基于量纲分析的平面冲击波经验模型研究

赵传荣; 孔德仁

doi:10.11858/gywlxb.2016.06.014

基于量纲分析的平面冲击波经验模型研究

doi: 10.11858/gywlxb.2016.06.014

赵传荣^{1, 2,},
孔德仁^1,*, ,

1.
南京理工大学机械工程学院, 江苏南京 210094
2.
安徽工业大学电气与信息工程学院，安徽马鞍山 243032

基金项目:

国家自然科学基金 11372143

详细信息

作者简介:
赵传荣(1989—), 男，博士研究生，主要从事冲击波加载及测试技术研究.E-mail:zhaochuanrong892@sina.cn

通讯作者:
孔德仁(1964—), 男，博士，教授，主要从事传感器技术研究.E-mail:derenkongnj@sina.com

中图分类号: O385
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出版历程
- 收稿日期: 2016-02-02
- 修回日期: 2016-06-25

Empirical Model of Plane Shock Wave on the Impact Surfaceof Target Based on Dimensional Analysis

ZHAO Chuan-Rong^{1, 2
,},
KONG De-Ren^{1,*
, ,}

1.
School of Mechanical Engineering, Nanjing University of Scienceand Technology, Nanjing 210094, China
2.
School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan 243032, China

摘要

摘要: 当飞片或靶板材料的冲击雨贡纽参数未知时，根据现有靶板撞击面冲击波压力的理论模型无法对其冲击波压力峰值和脉冲宽度进行准确预估。针对该问题，基于相似理论，对影响冲击波压力峰值和脉冲宽度的因素进行量纲分析，分别建立了冲击波压力峰值和脉冲宽度的经验模型，且模型中各项均有明确的物理意义。通过实例分析，获得了不同飞片厚度和冲击速度下，45钢冲击纯镍产生的平面冲击波的经验模型定量关系式，模型预测结果与实验测量值较为吻合。
- 平面冲击波 /
- 压力峰值 /
- 脉冲宽度 /
- 量纲分析 /
- 经验模型
Abstract: When the equation of state (EOS) and physical parameters of the projectile and the target plate materials are unknown, it is impossible to estimate accurately the peak value and the pulse width of the shock wave pressure on the impacting surface based on the existing theoretical models.To solve this problem, using the dimensional analysis, we studied the factors influencing the peak value and the pulse width of the shock wave pressure, and established an empirical model of the peak value, and that of the pulse width of the shock wave pressure respectively, with a clear physical meaning specified for each component in the formulas.This kind of model successfully avoided the problem of unknown EOS of the projectile and target materials.The obtained formulas can be used to predict the peak value and the pulse width of the shock wave pressure.We applied this model to an actual experiment of 45 steel impacting on a Ni plate, and found that the peak values and the pulse widths of the shock wave pressure calculated by this model match well with the measured results, which proves the feasibility of our model.
- plane shock wave /
- peak pressure /
- pulse width /
- dimensional analysis /
- empirical model

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表 1 相应物理量的量纲

Table 1. Dimensions of the corresponding physical quantities

Physical quantities	Dimension index
Physical quantities	M	L	T
p_m	1	-1	-2
τ	0	0	1
L	0	1	0
D	0	1	0
ρ₀₁	1	-3	0
C₀₁	0	1	-1
ρ₀₂	1	-3	0
C₀₂	0	1	-1
v	0	1	-1

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表 2 相似比求解

Table 2. Solution of similar ratio

π term	x₄	x₅	x₆	x₇	x₈	x₉	x₁	x₂	x₃
π₁	1	0	0	0	0	0	0	0	-1
π₂	0	1	0	0	0	0	-1	-2	2
π₃	0	0	1	0	0	0	0	1	-1
π₄	0	0	0	1	0	0	-1	-2	2
π₅	0	0	0	0	1	0	0	1	-1
π₆	0	0	0	0	0	1	0	1	-1

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表 3 实验数据

Table 3. Experimental data

Exp. No.	L/(cm)	v/(km/s)	p_m/(GPa)	τ/(μs)
1	0.3	0.334	7.39	0.960 0
2	0.3	0.711	14.52	0.900 0
3	0.3	0.977	19.12	0.879 0
4	0.5	0.449	7.75	2.680 0
5	0.3	0.461	8.50	0.925 0
6	0.4	0.464	8.75	1.900 0

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表 4 压力峰值和脉冲宽度的实测值与模型预测值的对比结果

Table 4. Comparison of the measured values of peak pressure and pulse widthwith those predicted by this model

L/(cm)	v/(km/s)	p_m/(GPa)	τ/(μs)	p_{m, j}/(GPa)	τ_j/(μs)	$\left\| {\frac{{{p_{\rm{m}}} - {p_{{\rm{m, j}}}}}}{{{p_{\rm{m}}}}}} \right\|/\left( \% \right)$	$\left\| {\frac{{\tau - {\tau _{\rm{j}}}}}{\tau }} \right\|/\left( \% \right)$
0.3	0.461	8.50	0.925 0	9.19	0.934 2	8.12	9.95
0.4	0.464	8.75	1.900 0	9.24	1.688 2	5.60	11.15
Note：p_{m, j} and τ_j are the predicted values of peak pressure (p_m) and pulse width (τ), respectively.

