含有预置缺陷的膨胀环动态断裂行为研究
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摘要
材料或结构的断裂位置及断裂形式一直是工程界和学术界关注的焦点。由于材料的样本个性,在动载作用下,裂纹的萌生往往会表现出特有的随机性,不会出现在某一个特定的位置。为了观测材料在高应变率加载下局部的断裂特征,本文采用预置缺陷的方法,使裂纹自然萌生于观测的视场范围内。利用爆炸膨胀环加载技术来实现对试样环的准一维加载,采用高速分幅相机观测膨胀环中预置圆孔的变形以及萌生裂纹的扩展。并利用LS-DYNA有限元程序再现整个过程。
(1)系统回顾调研了断裂研究的历史,分析了目前研究的难点、关注点以及研究方法,针对本课题实际,选择爆炸膨胀环作为加载手段,采用分幅相机作为测试手法,以获得膨胀环在高应变率下的局部断裂特征。
(2)为了清晰获得局部断裂特征,对膨胀环预置缺陷,并在试样前放置放大镜。无氧铜的实验发现,不同尺寸的缺陷会导致完全不同的断裂特征。通过改换材料20号钢,成功拍摄到预置圆孔应力集中最大位置处的裂纹萌生,及后期的扩展、止裂现象。
(3)针对含预置圆孔的20号钢膨胀环,起爆能量较低时,萌生于圆孔应力集中最大位置的裂纹会在一段时间之后止裂于某一裂纹长度；起爆能量较高时,萌生的裂纹失稳扩展,表现出特有的不稳定性。
(4)对于边缘预置缺口的实验,除了预置缺陷位置的裂纹萌生扩展之外,其它位置在内壁或者内部萌生缺陷,随着载荷穿透厚度方向,形成穿透裂纹,共同诱导整体的断裂破坏。
(5)实际测量中由于尺度原因往往会将裂纹断面的细节抹平,针对此,提出将裂纹扩展速度区分为测量速度与真实速度。通过这一理念上的区别,可以很简捷的解释极限裂纹扩展速度对其理论极限速度CR的较大偏离。
(6)通过对预置圆孔的20号钢膨胀环实验图像处理,得到了可视裂纹尖端的位移及速度随时间的变化。裂纹扩展速度随时间呈现一定的振荡,这体现出其特有的不稳定性。并以此估算裂纹的动态应力强度因子的变化。
(7)通过数值模拟探讨预置有圆孔的膨胀环在动态载荷作用下,圆孔的变形、裂纹的萌生以及扩展止裂的全过程。装药的多少决定了膨胀环内壁的载荷历史,由此决定膨胀环是否完全断裂。选择合适的参数,再现了膨胀环中圆孔诱导裂纹的萌生、扩展以及止裂现象。发现裂纹萌生于圆环的内壁,随时间穿透厚度方向,最终形成轴向裂纹。
Fracture position and fracture forms of materials and structures have been intensively researched by the academic and engineering circulars. Caused by sample personality, cracks usually initiate at different location under dynamic loading, showing its own randomness。In order to observe the local fracture characteristics of materials under high strain rate, a flaw is preset and the crack initiates naturally in the field range。The technique of expanding ring loading is used to achieve quasi one dimension tensile loading. The high-speed photography technique is serviced to gain the preset hole's deformation, the crack initiation and crack propagation。At last the whole fracture process is numerically simulated with LS-DYNA 3D finite element code.
(1) A review of fracture study is carried out。Current difficulties, focus and methods of the fracture mechanics are researched。The techniques of expanding ring loading and high-speed photography are used to observe the dynamic fracture characteristics for the subject。
(2) To obtain the local fracture characteristics, a flaw is preset。In addition, a magnifying glass is placed before the sample。From the experiments of copper, it is found that different flaw sizes caused different fracture forms。The circular hole's deformation, crack initiation and crack propagation process are obtained, by changing the material.
(3) At low explosive power, the crack stopped after a few of time in 20 steel expanding ring with a preset circular hole, while at high explosive power the crack propagating unstably。
(4) In addition to the location of crack initiation where preset an extended defect, other cracks initiate in the inner wall or inside for the experiment with a edged notch。As the load changes, defects penetrate through the thickness direction to form a through crack. The fracture induced the destruction of the whole.
