A review on rate-temperature coupling response and dynamic constitutive relation of metallic materials
-
摘要: 金属材料在冲击、爆炸等高应变率加载下的塑性流动行为具有不同于静载下的率-温耦合性和微观机制。航空航天、航海、能源开采、核工业、公共安全、灾害防治等方面的金属结构设计与性能评估需要进行大量的动载实验和数值模拟，建立准确的材料动态本构模型是结构数值模拟可靠性的基础和关键。本文中，总结了金属材料的率-温耦合变形行为及内在机理，回顾了金属动态本构关系研究的起源与发展脉络，分别针对唯象模型、具有物理基础的模型和人工神经网络模型进行了详细介绍和横向比较。唯象模型和人工神经网络模型分别因易应用和高预测精度而受到青睐，基于物理概念的宏观连续介质模型可以描述体现内部演化的真实物理量，从而涵盖更大的应变范围，更好地反映应变率、温度和应变的影响机制。Abstract: Different from static loading conditions, the plastic flow behavior of metallic materials under high strain rate loadings, such as impact and explosion, exhibits special rate-temperature coupling effect and deformation micro-mechanism. The design and evaluation of metallic structures used in aerospace and navigation, energy mining, nuclear industry, public safety, disaster prevention, etc. require a large number of experiments under dynamic loadings. In recent years, the rapid-developing computational mechanics can be used to analyze the structural mechanical response under complex loading, evaluate the structural safety and optimize the structural design, and can also save the experimental costs. Accurate dynamic constitutive description of materials is the basis for the reliability of structural numerical simulation. In this paper, the dynamic plastic deformation behavior and micro-mechanism of metals, as well as the origin and development of the dynamic constitutive relationship of metals are reviewed and summarized. Over wide ranges of strain rate and temperature, the metals exhibit complex rate-temperature coupling effect, such as dynamic strain aging and segmented strain rate sensitivity. The high strain rate may lead to dynamic recrystallization, deformation twinning and shock-induced phase transition. The existing constitutive models can be divided into three types: phenomenological models, physically based models and artificial neural network models. Phenomenological models refer to the constitutive models established merely by describing experimental phenomena without considering the internal physical mechanism. Physically based macro-scale continuum models can represent true physical quantities for documenting and tracking the evolution which takes place within metallic materials. Artificial neural network models are good at reproducing the plastic flow behavior as function of many factors, such as strain rate, temperature and plastic strain, without the need of identifying complex logic relationships and parameters within the system. The developments, prediction capabilities, and application scopes of the three types of dynamic constitutive models are illustrated in detail and compared horizontally. In addition, some objective suggestions for the further development of dynamic constitutive descriptions for metals are proposed. Phenomenological models are favored for their ease in application, artificial neural network models are favored for their high prediction accuracy. Recent trend has increased the focus on physically based models. This type of model extends application to a wider strain range and more clearly represents the influence mechanism of strain rate, temperature and strain.
-
Key words:
- metallic material /
- high strain rate /
- plastic deformation /
- dynamic constitutive model
-
图 1 低碳钢的屈服应力在不同温度和应变率区域内的应变率效应
Figure 1. Strain rate effect on yield stress of low-carbon steelin different temperature and strain rate regions
图 5 塑性流动曲线的4个阶段和绝热剪切引起的动态再结晶微观图片
Figure 5. Four stages of plastic flow curve and micro image of DRX caused by adiabatic shear
表 1 唯象动态本构模型之间的比较
Table 1. Comparison among phenomenological dynamic constitutive models
发表时间 模型名称 应变率/s−1 温度/℃ 待定参数/个 主要特点 1976 Voce-Kocks (VK) [80] 10−1 −173～327 7 饱和应力σs为温度和应变率的函数 1983 Johnson-Cook (JC)[77] 对数应变率的线性
函数，可达104温度的幂函数 5 兼顾温度和应变率效应
参数少，形式简单1992 Khan-Huang (KH) [82] 10−5～104 不考虑 5 未考虑温度效应
将总应变率分解为弹性和塑性分量1999 Khan-Huang-Liang (KHL) [83] 10−6～104 25～316 7 在KH模型基础上增加温度效应 2009 Khan-Liang-Farrokh (KLF) [115] 10−2～3×104 −50～250 9 基于KHL模型
兼顾温度和应变率效应
考虑晶粒尺寸2008 Improved Fields-Backofen (FB) model by Cheng[107] 10−1～10−4 150～300 5 兼顾温度和应变率效应
参数少，形式简单2005 Molinari-Ravichandran (MR) [81] 10−2～106 −196～200 9 基于微观结构的特征尺度
考虑温度、应变率和晶粒尺寸2010 Lin-Liu (LL) [117] 10−2～10 850～1150 8 可描述热成形过程达到应力峰值的
应力-应变曲线2010 Toros-Ozturk (TO) [118] 0.0016～0.16 室温～300 9 可描述大塑性应变下的软化行为 
下载: 导出CSV
表 2 具有物理基础的动态本构模型之间的比较
Table 2. Comparison among physically based dynamic constitutive models
年份 模型名称 建模思想 主要特点 1975 Bodner-Partom (BP) [93] 基于不可逆热力学，位错动力学和内变量理论 采用塑性功度量变形抗力
无需屈服函数
参数较少（不多于10），应用广泛1987 Zerilli-Armstrong (ZA) [45] 位错动力学理论
BCC和FCC晶体结构的塑性变形微观机制不同考虑温度、应变率和平均晶粒尺寸
不同晶体结构具有不同表达式
描述热激活区域的塑性流动行为1980 Steinberg-Guinan (SG) [94] 剪切模量和屈服应力具有相同的温度和
压强依赖性，将流体与冲击下的固体等效考虑温度、压强效应
未考虑应变率效应
（认为高应变率下应变率效应不明显）1989 Steinberg-Lund (SL) [96] 流动应力等于热分量和非热分量之和，
压强通过影响剪切模量影响流动应力考虑温度、应变率和压强效应
适用于10−4～106 s−1宽应变率范围1981 Mecking-Kocks (MK) [95] 针对FCC金属
位错累积是塑性变形主要障碍流动应力是应变硬化和率-温效应的乘积
在应变硬化项中考虑动态回复1988 Mechanical Threshold
Stress (MTS) [91]采用力学阈值应力作为内部结构参量，
不存在应变率效应的突然增大考虑温度、应变率和应变历史的影响
需要较多实验结果确定本构参数1998 Nemat-Nasser-Li (NN) [98] 位错动力学
热激活理论考虑FCC金属的应变历史对热激活行为的影响 1999 Nemat-Nasser-Guo
(NN) [100]位错动力学
热激活理论
高应变率下的黏性拖曳机制考虑高应变率加载下，金属塑性变形具有
黏性拖曳导致的强化2015 Guo-Wang (GW) [19] 位错动力学
热激活理论
动态应变时效经典理论描述第三型应变时效及其应变率效应 2021 Guo-Yuan (GY) [16] 沉淀强化理论
动态应变时效经典理论考虑晶粒尺寸、位错密度和沉淀相体积分数及尺寸
描述不同晶体结构的多相合金的塑性流动行为的区别2005 Voyiadjis-Abed (VA) [128] 位错动力学 考虑FCC和BCC金属热激活行为的区别 2008 Voyiadjis-Almasri (VA) [17] 热激活理论（热激活能与温度、应变率和
应变之间的关系）针对FCC金属，考虑应变历史的影响 2018–2020 Voyiadjis-Song (VS) [130-132] 动态应变时效发生符合韦伯概率分布 考虑动态应变时效，并结合韦伯分布进行描述 2001
2009
2010Rusinek-Klepaczko
(RK) [133-135]流动应力为描述应变强化的内应力和描述
率-温效应的有效应力之和考虑杨氏模量的温度效应
考虑动态应变时效引起的负应变率效应[134]
考虑FCC金属在高应变率下的黏性拖曳[135]2003 Preston-Tonks-Wallace
(PTW) [137]针对应变率效应机制的不同，分为3个区：
热激活控制的位错滑移区、过渡区和超高
应变率区应变率范围涵盖15个数量级
基于量纲分析法建模
考虑强冲击下非线性位错拖曳效应在塑性变形机制中
占主导地位1998 Cellular Automaton
(CA) [139]物理冶金原理
针对动态再结晶中的微观组织演化不同温度（高温）和应变率的动态再结晶
反向方法
下载: 导出CSV
-
