弹体侵彻超高性能混凝土反弹效应理论初探

朱擎 李述涛 陈叶青 马上

朱擎, 李述涛, 陈叶青, 马上. 弹体侵彻超高性能混凝土反弹效应理论初探[J]. 爆炸与冲击, 2023, 43(9): 091405. doi: 10.11883/bzycj-2022-0513
引用本文: 朱擎, 李述涛, 陈叶青, 马上. 弹体侵彻超高性能混凝土反弹效应理论初探[J]. 爆炸与冲击, 2023, 43(9): 091405. doi: 10.11883/bzycj-2022-0513
ZHU Qing, LI Shutao, CHEN Yeqing, MA Shang. Preliminary theoretical study on the rebound effect of projectiles penetrating ultra-high performance concrete targets[J]. Explosion And Shock Waves, 2023, 43(9): 091405. doi: 10.11883/bzycj-2022-0513
Citation: ZHU Qing, LI Shutao, CHEN Yeqing, MA Shang. Preliminary theoretical study on the rebound effect of projectiles penetrating ultra-high performance concrete targets[J]. Explosion And Shock Waves, 2023, 43(9): 091405. doi: 10.11883/bzycj-2022-0513

弹体侵彻超高性能混凝土反弹效应理论初探

doi: 10.11883/bzycj-2022-0513
详细信息
    作者简介:

    朱 擎(1997- ),男,博士研究生,zq953783236@163.com

    通讯作者:

    李述涛(1984- ),男,博士,高级工程师,list16@tsinghua.org.cn

  • 中图分类号: O385

Preliminary theoretical study on the rebound effect of projectiles penetrating ultra-high performance concrete targets

  • 摘要: 为了探究弹体在侵彻超高性能混凝土过程中弹体出现的反弹现象,基于空腔膨胀理论,分析了弹体从侵彻到反弹全过程的受力情况;分别以一维弹性杆弹性势能模型和一维应力波模型为理论基础,推导得到两种反弹速度的解析解,分析了影响反弹速度的物理量;通过数值模拟复现了弹体反弹现象,验证了理论模型的合理性,数值计算结果和两种解析解吻合良好。研究表明:侵彻阻力使弹体积累变形势能,侵彻结束后变形势能释放造成弹体反弹;反弹初速与着靶速度无关,与靶体材料的屈服强度和弹头形状系数等成正比,与弹体弹性模量和密度成反比。
  • 图  1  弹体侵彻阶段受力状态

    Figure  1.  Force state of projectile body in each stage of penetration

    图  2  侵彻过程中弹体侵彻阻力时程曲线

    Figure  2.  Time history curve of projectile penetration resistance during penetration

    图  3  一维杆弹性势能模型

    Figure  3.  One-dimensional rod elastic potential energy model

    图  4  一维弹性波模型

    Figure  4.  One-dimensional elastic wave model

    图  5  弹性杆中弹性波波系图及其相容关系

    Figure  5.  The pattern of elastic wave system in elastic rod and its compatibility relation

    图  6  弹体左端面最后一次反射的相容关系示意图

    Figure  6.  Schematic diagram of the compatibility relation of the last reflection of the left face of the projectile body

    图  7  文献[24]中侵彻试验的数值计算模型

    Figure  7.  Numerical calculation model of penetration test in reference [24]

    图  8  文献[24]中网格尺寸收敛性分析

    Figure  8.  Analysis of unit size convergence in reference [24]

    图  9  侵彻坑直径D的试验结果与数值计算结果对比

    Figure  9.  Comparison of test results and numerical results of penetration pit diameter D

    图  10  弹体速度时程曲线和反弹速度理论解

    Figure  10.  Time history curves of projectile velocity and theoretical solutions to rebound velocity

    图  11  弹体侵彻超高性能混凝土有限元模型

    Figure  11.  Numerical model of projectile penetration into ultra high performance concrete

    图  12  3925-105-700的速度与加速度时程曲线

    Figure  12.  3925-105-700 velocity and acceleration time history curve

    图  13  弹体侵彻方向的应力云图

    Figure  13.  Stress cloud diagram of projectile in penetration direction

    图  14  弹体7850-210速度时程曲线数值解和理论解的对比

    Figure  14.  Comparison of velocity time history curves of numerical and theoretical solutions of missile 7850-210

    图  15  弹体3925-105速度时程曲线数值解和理论解的对比

    Figure  15.  Comparison of velocity time history curves of numerical and theoretical solutions of missile 3925-105

