金属棒料下料是工业生产中的起点，也是最重要的一道工序，广泛存在于冷、热挤压件和模锻件、齿轮、轴承、轴套、链条、螺钉等各类机械零部件加工制造中，其下料效率和坯料断面质量直接影响着后续零件的加工质量、生产效率和成本。针对传统下料方法存在下料效率低、材料浪费、坯料断面质量低等问题，本文利用人为预制环状V型缺口的缺口效应、微裂纹萌生应力集中效应、疲劳裂纹扩展控制技术，提出一种新型低应力可控旋弯下料方法，并通过使用理论解析、数值模拟及试验方法对下料过程损伤机理及断裂行为进行深入研究。

根据304不锈钢棒料韧性断裂规律，建立了304不锈钢延性损伤宏观本构模型，利用数值模拟和单轴拉伸试验分析了环形缺口张角、缺口深度及缺口根部半径对304不锈钢棒料变形行为和损伤演变的影响，揭示了304不锈钢棒料变形规律及损伤演化机理。利用延性损伤宏观本构模型和单因素实验法相结合方法对不同下料工艺参数的缺口根部损伤场影响规律进行数值模拟，获取到加载速度5mm/s，载荷类型为线性递增载荷，加持位置L1=5mm，L2=10mm理想的下料工艺参数。通过构建的延性损伤宏观本构模型为耦合细观损伤模型奠定损伤状态参数与应力状态函数关系的理论基础。

304不锈钢棒料表面人为预制环状缺口由于缺口效应及应力集中效应是高效的下料辅助方法，通过有限元软件二次开发平台，建立了延性损伤与细观损伤的耦合本构模型，

利用理论解析、微观结构分析法和逆向求解法对模型参数识别，且分析不同应力状态的拉伸试样对304不锈钢棒料损伤演变影响，揭示了304不锈钢棒料微观损伤演化机理。通过利用耦合本构模型和单因素实验法分析不同缺口几何参数对缺口根部起裂损伤场的影响规律，获得缺口张角对称30°，缺口根部半径0.2mm，缺口深度0.8mm理想下料工艺参数。

根据低应力下料工艺的特点，详细阐述了新型低应力可控旋弯下料方法的工作原理，基于该下料的原理，研制由机械系统、液压系统及电气控制系统等三部分所构成的新型低应力可控旋弯下料系统，并对其进行调试以及试验。

根据新型低应力可控旋弯下料方法获得的坯料断面特征，提出一种适用于该下料方法的坯料断面评价指标为下料时间以及断面平整度。通过下料试验结果表明该下料方法较为合理。

根据304不锈钢棒料疲劳裂纹扩展规律，利用线弹性断裂力学理论，建立含环状缺口304不锈钢棒料的疲劳裂纹扩展模型，对下料载荷控制策略进行设计，并对直径D= 10mm的304不锈钢金属棒料进行下料试验。试验结果表明：当采用加载速度为1mm/s的线性递增载荷控制策略进行下料试验能够获得理想的坯料断面；为了进一步验证了所建立耦合本构模型以及延性损伤宏观本构模型的合理性，当缺口张角对称30^o、缺口根部半径0.2mm、棒料夹持位置L1= 5mm与L2=10mm时坯料断面的疲劳裂纹扩展区占比最大，能获取理想坯料断面及下料时间。

The metal bar cropping is the starting point and the most important process in industrial production. It is widely used in the processing and manufacturing ont color='red'>ofont> various mechanical parts such as gears, bearings, shaft sleeves, chains, screws, etc. Its cropping efficiency and cross-section quality directly affect the processing quality, production efficiency and cost ont color='red'>ofont> subsequent parts. Aiming at the problems ont color='red'>ofont> low cutting efficiency, waste ont color='red'>ofont> materials and low quality ont color='red'>ofont> cross-section in traditional cropping methods, this paper put forward a new low-stress controlled rotary bending cropping method by using the notch effect ont color='red'>ofont> artificially prefabricated annular V-notch, the stress concentration effect ont color='red'>ofont> micro-crack initiation and the control technology ont color='red'>ofont> fatigue crack propagation, and made an in-depth study on the damage mechanism and fracture behavior in the cropping process by using theoretical analysis, numerical simulation and experimental methods.

