KERK S . PELE:the future ammunition concept [C ] // Proceedings of the 21st International Symposium on Ballistics.Adelaide , Australia : International Ballistics Society , 2004 : 1134 - 1144 .

PAULUS G , CHANTERET P Y , WOLLMANN E . PELE:a new penetrator concept for generating lateral effects [C ] // Proceedings of the 21st International Symposium on ballistics.Adelaide , Australia : International Ballistics Society , 2004 : 104 - 110 .

朱建生 , 范智 , 杜忠华 . 外壳材料对PELE作用效果的影响 [J ] . 兵器材料科学与工程 , 2010 , 33 ( 6 ): 14 - 16 .

ZHU J S , FAN Z , DU Z H . The influence of shell material on the effect of PELE [J ] . Ordnance Materials Science and Engineering , 2010 , 33 ( 6 ): 14 - 16 . (in Chinese)

XU L Z , DU C X , CHENG C , et al . Effect of projectile parameters on opening behavior of PELE penetrating RC target [J ] . Defence Technology , 2021 , 17 ( 3 ): 859 - 873 . DOI: 10.1016/j.dt.2020.04.012 http://doi.org/10.1016/j.dt.2020.04.012 When a penetrator with enhanced lateral effect (PELE) impacts on a reinforced concrete (RC) target, the target is damaged with a large opening. An understanding of how PELE projectile parameters affect the opening dimension, is essential for effective design of the PELE projectile. In this study, under the condition that the impact velocity and target parameters (strength and thickness) were fixed values, the important influence factors of the PELE (jacket wall thickness B, jacket material strength Y1, filling material strength Y2 and angle of monolithic jacket θ) were determined by a dimensional analysis. Tests and simulations of the PELE penetrating the RC target were conducted to analyze the influence of these factors on opening diameter (D¯, an equivalent diameter under relative kinetic energy). Based on the test and simulation results, it is found that the influence of these factors B, Y1 and θ on the deformation mode of the jacket shows a similar trend: as values of the three factors decrease, the jacket deforms from small bending deformation to large one, and then to curling deformation. This causes the opening diameter to first increase with the decrease of these three factors, and then decreases. It is well known that the bending resistance of the jacket is related to these factors B, Y1 and θ. Therefore, a plastic limit bending moment (M0) of the jacket was quoted to characterize the influence of these factors on the bending deformation of the jacket and the opening diameter of the target. The influence factor Y2 causes D¯ to first increase with the increase of Y2, and then decreases. A formula was developed to predict the opening diameter, whose influence parameters were considered in a dimensionless way. It has been shown that the dimensionless opening diameter D¯/d1 is dependent on two dimensionless parameters [Formula presented] and [Formula presented], where d1 and fc are the outer diameter of the projectile and the compressive strength of the target, respectively. © 2020 The Authors

PAULUS G , SCHIRM V . Impact behaviour of PELE projectiles perforating thin target plates [J ] . International Journal of Impact Engineering , 2006 , 33 ( 1-12 ): 566 - 579 .

XU L Z , GAO G F , WANG X D , et al . A model to characterize the lateral expansion of a cylinder containing a polymer filler subjected to compression [J ] . Mechanics of Advanced Materials and Structures , 2021 , 28 ( 1 ): 102 - 109 .

朱建生 , 赵国志 , 杜忠华 . 装填材料对PELE效应的影响 [J ] . 弹道学报 , 2007 , 19 ( 2 ): 62 - 65 .

ZHU J S , ZHAO G Z , DU Z H . The influence of filling materials on the PELE effect [J ] . Journal of Ballistics , 2007 , 19 ( 2 ): 62 - 65 . (in Chinese)

ZHANG J H , WANG H F , ZHENG Y F , et al . Lateral enhancement effect of reactive PELE:two-step segmented simulation and analytical modeling [J ] . Thin-Walled Structures , 2023 , 192 : 111204 .

ZHOU J Y , RAN X W , TANG W H , et al . Research on the penetration characteristics of PELE projectile with reactive inner core [J ] . Polymers , 2023 , 15 ( 3 ): 617 .

