冲击载荷下金属材料的微结构-加载特性-层裂响应关系概述

蔡洋; 李超; 卢磊

doi:10.11858/gywlxb.20200648

冲击载荷下金属材料的微结构-加载特性-层裂响应关系概述

doi: 10.11858/gywlxb.20200648

蔡洋^1,,
李超^2,*, ,,
卢磊²

1.
顶峰多尺度科学研究所，四川成都　610027
2.
西南交通大学材料科学与工程学院，四川成都　610031

基金项目: 科学挑战计划（TZ2018001）

详细信息

作者简介:
蔡　洋（1990－），男，博士，副研究员，主要从事材料动态力学响应研究. E-mail：caiy@pims.ac.cn

通讯作者:
李　超（1990－），男，博士，助理教授，主要从事金属材料变形损伤研究. E-mail：cli@swjtu.edu.cn

中图分类号: O347.1
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出版历程
- 收稿日期: 2020-12-01
- 修回日期: 2021-02-01

Effects of Microstructure and Loading Characteristics on Spallation of Metallic Materials under Shock Loading

CAI Yang^1
,,
LI Chao^{2,*
, ,},
LU Lei²

1.
The Peac Institute of Multiscale Sciences, Chengdu 610027, Sichuan, China
2.
School of Materials Science and Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China

摘要

摘要: 鉴于冲击载荷下金属材料的变形损伤具有微结构和加载特征的依赖性，对国内外有关层裂现象的研究进展进行了简要梳理与总结。概述了晶粒尺寸、织构、晶界类型、相界和元素偏析带等结构对金属材料变形损伤的影响，重点阐述了脉冲宽度、应变率和峰值应力等加载特征对金属材料层裂强度的耦合作用，为了解冲击载荷下金属材料微结构、加载特征与变形损伤行为之间的关系提供参考。
- 损伤 /
- 层裂强度 /
- 微结构 /
- 加载特征
Abstract: Deformation and damage of metallic materials under shock loading depend on microstructure and loading characteristics. The effects of microstructures such as grain size, texture, grain boundary, phase boundary and element segregation bands on deformation and damage of metallic materials are reviewed, as well as the coupled effects of pulse duration, peak stress and strain rate on spall strength. This review provides a reference for establishing the relationship among microstructure, loading characteristics and deformation and damage behavior of metallic materials under shock loading.
- damage /
- spall strength /
- microstructure /
- loading characteristics

HTML全文

图 1 轻气炮加载装置示意图^[8]

Figure 1. Schematic setup for gas-gun experiment^[8]

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图 2 层裂原理示意图^[8]

Figure 2. Schematic illustration of spallation^[8]

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图 3 层裂强度及空隙密度与晶粒尺寸的关系^[27]

Figure 3. Contour map demonstrating the grain size dependence of spall strength as a function of void density^[27]

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图 4 金属钽层裂损伤的微结构表征^[14]

Figure 4. Microstructure characterization of spallation damage for tantalum^[14]

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图 5 不锈钢的自由面速度历史曲线^[43]

Figure 5. Representative free surface velocity histories for stainless steel^[43]

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图 6 镁合金层裂损伤的X射线计算机断层图像^[41]

Figure 6. X-ray computed tomography images of spallation damage for the magnesium alloy^[41]

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图 7 304不锈钢中的元素偏析带以及层裂损伤特征^[40]

Figure 7. Element segregation bands and damage features of 304 stainless steel^[40]

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图 8 304不锈钢层裂强度与冲击压力的关系^[40]

Figure 8. Spall strength of 304 stainless steel as a function of peak stress^[40]

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图 9 冲击加载下样品不同截面处的应力历史^[66]

Figure 9. Stress histories in different cross-sections of a sample under shock loading^[66]

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图 10 低碳钢的自由面速度历史^[28]

Figure 10. Free surface velocity histories of mild carbon steel^[28]

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图 11 金属材料的层裂强度与应变率的关系^[28]

Figure 11. Spall strength of metallic materials as a function of strain rate^[28]

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图 12 低碳钢层裂强度与峰值应力的关系^[28]

