弹丸超高速撞击薄板碎片云建模研究
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摘要
随着空间碎片日益增多,其超高速撞击对航天器特别是载人航天器在轨安全运行构成的威胁越来越严重。在航天器舱壁外间隔一定距离安装一层或多层薄板防护屏可以破碎空间碎片,分散其撞击能量,从而有效保护航天器的安全。铝合金薄板被广泛用来制作防护屏,直接承受空间碎片的撞击。
空间碎片穿透薄板防护屏后破碎形成的碎片云的特性直接影响后板(舱壁或后继防护屏)的撞击损伤效果,因此,对超高速撞击碎片云进行研究是航天器空间碎片防护结构设计与开发的一个重要技术基础。迄今,对碎片云形成过程的定量研究尚比较缺乏;另外,多数已有的碎片云模型只适合描述相对较高撞击速度范围内产生的碎片云,其中撞击体的破碎程度较高。
基于以上背景,本文针对处于相对较低撞击速度范围内的薄板超高速撞击现象(弹丸经历从塑性变形到完全破碎的过程,且所有材料均保持为固体状态),重点研究铝合金球形弹丸超高速正撞击铝合金薄板后撞击体的破碎过程、碎片云的形成过程、碎片云的组成结构与形态特点、碎片云的速度与质量特性、弹丸破碎特性、超高速撞击过程中的能量特性等,最终建立一个碎片云模型。本文的研究范围为:v0(撞击速度)介于2.00km/s与5.00km/s之间;t/D(薄板厚度与弹丸直径之比)介于0.032与0.315之间。
首先,应用二级轻气炮加载技术进行了弹丸超高速正撞击薄板实验研究,利用闪光X射线照相设备获取了碎片云图像,并在薄板后面放置观察板记录碎片云撞击造成的损伤。弹丸直径为6.35mm,薄板厚度介于0.50mm~2.00mm,撞击速度介于2.23km/s~5.26km/s。为了弥补实验手段在实验数量方面的不足并深入了解超高速撞击过程与机理,采用SPH算法进行了大量超高速撞击数值模拟研究,获取了碎片云多种特性的数据。通过比较数值模拟与实验两种手段得到的碎片云形态及特征点速度,发现二者结果吻合较好,验证了数值模拟手段的有效性。
第二,基于前人的研究成果,介绍了超高速撞击过程中弹丸与薄板内应力波的传播与相互作用规律以及撞击体材料的破碎机理,并利用实验与数值模拟结果进行了验证。根据实验观察结果,提出关于弹丸材料发生破碎与形成碎片云的临界问题;借助数值模拟手段,建立了上述现象发生时的临界撞击条件表达式,并描述了碎片云的形成过程。通过数值模拟分析,发现了薄板前表面材料发生破碎与产生反溅两种过程的差别,解释了其原因,并建立了相应临界撞击条件表达式。基于碎片云图像与观察板损伤实验结果分析,定义了不同撞击条件下碎片云的组成结构,总结并描述了碎片云的形态特点,确定了观察板损伤与碎片云的对应关系。
第三,根据碎片云形态特点,在碎片云上定义了4个能够表征碎片云形态特点的特征点;借助数值模拟研究结果,分析了所有特征点速度随撞击条件(v0、t/D)的变化规律,建立了特征点的归一化速度与撞击条件的定量关系式。综合利用理论分析、实验研究与数值模拟手段,提出了碎片云各组成部分的质量计算模型。基于数值模拟结果,建立了超高速撞击过程中能量耗散与撞击条件的定量关系。借助超高速撞击实验中获得的观察板损伤数据,分析了最大碎片尺寸等弹丸破碎程度表征量随撞击条件的变化规律,并讨论了主体碎片云质量分布与弹丸破碎程度的关系。
最后,在本文研究范围内,集成上述成果并基于对碎片云运动及碎片空间分布等规律的假设,提出了一个包含碎片云形状描述、速度分布及质量分布的碎片云模型,并给出了模型参数的计算方法。本模型刻画了碎片云的所有组成部分;以平面曲线方程描述碎片云不同组成部分的形状,进而建立了处于自由膨胀运动中的碎片云的速度分布模型。基于实验研究与数值模拟结果,提出了碎片云各组成部分的质量分布模型。应用质量、动量、能量守恒方程,计算碎片云模型中引入的待定参数。给出两个典型工况的算例,通过比较模型计算结果与数值模拟结果以及两个算例结果的互相比较,验证了模型的有效性。
本文的研究成果为防护结构撞击极限研究及航天器空间碎片防护结构设计提供了技术基础,揭示了弹板撞击过程中材料破碎并形成碎片云的机理,也为研发新型多层防护结构提供了超高速撞击碎片云特性研究的基础,具有一定的工程应用价值和理论指导意义。
With the increase of space debris, hypervelocity collisions between space debris and spacecrafts have became a more seriously hazard to space flights, espetially manned spacecrafts. The most useful shielding structure with one or multi-layer shielding walls in front the spacecraft bulkhead with a distant is used to break the space debris and disperse impact energy, in order to get effective protection effect. Generally, the material of shielding wall is aluminum alloy.
