基于板厚补偿的不同型号钢制靶板在舱内爆炸载荷作用下的等效方法

郑成; 朱业飞; 徐峰; 卢安格; 曹宇航; 周沪; 孔祥韶

doi:10.11883/bzycj-2024-0446

基于板厚补偿的不同型号钢制靶板在舱内爆炸载荷作用下的等效方法

doi: 10.11883/bzycj-2024-0446

郑成^1,,
朱业飞^{1, 2},
徐峰³,
卢安格^{1, 2},
曹宇航^{1, 2},
周沪^{1, 2},
孔祥韶^1, ,

1.
武汉理工大学绿色智能江海直达船舶与邮轮游艇研究中心，湖北武汉 430063
2.
武汉理工大学船海与能源动力工程学院，湖北武汉 430063
3.
中国舰船研究设计中心，湖北武汉 430064

基金项目: 国家自然科学基金（12202329，52171318）；武汉市自然科学基金探索计划（晨光计划）（2024040801020258）

详细信息

作者简介:
郑　成（1991－　），男，博士，研究员，zhengchengyeep@whut.edu.cn

通讯作者:
孔祥韶（1983－　），男，博士，教授，kongxs@whut.edu.cn

中图分类号: O383
计量
- 文章访问数: 157
- HTML全文浏览量: 15
- PDF下载量: 26
- 被引次数: 0
出版历程
- 收稿日期: 2024-11-13
- 修回日期: 2025-02-23
- 网络出版日期: 2025-02-28

Equivalent method of different grades of steel target plates under blast loads in the cabin based on plate thickness compensation

ZHENG Cheng^1
,,
ZHU Yefei^{1, 2},
XU Feng³,
LU Ange^{1, 2},
CAO Yuhang^{1, 2},
ZHOU Hu^{1, 2},
KONG Xiangshao^{1
, ,}

1.
Green & Smart River-Sea-Going Ship, Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, Hubei, China
2.
School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, Hubei, China
3.
China Ship Development and Design Center, Wuhan 430064, China

摘要

摘要: 针对舰船结构舱内爆炸响应实验，船用特种钢材价格昂贵，极大增加试验成本，开展舱内爆炸响应实验中普通钢材替代特种钢材的等效性研究。为确定不同材料靶板之间的等效关系，基于靶板结构中心变形相似原则，考虑靶板不破的情况下，结合薄板大变形理论分析，明确了板厚度与内爆响应的关系，提出靶板材料等效替换方法。运用有限元分析软件ATUODYN对封闭空间内爆炸载荷作用在921A钢、907A钢、Q235钢、Q355钢四种不同型号钢制靶板过程进行数值仿真，得到计算结果与试验结果最大误差值为5.6%，验证了数值仿真方法的正确性。通过对数值仿真计算得到的等效板厚拟合，结合不同材料靶板等效板厚与动态屈服强度之间的经验公式，验证了所提不同型号钢制靶板在舱内爆炸载荷作用下的等效方法具有合理性和良好的适用性。为用普通船用钢材替代船用特种钢材进行舱内爆炸实验提供了理论依据和数据参考。
- 舱内爆炸响应 /
- 靶板中心变形 /
- 板厚补偿 /
- 等效方法
Abstract: Experimental investigation of internal explosion effects on ship structures still faces fundamental challenges. The prohibitively high costs of specialized naval steel plates impose disproportionate financial burdens on experimental budgets. Additionally, the restricted availability of standardized thickness variants has dimensional scaling conflicts during reduced-scale internal explosion experiments. This research proposes an equivalent substitution method for scaled model testing. The methodology enables a strategic replacement of naval steel with conventional steel while maintaining response similitude during the internal explosion of ship structures. The primary research objective focuses on validating the equivalent substitution method for conventional steel as a replacement for specialized naval steel without degrading the accuracy of the recorded data. According to the principle of central deformation similarity, the equivalence relationship among target plates of different grades was established under the assumption of structural integrity during the explosion. Based on the theory of large deflection of thin plates, the relationship between plate thickness and deformation was clarified thoroughly. An equivalence substitution method for different plate grades was explained, and an equivalence substitution method for different plates was proposed. It provides a theoretical foundation for substituting specialized naval steel with conventional steel. Comprehensive numerical simulations were conducted using the finite element analysis software AUTODYN to validate the proposed method. The simulations modeled the dynamic response of four different grades of steel target plates (921A steel, 907A steel, Q235 steel, and Q355 steel) under internal blast loading. The maximum deviation between the simulation results and experimental data is only 5.6%, thereby fully confirming the accuracy and reliability of the numerical model. The equivalence relationships among grades under internal blast loading with different charge volume ratios (0.1, 0.2, 0.4, 0.8, and 1.0) were further explored through extensive numerical simulations involving four plates grades (Q235, Q355, 907A, and 921A) with various thicknesses. A fitting analysis of equivalent plate thickness was conducted. By integrating empirical formulas correlating equivalent plate thickness with dynamic yield strength, the substituted target plate showed less than 10% deviation in central deformation compared to the original plate. The proposed equivalence method for steel target plates of different grades under internal explosion loads has been demonstrated to be both rational and practically applicable. This provides a theoretical foundation and empirical reference for substituting specialized naval steel with ordinary steel in internal explosion experiments.
- structural response to internal explosion /
- central deformation similarity /
- thickness compensation /
- equivalence substitution method