(5) Details of the crack section are often ignored in actual measurement because of scale effects。It is recommended that the crack velocity can be distinguished as measuring velocity and real velocity。By the difference between these concepts, it is simple to explain why the limit velocity of crack propagation deviated to its theoretical limit speed。
(6) According to the image of the 20 steel expanding ring with a preset circular hole, the displacement and the velocity of crack tips are obtained。It is observed that the crack velocity oscillates with time because of the instability。And thus we estimate the dynamic stress intensity factors of the cracks。
(7) The circular hole's deformation, crack initiation, crack propagation and crack stop are numerically simulated with LS-DYNA 3D finite element code. Macro-crack can be found at the location of the hole under dynamic loading caused by stress concentration. Simulated results are in good agreement with experiments. It is found that crack initiation in the inner wall of the ring, which through the thickness direction。And axial cracks eventually are formed。
(1)系统回顾调研了断裂研究的历史,分析了目前研究的难点、关注点以及研究方法,针对本课题实际,选择爆炸膨胀环作为加载手段,采用分幅相机作为测试手法,以获得膨胀环在高应变率下的局部断裂特征。
(2)为了清晰获得局部断裂特征,对膨胀环预置缺陷,并在试样前放置放大镜。无氧铜的实验发现,不同尺寸的缺陷会导致完全不同的断裂特征。通过改换材料20号钢,成功拍摄到预置圆孔应力集中最大位置处的裂纹萌生,及后期的扩展、止裂现象。
(3)针对含预置圆孔的20号钢膨胀环,起爆能量较低时,萌生于圆孔应力集中最大位置的裂纹会在一段时间之后止裂于某一裂纹长度；起爆能量较高时,萌生的裂纹失稳扩展,表现出特有的不稳定性。
(4)对于边缘预置缺口的实验,除了预置缺陷位置的裂纹萌生扩展之外,其它位置在内壁或者内部萌生缺陷,随着载荷穿透厚度方向,形成穿透裂纹,共同诱导整体的断裂破坏。
(5)实际测量中由于尺度原因往往会将裂纹断面的细节抹平,针对此,提出将裂纹扩展速度区分为测量速度与真实速度。通过这一理念上的区别,可以很简捷的解释极限裂纹扩展速度对其理论极限速度CR的较大偏离。
(6)通过对预置圆孔的20号钢膨胀环实验图像处理,得到了可视裂纹尖端的位移及速度随时间的变化。裂纹扩展速度随时间呈现一定的振荡,这体现出其特有的不稳定性。并以此估算裂纹的动态应力强度因子的变化。
(7)通过数值模拟探讨预置有圆孔的膨胀环在动态载荷作用下,圆孔的变形、裂纹的萌生以及扩展止裂的全过程。装药的多少决定了膨胀环内壁的载荷历史,由此决定膨胀环是否完全断裂。选择合适的参数,再现了膨胀环中圆孔诱导裂纹的萌生、扩展以及止裂现象。发现裂纹萌生于圆环的内壁,随时间穿透厚度方向,最终形成轴向裂纹。
Fracture position and fracture forms of materials and structures have been intensively researched by the academic and engineering circulars. Caused by sample personality, cracks usually initiate at different location under dynamic loading, showing its own randomness。In order to observe the local fracture characteristics of materials under high strain rate, a flaw is preset and the crack initiates naturally in the field range。The technique of expanding ring loading is used to achieve quasi one dimension tensile loading. The high-speed photography technique is serviced to gain the preset hole's deformation, the crack initiation and crack propagation。At last the whole fracture process is numerically simulated with LS-DYNA 3D finite element code.
(1) A review of fracture study is carried out。Current difficulties, focus and methods of the fracture mechanics are researched。The techniques of expanding ring loading and high-speed photography are used to observe the dynamic fracture characteristics for the subject。
(2) To obtain the local fracture characteristics, a flaw is preset。In addition, a magnifying glass is placed before the sample。From the experiments of copper, it is found that different flaw sizes caused different fracture forms。The circular hole's deformation, crack initiation and crack propagation process are obtained, by changing the material.
(3) At low explosive power, the crack stopped after a few of time in 20 steel expanding ring with a preset circular hole, while at high explosive power the crack propagating unstably。
(4) In addition to the location of crack initiation where preset an extended defect, other cracks initiate in the inner wall or inside for the experiment with a edged notch。As the load changes, defects penetrate through the thickness direction to form a through crack. The fracture induced the destruction of the whole.