The damage of rear wall (spacecraft bulkhead or inner shielding wall) impacted by debris cloud which generates from the hypervelocity impact process between space debris and shielding structures depends on the characteristics of debris cloud. So, research on fundamental theory and technologies of debris cloud under hypervelocity impact has an important significance on shilding structure design and development. Nowadays, the quantitative investigation on debris cloud formation is still very limit and most models presented before are only for debris cloud produced by impacts with relatively higher velocties.
Based on the background mentioned above, within relatively lower velocity range, this paper mainly investigates the fragmentation process of hypervelocity impact for aluminum sphere and aluminum thin plate at normal angle, formation process of debris cloud, structure and morphology characteristics of debris cloud, velocity and mass characteristics of debris cloud, fragmentation properties of projectile and energy characteristics under hypervelocity impact phenomenon. Based on the individual results, a fresh analytical model of debris cloud is formed. In this paper the impact velocity (v0) is ranging from 2.00km/s and 5.00km/s, thickness of thin plate to projectile diameter ratio (t/D) is between 0.032and 0.315.
First, experiments of aluminum spherical projectiles impacting on aluminum thin plates at normal angle were performed by two stage light gas gun loading technique. Debris cloud radiographs were captured by flash X-ray radiography device. Damage patterns were recorded by witness plate placed behind the thin plate. The projectile diameter is 6.35mm. The thickness of thin plate is between 0.50mm~2.00mm. Impact velocity is ranging from 2.23km/s to 5.26km/s. Quantity of numerical simulations using SPH method were performed to remedy inadequacy of experiment results and mechanism studies. Results in numerical simulations and expreriments were nearly same for the debris cloud morphology and velocities on measurement points. These comparisons deduced the validity of simulation results.
Second, the stress wave propagation principle and marerial damage mechanism inside the projectile and thin plate under hypervelocity impact were discussed which are also verified by experimental and numerical results. According to experimental results, critical state problems are proposed on fragmentation of projectile material and debris cloud initial formation process. Critical impact conditions of projectile fragmentation and debris cloud formation are determined by numerical method. By analyzing the numerical simulation results, differences of material fragmentation and fragments ejection process on the front surface of thin plate are found. Possibly reasons are proposed and quantitative expressions are discussed. The composition and structure of debris cloud under different impact conditions are defined based on experimental and numerical results. Debris cloud morphological characteristics are described and summarized. By comparing the images of debris cloud with witness plate damage patterns, the corresponding relations are confirmed.
Third, four measurement points on debris cloud are defined based on the debris cloud morphology. With simulation data, variations of velocities on measurement points with impact condition (v0, t/D) are analyzed. Quantitative relationships between measurement point velocities and impact condition are obtained. By a comprehensive consideration on theoretical, experimental and numerical results, a mass calculation model on different parts of debris cloud is raised. Quantitative relationship between energy dissipation and impact condition during hypervelocity impact is fitted based on simulation data. By analyzing witness plate experimental damage patterns, variations of physical quantities, such as the maximum fragment’s dimension, characterizing the level of projectile fragmentation with impact condition are discussed. The relationship between major part of debris cloud mass distribution and damage degree of projectile is also discussed.
Last, Based on the previous study and reasonable assumptions, a debris cloud model including cloud shape description, velocity distribution and mass distribution is deduced. All components of debris cloud are described in this model. Plane curve equations are determined to describe different component contours of debris cloud. Furthermore, velocity distribution models for debris cloud being freely expanding are derived. Based on the experimental and numerical results, mass distribution models for different parts of debris cloud are discussed respectively, especially for the major part which has a complicate mass distribution. By using mass, momentum and energy conservation equations, parameters introduced in debris cloud model are determined. Finally, two typical simulation examples are used to verify the usefulness of the model.
The result of this paper is a basic technical knowledge for ballistic limit of shielding structure and design of spacecraft protection system. The mechanism of debris cloud formation is also explained in this paper. The results also can be the basic idea to develop the newly multi-layered shields. This paper has an effective and theoretical guidance values.
