Cavity expansion model and penetration mechanism of concrete with different strengths based on the Ottosen yield condition

ZHANG Xueyan; SUN Kai; LI Yuanlong; ZENG Feiyin; LI Guojie; WU Haijun

doi:10.11883/bzycj-2022-0511

Volume 43 Issue 9

Sep. 2023

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Explosion And Shock Waves > 2023 > 43(9): 091403

ZHANG Xueyan, SUN Kai, LI Yuanlong, ZENG Feiyin, LI Guojie, WU Haijun. Cavity expansion model and penetration mechanism of concrete with different strengths based on the Ottosen yield condition[J]. Explosion And Shock Waves, 2023, 43(9): 091403. doi: 10.11883/bzycj-2022-0511

Citation:

ZHANG Xueyan, SUN Kai, LI Yuanlong, ZENG Feiyin, LI Guojie, WU Haijun. Cavity expansion model and penetration mechanism of concrete with different strengths based on the Ottosen yield condition[J]. Explosion And Shock Waves, 2023, 43(9): 091403. doi: 10.11883/bzycj-2022-0511

Citation:

ZHANG Xueyan, SUN Kai, LI Yuanlong, ZENG Feiyin, LI Guojie, WU Haijun. Cavity expansion model and penetration mechanism of concrete with different strengths based on the Ottosen yield condition[J]. Explosion And Shock Waves, 2023, 43(9): 091403. doi: 10.11883/bzycj-2022-0511

PDF( 1615 KB)

Cavity expansion model and penetration mechanism of concrete with different strengths based on the Ottosen yield condition

doi: 10.11883/bzycj-2022-0511

ZHANG Xueyan^{1, 2
,},
SUN Kai¹,
LI Yuanlong¹,
ZENG Feiyin¹,
LI Guojie¹,
WU Haijun^{2
,
,}

1.
Beijing Aerospace Long March Aircraft Research Institute, Beijing 100076, China
2.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Received Date: 2022-11-14
Rev Recd Date: 2023-08-24

Available Online: 2023-08-28

Publish Date: 2023-09-11

Abstract

Abstract

Aiming at the urgent demand for theoretical research and engineering application of deep super hard targets in the field of damage and protection, the response zone and boundary conditions during the cavity expansding process are optimized in this paper based on the improved Ottosen yield condition. The entire process of cavity expansion is solved, the changes in the response zone of concrete with different strengths are analyzed. According to the relationship between cavity boundary stress and cavity expansion velocity, a calculation model of projectile penetration depth is established, and the penetration depth of projectile penetration into concrete with different strengths are calculated. The mechanism of the influence of target strength on penetration depth is also analyzed. The results show that the elastic and plastic cracking zone of high-strength concrete is larger and the compacted zone is smaller, indicating that high-strength concrete is more brittle and compact. And the addition of plastic cracking zone can better reflect the phenomenon of concrete with different strengths in penetration. By comparing with the experimental data, it can be seen that the cavity expansion theory established in this paper has good applicability for normal concrete and high-strength concrete. The relationship between radial stress and cavity boundary velocity and the penetration depth also can be accurately calculated by this theory. With the increase of concrete strength, the difference in the cavity boundary stress of the concrete becomes smaller, resulting in a smaller increase in the penetration depth of the projectile as the velocity increases, and the penetration depth of the projectile decreases and gradually tends to a certain value at the same speed.
- Ottosen yield condition,
- cavity expansion theory,
- high-strength concrete,
- depth of penetration

FullText(HTML)

References(35)

