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LIU Z H . Study on the characteristics of high-speed elliptical [D ] . Beijing : Beijing Institute of Technology , 2018 . (in Chinese)

DONG H , LIU Z H , WU H J , et al . Study on penetration characteristics of high-speed elliptical cross-sectional projectiles into concrete [J ] . International Journal of Impact Engineering , 2019 , 132 .

王文杰 , 张先锋 , 邓佳杰 , 等 . 椭圆截面弹体侵彻砂浆靶规律分析 [J ] . 爆炸与冲击 , 2018 , 38 ( 1 ): 164 - 173 .

WANG W J , ZHANG X F , DENG J J , et al . Analysis of projectile penetrating into mortar target with elliptical cross-section [J ] . Explosion and Shock Waves , 2018 , 38 ( 1 ): 164 - 173 . (in Chinese)

骆奎 . 非旋转对称的椭圆截面弹体对混凝土侵彻问题的研究 [D ] . 湘潭 : 湘潭大学 , 2020 .

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DAI X H , WANG K H , LI M R , et al . Rigid elliptical cross-section ogive-nose projectiles penetration into concrete targets [J ] . Defence Technology , 2021 , 17 ( 3 ): 800 - 811 . DOI: 10.1016/j.dt.2020.05.011 http://doi.org/10.1016/j.dt.2020.05.011 The elliptical cross-section ogive-nose projectile (ECOP) has recently attracted attention because it is well suited to the flattened shape of earth-penetrating weapons. However, the penetration performance of ECOPs has not been completely understood. The objective of this study was to investigate the penetration performance of ECOPs into concrete targets using a theoretical method. A general geometric model of ECOPs was introduced, and closed-form penetration equations were derived according to the dynamic cavity-expansion theory. The model was validated by comparing the predicted penetration depths with test data, and the maximum deviation was 15.8%. The increment in the penetration depth of the ECOP was evaluated using the proposed model, and the effect of the major–minor axis ratio on the increment was examined. Additionally, the mechanism of the penetration-depth increment was investigated with respect to the caliber radius head, axial stress, and resistance. © 2020 The Authors

董恒 . 椭圆截面弹体侵彻混凝土靶作用过程与结构响应研究 [D ] . 北京 : 北京理工大学 , 2021 .

DONG H . Penetration mechanism and structural response of elliptical cross-sectional projectile penetrating into concrete target [D ] . Beijing : Beijing Institute of Technology , 2021 . (in Chinese)

ZAID M , PAUL B . Oblique perforation of a thin plate by a truncated conical projectile [J ] . Journal of the Franklin Institute , 1959 , 268 ( 1 ): 24 - 45 . DOI: 10.1016/0016-0032(59)90354-0 http://doi.org/10.1016/0016-0032(59)90354-0 https://linkinghub.elsevier.com/retrieve/pii/0016003259903540 https://linkinghub.elsevier.com/retrieve/pii/0016003259903540

RECHT R F , IPSON T W . Ballistic perforation dynamics [J ] . Journal of Applied Mechanics , 1963 , 30 ( 3 ): 384 - 390 . DOI: 10.1115/1.3636566 http://doi.org/10.1115/1.3636566 https://asmedigitalcollection.asme.org/appliedmechanics/article/30/3/384/387842/Ballistic-Perforation-Dynamics https://asmedigitalcollection.asme.org/appliedmechanics/article/30/3/384/387842/Ballistic-Perforation-Dynamics Analytical equations of the types required to define ballistic perforation dynamics are developed. These equations concern both blunt and sharp-nosed fragments, perforating plates normally and at oblique impact angles. Residual velocities are defined in terms of magnitude and direction. Analytical models and confirming experimental data, which are presented here, specifically concern the ballistic velocity-impact range to about 25 percent of the velocity of longitudinal sonic waves in the impacting materials.

潘鑫 . 椭圆截面刚性弹体贯穿金属靶效能研究 [D ] . 北京 : 北京理工大学 , 2019 .