Figure 12. Spall strength of mild carbon steel as a function of peak compression stress^[28]

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图 13 拉应力历史对层裂强度影响的示意图^[28]

Figure 13. Schematic illustration of the effect of tensile stress history on spall strength^[28]

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图 14 低碳钢层裂损伤的微结构表征及层裂强度的减少量$\Delta\sigma\rm_{tw} $与孪晶密度的关系^[28]

Figure 14. Microstructure characterization of spallation damage for mild carbon steel, and reduction in spall strength $\Delta\sigma\rm_{tw} $ as a function of deformation twin density^[28]

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参考文献(99)

[1]	WHELCHEL R L, JR SANDERS T H, THADHANI N N. Spall and dynamic yield behavior of an annealed aluminum-magnesium alloy [J]. Scripta Materialia, 2014, 92: 59–62. doi: 10.1016/j.scriptamat.2014.08.014
[2]	ANTOUN T, CURRAN D R, SEAMAN L, et al. Spall fracture [M]. New York: Springer, 2003.
[3]	TRIVEDI P, ASAY J, GUPTA Y, et al. Influence of grain size on the tensile response of aluminum under plate-impact loading [J]. Journal of Applied Physics, 2007, 102(8): 083513. doi: 10.1063/1.2798497
[4]	LUO S N, AN Q, GERMANN T C, et al. Shock-induced spall in solid and liquid Cu at extreme strain rates [J]. Journal of Applied Physics, 2009, 106(1): 013502. doi: 10.1063/1.3158062
[5]	CHEN X, ASAY J, DWIVEDI S, et al. Spall behavior of aluminum with varying microstructures [J]. Journal of Applied Physics, 2006, 99(2): 023528. doi: 10.1063/1.2165409
[6]	ARMAN B, LUO S N, GERMANN T C, et al. Dynamic response of Cu₄₆Zr₅₄ metallic glass to high-strain-rate shock loading: plasticity, spall, and atomic-level structures [J]. Physical Review B, 2010, 81(14): 144201. doi: 10.1103/PhysRevB.81.144201
[7]	JOHNSON J N, GRAY Ⅲ G T, BOURNE N K. Effect of pulse duration and strain rate on incipient spall fracture in copper [J]. Journal of Applied Physics, 1999, 86(9): 4892–4901. doi: 10.1063/1.371527
[8]	BUTCHER B, BARKER L, MUNSON D, et al. Influence of stress history on time-dependent spall in metals [J]. AIAA Journal, 1964, 2(6): 977–990. doi: 10.2514/3.2484
[9]	桂毓林, 刘仓理, 王彦平, 等. AF1410钢的层裂断裂特性研究 [J]. 高压物理学报, 2006, 20(1): 34–38. doi: 10.11858/gywlxb.2006.01.008 GUI Y L, LIU C L, WANG Y P, et al. Spall fracture properties of AF1410 steel [J]. Chinese Journal of High Pressure Physics, 2006, 20(1): 34–38. doi: 10.11858/gywlxb.2006.01.008
[10]	DAVISON L, STEVENS A, KIPP M. Theory of spall damage accumulation in ductile metals [J]. Journal of the Mechanics and Physics of Solids, 1977, 25(1): 11–28. doi: 10.1016/0022-5096(77)90017-5
[11]	GRADY D. The spall strength of condensed matter [J]. Journal of the Mechanics and Physics of Solids, 1988, 36(3): 353–384. doi: 10.1016/0022-5096(88)90015-4
[12]	HANSEN N. Hall-Petch relation and boundary strengthening [J]. Scripta Materialia, 2004, 51(8): 801–806. doi: 10.1016/j.scriptamat.2004.06.002
[13]	JR CALLISTER W D. Fundamentals of materials science and engineering [M]. London: Wiley London, 2000.
[14]	CHENG M, LI C, TANG M, et al. Intragranular void formation in shock-spalled tantalum: mechanisms and governing factors [J]. Acta Materialia, 2018, 148: 38–48. doi: 10.1016/j.actamat.2018.01.029
[15]	REMINGTON T, HAHN E, ZHAO S, et al. Spall strength dependence on grain size and strain rate in tantalum [J]. Acta Materialia, 2018, 158: 313–329. doi: 10.1016/j.actamat.2018.07.048