According to the ductile fracture law ont color='red'>ofont> 304 stainless steel bar, the macroscopic constitutive model ont color='red'>ofont> ductile damage ont color='red'>ofont> 304 stainless steel bar was established. The effects ont color='red'>ofont> annular notch angle, notch depth and notch root radius on the deformation behavior and damage evolution ont color='red'>ofont> 304 stainless steel bar were analyzed by numerical simulation and tensile test, and the deformation law and damage evolution mechanism ont color='red'>ofont> 304 stainless steel bar were revealed. The macroscopic constitutive model ont color='red'>ofont> ductile damage and the single factor experiment method were used to numerically simulate the influence law ont color='red'>ofont> notch root damage field with different cropping process parameters, and the ideal cropping process parameters were obtained, such as loading speed ont color='red'>ofont> 5mm/s, linear increasing load, clamping position L1=5mm, L2=10mm. The macroscopic constitutive model ont color='red'>ofont> ductile damage established lays the theoretical foundation for the relationship between damage state parameters and stress state function for the coupled meso-damage model.

The artificially prefabricated annular notch on the surface ont color='red'>ofont> 304 stainless steel bar is an efficient cutting aid method due to notch effect and stress concentration effect. Through the secondary development platform ont color='red'>ofont> finite element sont color='red'>ofont>tware, the coupled constitutive model ont color='red'>ofont> ductile damage and microscopic damage is established. This model parameters were identified by theoretical analysis, microstructure analysis and reverse solution method. The influence ont color='red'>ofont> tensile specimens with different stress states on the damage evolution ont color='red'>ofont> 304 stainless steel bar was analyzed, and the micro-damage evolution mechanism ont color='red'>ofont> 304 stainless steel bar was revealed. By using the coupled constitutive model and single factor experiment method, the influence law ont color='red'>ofont> different notch geometric parameters on the crack initiation damage field at the notch root was analyzed, and the ideal cropping process parameters with the notch angle symmetry 30, notch root radius 0.2mm and notch depth 0.8mm were obtained.

According to the characteristics ont color='red'>ofont> the low-stress cropping process, the working principle ont color='red'>ofont> the new low-stress controllable rotary cropping method is described in detail. A new type ont color='red'>ofont> low stress controllable rotary bending cropping system is constructed, and it is debugged and tested.

According to the cross-section characteristics obtained by the new low-stress controllable rotary cropping method, a cross-section evaluation index suitable for the cropping method is proposed, which are cropping time and section flatness. The cropping test results show that the cropping method is more reasonable.

According to the fatigue crack propagation law ont color='red'>ofont> 304 stainless steel bar, the fatigue crack propagation model ont color='red'>ofont> 304 stainless steel bar with annular notch was established by using the theory ont color='red'>ofont> linear elastic fracture mechanics, and the load control strategy was designed. The cropping test ont color='red'>ofont> 304 stainless steel bar with diameter D= 10mm was carried out. The test results show that the ideal cross-section can be obtained when the cropping test is carried out with a linear incremental load control strategy with a loading speed ont color='red'>ofont> 1mm/s. In order to further verify the rationality ont color='red'>ofont> the established theory, when the notch opening angles is 30^o, the notch root radius is 0.2mm and the bar clamping positions is L1=5mm and L2=10mm, the proportion ont color='red'>ofont> fatigue crack propagation area ont color='red'>ofont> the cross-section is the largest, and the ideal cross-section and cropping time can be obtained.

[1]卢帆.中国制造2025视角下无锡市制造业现状及创新[J].管理观察, 2018(08):9-11.

[2]金菊. 工业4.0时代中国制造业的转型升级研究[D].云南大学, 2016:1-2.

[3]肖景容. 精密模锻[M]. 北京: 机械工业出版社, 1985:1-38.

