岩石类介质侵彻效应的理论研究进展

李杰; 程怡豪; 徐天涵; 王明洋

doi:10.11883/bzycj-2019-0286

岩石类介质侵彻效应的理论研究进展

doi: 10.11883/bzycj-2019-0286

李杰^1,,
程怡豪^{1, 2, ,},
徐天涵¹,
王明洋^{1, 3}

1.
陆军工程大学爆炸冲击防灾减灾国家重点实验室，江苏南京 210007
2.
陆军工程大学野战工程学院，江苏南京 210007
3.
南京理工大学机械工程学院，江苏南京 210094

基金项目: 国家自然科学基金面上项目(51679249)；中国博士后基金(2018M643853)

详细信息

作者简介:
李　杰（1981－　），男，博士，副教授，lijierf@163.com

通讯作者:
程怡豪（1986－　），男，博士，讲师，05105432@163.com

中图分类号: O347
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- 被引次数: 0
出版历程
- 收稿日期: 2019-07-19
- 修回日期: 2019-08-02
- 刊出日期: 2019-08-01

Review on theoretical research of penetration effects into rock-like material

LI Jie^1
,,
CHENG Yihao^{1, 2
, ,},
XU Tianhan¹,
WANG Mingyang^{1, 3}

1.
State Key Laboratory of Disaster Prevention and Mitigation of Explosive and Impact, Army Engineering University of PLA, Nanjing 210007, Jiangsu, China
2.
Field Engineering College, Army Engineering University of PLA, Nanjing 210007, Jiangsu, China
3.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

摘要

摘要: 近年来，随着超高速武器的发展，侵彻效应的研究重点逐渐由高速向超高速发展。随着弹体打击速度提高，侵彻机制发生变化，并触发强烈的成坑和地冲击效应。本文综述了大速度范围内岩石类介质侵彻效应的理论研究进展，讨论了长杆弹侵彻速度的分区，介绍了岩石类介质的侵彻、成坑、地冲击效应的理论模型，并对目前研究中尚有待解决的问题和下一步的研究方向进行了展望。
- 侵彻 /
- 岩石 /
- 混凝土 /
- 理论研究 /
- 成坑 /
- 地冲击
Abstract: In recent years, as the developing of hyper-velocity weapons, the research emphasis of penetration effects is shifting from high-velocity penetration to hyper-velocity penetration. With the increasing of impact velocity of projectiles, the penetration mechanism changes, where effects as cratering and ground shock are induced. In this paper, progress in theoretical research of penetration into rock-like materials in a wide velocity range is reviewed, where velocity range is divided into zones, and theoretical models of penetration, cratering and ground shock are introduced. The existing problems concerned and research orientation in the future are also forecasted.
- penetration /
- rock /
- concrete /
- theoretical research /
- cratering /
- ground shock

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图 1 钢杆弹撞击铝靶机理分区^[39]

Figure 1. Schematic of penetration of steel projectiles into aluminum targets^[39]

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图 2 岩石的动力压缩曲线^[50]

Figure 2. Dynamic compression curves of rock^[50]

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图 3 侵彻速度界定及介质压缩状态

Figure 3. Definition the scope of penetration velocity and medium compression state

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图 4 $v/c$与α关系曲线

Figure 4. Curve between $v/c$ and α

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图 5 花岗岩侵彻实验结果（撞击速度1～2.5 km/s）^[19]

Figure 5. Experimental results of penetration into granite targets with impact velocity from 1−2.5 km/s^[19]

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图 6 变形弹计算假设^[73]

Figure 6. Assumption of deformable projectile^[73]

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图 7 不同速度侵彻后回收弹体的形态^[19]

Figure 7. The morphology of the recovered projectiles after penetration under different velocities^[19]

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图 8 基于界面压力的超高速侵彻阶段划分^[74]

Figure 8. Phases during hypervelocity penetration based on interface pressure^[74]

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图 9 弧形弹头的几何参数

Figure 9. Ogive-nose projectile geometry

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图 10 花岗岩侵彻深度的实验结果与理论计算结果的预测效果^[32]

Figure 10. Comparison of calculation results with experimental results of penetration depth in granite^[32]

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图 11 岩石与金属靶体超高速撞击成坑的典型外观^{[106, 109]}

Figure 11. Typical appearance of craters formed by hypervelocity impact^{[106, 109]}

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图 12 不同条件下的成坑效应

Figure 12. Cratering effects under different conditions

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图 13 式（41）与混凝土超高速侵彻深度实验结果的对比^[114]