(5) Details of the crack section are often ignored in actual measurement because of scale effects。It is recommended that the crack velocity can be distinguished as measuring velocity and real velocity。By the difference between these concepts, it is simple to explain why the limit velocity of crack propagation deviated to its theoretical limit speed。
(6) According to the image of the 20 steel expanding ring with a preset circular hole, the displacement and the velocity of crack tips are obtained。It is observed that the crack velocity oscillates with time because of the instability。And thus we estimate the dynamic stress intensity factors of the cracks。
(7) The circular hole's deformation, crack initiation, crack propagation and crack stop are numerically simulated with LS-DYNA 3D finite element code. Macro-crack can be found at the location of the hole under dynamic loading caused by stress concentration. Simulated results are in good agreement with experiments. It is found that crack initiation in the inner wall of the ring, which through the thickness direction。And axial cracks eventually are formed。
引文
[1]金达曾,邓增杰,黄明志等,金属材料强度学[M],北京科学出版社,1989
[2]许锷俊,缺陷、损伤、微裂纹对航空发动机构件服役总寿命及可靠性的影响[J],航空发动机,Vol.29(2),2003：11-15
[3]包亦望,金宗哲,孙立,陶瓷的本征强度与常规强度[J],机械强度,Vol.16(3),1.994：29-32
[4]杨卫,宏微观断裂力学[M],国防工业出版社,1995
[5]Jay Fineberg, Close-up on cracks[J], Nature, Vol.426,2003:131-132
[6]L.B.Freund, Dynamic Fracture Mechanics[M], Cambridge University Press,1990
[7]Eran Sharon & Jay Fineberg, Confirming the continuum theory of dynamic brittle fracture for fast cracks[J], Nature, Vol.397,1999:333-335
[8]Jay Fineberg, Eran Sharon and G.Cohen, Crack Front Waves in Dynamic Fracture[J], International Journal of Fracture Vol.119,2003:247-261
[9]J. Fineberg, M. Marder, Instability in dynamic fracture, Physics Reports 313 (1999) 1-108
[10]Eran Sharon, Steven P. Gross and Jay Fineberg, Energy Dissipation in Dynamic Fracture[J], Physical Review Letters, Vol.76(12),1996:2117-2120
[11]Eran Sharon and Jay Fineberg, The Dynamics of Fast Fracture[J], Advanced Engineering Materials 1999,1, No.2 pp119-122
[12]T.D. Nguyen, S. Govindjee, P.A. Klein et.al, A rate-dependent cohesive continuum model for the study of crack dynamics[J], Comput. Methods Appl. Mech. Engrg. Vol.193,2004:3239-3265
[13]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅰ.Crack initiation and arrest[J]. International Journal of Fracture, Vol.25,1984:247-262
[14]K.Ravi-Chandar and W.G.Knauss. An experimental investigation into dynamic fracture: Ⅱ.Microstructural aspects[J]. International Journal of Fracture, Vol.26,1984:65-80
[15]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅲ.On steady-state crack propagation and crack branching[J]. International Journal of Fracture. Vol.26,1984: 141-154
