第三型应变时效的提出与研究进展

王建军; 袁康博; 张晓琼; 王瑞丰; 高猛; 郭伟国

doi:10.11883/bzycj-2020-0422

第三型应变时效的提出与研究进展

doi: 10.11883/bzycj-2020-0422

1.
太原理工大学机械与运载工程学院，山西太原 030024
2.
西北工业大学航空学院，陕西西安 710072

基金项目: 国家自然科学基金（11902272；11872051）；陕西省自然科学基金（2019JQ-129）

详细信息

作者简介:
王建军（1987－　），男，博士，副研究员，wangjianjun@tyut.edu.cn

通讯作者:
郭伟国（1960－　），男，博士，教授，weiguo@nwpu.edu.cn

中图分类号: O347.3
计量
- 文章访问数: 563
- HTML全文浏览量: 365
- PDF下载量: 226
- 被引次数: 0
出版历程
- 收稿日期: 2020-11-24
- 修回日期: 2021-01-19
- 网络出版日期: 2021-04-23
- 刊出日期: 2021-05-05

Proposition and research progress of the third-type strain aging

1.
College of Mechanical and Vehicle Engineering, Taiyuan Universtiy of Technology, Taiyuan 030024, Shanxi, China
2.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China

摘要

摘要: 第三型应变时效现象的发现使得传统的对于金属塑性流动行为的认识、位错的热激活理论以及常见的金属热粘塑性本构模型均需要进一步完善。为了系统地认识第三型应变时效，首先介绍了第三型应变时效现象区别于静态应变时效和Portevin-Le Chatelie动态应变时效的宏观特征，其次，对第三型应变时效的微观机理以及第三型应变时效与Portevin-Le Chatelier动态应变时效、蓝脆现象以及机械波谱的关联性进行了系统总结。最后，介绍了包含第三型应变时效的金属热黏塑性本构模型的发展。
- 应变时效 /
- 温度 /
- 应变率 /
- 微观机理 /
- 本构模型
Abstract: The traditional knowledge of plastic flow behavior of metal, dislocation activation theory, and thermoviscoplastic constitutive model of metal needs a further perfection due to the occurrence of third-type strain aging. Third-type strain aging leads to a bell-shaped flow stress-temperature curve, that is, the flow stress first increases as temperature increases, and after a peak value is reached, it decreases with further increase of temperature. Third-type strain aging occurs at both low and high strain rates. The bell-shaped segment induced by third-type strain aging on the flow stress-temperature curve shifts to higher temperature region as strain rate increases. In order to develop a systematic understanding of the third-type strain aging, firstly, macro characteristics of third-type stain aging effect that was distinguished from static strain aging effect and Portevin-Le Chatelier dynamic strain aging effect were introduced. Then, the micro mechanism of third-type strain aging and correlation of third-type strain aging, Portevin-Le Chatelier dynamic strain aging, blue brittleness phenomenon, and internal friction were systematically concluded. Third-type strain aging, Portevin-Le Chatelier dynamic strain aging, blue brittleness phenomenon, and mechanical spectroscopy are all resulted from the interaction of mobile dislocations with diffusion atoms. Third-type strain aging, Portevin-Le Chatelier dynamic strain aging, and blue brittleness phenomenon are different manifestations of dynamic strain aging. Third-type strain aging can be considered as another mode of mechanical spectroscopy. The common constitutive models are able to capture the plastic behavior of many metals under the coupling influence of strain rate and temperature in some cases. However, these thermoviscoplastic constitutive models do not take the effect of third-type strain aging into consideration, and they cannot describe the thermoviscoplastic behavior including the third-type strain aging effect. To accurately describe the plastic behavior of metals, some constitutive models including the effect of third type strain aging were proposed. The development of the thermoviscoplastic constitutive model of metal considering the effect of third type strain aging was finally introduced.
- strain aging /
- temperature /
- strain rate /
- microscopic mechanism /
- constitutive model

HTML全文

图 1 三种应变时效的表现形式

Figure 1. Manifestation of the three kinds of strain aging

下载: 全尺寸图片幻灯片

图 2 不同应变率下流动应力随温度变化曲线

Figure 2. Variation of flow stress with temperature at different strain rates

下载: 全尺寸图片幻灯片

图 3 扩散的溶质原子对运动位错的钉扎引起的第三型应变时效的示意图

Figure 3. Schematic of third-type strain aging caused by dislocation pinning by diffused solute atom

下载: 全尺寸图片幻灯片

图 4 API X70管线钢塑性流动行为中出现的第三型应变时效现象及本构模型预测结果^[88]

