A three-stage model for the perforation of finite metallic plates by long rods at high velocities
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摘要
A three-stage theoretical model is presented herein to predict the perforation of a thick metallic plate struck normally by a long rod at high velocities. The model is suggested on the basis of the assumption that the perforation of a thick metallic plate by a long rod can be divided into three stages:(1) initial penetration;(2) plug formation and(3) plug slipping and separation. Various analytical equations are derived which can be employed to predict the ballistic limit, residual velocity and residual length of the long rod. It is demonstrated that the present model predictions are in good agreement with available experimental results for the perforation of finite steel targets struck normally by steel as well as tungsten alloy long rods at high velocities. It is also demonstrated that the dynamic maximum shear stress of a plate material has strong effect on plug formation and plug thickness which, in turn, exerts considerable influence on the residual velocities and lengths of a long rod at impact velocities just above the ballistic limit.
A three-stage theoretical model is presented herein to predict the perforation of a thick metallic plate struck normally by a long rod at high velocities. The model is suggested on the basis of the assumption that the perforation of a thick metallic plate by a long rod can be divided into three stages:(1) initial penetration;(2) plug formation and(3) plug slipping and separation. Various analytical equations are derived which can be employed to predict the ballistic limit, residual velocity and residual length of the long rod. It is demonstrated that the present model predictions are in good agreement with available experimental results for the perforation of finite steel targets struck normally by steel as well as tungsten alloy long rods at high velocities. It is also demonstrated that the dynamic maximum shear stress of a plate material has strong effect on plug formation and plug thickness which, in turn, exerts considerable influence on the residual velocities and lengths of a long rod at impact velocities just above the ballistic limit.
A three-stage theoretical model is presented herein to predict the perforation of a thick metallic plate struck normally by a long rod at high velocities. The model is suggested on the basis of the assumption that the perforation of a thick metallic plate by a long rod can be divided into three stages:(1) initial penetration;(2) plug formation and(3) plug slipping and separation. Various analytical equations are derived which can be employed to predict the ballistic limit, residual velocity and residual length of the long rod. It is demonstrated that the present model predictions are in good agreement with available experimental results for the perforation of finite steel targets struck normally by steel as well as tungsten alloy long rods at high velocities. It is also demonstrated that the dynamic maximum shear stress of a plate material has strong effect on plug formation and plug thickness which, in turn, exerts considerable influence on the residual velocities and lengths of a long rod at impact velocities just above the ballistic limit.
引文
[1]Alekseevskii VP.Penetration of a rod into a target at high velocity.Combust Explos Shock Waves 1966;2:63e6.
[2]Tate A.A theory for the deceleration of long rods after impact.J Mech Phys Solid 1967;15:387e99.
[3]Tate A.Further results in the theory of long rod penetration.J Mech Phys Solid1969;17:141e50.
[4]Rosenberg Z.On the hydrodynamic theory of long-rod penetration.Int JImpact Eng 1990;10:483e6.
[5]Jones SE,Gillis PP,Foster JC.On the penetration of semi-infinite targets by long rods.J Mech Phys Solid 1987;35(1):121e31.
[6]Wang P,Jones SE.An elementary theory of one-dimensional rod penetration using a new estimate for pressure.Int J Impact Eng 1996;18(3):265e79.
[7]Grace FI.Nonsteady penetration of long rods into semi-infinite targets.Int JImpact Eng 1993;14:303e14.
[8]Walker JD,Anderson Jr CE.A time-dependent model for long-rod penetration.Int J Impact Eng 1995;16(1):19e48.
[9]Godwin RP,Chapyak EJ.Apparent target strength in long rod penetration.Int JImpact Eng 1998;21(1e2):77e88.
[10]Galanov BA,Ivanov SM,Kartuzov VV.On one new modification of Alekseevskii-Tate model for nonstationary penetration of long rods into targets.Int J Impact Eng 2001;26:201e10.
[11]Galanov BA,Ivanov SM,Kartuzov VV.Investigation of penetration resistance using a new modification of the Alekseevskii-Tate model.Int J Impact Eng2003;29:263e72.
[12]Rubin MB,Yarin AL.A generalized formula for the penetration depth of a deformable projectile.Int J Impact Eng 2001;27:387e98.