[16]	CHEN T, JIANG Z, PENG H, et al. Effect of grain size on the spall fracture behaviour of pure copper under plate-impact loading [J]. Strain, 2015, 51(3): 190–197. doi: 10.1111/str.12132
[17]	MINICH R W, CAZAMIAS J U, KUMAR M, et al. Effect of microstructural length scales on spall behavior of copper [J]. Metallurgical and Materials Transactions A, 2004, 35(9): 2663–2673. doi: 10.1007/s11661-004-0212-7
[18]	ESCOBEDO J, CERRETA E, DENNIS-KOLLER D. Effect of crystalline structure on intergranular failure during shock loading [J]. JOM, 2014, 66(1): 156–164. doi: 10.1007/s11837-013-0798-6
[19]	KANEL G I. Unusual behaviour of usual materials in shock waves [C]//Proceedings of the Journal of Physics Conference Series, 2014, 500: 012001.
[20]	GARKUSHIN G, IGNATOVA O, KANEL G, et al. Submicrosecond strength of ultrafine-grained materials [J]. Mechanics of Solids, 2010, 45(4): 624–632. doi: 10.3103/S0025654410040114
[21]	RAZORENOV S, GARKUSHIN G, IGNATOVA O. Resistance to dynamic deformation and fracture of tantalum with different grain and defect structures [J]. Physics of the Solid State, 2012, 54(4): 790–797. doi: 10.1134/S1063783412040233
[22]	BUCHAR J, ELICES M, CORTEZ R. The influence of grain size on the spall fracture of copper [J]. Journal de Physique Ⅳ, 1991, 1(C3): 623–630.
[23]	SCHWARTZ A J, CAZAMIAS J U, FISKE P S, et al. Grain size and pressure effects on spall strength in copper [C]//AIP Conference Proceedings. New York: American Institute of Physics, 2002.
[24]	MACKENCHERY K, VALISETTY R R, NAMBURU R R, et al. Dislocation evolution and peak spall strengths in single crystal and nanocrystalline Cu [J]. Journal of Applied Physics, 2016, 119(4): 044301. doi: 10.1063/1.4939867
[25]	DONGARE A M, RAJENDRAN A M, LAMATTINA B, et al. Atomic scale studies of spall behavior in nanocrystalline Cu [J]. Journal of Applied Physics, 2010, 108(11): 113518. doi: 10.1063/1.3517827
[26]	YUAN F, WU X. Shock response of nanotwinned copper from large-scale molecular dynamics simulations [J]. Physical Review B, 2012, 86(13): 134108. doi: 10.1103/PhysRevB.86.134108
[27]	WILKERSON J, RAMESH K. Unraveling the anomalous grain size dependence of cavitation [J]. Physical Review Letters, 2016, 117(21): 215503. doi: 10.1103/PhysRevLett.117.215503
[28]	LI C, YANG K, TANG X, et al. Spall strength of a mild carbon steel: effects of tensile stress history and shock-induced microstructure [J]. Materials Science and Engineering: A, 2019, 754: 461–469. doi: 10.1016/j.msea.2019.03.019
[29]	CAI Y, WU H A, LUO S N. A loading-dependent model of critical resolved shear stress [J]. International Journal of Plasticity, 2018, 109: 1–17. doi: 10.1016/j.ijplas.2018.03.011
[30]	TURLEY W, FENSIN S J, HIXSON R, et al. Spall response of single-crystal copper [J]. Journal of Applied Physics, 2018, 123(5): 055102. doi: 10.1063/1.5012267
[31]	PEREZ-BERGQUIST A, CERRETA E K, TRUJILLO C P, et al. Orientation dependence of void formation and substructure deformation in a spalled copper bicrystal [J]. Scripta Materialia, 2011, 65(12): 1069–1072. doi: 10.1016/j.scriptamat.2011.09.015
[32]	OWEN G, CHAPMAN D, WHITEMAN G, et al. Spall behaviour of single crystal aluminium at three principal orientations [J]. Journal of Applied Physics, 2017, 122(15): 155102. doi: 10.1063/1.4999559