PAN X . Study on the performance of elliptical cross-sectional rigid projectile perforating metal target [D ] . Beijing : Beijing Institute of Technology , 2019 . (in Chinese)

王浩 . 椭圆变截面弹体贯穿加筋板破坏模式与偏转机理研究 [D ] . 北京 : 北京理工大学 , 2020 .

WANG H . The failure mode and deflection mechanism of projectiles with tapered-elliptic cross-section perforation into stiffened plates [D ] . Beijing : Beijing Institute of Technology , 2020 . (in Chinese)

王浩 , 潘鑫 , 武海军 , 等 . 椭圆截面截卵形刚性弹体正贯穿加筋板能量耗散分析 [J ] . 爆炸与冲击 , 2019 , 39 ( 10 ): 103203 .

WANG H , PAN X , WU H J , et al . Energy dissipation analysis of elliptical truncated oval rigid projectile penetrating stiffened plate [J ] . Explosion and Shock Waves , 2019 , 39 ( 10 ): 69 - 80 . (in Chinese)

王浩 , 武海军 , 闫雷 , 等 . 椭圆横截面弹体斜贯穿双层间隔薄钢板失效模式 [J ] . 兵工学报 , 2020 , 41 ( 增刊2 ): 1 - 11 .

WANG H , WU H J , YAN L , et al . Research on oblique perforation of truncated ogive-nosed projectiles with elliptic cross-section into double-layered thin steel plate with gap space [J ] . Acta Armamentarii , 2020 , 41 ( S2 ): 1 - 11 . (in Chinese)

田泽 , 王浩 , 武海军 , 等 . 椭圆变截面弹体斜贯穿薄靶姿态偏转机理 [J ] . 兵工学报 , 2022 , 43 ( 7 ): 1537 - 1552 . DOI: 10.12382/bgxb.2021.0367 http://doi.org/10.12382/bgxb.2021.0367 随着新型武器平台的发展，具有良好平台适应性、高升阻比及隐身性能等特点的异形截面（椭圆形及变截面椭圆形）战斗部开始受到广泛关注。为探究椭圆变截面弹体斜贯穿薄靶机理与姿态偏转规律，对3种不同截面（圆形、椭圆形、变截面椭圆形）弹体斜贯穿双层945舰船薄钢板实验过程及结果进行整理与分析，根据椭圆变截面弹体贯穿过程、靶板破坏失效模式与弹体受力特征，将贯穿过程分为弹体头部压入阶段、弹体头部贯穿阶段、过渡阶段与弹身贯穿阶段。基于能量守恒、虚功原理分阶段分析弹体受力特征，建立弹体姿态偏转理论模型。通过对已有实验和数值模拟结果与理论模型所得结果进行对比，验证理论模型的可靠性。采用该理论模型着重讨论弹体撞击速度、初始倾角、质心位置、弹体翻滚角及椭圆截面长短轴之比等参数对椭圆变截面弹体姿态偏转的影响。结果表明：随着椭圆变截面弹体初始撞击速度的增加，弹体姿态偏转角度呈现指数型减小趋势；随着椭圆变截面弹体初始倾角的增大，弹体姿态偏转量增大；随着椭圆变截面弹体质心位置的后置，弹体姿态偏转角度增大；椭圆变截面弹体以不同的翻滚角撞击靶板时，弹体姿态偏转角度不同，γ_pt=0°较γ_pt=90°时弹体姿态偏转角度更大；当γ_pt=0°时，椭圆变截面弹体椭圆截面长短轴之比增大，弹体姿态偏转角度随之增大；当γ_pt=90°时，规律则相反。

TIAN Z , WANG H , WU H J , et al . Attitude deflection mechanism of projectiles with variable elliptical cross-section obliquely perforating thin target [J ] . Acta Armamentarii , 2020 , 43 ( 7 ): 1537 - 1552 . (in Chinese)

WEI H Y , ZHANG X F , LIU C , et al . A three-dimensional penetration trajectory model for ogive-nosed projectile into metal targets [J ] . International Journal of Impact Engineering , 2021 , 157 : 103998 . DOI: 10.1016/j.ijimpeng.2021.103998 http://doi.org/10.1016/j.ijimpeng.2021.103998 https://linkinghub.elsevier.com/retrieve/pii/S0734743X21001858 https://linkinghub.elsevier.com/retrieve/pii/S0734743X21001858

