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TANG Q Y . Study on the theoretical model of hypervelocity fluid penetration of long-rod projectile [D ] . Mianyang : Southwest University of Science and Technology , 2021 . (in Chinese)

ZAKI S , UDDIN E , MUBASHAR A . Experimental investigation of impact of long rod eroding projectiles against rolled homogeneous armour [J ] . Proceedings of the Institution of Mechanical Engineers , Part L: Journal of Materials: Design and Applications , 2020 , 234 ( 10 ): 1335 - 1342 .

张清源 . 长杆弹斜侵彻模型及仿真技术研究 [D ] . 长沙 : 国防科技大学 , 2020 .

ZHANG Q Y . Oblique penetration model of long rod projectile and simulation technology research [D ] . Changsha : National University of Defense Technology , 2020 . (in Chinese)

门建兵 , 蒋建伟 , 王树有 . 爆炸冲击数值模拟技术基础 [M ] . 北京 : 北京理工大学出版社 , 2015 .

MEN J B , JIANG J W , WANG S Y . Fundamentals of numerical simulation for explosion and shock problems [M ] . Beijing : Beijing Institute of Technology Press , 2015 . (in Chinese)

BOJANOWSKI C . Numerical modeling of large deformations in soil structure interaction problems using FE, EFG, SPH, and MM-ALE formulations [J ] . Archive of Applied Mechanics , 2014 , 84 : 743 - 755 . DOI: 10.1007/s00419-014-0830-5 http://doi.org/10.1007/s00419-014-0830-5 http://link.springer.com/10.1007/s00419-014-0830-5 http://link.springer.com/10.1007/s00419-014-0830-5

SU H , ZHANG C , YAN Z F , et al . Numerical simulation of penetration process of depleted uranium alloy based on an FEM-SPH coupling algorithm [J ] . Metals , 2023 , 13 ( 1 ): 79 . DOI: 10.3390/met13010079 http://doi.org/10.3390/met13010079 https://www.mdpi.com/2075-4701/13/1/79 https://www.mdpi.com/2075-4701/13/1/79 In order to quantitatively study the penetration capability of depleted uranium alloy, a simulation model of bullet impact on target plate with FEM-SPH coupling algorithm was established by using LS-DYNA software, which was combined with Johnson-Cook intrinsic model, Johnson-Cook fracture criterion, and equation of state to conduct a simulation study of alloy bullets made of depleted uranium alloy, tungsten alloy, and high-strength steel to penetrate target plate at 1400 m/s initial velocity. The results show that under the same conditions of initial kinetic energy, initial velocity, and initial volume, the residual kinetic energy of the depleted uranium alloy bullet is 1.14 times that of tungsten alloy and 1.20 times that of high-strength steel, and the residual velocity is 1.14 times that of tungsten alloy and 1.18 times that of steel, and the residual volume is 1.13 times that of tungsten alloy and 1.23 times that of steel after the penetration is completed. The shape of the bullet after penetrating the target plate is relatively sharp, and the diameter of the target hole formed is about 1.70 times the diameter of the projectile, which is significantly larger than 1.54 times that of tungsten alloy and 1.39 times that of high-strength steel, indicating the excellent penetration performance of depleted uranium alloy.

曲禹同 . 基于绝热剪切机制的细晶钨合金弹芯自锐行为研究 [D ] . 沈阳 : 沈阳理工大学 , 2022 .

QU Y T . Study on self-sharpening behavior of fine grain tungsten alloy projectile core based on adiabatic shear mechanism [D ] . Shenyang : Shenyang Ligong University , 2022 . (in Chinese)

GOH W L , ZHENG Y , YUAN J , et al . Effects of hardness of steel on ceramic armour module against long rod impact [J ] . International Journal of Impact Engineering , 2017 , 109 : 419 - 426 . DOI: 10.1016/j.ijimpeng.2017.08.004 http://doi.org/10.1016/j.ijimpeng.2017.08.004 https://linkinghub.elsevier.com/retrieve/pii/S0734743X17300969 https://linkinghub.elsevier.com/retrieve/pii/S0734743X17300969

唐奎 , 王金相 , 刘亮涛 , 等 . 长杆弹二次侵彻机理及影响因素研究 [J/OL ] . 兵工学报 , 2023 ( 2023-04-29 )[ 2023-05-12 ] .

