Theoretical Investigation on Failure Behavior of OgiveNose Projectile Subjected to Impact Loading
Abstract
:1. Introduction
2. Microscopic Analysis of the Recovered Projectile
3. Abrasion Model
3.1. Constitutive Model
3.2. Equations of Projectile Motion
Algorithm 1 The flow chat of cavity expansion theory. 

3.3. Mass Abrasion
Algorithm 2 Calculation of mass loss in any increment of time $\mathsf{\Delta}t$. 

4. Results and Discussion
4.1. Comparison of the Predicted Results with the Experimental Data
4.2. Comparison of the Predicted Results with Published Experimental Data and Other Abrasion Models
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
SEM  Scanning electron microscopy 
DOP  Depth of penetration 
HAZ  Heat affected zone 
CRH  Caliberradiushead 
References
 Xiao, X.K.; Mu, Z.C.; Pan, H.; Lou, Y.S. Effect of the Lode parameter in predicting shear cracking of 2024T351 aluminum alloy Taylor rods. Int. J. Impact Eng. 2018, 120, 185–201. [Google Scholar] [CrossRef]
 Hamed, S.; Keith, D.; Rooholamin, D.; Abolgazl, D. Scaled models for failure under impact loading. Int. J. Impact Eng. 2019, 129, 36–56. [Google Scholar]
 Ning, J.; Chen, L. Fuzzy interface treatment in Eulerian method. Sci. China Ser. E Technol. Sci. 2004, 47, 550–568. [Google Scholar] [CrossRef]
 Liu, B.; Guedes, C. Plastic response and failure of rectangular crosssection tubes subjected to transverse quasistatic and lowvelocity impact loads. Int. J. Impact Eng. 2015, 90, 213–227. [Google Scholar] [CrossRef]
 Li, J.; Hao, L.; Li, J. Theoretical modeling and numerical simulations of plasmas generated by shock waves. Sci. China Technol. Sci. 2019, 62, 2204–2212. [Google Scholar] [CrossRef]
 Rosenberg, Z.; Vayig, Y. The scaling issue in the penetration of concrete targets by rigid projectiles—Revisited. Int. J. Impact Eng. 2020, 140, 1–7. [Google Scholar] [CrossRef]
 Ning, J.; Song, W.; Yang, G. Failure analysis of plastic spherical shells impacted by a projectile. Int. J. Impact Eng. 2006, 32, 1464–1484. [Google Scholar] [CrossRef]
 Chen, X.W.; Li, Q.M. Transition from nondeformable projectile penetration to semihydrodynamic penetration. J. Eng. MechASCE 2004, 130, 123–127. [Google Scholar] [CrossRef]
 Li, Q.M.; Chen, X.W. Dimensionless formulae for penetration depth of concrete target impacted by a nondeformable projectile. Int. J. Impact Eng. 2003, 28, 93–116. [Google Scholar] [CrossRef]
 Forrestal, M.J.; Altman, B.S.; Cargile, J.D.; Hanchak, S.J. An empirical equation for penetration depth of ogivenose projectiles into concrete targets. Int. J. Impact Eng. 1994, 15, 395–405. [Google Scholar] [CrossRef]
 Forrestal, M.J.; Tzou, D.Y. A spherical cavityexpansion penetration model for concrete targets. Int. J. Solid Struct. 1997, 34, 4127–4146. [Google Scholar] [CrossRef]
 Xu, X.; Ma, T.; Liu, H.; Ning, J. A threedimensional coupled EulerPIC method for penetration problems. Int. J. Numer. Methods Eng. 2019, 119, 737–756. [Google Scholar] [CrossRef]
 Forrestal, M.J.; Frew, D.J.; Hanchak, S.J.; Brar, N.S. Penetration of grout and concrete targets with ogivenose steel projectiles. Int. J. Impact Eng. 1996, 18, 465–476. [Google Scholar] [CrossRef] [Green Version]
 Frew, D.J.; Hanchak, S.J.; Green, M.L.; Forrestal, M.J. Penetration of concrete targets with ogivenose steel rods. Int. J. Impact Eng. 1998, 21, 489–497. [Google Scholar] [CrossRef]
 Zhang, Y.D.; Lu, Z.C.; Wen, H.M. On the penetration of semiinfinite concrete targets by ogivalnosed projectiles at different velocities. Int. J. Impact Eng. 2019, 129, 128–140. [Google Scholar] [CrossRef]
 Feng, J.; Song, M.; Sun, W. Thick plain concrete targets subjected to high speed penetration of 30CrMnSiNi2A steel projectiles: Tests and analyses. Int. J. Impact Eng. 2018, 122, 305–317. [Google Scholar] [CrossRef]