[1] 杨桂通, 熊祝华. 塑性动力学 [M]. 北京: 清华大学出版社, 1984. [2] ARMSTRONG R W, WALLEY S M. High strain rate properties of metals and alloys [J]. International Materials Reviews, 2008, 53(3): 105–128. DOI: 10.1179/174328008X277795. [3] HOPKINSON J. On the rupture of iron wire by a blow [C] // Proceedings of the Literary and Philosophical Society of Manchester, 1872: 40–45. [4] HOPKINSON J. Further experiments on the rupture of iron wire [C] // Proceedings of the Literary and Philosophical Society of Manchester, 1872: 119–121. [5] HOPKINSON J. Original papers by the late John Hopkinson [J]. Cambridge, UK: Cambridge University Press, 1901, 2: 316–324. [6] HOPKINSON B. The effects of momentary stresses in metals [J]. Proceedings of the Royal Society of London, 1905, 74(497): 498–506. DOI: 10.1098/rspl.1904.0145. [7] CHARPY G. Note sur l’essai des métaux à la flexion par choc de barreaux entaillés [J]. Mémoires et comptes Rendus de la Société des Ingénieurs Civils de France, 1901: 848–877. [8] TÓTH L, ROSSMANITH H P, SIEWERT T A. Historical background and development of the Charpy test [J]. European Structural Integrity Society, 2002, 30: 3–19. DOI: 10.1016/S1566-1369(02)80002-4. [9] TRESCA M H. On further applications of the flow of solids [J]. Proceedings of the Institution of Mechanical Engineers, 1878, 29(1): 301–345. DOI: 10.1243/PIME_PROC_1878_029_017_02. [10] JOHNSON W. Henri Tresca as the originator of adiabatic heat lines [J]. International Journal of Mechanical Sciences, 1987, 29(5): 301–305; 307–310. DOI: 10.1016/0020-7403(87)90113-5. [11] JEFFRIES Z. Effect of temperature, deformation, and grain size on the mechanical properties of metals [J]. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers, 1919, 60: 474–576. [12] REMINGTON B A, ALLEN P, BRINGA E M, et al. Material dynamics under extreme conditions of pressure and strain rate [J]. Materials Science and Technology, 2006, 22(4): 474–488. DOI: 10.1179/174328406X91069. [13] 刘旭红, 黄西成, 陈裕泽, 等. 强动载荷下金属材料塑性变形本构模型评述 [J]. 力学进展, 2007, 37(3): 361–374. DOI: 10.3321/j.issn:1000-0992.2007.03.004.LIU X H, HUANG X C, CHEN Y Z, et al. A review on constitutive models for plastic deformation of metal materials under dynamic loading [J]. Advances in Mechanics, 2007, 37(3): 361–374. DOI: 10.3321/j.issn:1000-0992.2007.03.004. [14] SALVADO F C, TEIXEIRA-DIAS F, WALLEY S M, et al. A review on the strain rate dependency of the dynamic viscoplastic response of FCC metals [J]. Progress in Materials Science, 2017, 88: 186–231. DOI: 10.1016/j.pmatsci.2017.04.004. [15] YUAN K B, GUO W G, LI P H, et al. Thermomechanical behavior of laser metal deposited Inconel 718 superalloy over a wide range of temperature and strain rate: testing and constitutive modeling [J]. Mechanics of Materials, 2019, 135: 13–25. DOI: 10.1016/j.mechmat.2019.04.024. [16] YUAN K B, GUO W G, LI D W, et al. Influence of heat treatments on plastic flow of laser deposited Inconel 718: testing and microstructural based constitutive modeling [J]. International Journal of Plasticity, 2021, 136: 102865. DOI: 10.1016/j.ijplas.2020.102865. [17] VOYIADJIS G Z, ALMASRI A H. A physically based constitutive model for fcc metals with applications to dynamic hardness [J]. Mechanics of Materials, 2008, 40(6): 549–563. DOI: 10.1016/j.mechmat.2007.11.008. [18] 王建军, 袁康博, 张晓琼, 等. 第三型应变时效的提出与研究进展 [J]. 爆炸与冲击, 2021, 41(5): 051101. DOI: 10.11883/bzycj-2020-0422.WANG J J, YUAN K B, ZHANG X Q, et al. Proposition and research progress of the third-type strain aging [J]. Explosion and Shock Waves, 2021, 41(5): 051101. DOI: 10.11883/bzycj-2020-0422. [19] WANG J J, GUO W G, GAO X S, et al. The third-type of strain aging and the constitutive modeling of a Q235B steel over a wide range of temperatures and strain rates [J]. International Journal of Plasticity, 2015, 65: 85–107. DOI: 10.1016/j.ijplas.2014.08.017. [20] COTTRELL A H. LXXXVI. A note on the Portevin-Le Chatelier effect [J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1953, 44(355): 829–832. DOI: 10.1080/14786440808520347. [21] 钱匡武, 李效琦, 萧林钢, 等. 金属和合金中的动态应变时效现象 [J]. 福州大学学报(自然科学版), 2001, 29(6): 8–23. DOI: 10.3969/j.issn.1000-2243.2001.06.003.QIAN K W, LI X Q, XIAO L G, et al. Dynamic strain aging phenomenon in metals and alloys [J]. Journal of Fuzhou University (Natural Science), 2001, 29(6): 8–23. DOI: 10.3969/j.issn.1000-2243.2001.06.003. [22] 郭伟国, 左红星, 孟卫华, 等. 第三种应变时效与机械波谱关联性探讨 [J]. 材料科学与工艺, 2012, 20(1): 128–134. DOI: 10.11951/j.issn.1005-0299.20120126.GUO W G, ZUO H X, MENG W H, et al. Discussion of the relevancy of the third-type strain aging and mechanical spectroscopy [J]. Materials Science and Technology, 2012, 20(1): 128–134. DOI: 10.11951/j.issn.1005-0299.20120126. [23] GILAT A, WU X R. Plastic deformation of 1020 steel over a wide range of strain rates and temperatures [J]. International Journal of Plasticity, 1997, 13(6/7): 611–632. DOI: 10.1016/S0749-6419(97)00028-4. [24] CHENG J Y, NEMAT-NASSER S. A model for experimentally-observed high-strain-rate dynamic strain aging in titanium [J]. Acta Materialia, 2000, 48(12): 3131–3144. DOI: 10.1016/S1359-6454(00)00124-5. [25] GUO W G, GAO X S. On the constitutive modeling of a structural steel over a range of strain rates and temperatures [J]. Materials Science and Engineering: A, 2013, 561: 468–476. DOI: 10.1016/j.msea.2012.10.065. [26] 孟卫华, 郭伟国, 苏静, 等. DH-36钢的塑性流动统一本构关系研究 [J]. 力学学报, 2011, 43(5): 958–962. DOI: 10.6052/0459-1879-2011-5-lxxb2010-676.MENG W H, GUO W G, SU J, et al. Study of plastic flow unified constitutive relation for steel DH-36 [J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 958–962. DOI: 10.6052/0459-1879-2011-5-lxxb2010-676. [27] 孟卫华, 郭伟国, 王建军, 等. DH36钢拉伸塑性流动特性及本构关系 [J]. 