TANG K , WANG J X , LIU L T , et al . Study on the mechanism of secondary penetration of long rod and its influencing factors [J/OL ] . Acta Armamentarii , 2023 ( 2023-04-29 )[ 2023-05-12 ] . (in Chinese)

TANG K , WANG J X , SONG H P , et al . Investigation on the penetration of jacketed rods with striking velocities of 0.9-3.3km/s into semi-infinite targets [J ] . Defence Technology , 2022 , 18 ( 3 ): 476 - 489 . DOI: 10.1016/j.dt.2021.03.003 http://doi.org/10.1016/j.dt.2021.03.003 https://linkinghub.elsevier.com/retrieve/pii/S2214914721000295 https://linkinghub.elsevier.com/retrieve/pii/S2214914721000295

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ROSENBERG Z , MARMOR E , MAYSELESS M . On the hydrodynamic theory of long-rod penetration [J ] . International Journal of Impact Engineering , 1990 , 10 ( 1/2/3/4 ): 483 - 486 . DOI: 10.1016/0734-743X(90)90081-6 http://doi.org/10.1016/0734-743X(90)90081-6 https://linkinghub.elsevier.com/retrieve/pii/0734743X90900816 https://linkinghub.elsevier.com/retrieve/pii/0734743X90900816

WALKER J D , ANDERSON C E . A time-dependent model for long-rod penetration [J ] . International Journal of Impact Engineering , 1995 , 16 ( 1 ): 19 - 48 . DOI: 10.1016/0734-743X(94)00032-R http://doi.org/10.1016/0734-743X(94)00032-R https://linkinghub.elsevier.com/retrieve/pii/0734743X9400032R https://linkinghub.elsevier.com/retrieve/pii/0734743X9400032R

ZHU F L , CHEN Y , ZHU G L . Numerical simulation study on penetration performance of Depleted Uranium (DU) alloy fragments [J ] . Defence Technology , 2021 , 17 ( 1 ): 50 - 55 . DOI: 10.1016/j.dt.2020.01.002 http://doi.org/10.1016/j.dt.2020.01.002 Due to its high strength, high density, high hardness and good penetration capabilities, Depleted uranium alloys have already shined in armor-piercing projectiles. There should also be a lot of room for improvement in the application of fragment killing elements. Therefore, regarding the performance of the depleted uranium alloy to penetrate the target plate, further investigation is needed to analyze its advantages and disadvantages compared to tungsten alloy. To study the difference in penetration performance between depleted uranium alloy and tungsten alloy fragments, firstly, a theoretical analysis of the adiabatic shear sensitivity of DU and tungsten alloys was given from the perspective of material constitutive model. Then, taking the cylindrical fragment penetration target as the research object, the penetration process and velocity characteristics of the steel target plates penetrated by DU alloy fragment and tungsten alloy fragment were compared and analyzed, by using finite element software ANSYS/LS-DYNA and Lagrange algorithm. Lastly, the influence of different postures when impacting target and different fragment shapes on the penetration results is carried out in the research. The results show that in the penetration process of the DU and tungsten alloy fragments, the self-sharpening properties of the DU alloy can make the fragment head sharper and the penetrating ability enhance. Under the same conditions, the penetration capability of cylindrical fragment impacting target in vertical posture is better than that in horizontal posture, and the penetration capability of the spherical fragment is slightly better than that of cylindrical fragment. © 2020

FRAS T , MURZYN A , PAWLOWSKI P . Defeat mechanisms provided by slotted add-on bainitic plates against small-calibre 7.62mm×51 AP projectiles [J ] . International Journal of Impact Engineering , 2017 , 103 : 241 - 253 . DOI: 10.1016/j.ijimpeng.2017.01.015 http://doi.org/10.1016/j.ijimpeng.2017.01.015 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16303591 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16303591

