increase in ballistic limit for ogive and blunt nosed projectiles may be seen in Fig. 11. For ogive nosed projectile, the ballistic limit of 500 mm span diameter was found to be 9%, 13.7%, 20.2% and 24.6% higher than that of the 255 mm, 204 mm, 100 mm and 50 mm span diameter respectively. On the other hand, for blunt nosed projectile the same was found to be 3.3%, 6.2%, 51.5% and 76.6% higher respectively. The reason behind such behavior is the energy absorbed in bending that is higher for a larger span diameter. In

order to substantiate these results the energy absorbed in bending was calculated for each target span hit by blunt nosed projectile. The blunt nosed projectile was chosen because it experienced a larger increase in the ballistic limit velocity. It was assumed that the major portion of the kinetic energy of blunt nosed projectile is dissipated in shearing the target material, imparting momentum to the plug and global bending of the target. However, there was no sign of local stretching or thinning of the target material. The average thickness of plug was found to be 0.97 mm. The thickness of the target at the fractured region was found equivalent to that of the detached plug and the same has been confirmed from our previous experimental studies Gupta et al. [6,7]. The energy dissipated in shear was acquired from the numerical results. The values of average shear stress and the average shear strain were obtained at the narrow shear zone (the circular target region around the projectile) just before the occurrence of fracture. The shear strain energy (Eshear) was thus calculated as the product of average shear stress, average shear strain and the volume of the plug. The energy absorbed in target bending was calculated as;

Ebending ¼ Etotal  Eresidual  Eshear  Eplug

(4)

Plate deflection (mm)

16 14 12 Ogive 10 8 a 6 4 2 0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 Radial distance from center of plate (mm) Blunt

Plate deformation (mm)

Plate deflection (mm)

14 12 10 Ogive 8 6 4 b 2 0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 Radial distance from center of plate (mm) Blunt

10 Blunt Ogive

8 6

4

c

2

0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 Radial distance from center of plate (mm)

Fig. 17. Variation of plastic deformation of target with projectile nose shape at ballistic limit; (a) 1 mm thick monolithic target; (b) 0.5 mm thick double layered in-contact target; (c) 0.5 mm thick double layered spaced target with 10 mm spacing.

M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

23

Plate deflection (mm)

10 9 8 7 6 5 4 3 2 1 0 -1 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 Radial distance from center of plate (mm) Front plate Rear plate

a

Plate deflection (mm)

16 14 12 10 8 6 4 2 0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 Radial distance from center of plate (mm) Front plate Rear plate

b

Fig. 18. Plastic deformation of 0.5 mm thick double layered in-contact target impacted at ballistic limit by (a) ogive nosed projectile; (b) blunt nosed projectile.

Plate deflection (mm)

where Etotal and Eresidual is the initial and residual kinetic energy of projectile and Eplug is the kinetic energy of the sheared plug. Fig. 12 shows the energy absorbed in target bending for varying span diameter and describes a clear influence of span diameter on the absorbed energy. It is seen that energy absorbed in bending is increasing with increase in span diameter. It is also seen to decreasing with increase in projectile impact velocity except for 50 mm and 100 mm span diameter. For 100 mm span diameter the energy absorbed in bending slightly increased initially and then decreased with the increase in impact velocity, while for 50 mm span diameter it was found to increase continuously. Front plate Rear plate

Fig. 13(a)e(e) compares the resistance of a given target configuration for varying projectile nose shape. At each configuration, the target offered better resistance against blunt nosed projectile. The difference in the resistance of target increased with the decrease in impact velocity. The ballistic limit of monolithic, layered in-contact, 2 mm spaced, 5 mm spaced, 10 mm spaced, 20 mm spaced and 30 mm spaced target was found to be 32.5%, 51.8%, 54.3%, 54%, 53%, 46% and 46% higher respectively for blunt nosed projectile than for ogive nosed projectile, Table 6. Fig. 14(a)e(e) compares the ballistic resistance of a given span diameter for different projectile nose shapes. For 50 mm span

24

a

20 16 12 8

4

0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5

7.5

22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5

Plate deflection (mm)

Radial distance from center of plate (mm)

Front plate

30

Rear plate

25

b

20 15 10 5

0 -127.5-112.5 -97.5 -82.5 -67.5 -52.5 -37.5 -22.5 -7.5 7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5 127.5 Radial distance from center of plate (mm) Fig. 19. Plastic deformation of 0.5 mm thick double layered target with 10 mm spacing at ballistic limit by (a) ogive nosed projectile; (b) blunt nosed projectile.