空间碎片穿透薄板防护屏后破碎形成的碎片云的特性直接影响后板(舱壁或后继防护屏)的撞击损伤效果,因此,对超高速撞击碎片云进行研究是航天器空间碎片防护结构设计与开发的一个重要技术基础。迄今,对碎片云形成过程的定量研究尚比较缺乏;另外,多数已有的碎片云模型只适合描述相对较高撞击速度范围内产生的碎片云,其中撞击体的破碎程度较高。
基于以上背景,本文针对处于相对较低撞击速度范围内的薄板超高速撞击现象(弹丸经历从塑性变形到完全破碎的过程,且所有材料均保持为固体状态),重点研究铝合金球形弹丸超高速正撞击铝合金薄板后撞击体的破碎过程、碎片云的形成过程、碎片云的组成结构与形态特点、碎片云的速度与质量特性、弹丸破碎特性、超高速撞击过程中的能量特性等,最终建立一个碎片云模型。本文的研究范围为:v0(撞击速度)介于2.00km/s与5.00km/s之间;t/D(薄板厚度与弹丸直径之比)介于0.032与0.315之间。
首先,应用二级轻气炮加载技术进行了弹丸超高速正撞击薄板实验研究,利用闪光X射线照相设备获取了碎片云图像,并在薄板后面放置观察板记录碎片云撞击造成的损伤。弹丸直径为6.35mm,薄板厚度介于0.50mm~2.00mm,撞击速度介于2.23km/s~5.26km/s。为了弥补实验手段在实验数量方面的不足并深入了解超高速撞击过程与机理,采用SPH算法进行了大量超高速撞击数值模拟研究,获取了碎片云多种特性的数据。通过比较数值模拟与实验两种手段得到的碎片云形态及特征点速度,发现二者结果吻合较好,验证了数值模拟手段的有效性。
第二,基于前人的研究成果,介绍了超高速撞击过程中弹丸与薄板内应力波的传播与相互作用规律以及撞击体材料的破碎机理,并利用实验与数值模拟结果进行了验证。根据实验观察结果,提出关于弹丸材料发生破碎与形成碎片云的临界问题;借助数值模拟手段,建立了上述现象发生时的临界撞击条件表达式,并描述了碎片云的形成过程。通过数值模拟分析,发现了薄板前表面材料发生破碎与产生反溅两种过程的差别,解释了其原因,并建立了相应临界撞击条件表达式。基于碎片云图像与观察板损伤实验结果分析,定义了不同撞击条件下碎片云的组成结构,总结并描述了碎片云的形态特点,确定了观察板损伤与碎片云的对应关系。
第三,根据碎片云形态特点,在碎片云上定义了4个能够表征碎片云形态特点的特征点;借助数值模拟研究结果,分析了所有特征点速度随撞击条件(v0、t/D)的变化规律,建立了特征点的归一化速度与撞击条件的定量关系式。综合利用理论分析、实验研究与数值模拟手段,提出了碎片云各组成部分的质量计算模型。基于数值模拟结果,建立了超高速撞击过程中能量耗散与撞击条件的定量关系。借助超高速撞击实验中获得的观察板损伤数据,分析了最大碎片尺寸等弹丸破碎程度表征量随撞击条件的变化规律,并讨论了主体碎片云质量分布与弹丸破碎程度的关系。
最后,在本文研究范围内,集成上述成果并基于对碎片云运动及碎片空间分布等规律的假设,提出了一个包含碎片云形状描述、速度分布及质量分布的碎片云模型,并给出了模型参数的计算方法。本模型刻画了碎片云的所有组成部分;以平面曲线方程描述碎片云不同组成部分的形状,进而建立了处于自由膨胀运动中的碎片云的速度分布模型。基于实验研究与数值模拟结果,提出了碎片云各组成部分的质量分布模型。应用质量、动量、能量守恒方程,计算碎片云模型中引入的待定参数。给出两个典型工况的算例,通过比较模型计算结果与数值模拟结果以及两个算例结果的互相比较,验证了模型的有效性。
本文的研究成果为防护结构撞击极限研究及航天器空间碎片防护结构设计提供了技术基础,揭示了弹板撞击过程中材料破碎并形成碎片云的机理,也为研发新型多层防护结构提供了超高速撞击碎片云特性研究的基础,具有一定的工程应用价值和理论指导意义。
With the increase of space debris, hypervelocity collisions between space debris and spacecrafts have became a more seriously hazard to space flights, espetially manned spacecrafts. The most useful shielding structure with one or multi-layer shielding walls in front the spacecraft bulkhead with a distant is used to break the space debris and disperse impact energy, in order to get effective protection effect. Generally, the material of shielding wall is aluminum alloy.
The damage of rear wall (spacecraft bulkhead or inner shielding wall) impacted by debris cloud which generates from the hypervelocity impact process between space debris and shielding structures depends on the characteristics of debris cloud. So, research on fundamental theory and technologies of debris cloud under hypervelocity impact has an important significance on shilding structure design and development. Nowadays, the quantitative investigation on debris cloud formation is still very limit and most models presented before are only for debris cloud produced by impacts with relatively higher velocties.
Based on the background mentioned above, within relatively lower velocity range, this paper mainly investigates the fragmentation process of hypervelocity impact for aluminum sphere and aluminum thin plate at normal angle, formation process of debris cloud, structure and morphology characteristics of debris cloud, velocity and mass characteristics of debris cloud, fragmentation properties of projectile and energy characteristics under hypervelocity impact phenomenon. Based on the individual results, a fresh analytical model of debris cloud is formed. In this paper the impact velocity (v0) is ranging from 2.00km/s and 5.00km/s, thickness of thin plate to projectile diameter ratio (t/D) is between 0.032and 0.315.