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BADUROWICZ P , PACEK D . Determining ricocheting projectiles’ temperature using numerical and experimental approaches [J ] . Materials , 2022 , 15 ( 3 ): 928 . DOI: 10.3390/ma15030928 http://doi.org/10.3390/ma15030928 https://www.mdpi.com/1996-1944/15/3/928 https://www.mdpi.com/1996-1944/15/3/928 This paper describes the process of creating a numerical FEM (finite element method) model of the 5.56 × 45 mm SS109 projectile. The model was used to calculate the temperatures occurring in the projectile materials during the impact on the steel plate at an angle of 45°. The purpose of the investigation is to estimate the ability of a ricocheting projectile to cause ignition. For the same projectile, experimental tests were also carried out under the conditions adopted for the numerical investigation in order to validate the FEM model. During the experiment, temperature was measured with a thermal camera; the phenomenon was also recorded with a colour high-speed camera.

SONG W J , CHEN X W , CHEN P . Effect of compressibility on the hypervelocity penetration [J ] . Acta Mechanica Sinica , 2018 , 34 : 82 - 98 . DOI: 10.1007/s10409-017-0688-1 http://doi.org/10.1007/s10409-017-0688-1 http://link.springer.com/10.1007/s10409-017-0688-1 http://link.springer.com/10.1007/s10409-017-0688-1

孔繁家 . 并联组合式LEFP对杆式穿甲弹的毁伤仿真研究 [D ] . 太原 : 中北大学 , 2023 .

KONG F J . Simulation research on damage of parallel combined LEFP to rod armor-piercing projectiles [D ] . Taiyuan : North University of China , 2023 . (in Chinese)

HOLMQUIST T J , JOHNSON G R , GOOCH W A . Modeling the 14.5mm BS 41 projectile for ballistic impact computations[M]//SYNGELLAKIS S. Projectile Impact:Modelling Techniques and Target Performance Assessment . Ashurst Lodge, Southampton , UK : WIT Press , 2014 : 73 - 87 .

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HEDJERES S , TRIA D E , BOUDIAF A , et al . The influence of plasma nitriding hardness treatment on the dynamic compressive behavior of the Hardox 400 at a wide temperature range [J ] . Proceedings of the Institution of Mechanical Engineers , Part L: Journal of Materials: Design and Applications , 2023 , 237 ( 4 ): 867 - 885 .

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TRAJKOVSKI J , KUNC R , PEPEL V , et al . Flow and fracture behavior of high-strength armor steel PROTAC 500 [J ] . Materials & Design , 2015 , 66 : 37 - 45 . DOI: 10.1016/j.matdes.2014.10.030 http://doi.org/10.1016/j.matdes.2014.10.030 https://linkinghub.elsevier.com/retrieve/pii/S0261306914008188 https://linkinghub.elsevier.com/retrieve/pii/S0261306914008188

BØRVIK T , DEY S , CLAUSEN A H . Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles [J ] . International Journal of Impact Engineering , 2009 , 36 ( 7 ): 948 - 964 . DOI: 10.1016/j.ijimpeng.2008.12.003 http://doi.org/10.1016/j.ijimpeng.2008.12.003 https://linkinghub.elsevier.com/retrieve/pii/S0734743X08003229 https://linkinghub.elsevier.com/retrieve/pii/S0734743X08003229

ZHANG R , HAN B , LI L , et al . Influence of prestress on ballistic performance of bi-layer ceramic composite armors: experiments and simulations [J ] . Composite Structures , 2019 , 227 : 111258 . DOI: 10.1016/j.compstruct.2019.111258 http://doi.org/10.1016/j.compstruct.2019.111258 https://linkinghub.elsevier.com/retrieve/pii/S0263822318345173 https://linkinghub.elsevier.com/retrieve/pii/S0263822318345173

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WANG M , YANG M C , RONG G , et al . Failure model and numerical simulation of the tungsten alloy long rod when piercing into armor target [J ] . Rare Metal Materials and Engineering , 2015 , 45 ( 9 ): 2170 - 2174 . (in Chinese)

王晓东 , 王江波 , 徐立志 , 等 . 异型截面长杆弹侵彻半无限厚金属靶板实验研究 [J ] . 爆炸与冲击 , 2021 , 41 ( 3 ): 37 - 46 .