[4]Chunjian Hua, Shengdun Zhao, Lijun Zhang, et al. Investigation on the dynamic characteristic of a new type of precision cropping system with variant frequency vibration[J]. International Journal of Mechanical Science, 2006, 48(12):1333-1340.

[5]赵升吨, 雷净, 郝永江. 现代数控板材成形设备的现状[J]. 机械工人, 2006(6): 10-14.

[6]SD Z, J W, LH W, et al. Iterative learning control of electro-hydraulic proportional feeding system in slotting machine for metal bar cropping[J]. International Journal of Mechine Tools and Manufacture, 2005 (7-8):923-931.

[7]郭继富, 韩会杰, 赵东岩等. 金属冷热切圆锯片开裂、掉块原因分析及改进措施[J].轧钢, 2019, 36(05):93-96

[8]赵升吨, 景飞, 赵仁峰等. 金属管料下料技术概述[J]. 锻压装备与制造技术, 2015, 50 (02):11-14.

[9]郝海滨. 金属材料精密压力成形技术[M]. 北京: 化工工业出版社, 2004:87-90.

[10]Li WM, Cheng ZS and Gong ZY. Study on design and key technology of high-speed precision shear[J]. Mach Design Manuf , 2012 (05):136-138

[11]钟玮, 赵升吨, 王泽阳等. 提高棒料下料断面质量途径探讨[J]. 锻压装备与制造技术, 2016, 51(02):77-83.

[12]于德弘，赵升吨，陈金德. 回转式精密剪切机[P].中国, 92233678.4,1993-11-1

[13]Brabie.G. An analysis of the shearing stresses distribution on the cross-section of the twisted round bars[J]. Journal of Materials Processing Technology, 2003, 142(1):224-230.

[14]Mingan Chen, Huizhong Li, Xueqian Li, et al. Characterization of deformation microstructure and fractured surfure of plastic shearing of copper bar[J], Materials Science and Engineering A, 2007, 452-453(4):454-461.

[15]陈金德. 金属材料精密分离概论[J]. 模具工业, 1990, 6:5-9．

[16]Liu T, Ge P, Bi W, et al. Fracture strength of silicon wafers sawn by fixed diamond wire saw [J]. Solar Energy, 2017, 157:427-433.

[17]Chen Guojin, Zhu Miaofen, Ni Jing, et al. Study on online detection and fault diagnosis of and band saw equipment[J]. International Journal of Control andAutomation, 2014, 7(8): 1271-1281.

[18]Albrecht D, Mohring H-C. Potentials for the optimization of sawing processes using the example of bandsawing machines[J]. Procedia Manufac. 2018, 21:567-574.

[19]L. WM, C. ZS, G. ZY. Study on design and key technology of high-speed precision shear [J]. Mach Design Manuf. 2012, 05:136-138.

[20]陈金德, 邢广汉. 管材的偏心渐进精密剪切[J]. 模具工业, 1987, (4):7-11.

[21]田福祥. 圆钢径向夹紧精密剪切模设计[J]. 模具工业, 2006, 32(1):35-39.

[22]杜诗文, 李永堂. 金属圆柱棒的高速剪切断裂数值模拟及试验研究[J]. 机械强度, 2010, 32(3):451-454.

[23]付建华, 李永堂, 雷步芳等. 金属棒料高速精密剪切试验研究[J]. 机械工程学报, 2005, 41(5):154-156.

[24]李耀辉. 棒料高速精密剪切合理加载速度的探讨[J]. 锻压技术, 2007, 32(2):94-97.

[25]李耀辉, 李永堂. 影响高速剪切毛坯断面质量的技术参数[J]. 冲压, 2005, (2):72-74.

[26]李耀辉, 李永堂. 金属棒料高速精密剪切下料速度的研究与应用[J]. 金属铸锻焊技术, 2010, 39(15):8-11.

[27]付立壮. 一种棒料径向夹紧剪切模[J]. 锻压技术, 1995, 20(6):57-63.

[28]付立壮. 棒料的径向夹紧精密剪切[J]. 轴承, 1995, (7):25-27

[29]Chen, JD, Zhang, ZG, Xiong, GH. Precision cropping under axial load for shaped workpieces[C]. Proceedings of the 24th International Conference on Machine Tool Design and Research. UK: Elsevier Ltd, 1983.

