抗战斗部侵彻爆炸作用的混凝土遮弹层设计

程月华; 周飞; 吴昊

doi:10.11883/bzycj-2022-0346

抗战斗部侵彻爆炸作用的混凝土遮弹层设计

doi: 10.11883/bzycj-2022-0346

同济大学土木工程学院，上海 200092

基金项目: 国家自然科学基金（52208500）

详细信息

作者简介:
程月华（1994－　），女，博士研究生，yhcheng@tongji.edu.cn

通讯作者:
吴　昊（1981－　），男，博士，教授，wuhaocivil@tongji.edu.cn

中图分类号: O385
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- 被引次数: 0
出版历程
- 收稿日期: 2022-08-09
- 修回日期: 2023-01-09
- 网络出版日期: 2023-02-20
- 刊出日期: 2023-04-05

Design of concrete shield against the combination of penetration and explosion of warheads

College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 准确评估战斗部侵彻爆炸作用下混凝土遮弹层的损伤破坏可为防护工程设计提供重要参考。首先基于Karagozian & Case（K&C）模型框架建立了新型混凝土动态损伤本构模型，其中强度面综合考虑了静水压力、Lode角、应变率和损伤；独立描述了拉伸和压缩损伤，并考虑了拉压之间的连续过渡以及剪切变形和体积压缩对损伤的贡献。随后，开展了半无限厚混凝土靶体的105 mm口径弹体侵彻爆炸联合作用试验。进一步通过对上述试验和已有有限厚混凝土靶板的预制孔埋置装药爆炸试验进行数值仿真分析，验证了所建立的本构模型、参数取值和有限元分析方法在描述混凝土动态阻力、损伤演化和开裂行为方面的准确性。最后，确定了SDB、WDB-43/B和BLU-109/B三种典型战斗部以声速侵彻爆炸普通混凝土的临界贯穿和临界震塌厚度。结果表明：SDB、WDB-43/B和BLU-109/B战斗部侵彻爆炸作用下混凝土的临界贯穿厚度分别为1.4、3.4和3.8 m，临界震塌厚度分别为3.6、6.3和8.3 m；由于携带炸药量的差异，不同战斗部侵彻爆炸下的临界贯穿和临界震塌厚度与侵彻深度的比值非定值，相应的比值范围分别为1.49~2.13和2.90~4.66。
- 混凝土遮弹层 /
- 侵彻爆炸作用 /
- 临界贯穿厚度 /
- 临界震塌厚度 /
- 防护设计
Abstract: Accurately evaluating the damage and failure of concrete shield subjected to combination of penetration and explosion of warheads can provide an important reference for the design of protective structures. Firstly, based on the frame of Karagozian & Case (K&C) model, a newly dynamic-damage constitutive model was established. The hydrostatic pressure, Lode angle, strain rate, and damage were all considered in strength surface. The tension and compression damages were described separately with a continued transition. Besides, the contribution of shear deformation and hydrostatic compression were also considered. Then, the combined penetration and explosion test of 105-mm-caliber projectile on the semi-infinite concrete target was conducted. The corresponding numerical simulation was conducted to verify the accuracy of the constitutive model, the parameters, and the finite element analysis approach in describing the dynamic resistance of concrete. Furthermore, by conducting the numerical simulations of the existing prefabricated hole charge explosion test on the finite concrete plane, the accuracy of the established constitutive model, parameters, and finite element analysis approach in describing the damage evolution and cracking behavior of concrete was validated. Finally, the perforation limit and scabbing limit of normal strength concrete subjected to the combination of penetration and explosion of three typical warheads at sound velocity were determined. The results show that, the perforation limits of the SDB, WDU-43/B, and BLU-109/B warheads are 1.4, 3.4 and 3.8 m, respectively. The scabbing limit are 3.6, 6.3 and 8.3 m, respectively. Due to the differences of the explosive mass in warheads, the ratios of perforation limit and scabbing limit under combined penetration and explosion to the depth of penetration are not constant. The corresponding ratio ranges are 1.49−2.13 and 2.90−4.66, respectively.
- concrete shield /
- combined penetration and explosion /
- perforation limit /
- scabbing limit /
- protective design