爆炸与冲击, 2013, 33(4): 438–443. DOI: 10.11883/1001-1455(2013)04-0438-06.MENG W H, GUO W G, WANG J J, et al. Tensile plasticity flow characteristics of DH36 steel and its constitutive relation [J]. Explosion and Shock Waves, 2013, 33(4): 438–443. DOI: 10.11883/1001-1455(2013)04-0438-06. [28] HONG S I. Influence of dynamic strain aging on the apparent activation volume for deformation [J]. Materials Science and Engineering, 1985, 76: 77–81. DOI: 10.1016/0025-5416(85)90082-5. [29] LEE K W, KIM S K, KIM K T, et al. Ductility and strain rate sensitivity of zircaloy-4 nuclear fuel claddings [J]. Journal of Nuclear Materials, 2001, 295(1): 21–26. DOI: 10.1016/S0022-3115(01)00509-8. [30] LEE K O, LEE S B. Modeling of materials behavior at various temperatures of hot isostatically pressed superalloys [J]. Materials Science and Engineering: A, 2012, 541: 81–87. DOI: 10.1016/j.msea.2012.02.005. [31] SU J, GUO W, MENG W, et al. Plastic behavior and constitutive relations of DH-36 steel over a wide spectrum of strain rates and temperatures under tension [J]. Mechanics of Materials, 2013, 65: 76–87. DOI: 10.1016/j.mechmat.2013.06.002. [32] LIN Y C, CHEN X M. A critical review of experimental results and constitutive descriptions for metals and alloys in hot working [J]. Materials & Design, 2011, 32(4): 1733–1759. DOI: 10.1016/j.matdes.2010.11.048. [33] MEYERS M A, NESTERENKO V F, LASALVIA J C, et al. Observation and modeling of dynamic recrystallization in high-strain, high-strain rate deformation of metals [J]. Journal de Physique Ⅳ, 2000, 10(PR9): 51–56. DOI: 10.1051/jp4:2000909. [34] XU Y B, ZHANG J H, BAI Y L, et al. Shear localization in dynamic deformation: microstructural evolution [J]. Metallurgical and Materials Transactions A, 2008, 39(4): 811–843. DOI: 10.1007/s11661-007-9431-z. [35] WRIGHT T W. Physics and mathematics of adiabatic shear bands [M]. Cambridge, UK: Cambridge University Press, 2002. [36] GREBE H A, PAK H R, MEYERS M A. Adiabatic shear localization in titanium and Ti-6 pct Al-4 pct V alloy [J]. Metallurgical Transactions A, 1985, 16(5): 761–775. DOI: 10.1007/BF02814827. [37] RITTEL D, LANDAU P, VENKERT A. Dynamic recrystallization as a potential cause for adiabatic shear failure [J]. Physical Review Letters, 2008, 101(16): 165501. DOI: 10.1103/PhysRevLett.101.165501. [38] READ H E, TRIPLETT J R, CECIL R A. Dislocation dynamics and the formulation of constitutive equations for rate-dependent plastic flow in metals [R]. La Jolla, CA, USA: Systems Science and Software, 1970. [39] MURR L E, MEYERS M A, NIOU C S, et al. Shock-induced deformation twinning in tantalum [J]. Acta Materialia, 1997, 45(1): 157–175. DOI: 10.1016/S1359-6454(96)00145-0. [40] 李小飞, 左汝林, 林崇智. 镁合金塑性变形过程中孪生行为的研究 [J]. 热加工工艺, 2012, 41(4): 32–35. DOI: 10.3969/j.issn.1001-3814.2012.04.010.LI X F, ZUO R L, LIN C Z. Research on twinning behavior in plastic deformation of Mg alloy [J]. Hot Working Technology, 2012, 41(4): 32–35. DOI: 10.3969/j.issn.1001-3814.2012.04.010. [41] BARRETT C S, HALLER C T J R. Twinning in polycrystalline magnesium [J]. Transactions of the American Institute of Mining and Metallurgical Engineers, 1947, 171: 246–255. [42] MURR L E, ESQUIVEL E V. Observations of common microstructural issues associated with dynamic deformation phenomena: twins, microbands, grain size effects, shear bands, and dynamic recrystallization [J]. Journal of Materials Science, 2004, 39(4): 1153–1168. DOI: 10.1023/B:JMSC.0000013870.09241.c0. [43] CARRINGTON W E, GAYLER M L V. The use of flat-ended projectiles for determining dynamic yield stress Ⅲ: changes in microstructure caused by deformation under impact at high-striking velocities [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1948, 194(1038): 323–331. DOI: 10.1098/rspa.1948.0083. [44] MEYERS M A, XU Y B, XUE Q, et al. Microstructural evolution in adiabatic shear localization in stainless steel [J]. Acta Materialia, 2003, 51(5): 1307–1325. DOI: 10.1016/S1359-6454(02)00526-8. [45] ZERILLI F J, ARMSTRONG R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations [J]. Journal of Applied Physics, 1987, 61(5): 1816–1825. DOI: 10.1063/1.338024. [46] 唐志平. 冲击相变 [M]. 北京: 科学出版社, 2008. [47] 唐志平. 冲击相变研究的现状与趋势 [J]. 高压物理学报, 1994, 8(1): 14–22. DOI: 10.11858/gywlxb.1994.01.003.TANG Z P. Some topics in shock-induced phase transitions [J]. Chinese Journal of High Pressure Physics, 1994, 8(1): 14–22. DOI: 10.11858/gywlxb.1994.01.003. [48] WU L, WANG K, XIAO S F, et al. Atomistic studies of shock-induced phase transformations in single crystal iron with cylindrical nanopores [J]. Computational Materials Science, 2016, 122: 1–10. DOI: 10.1016/j.commatsci.2016.05.010. [49] HUANG Y F, XIONG Y N, LI P, et al. Atomistic studies of shock-induced plasticity and phase transition in iron-based single crystal with edge dislocation [J]. International Journal of Plasticity, 2019, 114: 215–226. DOI: 10.1016/j.ijplas.2018.11.004. [50] KADAU K, GERMANN T C, LOMDAHL P S, et al. Atomistic simulations of shock-induced transformations and their orientation dependence in bcc Fe single crystals [J]. Physical Review B, 2005, 72(6): 064120. DOI: 10.1103/PhysRevB.72.064120. [51] SRINIVASAN S G, BASKES M I, WAGNER G J. Atomistic simulations of shock induced microstructural evolution and spallation in single crystal nickel [J]. Journal of Applied Physics, 2007, 101(4): 043504. DOI: 10.1063/1.2423084. [52] KALANTAR D H, BELAK J F, COLLINS G W, et al. Direct observation of the α-ε transition in shock-compressed iron via nanosecond X-ray diffraction [J]. Physical Review Letters, 2005, 95(7): 075502. DOI: 10.1103/physrevlett.95.075502. [53] HAWRELIAK J, COLVIN J D, EGGERT J H, et al. Analysis of the X-ray diffraction signal for the α-ε transition in shock-compressed iron: simulation and experiment [J]. Physical Review B, 2006, 74(18): 184107. DOI: 10.1103/PHYSREVB.74.184107. [54] HAWRELIAK J A, EL-DASHER B, LORENZANA H, et al. In situ X-ray diffraction measurements of the c/a ratio in the high-pressure ε phase of shock-compressed polycrystalline iron [J]. Physical Review B, 2011, 83(14): 144114. DOI: 10.1103/PhysRevB.83.144114. [55] LUO S N, JENSEN B J, HOOKS D E, et al. Gas gun shock experiments with single-pulse X-ray phase contrast imaging and diffraction at the Advanced Photon Source [J]. Review of Scientific Instruments, 2012, 83(7): 073903. DOI: 10.1063/1.4733704. [56] FAHR D. Stress- and strain-induced formation of martensite and its effects on strength and ductility of metastable austenitic stainless steels [J]. Metallurgical Transactions, 1971, 2(7): 1883–1892. DOI: 10.1007/BF02913420. [57] TALONEN J. Effect of strain-induced α′-martensite transformation on mechanical properties of metastable austenitic stainless steels [D]. Helsinki, Finland: Helsinki University of Technology, 2007. [58] STRINGFELLOW R G, PARKS D M, OLSON