Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2015, Article ID 265321, 15 pages
http://dx.doi.org/10.1155/2015/265321
Review Article

Theoretical Research Progress in High-Velocity/Hypervelocity Impact on Semi-Infinite Targets

1State Key Laboratory for Disaster Prevention & Mitigation of Explosion & Impact, PLA University of Science and Technology, Nanjing 210007, China
2Beijing Canbao Architecture Design Institute, Beijing 100036, China
3The Fifth Department, 145 Erqi Road, Wuhan 430012, China

Received 3 November 2014; Revised 2 February 2015; Accepted 5 February 2015

Academic Editor: Mohammad Elahinia

Copyright © 2015 Yunhou Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Kinslow, High-Velocity Impact Phenomena, Academic Press, New York, NY, USA, 1970.
  2. W. Herrmann and J. S. Wilbeck, “Review of hypervelocity penetration theories,” International Journal of Impact Engineering, vol. 5, no. 1–4, pp. 307–322, 1987. View at Publisher · View at Google Scholar · View at Scopus
  3. Q.-M. Zhang and F. L. Huang, Hypervelocity Impact Kinetics Theory. First Version, Science Press, Beijing, China, 2000, (Chinese).
  4. T. H. Antoun, L. A. Glenn, O. R. Walton, P. Goldstein, I. N. Lomov, and B. Liu, “Simulation of hypervelocity penetration in limestone,” International Journal of Impact Engineering, vol. 33, no. 1–12, pp. 45–52, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. V. M. Fomin, A. I. Gulidov, G. A. Salozhnikov et al., The High-Speed Interaction between Solids, The Russian Academy of Science Siberian Branch Press, Novosibirsk, Russia, 1999, (Russian).
  6. T. J. Ahrens and M. L. Johnson, “Shock wave data for rocks,” in Mineral Physics and Crystallography, A Handbook of Physical Constants, T. J. Ahrens, Ed., pp. 35–44, American Geophysical Union, Washington, DC, USA, 1995. View at Google Scholar
  7. G. Weirauch, Das verhalfen von kupfersufen derm auftreffen auf verschiedene werkstuffe mit geschwindigkeiten zwischen 50m/s and 1650m/s, University of Karlsruhe, Karlsruhe, Germany, 1971.
  8. F.-Q. Jing, Experiment State Equation Guiding. Second Version, Science Press, Beijing, China, 1999, (Chinese).
  9. W. P. Walters and J. A. Zukas, Theory and Application of Shaped Charge, Weapon industry Press, Beijing, China, 1989, Translated 1992 by W. Shu-kui and B. Jing-fen.
  10. J. D. Walker, “Hypervelocity penetration modeling: momentum vs. energy and energy transfer mechanisms,” International Journal of Impact Engineering, vol. 26, no. 1–10, pp. 809–822, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. Q.-H. Qian and M.-Y. Wang, Shock and Explosion Effect in Rock, First Version, National Defense Industry Press, Beijing, China, 2010 (Chinese).
  12. G. H. Jonas and J. A. Zukas, “Mechanics of penetration: analysis and experiment,” International Journal of Engineering Science, vol. 16, no. 11, pp. 879–903, 1978. View at Publisher · View at Google Scholar · View at Scopus
  13. F.-Q. Jing, “Hypervelocity impact phenomena,” Explosion and Shock Waves, vol. 10, pp. 279–288, 1990 (Chinese). View at Google Scholar
  14. M.-Y. Wang, Calculating Research Progress on Protective Structure Anti-Penetration, Xiangshan Science Conferences Reports, Beijing, China, 2013, (Chinese).
  15. J. L. Summers and A. C. Charters, “High speed impact of metal projectiles in targets of various materials,” in Proceedings of the 3rd Symposium on Hypervelocity Impact, Chicago, Ill, USA, October 1958.