[33]	LIN E, SHI H, NIU L. Effects of orientation and vacancy defects on the shock Hugoniot behavior and spallation of single-crystal copper [J]. Modelling and Simulation in Materials Science and Engineering, 2014, 22(3): 035012. doi: 10.1088/0965-0393/22/3/035012
[34]	AN Q, RAVELO R, GERMANN T C, et al. Shock compression and spallation of single crystal tantalum [C]//AIP Conference Proceedings. New York: American Institute of Physics, 2012.
[35]	HAHN E N, FENSIN S J, GERMANN T C, et al. Orientation dependent spall strength of tantalum single crystals [J]. Acta Materialia, 2018, 159: 241–248. doi: 10.1016/j.actamat.2018.07.073
[36]	KANEL G, RAZORENOV S, UTKIN A, et al. Spall strength of molybdenum single crystals [J]. Journal of Applied Physics, 1993, 74(12): 7162–7165. doi: 10.1063/1.355032
[37]	VIGNJEVIC R, BOURNE N, MILLETT J, et al. Effects of orientation on the strength of the aluminum alloy 7010-T6 during shock loading: experiment and simulation [J]. Journal of Applied Physics, 2002, 92(8): 4342–4348. doi: 10.1063/1.1505996
[38]	GRAY G, BOURNE N, VECCHIO K, et al. Influence of anisotropy (crystallographic and microstructural) on spallation in Zr, Ta, HY-100 steel, and 1080 eutectoid steel [J]. International Journal of Fracture, 2010, 163(1/2): 243–258. doi: 10.1007/s10704-009-9440-6
[39]	TAN J, LU L, LI H, et al. Anisotropic deformation and damage of dual-phase Ti-6Al-4V under high strain rate loading [J]. Materials Science and Engineering: A, 2019, 742: 532–539. doi: 10.1016/j.msea.2018.10.088
[40]	MA L, LIU J, LI C, et al. Effects of alloying element segregation bands on impact response of a 304 stainless steel [J]. Materials Characterization, 2019, 153: 294–303. doi: 10.1016/j.matchar.2019.05.015
[41]	DAI Z H, LU L, CHAI H W, et al. Mechanical properties and fracture behavior of Mg-3Al-1Zn alloy under high strain rate loading [J]. Materials Science and Engineering: A, 2020, 789: 139690.
[42]	YU X, LI T, LI L, et al. Influence of initial texture on the shock property and spall behavior of magnesium alloy AZ31B [J]. Materials Science and Engineering: A, 2017, 700: 259–268. doi: 10.1016/j.msea.2017.06.015
[43]	LI C, HUANG J, TANG X, et al. Effects of structural anisotropy on deformation and damage of a duplex stainless steel under high strain rate loading [J]. Materials Science and Engineering: A, 2017, 705: 265–272. doi: 10.1016/j.msea.2017.08.091
[44]	GALITSKIY S, IVANOV D S, DONGARE A M. Dynamic evolution of microstructure during laser shock loading and spall failure of single crystal Al at the atomic scales [J]. Journal of Applied Physics, 2018, 124(20): 205901. doi: 10.1063/1.5051618
[45]	KOLLER D D, HIXSON R S, GRAY Ⅲ G T, et al. Influence of shock-wave profile shape on dynamically induced damage in high-purity copper [J]. Journal of Applied Physics, 2005, 98(10): 103518. doi: 10.1063/1.2128493
[46]	YU Y, LI C, MA H H, et al. Deformation and spallation of explosive welded steels under gas gun shock loading [J]. Chinese Physics Letters, 2018, 35(1): 104–108.
[47]	LI C, LI B, HUANG J Y, et al. Spall damage of a mild carbon steel: effects of peak stress, strain rate and pulse duration [J]. Materials Science and Engineering: A, 2016, 660: 139–147. doi: 10.1016/j.msea.2016.02.080
