Skip to main content
SpringerLink
Log in

Petal failure models of thin aluminum alloy plate penetrated by conical projectile nose

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

The process of the penetration of thin aluminum alloy plates which are widely used in satellites by conical projectile nose is studied in this paper. A new method of internal capture by flying anchor is proposed to capture and remove large space debris in this paper. The key problem to be solved in this method is the vertical and oblique penetration of satellite surface materials. According to the actual failure shapes, two theoretical models, the petal failure model of vertical penetration and the petal failure model of oblique penetration, are proposed by means of energy balance. For a thin aluminum alloy plate, where petal failure always occurs after penetration, the energy consumption of deformation region of plate involves the deformation energy of cylindrical wall, the petal tearing energy and the petal bending energy. The Thomson’s theory is used to calculate the plastic deformation energy of the cylinder wall. Dugdale’s narrow band theory which assumed that the width of the plastic zone near the crack tip is similar to the plate thickness is used in the calculation of petal tearing energy. For vertical penetration and oblique penetration, the shape of deformation region is circle and ellipse respectively. In the study of petal failure model of vertical penetration, the effect of half-cone angle on fracture stress is studied by numerical calculation using ANSYS Explicit Dynamics. In the study of oblique penetration, the functional relationship between deflection angle and initial obliquity angle is proposed through numerical calculation. Through the theoretical models, the energy consumption of target plate failure is calculated, so as to calculate the residual velocity or ballistic limit. Tests conducted on common aluminum alloy plates with a thickness of 2 mm. For most aluminum alloy targets, the experimental results are in good agreement with the theoretical results.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig.12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.
Fig. 18.
Fig. 19.
Fig. 20.
Fig. 21.
Fig. 22.
Fig. 23.
Fig. 24.
Fig. 25.
Fig. 26.
Fig. 27.

Similar content being viewed by others

REFERENCES

  1. D. J. Kessler and B. G. Cour-Palais, “Collision frequency of artificial satellites: The creation of a debris belt,” J. Geophys. Res-Space Phys. 83, 2637–2646 (1987). https://doi.org/10.1029/JA083iA06p02637

    Article  ADS  Google Scholar 

  2. R. F. Bishop, R. Hill, and N. F. Mott, “The theory of indentation and hardness tests,” Proc. Phys. Soc. 57, 147–159 (1945). https://doi.org/10.1088/0959-5309/57/3/301

    Article  ADS  Google Scholar 

  3. Y. J. Deng, W. J. Song, and X. W. Chen, “Spherical cavity-expansion model for penetration of reinforced-concrete targets,” Acta Mech. Sin. 35, 535–551 (2019). https://doi.org/10.1007/s10409-018-0821-9

    Article  MathSciNet  MATH  Google Scholar 

  4. Y. Peng, H. Wu, Q. Fang, X. Z. Kong, et al., “Modified spherical cavity expansion model for projectile penetration into concrete targets,” Acta Mech. Sin. 35, 518–534 (2019). https://doi.org/10.1007/s10409-018-0815-7

    Article  MathSciNet  Google Scholar 

  5. Q. F. Zhu, Z. X. Huang, Q. Q. Xiao, et al., “Theoretical considerations on cavity diameters and penetration depths of concrete materials generated by shaped charge jets using the targets response modes described by a modified HJC model,” Int. J. Impact. Eng. 138, 103439 (2020). https://doi.org/10.1016/j.ijimpeng.2019.103439

  6. Q. Tan, C. Meng, D. Song, et al., “Depth of penetration of steel-tube-confined concrete targets based on dynamic finite cylindrical cavity-expansion models,” SN Appl. Sci. 2, 613 (2020). https://doi.org/10.1007/s42452-020-2356-5

    Article  Google Scholar 

  7. R. Masri, “Low-velocity penetration of a rigid, hemispherical nose projectile in incompressible, elastoplastic, strain-hardening Mises media,” Int. J. Solids Struct. 167, 14–23 (2019). https://doi.org/10.1016/j.ijsolstr.2019.02.022

    Article  Google Scholar 

  8. Z. C. Lu and H. M. Wen, “On the penetration of high strength steel rods into semi-infinite aluminium alloy targets,” Int. J. Impact Eng. 111, 1–10 (2018). https://doi.org/10.1016/j.ijimpeng.2017.08.006

    Article  Google Scholar 

  9. X. W. Chen and Q. M. Li, “Perforation of a thick plate by rigid projectiles,” Int. J. Impact Eng. 28, 743–759 (2003). https://doi.org/10.1016/S0734-743X(02)00152-5