Figure 13. Comparison between Eq. (41) and experimental results of hyper-velocity penetration depth into concrete^[114]

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图 14 高速弹体侵彻岩石扩孔范围计算简图^[116]

Figure 14. Calculation diagram of cavitation induced by high-velocity projectile penetration into rocks^[116]

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图 15 径向裂纹区半径计算结果与实验结果对比^[32]

Figure 15. Comparison of crater radius between calculation results and experimental results^[32]

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图 16 Z模型在不同Z值下的速度场^[118]

Figure 16. Streamlines with different values of Z^[118]

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图 17 球形弹超高速撞击下介质中压力分布^[123]

Figure 17. Pressure distribution in medium under hypervelocity spherical projectile^[123]

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图 18 峰值压力随距离衰减曲线^[123]

Figure 18. Peak pressure decay with impact of distance^[123]

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图 19 弹速3 558 m/s时实测地冲击压力时程曲线^[32]

Figure 19. The experiment time history curve of ground shock with impact velocity 3 558 m/s^[32]

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图 20 弹速3 558 m/s时按公式（50）计算的地冲击压力时程曲线^[32]

Figure 20. the calculated time history curve of ground shock with impact velocity 3 558 m/s^[32]

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表 1 冲击压缩作用下典型硬岩分区行为特征^[51]

Table 1. Dynamic behaviors of hard rock in different ranges under shock compression^[51]

冲击压缩状态	波形时间特征	应变状态特征	应力状态特征	${c_0} = \sqrt {\displaystyle\frac{1}{{{\rho _0}}}\displaystyle\frac{{{\rm d}\sigma }}{{{\rm d}\varepsilon }}} $ 小扰动传播速度	$p\simfont\text{～} {{r}^{ - n}}$ 应力波衰减特征	冲击波速度特征(图2(a))
高应力流体状态	Δ=0～0.05 冲击波特征	ε_θ=0 一维应变	$\alpha = {\displaystyle\frac{{{\sigma _r}}}{{\sigma}_\theta} } \approx 1$	${c_0} = \sqrt {\frac{K}{{{\rho _0}}}} $	n=−2.2～3.0	D>>c_p
内摩擦拟流体状态	Δ=0.05～0.1 短波特征	${\varepsilon _r} \gg {\varepsilon _\theta } \ne 0$ 受限应变	$\begin{array}{l}\alpha = {\displaystyle\frac{\sigma _r}{{\sigma }_\theta} } = {\alpha ^}\\{\alpha _0} \simfont\text{＜} {\alpha ^} \simfont\text{＜} 1\end{array}$	${c_0} = \sqrt {\displaystyle\frac{{3K}}{{{\rho _0}\left( {1 + 2{\alpha ^*}} \right)}}} $ 介于流体与固体之间	n=1.4～1.8	D≈c_p
低应力固体状态	Δ＞0.1 弹塑性波特征	${\varepsilon _r} + 2{\varepsilon _\theta } = 0$ 相容应变	$\alpha = {\displaystyle\frac{{{\sigma _r}}}{{\sigma }_\theta }} = {\alpha _0}$	${c_0} = \sqrt {\frac{{\left( {K + \displaystyle\frac{4}{3}\mu } \right)}}{{{\rho _0}}}} $	n=1.1～1.2
注：$\alpha = \displaystyle\frac{{1 - {\rm{sin}}\phi }}{{1 + {\rm{sin}}\phi }}$，ϕ为介质内摩擦角；${\alpha _0} = \displaystyle\frac{\upsilon }{{1 - \upsilon }}$，$\upsilon $为介质泊松比；ρ₀为介质密度，K为体积模量，μ为剪切模量。

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表 2 不同修正流体动力学模型中[Y_p]和[R_t]值^[1]

Table 2. The value of [Y_p] and [R_t] in different models^[1]