[48]	MEYERS M A. Dynamic behavior of materials [M]. John Wiley & Sons, 1994.
[49]	ESCOBEDO J P, CERRETA E K, DENNIS-KOLLER D, et al. Influence of boundary structure and near neighbor crystallographic orientation on the dynamic damage evolution during shock loading [J]. Philosophical Magazine, 2013, 93(7): 833–846. doi: 10.1080/14786435.2012.734638
[50]	WAYNE L, KRISHNAN K, DIGIACOMO S, et al. Statistics of weak grain boundaries for spall damage in polycrystalline copper [J]. Scripta Materialia, 2010, 63(11): 1065–1068. doi: 10.1016/j.scriptamat.2010.08.003
[51]	BROWN A D, WAYNE L, PHAM Q, et al. Microstructural effects on damage nucleation in shock-loaded polycrystalline copper [J]. Metallurgical and Materials Transactions A, 2015, 46(10): 4539–4547. doi: 10.1007/s11661-014-2482-z
[52]	FENSIN S, VALONE S, CERRETA E, et al. Influence of grain boundary properties on spall strength: grain boundary energy and excess volume [J]. Journal of Applied Physics, 2012, 112(8): 083529. doi: 10.1063/1.4761816
[53]	FENSIN S, VALONE S, CERRETA E, et al. Effect of grain boundary structure on plastic deformation during shock compression using molecular dynamics [J]. Modelling and Simulation in Materials Science and Engineering, 2012, 21(1): 015011.
[54]	ZHANG W, KENNEDY G B, MULY K, et al. Effect of aging state on shock induced spall behavior of ultrahigh strength Al-Zn-Mg-Cu alloy [J]. International Journal of Impact Engineering, 2020, 146: 103725. doi: 10.1016/j.ijimpeng.2020.103725
[55]	ZHOU T T, HE A M, WANG P, et al. Spall damage in single crystal Al with helium bubbles under decaying shock loading via molecular dynamics study [J]. Computational Materials Science, 2019, 162: 255–267. doi: 10.1016/j.commatsci.2019.02.019
[56]	RAZORENOV S, KANEL G, HERRMANN B, et al. Influence of nano-size inclusions on spall fracture of copper single crystals [C]//AIP Conference Proceedings. New York: American Institute of Physics, 2007.
[57]	FENSIN S J, WALKER E K, CERRETA E K, et al. Dynamic failure in two-phase materials [J]. Journal of Applied Physics, 2015, 118(23): 235305. doi: 10.1063/1.4938109
[58]	TANG X, LI C, LI H, et al. Cup-cone structure in spallation of bulk metallic glasses [J]. Acta Materialia, 2019, 178: 219–227. doi: 10.1016/j.actamat.2019.08.006
[59]	TANG X, JIAN W, HUANG J, et al. Spall damage of a Ta particle-reinforced metallic glass matrix composite under high strain rate loading [J]. Materials Science and Engineering: A, 2018, 711: 284–292. doi: 10.1016/j.msea.2017.11.032
[60]	CHEN J, TSCHOPP M A, DONGARE A M. Shock wave propagation and spall failure of nanocrystalline Cu/Ta alloys: effect of Ta in solid-solution [J]. Journal of Applied Physics, 2017, 122(22): 225901. doi: 10.1063/1.5001761
[61]	CHEN J, MATHAUDHU S N, THADHANI N, et al. Unraveling the role of interfaces on the spall failure of Cu/Ta multilayered systems [J]. Scientific Reports, 2020, 10(1): 1–15. doi: 10.1038/s41598-019-56847-4
[62]	HAN W, CERRETA E, MARA N, et al. Deformation and failure of shocked bulk Cu-Nb nanolaminates [J]. Acta Materialia, 2014, 63: 150–161. doi: 10.1016/j.actamat.2013.10.019
[63]	YANG Y, JIANG Z, WANG C, et al. Effects of the phase interface on initial spallation damage nucleation and evolution in dual phase titanium alloy [J]. Materials Science and Engineering: A, 2018, 731: 385–393. doi: 10.1016/j.msea.2018.06.066