  16. A. C. Charters and G. S. Locke Jr., “A preliminary investigation of high speed impact: the penetration of small spheres into thick copper targets,” Tech. Rep. NASA RM A58B26, 1957. View at Google Scholar
  17. J. Frazier, “Hypervelocity impact experiments in wax,” BRL Report 1124, Aberdeen Proving Ground, Aberdeen, Md, USA, 1961. View at Google Scholar
  18. J. H. Kineke Jr., “An experimental study of crater formation in metallic targets,” in Proceedings of the 4th Symposium on Hypervelocity Impact, vol. 1, pp. 10–12, 1960.
  19. J. H. Kineke Jr., “Observation of crater formation in ductuile materials,” in Proceedings of the 5th Symposium on Hypervelocity Impact, pp. 339–370, Denver, Colo, USA, October 1961.
  20. W. Herrmann and A. Jones, “Correlation of hypervelocity impact data,” in Proceedings of the 5th Symposium on Hypervelocity Impact, pp. 389–438, Denver, Colo, USA, 1961.
  21. E. P. Bruce, “Review and analysis of high velocity impact data,” in Proceedings of the 5th Symposium on Hypervelocity Impact, pp. 439–474, Denver, Colo, USA, 1961.
  22. G.-C. Sun, Q.-M. Tan, C.-X. Zhao, and X.-Z. Ge, “Cratering experiments with hypervelocity impact upon thick metallic targets,” Acta Armamentarii, vol. 1, pp. 27–31, 1994 (Chinese). View at Google Scholar
  23. K. P. Stanyukovich, The Unsteady Motion of Continuum, Nauka, Moscow, Russia, 1971.
  24. L. V. Leontyev, “Comparison for effects of meteoroid collision with the surfaces of different targets,” Space Research, vol. 14, pp. 278–286, 1976. View at Google Scholar
  25. L. E. Murr, S. A. Quinones, E. Ferreyra T et al., “The low-velocity-to-hypervelocity penetration transition for impact craters in metal targets,” Materials Science and Engineering A, vol. 256, no. 1-2, pp. 166–182, 1998. View at Publisher · View at Google Scholar · View at Scopus
  26. J. R. Baker, “Hypervelocity crater penetration depth and diameter—a linear function of impact velocity?” International Journal of Impact Engineering, vol. 17, no. 1–3, pp. 25–35, 1995. View at Publisher · View at Google Scholar · View at Scopus
  27. S.-B. Yu, G.-C. Sun, and Q.-M. Tan, “Experimental laws of cratering for hypervelocity impacts of spherical projectiles into thick target,” International Journal of Impact Engineering, vol. 15, no. 1, pp. 67–77, 1994. View at Publisher · View at Google Scholar · View at Scopus
  28. E. J. Öpik, “The moon's surface,” Annual Review of Astronomy and Astrophysics, vol. 7, pp. 473–526, 1969. View at Publisher · View at Google Scholar
  29. D. E. Gault, “Displaced mass, depth, diameter, and effects of oblique trajectories for impact craters formed in dense crystalline rocks,” The Moon, vol. 6, no. 1-2, pp. 32–44, 1973. View at Publisher · View at Google Scholar
  30. M. R. Dence, R. A. F. Grieve, and P. B. Robertson, “Terrestrial impact structures: principal characteristics and energy consideration,” in Impact and Explosion Cratering, D. J. Roddy, R. O. Pepin, and R. B. Merrill, Eds., pp. 247–275, Pergamon Press, New York, NY, USA, 1977. View at Google Scholar
  31. Q.-M. Zhang and F.-L. Huang, “Effects on the earth resulted from the impact of a planetoid,” China Safety Science Journal, vol. 5, pp. 21–26, 1995. View at Google Scholar
  32. P. S. Westine and S. A. Mullin, “Scale modeling of hypervelocity impact,” International Journal of Impact Engineering, vol. 5, no. 1–4, pp. 693–701, 1987. View at Publisher · View at Google Scholar · View at Scopus
  33. Y.-M. Shen and J.-Q. Chen, “Numerically simulating verification of the comparability rule on hypervelocity impact,” Explosion and Shock Waves, vol. 31, no. 4, pp. 343–348, 2011 (Chinese). View at Google Scholar · View at Scopus
  34. R. T. Sedgwick, “Numerical techniques for modeling high velocity penetration and perforation processes,” in Ballistic Materials and Penetration Mechanics, R. C. Laible, Ed., vol. 5, pp. 253–272, Elsevier, New York, NY, USA, 1980. View at Publisher · View at Google Scholar
  35. J.-L. Xiang, The Effect of Compressible Effect of Metal Materials to Crater of Hypervelocity Impacting into Secondary Targets, Mechanics Research Institution of Chinese Academy of Sciences, Beijing, China, 1990, (Chinese).