Figure 4. Third type strain aging phenomenon in the plastic flow behavior of API X70 pipeline steel and prediction results of constitutive model^[88]

下载: 全尺寸图片幻灯片

图 5 本构模型预测得到的Q235B钢在应变为0.1下的流动应力随温度和应变率变化的情况^[6]

Figure 5. Constitutive model predicted variation of flow stress at the strain of 0.1 with temperature and strain rate for Q235B steel^[6]

下载: 全尺寸图片幻灯片

图 6 通过机器学习得到的DP800钢的流动应力随温度和等效应变率变化的情况^[18]

Figure 6. Variation of flow stress with temperature and strain rate obtained with machine learning for DP 800 steel^[18]

下载: 全尺寸图片幻灯片

参考文献(91)

[1]	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.
[2]	NEMAT-NASSER S, GUO W G. Thermomechanical response of HSLA-65 steel plates: experiments and modeling [J]. Mechanics of Materials, 2005, 37(2): 379–405. DOI: 10.1016/j.mechmat.2003.08.017.
[3]	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.
[4]	CORNET C, WACKERMANN K, STÖCKER C, et al. Effects of temperature and hold time on dynamic strain aging in a nickel based superalloy [J]. Materials at High Temperatures, 2014, 31(3): 226–232. DOI: 10.1179/1878641314Y.0000000018.
[5]	GANESAN V, LAHA K, NANDAGOPAL M, et al. Effect of nitrogen content on dynamic strain ageing behaviour of type 316LN austenitic stainless steel during tensile deformation [J]. Materials at High Temperatures, 2014, 31(2): 162–170. DOI: 10.1179/1878641314Y.0000000009.
[6]	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.
[7]	PORTEVIN A, LE-CHATELIER H. Heat treatment of aluminium-copper alloys [J]. Transaction of the American Society of Steel Treating, 1924, 5: 457–478.
[8]	MOTT N F, NABARRO F R N. Report of a conference on the strength of solids [M]. London: Physical Society, 1948.
[9]	COTTRELL A H, BILBY B A. Dislocation theory of yielding and strain ageing of iron [J]. Proceedings of the Physical Society: Section A, 1949, 62(1): 49–62. DOI: 10.1088/0370-1298/62/1/308.
[10]	SONG Y, GARCIA-GONZALEZ D, RUSINEK A. Constitutive models for dynamic strain aging in metals: strain rate and temperature dependences on the flow stress [J]. Materials, 2020, 13(7): 1794. DOI: 10.3390/ma13071794.
[11]	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.
[12]	ZHANG B, WANG J, WANG Y, et al. Dynamic strain-rate effect on uniaxial tension deformation of Ti5Al2.5Sn α-titanium alloy at various temperatures [J]. Materials at High Temperatures, 2019, 36(6): 479–488. DOI: 10.1080/09603409.2019.1638659.
[13]	RAN J Q, ZHANG G Q, CHEN G P, et al. A multi-strain-rate damage model on fracture prediction in single-point diamond turning process [J]. The International Journal of Advanced Manufacturing Technology, 2020, 110(9): 2753–2765. DOI: 10.1007/s00170-020-06023-0.
[14]	CHEN G, LU L P, REN C Z, et al. Temperature dependent negative to positive strain rate sensitivity and compression behavior for 2024-T351 aluminum alloy [J]. Journal of Alloys and Compounds, 2018, 765: 569–585. DOI: 10.1016/j.jallcom.2018.06.196.
[15]	JING L, SU X Y, ZHAO L M. The dynamic compressive behavior and constitutive modeling of D1 railway wheel steel over a wide range of strain rates and temperatures [J]. Results in Physics, 2017, 7: 1452–1461. DOI: 10.1016/j.rinp.2017.04.015.
[16]	WEAVER M L, NOEBE R D, KAUFMAN M J. Observations of dynamic strain aging in polycrystalline NiAl [J]. Intermetallics, 1996, 4(8): 593–600. DOI: 10.1016/0966-9795(96)00045-3.
[17]	SAMUEL K G, RAY S K, SASIKALA G. Dynamic strain ageing in prior cold worked 15Cr-15Ni titanium modified stainless steel (Alloy D9) [J]. Journal of Nuclear Materials, 2006, 355(1): 30–37. DOI: 10.1016/j.jnucmat.2006.03.016.
[18]	LI X Y, ROTH C C, MOHR D. Machine-learning based temperature-and rate-dependent plasticity model: application to analysis of fracture experiments on DP steel [J]. International Journal of Plasticity, 2019, 118: 320–344. DOI: 10.1016/j.ijplas.2019.02.012.