[16]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅳ.On the interaction of stress waves with propagating cracks[J]. International Journal of Fracture.Vol.26,1984: 189-200
[17]Su Hao, Wing Kam Liu, Patrick A.Klein et.al, Modeling and simulation of intersonic crack growth[J], International Journal of Solids and Structures Vol.41,2004:1773-1799
[18]P.Klein, H.Gao, Crack nucleation and growth as strain localization in a virtual-bond continuum[J], Engineering Fracture Mechanics Vol.61,1998:21-48
[19]张振南,葛修润,李永和,基于虚内键理论的材料多尺度力学模型[J],固体力学学报,Vol.27(4),2006：325-329
[20]张振南,葛修润,多维虚内键模型(VMIB)及其在岩体数值模拟中的应用[J],中国科学E：科学技术,Vol.37(5),2007：605-612
[21]张振南,葛修润,基于VMIB的非均质岩石材料破坏的数值模拟初探[J],岩石力学与工程学报,Vol.26(7),2007：1426-1431
[22]张振南,葛修润,张孟喜,基于VMIB的岩石围压破坏二维多尺度数值模拟[J],岩土力学,Vol.29(1),2008：219-224
[23]Zhennan Zhang, Xiurun Ge, Numerical simulation of two-dimensional shear fracture based on virtual multi-dimensional internal bonds[J], International Journal of Rock Mechanics & Mining Sciences Vol.45,2008:442-449
[24]张振南,多维虚内键模型理论与材料破坏模拟,北京科学出版社,2008
[25]白以龙,汪海英,夏蒙棼等,固体的统计宏观力学——连接多个耦合的时空尺度[J]。力学进展,Vol.36(2),2006：286-305
[26]白以龙,柯孚久,夏蒙棼,损伤断裂的确定性随机行为和对初始位形的敏感性[J],科学通报,Vol.39(10),1994：892-895
[27]黄克智,邱信明,姜汉卿,应变梯度理论的新进展(一)——偶应力理论和SG理论[J],机械强度,Vol.21(2),1999：81-87
[28]黄克智,邱信明,姜汉卿,应变梯度理论的新进展(二)——基于细观机制的MSG应变梯度塑性理论[J],机械强度,Vol.21(3),1999：161-165
[29]陈少华,王自强,应变梯度理论进展[J],力学进展,Vol.33(2),2003：207-216
[30]X.Y.Wu, K.T.Ramesh, T.W.Wright, The effects of thermal softening and heat conduction on the dynamic growth of voids[J], International Journal of Solids and Structures Vol.40,2003:4461-4478
[31]X.Y.Wu, K.T.Ramesh, T.W.Wright, The coupled effects of plastic strain gradient and thermal softening on the dynamic growth of voids[J], International Journal of Solids and Structures Vol.40,2003: 6633-6651
[32]Mel Vin F.Kanninen,Carl H.Popelar著,洪其麟、郑光华、郑祺选等译,高等断裂力学[M],北京航空学院出版社,1987.
[33]李振环,匡震邦,张克实,三轴应力场中不同形状孔洞的长大及其新模型[J],计算力学学报,Vol.17(4),2000：447-454
[34]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,Vol.18(1),1997：50-58
[35]K. S. Zhang, D. Zhang, and R. Feng, et al, Microdamage in polycrystalline ceramics under dynamic compression and tension, Journal of Applied Physics, Vol.98,,2005:023505-1-10
[36]李晓红,张克实,初始损伤非均匀性条件下的材料细观损伤演化[J],机械科学与技术,Vol.22(1),2003：118-120
[37]李振环,张克实,光滑拉伸试件中不同初始形状孔洞长大的有限元模拟[J],计算力学学报,Vol.14(4),1997：454-461
[38]张光,张克实,冯露等,截面形状对材料微孔洞损伤破坏的影响[J],机械工程学报,Vol.38(9),2002：22-26
[39]李晓红,张克实,延性材料损伤演化及材料软化的孔洞尺寸影响[J],机械强度,Vol.25(1)2003：81-84
[40]D. Grady et al. Investigation of Explosively Driven Fragmentation of Metals-----Two Dimensional Fracture and Fragmentation of Metal Shells--Progress Report Ⅱ
[41]汤铁钢、李庆忠、王健,等。爆炸膨胀环实验技术初步研究[J],高能量密度物理,2008(1)：68-70
[42]汤铁钢、李庆忠、陈永涛,等。实现材料高应变率拉伸加载的爆炸膨胀环技术,爆炸与冲击,2009,Vol.29(5)：546-549
