变形模式假定对冲击加载下圆板最终塑性变形的影响规律研究

徐维铮; 黄宇; 李彤; 李业勋; 傅华; 王彦平; 郑贤旭

doi:10.21656/1000-0887.450285

变形模式假定对冲击加载下圆板最终塑性变形的影响规律研究

doi: 10.21656/1000-0887.450285

中国工程物理研究院流体物理研究所，四川绵阳 621999

基金项目:

国家自然科学基金青年科学基金 12402444

装备预先研究领域基金 80928010101

详细信息

作者简介:
徐维铮(1991—)，男，副研究员，博士(E-mail: xuweizheng@whut.edu.cn)

通讯作者:
黄宇(1986—)，男，助理研究员，博士(通讯作者. E-mail: huangyu@buaa.edu.cn)

中图分类号: O342
计量
- 文章访问数: 49
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- 被引次数: 0
出版历程
- 收稿日期: 2024-10-23
- 修回日期: 2025-01-12
- 刊出日期: 2025-05-01

Study on the Influence of Deformation Mode Assumption on Plastic Deformation of Circular Plates Under Impact Loading

Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, Sichuan 621999, P.R.China

摘要

摘要: 为了找到一种适用于冲击加载条件下可靠普适的圆板塑性变形模式，首先基于能量法建立了冲击加载下可考虑不同变形模式及材料应变率效应的圆板塑性变形计算模型，然后利用计算模型与试验结果对比分析了不同变形模式假定对圆板最终塑性变形的影响规律. 研究表明：不同的变形模式假定给出了不同的膜拉伸应变空间分布以及膜拉伸平均应变率效应，改变了塑性变形吸能特性，最终影响圆板的塑性变形值；抛物线型变形模式具有误差小、材料适用范围广的优势，建议在后续的评估中采用.
- 圆板 /
- 冲击加载 /
- 变形模式 /
- 膜拉伸应变 /
- 应变率效应 /
- 塑性变形
Abstract: To find a reliable and universal plastic deformation mode of circular plates under impact loading, based on the energy method, a plastic deformation calculation model for circular plates under impact loading was established, with different deformation modes and material strain rate effects considered. Then the calculation model was compared with the experimental results to analyze the calculation deviation of plastic deformation of circular plates under different deformation modes. The results show that, different deformation mode assumptions give different spatial distributions of membrane tensile strain and different membrane tensile average strain rate effects, which changes the energy absorption characteristics of plastic deformations and finally affects the plastic deformation values of circular plates. The parabolic deformation mode has the advantages of small errors and wide application ranges for materials, and is suitable for the subsequent engineering evaluation.
- circular plate /
- impact loading /
- deformation mode /
- tensile strain of membrane /
- strain rate effect /
- plastic deformation

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图 1 瞬动加载下圆板最终变形示意图

Figure 1. Schematic diagram of the circular plate deformation under impulsive loading

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图 2 瞬动加载下的膜拉伸应变平均值计算示意图

Figure 2. Schematic diagram for calculating the average tensile strain of the membrane under impulsive loading

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图 3 三种变形模式下圆板变形轮廓空间分布

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. Spatial distributions of deformation profiles of the circular plate under 3 deformation modes

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图 4 三种变形模式下圆板膜拉伸应变空间分布及均值

Figure 4. Spatial distributions and mean values of tensile strains of the circular plate membrane under 3 deformation modes

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图 5 三种变形模式下圆板无量纲最终塑性变形值随无量纲加载冲量的变化图

Figure 5. Variations of dimensionless final plastic deformation values of the circular plate with dimensionless loading impulse under 3 deformation modes

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图 6 圆板瞬动加载试验布置图

Figure 6. The layout of the circular plate implusive loading test

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表 1 Nurick钢板试验工况与模型计算对比结果^[12]

Table 1. Comparative results of Nurick steel plate test conditions and model calculations^[12]