First, experiments of aluminum spherical projectiles impacting on aluminum thin plates at normal angle were performed by two stage light gas gun loading technique. Debris cloud radiographs were captured by flash X-ray radiography device. Damage patterns were recorded by witness plate placed behind the thin plate. The projectile diameter is 6.35mm. The thickness of thin plate is between 0.50mm~2.00mm. Impact velocity is ranging from 2.23km/s to 5.26km/s. Quantity of numerical simulations using SPH method were performed to remedy inadequacy of experiment results and mechanism studies. Results in numerical simulations and expreriments were nearly same for the debris cloud morphology and velocities on measurement points. These comparisons deduced the validity of simulation results.
Second, the stress wave propagation principle and marerial damage mechanism inside the projectile and thin plate under hypervelocity impact were discussed which are also verified by experimental and numerical results. According to experimental results, critical state problems are proposed on fragmentation of projectile material and debris cloud initial formation process. Critical impact conditions of projectile fragmentation and debris cloud formation are determined by numerical method. By analyzing the numerical simulation results, differences of material fragmentation and fragments ejection process on the front surface of thin plate are found. Possibly reasons are proposed and quantitative expressions are discussed. The composition and structure of debris cloud under different impact conditions are defined based on experimental and numerical results. Debris cloud morphological characteristics are described and summarized. By comparing the images of debris cloud with witness plate damage patterns, the corresponding relations are confirmed.
Third, four measurement points on debris cloud are defined based on the debris cloud morphology. With simulation data, variations of velocities on measurement points with impact condition (v0, t/D) are analyzed. Quantitative relationships between measurement point velocities and impact condition are obtained. By a comprehensive consideration on theoretical, experimental and numerical results, a mass calculation model on different parts of debris cloud is raised. Quantitative relationship between energy dissipation and impact condition during hypervelocity impact is fitted based on simulation data. By analyzing witness plate experimental damage patterns, variations of physical quantities, such as the maximum fragment’s dimension, characterizing the level of projectile fragmentation with impact condition are discussed. The relationship between major part of debris cloud mass distribution and damage degree of projectile is also discussed.
Last, Based on the previous study and reasonable assumptions, a debris cloud model including cloud shape description, velocity distribution and mass distribution is deduced. All components of debris cloud are described in this model. Plane curve equations are determined to describe different component contours of debris cloud. Furthermore, velocity distribution models for debris cloud being freely expanding are derived. Based on the experimental and numerical results, mass distribution models for different parts of debris cloud are discussed respectively, especially for the major part which has a complicate mass distribution. By using mass, momentum and energy conservation equations, parameters introduced in debris cloud model are determined. Finally, two typical simulation examples are used to verify the usefulness of the model.
The result of this paper is a basic technical knowledge for ballistic limit of shielding structure and design of spacecraft protection system. The mechanism of debris cloud formation is also explained in this paper. The results also can be the basic idea to develop the newly multi-layered shields. This paper has an effective and theoretical guidance values.
