Numerical analysis of impactor models penetration into a concrete barrier taking into account the detachable pallet influence
Numerical simulation within the framework of two-dimensional axisymmetric problem of continuum mechanics made it possible to analyze penetration into a semi-infinite concrete barrier with impactor models having diameter of 14 and 18 mm and initial speed of 1200 m/s. Influence of the detachable pallet used to accelerate the models in the ballistic installation barrel was both taken into account and not taken into account. Within the penetration process, the impactor models and the pallets were considered to be the absolutely rigid non-deformable bodies. The impactor model head was conical with or without a nasal blunt. Positive effect of blunting the head was established on the dynamics of penetration of the impactor models, which resulted in the increase in their penetration depth and the decrease in the maximum overload caused by the cavitation effect manifestation with the presence of blunting. When simulating penetration of the impactor models installed in a detachable pallet, a decrease was registered in the penetration depth by slightly more than 10% with an increase in the maximum overload compared to the case of penetration with a missing pallet. The negative influence reason of the pallet on the impactor models penetration was revealed. It consists in an increase in the shear stresses acting on the model contact surfaces with the adjacent layer of the destroyed concrete caused by compression of this layer by the pallet, until the pallet is completely separated from the impactor model.
 Bazhenov Yu.M. Beton pri dinamicheskom nagruzhenie [Concrete exposed to dynamic loading]. Moscow, Stroyizdat Publ., 1970, 271 p.
 Geniev G.A., Kissyuk V.N., Tyupin G.A. Teoriya plastichnosti betona i zhelezobetona [Theory of plasticity of concrete and reinforced concrete]. Moscow, Stroyizdat Publ., 1974, 306 p.
 Balagansky I.A., Merzhievsky L.A. Deystvie sredstv porazheniya i boepripasov [Destructive effects of ammunition]. Novosibirsk, NSTU Publ., 2012, 408 p.
 Yankelevsky D.Z. Local response of concrete slabs to low velocity missile impact. International Journal of Impact Engineering, 1997, vol. 19, no. 4, pp. 331–343.
 Dubinsky A.V. Obzor nekotorykh netraditsionnykh prilozheniy inzhenernoy teorii vysokoskorostnogo pronikaniya [A review of some non-traditional applications of the engineering theory of high-speed penetration]. Vestnik Permskogo natsionalnogo issledovatelskogo universiteta. Mekhanika — Perm National Research Polytechnic University Mechanics Bulletin, 2019, no. 3, pp. 125–139.
 Jinzhu L., Zhongjie L., Hongsong Zh., Fenglei H. Perforation experiments of concrete targets with residual velocity measurements. International Journal of Impact Engineering, 2013, vol. 57, pp. 1–6.
 Veldanov V.A., Daurskikh A.Yu., Dudik D.E., Isaev A.L., Sotskiy M.Yu., Fedorov S.V. Eksperimentalnye i teoreticheskie issledovaniya vliyaniya mekhani-cheskikh svoistv betona i betonnykh konstruktsiy na kharakter ikh deformirovaniya pri pronikanii skorostnogo udarnika [Experimental and theoretical research on effect of mechanical properties of concrete and concrete constructions on their deformation behaviour at speed striker penetration]. Izvestiya vuzov. Fizika — Russian Physics Journal, 2013, vol. 56, no. 7–3, pp. 26–28.
 Teland J.A., Sjol H. Penetration into concrete by truncated projectiles. International Journal of Impact Engineering, 2004, vol. 30, pp. 447–464.
 Dancygier A.N., Yankelevsky D.Z. High strength concrete response to hard projectile impact. International Journal of Impact Engineering, 1996, vol. 18, no. 6, pp. 583–599.
 Ben-Dor G., Dubinsky A., Elperin T. Optimization of penetration into geological and concrete shields by impactor with jet thruster. Journal of Mechanics of Materials and Structures, 2008, vol. 3, no. 4, pp. 707–727.
 Fedorov S.V., Fedorova N.A., Veldanov V.A. Ispolzovanie impulsa reaktivnoy tyagi dlya uvelicheniya glubiny pronikaniya issledovatelskikh moduley v maloprochnye gruntovye pregrady [Jet thrust impulse using for increase in research modules penetration depth into low-strength soil targets]. Izvestiya Rossiyskoy akademii raketnykh i artilleriyskikh nauk — Bulletin of the Russian Academy of Missile and Artillery Sciences, 2014, no. 4 (84), pp. 53−63.
 Fedorov S.V., Veldanov V.A., Fedorova N.A. O vozmozhnosti uvelicheniya glubiny pronikaniya v gruntovo-skalnye pregrady sostavnykh udarnikov s otstrelivaemoy v protsesse vzaimodeystviya khvosotovoy chastyu [On the possibility of increasing rocky target penetration depth for compound penetrators featuring a tail assembly jettisoned at impact]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie — Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2019, no. 1, pp. 30–50.
 Fedorov S.V., Fedorova N.A. Vliyanie prochnostnykh svoistv gruntovo-skalnoy pregrady na glubinu pronikaniya udarnikov pri dopolnitelnom deystvii impulsa reaktivnoy tyagi [Influence of the soil and rocky target strength properties on projectiles penetration depth with additional action of the jet thrust impulse]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie — Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2016, no. 4, pp. 40–56.
 Forrestal M.J., Lee L.M., Jenrette B.D. Laboratory-scale penetration experiments into geological targets to impact velocities of 2.1 km/s. Journal of Applied Mechanics, 1986, vol. 53, no. 2, pp. 317–320.