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参考文献(13)

[1]	KIM M, YOO C S.Highly repulsive interaction in novel inclusion D₂-N₂ compound at high pressure:Raman and X-ray evidence[J].J Chem Phys, 2011, 134(4):44-51. doi: 10.1063/1.3533957
[2]	罗宁, 胡强, 李尚升.人造金刚石的合成技术分析[J].应用技术, 2010(20):257. http://www.cqvip.com/Main/Detail.aspx?id=34216558 LUO N, HU Q, LI S S.Analysis of artificial diamond synthesis technology[J].The Application of Technology, 2010(20):257. http://www.cqvip.com/Main/Detail.aspx?id=34216558
[3]	PULHAM C R, MILLAR D I A, OSWALD I D H, et al.High-pressure studies of energetic materials[M]//Boldyreva E, Dera P.High-pressure crystallography.Netherlands: Springer Netherlands, 2010: 447-457.
[4]	曾代朋, 陈军, 谭多望.超压爆轰产物冲击绝热线的实验研究[J].高压物理学报, 2010, 24(1):76-80. doi: 10.3969/j.issn.1000-5773.2010.01.014 ZENG D P, CHEN J, TAN D W.Over pressure experimental study on detonation products shock Hugoniot[J].Chinese Journal of High Pressure Physics, 2010, 24(1):76-80. doi: 10.3969/j.issn.1000-5773.2010.01.014
[5]	PAVLENKO A V, BALABIN S I, KOZELKOV O E, et al.A one-stage light-gas gun for studying dynamic properties of structural materials in a range up to 40 GPa[J].Instrum Exp Tech+, 2013, 4(56):482-484. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=56a879292fe77c04c14d76c6a182a5ea
[6]	汤文辉, 张若棋, 陈雪芳.LY12-M铝中冲击波衰减机理的实验研究[J].高压物理学报, 1988, 2(3):218-226. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK000000974302 TANG W H, ZHANG R Q, CHEN X F.Experimental study on the mechanism of shock wave attenuation in LY12-M aluminum[J].Chinese Journal of High Pressure Physics, 1988, 2(3):218-226. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK000000974302
[7]	CHAN K S, TIAN J W, YANG B, et al.Evolution of slip morphology and fatigue crack initiation in surface grains of Ni200[J].Metall Mater Trans A, 2009, 40(11):2545-2556. doi: 10.1007/s11661-009-9980-4
[8]	杜晓松, 郝建德, 杨邦朝, 等.薄膜式锰铜传感器的超高压力标定[J].仪器仪表学报, 2001, 22(增刊2):151-152. http://d.old.wanfangdata.com.cn/Periodical/yqyb2001z2074 DU X S, HAO J D, YANG B C, et al.Calibration of thin-film ultrahigh pressure manganin gauges[J].Chinese Journal of Scientific Instrument, 2001, 22(Suppl 2):151-152. http://d.old.wanfangdata.com.cn/Periodical/yqyb2001z2074
[9]	陈卫东, 张忠, 刘家良.破片对屏蔽炸药冲击起爆的数值模拟和分析[J].兵工学报, 2009, 30(9):1187-1190. doi: 10.3321/j.issn:1000-1093.2009.09.007 CHEN W D, ZHANG Z, LIU J L.Numerical simulation and analysis of fragments impact initiation of shielded explosive[J].Acta Armamentarii, 2009, 30(9):1187-1190. doi: 10.3321/j.issn:1000-1093.2009.09.007
[10]	谈庆明.量纲分析[M].合肥:中国科学技术大学出版社, 2007:100-110. TAN Q M.Dimensional analysis[M].Hefei:University of Science and Technology of China Press, 2007:97-98.
[11]	KISELEV S P.Numerical simulation of wave formation in an oblique impact of plates by the method of molecular dynamics[J].Journal of Applied Mechanics and Technical Physics, 2012, 53(6):907-917. doi: 10.1134/S0021894412060144
[12]	杨超, 经福谦, 张万甲.冲击波压力和脉冲持续时间对铁和镍微结构的影响[J].兵器材料科学与工程, 1996, 19(3):38-44. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199600171784 YANG C, JING F Q, ZHANG W J.Effects of shock pressure and pulse duration on micro structure of iron and nickel[J].Ordnance Material Science and Engineering, 1996, 19(3):38-44. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199600171784
[13]	杨超, 经福谦, 张万甲, 等.冲击加载作用下铁和镍的高应变率变形[J].兵器材料科学与工程, 1996, 19(1):49-54. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199600171752 YANG C, JING F Q, ZHANG W J, et al.High strain rate deformation of Fe and Ni by shock loading[J].Ordnance Material Science and Engineering, 1996, 19(1):49-54. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199600171752