引文
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31 W. C. Turpin, J. M. Carson. Hole Growth in Thin Plates Perforated by Hypervelocity Pellets. AFML-TR-70-83, 1970
32 A. C. Charters. The Early Years of Aerodynamics Ranges, Light-Gas Guns, and High-Velocity Impact. Int. J. Impact Eng. 1995, 17:151~182
33王金贵.二级轻气炮超高速弹丸发射技术的研究.高压物理学报. 1992, 6(4):264~272
34沈金华,贾浩.电磁轨道炮及其应用.爆炸与冲击. 1984, 4(2):90-96
35周之奎,陈素年,邓利文.电热炮原理实验研究.爆炸与冲击. 1993, 13(2):186-192
36徐兴海,高顺受,陈素年.一种电炮装置.爆炸与冲击. 1982, (4):67-69
37 B. Stever, R. Frank. A Plasma Drag Hypervelocity Particle Accelerator. Int. J. Impact Eng. 1999, 23:67~76
38 J. D. Walker, D. J. Grosch. A Hypervelocity Fragment Launcher Based on an Inhibited Shaped Charge. Int. J. Impact Engng. 1993, 14:763-774
39张文兵.地基模拟空间碎片速度测试技术.航天器环境工程. 2006, 23(3):138~142
40 J. Williamsen, E. Howard. Video Imaging of Debris Clouds Following Penetration of Lightweight Spacecraft Materials. Int. J. Impact Eng. 2001, 26(1-10):865~877
41 M. L. Wilkins. Computer Simulation of Dynamic Phenomena. Springer. 1999
42 S. Hiermaier, D. Konke, A. J. Stilp, K. Thoma. Computational Simulation of the Hypervelocity Impact of Al-Spheres on Thin Plates of Different Materials. Int. J. Impact Eng. 1997, 20:363~374
43 D. Palmieri, M. Faraud, R. Destefanis. Whipple Shied Ballistic at Impact Velocity Higher Than 7 Km/S. Int. J. Impact Eng. 2001, 26:579~590
44张伟,庞宝君,贾斌,曲焱喆.弹丸超高速撞击防护屏碎片云数值模拟.高压物理学报. 2004, 18(1):47~52
45 C. J. Hayhurst, R. Clegg. A Cylindrically Symmetric Sph Simulations of Hypervelocity Impacts on Thin Plates. Int. J. Impact Eng. 1997, 20:337~348
46 T. G. Trucano, J. M. McGlaun. Hypervelocity Impact Calculations Using Cth: Case Studies. Int. J. Impact Eng. 1990, 10(1-4):601~613
47 J. M. McGlaun, S. L. Thompson, M. G. Elrick. Cth: A Three-Dimensional Shock Wave Physics Code. Int. J. Impact Eng. 1990, 10(1-4):351~360
48 P. H. L. Groenenboom. Groenenboom Numerical Simulation of 2d and 3d Hypervelocity Impact Using the Sph Option in Pam-Shocktm. Int. J. Impact Eng. 1997, 20(1-5):309~323
49 C. A. Wingate, R. F. Stellingwerf, R. F. Davidson, M. W. Burkett. Models of High Velocity Impact Phenomena. Int. J. Impact Eng. 1993, 14(1-4):819~830
50 J. D. Frey, F. Janicot, X. Garaud, P. Groenenboom, M. Lambert. The Validation of Hydrocodes for Orbital Debris Impact Simulation. Int. J. Impact Eng. 1993, 14(1-4):255~265
51 M. E. Kipp, D. E. Grady, J. W. Swegle. Numerical and Experimental Studies of High-Velocity Impact Fragmentation. Int. J. Impact Eng. 1993, 14:427~438
52 D. E. Grady, M. E. Kipp. Impact Failure and Fragmentation Properties ofMetals. SAND 98-0387, 1998
53 D. E. Grady, M. E. Kipp. Fragmentation Properties of Metals. Int. J. Impact Eng. 1997, 20:293~308
54 D. E. Grady, M. E. Kipp. Dynamic Fracture and Fragmentation. High-Pressure Shock Compression of Solids. 1992,
55 D. E. Grady. Local Inertial Effects in Dynamic Fragmentation. Journal of Applied Physics. 1982, 53(1):322~325
56 D. E. Grady. The Spall Strength of Condensed Matter. Journal of The Mechanics and Physics of Solids. 1998, 36(3):353~384
57 D. E. Grady, M. L. Olsen. A Statistics and Energy Based Theory of Dynamic Fragmentation. Int. J. Impact Eng. 2003, 29:293~306
58 D. E. Grady, M. E. Kipp. Geometric Statistics and Dynamic Fragmentation. Journal of Applied Physics. 1985, 58(3):1210~1222
59 D. E. Grady. Particle Size Statistics in Dynamic Fragmentation. Journal of Applied Physics. 1990, 68(12):6099~6105
60 A. J. Piekutowski. Formation and Description of Debris Cloud Produced by Hypervelocity Impact. NASA CR-4707, 1996:98~99
61 A. J. Piekutowski. Effects of Scale on Debris Cloud Properties. Int. J. Impact Engng. 1997, 20:639-650
62 A. J. Piekutowski. Fragmentation-Initiation Threshold for Spheres Impacting at Hypervelocity. Int. J. Impact Eng. 2003, 29:563~574
63 A. J. Piekutowski. Characteristics of Debris Clouds Produced by Hypervelocity Impact of Aluminum Spheres with Thin Aluminum Sheets. NASA CR-201003, 1995