WEI H Y , ZHANG X F , LIU C , et al . Oblique penetration of ogive-nosed projectile into aluminum alloy targets [J ] . International Journal of Impact Engineering , 2021 , 148 : 103745 . DOI: 10.1016/j.ijimpeng.2020.103745 http://doi.org/10.1016/j.ijimpeng.2020.103745 https://linkinghub.elsevier.com/retrieve/pii/S0734743X20308150 https://linkinghub.elsevier.com/retrieve/pii/S0734743X20308150

MA X H , ZHANG Q M , ZHANG X W . A model for rigid asymmetric ellipsoidal projectiles penetrating into metal plates [J ] . International Journal of Impact Engineering , 2021 , 163 : 104140 . DOI: 10.1016/j.ijimpeng.2021.104140 http://doi.org/10.1016/j.ijimpeng.2021.104140 https://linkinghub.elsevier.com/retrieve/pii/S0734743X21003158 https://linkinghub.elsevier.com/retrieve/pii/S0734743X21003158

MASRI R , COHEN T , DURBAN D . Enlargement of a Circular hole in a thin plastic sheet: taylor-bethe controversy in retrospect [J ] . Quarterly Journal of Mechanics and Applied Mathematics , 2010 , 63 ( 4 ): 589 - 616 . DOI: 10.1093/qjmam/hbq013 http://doi.org/10.1093/qjmam/hbq013 https://academic.oup.com/qjmam/article-lookup/doi/10.1093/qjmam/hbq013 https://academic.oup.com/qjmam/article-lookup/doi/10.1093/qjmam/hbq013

IQBAL M A , GUPTA N K , SEKHON G S . Behaviour of thin aluminium plates subjected to impact by ogive-nosed projectiles [J ] . Defence Science Journal , 2006 , 56 ( 5 ): 841 - 852 . DOI: 10.14429/dsj.56.1953 http://doi.org/10.14429/dsj.56.1953 http://publications.drdo.gov.in/ojs/index.php/dsj/article/view/1953 http://publications.drdo.gov.in/ojs/index.php/dsj/article/view/1953

GUPTA N K , IQBAL M A , SEKHON G S . Experimental and numerical studies on the behavior of thin aluminum plates subjected to impact by blunt-and hemispherical-nosed projectiles [J ] . International Journal of Impact Engineering , 2006 , 32 ( 12 ): 1921 - 1944 . DOI: 10.1016/j.ijimpeng.2005.06.007 http://doi.org/10.1016/j.ijimpeng.2005.06.007 https://linkinghub.elsevier.com/retrieve/pii/S0734743X05000953 https://linkinghub.elsevier.com/retrieve/pii/S0734743X05000953

GUPTA N K , IQBAL M A , SEKHON G S . Effect of projectile nose shape, impact velocity and target thickness on deformation behavior of aluminum plates [J ] . International Journal of Solids and Structures , 2007 , 44 ( 10 ): 3411 - 3439 . DOI: 10.1016/j.ijsolstr.2006.09.034 http://doi.org/10.1016/j.ijsolstr.2006.09.034 https://linkinghub.elsevier.com/retrieve/pii/S0020768306004045 https://linkinghub.elsevier.com/retrieve/pii/S0020768306004045

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

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IQBAL M A , SENTHIL K , MADHU V , et al . Oblique impact on single, layered and spaced mild steel targets by 7.62 AP projectiles [J ] . International Journal of Impact Engineering , 2017 , 110 : 26 - 38 . DOI: 10.1016/j.ijimpeng.2017.04.011 http://doi.org/10.1016/j.ijimpeng.2017.04.011 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16309113 https://linkinghub.elsevier.com/retrieve/pii/S0734743X16309113

BØRVIK T , HOPPERSTAD O S , BERSTAD T , et al . Perforation of 12mm thick steel plates by 20mm diameter projectiles with flat, hemispherical and, conical noses: Part II: numerical simulations [J ] . International Journal of Impact Engineering , 2002 , 27 ( 1 ): 37 - 64 . DOI: 10.1016/S0734-743X(01)00035-5 http://doi.org/10.1016/S0734-743X(01)00035-5 https://linkinghub.elsevier.com/retrieve/pii/S0734743X01000355 https://linkinghub.elsevier.com/retrieve/pii/S0734743X01000355