[30]Chen, JD, Zhang, XR, Yu, DH. The study of precision bar cropping under axial load[C]. Proceedings of the 24th International Conference on Machine Tool Design and Research. UK: Elsevier Ltd, 1981.

[31]陈明安，陈金德．轴向加压剪切过程中静水应力场及其作用分析[J]．湖南大学学报，1993, 20(1):71-75．

[32]Lattey JI, Sessions TMB, Harris LN. Precision metal cropping under high axial load [J]. Mach. Prod. Engng, 1971, 118(3057):920-924.

[33]陈明安, 李慧中, 李学谦等. 紫铜棒材轴向加压精密塑性剪切变形区的金相组织和断面特征[J]. 中国有色金属学报, 2005, 15(4):513-518.

[34]曹国强, 张睿. 高压水射流研究现状及应用[J]. 沈阳航空航天大学学报, 2017, 34(3): 1- 16.

[35]Hu Y, Kang Y, Wang X C, et al. Mechanism and experimental investigation of ultra high pressure water jet on rubber cutting[J]. International Journal of Precision Engineering and Manufacturing, 2014, 15(9):1973-1978.

[36]侯交义，康旭, 徐凯等. 基于拟水平正交实验法的磨料水射流切割性能研究[J]. 机床与液压, 2018, 46(3):95-98

[37]赵春红, 秦现生. 高压水射流技术及其应用[J]. 机床与液压, 2006, (2):1-3.

[38]赵松柏，韩永馗，曹亮等．超大厚度火焰切割工艺试验研究[J]．一重技术，2013，(1):27-29．

[39]蒋晓妍. 切割技术的发展现状及发展趋势[J]. 有色矿冶, 2016, 32(01):42-44.

[40]梁桂芳．切割技术手册[M]. 北京:机械工业出版社, 1997:1-62．

[41]Graham A. Thermal cutting process[J]. Welding Review, 1990, 9(4):184-190.

[42]陈月峰, 严得忠, 程定富等. 国内数控等离子弧切割技术得发展与应用[J]. 焊接技术. 2017, 46(8):1-4.

[43]Sullivan AB, Houldcroft PF. Gas-jet laser cutting[J]. Brit. Weld J. 1967, 46(8):443-445.

[44]孙晓东, 王松, 赵凯华等. 激光切割技术国内外研究现状[J]. 金属铸锻焊技术, 2012, 41 (9):214-216.

[45]李有堂, 魏庆同, 芮执元等. 一种弯曲限制型应力断料装置[P]: 中国, 98201457.0, 2000-02-09.

[46]Li YT, Yang CF, Wei YB. The application of fracture for middle carbon steel in extra-low cycle inverse rotating bending fatigue loading[J]. Key Engineering Materials, 2004, 261-263(2):1147-1152.

[47]陈金德, 王朝民, 于德宏. 低应力冲击剪切法[P]: 中国, 1989-10-04

[48]JD C, YW W, DH Y, et al. Plastic precision cropping of metal materials[J]. International Journal of Machine Tools Manufacture, 1992, 32(3):425-433.

[49]赵升吨, 赵仁峰, 钟斌等. 一种偏心套高速旋转式棒管料精密下料机[P]: 中国, 2012100 42371.7, 2012-02-23

[50]Chen J, Wang Y, Yu D. The controlled fracture technique and its application in metalworking [J]. Engineering Fracture Mechanics, 1991, 39(1):61-69.

[51]钟斌. 气动式弯曲疲劳下料方法及其断裂行为的研究[D]. 西安：西安交通大学, 2014.

[52]Zhang LJ, Zhao SD, Wang HX. Investigation on the precision cropping system with high-speed and centrifugal action[J]. Int. J. Adv. Manuf. Technol. 2015, 80:1311-1317.

[53]Zhang LJ, Chen XF, Wang HX, et al. Research on critical loading force in precision cropping system based on hydraulic compensation[J]. International Journal of Mechanical Sciences, 2018, 142-143:44-50.