64 A. J. Piekutowski. Fragmentation of a Sphere Initiated by Hypervelocity Impact with a Thin Sheet. Int. J. Impact Eng. 1995, 17:627~638
65 A. J. Piekutowski. Debris Clouds Produced by the Hypervelocity Impact of Nonspherical Projectiles. Int. J. Impact Engng. 2001, 26:613-624
66 C. J. Maiden, A. R. McMillan. An Investigation of the Protection Afforded a Spacecraft by a Thin Shield. AIAA. 1964, 2(11):1992-1998
67 J. W. Gehring, D. R. Christman, A. R. McMillan. Experimental Studies Concerning the Meteoroid Hazard to Aerospace Materials and Structures. J. Spacecraft Rocket. 1965, 2(5):731~737
68 A. J. Stilp, V. Hohler, E. Schneider, K. Weber. Debris Cloud Expansion Studies. Int. J. Impact Eng. 1990, 10:543~553
69 W. P. Schonberg, A. J. Bean, K. Darzi. Hypervelocity Impact Physics. NASA CR-4343, 1991
70 F. Horz, M. Cintala. Dimensionally Scaled Penetration Experiments: Aluminum Targets and Glass Projectiles 50um to 3.2mm in Diameter. Int. J. Impact Eng. 1994, 15:257~280
71 L. A. Merzhievsky. Statistical Characteristics of a Debris Cloud Behind a Shied. Int. J. Impact Engng. 1997, 20:569-577
72 L. A. Merzhievsky. Crater Formation in a Plastic Target under Hypervelocity Impact. Int. J. Impact Eng. 1997, 20:557~568
73 Y. Akahoshi, T. Nakamura. Construction of Mass, Three-Dimensional and Velocity Distribution for the Second Debris Clouds. Int. J. Impact Engng. 2001, 26:1-11
74 Y. Akahoshi, M. Kaji, H. Hata. Measurement of Mass, Spray Angle and Velocity Distribution of Fragment Cloud. Int. J. Impact Engng. 2003, 29:845-853
75 H. F. Swift, R. Bamford, R. Chen. Designing Space Vehicle Shields for Meteoroid Protection a New Analysis. Adv. Space Res. 1983, 2:219~234
76 W. P. Schonberg. A Comparison of Fragmentation Models. Int. J. Impact Eng. 1995, 17:739~750
77 A. J. Piekutowski. A Simple Dynamic Model for the Formation of Debris Clouds. Int. J. Impact Eng. 1990, 10:453~471
78 C. H. Yew, D. E. Grady, R. J. Lawrence. A Simple Model for Debris Clouds Produced by Hypervelocity Particle Impact. Int. J. Impact Eng. 1993, 14:853~862
79 E. Corvonato, R. Destefanis, M. Faraud. Integral Model for the Description of the Debris Cloud Structure and Impact. Int. J. Impact Eng. 2001, 26:115~128
80 D. E. Grady, N. A. Winfree. Impact Fragmentation of High-Velocity Compact Projectiles on Thin Plates: A Physical and Statistical Characterization of Fragment Debris. Int. J. Impact Eng. 2001, 26:246~262
81 F. K. Schafer. An Engineering Fragmentation Model for the Impact of Spherical Projectiles on Thin Metallic Plates. Int. J. Impact Eng. 2006, 33:745~762
82柳森,谢爱民,黄洁,李毅,罗锦阳,石安华.超高速碰撞碎片云的激光阴影照相技术.实验流体力学. 2005, 15(2):35~39
83张伟,庞宝君,罗德坤,张泽华.柱状弹丸撞击防护屏形成碎片云材料状态特性研究研究.中国空间科学技术. 2001, (3):53-59
84张伟,庞宝君,马文来,张泽华.弹丸撞击防护屏形成碎片云速度特性研究.中国空间科学技术. 2002, 2:67~71
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87何建,唐平,王善,欧阳志为.柱形杆高速碰撞薄靶板的数值仿真.系统仿真学报. 2005, 17(9):2107~2110
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89王海福,江增荣,蒋建委.高速碰撞下二次破片光滑粒子流体力学数值模拟.北京理工大学学报. 2004, 24(7):583~586
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91柳森,李毅,黄洁,罗锦阳,谢爱民,石安华.用于验证数值仿真的whipple屏超高速撞击实验结果.宇航学报. 2002, 26(4):505~508
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112 C. E. Anderson, T. G. Trucano, S. A. Mullin. Debris Cloud Dynamics. int. J. Impact Eng. 1990, 9:89~113
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2 R. Reynolds. Debris Environment Interactions with Low Earth Orbit Constellations. Proceedings of the Second Europe Conference on Space Debris, ESOC, Darmstadt, Germany, 1997
3庞宝君,韩增尧.建立空间碎片防护设计工程体系提高航天器在轨安全能力.中国第三届空间碎片会议文集,北京, 2005
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11 R. Destefanis, M. Callea. Meteoroid and Debris Impacts on Orbiting Structures: A Methodology. Proceeding of 1st European Conference on Space Debris. Darmstadt, Germany, 1993:523~533
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13 P. D. Anz-meador. Density and Mass Distributions of Orbital Debris. Acta Astronautica. 1996, 38(12):927~936