References

[1]	FORRESTAL M J, TZOU D Y. A spherical cavity-expansion penetration model for concrete targets [J]. International Journal of Solids and Structures, 1997, 34(31/32): 4127–4146. DOI: 10.1016/S0020-7683(97)00017-6.
[2]	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.
[3]	黄民荣, 顾晓辉, 高永宏. 脆性材料静态抗侵彻阻力简化计算模型与对比研究 [J]. 弹道学报, 2009, 21(2): 86–89. HUANG M R, GU X H, GAO Y H. Simplified analytical model and its contrast study on the static penetration resistance of brittle materials [J]. Journal of Ballistics, 2009, 21(2): 86–89.
[4]	黄民荣, 顾晓辉, 高永宏. 基于Griffith强度理论的空腔膨胀模型与应用研究 [J]. 力学与实践, 2009, 31(5): 30–34. DOI: 10.6052/1000-0879-2008-351. HUANG M R, GU X H, GAO Y H. Cavity expansion model based on the Griffith strength theory and its application [J]. Mechanics in Engineering, 2009, 31(5): 30–34. DOI: 10.6052/1000-0879-2008-351.
[5]	ZHANG S, WU H J, TAN Z J, et al. Theoretical analysis of dynamic spherical cavity expansion in reinforced concretes [J]. Key Engineering Materials, 2016, 715: 222–227. DOI: 10.4028/www.scientific.net/KEM.715.222.
[6]	曹扬悦也, 蒋志刚, 谭清华, 等. 基于Hoek-Brown准则的混凝土-岩石类靶侵彻模型 [J]. 振动与冲击, 2017, 36(5): 48–53, 60. DOI: 10.13465/j.cnki.jvs.2017.05.008. CAO Y Y Y, JIANG Z G, TAN Q H, et al. Penetration model for concrete-rock targets based on Hoek-Brown criterion [J]. Journal of Vibration and Shock, 2017, 36(5): 48–53, 60. DOI: 10.13465/j.cnki.jvs.2017.05.008.
[7]	詹昊雯, 曹扬悦也, 蒋志刚, 等. 约束混凝土靶的准静态柱形空腔膨胀理论 [J]. 弹道学报, 2017, 29(2): 13–18. ZHAN H W, CAO Y Y Y, JIANG Z G, et al. Quasi-static cylindrical cavity-expansion model for confined-concrete targets [J]. Journal of Ballistics, 2017, 29(2): 13–18.
[8]	XU H, WEN H M. A spherical cavity expansion penetration model for concrete based on Hoek-Brown strength criterion [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2012, 13(2): 145–152. DOI: 10.1515/ijnsns-2011-099.
[9]	FENG J, LI W B, WANG X M, et al. Dynamic spherical cavity expansion analysis of rate-dependent concrete material with scale effect [J]. International Journal of Impact Engineering, 2015, 84: 24–37. DOI: 10.1016/j.ijimpeng.2015.05.005.
[10]	SATAPATHY S. Dynamic spherical cavity expansion in brittle ceramics [J]. International Journal of Solids and Structures, 2001, 38(32/33): 5833–5845. DOI: 10.1016/S0020-7683(00)00388-7.
[11]	李志康, 黄风雷. 高速长杆弹侵彻半无限混凝土靶的理论分析 [J]. 北京理工大学学报, 2010, 30(1): 10–13. DOI: 10.15918/j.tbit1001-0645.2010.01.002. LI Z K, HUANG F L. High velocity long rod projectile’s penetration into semi-infinite concrete targets [J]. Transactions of Beijing Institute of Technology, 2010, 30(1): 10–13. DOI: 10.15918/j.tbit1001-0645.2010.01.002.
[12]	李志康. 弹体正侵彻半无限混凝土靶的理论分析 [D]. 北京: 北京理工大学, 2008.
[13]	王一楠. 动能弹体高速侵彻混凝土机理研究 [D]. 北京: 北京理工大学, 2009.
[14]	何涛. 动能弹在不同材料靶体中的侵彻行为研究 [D]. 合肥: 中国科学技术大学, 2007. HE T. A study on the penetration of projectiles into targets made of various materials [D]. Hefei: University of Science and Technology of China, 2007.
[15]	HE T, WEN H M, GUO X J. A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy [J]. Acta Mechanica Sinica, 2011, 27(6): 1001–1012. DOI: 10.1007/s10409-011-0505-1.
[16]	张欣欣, 闫雷, 武海军, 等. 考虑剪胀效应的混凝土动态球形空腔膨胀理论 [J]. 兵工学报, 2016, 37(1): 42–49. DOI: 10.3969/j.issn.1000-1093.2016.01.007. ZHANG X X, YAN L, WU H J, et al. A note on the dynamic spherical cavity expansion of concrete with shear dilatancy [J]. Acta Armamentarii, 2016, 37(1): 42–49. DOI: 10.3969/j.issn.1000-1093.2016.01.007.
[17]	ZHANG X Y, WU H J, LI J Z, et al. A constitutive model of concrete based on Ottosen yield criterion [J]. International Journal of Solids and Structures, 2020, 193/194: 79–89. DOI: 10.1016/j.ijsolstr.2020.02.013.