[19]	KREYCA J, KOZESCHNIK E. State parameter-based constitutive modelling of stress strain curves in Al-Mg solid solutions [J]. International Journal of Plasticity, 2018, 103: 67–80. DOI: 10.1016/j.ijplas.2018.01.001.
[20]	TSAI C W, LEE C, LIN P T, et al. Portevin-Le Chatelier mechanism in face-centered-cubic metallic alloys from low to high entropy [J]. International Journal of Plasticity, 2019, 122: 212–224. DOI: 10.1016/j.ijplas.2019.07.003.
[21]	WEAVER M L, NOEBE R D, KAUFMAN M J. The influence of C and Si on the flow behavior of NiAl single crystals [J]. Scripta Materialia, 1996, 34(6): 941–948. DOI: 10.1016/1359-6462(95)00590-0.
[22]	CUNIBERTI A. Serrated yielding in long-range ordered 18R Cu-Zn-Al single crystals [J]. Intermetallics, 2006, 14(7): 776–779. DOI: 10.1016/j.intermet.2005.11.011.
[23]	VARADHAN S, BEAUDOIN A J, FRESSENGEAS C. Lattice incompatibility and strain-aging in single crystals [J]. Journal of the Mechanics and Physics of Solids, 2009, 57(10): 1733–1748. DOI: 10.1016/j.jmps.2009.06.007.
[24]	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): 611–632. DOI: 10.1016/S0749-6419(97)00028-4.
[25]	ROBINSON J M, SHAW M P. Microstructural and mechanical influences on dynamic strain aging phenomena [J]. International Materials Reviews, 1994, 39(3): 113–122. DOI: 10.1179/imr.1994.39.3.113.
[26]	GIRONÈS A, LLANES L, ANGLADA M, et al. Dynamic strain ageing effects on superduplex stainless steels at intermediate temperatures [J]. Materials Science and Engineering: A, 2004, 367(1): 322–328. DOI: 10.1016/j.msea.2003.10.293.
[27]	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.
[28]	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.
[29]	张琼. 低碳钢拉伸形变时影响蓝脆的因素 [J]. 材料科学进展, 1988, 2(6): 87–91. ZHANG Q. Effect of factor of blue brittle of low-carbon steel for tensile deformation [J]. Materials Science Progress, 1988, 2(6): 87–91.
[30]	LI C C, LESLIE W C. Effects of dynamic strain aging on the subsequent mechanical properties of carbon steels [J]. Metallurgical Transactions A, 1978, 9(12): 1765–1775. DOI: 10.1007/BF02663406.
[31]	HONG S G, Lee S B. The tensile and low-cycle fatigue behavior of cold worked 316L stainless steel: influence of dynamic strain aging [J]. International Journal of Fatigue, 2004, 26(8): 899–910. DOI: 10.1016/j.ijfatigue.2003.12.002.
[32]	RODRIGUEZ P. Serrated plastic flow [J]. Bulletin of Materials Science, 1984, 6(4): 653–663. DOI: 10.1007/BF02743993.
[33]	FU S H, CHENG T, ZHANG Q C, et al. Two mechanisms for the normal and inverse behaviors of the critical strain for the Portevin-Le Chatelier effect [J]. Acta Materialia, 2012, 60(19): 6650–6656. DOI: 10.1016/j.actamat.2012.08.035.
[34]	钱匡武, 彭开萍, 陈文哲. 金属动态应变时效现象中的“锯齿屈服” [J]. 福建工程学院学报, 2003, 1(1): 4–8. DOI: 10.3969/j.issn.1672-4348.2003.01.002. QIAN K W, PENG K P, CHEN W Z. Features of serrated yielding of dynamic strain aging phenomenon in metals and alloys [J]. Journal of Fujian University of Technology, 2003, 1(1): 4–8. DOI: 10.3969/j.issn.1672-4348.2003.01.002.
[35]	YILMAZ A. The Portevin–Le Chatelier effect: a review of experimental findings [J]. Science and Technology of Advanced Materials, 2011, 12(6): 063001. DOI: 10.1088/1468-6996/12/6/063001.
[36]	SAKTHIVEL T, LAHA K, NANDAGOPAL M, et al. Effect of temperature and strain rate on serrated flow behaviour of Hastelloy X [J]. Materials Science and Engineering: A, 2012, 534: 580–587. DOI: 10.1016/j.msea.2011.12.011.
[37]	ROY A K, PAL J, MUKHOPADHYAY C. Dynamic strain ageing of an austenitic superalloy—Temperature and strain rate effects [J]. Materials Science and Engineering: A, 2008, 474(1): 363–370. DOI: 10.1016/j.msea.2007.05.056.
[38]	KARABULUT H, GÜNDÜZ S. Effect of vanadium content on dynamic strain ageing in microalloyed medium carbon steel [J]. Materials & Design, 2004, 25(6): 521–527. DOI: 10.1016/j.matdes.2004.01.005.