G B. A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels [J]. Acta Metallurgica et Materialia, 1992, 40(7): 1703–1716. DOI: 10.1016/0956-7151(92)90114-T. [59] BOUQUEREL J, VERBEKEN K, DE COOMAN B C. Microstructure-based model for the static mechanical behaviour of multiphase steels [J]. Acta Materialia, 2006, 54(6): 1443–1456. DOI: 10.1016/j.actamat.2005.10.059. [60] DAN W J, ZHANG W G, LI S H, et al. A model for strain-induced martensitic transformation of TRIP steel with strain rate [J]. Computational Materials Science, 2007, 40(1): 101–107. DOI: 10.1016/j.commatsci.2006.11.006. [61] GARION C, SKOCZEŃ B, SGOBBA S. Constitutive modelling and identification of parameters of the plastic strain-induced martensitic transformation in 316L stainless steel at cryogenic temperatures [J]. International Journal of Plasticity, 2006, 22(7): 1234–1264. DOI: 10.1016/j.ijplas.2005.08.002. [62] IWAMOTO T, TSUTA T. Computational simulation of the dependence of the austenitic grain size on the deformation behavior of TRIP steels [J]. International Journal of Plasticity, 2000, 16(7/8): 791–804. DOI: 10.1016/S0749-6419(99)00079-0. [63] TOMITA Y, IWAMOTO T. Computational prediction of deformation behavior of TRIP steels under cyclic loading [J]. International Journal of Mechanical Sciences, 2001, 43(9): 2017–2034. DOI: 10.1016/S0020-7403(01)00026-1. [64] TANG Z P, GUO Y B. Three-dimensional constitutive model for shock-induced phase transition with N transforming phases [C] // Conference of the APS Topical Group on Shock Compression of Condensed Matter. Seattle, USA: Association for the Advancement of High Pressure Science and Technology, 2013 [65] 郭扬波, 刘方平, 载翔宇, 等. TiNi 合金的动态伪弹性行为和率相关相变本构模型 [J]. 爆炸与冲击, 2003, 23(2): 105–110.GUO Y B, LIU F P, ZAI X Y, et al. Dynamic pseudoelastic behavior of TiNi alloys and a strain rate dependent phase transition constitutive model [J]. Explosion and Shock Waves, 2003, 23(2): 105–110. [66] BECKER R. Plasticity, tenacity and recrystallization [J]. Zeitschrift für Technische Physik, 1926, 7: 547–555. [67] EYRING H. The activated complex in chemical reactions [J]. The Journal of Chemical Physics, 1935, 3(2): 107–115. DOI: 10.1063/1.1749604. [68] TAYLOR G I. The mechanism of plastic deformation of crystals. PartⅠ: theoretical [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1934, 145(855): 362–387. DOI: 10.1098/rspa.1934.0106. [69] KAUZMAN W. Flow of solid metals from the standpoint of the chemical rate theory [J]. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers, 1941, 143(497): 57–83. [70] OROWAN E. Problems of plastic gliding [J]. Proceedings of the Physical Society, 1940, 52(1): 8. DOI: 10.1088/0959-5309/52/1/303. [71] ZENER C, HOLLOMON J H. Effect of strain rate upon plastic flow of steel [J]. Journal of Applied Physics, 1944, 15(1): 22–32. DOI: 10.1063/1.1707363. [72] TAYLOR G I. The testing of materials at high rates of loading [J]. Journal of the Institution of Civil Engineers, 1946, 26(8): 486–519. DOI: 10.1680/ijoti.1946.13699. [73] TAYLOR G I. The use of flat-ended projectiles for determining dynamic yield stressⅠ: theoretical considerations [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1948, 194(1038): 289–299. DOI: 10.1098/rspa.1948.0081. [74] WHIFFIN A C. The use of flat-ended projectiles for determining dynamic yield stressⅡ: tests on various metallic materials [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1948, 194(1038): 300–322. DOI: 10.1098/rspa.1948.0082. [75] DAVIES R M. A critical study of the Hopkinson pressure bar [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1948, 240(821): 375–457. DOI: 10.1098/rsta.1948.0001. [76] KOLSKY H. An investigation of the mechanical properties of materials at very high rates of loading [J]. Proceedings of the Physical Society: Section B, 1949, 62(11): 676–700. DOI: 10.1088/0370-1301/62/11/302. [77] JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures [C] // Proceedings of the 7th International Symposium on Ballistics. The Hague, 1983: 541–547. [78] FIELDS D S, BACKOFEN W A. Determination of strain hardening characteristics by torsion testing [C] // Proceedings, American Society for Testing and Materials. 1957, 57: 1259–1272. [79] VOCE E. The relationship between stress and strain for homogeneous deformation [J]. Journal of the Institute of Metals, 1948, 74: 537–562. [80] KOCKS U F. Laws for work-hardening and low-temperature creep [J]. Journal of Engineering Materials and Technology, 1976, 98(1): 76–85. DOI: 10.1115/1.3443340. [81] MOLINARI A, RAVICHANDRAN G. Constitutive modeling of high-strain-rate deformation in metals based on the evolution of an effective microstructural length [J]. Mechanics of Materials, 2005, 37(7): 737–752. DOI: 10.1016/j.mechmat.2004.07.005. [82] KHAN A S, HUANG S J. Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10–5 − 104 s–1 [J]. International Journal of Plasticity, 1992, 8(4): 397–424. DOI: 10.1016/0749-6419(92)90057-J. [83] KHAN A S, LIANG R Q. Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling [J]. International Journal of Plasticity, 1999, 15(10): 1089–1109. DOI: 10.1016/S0749-6419(99)00030-3. [84] KHAN A S, LIANG R Q. Behaviors of three BCC metals during non-proportional multi-axial loadings: experiments and modeling [J]. International Journal of Plasticity, 2000, 16(12): 1443–1458. DOI: 10.1016/S0749-6419(00)00016-4. [85] SEEGER A. Kristallplastizität [M] // SEEGER A, DEHLINGER U. Kristallphysik Ⅱ/Crystal Physics Ⅱ. Heidelberg, Berlin, Germany: Springer, 1958: 1–210. DOI: 10.1007/978-3-642-45890-3_1. [86] ZERILLI F J, ARMSTRONG R W. Dislocation mechanics based constitutive relations for dynamic straining to tensile instability [C] // Shock Compression of Condensed Matter–1989: Proceedings of the American Physical Society Topical Conference. Albuquerque, New Mexico, USA, 1989. [87] ZERILLI F J, ARMSTRONG R W. Description of tantalum deformation behavior by dislocation mechanics based constitutive relations [J]. Journal of Applied Physics, 1990, 68(4): 1580–1591. DOI: 10.1063/1.346636. [88] ZERILLI F J, ARMSTRONG R W. Modeling shock waves with dislocation mechanics based