 Yang, J.C.; Zuo, X.J.; He, X. Experimental Study of projectile mass loss in high velocity penetration of concrete target. J. Exp. Mech. 2012, 27, 122–127. [Google Scholar]
 Liu, C.; Zhang, X.F.; Chen, H.H. Experimental and theoretical study on steel longrod projectile penetration into concrete targets with elevated impact velocities. Int. J. Impact Eng. 2020, 138, 305–317. [Google Scholar] [CrossRef]
 Ning, J.; Ren, H.; Guo, T.; Li, P. Dynamic response of alumina ceramics impacted by long tungsten projectile. Int. J. Impact Eng. 2013, 62, 60–74. [Google Scholar] [CrossRef]
 Silling, S.A.; Forrestal, M.J. Mass loss from abrasion on ogivenose steel projectiles that penetrate concrete targets. Int. J. Impact Eng. 2007, 34, 1814–1820. [Google Scholar] [CrossRef]
 Wen, H.M.; Yang, Y.; He, T. Effects of abrasion on the penetration of ogivalnosed projectiles into concrete targets. Lat. Am. J. Solids Struct. 2010, 7, 413–422. [Google Scholar] [CrossRef] [Green Version]
 Chen, X.W.; He, L.L.; Yang, S.Q. Modeling on mass abrasion of kinetic energy penetrator. Eur. J. Mech. A Solids 2010, 29, 7–17. [Google Scholar] [CrossRef]
 Jones, S.E.; Foster, J.C.; Toness, O.A.; DeAngelis, R.J.; Rule, W.K. An estimate for mass loss from high velocity steel penetrators. In Proceedings of the ASME PVP435 Conference on Thermal–Hydraulic Problems, Sloshing Phenomena, and Extreme Loads on Structures, Vancouver, BC, Canada, 5–9 August 2002; pp. 227–237. [Google Scholar]
 Davis, R.N.; Neely, A.M.; Jones, S.E. Mass loss and blunting during highspeed penetration. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2004, 218, 1053–1062. [Google Scholar] [CrossRef]
 He, L.L.; Chen, X.W.; He, X. Parametric study on mass loss of penetrators. Acta Mech. Sin. 2010, 26, 585–597. [Google Scholar] [CrossRef]
 Ouyang, H.; Chen, X. Modeling on mass loss and nose blunting of highspeed penetrator into concrete target. Int. J. Prot. Struct. 2018, 10, 3–25. [Google Scholar]
 Guo, L.; He, Y.; Zhang, N.S.; Pang, C.X.; Hao, Z. On the mass loss of a projectile based on the Archard theory. Explos. Shock Waves 2014, 34, 622–629. [Google Scholar]
 Ning, J.; Ma, T.; Fei, G. Multimaterial Eulerian method and parallel computation for 3D explosion and impact problems. Int. J. Comput. Methods 2014, 11, 1350079. [Google Scholar] [CrossRef]
 Luk, V.K.; Forrestal, M.J. Penetration into semiinfinite reinforcedconcrete targets with spherical and ogival nose projectiles. Int. J. Impact Eng. 1987, 6, 291–301. [Google Scholar] [CrossRef]
 Meng, C.M.; Tan, Q.H.; Jiang, Z.G.; Song, D.Y.; Liu, F. Approximate solutions of finite dynamic spherical cavityexpansion models for penetration into elastically confined concrete targets. Int. J. Impact Eng. 2018, 114, 182–193. [Google Scholar] [CrossRef]
 Deng, Y.J.; Song, W.J.; Chen, X.W. Spherical cavityexpansion model for penetration of reinforcedconcrete targets. Acta Mech. Sin. 2019, 35, 535–551. [Google Scholar] [CrossRef]
 Ottosen, N.S. A failure criterion for concrete. J. Eng. Mech. Div. ASCE 1979, 105, 127–141. [Google Scholar]
 Holmquist, T.J.; Johnson, G.R.; Cook, W.H. A computational constitutive model for concrete subjected to large strains, high strain rate, and high pressures. In Proceedings of the 14th International Symposium on Ballistics, Quebec City, QC, Canada, 26–29 September 1993; pp. 591–600. [Google Scholar]
 Ren, G.M.; Wu, H.; Fang, Q.; Kong, X.Z. Parameters of HolmquistJohnsonCook model for highstrength concretelike materials under projectile impact. Int. J. Prot. Struct. 2017, 8, 352–367. [Google Scholar] [CrossRef]
