活性粉末混凝土抗多次侵彻实验研究及数值预测

徐世烺; 吴平; 周飞; 李庆华; 曾田; 蒋霄

doi:10.11883/bzycj-2020-0165

活性粉末混凝土抗多次侵彻实验研究及数值预测

doi: 10.11883/bzycj-2020-0165

浙江大学高性能建筑结构与材料研究所，浙江杭州 310058

基金项目: 国家自然科学基金（51678522，51622811）

详细信息

作者简介:
徐世烺（1953－　），男，博士，教授，slxu@zju.edu.cn

通讯作者:
李庆华（1981－　），女，博士，教授，liqinghua@zju.edu.cn

中图分类号: O383
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- 文章访问数: 994
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- 被引次数: 8
出版历程
- 收稿日期: 2020-05-25
- 修回日期: 2020-10-22
- 网络出版日期: 2021-04-21
- 刊出日期: 2021-06-05

Experimental investigation and numerical prediction on resistance of reactive powder concrete to multiple penetration

Institute of Advanced Engineering Structures and Materials, Zhejing University, Hangzhou 310058, Zhejiang, China

摘要

摘要: 活性粉末混凝土（reactive powder concrete，RPC）具有超高的强度和优异的阻裂性能。为了研究RPC在多次冲击荷载下的损伤规律，采用25 mm口径滑膛炮对直径为600 mm、高600 mm的RPC圆柱形靶体进行了多次侵彻实验，得到了每次侵彻后靶体的破坏数据，并根据实验数据确定了Forrestal经验公式中的相关系数。基于K&C本构模型和现有RPC基本力学性能的实验数据，修正了K&C模型的强度面参数、损伤参数、状态方程参数、损伤演化模型以及应变率效应相关参数，系统地确定了RPC的K&C模型参数。采用LS-DYNA软件中的重启动功能模拟了弹体多次侵彻RPC靶体的破坏结果，模拟结果与实验结果基本一致，验证了模拟方法的有效性。对长2 200 mm、宽2 200 mm、高1 260 mm的RPC靶体抗侵彻实验进行了数值预测，得到了侵彻深度与弹速之间的关系、弹体贯穿靶体时的极限速度以及弹体侵彻过程中的峰值加速度。
- 活性粉末混凝土 /
- K&C本构模型 /
- 多次侵彻 /
- 重启动 /
- 数值预测
Abstract: Reactive powder concrete (RPC) has ultra-high strength and excellent crack resistance. To study the damage law of the RPC subjected to multiple impact loads, a 25 mm caliber smoothbore gun was used to penetrate the RPC cylindrical target with the diameter of 600 mm and the height of 600 mm. In addition, the experimental data of the target after each penetration was obtained, and the correlation coefficient in the Forrestal empirical formula was determined. Based on the K&C constitutive model and the existing experimental data of the RPC, the model parameters for the RPC were determined systematically by modifying the strength and surface parameters, damage parameters, equation-of-state parameters, damage evolution model, the strain rate effect. The restart function in the LS-DYNA software was used to simulate the damage results of the projectile repeatedly penetrating the RPC target. The simulation results are basically consistent with the experimental results, and the effectiveness of the simulation method is verified. Finally, the numerical prediction of the penetration resistance experiment of the RPC target with the length of 2 200 mm, the width of 2 200 mm, and the height of 1 260 mm was carried out. The relationship between the penetration depth and the projectile velocity, the minimum velocity of the projectile passing through the target and the peak acceleration during projectile penetration were obtained.
- reactive powder concrete /
- K&C constitutive model /
- multiple penetrations /
- restart /
- numerical prediction

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图 1 弹体尺寸

Figure 1. Projectile sizes

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图 2 侵彻实验设备布置

Figure 2. Arrangement of penetration experiment equipments

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图 3 高速摄影机记录的弹体撞击靶体过程

Figure 3. Process of the projectile impacting the targetrecorded by a high-speed camera

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图 4 2%钢纤维掺量下不同强度RPC的Forrestal公式中的S^*

Figure 4. S* in the Forrestal formula of RPC with differentcompressive strengths at 2% steel fiber content

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图 5 RPC多次侵彻实验结果

Figure 5. Experimental results of RPC multiple penetrations

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图 6 多次侵彻实验后的靶体剖面

Figure 6. Profile of targets after multiple penetration experiments

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图 7 有限元模型

Figure 7. Finite element model

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图 8 混凝土和RPC三轴围压实验数据

Figure 8. Triaxial confining pressure experimental data of concrete and RPC

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图 9 拉伸和压缩应力应变曲线

Figure 9. Tensile and compressive stress-strain curves

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图 10 不同b₃值对应的三轴拉伸应力应变曲线

Figure 10. Triaxial tension strain stress curvescorresponding to different b₃ values

