Skip to main content
Log in

Alekseevskii-Tate revisited: An extension to the modified hydrodynamic theory of long rod penetration

  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

The modified hydrodynamic theory of long rod penetration into semi-infinite targets was established independently by Alekseevskii and Tate over forty years ago and since then many investigators contributed much to the development of the high speed penetration mechanics. However, in all the models proposed so far, the target resistance R t is not well defined and usually determined by adjusting it until the predicted depth of penetration comes to an agreement with experimental data. In this paper, assumptions are first made about particle velocity and pressure profiles together with response regions in the target and then an extension is made to the modified hydrodynamic theory of long rod penetration into semi-infinite targets, in which R t has explicit form and is dependent on penetration velocity as well as thermo-mechanical properties of target material. The present model is compared with long rod penetration tests for different material combinations. It transpires that the present model predictions are in good agreement with the experimental data and numerical simulations in terms of penetration depth although many assumptions and simplifications are introduced into the paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson Jr CE, Morris B L, Littlefield D L. A penetration mechanics database. SwRI Report 3593/001, Southwest Research Institute, San Antonio, TX, 1992

    Google Scholar 

  2. Hohler V, Stilp A J. Hypervelocity impact of rod projectiles with L/D from 1 to 32. Intl J Impact Eng, 1987, 5: 323–331

    Article  Google Scholar 

  3. Stilp A J, Hohler V. Aeroballistic and impact physics research at EMI — A historical overview. Intl J Impact Eng, 1995, 17: 785–805

    Article  Google Scholar 

  4. Zook J A, Frank K, Silsby G F. Terminal ballistics test and analysis guidelines for the penetration branch. BRL-MR-3960, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, 1992

    Google Scholar 

  5. Goldsmith W. Non-ideal projectile impact on targets. Intl J Impact Eng, 1999, 22: 95–395

    Article  Google Scholar 

  6. Orphal D L. Explosions and impacts. Intl J Impact Eng, 2006, 33: 496–545

    Article  Google Scholar 

  7. Eichelberger R J, Gehring J W. Effects of meteoroid impact on space vehicles. Am Rocket Soc J, 1962, 32: 1583–1591

    Google Scholar 

  8. Tate A. A theory for the deceleration of long rods after impact. J Mech Phys Solids, 1967, 15: 387–399

    Article  Google Scholar 

  9. Alekseevskii V P. Penetration of a rod into a target at high velocity. Combustion, Explosion and Shock Waves, 1966, 2: 63–66

    Article  Google Scholar 

  10. Tate A. Further results in the theory of long rod penetration. J Mech Phys Solids, 1969, 17: 141–150

    Article  MathSciNet  Google Scholar 

  11. Rosenberg Z. On the hydrodynamic theory of long-rod penetration. Intl J Impact Eng, 1990, 10: 483–486

    Article  Google Scholar 

  12. Jones S E, Gillis P P, Foster J C. On the penetration of semi-infinite targets by long rods. J Mech Phys Solids, 1987, 35: 121–131

    Article  Google Scholar 

  13. Wang P, Jones S E. An elementary theory of one-dimensional rod penetration using a new estimate for pressure. Intl J Impact Eng, 1996, 18: 265–279

    Article  Google Scholar 

  14. Cinnamon J D, Jones S E. A one-dimensional analysis of rod penetration. Intl J Impact Eng, 1992, 12: 145–166

    Article  Google Scholar 

  15. Galanov B A, Ivanov S M, Kartuzov V V. On one new modification of Alekseevskii-Tate model for nonstationary penetration of long rods into targets. Intl J Impact Eng, 2001, 26: 201–210

    Article  Google Scholar 

  16. Galanov B A, Ivanov S M, Kartuzov V V. Investigation of penetration resistance using a new modification of the Alekseevskii-Tate model. Int J Impact Eng, 2003, 29: 263–272

    Article  Google Scholar 

  17. Grace F I. Nonsteady penetration of long rods into semi-infinite targets. Intl J Impact Eng, 1993, 14: 303–314

    Article  MathSciNet  Google Scholar 

  18. Walker J D, Anderson Jr C E. A time-dependent model for long-rod penetration. Intl J Impact Eng, 1995, 16: 19–48

    Article  Google Scholar 

  19. Godwin R P, Chapyak E J. Apparent target strength in long rod penetration. Intl J Impact Eng, 1998, 21: 77–88

    Article  Google Scholar 

  20. Rubin M B, Yarin A L. A generalized formula for the penetration depth of a deformable projectile. Intl J Impact Eng, 2002, 27: 387–398