[18]	OTTOSEN N S. A failure criterion for concrete [J]. Journal of Engineering Mechanics Division, 1997, 103(4): 527–535.
[19]	过镇海. 混凝土的强度和变形-试验基础和本构关系 [M]. 北京: 清华大学出版社, 1997.
[20]	ČERVENKA J, PAPANIKOLAOU V K. Three dimensional combined fracture-plastic material model for concrete [J]. International Journal of Plasticity, 2008, 24(12): 2192–2220. DOI: 10.1016/j.ijplas.2008.01.004.
[21]	PAPANIKOLAOU V K, KAPPOS A J. Confinement-sensitive plasticity constitutive model for concrete in triaxial compression [J]. International Journal of Solids and Structures, 2007, 44(21): 7021–7048. DOI: 10.1016/j.ijsolstr.2007.03.022.
[22]	ARÁOZ G, LUCCIONI B. Modeling concrete like materials under sever dynamic pressures [J]. International Journal of Impact Engineering, 2015, 76: 139–154. DOI: 10.1016/j.ijimpeng.2014.09.009.
[23]	DAHL K K B. A constitutive model for normal and high strength concrete [R]. Anker Engelunds Vej: Technical University of Denmark, 1992.
[24]	KUPFER H, HILSDORF K H, RUSH H. Behavior of concrete under biaxial stresses [J]. Journal of the Engineering Mechanics Division Asce, 1969, 99(8): 656–666. DOI: 10.14359/7388.
[25]	IMRAN I, PANTAZOPOULOU S J. Plasticity model for concrete under triaxial compression[J]. Journal of Engineering Mechanics, 2001, 127(3): 281–290. DOI: 10.1061/(ASCE)0733-9399(2001)127:3(281).
[26]	GABET T, MALÉCOT Y, DAUDEVILLE L. Triaxial behaviour of concrete under high stresses: influence of the loading path on compaction and limit states [J]. Cement and Concrete Research, 2008, 38(3): 403–412. DOI: 10.1016/j.cemconres.2007.09.029.
[27]	VU X H, MALECOT Y, DAUDEVILLE L, et al. Experimental analysis of concrete behavior under high confinement: Effect of the saturation ratio [J]. International Journal of Solids and Structures, 2009, 46(5): 1105–1120. DOI: 10.1016/j.ijsolstr.2008.10.015.
[28]	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.
[29]	FORRESTAL M J, FREW D J, HANCHAK S J, et al. Penetration of grout and concrete targets with ogive-nose steel projectiles [J]. International Journal of Impact Engineering, 1996, 18(5): 465–476. DOI: 10.1016/0734-743X(95)00048-F.
[30]	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.
[31]	武海军, 黄风雷, 王一楠, 等. 高速侵彻混凝土弹体头部侵蚀终点效应实验研究 [J]. 兵工学报, 2012, 33(1): 48–55. WU H J, HUANG F L, WANG Y N, et al. Experimental investigation on projectile nose eroding effect of high-velocity penetration into concrete [J]. Acta Armamentarii, 2012, 33(1): 48–55.
[32]	张雪岩, 武海军, 李金柱, 等. 弹体高速侵彻两种强度混凝土靶的对比研究 [J]. 兵工学报, 2019, 40(2): 276–283. DOI: 10.3969/j.issn.1000-1093.2019.02.007. ZHANG X Y, WU H J, LI J Z, et al. Comparative study of projectiles penetrating into two kinds of concrete targets at high velocity [J]. Acta Armamentarii, 2019, 40(2): 276–283. DOI: 10.3969/j.issn.1000-1093.2019.02.007.
[33]	WU H, FANG Q, CHEN X W, et al. Projectile penetration of ultra-high performance cement based composites at 510-1320m/s [J]. Construction and Building Materials, 2015, 74: 188–200. DOI: 10.1016/j.conbuildmat.2014.10.041.
[34]	吴昊, 方秦, 龚自明. HSFRC靶体的弹体侵彻试验与理论分析 [J]. 弹道学报, 2012, 24(3): 19–24, 53. DOI: 10.3969/j.issn.1004-499X.2012.03.005. WU H, FANG Q, GONG Z M. Experiments and theoretical analyses on HSFRC target under the impact of rigid projectile [J]. Journal of Ballistics, 2012, 24(3): 19–24, 53. DOI: 10.3969/j.issn.1004-499X.2012.03.005.
[35]	ZHANG M H, SHIM V P W, LU G, et al. Resistance of high-strength concrete to projectile impact [J]. International Journal of Impact Engineering, 2005, 31(7): 825–841. DOI: 10.1016/j.ijimpeng.2004.04.009.