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图 1 舱内爆炸实验装置

Figure 1. Test device for explosion in the cabin

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图 2 1/4有限元对称模型

Figure 2. A 1/4 symmetric finite element model

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图 3 网格收敛性验证

Figure 3. Grid convergence verification

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图 4 空气域及边界条件设置

Figure 4. Air domain and boundary condition settings

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图 5 靶板变形云图实验结果与仿真结果对比

Figure 5. Comparison of target deformation cloud maps between experiment and simulation

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图 6 不同药量体积比下907A钢替换成其他材料靶板变形等效曲线

Figure 6. Equivalent deformation curves of 907A steel target plates replaced by other grades of steel under different charge volume ratios

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图 7 不同药量体积比下921A钢替换成其他材料靶板变形等效曲线

Figure 7. Equivalent deformation curves of 921A steel target plates replaced by other grades of steel under different charge volume ratios

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图 8 不同药量体积比材料等效替换关系

Figure 8. Equivalent substitution relationships of target materials at different charge mass-volume ratios

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图 9 计算值与换算值的结果对比

Figure 9. Comparison of the calculated value with the converted value

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表 1 靶板结构材料的本构参数

Table 1. Constitutive parameters for target plate structural materials

靶板材料	ρ₀/(kg·m⁻³）	E/MPa	μ	A/MPa	B/MPa	n	C	m
Q235^[20-21]	7850	206	0.28	293.8	230.2	0.578	0.0652	0.706
Q355^[22-23]	7850	206	0.28	339.45	405	0.403	0.02	0.659
907A^[24-25]	7850	220	0.3	580	395	0.62	0.055	1.03
921A^[25-26]	7870	212	0.31	651	395	0.62	0.055	1.03

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表 2 TNT炸药的JWL状态方程参数

Table 2. Parameters of the JWL equation of state for TNT explosive

C₁/GPa	C₂/GPa	r₁	r₂	ω	D/(m·s⁻¹)	p_CJ/GPa
373.8	3.747	4.15	0.9	035	6930	21

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表 3 TNT炸药的装药参数

Table 3. Parameters for TNT explosive charges

m_TNT/g	(m_TNT·V⁻¹_c)/(kg·m⁻³)	r_TNT/mm
120	0.1	25.99
230	0.2	32.23
466	0.4	40.71
920	0.8	51.29
1150	1.0	55.26

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表 4 数值仿真结果与实验实测数据^[12]对比

Table 4. Numerical simulation results compared with the experimental data^[12]

靶板材料	工况	(m_TNT·V⁻¹_c)/(kg·m⁻³)	δ/mm	w_exp/mm	w_sim/mm	$ \dfrac{w_{\text{sim}} - w_{\text{exp}}}{w_{{\text{exp}}}} /{\text{%}}$
Q235	1	0.1	2.3	56.8	54.2	−4.58
	2	0.1	3.7	33.9	35.8	5.60
	3	0.2	4.8	37.8	39.5	4.50