[54]Zhang LJ, Zhang DP, Wang HX, et al. Research on variable frequency-loading curve in precision cropping system with high-speed and centrifugal action[J]. Int. J. of Adv. Manuf. Technol. 2018, 97:2969-2978.

[55]Wang Zhenwei, Zhao Shengdun, Yu Yating. Study on the dynamic characteristics of the low-stress vibration cropping machine[J]. Journal of Materials Processing Technology，2007, 190 (1-3):89-95.

[56]Wang Zhenwei, Zhao Shengdun et al. Transistant analysis of the variant frequency vibration cropping system[J]. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, 2007, 7(221):769-778

[57]赵升吨, 任芋见, 杨昌群等．低应力疲劳裂纹可控式精密分离技术[J]. 塑性工程学报，2020, 27(12):1-8.

[58]余寿文, 冯西桥. 损伤力学[M]. 北京：清华大学出版社, 1997.

[59]Kachanov L. On the time to failure under deep condition, Izv[J]. AN SSSR, Otd. Tekhn. Nauk, 1958:26-31.

[60]Rabotnov Y N. On the equation of state for creep[J]. Progress in Applied Mechanics, 1963, 12:307-305.

[61]Lemaitre J. Evaluation of dissipation and damage in metals submitted to dynamic loading[J]. Mechancial behavior of materials, 1972:540-549.

[62]Voyiadjis. GZ, Kattan. PI. Healing and super healing in continuum damage mechanics[J]. International Journal of Damage Mechanics, 2014:245-260.

[63]H. Rokhgireh, M. Kästner, A. Nayebi. Modeling the Tensile Behavior of Specimens Manufactured by the Selective Laser Melting Method Using Continuum Damage Mechanics Theory[J]. Journal of Materials Engineering and Performance, 2021:1-7.

[64]Grandcoin. J, Boukamel. A, Lejeunes. S. A micro-mechanically based continuum damage model for fatigue life prediction of filled rubbers[J]. International Journal of Solids and Structures, 2014:1274-1286.

[65]Li. J, Leguillon. D, Martin. E. et al. Numerical implementation of the coupled criterion for damaged materials[J]. International Journal of Solids and Structures, 2019:93-103.

[66]Christopher J , Praveen C, Ganesan V. et al. Influence of varying nitrogen on creep deformation and damage behaviour of type 316L in the framework of continuum damage mechanics approach[J]. International Journal of Damage Mechanics, 2021, 30(1):3-24.

[67]周靖,王宝雨,徐伟力等.耦合损伤的22MnB5热变形本构模型[J].北京科技大学学报, 2013, 35(11):1450-1457.

[68]尹俊杰,李曙林,姚学玲等.含雷击热-力耦合损伤复合材料层压板拉伸剩余强度预测[J]. 复合材料学报, 2017, 34(01):83-90.

[69]张昉,金伟良,张军等.基于连续介质损伤力学的坑蚀钢筋高周疲劳寿命与损伤分析[J].建筑材料学报, 2021, 24(02):405-411

[70]拓宏亮,马晓平,卢智先.基于连续介质损伤模型的复合材料连接件失效分析[J].西北工业大学学报, 2018, 36(05):848-855.

[71]拓宏亮,马晓平,卢智先.基于连续介质损伤力学的复合材料层合板低速冲击损伤模型[J].复合材料学报, 2018, 35(07):1878-1888.

[72]盈亮,史栋勇,胡平等.基于连续介质损伤力学的高强度钢板热成形性数值预测[J].机械工程学报, 2016, 52(04):36-44.

[73]李爱民,崔海涛,温卫东等.基于非线性连续介质损伤力学方法的微动疲劳寿命预测[J].航空学报, 2013, 34(09):2122-2129.

[74]黄再兴.本构关系对连续介质损伤力学基本方程适定性的影响-一维弹性损伤情况[J].航空学报, 2000(02):124-127.

[75]McClintock FA. A criterion for ductile fracture by the growth of holes[J]. Journal of applied mechanics, 1968, 35(2):363-371.

