### Calculation of Collision Speed Corresponded to Maximum Penetration Using Hydrodynamic Theory

Document Type: Research Paper

Author

Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran

Abstract

One of the most valid and efficient models of long rod projectile penetration in homogeneous targets is Tate and Alekseevskii’s (A&t) model. Based on Tate’s model, the present research tries to calculate the optimum speeds to achieve the maximum penetration depth in the homogeneous targets. The proposed collision speed-penetration depth diagrams are developed using Tate’s model. In this way, various collision speed-penetration depth diagrams for different projectile dynamic resistances and targets are calculated and the optimum speed envelope is derived. According to Tate’s diagrams, the increase of collision speed is not followed by the increase of penetration depth; instead, it causes erosion phenomenon to happen. The comparison of the resulted optimum penetration speeds and the available data confirms the findings. Speed and rigidity both have a positive impact on the increase of penetration depth. With the increase of speed, the erosion issue finds a higher significance due to the increase of pressure on the projectile tip. Therefore, higher speed and erosion are opposed to each other; for the case of Y>R, there are some maximum points which indicate the optimum reciprocity of the two mentioned factors to obtain a maximum penetration depth. In the present research, an equation is developed indicating the optimum speeds resulting in the maximum penetration rate in the case of Y>R. For the reciprocity of speed and erosion, the target resistance against an erosive projectile should be 4 to 5 fold higher than the same target resistance against a rigid projectile penetration. [1]

Keywords

[1] Rosenberg and Z., Dekel E., 2008, A numerical study of the cavity expansion process and its application to long-rod penetration mechanics, International Journal of Impact Engineering 35: 147-154.
[2] Forrestal M. J., Frew D. J., Hickerson J. P. Rohwer T. A., 2003,Penetration of concrete targets with deceleration-time, International Journal of Impact Engineering 28: 479-497.
[3] Frew D.J., Forrestal M.J. Cargile J.D., 2006,The effect of concrete target diameter on projectile deceleration and penetration depth, International Journal of Impact Engineering 32: 1584-1594.
[4] Forrestal M. J., Frew D. J., Hanchak S. J. Brar N. S., 1996, Penetration of grout and concrete targets with ogive-nose steel projectiles, International Journal of Impact Engineering 18: 465-476.
[5] Vladimir M.G., 1996, Concrete penetration by eroding projectiles: experiments and analysis, Technical Report ARAED-TR-96014.
[6] Alekseeveskii V.P., 1966, Penetration of a Rod into a Target at High Velocity, Combus Explos Shock Waves 2: 63-66.
[7] Dullum O., Haugstad B., 1981, On the Effect of Finite Strength in Long Rod Penetration, Forsvarets Forskningstitutt, FFI/Rapport-81/4001, Kjeller, Norway .
[8] Tate A., 1967, A theory for the deceleration of long rods after impact, Journal of the Mechanics and Physics of Solids 15: 387-399.
[9] Tate A.,1969, Further results in the theory of long rod penetration, Journal of the Mechanics and Physics of Solids 17: 141-150.
[10] Zukas J. A., 1990, High Velocity Impact Dynamics, John Wiley & Sons.
[11] Williams A. E., 1976, Impact tests with mathematics method , Proceedings, 27th Meeting of the Aeroballistic Range Association, Centre, d Etudes de Vaujours, Sevran, France.