  36. Z.-W. Luo, Numerical Simulation of Metal Material Hypervelocity Impact, Mechanics Research Institution of Chinese Academy of Sciences, Beijing, China, 1990, (Chinese).
  37. Q. Guo, The Hypervelocity Impact Activity of TC4 Fibre and TiB2 Grains Enhanced Aluminum-Based Composite Material, Harbin Institute of Technology, Harbin, China, 2012.
  38. L. A. Merzhievsky, “Crater formation in a plastic target under hypervelocity impact,” International Journal of Impact Engineering, vol. 20, no. 6-10, pp. 557–568, 1997. View at Publisher · View at Google Scholar · View at Scopus
  39. A. J. Watts and D. Atkinson, “Dimensional scaling for impact cratering and perforation,” Tech. Rep. NASA-CR-188259, NASA, Washington, DC, USA, 1995. View at Google Scholar
  40. N. Zhou, “A simple analysis model for the hypervelocity cratering of semi-infinite targets by projectile,” International Journal of Impact Engineering, vol. 23, no. 1, pp. 989–994, 1999. View at Publisher · View at Google Scholar · View at Scopus
  41. T. Kadono and A. Fujiwara, “Cavity and crater depth in hypervelocity impact,” International Journal of Impact Engineering, vol. 31, no. 10, pp. 1309–1317, 2005. View at Publisher · View at Google Scholar · View at Scopus
  42. A. J. Piekutowski, M. J. Forrestal, K. L. Poormon, and T. L. Warren, “Penetration of 6061-T6511 aluminum targets by ogive-nose steel projectiles with striking velocities between 0.5 and 3.0 KM/S,” International Journal of Impact Engineering, vol. 23, no. 1, pp. 723–734, 1999. View at Publisher · View at Google Scholar · View at Scopus
  43. M. J. Forrestal and A. J. Piekutowski, “Penetration experiments with 6061-T6511 aluminum targets and spherical-nose steel projectiles at striking velocities between 0.5 and 3.0 km/s,” International Journal of Impact Engineering, vol. 24, no. 1, pp. 57–67, 2000. View at Publisher · View at Google Scholar · View at Scopus
  44. A. F. Savvateev, A. V. Budin, V. A. Kolikov, and P. G. Rutberg, “High-speed penetration into sand,” International Journal of Impact Engineering, vol. 26, no. 1-10, pp. 675–681, 2001. View at Publisher · View at Google Scholar · View at Scopus
  45. S. J. Bless, D. T. Berry, B. Pedersen et al., “Sand penetration by highspeed projectiles,” in Shock Compression of Condensed Matter, M. L. Elert, W. T. Buttler, M. D. Furnish, and etal, Eds., pp. 1361–1364, American Institute of Physics, 2009. View at Google Scholar
  46. J. Shen, X. Xu, X. He, S. Feng, and J. Yang, “Experimental study of effect of rock targets penetrated by high-velocity projectiles,” Chinese Journal of Rock Mechanics and Engineering, vol. 29, no. 2, pp. 4207–4212, 2010 (Chinese). View at Google Scholar · View at Scopus
  47. M. J. Forrestal, D. J. Frew, S. J. Hanchak, and N. S. Brar, “Penetration of grout and concrete targets with ogive-nose steel projectiles,” International Journal of Impact Engineering, vol. 18, no. 5, pp. 465–476, 1996. View at Publisher · View at Google Scholar · View at Scopus
  48. D. J. Frew, S. J. Hanchak, M. L. Green, and M. J. Forrestal, “Penetration of concrete targets with ogive-nose steel rods,” International Journal of Impact Engineering, vol. 21, no. 6, pp. 489–497, 1998. View at Publisher · View at Google Scholar · View at Scopus
  49. X.-W. Chen, B. Liang, Y.-Q. Ji et al., “Secondary-caliber experimental research on advanced high penetration ability earth penetrator,” in Proceedings of the Assembly Documents of the 6th National Conference on Security and Protective of Engineering Structure, pp. 1–6, Luoyang, China, 2007, (Chinese).
