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Journal of Pressure Vessel Technology | Volume 130 | Issue 3 | Research Paper
Research Papers: Design and Analysis

Low Velocity Perforation of Mild Steel Circular Plates With Projectiles Having Different Shaped Impact Faces

[+] Author and Article Information
Norman Jones1

Impact Research Centre, Department of Engineering, The University of Liverpool, Liverpool L69 3GH, UKnorman.jones@liv.ac.uk

R. S. Birch

Impact Research Centre, Department of Engineering, The University of Liverpool, Liverpool L69 3GH, UK

The value of k for a transverse shear failure is usually much smaller than k=1 and lies within the range of approximately 14 to 12(18-19).

A more rigorous analysis of material strain rate sensitive effects using equivalent stresses and strains is reported in a companion article.

ξ=0, 0.6, and 0.9 for the conical projectiles.

Note that equations (15) in Ref. 8 are not correct for 2R∕d>12 since the last term should be replaced by 4.553 and not unity as stated.

1

Corresponding author.

J. Pressure Vessel Technol 130(3), 031205 (Jun 20, 2008) (11 pages) doi:10.1115/1.2937768 History: Received October 30, 2006; Revised April 13, 2007; Published June 20, 2008
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This article studies the perforation of mild steel circular plates struck normally by cylindrical projectiles having blunt, hemispherical, and conical impact faces. Experimental results are obtained using a drop hammer rig for the perforation of 2–8mm thick plates struck by projectiles weighing between 1.75kg and 176kg and traveling up to about 12m∕s. The impact positions are at several radial locations across a plate, and it turns out that the perforation energy decreases as the impact location is moved away from a plate center toward the support. It transpires that the projectiles with hemispherical and blunt impact faces require the largest and the smallest impact perforation energies, respectively. Comparisons are made between the experimental results for the perforation energies and the predictions of several empirical equations. Design calculations for the impact perforation of plates could be undertaken using projectiles with blunt impact faces, which would provide a lower bound on the perforation energy of projectiles having hemispherical or conical impact faces, at least within the range of the parameters studied.
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Copyright © 2008 by American Society of Mechanical Engineers
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References