[76]Rice R J, Tracey DM. On the ductile fracture by the growth of holes [J]. Journal of the Mechanics and Physics of Solids, 1969(17):201-217.

[77]Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rules for porous ductile media[J]. Journal of engineering materials and technology, 1977, 99(1):2-15.

[78]Tvergaard V. Influence of voids on Shear Band Instabilities under Plane-strain Conditions[J]. International Journal of Fracture, 1981, 17(4):389-407.

[79]Tvergaard V, Needleman A. Flow localization in the plane strain tensile test[J]. Journal of the Mechanics and Physics of Soilds, 1981, 29(2):115-142

[80]Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta metallurgica, 1984, 32(1):157-169.

[81]Needleman A, Tvergaard V. An analysis of ductile rupture in notched bars[J]. Journal of the Mechanics and Physics of Solids, 1984, 32(6):461-490.

[82]He Wu, Wenchen Xu, Debin Shan, et al. An extended GTN model for low stress triaxiality and application in spinning forming[J]. Journal of Materials Processing Tech, 2019, 263:112-128.

[83]Shen Wang, Zhanghua Chen, Chaofang Dong. Tearing failure of ultra-thin sheet-metal involving size effffect in blanking process: Analysis based on modifified GTN model[J]. International Journal of Mechanical Sciences, 2017, 133:288-302.

[84]Pengjing Zhao, Zhanghua Chen, Chaofang Dong. Investigation and prediction of tearing failure during extrusion based on a modifified shear damage model[J]. Mechanics of Materials, 2017, 112:28-39.

[85]Wei Jiang, Yazhi Li, Jie Su. Modifified GTN model for a broad range of stress states and application to ductile fracture[J]. European Journal of Mechanics A/Solids, 2016, 57: 132-148

[86]Youbin Chen, Chunyu Zhang, Christophe Varé. An extended GTN model for indentation -induced damage[J]. Computational Materials Science, 2017, 128:229-235.

[87]Bao Y, Wierzbicki T. On fracture locus in the equivalent strain and stress triaxixlity space[J]. International Journal of Mechanical Sciences, 2004, 46(1):81-98.

[88]Xue L. Constitutive modeling of void shearing effect in ductile fracture of porous materials [J]. Engineering Fracture Mechanics, 2008, 75(11):3343-3366.

[89]Nahshon K, Hutchinson J. Modification of the Gurson model for shear failure[J]. European Journal of Mechanics-A/Solids, 2008, 27(1):1-17.

[90]Zhou J, Gao X, Sobatka J C, et al. On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions[J]. International Journal of Solids and Structures, 2014, 51(18):3273-3291.

[91]李振环,张克实.不同应力三维度条件下孔洞的演变及修正的Gurson模型[J].上海力学, 1997(01):50-58.

[92]郑长卿,雷登,周利等. 韧性断裂细观力学的初步研究及其应用[M].西安:西北工业大学出版社, 1988.

[93]王国珍,张贺全,蒲吉斌等.GTN损伤模型对C-Mn钢缺口拉伸试样延性断裂的预测[J].机械强度, 2008(04):647-652

[94]隋伟宁,陈茂明,陈彦文等.Q345B钢材GTN模型损伤参数标定及应用[J].沈阳建筑大学学报(自然科学版), 2018, 34(01):82-90.

[95]肖晋,胡玉梅,金晓清等.基于各向异性GTN模型的铝合金损伤参数确定[J].机械强度, 2018, 40(05):1189-1193.

[96]Yuxi Yan, Quan Sun, Jianjun Chen, et al. The initiation and propagation of edge cracks of silicon steel during tandem cold rolling process based on the Gurson- Tvergaard- Needleman Damage Model[J], 2013, 213:598-605.

[97]Q.Sun, D.Q. Zan, J.J. Cheng, H.L. Pan. Analysis of edge crack behavior of steel sheet in multi- pass cold rolling based on a shear modified GTN damage model[J]. Theoretical and Applied Fracture Mechanics, 2015, 80:259-266.