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陈小伟 , 梁冠军 , 姚勇 , 等 . 平头弹穿透金属靶板的模式分析 [J ] . 力学学报 , 2009 , 41 ( 1 ): 84 - 90 . DOI: 10.6052/0459-1879-2009-1-2007-572 http://doi.org/10.6052/0459-1879-2009-1-2007-572 对平头弹穿透金属靶的剪切冲塞和绝热剪切冲塞两种可能穿甲模式进行分析. 对作者先前提出的绝热剪切冲塞失效模型进一步发展，给出在绝热剪切冲塞条件下修正的终点弹道极限和剩余速度. 对相关的平头弹穿甲WeldoxE系列钢靶的试验数据进行分析比较，讨论靶板厚度、靶材强度对终点弹道性能的影响. 更多实验数据证实：在一定靶厚时由于靶板的结构响应导致弹道极限附近存在剩余速度跳跃；随靶厚和靶材强度增加，穿甲模式由剪切冲塞向绝热剪切冲塞转换.

CHEN X W , LIANG G J , YAO Y , et al . Perforation modes of metal plates struck by a blunt rigid projectile [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2009 , 41 ( 1 ): 84 - 90 . (in Chinese) DOI: 10.6052/0459-1879-2009-1-2007-572 http://doi.org/10.6052/0459-1879-2009-1-2007-572 The present paper analyzes the possible modes of shearplugging and adiabatic shear plugging in the perforation of metal platesstruck by a blunt rigid projectile. The modified ballistic limit andresidual velocity with adiabatic shear plugging are further formulated.Further experimental analyses are conducted on the perforations of Weldox Esteel plates, in order to discuss the effects of plate thickness andmaterial strength/hardness on the terminal ballistic performance. Moreexperimental evidences confirm the jump of residual velocity at ballisticlimit induced by the structural response of plate. With increasing thethickness of plate and the material strength, failure modes of plate maytransform from shear plugging to adiabatic shear plugging.

MAE H , TENG X , BAI Y , et al . Comparison of ductile fracture properties of aluminum castings: sand mold vs. metal mold [J ] . International Journal of Solids and Structures , 2008 , 45 ( 5 ): 1430 - 1444 . DOI: 10.1016/j.ijsolstr.2007.10.016 http://doi.org/10.1016/j.ijsolstr.2007.10.016 https://linkinghub.elsevier.com/retrieve/pii/S0020768307004350 https://linkinghub.elsevier.com/retrieve/pii/S0020768307004350

BAO Y , TREITLER R . Ductile crack formation on notched Al2024-T351 bars under compression-tension loading [J ] . Materials Science and Engineering: A , 2004 , 384 ( 1/2 ): 385 - 394 . DOI: 10.1016/S0921-5093(04)00883-4 http://doi.org/10.1016/S0921-5093(04)00883-4 https://linkinghub.elsevier.com/retrieve/pii/S0921509304008834 https://linkinghub.elsevier.com/retrieve/pii/S0921509304008834

BAO Y B , WIERZBICKI T . On fracture locus in the equivalent strain and stress triaxiality space [J ] . International Journal of Mechanical Sciences , 2004 , 46 ( 1 ): 81 - 98 . DOI: 10.1016/j.ijmecsci.2004.02.006 http://doi.org/10.1016/j.ijmecsci.2004.02.006 https://linkinghub.elsevier.com/retrieve/pii/S0020740304000360 https://linkinghub.elsevier.com/retrieve/pii/S0020740304000360