[43]汤铁钢、李庆忠、刘仓理。缺口膨胀环实验的设计分析与数值模拟研究[J],爆炸与冲击,2009,Vol.29(6).561-565
[44]汤铁钢、桂毓林、李庆忠等。爆炸膨胀环实验数据处理方法讨论[J],爆炸与冲击,已录用
[45]：汤铁钢、李庆忠、陈永涛等。爆炸膨胀环一维应力假定的分析与讨论[J],爆炸与冲击,已录用
[46]桂毓林、孙承伟、李强等,实现金属环动态拉伸的电磁加载技术研究[J],爆炸与冲击,Vol.26(6)2006：281-285
[47]桂毓林、孙承伟、路中华,一维快速拉伸下无氧铜的动态断裂与破碎[J],爆炸与冲击,Vol.27(1),2007：40-44
[48]桂毓林、谭多望、孙承伟,延性金属膨胀环的运动及断裂的三维数值模拟[J],计算力学学报,Vol.26(4),2009：579-584
[49]桂毓林,电磁加载下金属膨胀环的动态断裂与碎裂研究[D],博士学位论文
[50]余海东,林忠钦,张克实,薄板试样斜断口形成机制及损伤断裂过程分析[J],固体力学学报,Vol.27(2),2006：175-180
[51]余海东,张克实,郭运强等,中心圆孔薄板试样局部损伤破坏实验与数值分析[J],机械工程材料,Vol.29(1),2005：16-19
[1]余海东,张克实,郭运强等,中心圆孔薄板试样局部损伤破坏实验与数值分析[J],机械工程材料,Vol.29(1),2005：16-19
[2]汤铁钢、李庆忠、王健等。爆炸膨胀环实验技术初步研究[J],高能量密度物理,2008(1)：68-70
[3]汤铁钢、李庆忠、刘仓理。缺口膨胀环实验的设计分析与数值模拟研究[J],爆炸与冲击,2009,Vol.29(6).561-565
[4]桂毓林、孙承伟、路中华,一维快速拉伸下无氧铜的动态断裂与破碎[J],爆炸与冲击,Vol.27(1),2007：40-44
[5]桂毓林,电磁加载下金属膨胀环的动态断裂与碎裂研究[D],博士学位论文
[6]D. Grady et al. Investigation of Explosively Driven Fragmentation of Metals-----Two Dimensional Fracture and Fragmentation of Metal Shells--Progress Report Ⅱ
[7]汤铁钢、李庆忠、陈永涛,等。实现材料高应变率拉伸加载的爆炸膨胀环技术[J],爆炸与冲击,Vol.29(5),2009：546-549
[8]孙承伟,等。应用爆轰物理[M],国防工业出版社,2000
[1]Mikko J. Alava et al. Fracture size effects from disordered lattice models[J], International Journal of Fracture, Vol(154),2008:51-59
[2]Z.P.Bazant. Concrete fracture models:testing and practice. Engineering Fracture Mechanics Vol.(69),2002:165-205
[3]白以龙,柯孚久,夏蒙棼,损伤断裂的确定性随机行为和对初始位形的敏感性[J],科学通报,Vol.39(10),1994：892-895
[4]白以龙,汪海英,夏蒙棼等。固体的统计宏观力学——连接多个耦合的时空尺度[J]。力学进展,Vol.36(2),2006：286-305
[1]Mel Vin F.Kanninen,Carl H.Popelar著,洪其麟、郑光华、郑祺选等译,高等断裂力学[M],北京航空学院出版社,1987.
[2]L.B.Freund,Dynamic Fracture Mechanics[M],Cambridge University Press 1990.
[3]M.H.Aliabadi and D.P.Rooke.Numerical Fracture Mechanicd.Kluwer Academic Publisher 1991.
[4]杨卫,宏微观断裂力学,国防工业出版社,1995
[5]Norio Hasebe and Yasuhiro Kutanda,Caculation of stress intensity factor from stress concentration factor[J],Eng.Fra.Mech, Vol.(10),1978:215-221
[6]W.T.Koiter, Rectangular Tensile Sheet with Symmetric Edge Cracks[J],J.A.P,March1965:237-240
[7]J.Tweed and D.P.Rooke,The elastic problem for an infinite solid containing a circular hole with a pair of radial edge cracks of different lengths[J],Int.J.Engng Sci, Vol.14,1976:pp925-933
[8]西田正孝著,李安定,郭廷玮译,应力集中[M],机械工业出版社,1986
[9]程靳,赵树山,断裂力学[M],科学出版社,2006
[10]Eran Sharon, Steven P. Gross and Jay Fineberg, Energy Dissipation in Dynamic Fracture, Physical Review Letters, Vol.76 (12),1996:2117-2120
[11]J. Fineberg, M. Marder, Instability in dynamic fracture, Physics Reports 313 (1999) 1-108
[12]Eran Sharon & Jay Fineberg, Confirming the continuum theory of dynamic brittle fracture for fast cracks, Nature, Vol.397,1999:333-335
[13]Jay Fineberg, Eran Sharon and G.Cohen, Crack Front Waves in Dynamic Fracture, International Journal of Fracture 119:247-261,2003.