1
Backman, M. E., and Goldsmith, W., 1978, “The Mechanics of Penetration of Projectiles Into Targets,” Int. J. Eng. Sci.  [CrossRef], 16 , pp. 1–99.
2
Woodward, R. L., 1984, “The Interrelation of Failure Modes Observed in the Penetration of Metallic Targets,” Int. J. Impact Eng., 2 (2), pp. 121–129.
3
Forrestal, M. J., Rosenberg, Z., Luk, V. K., and Bless, S. J., 1987, “Perforation of Aluminium Plates With Conical-Nosed Rods,” ASME J. Appl. Mech., 54 (1), pp. 230–232.
4
Anderson, C. E., and Bodner, S. R., 1988, “Ballistic Impact: The Status of Analytical and Numerical Modelling,” Int. J. Impact Eng.  [CrossRef], 7 (1), pp. 9–35.
5
1990, "High Velocity Impact Dynamics", J.A.Zukas, ed., Wiley, New York.
6
Goldsmith, W., 1999, “Non-Ideal Projectile Impact on Targets,” Int. J. Impact Eng.  [CrossRef], 22 (2/3), pp. 95–395.
7
Jones, N., 1994, “Low Velocity Perforation of Metal Plates,” "Shock and Impact on Structures", C.A.Brebbia and V.Sanchez-Galvez, eds., Computational Mechanics, Southampton, UK, Chap. 3, pp. 53–71.
8
Corbett, G. G., Reid, S. R., and Johnson, W., 1996, “Impact Loading of Plates and Shells by Free-Flying Projectiles: A Review,” Int. J. Impact Eng.  [CrossRef], 18 (2), pp. 141–230.
9
Wen, H.-M., and Jones, N., 1992, “Semi-Empirical Equations for the Perforation of Plates Struck by a Mass,” "Structures Under Shock and Impact, II", P.S.Bulson, ed., Computational Mechanics, Southampton and Thomas Telford, London, pp. 369–380.
10
Wen, H.-M., and Jones, N., 1994, “Experimental Investigation Into the Dynamic Plastic Response and Perforation of a Clamped Circular Plate Struck Transversely by a Mass,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 208 , pp. 113–137.
11
Jones, N., and Kim, S.-B., 1997, “A Study on the Large Ductile Deformations and Perforation of Mild Steel Plates Struck by a Mass—Part 1: Experimental Results,” ASME J. Pressure Vessel Technol.  [CrossRef], 119 , pp. 178–184.
12
Birch, R. S., Jones, N., and Jouri, W. S., 1988, “Performance Assessment of an Impact Rig,” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 202 , pp. 275–285;Birch, R. S., and Jones, N., 1990, “Corrigenda,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 204 , p. 8.
13
Birch, R. S., and Jones, N., 1990, “Measurement of Impact Loads Using a Laser Doppler Velocimeter,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.  [CrossRef], 204 , pp. 1–8.
14
Ohte, S., Yoshizawa, H., Chiba, N., and Shida, S., 1982, “Impact Strength of Steel Plates Struck by Projectiles: Evaluation Formula for Critical Fracture Energy of Steel Plate,” Bull. JSME, 25 (206), pp. 1226–1231.
15
Yoshizawa, H., Ohte, S., Kashima, Y., Chiba, N., and Shida, S., 1984, “Impact Strength of Steel Plates Struck by Projectiles: Effect of Mechanical Properties on Critical Fracture Energy,” Bull. JSME, 27 (226), pp. 639–644.
16
Recht, R. F., and Ipson, T. W., 1963, “Ballistic Perforation Dynamics,” ASME J. Appl. Mech., 30 , pp. 384–390.
17
Jones, N., 1989, "Structural Impact", Cambridge University Press, Cambridge, England (Paperback edition, 1997).
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Jones, N., 1986, “Some Comments on the Dynamic Plastic Behaviour of Structures,” "Keynote Address, Proceedings International Symposium on Intense Dynamic Loading and Its Effects", Z.Zhemin and D.Jing, eds., Science, Beijing, China, pp. 49–71 and Pergamon Press, 1988.
19
Jouri, W. S., and Jones, N., 1988, “The Impact Behaviour of Aluminium Alloy and Mild Steel Double-Shear Specimens,” Int. J. Mech. Sci., 30 (3/4), pp. 153–172.
20
Jones, N., 2003, “On the Mass Impact Loading of Ductile Plates,” Def. Sci. J. (Def. Res. and Development Org., India), 53 (1), pp. 15–24.
21
Jones, N., Kim, S. B., and Li, Q. M., 1997, “Response and Failure Analysis of Ductile Circular Plates Struck by a Mass,” ASME J. Pressure Vessel Technol.  [CrossRef], 119 (3), pp. 332–342.
22
Corran, R. S. J., Shadbolt, P. J., and Ruiz, C., 1983, “Impact Loading of Plates—An Experimental Investigation,” Int. J. Impact Eng.  [CrossRef], 1 (1), pp. 3–22.
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Shadbolt, P. J., Corran, R. S. J., and Ruiz, C., 1983, “A Comparison of Plate Perforation Models in the Sub-Ordnance Impact Velocity Range,” Int. J. Impact Eng.  [CrossRef], 1 (1), pp. 23–49.
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Jones, N., 1989, “Some Comments on the Modelling of Material Properties for Dynamic Structural Plasticity,” "International Conference on the Mechanical Properties of Materials at High Rates of Strain", J.Harding, ed., Oxford, Institute of Physics Conference Series No. 102 , pp. 435–445.
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Liu, D., and Stronge, W. J., 2000, “Ballistic Limit of Metal Plates Struck by Blunt Deformable Missiles: Experiments,” Int. J. Solids Struct., 37 , pp. 1403–1423.
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Zhang, T., 1999, “Failure Map for Thin Ductile Targets by Normal Impact of Conical-Nosed Missiles,” "Impact Response of Materials and Structures, Proceedings of the Third International Symposium on Impact Engineering", V.P. W.Shim, S.Tanimura, and C.T.Lim, Singapore, Oxford University Press, New York, pp. 190–195.
27
Borvik, T., Langseth, M., and Hopperstad, O. S., 2003, “Ballistic Penetration and Perforation of Steel Plates—An Experimental and Numerical Investigation,” "Advances in Dynamics and Impact Mechanics", C.A.Brebbia and G.N.Nurick, eds., WIT, Southampton, pp. 181–202.
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Figures

Grahic Jump Location
+Variation of dimensionless perforation energies with ξ, d∕H, and striker nose geometry for 2mm thick mild steel plates with 2R=203.2mm. ——◻——, blunt; —⋅—⋅X—⋅—, conical; – – ○ – –, hemispherical. ▽: experimental results, blunt projectile with d∕H=2.54(10).
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Variation of dimensionless perforation energies with ξ, d∕H, and striker nose geometry for 2mm thick mild steel plates with 2R=203.2mm. ——◻——, blunt; —⋅—⋅X—⋅—, conical; – – ○ – –, hemispherical. ▽: experimental results, blunt projectile with d∕H=2.54(10).
Figure 2

Variation of dimensionless perforation energies with ξ, d∕H, and striker nose geometry for 2mm thick mild steel plates with 2R=203.2mm. ——◻——, blunt; —⋅—⋅X—⋅—, conical; – – ○ – –, hemispherical. ▽: experimental results, blunt projectile with d∕H=2.54(10).

