Advertisement

Retracted Article: Analysis of critical ricochet angle using two space discretization methods

  • Kamran Daneshjou
  • Majid Shahravi
Original Article

Abstract

Ricochet of a tungsten long-rod projectile from oblique steel plates with a finite thickness was investigated numerically using two explicit finite element methods. These two methods are Lagrange and smooth particle hydrodynamic (SPH). Three distinctive regimes resulting from oblique impact depending on the obliquity, namely simple ricochet, critical ricochet and target perforation, were investigated in detail. Critical ricochet angles were calculated for various impact velocities and strengths of the target plates in Lagrange and SPH methods. It was predicted that in every two methods, critical ricochet angle increases with decreasing impact velocities and that higher ricochet angles were expected if higher strength target materials are employed. The experimental results are discussed and compared with results predicted by the simulations and existing two-dimensional analytical model Through Investigation of the angles in which projectile only ricochets, both SPH and Lagrange methods represent approximate alike results. But in the cases that projectile begins to crack in head region out of high impact angles, the SPH method yields better results. One other advantage of the SPH against the Lagrange method is that no erosion happens though the method and therefore all the particles caused by impact are clearly seen. This means better satisfaction of the principle of conservation of mass. Therefore the correlation between the numerical results and the available experimental and observed data demonstrates that the SPH approach is an accurate and effective analysis technique for long rod ricochet phenomena in ricochet of tungsten rod with RHA target.

Keywords

Critical ricochet angle Numerical simulation Smooth particle hydrodynamic Lagrange method 