[98]赵雷,王逊,徐连勇等.基于GTN模型的小冲孔高温拉伸性能表征[J].天津大学学报(自然科学与工程技术版), 2022, 55(03):283-290.

[99]Zhao P J, Chen Z H, Dong C F. Investigation and prediction of tearing failure during extrusion on a modified shear damage model[J], Mechanics of Materials, 2017,112:28-39.

[100]Jiang W, Li YZ, Su J. Modified GTN model for a broad range of stress states and application to ductile fracture[J]. European Journal of Mechanics-A/Solids, 2016, 57: 132-148.

[101]He Wu, Wenchen Xu, Debin Shan, et al. Mechanism of increasing spinnability by multi-pass spinning forming Analysis of damage evolution using a modified GTN model[J], International Journal of Mechanical Science, 2019, 159:1-19.

[102]He Wu, Wenchen Xu, Debin Shan, et al. An extended GTN model for low stress triaxiality and application in spinning forming[J]. Journal of Materials Processing Tech., 2019, 263:112-128.

[103]T.S Cao, E. Maire, C. Verdu, et al. Characterization of ductile damage for a high carbon steel using 3D X-ray micro-tomography and mechanical tests-Application to the identification of a shear modified GTN model[J]. Computional Materials Science, 2014, 84:175-187.

[104]Wei Jiang, Yazhi Li, Jie Su. Modified GTN model for a broad range of stress states and application to ductile fracture[J]. European Journal of Mechanics A/Solids, 2016, 57: 132-148.

[105]韩蒙,李迪,孙彩凤等.基于修正GTN模型的双相钢断裂失效判据研究[J].塑性工程学报, 2020, 27(01):117-122.

[106]Rousselier G. Dissipation in porous metal plasticity and ductile fracture[J]. Journal of the Mechanics and Physics of Solids, 2001, 49 (8):1727-1746.

[107]Rousselier G. Ductile fracture models and their potential in local approach of fracture[J]. Nuclear Engineering and Design, 1987, 105 (1):97-111.

[108]Davison L, Stenvens A L. Thermomechanical constitution of spalling elastic bodies[J]. J Appl Phys, 1973(44):668-674.

[109]Vakulenko A A, Kachanov M. Continuum theory of cracked media[M]. Izc AN SSSR Mekh Tverdogo Tela, 1971(4):159-166.

[110]Murakami S, Ohno N. A Continuum Theory of Creep and Creep Damage Creep in Structures[J], 3rd Symposium of IUTAM, 1980:422-443.

[111]J.P. Cordebois, F. Sidoroff. Mechanical Behavior of Anisotropic Solid::Proceedings of the euromech colloquium 115[M]. Martinus Nijhoff, The Hague, 1979:761-774

[112]刘永平. 隧道脆性—准脆性围岩连续损伤特征研究[D]. 吉林大学, 2005.

[113]Bao Y, Wierzbicki T. On fracture locus in the equivalent strain and stress triaxiality space[J]. International Journal of Mechanical Sciences, 2004; 46(1) : 81-98

[114]Bao Y, Wierzbicki T. A comparative study on various ductile crack formation criteria[J]. Journal of Engineering Materials and Technology, 2004; 126(7): 314-324

[115]贾东,黄西成,莫军.基于应变路径和分布效应的应力三轴度确定方法[J].科学技术与工程,2013,13(10):2625-2629

[116]Bai YL, Wierzbicki T. A new model of metal plasticity and fracture with pressure and Lode dependence[J]. International Journal of Plasticity, 2008, 24(6): 1071-1096.

[117]Goto D M, Koss D A, Jablokov V. The influence of tensile stress states on the failure of HY-100 steel[J]. Metallurgical and Materials Transactions A, 1999; 30A: 2835-2842．

[118]Hooputra H, Metzmacher G, Werner H. Fracture criteria for crashworthiness simulation of wrought aluminum alloy components[C]. Proceedings of the 11th annual european conference, Europam, Heidelberg, Germany, 2001.