test	H/mm	I/(N·s)	W_e/mm	W_e/H	W₁/mm	W₁/H	error 1/%	W₂/mm	W₂/H	error 2/%	W₃/mm	W₃/H	error 3/%
1	1.6	9.0	10.62	6.64	10.43	6.52	-1.85	11.25	7.03	5.87	11.90	7.44	12.01
2	1.6	9.5	10.90	6.81	10.94	6.84	0.38	11.80	7.37	8.26	12.48	7.80	14.55
3	1.6	5.6	6.14	3.84	6.85	4.28	11.49	7.39	4.62	20.21	7.81	4.88	27.16
4	1.6	10.0	11.96	7.48	11.44	7.15	-4.39	12.34	7.71	3.13	13.06	8.16	9.11
5	1.6	9.9	12.08	7.55	11.34	7.09	-6.11	12.23	7.65	1.27	12.94	8.09	7.15
6	1.6	10.8	12.26	7.66	12.24	7.65	-0.10	13.21	8.25	7.76	13.97	8.73	14.02
7	1.6	10.6	12.20	7.63	12.04	7.53	-1.34	12.99	8.12	6.42	13.75	8.59	12.60
8	1.6	10.8	12.80	8.00	12.24	7.65	-4.34	13.21	8.25	3.18	13.97	8.73	9.17
9	1.6	11.5	13.62	8.51	12.94	8.09	-4.97	13.96	8.72	2.50	14.77	9.23	8.46
10	1.6	11.7	13.22	8.26	13.14	8.21	-0.60	14.17	8.86	7.22	14.99	9.37	13.45
11	1.6	11.4	14.00	8.75	12.84	8.02	-8.29	13.85	8.66	-1.07	14.66	9.16	4.68
12	1.6	12.6	14.90	9.31	14.02	8.76	-5.89	15.12	9.45	1.52	16.00	10.00	7.43
13	1.6	12.4	14.60	9.31	13.82	8.64	-7.20	14.91	9.32	0.11	15.78	9.86	5.93
14	1.6	12.9	15.28	9.55	14.31	8.94	-6.34	15.44	9.65	1.03	16.34	10.21	6.91
15	1.6	12.8	16.08	10.05	14.21	8.88	-11.61	15.33	9.58	-4.65	16.22	10.14	0.90
16	1.6	13.6	16.30	10.19	14.99	9.37	-8.07	16.17	10.11	-0.82	17.11	10.69	4.95
17	1.6	13.4	16.38	10.24	14.80	9.25	-9.69	15.96	9.98	-2.58	16.89	10.56	3.09
18	1.6	14.1	17.70	11.06	15.47	9.67	-12.58	16.69	10.43	-5.69	17.66	11.04	-0.20
19	1.6	13.8	17.06	10.66	15.18	9.49	-10.99	16.38	10.24	-3.97	17.33	10.83	1.61
20	1.6	14.7	18.56	11.60	16.04	10.03	-13.55	17.31	10.82	-6.73	18.32	11.45	-1.31
21	1.6	15.6	19.60	12.40	16.90	10.56	-14.82	18.23	11.40	-8.10	19.30	12.06	-2.75

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表 2 Symonds钢板试验工况与模型计算对比结果^[13]

Table 2. Comparative results of Symonds steel plate test conditions and model calculations^[13]

test	H/mm	I/(N·s)	W_e/mm	W_e/H	W₁/mm	W₁/H	error 1/%	W₂/mm	W₂/H	error 2/%	W₃/mm	W₃/H	error 3/%
1	1.9	7.09	12.29	6.37	11.03	5.71	-10.29	11.90	6.16	-3.20	12.59	6.52	2.44
2	1.9	3.12	5.00	2.59	5.37	2.78	7.26	5.79	3.00	15.68	6.12	3.17	22.39
3	1.9	5.41	9.88	5.11	8.71	4.51	-11.84	9.40	4.87	-4.89	9.94	5.15	0.65
4	1.9	5.54	9.75	5.05	8.90	4.61	-8.79	9.60	4.97	-1.59	10.16	5.26	4.14
5	1.9	3.15	5.28	2.74	5.41	2.80	2.47	5.84	3.02	10.52	6.18	3.20	16.93
6	1.9	4.55	7.98	4.13	7.48	3.87	-6.22	8.07	4.18	1.16	8.54	4.42	7.05
7	1.9	6.95	12.34	6.39	10.84	5.62	-12.16	11.70	6.06	-5.22	12.38	6.41	0.30

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表 3 Symonds钛板试验工况与模型计算对比结果^[13]

Table 3. Comparative results of Symonds titanium plate test conditions and model calculations^[13]

test	H/mm	I/(N·s)	W_e/mm	W_e/H	W₁/mm	W₁/H	error 1/%	W₂/mm	W₂/H	error 2/%	W₃/mm	W₃/H	error 3/%
1	2.3	5.26	8.41	3.60	9.56	4.09	13.65	10.29	4.40	22.34	10.87	4.65	29.25
2	2.3	7.06	11.33	4.84	12.59	5.39	11.11	13.55	5.80	19.61	14.32	6.13	26.37
3	2.3	5.57	9.22	3.95	10.09	4.32	9.41	10.86	4.65	17.77	11.47	4.91	24.42
4	2.3	5.43	8.92	3.82	9.85	4.21	10.46	10.60	4.54	18.90	11.20	4.79	25.61
5	2.3	3.54	5.77	2.47	6.60	2.82	14.42	7.10	3.04	23.15	7.50	3.21	30.10
6	2.3	6.58	11.13	4.76	11.79	5.05	5.98	12.69	5.43	14.08	13.41	5.74	20.53
7	2.3	5.94	10.24	4.38	10.71	4.58	4.60	11.53	4.93	12.60	12.18	5.21	18.95
8	2.3	6.34	10.85	4.64	11.38	4.87	4.95	12.25	5.24	12.98	12.95	5.54	19.36
9	2.3	4.71	8.00	3.42	8.62	3.69	7.74	9.28	3.97	15.98	9.80	4.20	22.52
10	2.3	3.60	5.97	2.55	6.69	2.86	12.08	7.20	3.08	20.63	7.61	3.26	27.43
11	2.3	7.06	12.67	5.43	12.58	5.38	-0.75	13.54	5.80	6.84	14.31	6.12	12.88

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表 4 三种变形模式假定下模型与试验平均误差

Table 4. Average errors of the model and the test under the assumption of 3 deformation modes

test case	deformation mode 1	deformation mode 2	deformation mode 3
Nurick’steel plate	6.89%	4.86%	7.97%
Symonds’steel plate	8.43%	6.04%	7.70%
Symonds’titanium plate	8.65%	16.81%	23.40%

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参考文献(13)

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