  50. X. He, X.-Y. Xu, G.-J. Sun, J. Shen, J.-C. Yang, and D.-L. Jin, “Experimental investigation on projectiles' high-velocity penetration into concrete targets,” Explosion and Shock Waves, vol. 30, no. 1, pp. 1–6, 2010 (Chinese). View at Google Scholar · View at Scopus
  51. X.-N. Zhao, Effect Research on High Velocity Projectile Penetrating into Concrete, Nanjing University of Science and Technology, Nanjing, China, 2011, (Chinese).
  52. Z. Mu and W. Zhang, “An investigation on mass loss of ogival projectiles penetrating concrete targets,” International Journal of Impact Engineering, vol. 38, no. 8-9, pp. 770–778, 2011. View at Publisher · View at Google Scholar · View at Scopus
  53. H.-J. Wu, F.-L. Huang, Y.-N. Wang, Z.-P. Duan, and A.-G. Pi, “Experimental investigation on projectile nose eroding effect of high-velocity penetration into concrete,” Acta Armamentarii, vol. 33, no. 1, pp. 48–55, 2012 (Chinese). View at Google Scholar · View at Scopus
  54. L.-L. He, X.-W. Chen, and Y.-M. Xia, “A review on the mass loss of projectile,” Acta Armamentarii, vol. 31, no. 7, pp. 950–966, 2010 (Chinese). View at Google Scholar · View at Scopus
  55. M. A. Lavrent'ev, “Cumulative charge and the principles of its operation,” Uspekhi Matematicheskikh Nauk, vol. 12, no. 4, article 76, pp. 41–56, 1957. View at Google Scholar · View at MathSciNet
  56. F. F. Vitman and N. A. Zlatin, “On collision of deformable bodies and its modeling,” Journal of Technology Physics, vol. 33, pp. 982–989, 1963 (Russian). View at Google Scholar
  57. A. Tate, “A theory for the deceleration of long rods after impact,” Journal of the Mechanics and Physics of Solids, vol. 15, no. 6, pp. 387–399, 1967. View at Publisher · View at Google Scholar · View at Scopus
  58. S. Satapathy, “Dynamic spherical cavity expansion in brittle ceramics,” International Journal of Solids and Structures, vol. 38, no. 32-33, pp. 5833–5845, 2001. View at Publisher · View at Google Scholar · View at Scopus
  59. M. J. Forrestal, K. Okajima, and V. K. Luk, “Penetration of 6061-T651 aluminum targets with rigid long rods,” Journal of Applied Mechanics, Transactions ASME, vol. 55, no. 4, pp. 755–760, 1988. View at Publisher · View at Google Scholar · View at Scopus
  60. S. C. Hunter and R. J. M. Crozier, “Similarity solution for the rapid uniform expansion of a spherical cavity in a compressible elastic-plastic solid,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 21, no. 4, pp. 467–486, 1968. View at Publisher · View at Google Scholar · View at Scopus
  61. X. W. Chen and Q. M. Li, “Deep penetration of a non-deformable projectile with different geometrical characteristics,” International Journal of Impact Engineering, vol. 27, no. 6, pp. 619–637, 2002. View at Publisher · View at Google Scholar · View at Scopus
  62. Q. M. Li and X. W. Chen, “Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile,” International Journal of Impact Engineering, vol. 28, no. 1, pp. 93–116, 2003. View at Publisher · View at Google Scholar · View at Scopus
  63. M.-Y. Wang, X.-L. Rong, Q.-H. Qian, and T. Ge, “Calculation principle for penetration and perforation of projectiles into rock,” Chinese Journal of Rock Mechanics and Engineering, vol. 22, no. 11, pp. 1811–1806, 2003. View at Google Scholar · View at Scopus
  64. M.-Y. Wang, D.-L. Zheng, and Q.-H. Qian, “Scaling problems of penetration and perforation for projectile into concrete media,” Explosion and Shock Waves, vol. 24, no. 2, pp. 108–114, 2004 (Chinese). View at Google Scholar · View at Scopus
  65. W. Chen, M.-Y. Wang, and L.-Y. Gu, “Calculation of oblique penetration depth of projectiles into an intrinsic friction medium,” Explosion and Shock Waves, vol. 28, no. 6, pp. 521–526, 2008 (Chinese). View at Google Scholar · View at Scopus
  66. Q.-H. Qian and M.-Y. Wang, Calculation Theory for Advanced Protective Structures, first version, Jiangsu Science and Technology Press, Nanjing, China, 2009, (Chinese).