[13]Walters WP,Segletes SB.An exact solution of the long rod penetration equations.Int J Impact Eng 1991;11(2):225e31.
[14]Segletes SB,Walters WP.Extensions to the exact solution of the long-rod penetration/erosion equations.Int J Impact Eng 2003;28:363e76.
[15]Orphal DL.Explosions and impacts.Int J Impact Eng 2006;33:496e545.
[16]Anderson Jr CE,Walker JD.An examination of long-rod penetration.Int JImpact Eng 1991;11(4):481e501.
[17]Anderson Jr CE,Littlefield DL,Walker JD.Long-rod penetration,target resistance,and hypervelocity impact.Int J Impact Eng 1993;14:1e12.
[18]Lan B,Wen HM.Alekseevskii-Tate revisited:an extension to the modified hydrodynamic theory of long-rod penetration.Sci China Technol Sci2010;53(5):1364e73.
[19]Wen HM,Lan B.Analytical models for the penetration of semi-infinite targets by rigid,deformable and erosive long rods.Acta Mech Sin 2010;26(4):573e83.
[20]Wen HM,He Y,Lan B.Analytical model for cratering of semi-infinite metallic targets by long rod penetrators.Sci China Technol Sci 2010;53(12):3189e96.
[21]Wen HM,He Y,Lan B.A combined numerical and theoretical study on the penetration of a jacketed rod into semi-infinite targets.Int J Impact Eng2011;38:1001e10.
[22]He Y,Wen HM.Predicting the penetration of long rods into semi-infinite metallic targets.Sci China Technol Sci 2013;56(11):2814e20.
[23]Lu ZC,Wen HM.On the penetration of high strength steel rods into semiinfinite aluminium alloy targets.Int J Impact Eng 2018;111:1e10.
[24]Grace FI.Long-rod penetration into targets of finite thickness at normal impact.Int J Impact Eng 1995;16:419e33.
[25]Grace FI.Ballistic limit velocity for long rods from ordinance velocity through hypervelocity impact.Int J Impact Eng 1999;23:295e306.
[26]Anderson CE,Hohler V,Walker JD,et al.Time-resolved penetration of long rods into steel targets.Int J Impact Eng 1995;16:1e18.
[27]Ravid M,Bodner SR.Dynamic perforation of viscoplastic plates by rigid projectiles.Int J Eng Sci 1983;21(6):577e91.
[28]Wen HM,Jones N.Experimental investigation of the scaling laws for metal plates struck by large masses.Int J Impact Eng 1993;13(3):485e505.
[29]Anderson Jr CE,Hohler V,Walker JD,et al.The influence of projectile hardness on ballistic performance.Int J Impact Eng 1999;22(6):619e32.
[30]BФrvik T,Hopperstad OS,Langseth M,et al.Effect of target thickness in blunt projectile penetration of Weldox 460 E steel plates.Int J Impact Eng2003;28(4):413e64.
[31]Wen HM,Sun WH.Transition of plugging failure models for ductile metal plates under impact by flat-nosed projectiles.Mech Base Des Struct Mach2010;38:1001e10.
[32]Hohler V,Stilp AJ.In A penetration mechanics database.In:Anderson Jr CE,Morris BL,Littlefeld DL,editors.SwRI report 3593/001.San Antonio,TX:Southwest Research Institute;1992.
[33]Rohr I,Nahme H,Thoma K.Material characterization and constitutive modelling of ductile high strength steel for a wide range of strain rates.Int JImpact Eng 2004;31(4):401e33.
[2]Tate A.A theory for the deceleration of long rods after impact.J Mech Phys Solid 1967;15:387e99.
[3]Tate A.Further results in the theory of long rod penetration.J Mech Phys Solid1969;17:141e50.
[4]Rosenberg Z.On the hydrodynamic theory of long-rod penetration.Int JImpact Eng 1990;10:483e6.
[5]Jones SE,Gillis PP,Foster JC.On the penetration of semi-infinite targets by long rods.J Mech Phys Solid 1987;35(1):121e31.
[6]Wang P,Jones SE.An elementary theory of one-dimensional rod penetration using a new estimate for pressure.Int J Impact Eng 1996;18(3):265e79.
[7]Grace FI.Nonsteady penetration of long rods into semi-infinite targets.Int JImpact Eng 1993;14:303e14.
