弹体侵彻混凝土靶体的尺寸效应分析

彭永; 卢芳云; 方秦; 吴昊; 李翔宇

doi:10.11883/bzycj-2018-0402

弹体侵彻混凝土靶体的尺寸效应分析

doi: 10.11883/bzycj-2018-0402

1.
国防科技大学文理学院，湖南长沙 410073
2.
陆军工程大学国防工程学院，江苏南京 210007
3.
同济大学土木工程学院结构工程与防灾研究所，上海 200092

基金项目: 国家自然科学基金（11902355）

详细信息

作者简介:
彭　永（1989－　），男，博士，讲师，pengy116@163.com

中图分类号: O385; TU528
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- 被引次数: 1
出版历程
- 收稿日期: 2018-10-18
- 修回日期: 2019-01-30
- 网络出版日期: 2019-10-25
- 刊出日期: 2019-11-01

Analyses of the size effect for projectile penetrations into concrete targets

1.
College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, Hunan, China
2.
College of Defense Engineering, PLA Amy Engineering University, Nanjing 210007, Jiangsu, China
3.
Research Institute of Structural Engineering and Disaster Reduction, College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 由于混凝土靶体抗刚性弹侵彻实验大多基于缩比弹体展开，侵彻深度相似律是否成立显得尤为重要。在侵彻相似模型基础上，综合分析已有侵彻实验数据及经验公式，发现侵彻深度在通常情况下存在尺寸效应，且无量纲侵彻深度随弹体尺寸变大而增大。但如果模型以及原型实验中弹体与混凝土靶体（包括粗骨料）严格等比例设计，侵彻深度相似律是成立的。不变的骨料特征（粗骨料未随弹体尺寸缩放）是引起侵彻实验以及侵彻经验公式中尺寸效应的主要原因。为研究由粗骨料引起的侵彻尺寸效应，开发了混凝土二维细观有限元建模程序，细观数值实验成功地反映出了侵彻尺寸效应，考虑模拟尺寸效应后的侵彻公式能较好地预测不同尺寸侵彻实验。
- 侵彻深度 /
- 混凝土 /
- 尺寸效应 /
- 细观模型
Abstract: Whether the replica scaling law holds or not is of great significance because penetration tests of concrete targets against rigid projectiles are commonly conducted in a reduced scale. In this paper, based on the replica scaling model and the analyses of penetration tests with various sizes and empirical formulae, we found that there exists a size effect in general for penetration depth, and the dimensionless depth increases with as does the size. However, the replica scaling law is satisfied for the penetration depth in rigid projectile penetrations, as long as the scaling is done strictly for both projectiles and concrete targets, including the coarse aggregates. We also found that the coarse aggregates of an invariant size (not replica-scaled) are the major factor accounting for the size effect in penetration depth found in tests and empirical formulae. To find out about the size effect resulting from aggregates, we developed a 2D mesoscopic finite element model for concrete target and conducted numerical simulations that successfully represent the size effect, thereby proving that penetration formula with size effect considered could well predict the penetration tests with different size.
- penetration depth /
- concrete /
- size effect /
- mesoscopic model

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图 1 侵彻相似律成立前提下几何相似弹体的无量纲侵彻深度

Figure 1. Dimensionless penetration depth of geometrically similar projectiles, given the scaling law as true

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图 2 几何相似弹体的无量纲侵彻深度（P/d）与侵彻初速度的关系^[8]

Figure 2. Dimensionless penetration depth of geometrically similar projectiles vs. initial penetrating velocities ^[8]

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图 3 Forrestal半理论侵彻深度公式计算结果

Figure 3. Calculated results based on the semi-analytical formula for penetration depth proposed by Forrestal et al

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图 4 经验公式中几何相似弹体的无量纲侵彻深度

Figure 4. Dimensionless penetration depth of the geometrically similar projectiles predicted by the empirical formulae

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图 5 模型以及原型侵彻实验的无量纲侵彻深度^[25]

Figure 5. Normalized penetration depth for the two sets of scaled penetration experiments ^[25]

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图 6 二维粗骨料几何随机模型的生成

Figure 6. Procedures for 2D geometric model of an aggregate of random size and shape

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图 7 混凝土二维细观有限元模型

Figure 7. 2D mesoscopic finite element model for concrete specimen

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图 8 侵彻作用下非均质混凝土靶体内的von Mises应力分布

Figure 8. Von Mises stress distributions in the inhomogeneous regarded concrete target under projectile penetrations

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图 9 侵彻作用下均质混凝土靶体内的von Mises应力分布

Figure 9. Von Mises stress distributions in the homogeneous regarded concrete target under projectile penetrations

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图 10 几何相似弹体侵彻相同材质靶体时的无量纲相对侵彻深度

Figure 10. Relative dimensionless penetration depth of replica-scaled projectiles into targets of identical materials

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图 11 考虑尺寸效应后半理论公式计算结果与不同尺寸侵彻实验数据的对比

Figure 11. Comparison between predictions of semi-analytical formula with size effect added and test data of different sizes

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表 1 相似模型中原型相对于模型的各物理量

Table 1. Parameters in the prototype model relative to the reduced model

变量	比例	变量	比例
弹径	λ	侵彻深度	λ
弹长	λ	加速度	λ⁻¹
弹体密度	1	侵彻持续时间	λ
弹体质量	λ³	弹体轴向阻力	λ²
侵彻初速度	1	阻应力	1

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表 2 确定S值的侵彻实验相关信息^{[7-8, 19]}

Table 2. Experimental parameters for tests for determining S ^{[7-8, 19]}

f_c/MPa	13.5	21.6	36.2	51	58.4	62.8	96.7
a¹⁾/mm	4.8	4.8	9.5²⁾	9.5	9.5	9.5	9.5²⁾
d/mm	12.9	12.9	26.9	30.5	20.3/30.5	20.3	26.9
d/a	2.69	2.69	2.83	3.21	2.14/3.21	2.14	2.83
M/kg	0.064	0.064	0.906	1.6	0.478/1.62	0.478	0.904
注：1) a 为混凝土靶体中粗骨料的最大粒径，2) 表示粒径没有明确给出。

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表 3 砂浆及粗骨料的HJC材料模型参数

Table 3. Parameters of the HJC material model for cement and aggregate

参数	砂浆	骨料	参数	砂浆	骨料
单轴抗压强度 f_c/MPa	12	120	弹性极限静水压力P_crush/MPa	4.0	40
密度 ρ/（kg·m⁻³）	2 000	2 660	弹性极限体积应变U_crush	5.4×10⁻⁴	1.1×10⁻³
剪切模量 G/GPa	5.55	26.93	转折静水压力P_lock/GPa	1	1
极限面参数A	0.79	0.79	压实体积应变U_lock	0.1	0.1
极限面参数B	1.6	1.6	压力系数K₁/GPa	17	17
压力硬化系数 N	0.61	0.61	压力系数K₂/GPa	38	38
抗拉强度 T/MPa	1.1	12	压力系数K₃/GPa	29.8	29.8

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