Grahic Jump Location
+Variation of dimensionless perforation energies with ξ, d∕H, and striker nose geometry for 4mm thick mild steel plates with 2R=203.2mm. The notation is defined in Fig. 2. ▽: experimental results, blunt projectile with d∕H=1.27(10).
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation of dimensionless perforation energies with ξ, d∕H, and striker nose geometry for 4mm thick mild steel plates with 2R=203.2mm. The notation is defined in Fig. 2. ▽: experimental results, blunt projectile with d∕H=1.27(10).
Figure 3

Variation of dimensionless perforation energies with ξ, d∕H, and striker nose geometry for 4mm thick mild steel plates with 2R=203.2mm. The notation is defined in Fig. 2. ▽: experimental results, blunt projectile with d∕H=1.27(10).

Grahic Jump Location
+(a) Idealized experimental arrangement with a blunt-faced projectile striking a circular plate normally at a radial distance ri from the plate center. (b) Projectile with a conical nose having a 90deg included angle. (c) Projectile with a hemispherical nose of radius d∕2.
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(a) Idealized experimental arrangement with a blunt-faced projectile striking a circular plate normally at a radial distance ri from the plate center. (b) Projectile with a conical nose having a 90deg included angle. (c) Projectile with a hemispherical nose of radius d∕2.
Figure 1

(a) Idealized experimental arrangement with a blunt-faced projectile striking a circular plate normally at a radial distance ri from the plate center. (b) Projectile with a conical nose having a 90deg included angle. (c) Projectile with a hemispherical nose of radius d∕2.

Grahic Jump Location
+Variation of dimensionless energies for perforation and cracking with ξ and striker nose geometry for 6mm thick mild steel plates with d∕H=2.54 and 2R=203.2mm. ○ and ◻, defined in Fig. 2; ◼, +, and ●, energies for cracking caused by blunt, conical, and hemispherical shaped projectiles, respectively.
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Variation of dimensionless energies for perforation and cracking with ξ and striker nose geometry for 6mm thick mild steel plates with d∕H=2.54 and 2R=203.2mm. ○ and ◻, defined in Fig. 2; ◼, +, and ●, energies for cracking caused by blunt, conical, and hemispherical shaped projectiles, respectively.
Figure 4

Variation of dimensionless energies for perforation and cracking with ξ and striker nose geometry for 6mm thick mild steel plates with d∕H=2.54 and 2R=203.2mm. ○ and ◻, defined in Fig. 2; ◼, +, and ●, energies for cracking caused by blunt, conical, and hemispherical shaped projectiles, respectively.

Grahic Jump Location
+Variation of dimensionless perforation energies with ξ, d∕H, and projectile nose geometry for 8mm thick mild steel plates with 2R=203.2mm. The notation is defined in Fig. 2.
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Variation of dimensionless perforation energies with ξ, d∕H, and projectile nose geometry for 8mm thick mild steel plates with 2R=203.2mm. The notation is defined in Fig. 2.
Figure 5

Variation of dimensionless perforation energies with ξ, d∕H, and projectile nose geometry for 8mm thick mild steel plates with 2R=203.2mm. The notation is defined in Fig. 2.

Grahic Jump Location
+Photographs of some typical circular plate failures. (a) H=8mm, ξ=0, blunt-faced projectile, d∕H=1.27. (b) H=6mm, ξ=0.8, blunt-faced projectile, d∕H=2.54. (c) H=4mm, ξ=0, hemispherical projectile, d∕H=1.27. (d) H=2mm, ξ=0, conical projectile, d∕H=5.08. (e) H=6mm, ξ=0.8, hemispherical projectile, d∕H=2.54. (f) H=8mm, ξ=0, conical projectile, d∕H=2.54.
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Photographs of some typical circular plate failures. (a) H=8mm, ξ=0, blunt-faced projectile, d∕H=1.27. (b) H=6mm, ξ=0.8, blunt-faced projectile, d∕H=2.54. (c) H=4mm, ξ=0, hemispherical projectile, d∕H=1.27. (d) H=2mm, ξ=0, conical projectile, d∕H=5.08. (e) H=6mm, ξ=0.8, hemispherical projectile, d∕H=2.54. (f) H=8mm, ξ=0, conical projectile, d∕H=2.54.
Figure 6

Photographs of some typical circular plate failures. (a) H=8mm, ξ=0, blunt-faced projectile, d∕H=1.27. (b) H=6mm, ξ=0.8, blunt-faced projectile, d∕H=2.54. (c) H=4mm, ξ=0, hemispherical projectile, d∕H=1.27. (d) H=2mm, ξ=0, conical projectile, d∕H=5.08. (e) H=6mm, ξ=0.8, hemispherical projectile, d∕H=2.54. (f) H=8mm, ξ=0, conical projectile, d∕H=2.54.