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图 1 三维双曲线强度面

Figure 1. Sketch map of the 3D hyperbolic strength surface

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图 2 状态方程示意

Figure 2. Sketch sof equation of state

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图 3 应变硬化和软化函数

Figure 3. Strain hardening and softening functions

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图 4 体积压缩损伤函数

Figure 4. Damage function of volumetric compaction

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图 5 普通混凝土单轴压缩应力-应变曲线

Figure 5. Compressive stress-strain relation of normal strength concrete

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图 6 试验弹体、TNT炸药和靶体

Figure 6. Test projectile, TNT and target

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图 7 侵彻爆炸联合作用试验

Figure 7. Combined penetration and explosion test

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图 8 侵彻作用有限元模型

Figure 8. Finite element model of penetration

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图 9 侵彻试验模拟结果

Figure 9. Simulation results of penetration test

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图 10 爆炸作用有限元模型

Figure 10. Finite element model of explosion

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图 11 爆炸试验模拟结果

Figure 11. Simulation results of explosion test

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图 12 预制孔装药爆炸试验

Figure 12. Prefabricated hole charge explosion test

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图 13 试验^[23]与数值模拟结果对比

Figure 13. Comparsions of test^[23] and numerical simulation results

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图 14 有限元模型

Figure 14. Finite element model

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图 15 三种厚度靶体的开裂破坏

Figure 15. Cracking failure of targets with three thicknesses

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图 16 三种战斗部打击下混凝土靶体的损伤云图

Figure 16. Damage contours of concrete targets subjected to three warheads

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图 17 三种厚度靶体的开裂破坏

Figure 17. Cracking failure of targets with three thicknesses

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图 18 三种战斗部打击下混凝土靶体的损伤云图

Figure 18. Damage contours of concrete targets subjected to three warheads

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表 1 动态损伤本构模型中的强度面和损伤参数

Table 1. Parameters of the strength surface and the damage for the dynamic-damage constitutive model

S_max	p₀	$ d_{\text{1}}^{\text{h}} $	$ d_{\text{1}}^{\text{s}} $	d₂	ε_frac	A	m
13f_c	−0.16f_c	0.000 35	0.000 84	1	0.007	1.03	0

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表 2 动态损伤本构模型的状态方程参数

Table 2. Parameters of the equation of state for the dynamic-damage constitutive model

μ₁	μ₂	μ₃	μ₄	μ₅	μ₆	μ₇	μ₈	μ₉	μ₁₀
0	0.0015	0.0043	0.0101	0.0305	0.0513	0.0726	0.0943	0.1740	0.2080

p₁/μ₂	p₂/μ₂	p₃/μ₂	p₄/μ₂	p₅/μ₂	p₆/μ₂	p₇/μ₂	p₈/μ₂	p₉/μ₂	p₁₀/μ₂
0	1	2.18	3.50	6.65	10.03	14.23	21.77	127.10	194.40

K_u,1	K_u,2	K_u,3	K_u,4	K_u,5	K_u,6	K_u,7	K_u,8	K_u,9	K_u,10
1	1	1.014	1.065	1.267	1.470	1.672	1.825	4.107	5.000

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表 3 试验与数值模拟结果对比

Table 3. Comparisons of test data and simulation results

试验	深度			开坑直径
试验	试验/mm	模拟/mm	相对误差/%	试验/mm	模拟/mm	相对误差/%
侵彻	515	519	0.8	1 176	948	−19.4
爆炸	680	648	−4.7	1 671	1 728	3.4

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表 4 TNT炸药的模型和状态方程参数

Table 4. Parameters for material model and the equation of state of the explosive TNT

密度/(kg·m⁻³)	爆速/(m·s⁻¹)	CJ爆压/GPa	A_JWL/GPa	B_JWL/GPa	R₁	R₂	ω
1630	6930	21	374	375	4.15	1.0	0.35

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表 5 空气的模型和状态方程参数

Table 5. Parameters for material model and the equation of state of the air

ρ/(kg·m⁻³)	C₄	C₅	E₀/Pa
1.29	0.4	0.4	2.5×10⁵

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表 6 三种战斗部参数

Table 6. Parameters of three warheads

战斗部	直径/ mm	总质量/ kg	长度/ mm	壁厚/ mm	头部曲径比	等效TNT 质量/kg
SDB	152	113	1800	10.8	3	23
WDU-43/B	234	454	2400	41.5	9	100
BLU-109/B	368	874	2510	25.4	3	324

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表 7 三种战斗部打击下的模拟结果

Table 7. Simulation results of three warheads

战斗部	侵彻作用		侵彻爆炸联合作用		临界贯穿厚度/m	D₁	D₂	临界震塌厚度/m	D₃	D₄
战斗部	深度/m	开坑直径/mm	深度/m	开坑直径/mm	临界贯穿厚度/m	D₁	D₂	临界震塌厚度/m	D₃	D₄
SDB	0.94	1066	1.03	1656	1.4	1.49	1.36	3.6	3.83	3.50
WDU-43/B	2.17	1806	2.45	2180	3.4	1.57	1.39	6.3	2.90	2.57
BLU-109/B	1.78	2554	2.18	3556	3.8	2.13	1.74	8.3	4.66	3.81

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