张甲浩 , 王海福 , 葛超 , 等 . 活性PELE侵彻钢筋混凝土靶扩孔增强行为 [J ] . 兵工学报 , 2025 , 46 ( 3 ): 240307 . DOI: 10.12382/bgxb.2024.0307 http://doi.org/10.12382/bgxb.2024.0307 活性横向效应增强弹(Penetrator with Enhanced Lateral Effect,PELE)在侵彻钢筋混凝土靶的过程中会发生剧烈的爆燃反应,较惰性芯体PELE对靶板的扩孔效应更加显著。为揭示活性PELE侵彻钢筋混凝土靶扩孔增强机理,建立活性PELE侵彻钢筋混凝土靶扩孔分析模型,模型充分考虑径向稀疏波和活性材料的冲击爆燃反应。开展5种撞击速度下的活性PELE侵彻钢筋混凝土靶实验,综合实验和理论对活性PELE芯体反应特性、壳体变形角度-长度演化及扩孔增强行为进行讨论。研究结果表明:新的分析模型能够有效预测活性PELE壳体变形和钢筋混凝土靶扩孔,平均误差分别为6.9%和8.5%;活性PELE壳体表现出双弯曲变形和卷曲变形两种典型变形模式,给出壳体变形角度-长度演化过程;当撞击压力大于2.32GPa时,忽略径向稀疏波会高估活性PELE芯体反应程度和壳体径向变形,验证了考虑径向稀疏波的必要性;量化比较后发现活性材料的爆燃反应使钢筋混凝土靶的最大开孔提高了24.3%。

ZHANG J H , WANG H F , GE C , et al . Enhanced opening behavior of reactive PELE penetrating reinforced concrete target [J ] . Acta Armamentarii , 2025 , 46 ( 3 ): 240307 . (in Chinese)

张洪成 , 尹建平 , 王志军 . 着靶角对PELE横向效应的影响 [J ] . 兵器材料科学与工程 , 2012 , 35 ( 4 ): 46 - 49 .

ZHANG H C , YIN J P , WANG Z J . The influence of target angle on the lateral effect of PELE [J ] . Ordnance Materials Science and Engineering , 2012 , 35 ( 4 ): 46 - 49 . (in Chinese)

刘宇珩 , 霸书红 , 杜忠华 , 等 . 着靶角度对PELE侵彻钢筋混凝土扩孔效应的影响研究 [J ] . 弹道学报 , 2022 , 34 ( 4 ): 15 - 22 . DOI: 10.12115/j.issn.1004-499X(2022)04-003 http://doi.org/10.12115/j.issn.1004-499X(2022)04-003 为了探究着靶角度对PELE侵彻钢筋混凝土靶扩孔效应的影响规律,建立了PELE侵彻钢筋混凝土靶的仿真模型,并且利用侵彻试验结果对仿真模型的准确性进行验证。在0～75°着靶角度范围内,从壳体变形模式、靶板扩孔直径等角度开展了PELE侵彻钢筋混凝土扩孔效应的影响规律与机理研究。研究结果表明:在0～30°着靶角度内,靶板的扩孔尺寸随着角度增大而增大,最大约为4.4倍弹径,并且PELE对钢筋混凝土靶板的破坏功增多; 随着着靶角度进一步增大,靶板的扩孔尺寸反而减小,PELE对钢筋混凝土靶板的破坏功也随之减少。此研究规律可对侵彻毁伤评估、新型动能武器系统设计提供技术支持和理论依据,并可用于指导钢筋混凝土防御工事设计。

LIU Y H , BA S H , DU Z H , et al . Study on the influence of target angle on the dilation effect of PELE penetration into reinforced concrete [J ] . Journal of Ballistics , 2022 , 34 ( 4 ): 15 - 22 . (in Chinese)