References

  1. 1.
    Zukas JA (1990) High velocity impact dynamics. A Wiley-Inter science Publication. Wiley, New YorkGoogle Scholar
  2. 2.
    Ogorkiewicz RM (1991) Technology of tanks. Janes’s Information Group, CoulsdonGoogle Scholar
  3. 3.
    Goldsmith W, Cunningham PM (1956) Kinematic phenomena observed. During the oblique impact of a sphere on a beam. J Appl Mech (Trans ASME) 78:612Google Scholar
  4. 4.
    Recht RF, Ipson TW (1962) The dynamics of terminal ballistics” Final Report No AD274128. Denver Research Institute, DenverGoogle Scholar
  5. 5.
    Finnegan SA, Dimaranan LF, Heimdahl DER, Pringle JK (1993) A study of obliquity effects on perforation and ricochet processes in thin plates impacted by compact fragments. In: Proc. 14th Int. Symp. Ballistics, p 661Google Scholar
  6. 6.
    Tate A (1979) A simple estimate of the minimum target obliquity required for the ricochet of a high speed long rod projectile. J Phys D Appl Phys 12:1825CrossRefGoogle Scholar
  7. 7.
    Rosenberg Z, Yeshurun Y, Mayseless M (1989) On the ricochet of long rod projectiles. In: Proc. 11th Int. Symp. Ballistics, p 501Google Scholar
  8. 8.
    Senf H, Rothenhausler H, Scharpf F, Both A, Pfang W (1981) Experimental and numerical investigation of the ricocheting of projectiles from metallic surfaces. In: Proc. 6th Int. Symp. Ballistics, p 510Google Scholar
  9. 9.
    Zukas JA, Gaskill B (1996) Ricochet of deforming projectiles from deforming plates. Int J Impact Eng 18:601CrossRefGoogle Scholar
  10. 10.
    Johnson W, Sengupta AK, Ghosh SK (1981) High velocity oblique impact and ricochet mainly of long rod projectile: an overview. Int J Mech Sci 24:425CrossRefGoogle Scholar
  11. 11.
    Johnson W, Sengupta AK, Ghosh SK (1981) Plasticine modelled high velocity oblique impact and ricochet of long-rods. Int J Mech Sci 24:437–455CrossRefGoogle Scholar
  12. 12.
    Reid SR, Edmonds AJ, Johnson W (1981) Bending of long steel and aluminum rods during end impact with a rigid target. J Mech Eng Sci 23:85CrossRefGoogle Scholar
  13. 13.
    Jonas GH, Zukas JA (1978) Mechanics of penetration: analysis, experiment. Int J Eng Sci 16:879CrossRefGoogle Scholar
  14. 14.
    Tate A (1967) A theory for the deceleration of long rods after impact. J Mech Phys Solids 15:387CrossRefGoogle Scholar
  15. 15.
    Tate A (1969) Further results in the theory of long rod penetration. J Mech Phys Solids 17:141–150CrossRefMathSciNetGoogle Scholar
  16. 16.
    Tate A (1977) Int J Mech Sci 28:535CrossRefGoogle Scholar
  17. 17.
    Goldsmith W, Finnegan SA (1986) Normal and oblique impact of cylindro-conical and cylindrical projectiles on metallic plates. Int J Impact Eng 4:83CrossRefGoogle Scholar
  18. 18.
    Roecker E, Grabarek C (1986) The effect of Yaw and Pitch on long rod penetration into rolled homogeneous armor at various obliquities. In: Proc. 9th Int. Symp. Ballistics, vol 2, pp 467–473Google Scholar
  19. 19.
    Falcovitz J, Mayseless M, Tauber Z, Keck D, Kennedy R, Ofstedhal K, Sing P (1989) A computer model for oblique impact of a rigid projectile at ductile layered targets. In: Proc. 11th Int. Symp. Ballistics, p 311Google Scholar
  20. 20.
    Johnson GR, Stryk RA, Holmquist TJ, Souka A (1990) Int J Impact Eng 10:281CrossRefGoogle Scholar
  21. 21.
    Cullis IG, Lynch NJ (1995) Performance of model scale long rod projectiles against complex targets over the velocity range 1700–2200 m/s. Int J Impact Eng 17:263–274CrossRefGoogle Scholar
  22. 22.
    Luttwak G, Rosenberg Z, Kivity Y (1996) Long rod penetration in oblique impact. In: AlP Conf ProcGoogle Scholar
  23. 23.
    Pierazzo E, Melosh HJ (2000) Understanding oblique impacts from experiments, observations, and modeling. Ann Rev Earth Planet Sci 28:141–167CrossRefGoogle Scholar
  24. 24.
    Hohler V, Stilp AJ (1981) Interferometric investigation of rod deceleration during impact process. In: Proc. 6th Int. Symp. Ballistics, p 333Google Scholar
  25. 25.
    Sislby GF (1984) Penetration of semi-itilnite steel targets by tungsten rods at. 1.3 to 4.5 lcds. In: Proc 8th Int Symp. Ballistics, p 31Google Scholar
  26. 26.
    Cagliostro DJ, Mandell DA, Schwalbe LA, Adams TF, Chapyak EJ (1990) Armor penetration by projectile with combined obliquity, yaw. Int J Impact Eng 10:81–92CrossRefGoogle Scholar
  27. 27.
    Bjerke TW, Silsby GF, Scheffler DR, Mudd RM (1992) Yawed long-rod armor penetration. Int J Impact Eng 12:281–292CrossRefGoogle Scholar
  28. 28.
    Bukharev YI, Zhukov VI (1995) Model of the penetration of a metal barrier by a rod projectile with an angle of attack, combustion, explosion and shock waves. Comb Expl Shock Waves Fiz Goren Vzryva 31:362CrossRefGoogle Scholar
  29. 29.
    Goldsmith W, Tam E, Tomer D (1995) Yawing impact on thin plates by blunt projectiles. Int J Impact Eng 16:479–498CrossRefGoogle Scholar
  30. 30.
    Anderson CE, Bless SJ, Sharron TR, Satapathy S, Normandia MJ (1998) Investigation of yawed impact into a finite target. In: AlP Conf Proc., p 925Google Scholar
  31. 31.
    Lee M, Bless SJ (1998) AIP Conf Proc., pp 925–928Google Scholar
  32. 32.
    Woong L, Heon JL, Hyunho S (2002) Ricochet of a tungsten heavy alloy long-rod projectile from deformable steel plates. Int J Appl Phys 35:2676–2686Google Scholar
  33. 33.
    Livermore Software Technology Corporation (2007) Ls Dyna User’s Manual version 970Google Scholar
  34. 34.
    Meyers MA (1994) Dynamic behavior of materials. Wiley, New YorkzbMATHCrossRefGoogle Scholar
  35. 35.
    Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non spherical stars. Mon Not Roy Astron Soc 181:375–389zbMATHGoogle Scholar
  36. 36.
    Swegle JW, Hicks DL, Attaway SW (1995) Smoothed particle hydrodynamics stability analysis. J Comp Phys 116:123–134zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Balsara DS (1995) Von Neumann stability analysis of smooth particle hydrodynamics—suggestions for optimal algorithms. J Comp Phys 121:357–372zbMATHCrossRefGoogle Scholar
  38. 38.
    Guenther C, Hicks DL, Swegle JW (1994) Conservative Smoothing Versus Artificial Viscosity. Sandia Report SAND94-1853, AlbuquerqueGoogle Scholar
  39. 39.
    Quan X, Birnbaum NK, Cowler MS, Gerber BI (2003) Numerical simulation of structural deformation under shock and impact loads using a coupled multi-solver approach. In: 5th Asia-pacific conference on shock & impact loads on structures, November 2003, pp 71–78Google Scholar
  40. 40.
    Yaziv D, Mayseless M, Reifen Y (2001) The penetration process of long rods into thin metallic targets at high obliquity. In: 19th International Symposium of Ballistics, 7–11 May 2001Google Scholar
  41. 41.
    Rosenberg Z, Dekel E (1998) A computational study of the relations between material properties of long-rod penetrators, their ballistic performance. Int J Impact Eng 21(283):296Google Scholar
  42. 42.
    Anderson CE, Walker JD, Bless SJ, Partom Y (1996) On the L/D effect for long-rod penetrators. Int J Impact Eng 18(247):264Google Scholar
  43. 43.
    Anderson CE, Walker JD (1991) An examination of long-rod penetration. Int J Impact Eng 11(481):501Google Scholar
  44. 44.
    Wilkins ML (1973) Calculation of elastic-plastic flow. Lawrence Livermore Laboratory Report UCRL 7322, revision 1Google Scholar
  45. 45.
    US DOD (2000) Armour plate, steel, wrought, homogeneous military specification MIL-A-12560H (Amendment 3)Google Scholar
  46. 46.
    Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, large strain rates, and high temperatures. In: Proc. 7th Int. Symp. Ballistics, pp 541–547Google Scholar
  47. 47.
    Yaziv D, Mayseless M, Reifen Y (2001) The penetration process of long rods into thin metallic targets at high obliquity. In: Crewther IR (ed) Proc. 19th Int. Symp. On Ballistics. Interlaken, Switzerland, pp 1257–1264Google Scholar

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIran University of Science and TechnologyTehranIran

Personalised recommendations