  67. M.-Y. Wang, T. Ge, P. Wu, and Q.-H. Qian, “Study on problems of near cavity of penetration and explosion in rock,” Chinese Journal of Rock Mechanics and Engineering, vol. 23, pp. 2859–2863, 2005 (Chinese). View at Google Scholar
  68. D.-R. Wang, T. Ge, Z.-P. Zhou, and M.-Y. Wang, “Investigation of calculation method for anti-penetration of reactive power steel fiber concrete (RPC),” Explosion and Shock Waves, vol. 26, no. 4, pp. 367–372, 2006 (Chinese). View at Google Scholar · View at Scopus
  69. M.-Y. Wang, K.-K. Tan, H.-J. Wu, and Q. Qian, “New method of calculation of projectile penetration into rock,” Chinese Journal of Rock Mechanics and Engineering, vol. 28, no. 9, pp. 1863–1869, 2009 (Chinese). View at Google Scholar · View at Scopus
  70. X. W. Chen and Q. M. Li, “Transition from nondeformable projectile penetration to semihydrodynamic penetration,” Journal of Engineering Mechanics, vol. 130, no. 1, pp. 123–127, 2004. View at Publisher · View at Google Scholar · View at Scopus
  71. M. J. Forrestal, B. S. Altman, J. D. Cargile, and S. J. Hanchak, “An empirical equation for penetration depth of ogive-nose projectiles into concrete targets,” International Journal of Impact Engineering, vol. 15, no. 4, pp. 395–405, 1994. View at Publisher · View at Google Scholar · View at Scopus
  72. Z.-C. Mu, The Research on Penetration Characters of Concrete Material under Steel Penetrating Model, Harbin Institute of Technology, Harbin, China, 2012, (Chinese).
  73. S. B. Segletes, “The erosion transition of tungsten-alloy long rods into aluminum targets,” International Journal of Solids and Structures, vol. 44, no. 7-8, pp. 2168–2191, 2007. View at Publisher · View at Google Scholar · View at Scopus
  74. J.-F. Lou, Theory Model and Numerical Simulation Research on Penetrating into Semi-Infinite Targets, China Academy of Engineering Physics, Mianyang, China, 2012, (Chinese).
  75. R. F. Bishop, R. Hill, and N. F. Mott, “The theory of indentation and hardness tests,” Proceedings of the Physical Society, vol. 57, no. 3, article 301, pp. 147–159, 1945. View at Publisher · View at Google Scholar · View at Scopus