    图  16  反弹速度数值解和理论解与侵彻初速之间的关系

    Figure  16.  The relationship between numerical and theoretical solutions of rebound velocity and initial penetration velocity

    图  17  两类弹体侵彻速度与反弹速度的对比

    Figure  17.  Comparison of penetration velocity and rebound velocity of two types of projectile bodies

    表  1  超高性能混凝土K&C模型参数[24]

    Table  1.   K&C model parameters fot the ultra-high performance concrete[24]

    a0/MPaa1a2/MPa−1a1fa2f/MPa−1a0y/MPaa1ya2y/MPa−1
    60.480.446 30.001 0520.44170.000 98938.320.6250.003 090
    ρc/(kg·m−3)νft/MPab1b2b3ΩW/mm
    2 5670.2120.15−4.391.150.752
    注:a0a1a2a1fa2fa0ya1y为失效面参数,ν为泊松比,ft为抗拉强度,b1b2b3为损伤参数,Ω为剪胀参数,W为试件宽度。
    下载: 导出CSV

    表  2  侵彻深度的试验与数值计算结果

    Table  2.   Experimental and numerical results of penetration depth

    侵彻初速/(m·s−1)试验侵彻深度/mm数值模拟侵彻深度/mm误差/%
    40570691.43
    6161201099.17
    下载: 导出CSV

    表  3  反弹速度的数值计算结果和理论预测值

    Table  3.   The results of numerical calculation and theoretical prediction of the rebound velocity

    弹体vi/(m·s−1)vr/(m·s−1) 与数值模拟的误差/%
    数值模拟弹性势能模型一维弹性波模型 弹性势能模型一维弹性波模型
    7850-2103008.214.1219.244.057.3
    40010.614.1219.224.444.8
    50017.014.1219.2−20.011.5
    60013.314.1219.25.730.7
    70016.714.1219.2−17.913.0
    80015.914.1219.2−12.417.2
    3925-10530016.328.2538.4 42.857.5
    40024.528.2538.414.036.2
    50025.828.2538.49.432.8
    60034.228.2538.4−20.010.9
    70037.128.2538.4−30.23.40
    80033.728.2538.4−18.312.2
    下载: 导出CSV
  • [1] YU R, SPIESZ P, BROUWERS H J H. Mix design and properties assessment of Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) [J]. Cement and Concrete Research, 2014, 56: 29–39. DOI: 10.1016/j.cemconres.2013.11.002.
    [2] 戎志丹, 孙伟. 粗集料对超高性能水泥基材料动态力学性能的影响 [J]. 爆炸与冲击, 2009, 29(4): 361–366. DOI: 10.11883/1001-1455(2009)04-0361-06.

    RONG Z D, SUN W. Influences of coarse aggregate on dynamic mechanical behaviors of ultrahigh-performance cementitious composites [J]. Explosion and Shock Waves, 2009, 29(4): 361–366. DOI: 10.11883/1001-1455(2009)04-0361-06.
    [3] 张文华, 张云升, 陈振宇. 超高性能混凝土抗缩比钻地弹侵彻试验及数值仿真 [J]. 工程力学, 2018, 35(7): 167–175, 186. DOI: 10.6052/j.issn.1000-4750.2017.03.0237.

    ZHANG W H, ZHANG Y S, CHEN Z Y. Penetration test and numerical simulation of ultral-high performance concrete with a scaled earth penetrator [J]. Engineering Mechanics, 2018, 35(7): 167–175, 186. DOI: 10.6052/j.issn.1000-4750.2017.03.0237.
    [4] ZHANG W H, ZHANG Y S, ZHANG G R. Static, dynamic mechanical properties and microstructure characteristics of ultra-high performance cementitious composites [J]. Science and Engineering of Composite Materials, 2012, 19(3): 237–245. DOI: 10.1515/secm-2011-0136.
    [5] 任辉启, 穆朝民, 刘瑞朝, 等. 精确制导武器侵彻效应与工程防护 [M]. 北京: 科学出版社, 2016.
    [6] 程月华, 吴昊, 谭可可, 等. 装甲钢/UHPC复合靶体抗侵彻性能试验与数值模拟研究 [J]. 爆炸与冲击, 2022, 42(5): 053302. DOI: 10.11883/bzycj-2021-0278.