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表 5 靶板变形计算结果

Table 5. Calculation results of target deformation

α/(kg·m⁻³)	Q235		Q355		907A		921A
α/(kg·m⁻³)	δ/mm	w/mm	δ/mm	w/mm	δ/mm	w/mm	δ/mm	w/mm
0.1	2.0	60.6	2.0	58.8	1.0	65.2	1.0	63.5
	2.5	50.3	2.5	48.7	1.5	45.9	1.5	44.9
	3.0	42.7	3.0	40.2	2.0	38.5	2.0	37.5
	3.5	37.0	3.5	35.2	2.5	33.2	2.5	32.5
	4.0	33.2	4.0	30.8
0.2	2.5	72.6	2.5	70.9	1.0	94.9	1.0	91.1
	3.0	61.9	3.0	60.4	1.5	67.6	1.5	65.5
	3.5	53.8	3.5	51.5	2.0	53.7	2.0	52.9
	4.0	48.1	4.0	44.9	2.5	45.5	2.5	43.8
	5.0	38.6	5.0	37.8	3.0	39.3	3.0	35.9
0.4	3.0	104.2	3.0	102.4	2.0	88.6	2.0	85.5
	3.5	90.8	3.5	88.9	3.0	62.9	2.5	71.4
	4.0	80.1	4.0	78.8	3.5	54.8	3.0	60.1
	5.0	64.3	5.0	62.3	4.0	48.9	4.0	46.3
	6.0	48.8	6.0	46.8	5.0	40.5	5.0	38.5
0.8	4.0	144.7	4.0	143.5	2.0	159.2	2.5	122.5
	4.5	128.2	4.5	127.4	2.5	127.9	3.0	103.8
	5.0	115.4	5.0	114.4	3.0	109.0	3.5	90.4
	6.0	96.4	6.0	94.6	4.0	83.5	4.0	80.8
	7.0	81.4	7.0	80.3	5.0	67.3	5.0	64.6
1.0	5.0	143.7	5.5	130.2	3.0	133.2	3.0	127.5
	5.5	130.5	6.0	118.6	3.5	115.2	3.5	110.9
	6.0	119.1	6.5	109.5	4.0	101.5	4.0	98.2
	7.0	101.8	7.0	100.6	5.0	82.4	5.0	79.0
	8.0	88.0	8.0	86.7	6.0	68.8	6.0	65.9

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表 6 不同的屈服强度

Table 6. Yield strength of different target materials

靶材	屈服强度/MPa
Q235	235
Q355	355
907A	390
921A	590

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表 7 不同药量体积比和不同靶材对应的等效系数

Table 7. Equivalent coefficients corresponding to target materials at different charge mass-volume ratios

α/(kg·m⁻³)	β
α/(kg·m⁻³)	907A换成Q235	907A换成Q355	921A换成Q235	921A换成Q355	921A换成907A
0.1	1.05	5.03	0.61	0.98	0.08
0.2	1.06	5.28	0.64	1.07	0.10
0.4	1.06	5.32	0.64	1.12	0.10
0.8	1.12	5.88	0.65	1.16	0.10
1.0	1.13	5.94	0.66	1.19	0.10

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表 8 907A替换成Q235后靶板变形

Table 8. Target plate deformation after 907A steel was replaced by Q235 steel

药量体积比/(kg/m³)	907A板厚/mm	等效系数β	Q235板厚/mm	907A靶板中心变形/mm	Q235靶板中心变形/mm	误差%
0.1	1.5	1.05	2.77	45.9	46.1	0.46
0.1	2.0	1.05	3.34	38.5	38.7	0.52
0.1	4.0	1.05	4.00	33.2	33.4	0.60
0.2	1.5	1.06	2.70	67.6	68.5	1.33
0.2	2.0	1.06	3.46	53.7	54.7	1.86
0.2	2.5	1.06	4.17	45.5	45.9	0.88
0.4	2.0	1.06	3.65	88.6	87.5	−1.24
0.8	2.5	1.12	4.54	127.9	127.0	−0.70
1.0	3.0	1.13	5.40	133.2	132.9	−0.23