模型	[Y_p]	[R_t]	备注
A-T^[42-44]	Y_p	R_t	${Y_{\rm p}}{\rm{ = HEL = }}{\sigma _{\rm{yp}}}\left( {1 + \upsilon } \right)/\left( {1 - 2\upsilon } \right)$
A-T^[42-44]	Y_p	R_t	${R_{\rm t}}={\sigma _{\rm{yt} } }\left[ {\left( {2/3} \right) + \ln \left( {0.57{E_{\rm t} }/{\sigma _{\rm{yt} } } } \right)} \right]$
S-W-Z-S^[78]	$\displaystyle\frac{{{Y_{\rm p}}}}{4}$	$\displaystyle\frac{A}{{4{A_{\rm p}}}}{R_{\rm t}} + \displaystyle\frac{{3A - 4{A_{\rm p}}}}{{8{A_{\rm p}}}}{\rho _{\rm t}}{u^2}$	${A_{\rm p}}$为长杆弹截面积
S-W-Z-S^[78]	$\displaystyle\frac{{{Y_{\rm p}}}}{4}$		$A$为坑底面积，$A \simfont\text{≥} 2{A_{\rm p}}$
R-M-M^[79]	${Y_{\rm p}}$	$\displaystyle\frac{{{A_{\rm t}}}}{{{A_{\rm p}}}}{R_{\rm t}} + \displaystyle\frac{{{A_{\rm t}} - {A_{\rm p}}}}{{2{A_{\rm p}}}}{\rho _{\rm t}}{u^2}$	${A_{\rm p}}$为长杆弹截面积
			${A_{\rm p}}$为蘑菇头等效面积
			${R_{\rm t}}=\left( {{\sigma _{\rm{yt}}}/\sqrt 3 } \right)\left[ {1 + \ln \left( {\sqrt 3 {E_{\rm t}}/\left( {5 - 4v} \right){\sigma _{\rm{yt}}}} \right)} \right]$
A-W^[80]	${\sigma _{\rm{yp}}}$	$\displaystyle\frac{7}{3}\ln \left( \alpha \right){\sigma _{\rm{yt}}}$	$\alpha $为靶体中塑性流动区的无量纲长度，由柱形空腔膨胀模型得到（${K_{\rm t}}$${G_{\rm t}}$为靶体的体积模量和剪切模量）： $\left( {1{\rm{ + }}\displaystyle\frac{{{\rho _{\rm t}}{u^2}}}{{{\sigma _{\rm{yt}}}}}} \right)\sqrt {{K_{\rm t}} - {\rho _{\rm t}}{\alpha ^2}{u^2}} = \left( {1{\rm{ + }}\displaystyle\frac{{{\rho _{\rm t}}{\alpha ^2}{u^2}}}{{2{G_{\rm t}}}}} \right)\sqrt {{K_{\rm t}} - {\rho _{\rm t}}{u^2}} $
Z-H^[81]	$\displaystyle\frac{{{Y_{\rm p}}}}{4}$	$\displaystyle\frac{{{D^2}}}{{4D_{\rm p}^2}}{R_{\rm t}} + \displaystyle\frac{{\beta {D^2} - 4D_{\rm p}^2}}{{8D_{\rm p}^2}}{\rho _{\rm t}}{u^2}$	$\beta $为动阻力系数
L-W^[73]	${Y_{\rm p}}$	$ S - {\rho _{\rm t}}u{U_{{\rm F}0}}\exp \left[ { - {{\left( {\displaystyle\frac{{u - {U_{{\rm F}0}}}}{{n{U_{{\rm F}0}}}}} \right)}^2}} \right] + 2{\rho _{\rm t}}U_{{\rm F}0}^2\exp \left[ { - 2{{\left( {\displaystyle\frac{{u - {U_{{\rm F}0}}}}{{n{U_{{\rm F}0}}}}} \right)}^2}} \right] $	$S$为静阻力，${U_{ {\rm F}0} } = \sqrt {{\rm HEL}/{\rho _{\rm t} } } $为临界侵彻速度， $n$为可调系数