    CHENG Y H, WU H, TAN K K, et al. Experimental and numerical studies on penetration resistance of armor steel/UHPC composite target [J]. Explosion and Shock Waves, 2022, 42(5): 053302. DOI: 10.11883/bzycj-2021-0278.
    [7] 隋树元, 王树山. 终点效应学 [M]. 北京: 国防工业出版社, 2000: 7.
    [8] FORRESTAL M J, LUK V K. Dynamic spherical cavity-expansion in a compressible elastic-plastic solid [J]. Journal of Applied Mechanics, 1988, 55(2): 275–279. DOI: 10.1115/1.3173672.
    [9] FORRESTAL M J, LUK V K, BRAR N S. Perforation of aluminum armor plates with conical-nose projectiles [J]. Mechanics of Materials, 1990, 10(1/2): 97–105. DOI: 10.1016/0167-6636(90)90020-G.
    [10] FORRESTAL M J, BRAR N S, LUK V K. Penetration of strain-hardening targets with rigid spherical-nose rods [J]. Journal of Applied Mechanics, 1991, 58(1): 7–10. DOI: 10.1115/1.2897183.
    [11] 陈小伟. 穿甲/侵彻力学的理论建模与分析 [M]. 北京: 科学出版社, 2019: 9.
    [12] CHEN X W, LI Q M. Deep penetration of a non-deformable projectile with different geometrical characteristics [J]. International Journal of Impact Engineering, 2002, 27(6): 619–637. DOI: 10.1016/S0734-743X(02)00005-2.
    [13] BATRA R C, WRIGHT T W. Steady state penetration of rigid perfectly plastic targets [J]. International Journal of Engineering Science, 1986, 24(1): 41–54. DOI: 10.1016/0020-7225(86)90147-3.
    [14] FORRESTAL M J, FREW D J, HICKERSON J P, et al. Penetration of concrete targets with deceleration-time measurements [J]. International Journal of Impact Engineering, 2003, 28(5): 479–497. DOI: 10.1016/S0734-743X(02)00108-2.
    [15] FORRESTAL M J, WARREN T L. Penetration equations for ogive-nose rods into aluminum targets [J]. International Journal of Impact Engineering, 2008, 35(8): 727–730. DOI: 10.1016/j.ijimpeng.2007.11.002.
    [16] FREW D J, FORRESTAL M J, CARGILE J D. The effect of concrete target diameter on projectile deceleration and penetration depth [J]. International Journal of Impact Engineering, 2006, 32(10): 1584–1594. DOI: 10.1016/j.ijimpeng.2005.01.012.
    [17] ROSENBERG Z, DEKEL E. The penetration of rigid long rods-revisited [J]. International Journal of Impact Engineering, 2009, 36(4): 551–564. DOI: 10.1016/j.ijimpeng.2008.06.001.
    [18] 陈小伟, 李继承. 刚性弹侵彻深度和阻力的比较分析 [J]. 爆炸与冲击, 2009, 29(6): 584–589. DOI: 10.11883/1001-1455(2009)06-0584-06.

    CHEN X W, LI J C. Analysis of penetration depth and resistive force in the deep penetration of a rigid projectile [J]. Explosion and Shock Waves, 2009, 29(6): 584–589. DOI: 10.11883/1001-1455(2009)06-0584-06.
    [19] FORRESTAL M J, ALTMAN B S, CARGILE J D, et al. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets [J]. International Journal of Impact Engineering, 1994, 15(4): 395–405. DOI: 10.1016/0734-743X(94)80024-4.
    [20] CHEN X W. Dynamics of metallic and reinforced concrete targets subjected to projectile impact [D]. Singapore: Nanyang Technological University, 2003.
    [21] ROSENBERG Z, VAYIG Y, MALKA-MARKOVITZ A. The scaling issue in the penetration of concrete targets by rigid projectiles: revisited [J]. International Journal of Impact Engineering, 2020, 140: 103561. DOI: 10.1016/j.ijimpeng.2020.103561.
    [22] ROSENBERG Z, VAYIG Y, MALKA-MARKOVITZ A, et al. More on the perforation of concrete slabs by rigid projectiles [J]. International Journal of Impact Engineering, 2022, 162: 104138. DOI: 10.1016/j.ijimpeng.2021.104138.
    [23] 余同希, 邱信明. 冲击动力学 [M]. 北京: 清华大学出版社, 2011.
    [24] ZHANG F L, SHEDBALE A S, ZHONG R, et al. Ultra-high performance concrete subjected to high-velocity projectile impact: implementation of K&C model with consideration of failure surfaces and dynamic increase factors [J]. International Journal of Impact Engineering, 2021, 155: 103907. DOI: 10.1016/j.ijimpeng.2021.103907.
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出版历程
  • 收稿日期:  2022-11-14
  • 修回日期:  2023-03-01
  • 网络出版日期:  2023-03-24
  • 刊出日期:  2023-09-11

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