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M.A. Iqbal et al. / International Journal of Impact Engineering 42 (2012) 11e24

diameter the target offered almost same resistance for both the projectiles and the ballistic limit velocity of ogive nosed projectile was found to be slightly higher than that of the blunt nosed projectile, Table 7. However, at all other spans the target offered better resistance to the blunt nosed projectile. Moreover, the difference in the ballistic resistance offered by the target also increased with an increase in span diameter and the decrease in impact velocity. The ballistic limit velocity of blunt nosed projectile was found to be 4%, 40.5%, 38.5% and 31% higher for 100 mm, 204 mm, 255 mm and 500 mm span diameter respectively, while for 50 mm span diameter it was found to be 7.4% lower than that of ogive nosed projectile. Fig. 15(a)e(c) shows the variation in the global target deformation with impact velocity of ogive nosed projectile. For each target span the plastic deformation was found to increase with the decrease in projectile impact velocity such that the highest plastic deformation was found at ballistic limit. It was also observed that the plastic deformation of target increased with an increase in target span diameter which has also been justified earlier in this paper. This is the fact due to which the ballistic limit increased with an increase in target span diameter. Fig. 16(a)e(c) shows the variation in the global target deformation with the impact velocity of blunt nosed projectile. In this case also the plastic deformation of target was found to increase with the decrease in impact velocity and increase in effective span diameter. While at each span diameter the deformation of target was found to be higher for blunt nosed projectile as compared to ogive nosed projectile. Fig. 17(a)e(c) compare the global target deformation with projectile nose shape for monolithic, double layered in-contact and double layered spaced targets with 10 mm spacing respectively at ballistic limit. For layered and spaced targets the deformation is that of the rear layer. At each configuration the blunt nosed projectile caused higher plastic deformation than ogive nosed projectile. Further, the highest deformation was observed in the case of monolithic target for each projectile. Fig. 18 show the deformation of 0.5 mm thick double layered incontact targets impacted by ogive and blunt nosed projectile respectively at ballistic limit. Mode of deformation of both the layers was found to be identical. However, the rear layer deformed more as compared to that of the front layer. Fig. 19(a) and (b) show the global deformation of 0.5 mm thick double layered spaced target with 10 mm spacing impacted by ogive and blunt nosed projectile respectively at ballistic limit. In this case also the deformation of rear layer was found to be higher than that of the front layer for each projectile. Experiments [7] revealed that the plastic deformation in the layered target increased with each successive layer from the front plate. 5. Conclusions Three-dimensional numerical simulations were performed wherein ogive and blunt nosed projectiles were hit normally on

1 mm thick 1100-H12 aluminum target with varying configuration and span diameter. For ogive nosed projectile the ballistic limit of monolithic target was found to be 17.7% and 25.8% higher than the double layered incontact and 2 mm spaced target respectively. The ballistic limit of layered in-contact target was found to be 7% higher than 2 mm spaced target. The variation of spacing had insignificant effect on the ballistic limit. For blunt nosed projectile, the ballistic limit of monolithic target was found to be 2.7% and 8% higher than double layered in-contact and 2 mm spaced target respectively. The ballistic limit of layered in-contact target was found to be 5.2% higher than the 2 mm spaced target. While, the ballistic limit of 2 mm spaced target was found to be 1%, 1.2%, 6.6% and 6.6% higher than 5 mm, 10 mm, 20 mm and 30 mm spaced target. The ballistic limit velocity of both the projectiles consistently increased with an increase in target span diameter. The increase in ballistic limit occurred due to the increase in bending energy. For ogive nosed projectile, the ballistic limit of 500 mm span diameter was found to be 9%, 13.7%, 20.2% and 24.6% higher than that of the 255 mm, 204 mm, 100 mm and 50 mm span diameter respectively. On the other hand, for blunt nosed projectile the same was found to be 3.3%, 6.2%, 51.5% and 76.6% higher respectively.

References [1] Marom I, Bonder SR. Projectile perforation of multi-layered beams. Int J Mech Sci 1979;21:489e504. [2] Corran RSJ, Shadbolt PJ, Ruiz C. Impact loading of plates e an experimental investigation. Int J Impact Eng 1983;1(1):3e22. [3] Radin J, Goldsmith W. Normal projectile penetration and perforation of layered targets. Int J Impact Eng 1988;7:229e59. [4] Nurick GN, Walters CE. The ballistic penetration of multiple thin plates separated by an air gap. In: Proceedings of SEM conference on experimental mechanics. Albuquerque, USA; 1990. p. 631e7. [5] Almohandes AA, Abdel-Kader MS, Eleiche AM. Experimental investigation of the ballistic resistance of steelefiberglass reinforced polyester laminated plates. Compos Part B Eng 1996;27(5):447e58. [6] Gupta NK, Iqbal MA, Sekhon GS. Effect of projectile nose shape, impact velocity and target thickness on deformation behavior of aluminum plates. Int J Solids Struct 2007;44:3411e39. [7] Gupta NK, Iqbal MA, Sekhon GS. Effect of Projectile nose shape, impact velocity and target thickness on the deformation behavior of layered plates. Int J Impact Eng 2008;35:37e60. [8] Dey S, Borvik T, Teng X, Wierzbicki T, Hopperstad OS. On the ballistic resistance of double-layered steel plates: an experimental and numerical investigation. Int J Solids Struct 2007;44:6701e23. [9] Teng X, Wierzbicki T, Huang M. Ballistic resistance of double-layered armor plates. Int J Impact Eng 2008;35:870e84. [10] ABAQUS/Explicit user’s manual. Version 6.7: vol. 1(2), 2007. [11] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proc. the seventh International symposium on ballistics. The Hague, Netherlands; 1983. p. 541e7. [12] Johnson GR, Cook WH. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 1985;21(1):31e48. [13] Gupta NK, Iqbal MA, Sekhon GS. Experimental and numerical studies on the behavior of thin aluminum plates subjected to impact by blunt- and hemispherical e nosed projectiles. Int J Impact Eng 2006;32:1921e44.