Grahic Jump Location
+Variation of dimensionless perforation energies with plate thickness for d∕H=2.54 and 2R=203.2mm. The notation is defined in Fig. 4. (a) ξ=0, (b) ξ=0.5 (ξ=0.6 for × at H=8mm), and (c) ξ=0.8 (ξ=0.9 for × at H=8mm)
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Variation of dimensionless perforation energies with plate thickness for d∕H=2.54 and 2R=203.2mm. The notation is defined in Fig. 4. (a) ξ=0, (b) ξ=0.5 (ξ=0.6 for × at H=8mm), and (c) ξ=0.8 (ξ=0.9 for × at H=8mm)
Figure 7

Variation of dimensionless perforation energies with plate thickness for d∕H=2.54 and 2R=203.2mm. The notation is defined in Fig. 4. (a) ξ=0, (b) ξ=0.5 (ξ=0.6 for × at H=8mm), and (c) ξ=0.8 (ξ=0.9 for × at H=8mm)

Grahic Jump Location
+Comparison of dimensionless perforation energies with empirical equations for fully clamped circular plates (2R=203.2mm) struck at the center (ξ=0) by blunt-faced projectiles having d∕H=2.54. Experimental results: ——◻——. Empirical results: – – – – – – 1, SRI equation (Eq. 1); – – – – – –- 2, BRL equation (Eq. 2); – – – – – – 3, Neilson equation (Eq. 3) (lower curve has a coefficient 1.0 instead of 1.4); – – – – – – 4, Jowett equation (Eq. 7); —⋅—⋅— 5, Eq. 8.
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Comparison of dimensionless perforation energies with empirical equations for fully clamped circular plates (2R=203.2mm) struck at the center (ξ=0) by blunt-faced projectiles having d∕H=2.54. Experimental results: ——◻——. Empirical results: – – – – – – 1, SRI equation (Eq. 1); – – – – – –- 2, BRL equation (Eq. 2); – – – – – – 3, Neilson equation (Eq. 3) (lower curve has a coefficient 1.0 instead of 1.4); – – – – – – 4, Jowett equation (Eq. 7); —⋅—⋅— 5, Eq. 8.
Figure 8

Comparison of dimensionless perforation energies with empirical equations for fully clamped circular plates (2R=203.2mm) struck at the center (ξ=0) by blunt-faced projectiles having d∕H=2.54. Experimental results: ——◻——. Empirical results: – – – – – – 1, SRI equation (Eq. 1); – – – – – –- 2, BRL equation (Eq. 2); – – – – – – 3, Neilson equation (Eq. 3) (lower curve has a coefficient 1.0 instead of 1.4); – – – – – – 4, Jowett equation (Eq. 7); —⋅—⋅— 5, Eq. 8.

Grahic Jump Location
+Comparison of dimensionless perforation energies at several positions, ξ, with an empirical equation (Eq. 6) for blunt projectiles having d∕H=2.54(2R=203.2mm). Experimental results: ——◻——, ξ=0; ——▽—— (▼ severe cracking), ξ=0.5; ——△——, ξ=0.8. — ⋅ —: empirical equation (Eq. 6) (Eq. 8 at ξ=0).
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Comparison of dimensionless perforation energies at several positions, ξ, with an empirical equation (Eq. 6) for blunt projectiles having d∕H=2.54(2R=203.2mm). Experimental results: ——◻——, ξ=0; ——▽—— (▼ severe cracking), ξ=0.5; ——△——, ξ=0.8. — ⋅ —: empirical equation (Eq. 6) (Eq. 8 at ξ=0).
Figure 9

Comparison of dimensionless perforation energies at several positions, ξ, with an empirical equation (Eq. 6) for blunt projectiles having d∕H=2.54(2R=203.2mm). Experimental results: ——◻——, ξ=0; ——▽—— (▼ severe cracking), ξ=0.5; ——△——, ξ=0.8. — ⋅ —: empirical equation (Eq. 6) (Eq. 8 at ξ=0).

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