Ballistic limit velocities of carbon fiber material target plate against fragment penetration
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摘要: 碳纤维复合材料(CFRPs)在国防科技中广泛应用，已经成为主承力构件及部分结构的防护材料，研究其抗破片侵彻性能为科研人员提高碳纤维复合材料性能、进行防护结构设计提供依据。为研究碳纤维复合材料靶板受破片侵彻的毁伤机理及弹道极限速度，进行8 g立方体钢破片分别侵彻厚5 mm、10 mm、15 mm碳纤维复合材料靶板数值仿真与试验，得到破片侵彻碳纤维复合材料靶板的数值仿真弹道极限与六射弹弹道极限速度，数值仿真弹道极限与六射弹弹道极限最大误差为6.21%。利用数值仿真方法得到大量不同着靶速度与对应的剩余速度，基于THOR公式建立破片侵彻碳纤维复合材料靶板剩余速度模型与弹道极限计算公式。对弹道极限公式进行试验验证，选取不同工况下的六射弹弹道极限，与理论计算值进行对比，结果表明，同一工况下，试验结果与计算结果最大误差为4.54%。
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关键词:
- 碳纤维复合材料(CFRPs) /
- 弹道侵彻试验 /
- 毁伤模式 /
- 弹道极限
Abstract: Carbon fiber reinforced plastics (CFRPs) are widely used in national defense science and technology and have become the protective materials for main load-bearing components and some structures. Research on their fragment penetration resistance provides a basis for scientific researchers to improve the performance of CFRPs and design protective structures. To study the damage mechanism and ballistic limit velocity of CFRP target plates penetrated by fragments, numerical simulations and tests were conducted on 8g cubic steel fragments penetrating CFRP target plates with thicknesses of 5 mm, 10 mm and 15 mm, respectively. The numerical simulation of the ballistic limit velocities of the fragments penetrating CFRP target plates and the six-projectile ballistic limit velocities were obtained, and the maximum error between the numerical simulation of the ballistic limit velocity and the six-projectile ballistic limit velocity was 6.21%. A large number of different impact velocities and corresponding residual velocities were obtained by numerical simulations. Based on the THOR formula, the residual velocity model of the fragments penetrating CFRP target plates and the ballistic limit calculation formula were established. The ballistic limit formula was verified experimentally, and the six-projectile ballistic limits under different working conditions were selected and compared with the theoretical calculated values. The results show that under the same working condition, the maximum error between the test and calculated results is 4.54%. -
图 1 破片不同姿态侵彻碳纤维复合靶板：(a)面接触；(b)棱接触；(c)点接触
Figure 1. Fragments penetrate CFRPs in different attitudes: (a) Face contact; (b) Edge contact ; (c) Point contact
图 2 破片侵彻5 mm CFRPs靶板结果对比图
Figure 2. Comparison of the results of fragment penetrating 5 mm CFRPs target
图 3 破片侵彻10 mm CFRPs靶板结果对比图
Figure 3. Comparison of the results of fragment penetrating 10 mm CFRPs target
图 4 破片侵彻15 mm CFRPs靶板结果对比图
Figure 4. Comparison of the results of fragment penetrating 15 mm CFRPs target
图 5 破片侵彻碳纤维复合材料靶板试验系统：(a)试验系统示意图；(b)试验现场布置图
Figure 5. Test system of fragments penetrating CFRPs: (a)Schematic diagram;(b)Site layout
①target and high speed camera; ②velocity measurement network target and electronic timer; ③ ballistic musket
图 9 碳纤维复合材料靶板：(a)靶板正面；(b)不同厚度靶板侧面
Figure 9. carbon fiber reinforced plastics target: (a) Front of target plate;(b) Different thickness of the target plate side
图 10 破片侵彻碳纤维复合材料靶板情况：(a)~(b)局部侵彻靶板正反面效果；(c)~(d)完全侵彻靶板正反面效果
Figure 10. fragment penetrating CFRPs: (a)-(b) Front and back effect of local penetration target plate; (c)-(d) Front and back effect of complete penetration target plate
表 1 钢破片材料参数
Table 1. Material parameters of the steel fragment
ρ/(g·cm−3) G/GPa σ/MPa B/MPa n 7.83 0.77 792 510 0.26 c M TM/K TR/K 0.014 1.03 1793 294 Notes: ρ is density ; G is the shear modulus ; σis the yield stress ; B is the hardening coefficient ; n is the hardening index ; c is the strain rate coefficient; M is the temperature coefficient ; TM is the melting temperature ; TR is the ambient temperature. 