constitutive relations [C] // SCHMIDT S C, DICK R D, FORBES J W, et al. Shock Compression of Condensed Matter–1991. Williamsburg, Virginia, USA: Elsevier, 1992: 257–260. DOI: 10.1016/b978-0-444-89732-9.50058-3. [89] ZERILLI F J, ARMSTRONG R W. Constitutive relations for titanium and Ti-6Al-4V [J]. AIP Conference Proceedings, 1996, 370(1): 315–318. DOI: 10.1063/1.50713. [90] ZERILLI F J, ARMSTRONG R W. Dislocation mechanics based analysis of material dynamics behavior: enhanced ductility, deformation twinning, shock deformation, shear instability, dynamic recovery [J]. Journal de Physique Ⅳ, 1997, 7(C3): 637–642. DOI: 10.1051/jp4:19973109. [91] FOLLANSBEE P S, KOCKS U F. A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable [J]. Acta Metallurgica, 1988, 36(1): 81–93. DOI: 10.1016/0001-6160(88)90030-2. [92] NEMAT-NASSER S, LI Y F, ISAACS J B. Experimental/computational evaluation of flow stress at high strain rates with application to adiabatic shear banding [J]. Mechanics of Materials, 1994, 17(2/3): 111–134. DOI: 10.1016/0167-6636(94)90053-1. [93] BODNER S R, PARTOM Y. Constitutive equations for elastic-viscoplastic strain-hardening materials [J]. Journal of Applied Mechanics, 1975, 42(2): 385–389. DOI: 10.1115/1.3423586. [94] STEINBERG D J, COCHRAN S G, GUINAN M W. A constitutive model for metals applicable at high-strain rate [J]. Journal of Applied Physics, 1980, 51(3): 1498–1504. DOI: 10.1063/1.327799. [95] MECKING H, KOCKS U F. Kinetics of flow and strain-hardening [J]. Acta Metallurgica, 1981, 29(11): 1865–1875. DOI: 10.1016/0001-6160(81)90112-7. [96] STEINBERG D J, LUND C M. A constitutive model for strain rates from 10–4 to 106 s–1 [J]. Journal de Physique Colloques, 1988, 49(C3): 433–440. DOI: 10.1051/jphyscol:1988362. [97] NEMAT-NASSER S, ISAACS J B. Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and Ta-W alloys [J]. Acta Materialia, 1997, 45(3): 907–919. DOI: 10.1016/S1359-6454(96)00243-1. [98] NEMAT-NASSER S, LI Y L. Flow stress of f.c.c. polycrystals with application to OFHC Cu [J]. Acta Materialia, 1998, 46(2): 565–577. DOI: 10.1016/S1359-6454(97)00230-9. [99] NEMAT-NASSER S, GUO W G, CHENG J Y. Mechanical properties and deformation mechanisms of a commercially pure titanium [J]. Acta Materialia, 1999, 47(13): 3705–3720. DOI: 10.1016/S1359-6454(99)00203-7. [100] NEMAT-NASSER S, GUO W G, LIU M Q. Experimentally-based micromechanical modeling of dynamic response of molybdenum [J]. Scripta Materialia, 1999, 40(7): 859–872. DOI: 10.1016/S1359-6462(99)00041-X. [101] NEMAT-NASSER S, GUO W G. Flow stress of commercially pure niobium over a broad range of temperatures and strain rates [J]. Materials Science and Engineering: A, 2000, 284(1/2): 202–210. DOI: 10.1016/S0921-5093(00)00740-1. [102] NEMAT-NASSER S, GUO W G. High strain-rate response of commercially pure vanadium [J]. Mechanics of Materials, 2000, 32(4): 243–260. DOI: 10.1016/S0167-6636(99)00056-3. [103] NEMAT-NASSER S, GUO W G, KIHL D P. Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures [J]. Journal of the Mechanics and Physics of Solids, 2001, 49(8): 1823–1846. DOI: 10.1016/S0022-5096(00)00069-7. [104] NEMAT-NASSER S, GUO W G. Thermomechanical response of DH-36 structural steel over a wide range of strain rates and temperatures [J]. Mechanics of Materials, 2003, 35(11): 1023–1047. DOI: 10.1016/S0167-6636(02)00323-X. [105] NEMAT-NASSER S, GUO W G. Thermomechanical response of HSLA-65 steel plates: experiments and modeling [J]. Mechanics of Materials, 2005, 37(2/3): 379–405. DOI: 10.1016/j.mechmat.2003.08.017. [106] GUO W G, NEMAT-NASSER S. Flow stress of Nitronic-50 stainless steel over a wide range of strain rates and temperatures [J]. Mechanics of Materials, 2006, 38(11): 1090–1103. DOI: 10.1016/j.mechmat.2006.01.004. [107] CHENG Y Q, ZHANG H, CHEN Z H, et al. Flow stress equation of AZ31 magnesium alloy sheet during warm tensile deformation [J]. Journal of Materials Processing Technology, 2008, 208(1): 29–34. DOI: 10.1016/j.jmatprotec.2007.12.095. [108] LIANG R Q, KHAN A S. A critical review of experimental results and constitutive models for BCC and FCC metals over a wide range of strain rates and temperatures [J]. International Journal of Plasticity, 1999, 15(9): 963–980. DOI: 10.1016/S0749-6419(99)00021-2. [109] RULE W K, JONES S E. A revised form for the Johnson-Cook strength model [J]. International Journal of Impact Engineering, 1998, 21(8): 609–624. DOI: 10.1016/s0734-743x(97)00081-x. [110] ZHANG H J, WEN W D, CUI H T. Behaviors of IC10 alloy over a wide range of strain rates and temperatures: experiments and modeling [J]. Materials Science and Engineering: A, 2009, 504(1/2): 99–103. DOI: 10.1016/j.msea.2008.10.056. [111] WANG J J, GUO W G, LI P H, et al. Modified Johnson-Cook description of wide temperature and strain rate measurements made on a nickel-base superalloy [J]. Materials at High Temperatures, 2017, 34(3): 157–165. DOI: 10.1080/09603409.2016.1252164. [112] KHAN A S, SUH Y S, KAZMI R. Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys [J]. International Journal of Plasticity, 2004, 20(12): 2233–2248. DOI: 10.1016/j.ijplas.2003.06.005. [113] KHAN A S, ZHANG H Y. Mechanically alloyed nanocrystalline iron and copper mixture: behavior and constitutive modeling over a wide range of strain rates [J]. International Journal of Plasticity, 2000, 16(12): 1477–1492. DOI: 10.1016/S0749-6419(00)00024-3. [114] KHAN A S, SUH Y S, CHEN X, et al. Nanocrystalline aluminum and iron: mechanical behavior at quasi-static and high strain rates, and constitutive modeling [J]. International Journal of Plasticity, 2006, 22(2): 195–209. DOI: 10.1016/j.ijplas.2004.07.008. [115] FARROKH B, KHAN A S. Grain size, strain rate, and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: synthesis, experiment, and constitutive modeling [J]. International Journal of Plasticity, 2009, 25(5): 715–732. DOI: 10.1016/j.ijplas.2008.08.001. [116] DURRENBERGER L, MOLINARI A, RUSINEK A. Internal variable modeling of the high strain-rate behavior of metals with applications to multiphase steels [J]. Materials Science and Engineering: A, 2008, 478(1/2): 297–304. DOI: 