[64]	YANG Y, WANG H, WANG C, et al. Effects of the phase interface on spallation damage nucleation and evolution in dual-phase steel [J]. Steel Research International, 2020, 91(6): 1900583. doi: 10.1002/srin.201900583
[65]	RIVERA-DIAZ-DEL-CASTILLO P, VAN DER ZWAAG S, SIETSMA J. A model for ferrite/pearlite band formation and prevention in steels [J]. Metallurgical and Materials Transactions A, 2004, 35(2): 425–433. doi: 10.1007/s11661-004-0353-8
[66]	KANEL G. Spall fracture: methodological aspects, mechanisms and governing factors [J]. International Journal of Fracture, 2010, 163(1): 173–91.
[67]	MEYERS M. Shock waves and high-strain-rate phenomena in metals: concepts and applications [M]. New York: Springer Science & Business Media, 2012.
[68]	LUO S N, GERMANN T C, AN Q, et al. Shock-induced spall in copper: the effects of anisotropy, temperature, defects and loading pulse [C]//AIP Conference Proceedings. New York: American Institute of Physics, 2009.
[69]	GRAY Ⅲ G T, BOURNE N K, HENRIE B L. On the influence of loading profile upon the tensile failure of stainless steel [J]. Journal of Applied Physics, 2007, 101(9): 093507. doi: 10.1063/1.2720099
[70]	CAI Y, WU H A, LUO S N. Spall strength of liquid copper and accuracy of the acoustic method [J]. Journal of Applied Physics, 2017, 121(10): 105901. doi: 10.1063/1.4978251
[71]	MOSHE E, ELIEZER S, DEKEL E, et al. An increase of the spall strength in aluminum, copper, and Metglas at strain rates larger than 10⁷ s⁻¹ [J]. Journal of Applied Physics, 1998, 83(8): 4004–4011. doi: 10.1063/1.367222
[72]	JONES D R, FENSIN S J, MARTINEZ D T, et al. Effect of peak stress and tensile strain-rate on spall in tantalum [J]. Journal of Applied Physics, 2018, 124(8): 085901. doi: 10.1063/1.5045045
[73]	TULER F R, BUTCHER B M. A criterion for the time dependence of dynamic fracture [J]. International Journal of Fracture Mechanics, 1968, 4(4): 431–437.
[74]	HAHN E N, GERMANN T C, RAVELO R, et al. On the ultimate tensile strength of tantalum [J]. Acta Materialia, 2017, 126: 313–328. doi: 10.1016/j.actamat.2016.12.033
[75]	WHITEMAN G, KEIGHTLEY P, MILLETT J. The behaviour of 2169 steel under uniaxial stress and uniaxial strain loading [J]. Journal of Dynamic Behavior of Materials, 2016, 2(3): 337–346. doi: 10.1007/s40870-016-0069-z
[76]	PAVLENKO A V, MALUGINA S, KAZAKOV D N, et al. Plastic deformation and spall fracture of structural 12Cr18Ni10Ti steel [C]//AIP Conference Proceedings. New York: American Institute of Physics, 2012.
[77]	STEVENS A, TULER F. Effect of shock precompression on the dynamic fracture strength of 1020 steel and 6061-T6 aluminum [J]. Journal of Applied Physics, 1971, 42(13): 5665–5670. doi: 10.1063/1.1659997
[78]	WANG G. Influence of shock pre-compression stress and tensile strain rate on the spall behaviour of mild steel [J]. Strain, 2011, 47(5): 398–404. doi: 10.1111/j.1475-1305.2009.00700.x
[79]	NGUYEN T, LUSCHER D, WILKERSON J. A physics-based model and simple scaling law to predict the pressure dependence of single crystal spall strength [J]. Journal of the Mechanics and Physics of Solids, 2020, 137: 103875. doi: 10.1016/j.jmps.2020.103875