CHENG C , DU Z H , CHEN X , et al . Damage of multi-layer spaced metallic target plates impacted by radial layered PELE [J ] . Defence Technology , 2020 , 16 ( 1 ): 201 - 207 . DOI: 10.1016/j.dt.2019.05.002 http://doi.org/10.1016/j.dt.2019.05.002 Three different kinds of PELE (the penetrator with lateral efficiency) were launched by ballistic artillery to impact the multi-layer spaced metal target plates. The impact velocities of the projectiles were measured by the velocity measuring system. The damage degree and process of each layer of target plate impacted by the three kinds of projectiles were analyzed. The experimental results show that all the three kinds of projectiles have the effect of expanding holes on the multi-layer spaced metal target plates. For the normal structure PELE(without layered) with tungsten alloy jacket and the radial layered PELE with tungsten alloy jacket, the diameters of holes on the second layer of plates are 3.36 times and 3.76 times of the diameter of the projectile, respectively. For radial layered PELE with W/Zr-based amorphous composite jacket, due to the large number of tungsten wires dispersed after the impact, the diameter of the holes on the four-layer spaced plates can reach 2.4 times, 3.04 times, 5.36 times and 2.68 times of the diameter of the projectile. Besides, the normal structure PELE with tungsten alloy jacket and the radial layered PELE whit tungsten alloy jacket formed a large number of fragments impact marks on the third target plate. Although the number of fragments penetrating the third target plate is not as large as that of the normal structure PELE, the area of dispersion of fragments impact craters on the third target plate is larger by the radial layered PELE. The radial layered PELE with W/Zr-based amorphous composite jacket released a lot of heat energy due to the impact of the matrix material, and formed a large area of ablation marks on the last three target plates. © 2019 The Authors

姬鹏远 . 侵彻膨胀弹终点效应数值模拟研究 [D ] . 北京 : 北京理工大学 , 2007 .

JI P Y . Numerical simulation study on the endpoint effect of penetrating expansion projectiles [D ] . Beijing : Beijing Institute of Technology , 2007 . (in Chinese)

凃胜元 , 沈晓军 , 王军波 , 等 . 着速和靶厚对钢弹体PELE侵彻后效影响的实验研究 [J ] . 弹箭与制导学报 , 2010 , 30 ( 3 ): 69 - 71 .

TU S Y , SHEN X J , WANG J B , et al . Experimental study on the effects of landing speed and target thickness on the post penetration effect of steel projectile PELE [J ] . Journal of Missile and Guidance , 2010 , 30 ( 3 ): 69 - 71 . (in Chinese)

朱建生 , 赵国志 , 杜忠华 , 等 . 小口径PELE作用薄靶板影响因素的实验研究 [J ] . 实验力学 , 2007 , 22 ( 5 ): 505 - 510 .

ZHU J S , ZHAO G Z , DU Z H , et al . Experimental study on the influencing factors of small caliber PELE acting on thin target plates [J ] . Experimental Mechanics , 2007 , 22 ( 5 ): 505 - 510 . (in Chinese)

朱建生 , 赵国志 , 杜忠华 , 等 . 靶板厚度对横向效应增强型侵彻体作用效果的影响 [J ] . 南京理工大学学报(自然科学版) , 2009 , 33 ( 4 ): 474 - 479 .

ZHU J S , ZHAO G Z , DU Z H , et al . The influence of target plate thickness on the effect of lateral effect enhanced penetrator [J ] . Journal of Nanjing University of Technology (Natural Science Edition) , 2009 , 33 ( 4 ): 474 - 479 . (in Chinese)

YIN J P , LIU Y K , WANG Z J , et al . Formation and penetration of PELE/EFP multi-mode warhead based on double-layer shaped charge [J ] . Journal of Energetic Materials , 2023 , 41 ( 1 ): 4 - 26 .

XU L Z , REN W K , WANG X D , et al . Analytical investigation on deformation of PELE projectile and opening damage to concrete target [J ] . Thin-Walled Structures , 2021 , 161 : 107408 .