10.1016/j.msea.2007.06.011. [117] LIN Y C, LIU G. A new mathematical model for predicting flow stress of typical high-strength alloy steel at elevated high temperature [J]. Computational Materials Science, 2010, 48(1): 54–58. DOI: 10.1016/j.commatsci.2009.06.026. [118] TOROS S, OZTURK F. Modeling uniaxial, temperature and strain rate dependent behavior of Al-Mg alloys [J]. Computational Materials Science, 2010, 49(2): 333–339. DOI: 10.1016/j.commatsci.2010.05.019. [119] ABED F H, VOYIADJIS G Z. A consistent modified Zerilli-Armstrong flow stress model for BCC and FCC metals for elevated temperatures [J]. Acta Mechanica, 2005, 175(1): 1–18. DOI: 10.1007/s00707-004-0203-1. [120] NOBLE J P, HARDING J. An evaluation of constitutive relations for high-rate material behaviour using the tensile Hopkinson-bar [J]. Journal de Physique Ⅳ, 1994, 4(C8): 477–482. DOI: 10.1051/jp4:1994874. [121] LEE W S, LIU C Y. The effects of temperature and strain rate on the dynamic flow behaviour of different steels [J]. Materials Science and Engineering: A, 2006, 426(1/2): 101–113. DOI: 10.1016/j.msea.2006.03.087. [122] ÖZEL T, KARPAT Y. Identification of constitutive material model parameters for high-strain rate metal cutting conditions using evolutionary computational algorithms [J]. Materials and Manufacturing Processes, 2007, 22(5): 659–667. DOI: 10.1080/10426910701323631. [123] ZHANG H J, WEN W D, CUI H T, et al. A modified Zerilli-Armstrong model for alloy IC10 over a wide range of temperatures and strain rates [J]. Materials Science and Engineering: A, 2009, 527(1/2): 328–333. DOI: 10.1016/j.msea.2009.08.008. [124] SAMANTARAY D, MANDAL S, BORAH U, et al. A thermo-viscoplastic constitutive model to predict elevated-temperature flow behaviour in a titanium-modified austenitic stainless steel [J]. Materials Science and Engineering: A, 2009, 526(1/2): 1–6. DOI: 10.1016/j.msea.2009.08.009. [125] GAO C Y, ZHANG L C. A constitutive model for dynamic plasticity of FCC metals [J]. Materials Science and Engineering: A, 2010, 527(13/14): 3138–3143. DOI: 10.1016/j.msea.2010.01.083. [126] MCCORMIGK P G. A model for the Portevin-Le Chatelier effect in substitutional alloys [J]. Acta Metallurgica, 1972, 20(3): 351–354. DOI: 10.1016/0001-6160(72)90028-4. [127] LEE M H, KIM J H, CHOI B K, et al. Mechanical properties and dynamic strain aging behavior of Zr-1.5Nb-0.4Sn-0.2Fe alloy [J]. Journal of Alloys and Compounds, 2007, 428(1/2): 99–105. DOI: 10.1016/j.jallcom.2006.03.076. [128] VOYIADJIS G Z, ABED F H. Microstructural based models for bcc and fcc metals with temperature and strain rate dependency [J]. Mechanics of Materials, 2005, 37(2/3): 355–378. DOI: 10.1016/j.mechmat.2004.02.003. [129] TABEI A, ABED F H, VOYIADJIS G Z, et al. Constitutive modeling of Ti-6Al-4V at a wide range of temperatures and strain rates [J]. European Journal of Mechanics: A/Solids, 2017, 63: 128–135. DOI: 10.1016/j.euromechsol.2017.01.005. [130] VOYIADJIS G Z, SONG Y, RUSINEK A. Constitutive model for metals with dynamic strain aging [J]. Mechanics of Materials, 2019, 129: 352–360. DOI: 10.1016/j.mechmat.2018.12.012. [131] VOYIADJIS G Z, SONG Y. A physically based constitutive model for dynamic strain aging in Inconel 718 alloy at a wide range of temperatures and strain rates [J]. Acta Mechanica, 2020, 231(1): 19–34. DOI: 10.1007/s00707-019-02508-6. [132] SONG Y, VOYIADJIS G Z. Constitutive modeling of dynamic strain aging for HCP metals [J]. European Journal of Mechanics: A/Solids, 2020, 83: 104034. DOI: 10.1016/j.euromechsol.2020.104034. [133] RUSINEK A, KLEPACZKO J R. Shear testing of a sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress [J]. International Journal of Plasticity, 2001, 17(1): 87–115. DOI: 10.1016/S0749-6419(00)00020-6. [134] RUSINEK A, RODRÍGUEZ-MARTÍNEZ J A. Thermo-viscoplastic constitutive relation for aluminium alloys, modeling of negative strain rate sensitivity and viscous drag effects [J]. Materials & Design, 2009, 30(10): 4377–4390. DOI: 10.1016/j.matdes.2009.04.011. [135] RUSINEK A, RODRÍGUEZ-MARTÍNEZ J A, ARIAS A. A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper [J]. International Journal of Mechanical Sciences, 2010, 52(2): 120–135. DOI: 10.1016/j.ijmecsci.2009.07.001. [136] KAPOOR R, NEMAT-NASSER S. Comparison between high and low strain-rate deformation of tantalum [J]. Metallurgical and Materials Transactions A, 2000, 31(3): 815–823. DOI: 10.1007/s11661-000-0025-2. [137] PRESTON D L, TONKS D L, WALLACE D C. Model of plastic deformation for extreme loading conditions [J]. Journal of Applied Physics, 2003, 93(1): 211–220. DOI: 10.1063/1.1524706. [138] KIM J B, SHIN H. Comparison of plasticity models for tantalum and a modification of the PTW model for wide ranges of strain, strain rate, and temperature [J]. International Journal of Impact Engineering, 2009, 36(5): 746–753. DOI: 10.1016/j.ijimpeng.2008.11.003. [139] GOETZ R L, SEETHARAMAN V. Modeling dynamic recrystallization using cellular automata [J]. Scripta Materialia, 1998, 38(3): 405–413. DOI: 10.1016/s1359-6462(97)00500-9. [140] ROWLEY M A, THORNTON E A. Constitutive modeling of the visco-plastic response of Hastelloy-X and aluminum alloy 8009 [J]. Journal of Engineering Materials and Technology, 1996, 118(1): 19–27. DOI: 10.1115/1.2805928. [141] 宋迎东, 王舸, 高德平. 一种弹-粘塑性本构模型材料常数的估计方法 [J]. 固体力学学报, 2000, 21(2): 152–156. DOI: 10.19636/j.cnki.cjsm42-1250/o3.2000.02.009.SONG Y D, WANG G, GAO D P. Material constants estimation method of an elastic-viscoplastic constitutive model [J]. Acta Mechanica Solida Sinica, 2000, 21(2): 152–156. DOI: 10.19636/j.cnki.cjsm42-1250/o3.2000.02.009. [142] SHI D Q, YANG X G, WANG Y R. Improvement on the modeling of rate-dependent plasticity and cyclic hardening by bodner-partom model [J]. Chinese Journal of Aeronautics, 2005, 18(1): 83–89. DOI: 10.1016/S1000-9361(11)60287-2. [143] 石多奇, 杨晓光, 王延荣, 等. Udimet 720 Li材料BP型粘塑性本构建模研究 [J]. 