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表 2 数值仿真弹道极限
Table 2. Numerical simulation of ballistic limit
Target thickness/mm Simulation of ballistic limit velocity/ (m·s-1) 5 307.76 10 394.78 15 437.55
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表 3 发射药量与破片着靶速度
Table 3. Amount of propellant and the velocity of fragment hitting the target
Target
thickness/mmDosage of
propellant/gRange of speed/
((m·s−1))5 2.5-3 290-340 10 3.5-4 370-420 15 4.5-5 425-460
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表 4 碳纤维复合材料力学性能
Table 4. Mechanical properties of CFRPs
Mechanical property Parameter Longitudinal tensile strength $ {\sigma }_{\mathrm{x}\mathrm{t}} $ /MPa 1755 Longitudinal tensile modulus $ {E}_{1\mathrm{t}} $ / GPa 138 Main Poisson's ratio $ {V}_{12} $ 0.27 Transverse tensile strength $ {\sigma }_{\mathrm{y}\mathrm{t}} $ /MPa 48 Transverse tensile modulus $ {E}_{2\mathrm{t}} $ /GPa 8.36 Longitudinal compressive strength $ {\sigma }_{\mathrm{x}\mathrm{c}} $ /MPa 1248 Longitudinal compression modulus $ {E}_{1\mathrm{C}} $ /GPa 128 Transverse compressive strength$ {\sigma }_{\mathrm{y}\mathrm{c}} $ /MPa 214 Transverse compression modulus $ {E}_{2\mathrm{C}} $ /GPa 8.48 Longitudinal and transverse shear strength $ {\tau }_{12} $ /MPa 113 Longitudinal and transverse shear modulus $ {G}_{12} $ /GPa 4.51 Shear strength of bonded structure $ {\tau }_{\mathrm{J}} $/MPa 21.5
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表 5 六射弹弹道极限
Table 5. Six-shot limit velocity
Target thickness/mm Experimental data/ (m·s-1) Six-shot limit velocity/(m·s-1) Local penetration Complete penetration 5 312 335 328.17 318 340 318 342 10 379 404 394.67 384 406 386 409 15 423 439 436.50 429 447 432 449
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表 6 数值仿真与试验结果误差表
Table 6. Error table between numerical simulation and test results
Target
thickness/mmBallistic limit
velocity/(m·s−1)Six-shot limit
velocity/(m·s−1)Deviation/% 5 307.76 328.17 6.21 10 394.78 394.67 0 15 437.55 436.50 0.23
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表 7 不同速度碳纤维复合靶板破坏形式
Table 7. Failure modes of CFRPs with different velocities
Velocity Damage pattern Shear failure Fiber tensile failure Matrix damage Delamination damage (bulging) >limit velocity √ =limit velocity √ √ <imit velocity √ √ Multiple minor collisions √
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表 8 拟合系数
Table 8. Fit coefficient
$ {C}_{1} $ $ {C}_{2} $ $ {C}_{3} $ $ {C}_{4} $ $ {C}_{5} $ 6.422 0.302 −0.968 1.254 −0.306
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表 9 碳纤维复合靶板弹道极限理论计算值
Table 9. Ballistic limit calculation value of CFRPs
Target thickness/mm Theoretical calculation of ballistic
limit velocity/(m·s−1)5 323.32 10 379.46 15 416.72
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表 10 理论计算与试验结果误差
Table 10. Error between theoretical calculation and test results
Target
thickness/mmTheoretical
velocity /(m·s−1)Six-shot limit
velocity/(m·s−1)Deviation/% 5 323.32 328.17 1.47 10 379.46 394.67 3.88 15 416.72 436.50 4.54
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