Relative Articles

[1]	HE Yong, XU Tianhan, ZHANG Xiaohan, SUI Yaguang, XING Haozhe. Analysis of the size effect on the penetration depth of earth-penetrating projectiles and practical calculating formula[J]. Explosion And Shock Waves, 2025, 45(4): 043301. doi: 10.11883/bzycj-2024-0248
[2]	ZHAO Hongyuan, WU Haijun, DONG Heng, LYU Yingqing, HUANG Fenglei. An experimental study of anti-penetration performance of concrete-filled steel tube with honeycomb structure[J]. Explosion And Shock Waves, 2023, 43(5): 053101. doi: 10.11883/bzycj-2022-0050
[3]	CHENG Yuehua, JIANG Pengfei, WU Hao, TAN Keke, FANG Qin. On penetration depth of typical earth-penetrating projectilesinto concrete targets considering the scaling effect[J]. Explosion And Shock Waves, 2022, 42(6): 063302. doi: 10.11883/bzycj-2021-0373
[4]	CHEN Beibei, ZHANG Xianfeng, DENG Jiajie, ZHANG Jian, BAO Kuo, TAN Mengting. Residual penetration depth of a projectile into YAG transparent ceramic/glass[J]. Explosion And Shock Waves, 2020, 40(8): 083301. doi: 10.11883/bzycj-2019-0372
[5]	QIAN Bingwen, ZHOU Gang, LI Jin, LI Yunliang, ZHANG Dezhi, ZHANG Xiangrong, ZHU Yurong, TAN Shushun, JING Jiyong, ZHANG Zidong. Penetration depth of hypervelocity tungsten alloy projectile penetrating concrete target[J]. Explosion And Shock Waves, 2019, 39(8): 083301. doi: 10.11883/bzycj-2019-0141
[6]	PENG Yong, LU Fangyun, FANG Qin, WU Hao, LI Xiangyu. Analyses of the size effect for projectile penetrations into concrete targets[J]. Explosion And Shock Waves, 2019, 39(11): 113301. doi: 10.11883/bzycj-2018-0402
[7]	WANG Wenjie, ZHANG Xianfeng, DENG Jiajie, ZHENG Yingmin, LIU Chuang. Analysis of projectile penetrating into mortar target with elliptical cross-section[J]. Explosion And Shock Waves, 2018, 38(1): 164-173. doi: 10.11883/bzycj-2017-0020
[8]	DENG Jiajie, ZHANG Xianfeng, LIU Chuang, WANG Wenjie, XU Chenyang. Experimental and theoretical study of symmetrical grooved-nose projectile penetrating into semi-infinite aluminum target[J]. Explosion And Shock Waves, 2018, 38(6): 1231-1240. doi: 10.11883/bzycj-2017-0413
[9]	WU Cheng, SHEN Xiaojun, WANG Xiaoming, YAO Wenjin. Numerical simulation on anti-penetration and penetration depth model of mesoscale concrete target[J]. Explosion And Shock Waves, 2018, 38(6): 1364-1371. doi: 10.11883/bzycj-2017-0123
[10]	JIAO Chujie, LI Xibo, CHENG Congmi, LI Congbo. Dynamic damage constitutive relationship of high strength concrete based on fractal theory[J]. Explosion And Shock Waves, 2018, 38(4): 925-930. doi: 10.11883/bzycj-2016-0377