[39]	GÜNDÜZ S, ACARER M. The effect of heat treatment on high temperature mechanical properties of microalloyed medium carbon steel [J]. Materials & Design, 2006, 27(10): 1076–1085. DOI: 10.1016/j.matdes.2005.01.020.
[40]	XIAO J Y, WANG J J, GUO W G, et al. The influence of heat treatment and strain rate on the third type strain ageing phenomenon [J]. Materials at High Temperatures, 2019, 36(2): 104–110. DOI: 10.1080/09603409.2018.1467108.
[41]	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.
[42]	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.
[43]	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.
[44]	VAN DEN BEUKEL A, KOCKS U F. The strain dependence of static and dynamic strain-aging [J]. Acta Metallurgica, 1982, 30(5): 1027–1034. DOI: 10.1016/0001-6160(82)90211-5.
[45]	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.
[46]	CUDDY L J, LESLIE W C. Some aspects of serrated yielding in substitutional solid solutions of iron [J]. Acta Metallurgica, 1972, 20(10): 1157–1167. DOI: 10.1016/0001-6160(72)90164-2.
[47]	SCHWARZ R B, FUNK L L. Kinetics of the Portevin-Le Chatelier effect in Al 6061 alloy [J]. Acta Metallurgica, 1985, 33(2): 295–307. DOI: 10.1016/0001-6160(85)90148-8.
[48]	PICU R C, ZHANG D. Atomistic study of pipe diffusion in Al-Mg alloys [J]. Acta Materialia, 2004, 52(1): 161–171. DOI: 10.1016/j.actamat.2003.09.002.
[49]	PENG K P, QIAN K W, CHEN W Z. Effect of dynamic strain aging on high temperature properties of austenitic stainless steel [J]. Materials Science and Engineering: A, 2004, 379(1): 372–377. DOI: 10.1016/j.msea.2004.03.004.
[50]	CORBY C, CÁCERES C H, LUKÁČ P. Serrated flow in magnesium alloy AZ91 [J]. Materials Science and Engineering: A, 2004, 387: 22–24. DOI: 10.1016/j.msea.2004.01.077.
[51]	FRIEDEL J. Dislocations: international series of monographs on solid state physics [M]. Oxford: Pergamon Press, 1964: 491.
[52]	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.
[53]	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.
[54]	张质良, 余大伟, 阮雪榆. “蓝脆”温度挤压特性的研究 [J]. 模具技术, 1983(2): 1–13.
[55]	王敏杰, 胡荣生, 刘培德. 金属切削中的蓝脆效应与热塑剪切失稳 [J]. 科学通报, 1990, 35(8): 634–636. DOI: 10.1360/csb1990-35-8-634.
[56]	KIM I S, KANG S S. Dynamic strain aging in SA508-class 3 pressure vessel steel [J]. International Journal of Pressure Vessels and Piping, 1995, 62(2): 123–129. DOI: 10.1016/0308-0161(95)93969-C.
[57]	CAILLARD D. Dynamic strain ageing in iron alloys: the shielding effect of carbon [J]. Acta Materialia, 2016, 112: 273–284. DOI: 10.1016/j.actamat.2016.04.018.
[58]	KOYAMA M, SHIMOMURA Y, CHIBA A, et al. Room-temperature blue brittleness of Fe-Mn-C austenitic steels [J]. Scripta Materialia, 2017, 141: 20–23. DOI: 10.1016/j.scriptamat.2017.07.017.
[59]	VERMA P, RAO G S, CHELLAPANDI P, et al. Dynamic strain ageing, deformation, and fracture behavior of modified 9Cr-1Mo steel [J]. Materials Science and Engineering: A, 2015, 621: 39–51. DOI: 10.1016/j.msea.2014.10.011.
[60]	SCHWINK C, NORTMANN A. The present experimental knowledge of dynamic strain ageing in binary f.c.c. solid solutions [J]. Materials Science and Engineering: A, 1997, 234(97): 1–7. DOI: 10.1016/S0921-5093(97)00139-1.
[61]	WOLFENDEN A, KINRA V K. M3D III: mechanics and mechanisms of materials damping [M]. West Conshohocken, PA: ASTM International, 1997.
[62]	MARTIN R, TKALCEC I, MARI D, et al. Tempering effects on three martensitic carbon steels studied by mechanical spectroscopy [J]. Philosophical Magazine, 2008, 88(22): 2907–2920. DOI: 10.1080/14786430802406249.
[63]	TKALCEC I, MARI D. Internal friction in martensitic, ferritic and bainitic carbon steel; cold work effects [J]. Materials Science and Engineering: A, 2004, 370(1): 213–217. DOI: 10.1016/j.msea.2003.04.004.
[64]	TKALCEC I, MARI D, BENOIT W. Correlation between internal friction background and the concentration of carbon in solid solution in a martensitic steel [J]. Materials Science and Engineering: A, 2006, 442(1): 471–475. DOI: 10.1016/j.msea.2006.03.115.