[119]Hooputra H, Gese H, Dell H, et al. A comprehensive failure model for crashworthiness simulation of aluminum extrusions[J]. International Journal of Crashworthiness, 2004, 9: 449-464.

[120]谭积钻. HRB400钢在较低三轴应力下变形破坏的试验与数值研究[D].广西大学,2018.

[121]Verkhovsky A B. Stress Determination of Dangerous Section of Complicated Shape Parts[M]. China Machine Press,1962:18.

[122]Science and Technology Committee of the Ministry of Aviation Industry.Stress Concentration Factor Manual[M].Beijing:Higher Education Press,1990.

[123]Nada Nao-Aki, Yasushi Takase. Stress concentration formula useful for all notch shape in a round bar(comparsion between torsion, tension and bending)[J]. International Journal of Fatigue, 2006, 28: 151-163

[124]Nada Nao-Aki, Rei Takaki, Yunong Shen, et al. Strain rate concentration factor for flat notched specimen to predict impact strength for polymeric materials[J]. Mechanics of Materials, 2019, 131:141-157.

[125]Nada Nao-Aki, H. OHTSUKA, H. ZHENG, et al. Strain rate concentration and dynamic stress concentration for double-edge-notched specimens subjected to high-speed tensile loads[J]. Fatigue & Fracture of Engineering Materials & Structures, 2015, 38: 125-138.

[126]Nada Nao-Aki, Yunong Shen, Rei Takaki, et al. Relationship bewteen strain rate concentration factor and stress concentration factor[J]. Theoretical and Applied Fracture Mechanics, 2017, 90:218-227.

[127]Nielsen K L, Tvergaard V. Effect of a shear modified Gurson model on damage development in a FSW tensile specimen[J]. Internatioanal Jorunal of Solid and Structures,

2009, 46(3):587-601.

[128]Malcher L, Andrade Pires F M. An assessment of isotropic constitutive models for ductile fracture under high and low stress triaxiality[J]. International Journal of Plasticity, 2012, 30:81-115

[129]姜薇. 基于细观损伤机理的韧性断裂研究[D]. 西安: 西北工业大学, 2016.

[130]P.J. Zhao, Z.H. Chen, C.F. Dong. Experimental and numerical analysis of micromechanical damage for DP600 steel in fine-blanking process[J]. Journal of Materials Processing Technology, 2016, 236:16-25.

[131]Zhang, XC, Tu, ST, Xuan, FZ. Creep-fatigue endurance of 304 stainless steels[J]. Theoretical and Applied Fracture Mechanics, 2014:51-66.

[132]L. Gardner. Stability and design of stainless steel structures – Review and outlook[J]. Thin - Walled Structures, 2019(141):208-216

[133]Abendroth M, Kuna M. Determination of deformation and failure properties of ductile materials by means of the small punch test and neural networks[J]. Computional Materials Science, 2003 ,28(3):633-644

[134]Cuest I I, Alegre J M, Lacalle R. Determination of the Gurson-Tvergaard damage model parameters for simulating small punch test[J]. Fatigue&Fracture of Engineering Materials & Structures, 2010, 33(11):703-713.

[135]Coffin LF. Fatigue and Microstructure. Fatigue in machines and structures-power generation[S]. ASM, 1978.

[136]郑修麟. 切口件的断裂力学[M]. 西安：西北工业大学出版社, 2005:21-29.

[137]郦正能，关志东，张继奎. 应用断裂力学[M]. 北京：北京航空航天大学出版社，2012.

[138]钟斌,李雪伍,于正洋等.304不锈钢棒气动式可控旋弯下料工艺及试验[J].机械工程学报, 2018,54 (22):47-54.

[139]Zheng XL, Hirt MA. Fatigue crack propagation in steels[J]. Engineering Fracture Mechanics, 1983, 18(5):965-973.

[140]PARIS.P, ERDOGAN. F. A critical analysis of crack propagation laws[J]. Journal of Basic Engineering, 1963:528-534.

付远,廖岩松,陆德平, 等.XFEM研究304不锈钢单边裂纹的高周疲劳扩展[J].钢铁,2018,53(09):63-68