14 F. Alby, E. Lansard, T. Michal. Collision of Cerise with Space Debris. Proceeding of 2ed European Conference on Space Debris, Darmstadt, Germany, 1997:589~596
15 E. L. Christiansen. Design and Performance Equations for Advanced Meteoroid and Debris Shields. Int. J. Impact Eng. 1993, 14:145~156
16 J. Davey, E. A. Taylor. Development of Iso Standards Addressing Mitigation of Orbital Debris. Proceeding the 4th European Conference on Space Debris,Darmstadt, Germany, 2005:145~156
17 F. L. Whipple. Meteorites and Space Travel. The Astronomical Journal. 1947, 52:132-137
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20 R. Janovsky, I. Kalninsch, A. Stichternath. The Meteoroid and Debris Protection System for the Atv-Spacecraft. Acta Astronautica. 2000, 47(2-9):281~287
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23李清源.哥伦布航天器对轨道碎片撞击危害的设计考虑.强度与环境. 1997, (3):47~54
24张伟,庞宝君,张泽华,邹经湘.航天器空间碎片防护方案的评价方法.中国空间科学技术. 1998, (6):30~36
25张伟,庞宝君,邹经湘,张泽华.航天器微流星和空间碎片的防护方案.哈尔滨工业大学学报. 1999, 32(2):18~22
26 M. Lamber, E. Schneider. Shield against Space Debris. A Comparison between Different Shield: The Effect of Materials on Their Performance. Int. J. Impact Eng. 1995, 17(4-6):477~485
27钱伟长.穿甲力学.国防工业出版社. 1984
28 R. Kinslow. High-Velocity Impact Phenomena. Academic Press. 1970
29张庆明,黄凤雷.超高速碰撞动力学引论.科学出版社. 2000
30马晓青,韩峰.高速碰撞动力学.国防工业出版社. 1998
31 W. C. Turpin, J. M. Carson. Hole Growth in Thin Plates Perforated by Hypervelocity Pellets. AFML-TR-70-83, 1970
32 A. C. Charters. The Early Years of Aerodynamics Ranges, Light-Gas Guns, and High-Velocity Impact. Int. J. Impact Eng. 1995, 17:151~182
33王金贵.二级轻气炮超高速弹丸发射技术的研究.高压物理学报. 1992, 6(4):264~272
34沈金华,贾浩.电磁轨道炮及其应用.爆炸与冲击. 1984, 4(2):90-96
35周之奎,陈素年,邓利文.电热炮原理实验研究.爆炸与冲击. 1993, 13(2):186-192
36徐兴海,高顺受,陈素年.一种电炮装置.爆炸与冲击. 1982, (4):67-69
37 B. Stever, R. Frank. A Plasma Drag Hypervelocity Particle Accelerator. Int. J. Impact Eng. 1999, 23:67~76
38 J. D. Walker, D. J. Grosch. A Hypervelocity Fragment Launcher Based on an Inhibited Shaped Charge. Int. J. Impact Engng. 1993, 14:763-774
39张文兵.地基模拟空间碎片速度测试技术.航天器环境工程. 2006, 23(3):138~142
40 J. Williamsen, E. Howard. Video Imaging of Debris Clouds Following Penetration of Lightweight Spacecraft Materials. Int. J. Impact Eng. 2001, 26(1-10):865~877
41 M. L. Wilkins. Computer Simulation of Dynamic Phenomena. Springer. 1999
42 S. Hiermaier, D. Konke, A. J. Stilp, K. Thoma. Computational Simulation of the Hypervelocity Impact of Al-Spheres on Thin Plates of Different Materials. Int. J. Impact Eng. 1997, 20:363~374
43 D. Palmieri, M. Faraud, R. Destefanis. Whipple Shied Ballistic at Impact Velocity Higher Than 7 Km/S. Int. J. Impact Eng. 2001, 26:579~590
44张伟,庞宝君,贾斌,曲焱喆.弹丸超高速撞击防护屏碎片云数值模拟.高压物理学报. 2004, 18(1):47~52
45 C. J. Hayhurst, R. Clegg. A Cylindrically Symmetric Sph Simulations of Hypervelocity Impacts on Thin Plates. Int. J. Impact Eng. 1997, 20:337~348
46 T. G. Trucano, J. M. McGlaun. Hypervelocity Impact Calculations Using Cth: Case Studies. Int. J. Impact Eng. 1990, 10(1-4):601~613
47 J. M. McGlaun, S. L. Thompson, M. G. Elrick. Cth: A Three-Dimensional Shock Wave Physics Code. Int. J. Impact Eng. 1990, 10(1-4):351~360
48 P. H. L. Groenenboom. Groenenboom Numerical Simulation of 2d and 3d Hypervelocity Impact Using the Sph Option in Pam-Shocktm. Int. J. Impact Eng. 1997, 20(1-5):309~323
49 C. A. Wingate, R. F. Stellingwerf, R. F. Davidson, M. W. Burkett. Models of High Velocity Impact Phenomena. Int. J. Impact Eng. 1993, 14(1-4):819~830
50 J. D. Frey, F. Janicot, X. Garaud, P. Groenenboom, M. Lambert. The Validation of Hydrocodes for Orbital Debris Impact Simulation. Int. J. Impact Eng. 1993, 14(1-4):255~265
51 M. E. Kipp, D. E. Grady, J. W. Swegle. Numerical and Experimental Studies of High-Velocity Impact Fragmentation. Int. J. Impact Eng. 1993, 14:427~438
52 D. E. Grady, M. E. Kipp. Impact Failure and Fragmentation Properties ofMetals. SAND 98-0387, 1998