北京航空航天大学学报, 2003, 29(7): 627–630. DOI: 10.13700/j.bh.1001-5965.2003.07.015.SHI D Q, YANG X G, WANG Y R, et al. B-P viscoplastic constitutive modeling of Udimet 720 Li [J]. Journal of Beijing University of Aeronautics and Astronautics, 2003, 29(7): 627–630. DOI: 10.13700/j.bh.1001-5965.2003.07.015. [144] HOLMQUIST T J, JOHNSON G R. Determination of constants and comparison of results for various constitutive models [J]. Journal de Physique Ⅳ, 1991, 1(C3): 853–860. DOI: 10.1051/jp4:19913119. [145] SAMANTARAY D, MANDAL S, BHADURI A K. A comparative study on Johnson Cook, modified Zerilli-Armstrong and Arrhenius-type constitutive models to predict elevated temperature flow behaviour in modified 9Cr-1Mo steel [J]. Computational Materials Science, 2009, 47(2): 568–576. DOI: 10.1016/j.commatsci.2009.09.025. [146] LI H Y, WANG X F, WEI D D, et al. A comparative study on modified Zerilli-Armstrong, Arrhenius-type and artificial neural network models to predict high-temperature deformation behavior in T24 steel [J]. Materials Science and Engineering: A, 2012, 536: 216–222. DOI: 10.1016/j.msea.2011.12.108. [147] CHEN C, YIN H Q, HUMAIL I S, et al. A comparative study of a back propagation artificial neural network and a Zerilli-Armstrong model for pure molybdenum during hot deformation [J]. International Journal of Refractory Metals and Hard Materials, 2007, 25(5/6): 411–416. DOI: 10.1016/j.ijrmhm.2006.11.004. [148] LI J, LI F G, CAI J, et al. Comparative investigation on the modified Zerilli-Armstrong model and Arrhenius-type model to predict the elevated-temperature flow behaviour of 7050 aluminium alloy [J]. Computational Materials Science, 2013, 71: 56–65. DOI: 10.1016/j.commatsci.2013.01.010. [149] SHAMSOLHODAEI A, ZAREI-HANZAKI A, GHAMBARI M, et al. The high temperature flow behavior modeling of NiTi shape memory alloy employing phenomenological and physical based constitutive models: a comparative study [J]. Intermetallics, 2014, 53: 140–149. DOI: 10.1016/j.intermet.2014.04.015. [150] CAI J, WANG K S, HAN Y Y. A comparative study on Johnson Cook, modified Zerilli-Armstrong and Arrhenius-type constitutive models to predict high-temperature flow behavior of Ti-6Al-4V alloy in α+β phase [J]. High Temperature Materials and Processes, 2016, 35(3): 297–307. DOI: 10.1515/htmp-2014-0157. [151] WANG J, ZHAO G Q, CHEN L, et al. A comparative study of several constitutive models for powder metallurgy tungsten at elevated temperature [J]. Materials & Design, 2016, 90: 91–100. DOI: 10.1016/j.matdes.2015.10.114. [152] LIU Y, LI M, REN X W, et al. Flow stress prediction of Hastelloy C-276 alloy using modified Zerilli-Armstrong, Johnson-Cook and Arrhenius-type constitutive models [J]. Transactions of Nonferrous Metals Society of China, 2020, 30(11): 3031–3042. DOI: 10.1016/S1003-6326(20)65440-1. [153] ZHANG W W, YAO Y L. Micro scale laser shock processing of metallic components [J]. Journal of Manufacturing Science and Engineering, 2002, 124(2): 369–378. DOI: 10.1115/1.1445149. [154] FAN Y, WANG Y, VUKELIC S, et al. Wave-solid interactions in laser-shock-induced deformation processes [J]. Journal of Applied Physics, 2005, 98(10): 104904. DOI: 10.1063/1.2134882. [155] COLOMBIER J P, COMBIS P, BONNEAU F, et al. Hydrodynamic simulations of metal ablation by femtosecond laser irradiation [J]. Physical Review B, 2005, 71(16): 165406. DOI: 10.1103/PhysRevB.71.165406. [156] AUSTIN R A, MCDOWELL D L. A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates [J]. International Journal of Plasticity, 2011, 27(1): 1–24. DOI: 10.1016/j.ijplas.2010.03.002. [157] DEITERDING R, RADOVITZKY R, MAUCH S P, et al. A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading [J]. Engineering with Computers, 2006, 22(3/4): 325–347. DOI: 10.1007/s00366-006-0043-9. [158] REMINGTON B A, BAZAN G, BELAK J, et al. Materials science under extreme conditions of pressure and strain rate [J]. Metallurgical and Materials Transactions A, 2004, 35(9): 2587–2607. DOI: 10.1007/s11661-004-0205-6. [159] PIERAZZO E, ARTEMIEVA N, ASPHAUG E, et al. Validation of numerical codes for impact and explosion cratering: impacts on strengthless and metal targets [J]. Meteoritics & Planetary Science, 2008, 43(12): 1917–1938. DOI: 10.1111/j.1945-5100.2008.tb00653.x. [160] POLIAK E I, JONAS J J. A one-parameter approach to determining the critical conditions for the initiation of dynamic recrystallization [J]. Acta Materialia, 1996, 44(1): 127–136. DOI: 10.1016/1359-6454(95)00146-7. [161] NES E. Modelling of work hardening and stress saturation in FCC metals [J]. Progress in Materials Science, 1997, 41(3): 129–193. DOI: 10.1016/S0079-6425(97)00032-7. [162] CHICHILI D R, RAMESH K T, HEMKER K J. The high-strain-rate response of alpha-titanium: experiments, deformation mechanisms and modeling [J]. Acta Materialia, 1998, 46(3): 1025–1043. DOI: 10.1016/S1359-6454(97)00287-5. [163] BOUAZIZ O, GUELTON N. Modelling of TWIP effect on work-hardening [J]. Materials Science and Engineering: A, 2001, 319/320/321: 246–249. DOI: 10.1016/S0921-5093(00)02019-0. [164] DING R, GUO Z X. Coupled quantitative simulation of microstructural evolution and plastic flow during dynamic recrystallization [J]. Acta Materialia, 2001, 49(16): 3163–3175. DOI: 10.1016/S1359-6454(01)00233-6. [165] KNEZEVIC M, LEVINSON A, HARRIS R, et al. Deformation twinning in AZ31: influence on strain hardening and texture evolution [J]. Acta Materialia, 2010, 58(19): 6230–6242. DOI: 10.1016/j.actamat.2010.07.041. [166] BANERJEE B. The Mechanical Threshold Stress model for various tempers of AISI 4340 steel [J]. International Journal of Solids and Structures, 2007, 44(3/4): 834–859. DOI: 10.1016/j.ijsolstr.2006.05.022. [167] GATTIKER J, HIGDON D, KELLER-MCNULTY S, et al. Combining experimental data and computer simulations, with an application to flyer plate experiments [J]. Bayesian Analysis, 2006, 1(4): 765–792. DOI: 10.1214/06-BA125. [168] PARK H S, LORENZ K T, CAVALLO R M, et al. Viscous Rayleigh-Taylor instability experiments at high pressure and strain rate [J]. Physical Review Letters, 2010, 104(13): 135504. DOI: 10.1103/PhysRevLett.104.135504. [169] BARTON N R, BERNIER J V, BECKER R, et al. A multiscale strength model for extreme loading conditions [J]. Journal of Applied Physics, 2011, 109(7): 073501. DOI: 10.1063/1.3553718. [170] RAVELO R, GERMANN T C, GUERRERO O, et al. Shock-induced