    Article  Google Scholar 

  21. Walters W P, Segletes S B. An exact solution of the long rod penetration equations. Intl J Impact Eng, 1991, 11: 225–231

    Article  Google Scholar 

  22. Segletes S B, Walters W P. Extensions to the exact solution of the long-rod penetration/erosion equations. Intl J Impact Eng, 2003, 28: 363–376

    Article  Google Scholar 

  23. Anderson Jr C E, Walker J D. An examination of long-rod penetration. Intl J Impact Eng, 1991, 11: 481–501

    Article  Google Scholar 

  24. Anderson Jr C E, Littlefield D L, Walker J D. Long-rod penetration, target resistance, and hypervelocity impact. Intl J Impact Eng, 1993, 14: 1–12

    Article  MATH  Google Scholar 

  25. Sorensen B R, Kimsey K D, Silsby G F, et al. High velocity penetration of steel targets. Intl J Impact Eng, 1991, 11: 107–119

    Article  Google Scholar 

  26. Lan B, Wen H M. Numerical simulation and analysis of the penetration of tungsten alloy long rods into semi-infinite armor steel targets. Chinese J High Pressure Phys, 2008, 22: 245–252

    Google Scholar 

  27. Tan H. Introduction to Experimental Shock-Wave Physics. Beijing: National Defense Industry Press, 2007

    Google Scholar 

  28. Li T, Tang Z P, Cai J. Micro-obervation of shear wave attenuation mechanism in Nylon-66. Mater Lett, 2007, 61: 1436–1438

    Article  Google Scholar 

  29. Tang Z P, Xu S L, Dai X Y, et al. S-wave tracing technique to investigate the damage and failure behaviour of brittle materials subjected to shock loading. Intl J Impact Eng, 2005, 31: 1172–1191

    Article  Google Scholar 

  30. Forrestal M J, Luk V K. Dynamic spherical cavity-expansion in a compressible elastic-plastic solid. J Appl Mech, 1988, 55: 275–279

    Article  Google Scholar 

  31. Hill R. The Mathematical Theory of Plasticity. London: Oxford University Press, 1950

    MATH  Google Scholar 

  32. Zhou H, Wen H M. Penetration of bilinear strain-hardening targets subjected to impact by ogival-nosed projectiles. Proceeding of 2003 International Autumn Seminar on Propellants, Explosives and Pyrotechnics, In: Huang P et al. eds. Theory and Practice of Energetic Materials, Vol.5. Beijing/New York: Science Press, 2003. 933–942

    Google Scholar 

  33. Luk V K, Forrestal M J, Amos D E. Dynamic spherical cavity expansion of strain-hardening materials. J Appl Mech, 1991, 58: 1–6

    Article  Google Scholar 

  34. Tate A. Long rod penetration models-Part II. Extensions to the hydrodynamic theory of penetration. Intl J Mech Sci, 1986, 28: 599–612

    Article  Google Scholar 

  35. Silsby G F. Penetration of semi-infinite steel targets by tungsten rods at 1.3 to 4.5 km/s. Proceeding of the Eighth International Symposium on Ballistics, TB/31-35, Orlando, Florida, 1984

  36. Mchenry M R, Choo Y, Orphal D L. Numerical simulations of low L/D rod aluminum into aluminum impacts compared to the Tate cratering model. Intl J Impact Eng, 1999, 23: 621–628

    Article  Google Scholar 

  37. Lan B, Wen H M. Numerical simulation of the penetration of a spherical-nosed 4340 steel long rod into semi-infinite 6061-T6511 aluminum targets (in Chinese). J Eng Mech, 2009, 26: 183–190

    Google Scholar 

  38. Orphal D L, Anderson Jr C E. The dependence of penetration velocity on impact velocity. Intl J Impact Eng, 2006, 33: 546–554

    Article  Google Scholar 

  39. Hohler V, Stilp A J. In: Anderson Jr C E, Morris B L, Littlefeld D L, eds. A Penetration Mechanics Database. SwRI Report 3593/001, Southwest Research Institute, San Antonio, TX, 1992. A76–A82

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to HeMing Wen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lan, B., Wen, H. Alekseevskii-Tate revisited: An extension to the modified hydrodynamic theory of long rod penetration. Sci. China Technol. Sci. 53, 1364–1373 (2010). https://doi.org/10.1007/s11431-010-0011-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-010-0011-x

Keywords

Navigation