  76. R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, London, UK, 1950.
  77. Z. Rosenberg and E. Dekel, “Numerical study of the transition from rigid to eroding-rod penetration,” Journal de Physique Archives, vol. 110, pp. 681–686, 2003. View at Google Scholar
  78. Z. Rosenberg and E. Dekel, “On the deep penetration of deforming long rods,” International Journal of Solids and Structures, vol. 47, no. 2, pp. 238–250, 2010. View at Publisher · View at Google Scholar · View at Scopus
  79. A. Tate, “A possible explanation for the hydrodynamic transition in high speed impact,” International Journal of Mechanical Sciences, vol. 19, no. 2, pp. 121–123, 1977. View at Publisher · View at Google Scholar · View at Scopus
  80. V. P. Alekseevskii, “Penetration of a rod into a target at high velocity,” Combustion, Explosion, and Shock Waves, vol. 2, no. 2, pp. 63–66, 1969. View at Publisher · View at Google Scholar · View at Scopus
  81. F. F. Vitaman, N. A. Zlatin, and B. S. Loffe, “Deformable resistance of metals at velocities 10−6-102m/s,” Journal of Technical Physics, vol. 19, pp. 300–326, 1949. View at Google Scholar
  82. F. F. Vitman and N. A. Zlatin, “On collision of deformable bodies and its modeling. I,” Journal of Technical Physics, vol. 33, pp. 982–989, 1963. View at Google Scholar
  83. L. V. Belyakov, F. F. Vitman, and N. A. Zlatin, “On collision of deformable bodies and its modeling. II,” Journal of Technical Physics, vol. 33, pp. 990–995, 1963. View at Google Scholar
  84. N. A. Zlatin and G. I. Mishin, Ballistic Ranges and Their Application in Experimental Research, Nauka Press, Moscow, Russia, 1974.
  85. A. Tate, “Long rod penetration models—part I. A flow field model for high speed long rod penetration,” International Journal of Mechanical Sciences, vol. 28, no. 8, pp. 535–548, 1986. View at Publisher · View at Google Scholar · View at Scopus
  86. A. Tate, “Long rod penetration models. Part II. Extensions to the hydrodynamic theory of penetration,” International Journal of Mechanical Sciences, vol. 28, no. 9, pp. 599–612, 1986. View at Publisher · View at Google Scholar · View at Scopus
  87. G. C. Sun, J. Y. Wu, G. Z. Zhao et al., “A simplified model of long-rod projectile penetration of semi-infinite targets at normal incidence,” Acta Armamentarii, vol. 3, pp. 1–8, 1981 (Chinese). View at Google Scholar
  88. Z. Rosenberg, E. Marmor, and M. Mayseless, “On the hydrodynamic theory of long-rod penetration,” International Journal of Impact Engineering, vol. 10, no. 1–4, pp. 483–486, 1990. View at Publisher · View at Google Scholar · View at Scopus
  89. L.-S. Zhang and F.-L. Huang, “Model for long-rod penetration into semi-infinite targets,” Journal of Beijing Institute of Technology, vol. 13, no. 3, pp. 285–289, 2004. View at Google Scholar · View at Scopus
  90. C. E. Anderson Jr., J. D. Walker, S. J. Bless, and Y. Partom, “On the L/D effect for long-rod penetrators,” International Journal of Impact Engineering, vol. 18, no. 3, pp. 247–264, 1996. View at Publisher · View at Google Scholar · View at Scopus
  91. B. Lan and H. Wen, “Alekseevskii-Tate revisited: an extension to the modified hydrodynamic theory of long rod penetration,” Science China Technological Sciences, vol. 53, no. 5, pp. 1364–1373, 2010. View at Publisher · View at Google Scholar · View at Scopus
  92. H. Wen, Y. He, and B. Lan, “Analytical model for cratering of semi-infinite metallic targets by long rod penetrators,” Science China Technological Sciences, vol. 53, no. 12, pp. 3189–3196, 2010. View at Publisher · View at Google Scholar · View at Scopus
  93. A. A. Kozhushko, A. D. Izotov, V. B. Lazarev et al., “Hydrodynamic model concepts in the problem of the dyanmic strength of materials of various physicochemica nature. II. Effets of the strength characterisitics of media,” Neorganicheskie Materialy, vol. 29, pp. 1189–1209, 1993. View at Google Scholar
  94. J. Zhao, X. W. Chen, F. N. Jin, and Y. Xu, “Depth of penetration of high-speed penetrator with including the effect of mass abrasion,” International Journal of Impact Engineering, vol. 37, no. 9, pp. 971–979, 2010. View at Publisher · View at Google Scholar · View at Scopus
  95. S. A. Silling and M. J. Forrestal, “Mass loss from abrasion on ogive-nose steel projectiles that penetrate concrete targets,” International Journal of Impact Engineering, vol. 34, no. 11, pp. 1814–1820, 2007. View at Publisher · View at Google Scholar · View at Scopus
  96. L.-L. He, X.-W. Chen, and X. He, “Parametric study on mass loss of penetrators,” Acta Mechanica Sinica, vol. 26, no. 4, pp. 585–597, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  97. L.-L. He, Dynamic Behavior Research on the Projectile Penetrating into Concrete with Considering Mass Losing and Nose Passivation, China University of Sciences and Technology, Hefei, China, 2012 (Chinese).