 Roscoe, K.H.; Schofied, M.A. On the yielding of soils. Geotechnique 1958, 8, 22–53. [Google Scholar] [CrossRef]
 Sandler, I.S. Review of the development of Cap Models for geomaterials. Shock Vib. 2005, 21, 67–71. [Google Scholar] [CrossRef]
 Feng, J.; Li, W.; Wang, X.; Song, M.; Ren, H.; Li, W. Dynamic spherical cavity expansion analysis of ratedependent concrete material with scale effect. Int. J. Impact Eng. 2015, 84, 24–37. [Google Scholar] [CrossRef]
 Liu, Z.L.; Sun, W.W.; Wang, X.M.; Feng, J. Spherical cavityexpansion model for concrete targets based on cap model and penetration resistance analysis. Acta Armamentarii 2015, 32, 2209–2216. [Google Scholar]
 Hanchak, S.J.; Forrestal, M.J.; Young, E.R.; Ehrgott, J.Q. Perforation of concrete slabs with 48 MPa (7 ksi) and 140 MPa (20 ksi) unconfined compressive strengths. Int. J. Impact Eng. 1992, 12, 1–7. [Google Scholar] [CrossRef]
 Gebbeken, N.; Greulich, S.; Pietzsch, A. Hugoniot properties for concrete determined by fullscale detonation experiments and flyerplateimpact tests. Int. J. Impact Eng. 2006, 32, 2017–2031. [Google Scholar] [CrossRef]
 Satapathy, S. Dynamic spherical cavity expansion in brittle ceramics. Int. J. Solids Struct. 2001, 38, 5833–5845. [Google Scholar] [CrossRef]
 He, L.; Chen, X. Analyses of the penetration process considering mass loss. Eur. J. Mech. A Solids 2011, 30, 145–157. [Google Scholar] [CrossRef]
 Rabinowicz, E.; Dunn, L.; Russell, P. A study of abrasive wear under threebody conditions. Wear 1961, 4, 345–355. [Google Scholar] [CrossRef]
 Guo, L.; He, Y.; Zhang, X.; He, Y.; Deng, J.; Guan, Z. Thermalmechanical analysis on the mass loss of highspeed projectiles penetrating concrete targets. Eur. J. Mech. A Solids 2017, 65, 159–177. [Google Scholar] [CrossRef]
${\mathit{f}}_{\mathit{c}}\mathbf{/}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$  ${\mathit{f}}_{\mathit{t}}\mathbf{/}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$  ${\mathit{p}}_{\mathit{m}}\mathbf{/}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$  ${\mathit{p}}_{\mathit{l}}\mathbf{/}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$  ${\mathit{\kappa}}_{\mathit{e}}$  ${\mathit{\kappa}}_{\mathit{p}}$  R  ${\mathit{\rho}}_{0}\mathbf{/}\mathbf{(}\mathbf{kg}\mathbf{/}{\mathit{m}}^{\mathbf{3}}\mathbf{)}$ 
50.0  4.0  476.0  800.0  0.0013  0.11  0.91  2300.0 
${\mathit{K}}_{\mathit{c}}\mathbf{/}\mathbf{\left(}\mathbf{GPa}\mathbf{\right)}$  ${\mathit{K}}_{\mathit{l}}\mathbf{/}\mathbf{\left(}\mathbf{GPa}\mathbf{\right)}$  ${\mathit{A}}^{\mathbf{\prime}}$  ${\mathit{k}}_{\mathbf{1}}$  ${\mathit{k}}_{\mathbf{2}}$  ${\mathit{B}}^{\prime}$  $\mathbf{\nu}$  $\mathit{E}\mathbf{/}\mathbf{\left(}\mathbf{GPa}\mathbf{\right)}$ 
7.18  52.8  1.8076  14.4863  0.9914  4.0962  0.22  209 
Test No.  Initial Impact Velocity (m/s)  DOP (m)  Test Data (m)  Error  Mass Loss Rate (%)  Test Data (%)  Error 

No. 1  1325  0.79  0.74  6.7%  9.6  9.05  6.1% 
No. 2  1385  0.83  0.82  1.2%  10.4  9.06  14.8% 
No. 3  1386  0.83  0.70  18.6%  10.5  9.77  7.5% 
No. 4  1425  0.86  0.86  0.1%  11.4  10.42  9.4% 
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Li, Z.; Xu, X. Theoretical Investigation on Failure Behavior of OgiveNose Projectile Subjected to Impact Loading. Materials 2020, 13, 5372. https://doi.org/10.3390/ma13235372
Li Z, Xu X. Theoretical Investigation on Failure Behavior of OgiveNose Projectile Subjected to Impact Loading. Materials. 2020; 13(23):5372. https://doi.org/10.3390/ma13235372
Chicago/Turabian StyleLi, Zhao, and Xiangzhao Xu. 2020. "Theoretical Investigation on Failure Behavior of OgiveNose Projectile Subjected to Impact Loading" Materials 13, no. 23: 5372. https://doi.org/10.3390/ma13235372