WANG X D , WANG J B , XU L Z , et al . Experimental study on penetration of non-circular cross-section long-rod projectiles into semi-infinite metal target [J ] . Explosion and Shockwaves , 2021 , 41 ( 3 ): 37 - 46 . (in Chinese)

刘铁磊 , 徐豫新 , 王晓锋 , 等 . 钨合金球形破片侵彻低碳钢的弹道极限速度计算模型 [J ] . 兵工学报 , 2022 , 43 ( 4 ): 768 - 779 .

LIU T L , XU Y X , WANG X F , et al . Ballistic limit calculation model of tungsten alloy spherical fragments penetrating into low carbon steel plate [J ] Acta Armamentarii , 2022 , 43 ( 4 ): 768 - 779 . (in Chinese) DOI: 10.12382/bgxb.2021.0448 http://doi.org/10.12382/bgxb.2021.0448 The penetration failure characteristics of tungsten alloy spherical fragments penetrating into low-carbon steel plate at different target speeds are analyzed to obtain a ballistic limit calculation model of tungsten alloy spherical fragments penetrating into low-carbon steel plate in a wider speed range. A ballistic limit calculation model including the main mechanical parameters of projectile and target is proposed. The fragment rigidity，plasticity, erosion and fragmentation penetration iare considered in the proposed model. A calculation method of velocity threshold for different failure characteristics of tungsten alloy is established for the need of solving the model. Based on the existing experimental data, the model coefficients are obtained by using trust region method. In addition, the ballistic limit of fragments penetrating into Q235 and Q345E steel plates is test，and the calculation accuracy of the model is analyzed according to the test results. The results show that the calculated average error and maximum error of the model are 10% lower than those of the test results，and the average error of the model is reduced by 60% compared with the existing ballistic limit calculation model.

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JIAO W J , CHEN X W . Review on long-rod penetration at hypervelocity [J ] . Advances in Mechanics , 2019 , 49 ( 1 ): 201904 . (in Chinese)

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TRIA D E , TREBIŃSKI R . On the influence of fracture criterion on perforation of high-strength steel plates subjected to armour piercing projectile [J ] . Archive of mechanical engineering , 2015 , 62 ( 2 ): 157 - 179 . DOI: 10.1515/meceng-2015-0010 http://doi.org/10.1515/meceng-2015-0010 http://journals.pan.pl/dlibra/publication/98553/edition/84993/content http://journals.pan.pl/dlibra/publication/98553/edition/84993/content This paper presents a numerical investigation of fracture criterion influence on perforation of high-strength 30PM steel plates subjected to 7.62x51 mm Armour Piercing (AP) projectile. An evaluation of four ductile fracture models is performed to identify the most suitable fracture criterion. Included in the paper is the Modified Johnson-Cook (MJC) constitutive model coupled separately with one of these fracture criteria: the MJC fracture model, the Cockcroft-Latham (CL), the maximum shear stress and the constant failure strain models. A 3D explicit Lagrangian algorithm that includes both elements and particles, is used in this study to automatically convert distorted elements into meshless particles during the course of the computation. Numerical simulations are examined by comparing with the experimental results. The MJC fracture model formulated in the space of the stress triaxiality and the equivalent plastic strain to fracture were found capable of predicting the realistic fracture patterns and at the same time the correct projectile residual velocities. However, this study has shown that CL one parameter fracture criterion where only one simple material test is required for calibration is found to give good results as the MJC failure criterion. The maximum shear stress fracture criterion fails to capture the shear plugging failure and material fracture properties cannot be fully characterized with the constant fracture strain

CHOUDHARY S , SINGH P K , KHARE S , et al . Ballistic impact behaviour of newly developed armour grade steel: an experimental and numerical study [J ] . International Journal of Impact Engineering , 2020 , 140 : 103557 . DOI: 10.1016/j.ijimpeng.2020.103557 http://doi.org/10.1016/j.ijimpeng.2020.103557 https://linkinghub.elsevier.com/retrieve/pii/S0734743X19313168 https://linkinghub.elsevier.com/retrieve/pii/S0734743X19313168

