Experimental Study and Theoretical Analysis of the Size Effect for Scale Model Projectile Penetrating into Rock Target

doi:10.12382/bgxb.2023.0014

Abstract

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

CLC Number:

O385

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.

Figures/Tables 19

Fig.1 Sketch of granite target

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

Fig.2 Dimensions and photographs of projectile

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

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

Fig.3 Frontview of macroscopic damage pattern of target

Fig.4 Sketch of damage section of the targets

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

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

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

Fig.8 Rt of granite varying with impact velocity

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

Fig.10 Ogive nose geometry

Fig.11 Nose geometry λ1 varying with ln/d

Fig.12 Sketch of deformation and failure zone

Fig.13 Dependence of χpm on κ

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

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

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

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