缩比模型弹侵彻岩石靶尺寸效应试验研究与理论分析

doi:10.12382/bgxb.2023.0014

摘要/Abstract

摘要：

为研究弹体侵彻岩体介质尺寸效应产生的内在机理,开展两种弹形几何相似的钢质弹体对高强度花岗岩靶的侵彻效应试验。根据侵彻深度试验结果,评估常用的经验公式对于高强度岩石侵彻深度预测的适用性,发展以弹形系数和弹径系数为控制变量的侵彻深度计算方法,建立不同缩尺比下模型弹与原型弹侵彻深度换算关系。研究结果表明:模型弹与原型弹的比例侵彻深度存在弹体口径放大效应,该效应系数不仅与缩比系数有关,也与原型弹直径以及靶体材料参数有关,且随着原型弹直径的增大而增大,随着缩比系数的增大而减小;建立的侵彻深度换算关系解释了采用传统模型试验方法导致模型与原型试验结果之间产生误差的原因,揭示了弹体侵彻岩石类介质中尺寸效应产生的机理。

关键词: 花岗岩, 模型试验, 侵彻深度, 尺寸效应

Abstract:

The penetration effects of geometrically similar projectiles on high-strength granite targets are tests to study the inherent mechanism of the size effect of the projectile penetrating into rock medium. According to the penetration test results, the applicability of typical empirical formulae for predicting the penetration depth of projectile into high strength rock is evaluated, a penetration depth calculation method with the shape and diameter coefficients as the control variables is developed, and the conversion relationship between the penetration depths of model projectile and prototype projectile under different scale ratios is established. The research results show that the proportional penetration depth of model projectile and the prototype projectile has the caliber effect. The effect coefficient is not only related to the scale ratios, but also related to the diameter of prototype projectile and the material parameters of target. It increases with the increase in the prototype projectile diameter, and decreases with the increase in the scale ratio. The established conversion relation of penetration depth explains the reason for the error between the model test result and the prototype test result caused by the traditional model test method, and reveals the mechanism of the size effect of projectile penetrating into rock-like materials.

Key words: granite, model test, penetration depth, size effect

中图分类号:

O385

高飞, 邓树新, 张国凯, 纪玉国, 刘晨康, 王明洋. 缩比模型弹侵彻岩石靶尺寸效应试验研究与理论分析[J]. 兵工学报, 2023, 44(12): 3601-3612.

GAO Fei, DENG Shuxin, ZHANG Guokai, JI Yuguo, LIU Chenkang, WANG Mingyang. Experimental Study and Theoretical Analysis of the Size Effect for Scale Model Projectile Penetrating into Rock Target[J]. Acta Armamentarii, 2023, 44(12): 3601-3612.

图/表 19

图1 花岗岩靶标示意图

Fig.1 Sketch of granite target

表1 花岗岩基本力学性能参数

Table 1 Basic mechanical properties parameters of granite

密度/ (kg·m^-3)	静态抗压强度/MPa	动态抗压强度/MPa	弹性模量/ GPa	泊松比
2670	147	246	54.6	0.25

图2 弹体尺寸及实物图

Fig.2 Dimensions and photographs of projectile

表2 弹体材料参数[22]

Table 2 Material parameters of projectile[22]

密度/ (kg·m^-3)	洛氏硬度/ HRC	抗拉强度/ MPa	延伸率/ %	截面收缩率/%
7850	45	1400	12	58
屈服强度/ MPa	硬化系数/ MPa	硬化指数	应变率系数	温度软化系数
1270	810	0.48	0.04	1

表3 侵彻试验结果汇总

Table 3 Summary of penetration test results

编号	弹径 d/mm	弹体质量 m/g	速度v₀/ (m·s^-1)	侵彻深度 h/mm	h/d	靶体阻力常数R_t/GPa
A-1	20	206.1	488	63.0	3.15	1.78
A-2	20	206.4	607	78.0	3.90	2.04
A-3	20	206.2	659	89.0	4.45	2.01
A-4	20	206.0	772	108.0	5.40	2.14
A-5	20	206.3	842	119.0	5.95	2.25
A-6	20	206.4	920	128.0	6.40	2.45
A-7	20	206.3	986	138.0	6.90	2.57
A-8	20	206.3	1070	177.0	8.85	2.23
B-1	10	25.72	646	39.4	3.94	2.26
B-2	10	25.73	754	46.8	4.68	2.44
B-3	10	25.75	830	53.9	5.39	2.46
B-4	10	25.75	926	60.4	6.04	2.64
B-5	10	25.72	1016	69.5	6.95	2.67

图3 靶体宏观破坏形态正视图

Fig.3 Frontview of macroscopic damage pattern of target

图4 靶体宏观破坏形态剖面示意图

Fig.4 Sketch of damage section of the targets

图5 试验前和试验后回收弹体(d=20mm)

Fig.5 Photograph of unfired and recovered projectiles with d=20mm

图6 两组模型弹侵彻花岗岩无量纲侵彻深度

Fig.6 Dimensionless penetration depths for the two sets of scaled penetration tests

图7 无量纲侵彻深度试验结果与经验公式对比

Fig.7 Comparison between dimensionless penetration depth empirical formulae and test data

图8 花岗岩靶体Rt随撞击速度的变化规律

Fig.8 Rt of granite varying with impact velocity

图9 不同速度飞片加载下试样自由面粒子速度变化历程

Fig.9 Velocity variation of particles on the free surface of specimen under the action of different velocity flyers

图10 卵形弹头示意图

Fig.10 Ogive nose geometry

图11 弹形系数λ1随弹头长径比ln/d变化关系

Fig.11 Nose geometry λ1 varying with ln/d

图12 介质的变形与破坏区示意图

Fig.12 Sketch of deformation and failure zone

图13 χpm与κ的关系

Fig.13 Dependence of χpm on κ

图14 hp/hm与κ的关系

Fig.14 Dependence of hp/hm on κ based on Eq.(24)

表4 原型与模型试验的无量纲侵彻深度[6]

Table 4 Dimensionless penetration depths for the prototype and model penetration tests[6]

α	d_p/mm	d_m/mm	h_p/d_p	h_m/d_m	χ_pm
1/10	100	10.1	10.5	7.7	1.36
1/5	100	20.3	10.5	8.5	1.23
1/2	20.3	10.1	8.5	7.7	1.10

图15 几何相似弹体侵彻混凝土口径放大效应

Fig.15 Caliber effects of geometrical similar projectiles penetrating into concrete

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