XU L Z , WANG J B , WANG X D , et al Opening behavior of PELE perforation on reinforced concrete target [J ] . Defence Technology , 2021 , 17 ( 3 ): 898 - 911 . DOI: 10.1016/j.dt.2020.05.019 http://doi.org/10.1016/j.dt.2020.05.019 Impact velocity (v0), target strength (fc) and target thickness (hc) are important factors affecting opening damage (D¯) of PELE penetration into RC target. In this paper, based on the three influence factors of v0, fc and hc, experimental and numerical simulation studies on PELE penetration into RC target were carried out. The study results show that: (1) Since interaction force (or penetration resistance) between projectile and target is positively correlated with v0 and fc, with the increase of v0 and fc, deformation mode of jacket is changed from small bending deformation to large bending deformation and then to curling deformation. Therefore, the variation of jacket deformation mode causes opening diameter of RC target to increase first and then to decrease. It is found that the two factors approximately satisfy a quadratic function relationship, respectively. (2) For PELE projectile penetrating RC targets with thickness of 80–400 mm, the opening diameter of six sets of RC targets grows from 240 to 500 mm, and hc with D¯ approximately satisfy a linear relationship. (3) Based on the above study results, the relationship between two dimensionless parameters ([Formula presented] and [Formula presented]) and dimensionless opening diameter (D¯/d1) was determined. Combined with the results of previous research, a dimensionless opening diameter model [Formula presented] was established. By tests verified, the test results are all within ±10% error of the theoretical model, which verifies the accuracy of the model. © 2020 The Authors

FAN Z J , RAN X W , TANG W H , et al . The model to calculate the radial velocities of fragments after PELE perforating a thin plate [J ] . International Journal of Impact Engineering , 2016 , 95 : 12 - 16 .

范少博 , 陈智刚 , 郭光全 , 等 . 装填材料对PELE侵彻混凝土效能影响研究 [J ] . 兵器材料科学与工程 , 2012 , 35 ( 5 ): 47 - 50 .

FAN S B , CHEN Z H , GUO G Q , et al . A study on the effect of filling materials on the penetration efficiency of PELE into concrete [J ] . Ordnance Materials Science and Engineering , 2012 , 35 ( 5 ): 47 - 50 . (in Chinese)

ZHU J S , ZHAO G Z , DU Z H , et al . Mechanism of PELE projectiles perpendicularly impacting on thin target plates [J ] . Explos Shock Waves , 2009 , 29 : 281 - 288 .

DU Z H , SONG L L , ZHONG K , et al . Influence of the ratio of inner to outer diameter on penetrator with enhanced lateral efficiency [J ] . Advanced Science Letters , 2011 , 4 ( 4/5 ): 1525 - 1528 .

LEI M A , WANG H F , YU Q B , et al . Fragmentation behavior of large-caliber PELE impacting RHA plate at low velocity [J ] . Defence Technology , 2019 , 15 ( 6 ): 912 - 922 . DOI: 10.1016/j.dt.2019.04.004 http://doi.org/10.1016/j.dt.2019.04.004 Impact experiments of large-caliber PELE with various inner-outer diameter ratio perforating RHA plate at low velocity were performed. Experimental results showed the size of perforated holes on plate, average diameter of damage area on witness plate, and number of behind-armor fragments will increase as d/D increasing from 0.72 to 0.84. Expansion and fragmentation of large-caliber PELE in this condition were also numerically studied with ANSYS Autodyn. Then, an analytical model accounting for an additional radial shock wave was presented to predict radial expansion velocity and fragmentation of jacket, as well as an empirical approach to estimate diameter of damage area. Calculation results by these approaches were in good agreement with experiments and numerical simulations. Further discussion revealed that Shock/rarefaction wave interactions behavior varying with inner-outer diameter ratio is an important mechanism resulting in different lateral effect by PELE projectiles with various configurations. © 2019

张甲浩 , 郭萌萌 , 周晟 , 等 . 活性横向增强弹靶后横向效应实验与数值模拟 [J ] . 兵工学报 , 2024 , 45 ( 7 ): 2270 - 2281 . DOI: 10.12382/bgxb.2023.0537 http://doi.org/10.12382/bgxb.2023.0537 为揭示活性横向增强弹(Penetrator with Enhanced Lateral Effect,PELE)的靶后横向增强机理,开展活性PELE冲击钢靶毁伤效应实验,在钢靶后设置效应铝靶,得到不同前置钢靶厚度条件下的穿孔毁伤情况。基于点火增长模型建立活性PELE冲击爆燃反应过程的两步仿真分析模型。综合实验和仿真对活性PELE在780m/s速度条件下冲击6~20mm厚度范围内钢靶的靶后横向增强效应进行讨论,从效应靶毁伤、芯体反应、波相互作用及壳体破片飞散4个方面进行深入分析。分析结果表明:仿真分析模型有效模拟了活性PELE冲击靶板的爆燃反应过程;靶板厚度对活性PELE在效应靶上的穿孔散布尺寸影响显著,随着靶板厚度的增加,活性PELE的靶后横向增强效应先增大后减小;活性芯体的爆燃反应释能使壳体最大径向速度提高了40%以上。

