Theoretical model of interface defeat/penetration transition velocity of ceramic armor impacted by long-rod projectile
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摘要: 为预测长杆弹撞击装甲陶瓷界面击溃/侵彻转变过程，采用Hertz接触理论确定靶体内部应力，将其分别应用于陶瓷锥裂纹与翼型裂纹扩展理论。通过比较两种裂纹扩展模型计算得到的界面击溃/侵彻转变速度，提出准确预测界面击溃/侵彻转变速度的理论模型。结果表明：将两种裂纹扩展理论相结合的理论模型可以合理地解释界面击溃/侵彻转变过程，转变速度计算结果与已有实验结果吻合较好。弹体半径较小时，锥裂纹扩展控制界面击溃/侵彻转变过程；弹体半径较大时，翼型裂纹扩展控制界面击溃/侵彻转变过程。Abstract: In this study a theoretical model was established to predict the interface defeat/penetration transition velocity of a ceramic armor impacted by a long-rod projectile. Predications of the transition velocity were obtained by measuring the stress inside the target and then applying it in turn to the conical crack and the wing crack propagation theory. After that, a theoretical model consisting of the conical and the wing crack propagation theory was presented. The results show that the theoretical model can reasonably well describe the interface defeat/penetration transition process. The interface defeat/penetration transition velocity calculated by the theoretical model agrees well with the experimental results from the previously published literature. The conical crack propagation dominates the interface defeat/penetration transition process when the projectile radius is small, while the wing crack dominates the transition when the projectile radius is large.
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图 3 基于裂纹扩展的转变速度理论模型
Figure 3. Combined criterion of interface defeat/penetration transition velocity based on crack propagation model
图 5 弹体半径为0.5 mm、撞击速度为1 000 m/s时，等效应力与裂纹长度的关系
Figure 5. Relation between normalized stress and crack length at impact velocity of 1 000 m/s with projetcile radius of 0.5 mm
图 8 不同弹体材料转变速度与弹体半径的关系
Figure 8. Relation between transition velocity and projectile radius of different projectile materials
表 1 不同靶体材料参数
Table 1. Target material data
材料 ν d/μm KIC/(MPa·m1/2) σHEL/GPa τy/GPa Δ B4C 0.16 3 2.5 22.2 4.19 0.37 TiB2 0.11 10 6.9 17 7.45 0.32 
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表 2 弹体材料参数
Table 2. Projctile matearil data
材料 ρp/(kg·m-3) Kp/GPa σyp/GPa WHA 17 700 285 1.3 Au 19 300 180 0.2
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表 3 转变速度计算值与实验值对比
Table 3. Comparison of transition velocity between experimental data and theoretical calculation
材料 Pm/GPa vexp/(m·s-1)[4] vcal/(m·s-1) Error/% B4C 24.2 1 430~1 480 1493 0.8~4.4 TiB2 25.6 1 465~1 545 1526 0.0~4.2
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表 4 不同靶体材料参数
Table 4. Target material data
材料 ν d/μm KIC/(MPa·m1/2) σHEL/GPa τy/GPa Δ SiC 0.16 4.8 2.6 16 6.48 0.20
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