[14]T.D. Nguyen, S. Govindjee, P.A. Klein et.al, A rate-dependent cohesive continuum model for the study of crack dynamics, Comput. Methods Appl. Mech. Engrg. Vol.193,2004:3239-3265
[15]K.Ravi-Chandar and W.G.Knauss. An experimental investigation into dynamic fracture:Ⅰ.Crack initiation and arrest. International Journal of Fracture Vol.25,1984:247-262
[16]K.Ravi-Chandar and W.G.Knauss. An experimental investigation into dynamic fracture: II.Microstructural aspects[J]. International Journal of Fracture Vol.26,1984:65-80
[17]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅲ.On steady-state crack propagation and crack branching[J]. International Journal of Fracture. Vol.26,1984: 141-154
[18]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅳ.On the interaction of stress waves with propagating cracks [J]. International Journal of Fracture. Vol. 26,1984:189-200
[1]LS-DYNA Keyword user's manual, March 2001 version 960, Livermore Software Technology Corporation
[2]工程材料实用手册,结构钢、不锈钢[M],中国标准出版社,1988
[3]汤铁钢、李庆忠、陈永涛,等。实现材料高应变率拉伸加载的爆炸膨胀环技术[J],爆炸与冲击,2009,Vol.29(5)：546-549
[2]许锷俊,缺陷、损伤、微裂纹对航空发动机构件服役总寿命及可靠性的影响[J],航空发动机,Vol.29(2),2003：11-15
[3]包亦望,金宗哲,孙立,陶瓷的本征强度与常规强度[J],机械强度,Vol.16(3),1.994：29-32
[4]杨卫,宏微观断裂力学[M],国防工业出版社,1995
[5]Jay Fineberg, Close-up on cracks[J], Nature, Vol.426,2003:131-132
[6]L.B.Freund, Dynamic Fracture Mechanics[M], Cambridge University Press,1990
[7]Eran Sharon & Jay Fineberg, Confirming the continuum theory of dynamic brittle fracture for fast cracks[J], Nature, Vol.397,1999:333-335
[8]Jay Fineberg, Eran Sharon and G.Cohen, Crack Front Waves in Dynamic Fracture[J], International Journal of Fracture Vol.119,2003:247-261
[9]J. Fineberg, M. Marder, Instability in dynamic fracture, Physics Reports 313 (1999) 1-108
[10]Eran Sharon, Steven P. Gross and Jay Fineberg, Energy Dissipation in Dynamic Fracture[J], Physical Review Letters, Vol.76(12),1996:2117-2120
[11]Eran Sharon and Jay Fineberg, The Dynamics of Fast Fracture[J], Advanced Engineering Materials 1999,1, No.2 pp119-122
[12]T.D. Nguyen, S. Govindjee, P.A. Klein et.al, A rate-dependent cohesive continuum model for the study of crack dynamics[J], Comput. Methods Appl. Mech. Engrg. Vol.193,2004:3239-3265
[13]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅰ.Crack initiation and arrest[J]. International Journal of Fracture, Vol.25,1984:247-262
[14]K.Ravi-Chandar and W.G.Knauss. An experimental investigation into dynamic fracture: Ⅱ.Microstructural aspects[J]. International Journal of Fracture, Vol.26,1984:65-80
[15]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅲ.On steady-state crack propagation and crack branching[J]. International Journal of Fracture. Vol.26,1984: 141-154
[16]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅳ.On the interaction of stress waves with propagating cracks[J]. International Journal of Fracture.Vol.26,1984: 189-200