  98. S. E. Jones, J. C. Foster, O. A. Toness et al., “An estimate for mass loss from high velocity steel penetrators,” in Proceedings of the ASME PVP-435 Conference on Thermal-Hydraulic Problems, Sloshing Phenomena, and Extreme Loads on Structures, vol. 422, pp. 227–237, ASME, New York, NY, USA, 2002.
  99. L.-L. He and X.-W. Chen, “Analyses of the penetration process considering mass loss,” European Journal of Mechanics A/Solids, vol. 30, no. 2, pp. 145–157, 2011. View at Publisher · View at Google Scholar · View at Scopus
  100. Y. Yang, Problems Research on Penetration and Run Through of Concrete, China University of Sciences and Technology, Hefei, China, 2012, (Chinese).
  101. H.-M. Wen and B. Lan, “Analytical models for the penetration of semi-infinite targets by rigid, deformable and erosive long rods,” Acta Mechanica Sinica, vol. 26, no. 4, pp. 573–583, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  102. M. J. Forrestal and T. L. Warren, “Penetration equations for ogive-nose rods into aluminum targets,” International Journal of Impact Engineering, vol. 35, no. 8, pp. 727–730, 2008. View at Publisher · View at Google Scholar · View at Scopus
  103. C.-B. Li, Z.-W. Shen, and M.-J. Pei, “Calculation analysis of rod-shaped projectile penetrating into concrete targets,” Journal of University of Science and Technoloty China, vol. 28, pp. 215–219, 2008 (Chinese). View at Google Scholar
  104. J. Zhao, Y.-H. Zhao, J.-L. Shan et al., “The Hugoniot equation of state for Bukit Timah granite,” Chinese Journal of Geotechnical Engineering, vol. 21, pp. 315–318, 1999 (Chinese). View at Google Scholar
  105. A. C. Charters and J. L. Summers, “Some comments on the phenomena of high speed impact,” in Proceedings of the Dicennial Symposium, U.S. Naval Ordnance Laboratory, White Oak, Md, USA, 1959.
  106. R. J. Eichelberger, “Effects of meteoroid impacts on space vehicles,” ARS Journal, vol. 32, no. 10, pp. 1583–1591, 1962. View at Publisher · View at Google Scholar
  107. I. J. Loeffler, S. Liebleln, and N. Clough, “Meteoroid protection for space radiators, progress in astronautics and aeronautics,” in Power Systems for Space Flight, M. A. Zipkin and R. N. Edwards, Eds., Academic Press, 1963. View at Google Scholar
  108. D. R. Christman and J. W. Gehring, “Analysis of high-velocity projectile penetration mechanics,” Journal of Applied Physics, vol. 37, no. 4, pp. 1579–1587, 1966. View at Publisher · View at Google Scholar · View at Scopus
  109. J. M. Walsh and W. E. Johnson, “On the theory of hypervelocity impact,” in Proceedings of the 7th Symposium on Hypervelocity Impact, Tampa, Fla, USA, 1964.
  110. E. L. Christiansen, “Design and performance equations for advanced meteoroid and debris shields,” International Journal of Impact Engineering, vol. 14, no. 1–4, pp. 145–156, 1993. View at Publisher · View at Google Scholar · View at Scopus
  111. J.-S. Zhou, L. Zhen, and D.-Z. Yang, “ Damage behaviors of several metal materials under impacts of projectiles with hypervelocities of 2.6~7 km/s,” Journal of Astronautics, vol. 21, pp. 75–81, 2000 (Chinese). View at Google Scholar