Volume 43 Issue 9
Sep.  2023
Turn off MathJax
Article Contents
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

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

doi: 10.11883/bzycj-2022-0513
  • Received Date: 2022-11-14
  • Rev Recd Date: 2023-03-01
  • Available Online: 2023-03-24
  • Publish Date: 2023-09-11
  • It is a developing trend of protection engineering to use high resistance materials such as ultra-high performance concrete to construct bullet-shielding structures. The phenomenon of projectile body rebound was found in the tests of projectile body penetrating ultra-high performance concrete. The projectile rebound effect is very important in the study of engineering protection, weapon damage and warhead design. In order to study the rebound velocity of projectile body after penetration and its influencing factors, the stress of projectile body from penetration to rebound was analyzed. Based on the expression of penetration resistance given by the cavity expansion theory, a one-dimensional elastic bar potential energy model was established from the perspective of the accumulation of deformation energy by penetration resistance, and a one-dimensional stress wave model was established from the perspective of stress wave generated by penetration resistance. The analytical solutions of the rebound velocity were derived from the two models respectively, and the physical quantities affecting the rebound velocity were analyzed. Through numerical simulation, the rebound phenomenon of the projectile body after penetrating the ultra-high performance concrete is reproduced, and the numerical results of the rebound velocity agree well with the two analytical solutions. Through numerical calculation of the same penetration model with different material parameters, the relationship between the rebound velocity and the material parameters in the analytical solution is verified, and the reliability of the theoretical model is proved. The results show that the projectile body accumulates deformation potential energy due to penetration resistance, and the projectile body bounces back due to the release of deformation potential energy after penetration. The initial rebound velocity is independent of the target velocity, proportional to the target material, yield strength and warhead shape coefficient, and inversely proportional to the elastic modulus and density of the projectile body. The results can preliminarily predict the rebound velocity and provide a reference for the design of ultra-high performance concrete protective structure and warhead.
  • loading
  • [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.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(17)  / Tables(3)

    Article Metrics

    Article views (360) PDF downloads(123) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return