ZHANG J H , GUO M M , ZHOU S , et al . Experimental and numerical research on behind-plate enhanced lateral effect of reactive PELE [J ] . Acta Armamentarii , 2024 , 45 ( 7 ): 2270 - 2281 . (in Chinese) DOI: 10.12382/bgxb.2023.0537 http://doi.org/10.12382/bgxb.2023.0537 To reveal the behind-plate enhanced lateral mechanism of reactive penetrator with enhanced lateral effect (PELE), the damage effect experiment of reactive PELE impacting steel plate is made to obtain the perforation damage of witness aluminum plate set behind the steel plate under the conditions of different front steel plate thicknesses. A two-step numerical simulation model of reactive PELE impact-induced deflagration reaction is developed based on the ignition growth model. The behind-plate enhanced lateral effect of reactive PELE impacting a steel target with a thickness of 6-20mm at 780m/s velocity is discussed by experiment and simulation. The damage effect of witness aluminum plate, filling reaction, wave interaction and jacket fragments dispersion are analyzed. The results show that the numerical simulation model can effectively simulate the deflagration reaction of reactive PELE impacting plate. The perforation dispersion on the witness plate significantly depends on the front steel plate thickness, the behind-plate enhanced lateral effect of the reactive PELE increases first and then decreases with the increase in the plate thickness, and the released energy of the reactive filling increases the maximum radial velocity of jacket fragments by more than 40%.

DING L L , ZHOU J Y , TANG W H , et al . Damage characteristics analysis of the truncated cone-shaped PELE Projectile [J ] . Symmetry , 2019 , 11 ( 8 ): 1025 .

杜忠华 , 宋丽丽 . 横向效应增强型侵彻体撞击金属薄板理论模型 [J ] . 南京理工大学学报(自然科学版) , 2011 , 35 ( 6 ): 822 - 826 .

DU Z H , SONG L L . Theoretical model of lateral effect enhanced penetrator impacting metal thin plates [J ] . Journal of Nanjing University of Technology (Natural Science Edition) , 2011 , 35 ( 6 ): 822 - 826 . (in Chinese)

VERREAULT J , VAN H N P , ABADJIEVA E . PELE fragmentation dynamics [C ] // Proceedings of the 27th International Symposium on Ballistics.Freiburg , Germany : International Ballistics Society , 2013 : 1289 - 1300 .

VERREAULT J . Analytical and numerical description of the PELE fragmentation upon impact with thin target plates [J ] . International Journal of Impact Engineering , 2015 , 76 : 196 - 206 .

DING L L , ZHOU J Y , TANG W H , et al . Damage characteristics of PELE projectile with gradient density inner core material [J ] . Materials , 2018 , 11 ( 12 ): 2389 .

DING L L , ZHOU J Y , TANG W H , et al . Research on the crushing process of PELE casing material based on the crack-softening algorithm and stochastic failure algorithm [J ] . Materials , 2018 , 11 ( 9 ): 1561 .

KIM H S , YEOM K S , KIM S , SOTSKY L . Numerical simulation for the front section effect of missile on the target perforation [C ] // Proceedings of the 22nd International Symposium on ballistics.Vancouver,BC , Canada : International Ballistics Society , 2005 .

王礼立 . 应力波基础 [M ] . 北京 : 国防工业出版社 , 1985 .

WANG L L . Stress wave fundamentals [M ] . Beijing : National Defense Industry Press , 1985 . (in Chinese)

王仲仁 , 苑世剑 . 弹性与塑性力学基础 [M ] . 哈尔滨 : 哈尔滨工业大学出版社 , 1997 .

WANG Z R , YUAN S J . Fundamentals of elasticity and plasticity [M ] . Harb in: Harbin Institute of Technology Press , 1997 . (in Chinese)

MOTT N F . Fragmentation of shell cases [J ] . Proceedings of the Royal Society A , 1947 , 189 : 300 - 308 .