RYAN S , LI H , EDGERTON M , et al . The ballistic performance of an ultra-high hardness armour steel: an experimental investigation [J ] . International journal of impact engineering , 2016 , 94 : 60 - 73 . DOI: 10.1016/j.ijimpeng.2016.03.011 http://doi.org/10.1016/j.ijimpeng.2016.03.011 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16301270 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16301270

MA D , GIGLIO M , MANES A . Numerical investigation on the uniaxial compressive behaviour of an epoxy resin and a nanocomposite [J ] . European Journal of Mechanics-A/Solids , 2022 , 92 : 104500 . DOI: 10.1016/j.euromechsol.2021.104500 http://doi.org/10.1016/j.euromechsol.2021.104500 https://linkinghub.elsevier.com/retrieve/pii/S0997753821002424 https://linkinghub.elsevier.com/retrieve/pii/S0997753821002424

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MEYER H W , KLEPONIS D S . An analysis of parameters for the Johnson-Cook strength model for 2-in-thick Rolled Homogeneous Armor: ARL-TR-2528 [R ] . Adelphi, MD , US : Army Research Laboratory , 2001 .

ANDERSON C E , HOHLER V , WALKER J D , et al . Time-resolved penetration of long rods into steel targets [J ] . International Journal of Impact Engineering , 1995 , 16 ( 1 ): 1 - 18 . DOI: 10.1016/0734-743X(94)E0030-Y http://doi.org/10.1016/0734-743X(94)E0030-Y https://linkinghub.elsevier.com/retrieve/pii/0734743X94E0030Y https://linkinghub.elsevier.com/retrieve/pii/0734743X94E0030Y

WANG X , JIANG J W , SUN S J , et al . Investigation on the spatial distribution characteristics of behind-armor debris formed by the perforation of EFP through steel target [J ] . Defence Technology , 2020 , 16 ( 1 ): 119 - 135 . DOI: 10.1016/j.dt.2019.05.016 http://doi.org/10.1016/j.dt.2019.05.016 The behind-armor debris (BAD) formed by the perforation of an EFP is the main damage factor for the secondary destruction to the behind-armor components. Aiming at investigating the BAD caused by EFP, flash X-ray radiography combined with an experimental witness plate test method was used, and the FEM-SPH adaptive conversion algorithm in LS-DYNA software was employed to model the perforation process. The simulation results of the debris cloud shape and number of debris were in good agreement with the flash X-ray radiographs and perforated holes on the witness plate, respectively. Three-dimensional numerical simulations of EFP's penetration under various impact conditions were conducted. The results show that, an ellipsoidal debris cloud, with the major-to-minor axis radio (a/b) smaller than that caused by shaped charge jets, was formed behind the target. With the increase of target thickness (h) and decrease of impact velocity (v0) and obliquity (θ), the value of a/b decreases. The number of debris ejected from target is significantly higher than that from EFP. Based on the statistical analysis of the spatial distribution of the BAD, An engineering calculation model was established considering the influence of h, v0 and θ. The model can with reasonable accuracy predict the quantity and velocity distribution characteristics of BAD formed by EFP. © 2019 The Authors

BERGS T , HARDT M , SCHRAKNEPPER D . Determination of Johnson-Cook material model parameters for AISI 1045 from orthogonal cutting tests using the Downhill-Simplex algorithm [J ] . Procedia Manufacturing , 2020 , 48 : 541 - 552 . DOI: 10.1016/j.promfg.2020.05.081 http://doi.org/10.1016/j.promfg.2020.05.081 https://linkinghub.elsevier.com/retrieve/pii/S235197892031533X https://linkinghub.elsevier.com/retrieve/pii/S235197892031533X

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BOYCE B L , DILMORE M F . The dynamic tensile behavior of tough, ultrahigh-strength s teels at strain-rates from 0.0002s -1 to 200s -1 [J ] . International Journal of Impact Engineering , 2009 , 36 ( 2 ): 263 - 271 . DOI: 10.1016/j.ijimpeng.2007.11.006 http://doi.org/10.1016/j.ijimpeng.2007.11.006 https://linkinghub.elsevier.com/retrieve/pii/S0734743X08000808 https://linkinghub.elsevier.com/retrieve/pii/S0734743X08000808