[8]Walker JD,Anderson Jr CE.A time-dependent model for long-rod penetration.Int J Impact Eng 1995;16(1):19e48.
[9]Godwin RP,Chapyak EJ.Apparent target strength in long rod penetration.Int JImpact Eng 1998;21(1e2):77e88.
[10]Galanov BA,Ivanov SM,Kartuzov VV.On one new modification of Alekseevskii-Tate model for nonstationary penetration of long rods into targets.Int J Impact Eng 2001;26:201e10.
[11]Galanov BA,Ivanov SM,Kartuzov VV.Investigation of penetration resistance using a new modification of the Alekseevskii-Tate model.Int J Impact Eng2003;29:263e72.
[12]Rubin MB,Yarin AL.A generalized formula for the penetration depth of a deformable projectile.Int J Impact Eng 2001;27:387e98.
[13]Walters WP,Segletes SB.An exact solution of the long rod penetration equations.Int J Impact Eng 1991;11(2):225e31.
[14]Segletes SB,Walters WP.Extensions to the exact solution of the long-rod penetration/erosion equations.Int J Impact Eng 2003;28:363e76.
[15]Orphal DL.Explosions and impacts.Int J Impact Eng 2006;33:496e545.
[16]Anderson Jr CE,Walker JD.An examination of long-rod penetration.Int JImpact Eng 1991;11(4):481e501.
[17]Anderson Jr CE,Littlefield DL,Walker JD.Long-rod penetration,target resistance,and hypervelocity impact.Int J Impact Eng 1993;14:1e12.
[18]Lan B,Wen HM.Alekseevskii-Tate revisited:an extension to the modified hydrodynamic theory of long-rod penetration.Sci China Technol Sci2010;53(5):1364e73.
[19]Wen HM,Lan B.Analytical models for the penetration of semi-infinite targets by rigid,deformable and erosive long rods.Acta Mech Sin 2010;26(4):573e83.
[20]Wen HM,He Y,Lan B.Analytical model for cratering of semi-infinite metallic targets by long rod penetrators.Sci China Technol Sci 2010;53(12):3189e96.
[21]Wen HM,He Y,Lan B.A combined numerical and theoretical study on the penetration of a jacketed rod into semi-infinite targets.Int J Impact Eng2011;38:1001e10.
[22]He Y,Wen HM.Predicting the penetration of long rods into semi-infinite metallic targets.Sci China Technol Sci 2013;56(11):2814e20.
[23]Lu ZC,Wen HM.On the penetration of high strength steel rods into semiinfinite aluminium alloy targets.Int J Impact Eng 2018;111:1e10.
[24]Grace FI.Long-rod penetration into targets of finite thickness at normal impact.Int J Impact Eng 1995;16:419e33.
[25]Grace FI.Ballistic limit velocity for long rods from ordinance velocity through hypervelocity impact.Int J Impact Eng 1999;23:295e306.
[26]Anderson CE,Hohler V,Walker JD,et al.Time-resolved penetration of long rods into steel targets.Int J Impact Eng 1995;16:1e18.
[27]Ravid M,Bodner SR.Dynamic perforation of viscoplastic plates by rigid projectiles.Int J Eng Sci 1983;21(6):577e91.
[28]Wen HM,Jones N.Experimental investigation of the scaling laws for metal plates struck by large masses.Int J Impact Eng 1993;13(3):485e505.
[29]Anderson Jr CE,Hohler V,Walker JD,et al.The influence of projectile hardness on ballistic performance.Int J Impact Eng 1999;22(6):619e32.
[30]BФrvik T,Hopperstad OS,Langseth M,et al.Effect of target thickness in blunt projectile penetration of Weldox 460 E steel plates.Int J Impact Eng2003;28(4):413e64.
[31]Wen HM,Sun WH.Transition of plugging failure models for ductile metal plates under impact by flat-nosed projectiles.Mech Base Des Struct Mach2010;38:1001e10.
[32]Hohler V,Stilp AJ.In A penetration mechanics database.In:Anderson Jr CE,Morris BL,Littlefeld DL,editors.SwRI report 3593/001.San Antonio,TX:Southwest Research Institute;1992.
[33]Rohr I,Nahme H,Thoma K.Material characterization and constitutive modelling of ductile high strength steel for a wide range of strain rates.Int JImpact Eng 2004;31(4):401e33.