[17]Su Hao, Wing Kam Liu, Patrick A.Klein et.al, Modeling and simulation of intersonic crack growth[J], International Journal of Solids and Structures Vol.41,2004:1773-1799
[18]P.Klein, H.Gao, Crack nucleation and growth as strain localization in a virtual-bond continuum[J], Engineering Fracture Mechanics Vol.61,1998:21-48
[19]张振南,葛修润,李永和,基于虚内键理论的材料多尺度力学模型[J],固体力学学报,Vol.27(4),2006：325-329
[20]张振南,葛修润,多维虚内键模型(VMIB)及其在岩体数值模拟中的应用[J],中国科学E：科学技术,Vol.37(5),2007：605-612
[21]张振南,葛修润,基于VMIB的非均质岩石材料破坏的数值模拟初探[J],岩石力学与工程学报,Vol.26(7),2007：1426-1431
[22]张振南,葛修润,张孟喜,基于VMIB的岩石围压破坏二维多尺度数值模拟[J],岩土力学,Vol.29(1),2008：219-224
[23]Zhennan Zhang, Xiurun Ge, Numerical simulation of two-dimensional shear fracture based on virtual multi-dimensional internal bonds[J], International Journal of Rock Mechanics & Mining Sciences Vol.45,2008:442-449
[24]张振南,多维虚内键模型理论与材料破坏模拟,北京科学出版社,2008
[25]白以龙,汪海英,夏蒙棼等,固体的统计宏观力学——连接多个耦合的时空尺度[J]。力学进展,Vol.36(2),2006：286-305
[26]白以龙,柯孚久,夏蒙棼,损伤断裂的确定性随机行为和对初始位形的敏感性[J],科学通报,Vol.39(10),1994：892-895
[27]黄克智,邱信明,姜汉卿,应变梯度理论的新进展(一)——偶应力理论和SG理论[J],机械强度,Vol.21(2),1999：81-87
[28]黄克智,邱信明,姜汉卿,应变梯度理论的新进展(二)——基于细观机制的MSG应变梯度塑性理论[J],机械强度,Vol.21(3),1999：161-165
[29]陈少华,王自强,应变梯度理论进展[J],力学进展,Vol.33(2),2003：207-216
[30]X.Y.Wu, K.T.Ramesh, T.W.Wright, The effects of thermal softening and heat conduction on the dynamic growth of voids[J], International Journal of Solids and Structures Vol.40,2003:4461-4478
[31]X.Y.Wu, K.T.Ramesh, T.W.Wright, The coupled effects of plastic strain gradient and thermal softening on the dynamic growth of voids[J], International Journal of Solids and Structures Vol.40,2003: 6633-6651
[32]Mel Vin F.Kanninen,Carl H.Popelar著,洪其麟、郑光华、郑祺选等译,高等断裂力学[M],北京航空学院出版社,1987.
[33]李振环,匡震邦,张克实,三轴应力场中不同形状孔洞的长大及其新模型[J],计算力学学报,Vol.17(4),2000：447-454
[34]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,Vol.18(1),1997：50-58
[35]K. S. Zhang, D. Zhang, and R. Feng, et al, Microdamage in polycrystalline ceramics under dynamic compression and tension, Journal of Applied Physics, Vol.98,,2005:023505-1-10
[36]李晓红,张克实,初始损伤非均匀性条件下的材料细观损伤演化[J],机械科学与技术,Vol.22(1),2003：118-120
[37]李振环,张克实,光滑拉伸试件中不同初始形状孔洞长大的有限元模拟[J],计算力学学报,Vol.14(4),1997：454-461
[38]张光,张克实,冯露等,截面形状对材料微孔洞损伤破坏的影响[J],机械工程学报,Vol.38(9),2002：22-26
[39]李晓红,张克实,延性材料损伤演化及材料软化的孔洞尺寸影响[J],机械强度,Vol.25(1)2003：81-84
[40]D. Grady et al. Investigation of Explosively Driven Fragmentation of Metals-----Two Dimensional Fracture and Fragmentation of Metal Shells--Progress Report Ⅱ
[41]汤铁钢、李庆忠、王健,等。爆炸膨胀环实验技术初步研究[J],高能量密度物理,2008(1)：68-70
[42]汤铁钢、李庆忠、陈永涛,等。实现材料高应变率拉伸加载的爆炸膨胀环技术,爆炸与冲击,2009,Vol.29(5)：546-549
[43]汤铁钢、李庆忠、刘仓理。缺口膨胀环实验的设计分析与数值模拟研究[J],爆炸与冲击,2009,Vol.29(6).561-565
[44]汤铁钢、桂毓林、李庆忠等。爆炸膨胀环实验数据处理方法讨论[J],爆炸与冲击,已录用
[45]：汤铁钢、李庆忠、陈永涛等。爆炸膨胀环一维应力假定的分析与讨论[J],爆炸与冲击,已录用
[46]桂毓林、孙承伟、李强等,实现金属环动态拉伸的电磁加载技术研究[J],爆炸与冲击,Vol.26(6)2006：281-285
[47]桂毓林、孙承伟、路中华,一维快速拉伸下无氧铜的动态断裂与破碎[J],爆炸与冲击,Vol.27(1),2007：40-44
[48]桂毓林、谭多望、孙承伟,延性金属膨胀环的运动及断裂的三维数值模拟[J],计算力学学报,Vol.26(4),2009：579-584
[49]桂毓林,电磁加载下金属膨胀环的动态断裂与碎裂研究[D],博士学位论文