[11]	Xiao Yunkai, Fang Qin, Wu Hao, Kong Xiangzhen, Peng Yong. A model for rigid sharp-nosed projectile perforating metallic targets considering free-surface and cracking effects[J]. Explosion And Shock Waves, 2016, 36(3): 359-369. doi: 10.11883/1001-1455(2016)03-0359-11
[12]	Deng Jiajie, Zhang Xianfeng, Qiao Zhijun, Guo Lei, He Yong, Chen Dongdong. An analytic model of penetration for oval-nosed projectile penetrating into pre-drilled target[J]. Explosion And Shock Waves, 2016, 36(5): 625-632. doi: 10.11883/1001-1455(2016)05-0625-08
[13]	Liu Jian-cheng, Huang Feng-lei, Pi Ai-guo, Chai Chuan-guo, Wu Hai-jun. On enhanced penetration performance of modified nose projectiles[J]. Explosion And Shock Waves, 2014, 34(4): 409-414. doi: 10.11883/1001-1455(2014)04-0409-06
[14]	LaiJian-zhong, ZhuYao-yong, XuSheng, GuoXu-jia. Resistanceofultra-high-performancecementitious compositestomultipleimpactpenetration[J]. Explosion And Shock Waves, 2013, 33(6): 601-607. doi: 10.11883/1001-1455(2013)06-0601-07
[15]	WU Hao, FANGQin, GONG Zi-ming. Semi-theoreticalanalysesforpenetrationdepthofrigidprojectiles withdifferentnosegeometriesintoconcrete(rock)target[J]. Explosion And Shock Waves, 2012, 32(6): 573-580. doi: 10.11883/1001-1455(2012)06-0573-08
[16]	LANG Lin, CHEN Xiao-wei, LEI Jing-song. Numericalsimulationsonlongrodsandsegmentedrods penetratingintosteeltarget[J]. Explosion And Shock Waves, 2011, 31(2): 127-134. doi: 10.11883/1001-1455(2011)02-0127-08
[17]	SUN Chuan-Jie, LU Yong-Gang, ZHANG Fang-Ju, LI Hui-Min. Penetration of cylindrical-nose-tip projectiles into concrete targets[J]. Explosion And Shock Waves, 2010, 30(3): 269-275. doi: 10.11883/1001-1455(2010)03-0269-07
[18]	PI Ai-guo, HUANG Feng-lei. Elastic-plastic dynamic response of slender projectiles penetrating into 2024-O aluminum targets[J]. Explosion And Shock Waves, 2008, 28(3): 252-260. doi: 10.11883/1001-1455(2008)03-0252-09
[19]	ZHOU Ning, REN Hui-qi, SHEN Zhao-wu, HE Xiang, LIU Rui-zhao, WU Biao. An engineering analytical model for projectiles to penetrate into semi-infinite reinforced concrete targets[J]. Explosion And Shock Waves, 2007, 27(6): 529-534. doi: 10.11883/1001-1455(2007)06-0529-06
[20]	PI Ai-guo, HUANG Feng-lei. Dynamic behavior of a slender projectile on oblique penetrating into concrete target[J]. Explosion And Shock Waves, 2007, 27(4): 331-338. doi: 10.11883/1001-1455(2007)04-0331-08