    Article  Google Scholar 

  10. H. Yang, J. Zhang, Z. Wang, et al., “Numerical study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets,” Acta Mech. Sin. 37, 482–493 (2021). https://doi.org/10.1007/s10409-021-01054-6

    Article  ADS  Google Scholar 

  11. C. E. Anderson, “Analytical models for penetration mechanics: a review,” Int. J. Impact Eng. 108, 3–26 (2017). https://doi.org/10.1016/j.ijimpeng.2017.03.018

    Article  Google Scholar 

  12. Z. Melvin and P. Burton, “Mechanics of high speed projectile perforation,” J. Franklin Inst. 264, 117–126 (1957). https://doi.org/10.1016/0016-0032(57)90892-X

    Article  MathSciNet  Google Scholar 

  13. B. Lankof and W. Goldsmith, “Petalling of thin metallic plates during penetration by cylindro-conical projection,” Int. J. Solids Struct. 21, 245–266 (1985). https://doi.org/10.1016/0020-7683(85)90021-6

    Article  Google Scholar 

  14. N. K. Gupta, R. Ansari, and S. K. Gupta, “Normal impact of ogive nosed projectiles on thin plates,” Int. J. Impact Eng. 25, 641–660 (2001). https://doi.org/10.1016/S0734-743X(01)00003-3

    Article  Google Scholar 

  15. Z. Mohammad, P. K. Gupta, and A. Baqi, “Experimental and numerical investigations on the behavior of thin metallic plate targets subjected to ballistic impact,” Int. J. Impact Eng. 146, 103717 (2020). https://doi.org/10.1016/j.ijimpeng.2020.103717

  16. D. W. Zhou and W. J. Stronge, “Ballistic limit for oblique impact of thin sandwich panels and spaced,” Int. J. Impact Eng. 35, 1339–1354 (2008). https://doi.org/10.1016/j.ijimpeng.2007.08.004

    Article  Google Scholar 

  17. Vishal Mehra, Sambaran Pahari, Aditya Nandan Savita, et al., “Tip failure and residual velocity in impact of hollow Al-6061 T6 projectiles on thin Al-6061 T6 plates,” Proc. Eng. 173, 271–277 (2017). https://doi.org/10.1016/j.proeng.2016.12.012

    Article  Google Scholar 

  18. Yu. K. Bivin, “Fracture of circular plates on normal impact by a rigid spherical body,” Mech. Solids. 46 (4), 597–609 (2011). https://doi.org/10.3103/S0025654411040108

    Article  ADS  Google Scholar 

  19. Yu. K. Bivin and I. V. Simonov, “Fracture mechanisms of metal plates under off-centred impact,” Key Eng. Mater. 417–418, 249-252 (2010). https://doi.org/10.4028/www.scientific.net/KEM.417-418.249

  20. Yu. K. Bivin, “Fracture of metal plates on normal impact by a rigid conical body,” Mech. Solids. 49 (4), 445–452 (2014). https://doi.org/10.3103/S0025654414040098

    Article  ADS  Google Scholar 

  21. N. V. Banichuk, S. Y. Ivanova, and K. Y. Osipenko, “Perforation of layered structures by a spherical rigid body,” Mech. Solids. 56, 189–196 (2021). https://doi.org/10.3103/S0025654421020035

    Article  ADS  Google Scholar 

  22. V. V. Vershinin, “Validation of metal plasticity and fracture models through numerical simulation of high-velocity perforation,” Int. J. Solids Struct. 67-68, 127–138 (2015). https://doi.org/10.1016/j.ijsolstr.2015.04.007

    Article  Google Scholar 

  23. P. A. Mossakovsky, F. K. Antonov, A. M. Bragov, et al., “On fracture criterion of titanium alloy under dynamic loading conditions,” in Proc. of 8th European LS-DYNA Users Conference (Straßburg, 2011). https://www.dynalook.com/conferences/8th-european-ls-dyna-conference/session-10/Session10_Paper4.pdf/view

  24. A. Rusinek, J. A. Rodríguez-Martínezb, A. Arias, et al., “Influence of conical projectile diameter on perpendicular impact of thin steel plate,” Eng. Fract. Mech. 75, 2946–2967 (2008). https://doi.org/10.1016/j.engfracmech.2008.01.011

    Article  Google Scholar 

  25. Vivek Bhurea, Gaurav Tiwaria, M. A. Iqbalb, et al., “The effect of target thickness on ballistic resistance of thin aluminium plates,” Mater. Today: Proc. 21, 1999–2013 (2020). https://doi.org/10.1016/j.matpr.2020.01.317

  26. R. Dudzia, S. Tuttle, and S. Barraclough, “Harpoon technology development for the active removal of space debris,” Adv. Space Res. 56, 509–527 (2015). https://doi.org/10.1016/j.asr.2015.04.012