plasticity in tantalum single crystals: interatomic potentials and large-scale molecular-dynamics simulations [J]. Physical Review B, 2013, 88(13): 134101. DOI: 10.1103/PhysRevB.88.134101. [171] JIN Z Y, LIU J, CUI Z S, et al. Identification of nucleation parameter for cellular automaton model of dynamic recrystallization [J]. Transactions of Nonferrous Metals Society of China, 2010, 20(3): 458–464. DOI: 10.1016/S1003-6326(09)60162-X. [172] JIN Z Y, CUI Z S. Investigation on strain dependence of dynamic recrystallization behavior using an inverse analysis method [J]. Materials Science and Engineering: A, 2010, 527(13/14): 3111–3119. DOI: 10.1016/j.msea.2010.01.062. [173] CHEN F, CUI Z S, LIU J, et al. Mesoscale simulation of the high-temperature austenitizing and dynamic recrystallization by coupling a cellular automaton with a topology deformation technique [J]. Materials Science and Engineering: A, 2010, 527(21/22): 5539–5549. DOI: 10.1016/j.msea.2010.05.021. [174] LIN Y C, ZHANG J, ZHONG J. Application of neural networks to predict the elevated temperature flow behavior of a low alloy steel [J]. Computational Materials Science, 2008, 43(4): 752–758. DOI: 10.1016/j.commatsci.2008.01.039. [175] LI H Y, WEI D D, LI Y H, et al. Application of artificial neural network and constitutive equations to describe the hot compressive behavior of 28CrMnMoV steel [J]. Materials & Design, 2012, 35: 557–562. DOI: 10.1016/j.matdes.2011.08.049. [176] RAO K P, PRASAD Y K D V. Neural network approach to flow stress evaluation in hot deformation [J]. Journal of Materials Processing Technology, 1995, 53(3/4): 552–566. DOI: 10.1016/0924-0136(94)01744-L. [177] HODGSON P D, KONG L X, DAVIES C H J. The prediction of the hot strength in steels with an integrated phenomenological and artificial neural network model [J]. Journal of Materials Processing Technology, 1999, 87(1): 131–138. DOI: 10.1016/S0924-0136(98)00344-6. [178] JI G L, LI F G, LI Q H, et al. A comparative study on Arrhenius-type constitutive model and artificial neural network model to predict high-temperature deformation behaviour in Aermet100 steel [J]. Materials Science and Engineering: A, 2011, 528(13/14): 4774–4782. DOI: 10.1016/j.msea.2011.03.017. [179] SABOKPA O, ZAREI-HANZAKI A, ABEDI H R, et al. Artificial neural network modeling to predict the high temperature flow behavior of an AZ81 magnesium alloy [J]. Materials & Design, 2012, 39: 390–396. DOI: 10.1016/j.matdes.2012.03.002. [180] HAGHDADI N, ZAREI-HANZAKI A, KHALESIAN A R, et al. Artificial neural network modeling to predict the hot deformation behavior of an A356 aluminum alloy [J]. Materials & Design, 2013, 49: 386–391. DOI: 10.1016/j.matdes.2012.12.082. [181] GAO T J, ZHAO D, ZHANG T W, et al. Strain-rate-sensitive mechanical response, twinning, and texture features of NiCoCrFe high-entropy alloy: experiments, multi-level crystal plasticity and artificial neural networks modeling [J]. Journal of Alloys and Compounds, 2020, 845: 155911. DOI: 10.1016/j.jallcom.2020.155911. [182] EDGERTON M, RYAN S. An artificial neural network based constitutive model for predicting the response of a high-strength steel [C] // 30th International Symposium on Ballistics. Long Beach, CA, USA, 2017: 11–15. [183] BOBBILI R, MADHU V. Constitutive modeling and fracture behavior of a biomedical Ti-13Nb-13Zr alloy [J]. Materials Science and Engineering: A, 2017, 700: 82–91. DOI: 10.1016/j.msea.2017.05.113. [184] STOFFEL M, BAMER F, MARKERT B. Neural network based constitutive modeling of nonlinear viscoplastic structural response [J]. Mechanics Research Communications, 2019, 95: 85–88. DOI: 10.1016/j.mechrescom.2019.01.004. [185] 黄志斌, 万敏, 伍惠, 等. TC4钛合金神经网络本构模型及在有限元模拟中应用 [J]. 塑性工程学报, 2013, 20(1): 89–94. DOI: 10.3969/j.issn.1007-2012.2013.01.019.HUANG Z B, WAN M, WU H, et al. Constitutive model of Ti-6Al-4V alloy based on artificial neural network and its application on FEM simulation [J]. Journal of Plasticity Engineering, 2013, 20(1): 89–94. DOI: 10.3969/j.issn.1007-2012.2013.01.019. [186] LEFIK M, SCHREFLER B A. Artificial neural network as an incremental non-linear constitutive model for a finite element code [J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(28): 3265–3283. DOI: 10.1016/S0045-7825(03)00350-5. [187] ALI U, MUHAMMAD W, BRAHME A, et al. Application of artificial neural networks in micromechanics for polycrystalline metals [J]. International Journal of Plasticity, 2019, 120: 205–219. DOI: 10.1016/j.ijplas.2019.05.001. 期刊类型引用(9)
1. 杜天冬, 薛冰, 林谋金, 高鹏飞, 章欣宇, 张露, 周俊琪. SBF-AlSi12复合材料的力学性能及本构模型研究. 兵器装备工程学报. 2025(06) 
百度学术2. 李祥辉，张兴渝，胡家豪，刘洋，马伯翰，王永刚，蒋招绣. AISI 4340钢靶大塑性模型及断裂起始模型参数研究. 兵工学报. 2025(01): 301-316 . 百度学术3. 谭毅，杨书仪，孙要兵，郭小军. ZL114A铝合金本构关系与失效准则参数的确定. 爆炸与冲击. 2024(01): 88-107 . 
本站查看4. 王冉，武毅，白龙，张益铭，王宁飞. 宽温域宽应变率下丁羟四组元HTPB推进剂单轴压缩力学行为. 含能材料. 2024(02): 183-192 . 百度学术5. 苏鹏程，赵长安，王佩艳，袁康博，连晨晨. 激光增材制造镍基高温合金的高温变形行为与本构模型. 火箭推进. 2024(01): 135-146 . 百度学术6. 刘晓燕，李帅康，陈文文，王子轩. TA1纯钛绝热剪切行为及变形机制. 有色金属工程. 2024(07): 60-67 . 百度学术7. 呙程祥，王家昌，张明磊，张松. H13模具钢的热变形行为及本构模型建立. 锻压技术. 2024(10): 221-229 . 百度学术8. 熊启林，曾昭泉，安稳，黄西成. 超高应变率下金属热力学塑性变形研究进展. 华中科技大学学报(自然科学版). 2023(01): 67-81 . 百度学术9. 苏宏华，王禹封，谯木，赵正彩，赵彪，徐宝德. 切削加工有限元仿真技术的现状与展望. 南京航空航天大学学报. 2023(03): 361-378 . 百度学术其他类型引用(16)
-
百度学术推荐阅读
用于软材料的中应变率lshpb系统及应用
徐沛栋 等, 爆炸与冲击, 2025
考虑动态拉压比影响的岩石损伤本构模型
胡学龙 等, 爆炸与冲击, 2025
考虑微结构特征的陶瓷材料含损伤本构模型
刘慕皓 等, 爆炸与冲击, 2024
高应变率载荷下纯钛的非连续冲击疲劳失效模型及其微观机理
惠煜中 等, 爆炸与冲击, 2024
率温联合条件下混凝土材料压缩强度的变化规律
李平 等, 高压物理学报, 2022
考虑超细晶金属材料应变软化效应的晶体塑性本构模型研究
郑战光 等, 机械强度, 2025
应变率相关的橡胶本构模型研究
魏家威 等, 高压物理学报, 2022
Biofilms in plastisphere from freshwater wetlands: biofilm formation, bacterial community assembly, and biogeochemical cycles
Meng, Liang et al., JOURNAL OF HAZARDOUS MATERIALS, 2024
Machine learning method to predict dynamic compressive response of concrete-like material at high strain rates
DEFENCE TECHNOLOGY, 2024
Mechanical response behavior, constitutive modeling and microstructural evolution of a 7003-t6 al alloy rolled plate under high-speed impact loading
JOURNAL OF MATERIALS RESEARCH AND TECHNOLOGY-JMR&T, 2025
Powered by 
图(7) / 表(2)
计量
- 文章访问数: 1256
- HTML全文浏览量: 622
- PDF下载量: 305
- 被引次数: 25