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表 9 907A替换成Q355后靶板变形

Table 9. Target plate deformation after 907A steel was replaced by Q355 steel

药量体积比/(kg/m³)	907A板厚/mm	等效系数β	Q355板厚/mm	907A靶板中心变形/mm	Q355靶板中心变形/mm	误差%
0.1	1.5	5.03	2.66	45.9	45.2	−1.53
0.1	2.0	5.03	3.16	38.5	38.9	1.04
0.1	4.0	5.03	3.67	33.2	33.3	0.30
0.2	1.5	5.28	2.65	67.6	67.4	−0.30
0.2	2.0	5.28	3.37	53.7	53.5	−0.37
0.2	2.5	5.28	3.95	45.5	45.7	0.44
0.4	2.0	5.32	3.56	88.6	88.0	−0.68
0.8	2.5	5.88	4.5	127.9	127.8	−0.08
1.0	3.0	5.94	5.25	133.2	135.7	1.88

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表 10 921A替换成Q235后靶板变形

Table 10. Target plate deformation after 921A steel was replaced by Q235 steel

药量体积比/(kg/m³)	921A板厚/mm	等效系数β	Q235板厚/mm	921A靶板中心变形/mm	Q235靶板中心变形/mm	误差%
0.1	1.5	0.61	2.84	44.9	46.6	3.79
0.1	2.0	0.61	3.44	37.5	37.2	−0.80
0.1	2.5	0.61	4.12	32.5	31.2	−4.00
0.2	1.5	0.64	2.84	65.5	65.2	−0.46
0.2	2.0	0.64	3.58	52.9	52.8	−0.19
0.2	2.5	0.64	4.34	43.8	43.6	−0.46
0.4	2.0	0.64	3.78	85.5	84.2	−1.52
0.4	2.5	0.64	4.53	71.4	71.2	−0.28
0.8	2.5	0.65	4.74	122.5	121.5	−0.82
1.0	3.0	0.66	5.64	127.5	128.0	0.39

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表 11 921A替换成Q355后靶板变形

Table 11. Target plate deformation after 921A steel was replaced by Q355 steel

药量体积比/(kg/m³)	921A板厚/mm	等效系数β	Q355板厚/mm	921A靶板中心变形/mm	Q355靶板中心变形/mm	误差%
0.1	1.5	0.98	2.72	44.9	44.5	−0.89
0.1	2.0	0.98	3.24	37.5	37.7	0.53
0.1	2.5	0.98	3.76	32.5	32.4	−0.31
0.2	1.5	1.07	2.74	65.5	64.7	−1.22
0.2	2.0	1.07	3.42	52.9	53.1	0.38
0.2	2.5	1.07	4.10	43.8	43.2	−1.37
0.4	2.0	1.12	3.70	85.5	84.3	−1.40
0.4	2.5	1.12	4.41	71.4	71.1	−0.42
0.8	2.5	1.16	4.70	122.5	122.0	−0.41
0.1	3.0	1.19	5.61	127.5	127.7	0.16

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表 12 921A替换907A后靶板变形

Table 12. Target plate deformation after 921A steel was replaced by 90A steel

药量体积比/(kg/m³)	921A板厚/mm	等效系数β	907A板厚/mm	921A靶板中心变形/mm	907A靶板中心变形/mm	误差%
0.1	1.5	0.08	1.57	44.9	45.1	0.44
0.1	2.0	0.08	2.05	37.5	39.8	6.13
0.1	2.5	0.08	2.55	32.5	34.1	4.92
0.2	1.5	0.10	1.59	65.5	65.6	0.15
0.2	2.0	0.10	2.06	52.9	51.7	−2.28
0.2	2.5	0.10	2.58	43.8	43.9	0.23
0.4	2.0	0.10	2.08	85.5	85.7	0.23
0.4	2.5	0.10	2.61	71.4	70.6	−1.12
0.8	2.5	0.10	2.69	122.5	119.6	−2.37
1.0	3.0	0.10	3.15	127.5	127.2	−0.24

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