BAO Y B , WIERZBICKI T . A comparative study on various ductile crack formation criteria [J ] . Journal of Engineering Materials and Technology , 2004 , 126 ( 3 ): 314 - 324 . DOI: 10.1115/1.1755244 http://doi.org/10.1115/1.1755244 https://asmedigitalcollection.asme.org/materialstechnology/article/126/3/314/464882/A-Comparative-Study-on-Various-Ductile-Crack https://asmedigitalcollection.asme.org/materialstechnology/article/126/3/314/464882/A-Comparative-Study-on-Various-Ductile-Crack Various fracture criteria, based on different assumptions and different mechanical models, have been proposed in the past to predict ductile fracture. The objective of this study is to assess their effectiveness and accuracy in a wide range of process parameters. A series of tests on 2024-T351 aluminum alloy, including upsetting tests and tensile tests is carried out. It is found that none of the existing fracture criteria give consistent results. Two totally different fracture mechanisms are clearly observed from microfractographs of upsetting and tensile specimens. This observation confirms that it is impossible to capture all features of ductile crack formation in different stress states with a single criterion. It is shown that different functions are necessary to predict crack formation for different ranges of stress triaxiality. Weighting functions in a wide range of stress states can be obtained by determining the fracture locus in the space of equivalent strain to fracture and stress triaxiality.

BAO Y B , WIERZBICKI T . On the cut-off value of negative triaxiality for fracture [J ] . Engineering Fracture Mechanics , 2005 , 72 ( 7 ): 1049 - 1069 . DOI: 10.1016/j.engfracmech.2004.07.011 http://doi.org/10.1016/j.engfracmech.2004.07.011 https://linkinghub.elsevier.com/retrieve/pii/S0013794404001869 https://linkinghub.elsevier.com/retrieve/pii/S0013794404001869

BAI Y L , BAO Y B , WIERZBICKI T . Fracture of prismatic aluminum tubes under reverse straining [J ] . International Journal of Impact Engineering , 2006 , 32 ( 5 ): 671 - 701 . DOI: 10.1016/j.ijimpeng.2005.05.002 http://doi.org/10.1016/j.ijimpeng.2005.05.002 https://linkinghub.elsevier.com/retrieve/pii/S0734743X05000837 https://linkinghub.elsevier.com/retrieve/pii/S0734743X05000837

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吴子奇 . 弹目结合的反舰导弹对目标舰船靶标侵彻毁伤研究 [D ] . 哈尔滨 : 哈尔滨工程大学 , 2019 .

WU Z Q . Study on damage of ship target penetrated by anti-ship missile with missile-target combination [D ] . Harbin : Harbin Engineering University , 2019 . (in Chinese)

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GANJIANI M . A damage model for predicting ductile fracture with considering the dependency on stress triaxiality and Lode angle [J ] . European Journal of Mechanics—A/Solids , 2020 , 84 : 104048 . DOI: 10.1016/j.euromechsol.2020.104048 http://doi.org/10.1016/j.euromechsol.2020.104048 https://linkinghub.elsevier.com/retrieve/pii/S0997753820304368 https://linkinghub.elsevier.com/retrieve/pii/S0997753820304368

MUIRURI A , MARINGA M , DU PREEZ W . Development of VUMAT and VUHARD subroutines for simulating the dynamic mechanical properties of additively manufactured parts [J ] . Materials , 2022 , 15 ( 1 ): 372 . DOI: 10.3390/ma15010372 http://doi.org/10.3390/ma15010372 https://www.mdpi.com/1996-1944/15/1/372 https://www.mdpi.com/1996-1944/15/1/372 Numerical modelling and simulation can be useful tools in qualification of additive manufactured parts for use in demanding structural applications. The use of these tools in predicting the mechanical properties and field performance of additive manufactured parts can be of great advantage. Modelling and simulation of non-linear material behaviour requires development and implementation of constitutive models in finite element analysis software. This paper documents the implementation and verification process of a microstructure-variable based model for DMLS Ti6Al4V (ELI) in two separate ABAQUS/Explicit subroutines, VUMAT and VUHARD, available for defining the yield surface and plastic deformation of materials. The verification process of the implemented subroutines was conducted for single and multiple element tests with varying prescribed loading conditions. The simulation results obtained were then compared with the analytical solutions at the same conditions of strain rates and temperatures. This comparison showed that both developed subroutines were accurate in predicting the flow stress of various forms of DMLS Ti6Al4V (ELI) under different conditions of strain rates and temperatures.

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