[80]	WANG Y, HE H, WANG L. Critical damage evolution model for spall failure of ductile metals [J]. Mechanics of Materials, 2013, 56: 131–141. doi: 10.1016/j.mechmat.2012.10.004
[81]	ZENG Z H, LI X Z, LI C, et al. Deformation twinning in a mild steel: loading dependence and strengthening [J]. Materials Science and Engineering: A, 2019, 751: 332–339. doi: 10.1016/j.msea.2019.02.079
[82]	LI C, ZENG Z H, LI Y, et al. Shock-induced twinning and texture in a mild carbon steel [J]. Materials Science and Engineering: A, 2020, 773: 138832.
[83]	CURRAN D, SEAMAN L, SHOCKEY D. Dynamic failure of solids [J]. Physics Reports, 1987, 147(5/6): 253–388. doi: 10.1016/0370-1573(87)90049-4
[84]	SEAMAN L, CURRAN D R, SHOCKEY D A. Computational models for ductile and brittle fracture [J]. Journal of Applied Physics, 1976, 47(11): 4814–4826. doi: 10.1063/1.322523
[85]	TONG W, RAVICHANDRAN G. Inertial effects on void growth in porous viscoplastic materials [J]. ASME Journal of Applied Mechanics, 1995, 62(3): 633–639. doi: 10.1115/1.2895993
[86]	WU X, RAMESH K, WRIGHT T. The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading [J]. Journal of the Mechanics and Physics of Solids, 2003, 51(1): 1–26. doi: 10.1016/S0022-5096(02)00079-0
[87]	WILKERSON J, RAMESH K. A dynamic void growth model governed by dislocation kinetics [J]. Journal of the Mechanics and Physics of Solids, 2014, 70: 262–280. doi: 10.1016/j.jmps.2014.05.018
[88]	THOMASON P. Ductile spallation fracture and the mechanics of void growth and coalescence under shock-loading conditions [J]. Acta Materialia, 1999, 47(13): 3633–3646. doi: 10.1016/S1359-6454(99)00223-2
[89]	CHEN D, TAN H, YU Y, et al. A void coalescence-based spall model [J]. International Journal of Impact Engineering, 2006, 32(11): 1752–1767. doi: 10.1016/j.ijimpeng.2005.04.009
[90]	白以龙, 柯孚久, 夏蒙棼. 固体中微裂纹系统统计演化的基本描述 [J]. 力学学报, 1991, 23(3): 290–298. BAI Y L, KE F J, XIA M F. Formulation of statistical evolution of microcracks in solids [J]. Chinese Journal of Theoretical and Applied Mechani, 1991, 23(3): 290–298.
[91]	GURSON A. Plastic flow and fracture behavior of ductile materials incorporating void nucleation, growth and coalescence [D]. Providence, RI: Brown University, 1975.
[92]	TVERGAARD V. Material failure by void growth to coalescence [J]. Advances in Applied Mechanics, 1990, 27: 83–151.
[93]	BENZERGA A, LEBLOND J. Ductile fracture by void growth to coalescence [J]. Advances in Applied Mechanics, 2010, 44: 169–305.
[94]	TANG X C, YAO X H, WILKERSON J W. A micromechanics-based framework to predict transitions between dimple and cup-cone fracture modes in shocked metallic glasses [J]. International Journal of Plasticity, 2021, 137: 102884. doi: 10.1016/j.ijplas.2020.102884
[95]	JIANG M Q, DAI L H. On the origin of shear banding instability in metallic glasses [J]. Journal of the Mechanics and Physics of Solids, 2009, 57(8): 1267–1292. doi: 10.1016/j.jmps.2009.04.008
[96]	CORTES R. The growth of microvoids under intense dynamic loading [J]. International Journal of Solids and Structures, 1992, 29(11): 1339–1350. doi: 10.1016/0020-7683(92)90082-5
[97]	SEAMAN L, CURRAN D R. Inertia and temperature effects in void growth [C]//AIP Conference Proceedings. New York: American Institute of Physics, 2002, 620: 607–610.
[98]	封加波. 金属动态延性破坏的损伤度函数模型[D]. 北京: 北京理工大学, 1992.
[99]	王永刚. 延性金属动态拉伸断裂及其临界损伤度研究[D]. 绵阳: 中国工程物理研究院, 2006.