    Article  ADS  Google Scholar 

  27. K. Senthil, B. Arindamb, R. Mittalb, et al., “Numerical investigations on the impact of hemi spherically tipped projectiles on thin plates,” Proc. Engi. 173, 1926–1931 (2017). https://doi.org/10.1016/j.proeng.2016.12.254

    Article  Google Scholar 

  28. A. Ariasa, J. A. Rodríguez-Martíneza, and A. Rusinekb, “Numerical simulations of impact behaviour of thin steel plates subjected to cylindrical, conical and hemispherical non-deformable projectiles,” Eng. Fract. Mech. 75, 1635–1656 (2008). https://doi.org/10.1016/j.engfracmech.2007.06.005

    Article  Google Scholar 

  29. P. Teixeira, L. Pina, R. Rocha, et al., “Parametric analysis of energy absorption capacity of thin aluminum plates impacted by rigid spherical projectiles,” Thin-Walled Struct. 159, 107240 (2021) https://doi.org/10.1016/j.tws.2020.107240

  30. C. Y. Thams, “Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile,” Finite. Elem. Anal. Des. 42, 1258–1268 (2006). https://doi.org/10.1016/j.finel.2006.06.011

    Article  Google Scholar 

  31. J. G. Shin, K. Park, and G. I. Kim, “Estimation of exit angle for oblique penetration using numerical analysis,” J. Mech. Sci. Technol. 32, 5767–5776 (2018). https://doi.org/10.1007/s12206-018-1124-6

    Article  Google Scholar 

  32. M. Zaid, and B. Paul, “Oblique perforation of a thin plate by truncated projectile,” J. Franklin Inst. 268, 22–44 (1958). https://doi.org/10.1016/0016-0032(59)90354-0

    Article  MathSciNet  Google Scholar 

  33. Yu. K. Bivin, “Oblique impact by a spherical solid on a metal plate,” Mech. Solids. 48 (2), 228–233 (2013). https://doi.org/10.3103/s0025654413020155

    Article  ADS  Google Scholar 

  34. W. T. Thomson, “An approximate theory of armor penetration,” J. Appl. Phys. 26, 80–2 (1955). https://doi.org/10.1063/1.1721868

    Article  ADS  Google Scholar 

  35. J. Rabin and W. Goldsmith, “Normal projectile penetration and perforation of layered targets,” Int. J. Impact Eng. 7, 229–259 (1988). https://doi.org/10.1016/0734-743X(88)90028-0

    Article  Google Scholar 

  36. D. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids. 8, 100–108 (1960). https://doi.org/10.1016/0022-5096(60)90013-2

    Article  ADS  Google Scholar 

  37. X. U. Shuang-xi, W. U. Wei-guo, L. I. Xiao-bin, et al., “Theoretical analysis on residual velocity of conical projectile after penetrating thin plate at low oblique angle,” J. Ballist. 22, 58–62 (2010). https://doi.org/10.3184/030823410X12680741110954

    Article  Google Scholar 

  38. W. Goldsmith and S. A. Finnegan, “Normal and oblique impact of cylindro-conical and cylindrical projectiles on metallic plates,” Int. J. Impact Eng. 4, 83–105 (1986). https://doi.org/10.1016/0734-743X(86)90010-2

    Article  Google Scholar 

  39. J. Rabin and W. Goldsmith, “Normal projectile penetration and perforation of layered targets,” Int. J. Impact Eng. 7, 229–259 (1988). https://doi.org/10.1016/0734-743X(88)90028-0

    Article  Google Scholar 

  40. C. A. Calder and W. Goldsmith, “Plastic deformation and perforation of thin plates resulting from projectile impact,” Int. J. Solids Struct. 7, 863–881 (1974). https://doi.org/10.1016/0020-7683(71)90096-5

    Article  Google Scholar 

Download references

Funding

This work was financially supported by the National Natural Science Foundation of China (grant no. 51775129).

Author information

Authors and Affiliations

  1. State Key Laboratory of Robotics and System, Harbin Institute of Technology, 150001, Harbin, China

    Yuntao Li, Jingdong Zhao & Hong Liu

  2. Beijing Key Laboratory of Intelligent Space Robotic Systems Technology and Applications, Beijing Institute of Spacecraft System Engineering, 100094, Beijing, China

    Zhijun Zhao

Authors
  1. Yuntao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingdong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhijun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jingdong Zhao.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Zhao, J., Liu, H. et al. Petal failure models of thin aluminum alloy plate penetrated by conical projectile nose. Mech. Solids 57, 427–450 (2022). https://doi.org/10.3103/S0025654422020170

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654422020170

Keyword:

Search

Navigation