[65]	NIEMEYER T C, GRANDINI C R, FLORÊNCIO O. Stress-induced ordering due heavy interstitial atoms in Nb–0.3 wt.% Ti alloys [J]. Materials Science and Engineering: A, 2005, 396(1): 285–289. DOI: 10.1016/j.msea.2005.01.045.
[66]	STRAHL A, GOLOVINA S B, GOLOVIN I S, et al. On dislocation-related internal friction in Fe-22-31 at.% Al [J]. Journal of Alloys and Compounds, 2004, 378(1): 268–273. DOI: 10.1016/j.jallcom.2003.10.066.
[67]	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, 127. 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, 127. DOI: 10.11951/j.issn.1005-0299.20120126.
[68]	彭开萍, 陈文哲, 钱匡武. 3004铝合金“反常”锯齿屈服现象的研究 [J]. 物理学报, 2006, 55(7): 3569–3575. DOI: 10.3321/j.issn:1000-3290.2006.07.061. PENG K P, CHEN W Z, QIAN K W. Study of an anomalous serrated yielding phenomenon in 3004 aluminum alloy [J]. Acta Physica Sinica, 2006, 55(7): 3569–3575. DOI: 10.3321/j.issn:1000-3290.2006.07.061.
[69]	LEE S J, KIM J, KANE S N, et al. On the origin of dynamic strain aging in twinning-induced plasticity steels [J]. Acta Materialia, 2011, 59(17): 6809–6819. DOI: 10.1016/j.actamat.2011.07.040.
[70]	KARLSEN W, IVANCHENKO M, EHRNSTÉN U, et al. Microstructural manifestation of dynamic strain aging in AISI 316 stainless steel [J]. Journal of Nuclear Materials, 2009, 395(1): 156–161. DOI: 10.1016/j.jnucmat.2009.10.047.
[71]	IVANCHENKO M, NEVDACHA V, YAGODZINSKYY Y, et al. Internal friction studies of carbon and its redistribution kinetics in Inconel 600 and 690 alloys under dynamic strain aging conditions [J]. Materials Science and Engineering: A, 2006, 442(1): 458–461. DOI: 10.1016/j.msea.2006.02.207.
[72]	JOHNSON G R, COOK W H. A constitutive model and date for metals subjected to large strains, high strain rates, and high temperatures [C] // Proceedings of the 7th International Symposium on Ballistics. The Hague, Netherlands, 1983: 541−547.
[73]	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.
[74]	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.
[75]	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.
[76]	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.
[77]	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.
[78]	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.
[79]	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.
[80]	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.
[81]	GAO C Y, ZHANG L C. Constitutive modelling of plasticity of fcc metals under extremely high strain rates [J]. International Journal of Plasticity, 2012, 32: 121–133. DOI: 10.1016/j.ijplas.2011.12.001.
[82]	KHAN A S, LIU H W. Variable strain rate sensitivity in an aluminum alloy: response and constitutive modeling [J]. International Journal of Plasticity, 2012, 35: 1–14. DOI: 10.1016/j.ijplas.2012.02.001.
[83]	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.
[84]	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.
[85]	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.
[86]	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.
[87]	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.
[88]	SHEN F H, MÜNSTERMANN S, LIAN J H. An evolving plasticity model considering anisotropy, thermal softening and dynamic strain aging [J]. International Journal of Plasticity, 2020, 132: 102747. DOI: 10.1016/j.ijplas.2020.102747.
[89]	郭扬波, 唐志平, 程经毅. 一种基于位错机制的动态应变时效模型 [J]. 固体力学学报, 2002, 23(3): 249–256. DOI: 10.3969/j.issn.0254-7805.2002.03.001. GUO Y B, TANG Z P, CHENG J Y. A dislocation-mechanics-based constitutive model for dynamic strain aging [J]. Acta Mechanica Solida Sinica, 2002, 23(3): 249–256. DOI: 10.3969/j.issn.0254-7805.2002.03.001.
[90]	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.
[91]	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.