 Kaminsky M.V., Kopytov G.F., Kiselev Yu.G., Kochnev Yu.V., Mogilev V.A., Fateev Yu.A. Kriticheskaya skorost pri vnedrenii udarnikov s konicheskoy nosovoy formoy v gruntovye pregrady [Critical velocity at penetration of projectiles with a conic nose form into soil targets]. In: Sbornik materialov III Nauchnoy konferentsii Volzhskogo regionalnogo tsentra PAPAN “Sovremennye metody proektirovaniya i otrabotki raketno-artilleriyskogo vooruzheniya” [Proceedings of the III Scientific conference of the RAMAS Volga regional center “Advanced methods of design and development of missile and artillery weapons”]. In 2 vols. Sarov, RFYaC–VNIIEF Publ., 2004, vol. 2, pp. 642–647.
 Chen X.W., Fan S.C., Li Q.M. Oblique and normal perforation of concrete targets by a rigid projectile. International Journal of Impact Engineering, 2004, vol. 30, pp. 617–637.
 Chen X.W., Li X.L., Huang F.L., Wu H.J., Chen Y.Z. Normal perforation of reinforced concrete target by rigid projectile. International Journal of Impact Engineering, 2008, vol. 35, pp. 1119–1129.
 Ben-Dor G., Dubinsky A., Elperin T. Analytical engineering models for predicting high speed penetration of hard projectiles into concrete shields: a review. International Journal of Damage Mechanics, 2015, vol. 24, no. 1, pp. 76–94.
 Forrestal M.J., Altman B.S., Cargile J.D., Hanchak S.J. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets. International Journal of Impact Engineering, 1994, vol. 15, no. 4, pp. 395–405.
 Li Q.M., Chen X.W. Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile. International Journal of Impact Engineering, 2003, vol. 28, pp. 93–116.
 Ben-Dor G., Dubinsky A., Elperin T. High-speed penetration modeling and shape optimization of the projectile penetrating into concrete shields. Mechanics Based Design of Structures and Machines, 2009, vol. 37, no. 4, pp. 538–549.
 Warren T.L., Fossum A.F., Frew D.J. Penetration into low-strength (23 MPa) concrete: target characterization and simulations. International Journal of Impact Engineering, 2004, vol. 30, pp. 477–503.
 Unosson M., Nilsson L. Projectile penetration and perforation of high performance concrete: experimental results and macroscopic modeling. International Journal of Impact Engineering, 2006, vol. 32, pp. 1068–1085.
 Isaev A.L., Veldanov V.A. Model uprochneniya betona pri armirovanii [Model for concrete strengthening due to reinforcement]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie — Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2018, no. 6, pp. 34–43.
 Forrestal M.J., Frew D.J., Hickerson J.P., Rohwer T.A. Penetration of concrete targets with deceleration-time measurements. International Journal of Impact Engineering, 2003, vol. 28, pp. 479–497.
 Luk V.K., Forrestal M.J. Penetration into semi-infinite reinforced concrete targets with spherical and ogival nose projectiles. International Journal of Impact Engineering, 1987, vol. 6, no. 4, pp. 291–301.
 Balandin P.P. K voprosu o gipotezakh prochnosti [On problem of strength theory]. Vestnik inzhenerov i tekhnikov, 1937, no. 1, pp. 19–24.
 Belov N.N., Yugov N.T., Kopanitsa D.G., Yugov A.A. Raschet prochnosti konstruktsiy iz betonnykh i zhelezobetonnykh plit pri vysokoskorostnom udare [Stress analysis of concrete and reinforced-concrete slab structures under a high-velocity impact]. Prikladnaya mekhanika i tekhnicheskaya fizika — Journal of Applied Mechanics and Technical Physics, 2005, vol. 46, no. 3, pp. 165–173.
 Isaev A.L., Selivanov V.V. Chislennaya realizatsiya fizicheskikh sootnosheniy dlya uprochnyayuscheysya uprugoplastichnoy sredy [Numerical realization of physical relations for a strain-hardening elastoplastic medium]. Problemy prochnosti — Journal Strength of Materials, 1989, vol. 5, pp. 47–49.
 Grigoryan S.S. Ob osnovnykh predstavleniyakh dinamiki gruntov [On basic concepts in soil dynamics]. Prikladnaya matematika i mekhanika — Journal of Applied Mathematics and Mechanics, 1960, vol. 24, no. 6, pp. 1057–1072.
 Fedorov S.V., Veldanov V.A., Smirnov V.E. Chislennyi analiz vliyaniya skorosti i prochnosti udlinennykh udarnikov iz vysokoplotnogo splava na glubinu ikh pronikaniya v stalnuyu pregradu [Numerical analysis of high density alloys and elongated projectiles’ velocity and strength effect on their penetration into a steel target]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie — Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2015, no. 1, pp. 65–83.
 Fedorov S.V. Chislennoe modelirovanie formirovaniya kumulyativnykh struy polusfericheskimi oblitsovkami degressivnoy tolschiny [Numerical simulation of the formation of shaped-charge jets from hemispherical liners of digressive thickness]. Fizika goreniya i vzryva — Combustion, Explosion, and Shock Waves, 2016, vol. 52, no. 5, pp. 116–130.
 Fedorov S.V., Babkin A.V., Veldanov V.A., Gladkov N.A., Ladov S.V. O vysokoskorostnom pronikanii sterzhney iz poristogo materiala [High-velocity penetration of porous material rods]. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2016, no. 5, pp. 18–32.
 Frew D.J., Hanchak S.J., Green M.L., Forrestal M.J. Penetration of concrete targets with ogive-nose steel rods. International Journal of Impact Engineering, 1998, vol. 21, no. 6, pp. 489–497.
 Chernyak G.B., Povarova K.B. Volfram v boepripasakh [Tungsten in ammunition]. Moscow, CNIIKhM Publ., 2014, 355 p.