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图 11 状态方程

Figure 11. State equation

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图 12 第1次侵彻RPC靶体的模拟结果

Figure 12. Simulation results of the first penetration of the RPC target

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图 13 第2次侵彻RPC靶体的模拟结果

Figure 13. Simulation results of the second penetration of the RPC target

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图 14 第3次侵彻RPC靶体的模拟结果

Figure 14. Simulation results of the third penetration of the RPC target

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图 15 弹体与钢筋分布示意图（单位：mm）

Figure 15. Schematic diagram of the distribution of projectiles and reinforcement (unit: mm)

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图 16 有限元模型

Figure 16. Finite element model

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图 17 850 m/s弹速下的侵彻结果

Figure 17. Penetration results at the projectile velocity of 850 m/s

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图 18 1 150 m/s弹速下的贯穿结果

Figure 18. Penetration results at the projectile velocity of 1 150 m/s

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图 19 弹速与侵彻深度之间的关系

Figure 19. Relationship between projectile velocity and penetration depth

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表 1 RPC材料配合比

Table 1. Mixture proportions of RPC

kg/m³
材料	胶凝材料	砂	减水剂	水	钢纤维
RPC	1 238	928	17.7	234.3	159

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表 2 RPC基本力学性能参数

Table 2. Basic mechanical performance parameters of RPC

材料	f_c/MPa	f_t/MPa	E/GPa	μ	ρ/（g·cm⁻³）
RPC	120	9.27	46.2	0.22	2.44

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表 3 靶体多次侵彻实验结果

Table 3. Experimental results of targets subjected to multiple penetrations

侵彻次数	v₀/（m·s⁻¹）	h/mm	S/cm²	H/mm	N	W_max/mm
1	511.5	129.1	329.7	59.5	0	0
2	552.5	257.4	344.1	79.8	12	2
3	560.0	290.3	354.8	114.9	13	13

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表 4 弹体、钢箍以及钢筋材料模型参数

Table 4. Model parameters of projectile, steel culvert and steel bar material

材料	ρ/（kg·m⁻³）	E/GPa	μ	σ_y/MPa
弹体	7 850	210	0.3	1 650
钢箍/钢筋	7 800	210	0.3	300

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表 5 损伤演化函数η(λ)

Table 5. Damage evolution function η(λ)

λ	η	λ	η
0	0	4.0×10⁻⁶	0.51
2.7×10⁻⁵	0.62	6.7×10⁻⁴	0.37
6.8×10⁻⁵	0.92	1.2×10⁻³	0.27
8.0×10⁻⁵	0.99	2.0×10⁻³	0.20
1.0×10⁻⁴	1.00	5.5×10⁻³	0.10
1.4×10⁻⁴	0.96	1.6×10⁻²	0
2.6×10⁻⁴	0.66

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表 6 活性粉末混凝土的K&C模型应变率效应特征点取值

Table 6. K&C model strain rate characteristic points of reactive powder concrete

$\dot \varepsilon/{\rm{s}^{-1} }$	$\psi$	$\dot \varepsilon/{\rm{s}^{-1} }$	$\psi$	$\dot \varepsilon/{\rm{s}^{-1} }$	$\psi$
–30 000	9.97	–10	1.27	–1×10^–4	1.07
–4 782	9.97	–3	1.24	–1×10^–5	1.03
–1 000	5.41	–1	1.22	0	1.00
–300	3.45	–0.1	1.18	30	1.00
–100	2.29	–0.01	1.14	265	2.94
–25	1.28	–1×10^–3	1.11	30 000	2.94

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表 7 RPC的K&C模型8号状态方程参数

Table 7. Parameters of No. 8 equation of state in the K&C model of RPC

ε_V
ε_V₁	ε_V₂	ε_V₃	ε_V₄	ε_V₅	ε_V₆	ε_V₇	ε_V₈	ε_V₉	ε_V₁₀
0	0.0015	0.0043	0.0101	0.0305	0.0513	0.0726	0.0943	0.174	0.208

σ_V/GPa
σ_V₁	σ_V₂	σ_V₃	σ_V₄	σ_V₅	σ_V₆	σ_V₇	σ_V₈	σ_V₉	σ_V₁₀
0	0.041	0.094	0.292	0.881	1.622	2.511	3.573	8.714	11.579

K_av/GPa
K_av1	K_av2	K_av3	K_av4	K_av5	K_av6	K_av7	K_av8	K_av9	K_av10
27.5	27.5	27.885	29.288	34.843	40.425	45.980	50.186	112.915	137.5

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