53 D. E. Grady, M. E. Kipp. Fragmentation Properties of Metals. Int. J. Impact Eng. 1997, 20:293~308
54 D. E. Grady, M. E. Kipp. Dynamic Fracture and Fragmentation. High-Pressure Shock Compression of Solids. 1992,
55 D. E. Grady. Local Inertial Effects in Dynamic Fragmentation. Journal of Applied Physics. 1982, 53(1):322~325
56 D. E. Grady. The Spall Strength of Condensed Matter. Journal of The Mechanics and Physics of Solids. 1998, 36(3):353~384
57 D. E. Grady, M. L. Olsen. A Statistics and Energy Based Theory of Dynamic Fragmentation. Int. J. Impact Eng. 2003, 29:293~306
58 D. E. Grady, M. E. Kipp. Geometric Statistics and Dynamic Fragmentation. Journal of Applied Physics. 1985, 58(3):1210~1222
59 D. E. Grady. Particle Size Statistics in Dynamic Fragmentation. Journal of Applied Physics. 1990, 68(12):6099~6105
60 A. J. Piekutowski. Formation and Description of Debris Cloud Produced by Hypervelocity Impact. NASA CR-4707, 1996:98~99
61 A. J. Piekutowski. Effects of Scale on Debris Cloud Properties. Int. J. Impact Engng. 1997, 20:639-650
62 A. J. Piekutowski. Fragmentation-Initiation Threshold for Spheres Impacting at Hypervelocity. Int. J. Impact Eng. 2003, 29:563~574
63 A. J. Piekutowski. Characteristics of Debris Clouds Produced by Hypervelocity Impact of Aluminum Spheres with Thin Aluminum Sheets. NASA CR-201003, 1995
64 A. J. Piekutowski. Fragmentation of a Sphere Initiated by Hypervelocity Impact with a Thin Sheet. Int. J. Impact Eng. 1995, 17:627~638
65 A. J. Piekutowski. Debris Clouds Produced by the Hypervelocity Impact of Nonspherical Projectiles. Int. J. Impact Engng. 2001, 26:613-624
66 C. J. Maiden, A. R. McMillan. An Investigation of the Protection Afforded a Spacecraft by a Thin Shield. AIAA. 1964, 2(11):1992-1998
67 J. W. Gehring, D. R. Christman, A. R. McMillan. Experimental Studies Concerning the Meteoroid Hazard to Aerospace Materials and Structures. J. Spacecraft Rocket. 1965, 2(5):731~737
68 A. J. Stilp, V. Hohler, E. Schneider, K. Weber. Debris Cloud Expansion Studies. Int. J. Impact Eng. 1990, 10:543~553
69 W. P. Schonberg, A. J. Bean, K. Darzi. Hypervelocity Impact Physics. NASA CR-4343, 1991
70 F. Horz, M. Cintala. Dimensionally Scaled Penetration Experiments: Aluminum Targets and Glass Projectiles 50um to 3.2mm in Diameter. Int. J. Impact Eng. 1994, 15:257~280
71 L. A. Merzhievsky. Statistical Characteristics of a Debris Cloud Behind a Shied. Int. J. Impact Engng. 1997, 20:569-577
72 L. A. Merzhievsky. Crater Formation in a Plastic Target under Hypervelocity Impact. Int. J. Impact Eng. 1997, 20:557~568
73 Y. Akahoshi, T. Nakamura. Construction of Mass, Three-Dimensional and Velocity Distribution for the Second Debris Clouds. Int. J. Impact Engng. 2001, 26:1-11
74 Y. Akahoshi, M. Kaji, H. Hata. Measurement of Mass, Spray Angle and Velocity Distribution of Fragment Cloud. Int. J. Impact Engng. 2003, 29:845-853
75 H. F. Swift, R. Bamford, R. Chen. Designing Space Vehicle Shields for Meteoroid Protection a New Analysis. Adv. Space Res. 1983, 2:219~234
76 W. P. Schonberg. A Comparison of Fragmentation Models. Int. J. Impact Eng. 1995, 17:739~750
77 A. J. Piekutowski. A Simple Dynamic Model for the Formation of Debris Clouds. Int. J. Impact Eng. 1990, 10:453~471
78 C. H. Yew, D. E. Grady, R. J. Lawrence. A Simple Model for Debris Clouds Produced by Hypervelocity Particle Impact. Int. J. Impact Eng. 1993, 14:853~862
79 E. Corvonato, R. Destefanis, M. Faraud. Integral Model for the Description of the Debris Cloud Structure and Impact. Int. J. Impact Eng. 2001, 26:115~128
80 D. E. Grady, N. A. Winfree. Impact Fragmentation of High-Velocity Compact Projectiles on Thin Plates: A Physical and Statistical Characterization of Fragment Debris. Int. J. Impact Eng. 2001, 26:246~262
81 F. K. Schafer. An Engineering Fragmentation Model for the Impact of Spherical Projectiles on Thin Metallic Plates. Int. J. Impact Eng. 2006, 33:745~762
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