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表 3 地质类材料成坑效应的相似关系

Table 3. Similarity laws of cratering effects in geological material

成坑参数	强度控制区域	重力控制区域
V_c	$\displaystyle\frac{ { {\rho _{\rm{t} } }{V_{\rm c} } } }{ { {m_{\rm{p} } } }} = {f_{ {V_{\rm{c} } }s} }\left( \varepsilon \right){\left( {\displaystyle\frac{ { {\rho _{\rm{p} } }v_0^2} }{ { {Y_{\rm t}} } } } \right)^{\frac{ {3{\xi _1} } }{2} } }{\left( {\displaystyle\frac{ { {\rho _{\rm{t} } } }}{ { {\rho _{\rm{p} } } } } } \right)^{1 - 3{\xi _2} + \frac{3}{2}{\xi _1} } }$	$\displaystyle\frac{{{\rho _{\rm{t}}}{V_{\rm c}}}}{{{m_{\rm{p}}}}} = {f_{{V_{\rm{c}}}g}}\left( \varepsilon \right){\left( {\displaystyle\frac{{v_0^2}}{{g{a_0}}}} \right)^{\frac{{3{\xi _1}}}{{2 + {\xi _1}}}}}{\left( {\displaystyle\frac{{{\rho _{\rm{t}}}}}{{{\rho _{\rm{p}}}}}} \right)^{\frac{{2 + {\xi _1} - 6{\xi _2}}}{{2 + {\xi _1}}}}}$
D_c	${D_{\rm{c} } }{\left( {\displaystyle\frac{ { {\rho _{\rm{t} } } }}{ { {m_{\rm{p} } } } } } \right)^{1/3} } = {f_{ {D_{\rm{c} } }s} }\left( \varepsilon \right){\left( {\displaystyle\frac{ { {\rho _{\rm{p} } }v_0^2} }{ { {Y_{\rm t}} } } } \right)^{\frac{ { {\xi _1} } }{2} } }{\left( {\displaystyle\frac{ { {\rho _{\rm{t} } } }}{ { {\rho _{\rm{p} } } } } } \right)^{\frac{1}{3} - {\xi _2} + \frac{1}{2}{\xi _1} } }$	${D_{\rm c}}{\left( {\displaystyle\frac{{{\rho _{\rm{t}}}}}{{{m_{\rm{p}}}}}} \right)^{1/3}} = {f_{{D_{\rm{c}}}g}}\left( \varepsilon \right){\left( {\displaystyle\frac{{v_0^2}}{{g{a_0}}}} \right)^{\frac{{{\xi _1}}}{{2 + {\xi _1}}}}}{\left( {\displaystyle\frac{{{\rho _{\rm{t}}}}}{{{\rho _{\rm{p}}}}}} \right)^{\frac{{2 + {\xi _1} - 6{\xi _2}}}{{3\left( {2 + {\xi _1}} \right)}}}}$
h	$h{\left( {\displaystyle\frac{ { {\rho _{\rm{t} } } }}{ { {m_{\rm{p} } } } } } \right)^{1/3} } = {f_{ {h_{\rm{c} } }s} }\left( \varepsilon \right){\left( {\displaystyle\frac{ { {\rho _{\rm{p} } }v_0^2} }{ { {Y_{\rm t}} } } } \right)^{\frac{ { {\xi _1} } }{2} } }{\left( {\displaystyle\frac{ { {\rho _{\rm{t} } } }}{ { {\rho _{\rm{p} } } } } } \right)^{\frac{1}{3} - {\xi _2} + \frac{1}{2}{\xi _1} } }$	$h{\left( {\displaystyle\frac{{{\rho _{\rm{t}}}}}{{{m_{\rm{p}}}}}} \right)^{1/3}} = {f_{{h_{\rm{c}}}g}}\left( \varepsilon \right){\left( {\displaystyle\frac{{v_0^2}}{{g{a_0}}}} \right)^{\frac{{{\xi _1}}}{{2 + {\xi _1}}}}}{\left( {\displaystyle\frac{{{\rho _{\rm{t}}}}}{{{\rho _{\rm{p}}}}}} \right)^{\frac{{2 + {\xi _1} - 6{\xi _2}}}{{3\left( {2 + {\xi _1}} \right)}}}}$

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表 4 地质类材料地冲击衰减指数n

Table 4. Power exponent n for attenuation of ground shock in geological material

介质类型	作用类型	研究方法	爆炸当量（TNT）或撞击速度	n
花岗岩	化学爆炸	试验拟合	0.12 kg	2.12
花岗岩	核爆炸	试验拟合	4.8 kt/12.2 kt/56 kt	1.6
砂岩	化学爆炸	试验拟合	0.1 kg	2
石灰岩	化学爆炸	试验拟合	0.18～0.2 kg	2
石灰岩	撞击	数值计算	4～6 km/s	2
玄武岩	撞击	试验拟合	0.6～2.7 km/s	1.7±0.2
辉长-钙长岩	撞击	数值计算	4～45 km/s	0.2～2.95
冰	撞击	试验拟合	3.9～4.6 km/s	0.9～1.8
盐岩	核爆炸	试验拟合	1.1 kt/3.1 kt/25 kt	1.6
混凝土	化学爆炸	试验拟合	0.12 kg	1.53
细粘土	化学爆炸	试验拟合	0.2 kg	2.6
黏土	化学爆炸	试验拟合	0.4 kg	2.34

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