[50]余海东,林忠钦,张克实,薄板试样斜断口形成机制及损伤断裂过程分析[J],固体力学学报,Vol.27(2),2006：175-180
[51]余海东,张克实,郭运强等,中心圆孔薄板试样局部损伤破坏实验与数值分析[J],机械工程材料,Vol.29(1),2005：16-19
[1]余海东,张克实,郭运强等,中心圆孔薄板试样局部损伤破坏实验与数值分析[J],机械工程材料,Vol.29(1),2005：16-19
[2]汤铁钢、李庆忠、王健等。爆炸膨胀环实验技术初步研究[J],高能量密度物理,2008(1)：68-70
[3]汤铁钢、李庆忠、刘仓理。缺口膨胀环实验的设计分析与数值模拟研究[J],爆炸与冲击,2009,Vol.29(6).561-565
[4]桂毓林、孙承伟、路中华,一维快速拉伸下无氧铜的动态断裂与破碎[J],爆炸与冲击,Vol.27(1),2007：40-44
[5]桂毓林,电磁加载下金属膨胀环的动态断裂与碎裂研究[D],博士学位论文
[6]D. Grady et al. Investigation of Explosively Driven Fragmentation of Metals-----Two Dimensional Fracture and Fragmentation of Metal Shells--Progress Report Ⅱ
[7]汤铁钢、李庆忠、陈永涛,等。实现材料高应变率拉伸加载的爆炸膨胀环技术[J],爆炸与冲击,Vol.29(5),2009：546-549
[8]孙承伟,等。应用爆轰物理[M],国防工业出版社,2000
[1]Mikko J. Alava et al. Fracture size effects from disordered lattice models[J], International Journal of Fracture, Vol(154),2008:51-59
[2]Z.P.Bazant. Concrete fracture models:testing and practice. Engineering Fracture Mechanics Vol.(69),2002:165-205
[3]白以龙,柯孚久,夏蒙棼,损伤断裂的确定性随机行为和对初始位形的敏感性[J],科学通报,Vol.39(10),1994：892-895
[4]白以龙,汪海英,夏蒙棼等。固体的统计宏观力学——连接多个耦合的时空尺度[J]。力学进展,Vol.36(2),2006：286-305
[1]Mel Vin F.Kanninen,Carl H.Popelar著,洪其麟、郑光华、郑祺选等译,高等断裂力学[M],北京航空学院出版社,1987.
[2]L.B.Freund,Dynamic Fracture Mechanics[M],Cambridge University Press 1990.
[3]M.H.Aliabadi and D.P.Rooke.Numerical Fracture Mechanicd.Kluwer Academic Publisher 1991.
[4]杨卫,宏微观断裂力学,国防工业出版社,1995
[5]Norio Hasebe and Yasuhiro Kutanda,Caculation of stress intensity factor from stress concentration factor[J],Eng.Fra.Mech, Vol.(10),1978:215-221
[6]W.T.Koiter, Rectangular Tensile Sheet with Symmetric Edge Cracks[J],J.A.P,March1965:237-240
[7]J.Tweed and D.P.Rooke,The elastic problem for an infinite solid containing a circular hole with a pair of radial edge cracks of different lengths[J],Int.J.Engng Sci, Vol.14,1976:pp925-933
[8]西田正孝著,李安定,郭廷玮译,应力集中[M],机械工业出版社,1986
[9]程靳,赵树山,断裂力学[M],科学出版社,2006
[10]Eran Sharon, Steven P. Gross and Jay Fineberg, Energy Dissipation in Dynamic Fracture, Physical Review Letters, Vol.76 (12),1996:2117-2120
[11]J. Fineberg, M. Marder, Instability in dynamic fracture, Physics Reports 313 (1999) 1-108
[12]Eran Sharon & Jay Fineberg, Confirming the continuum theory of dynamic brittle fracture for fast cracks, Nature, Vol.397,1999:333-335
[13]Jay Fineberg, Eran Sharon and G.Cohen, Crack Front Waves in Dynamic Fracture, International Journal of Fracture 119:247-261,2003.
[14]T.D. Nguyen, S. Govindjee, P.A. Klein et.al, A rate-dependent cohesive continuum model for the study of crack dynamics, Comput. Methods Appl. Mech. Engrg. Vol.193,2004:3239-3265
[15]K.Ravi-Chandar and W.G.Knauss. An experimental investigation into dynamic fracture:Ⅰ.Crack initiation and arrest. International Journal of Fracture Vol.25,1984:247-262
[16]K.Ravi-Chandar and W.G.Knauss. An experimental investigation into dynamic fracture: II.Microstructural aspects[J]. International Journal of Fracture Vol.26,1984:65-80
[17]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅲ.On steady-state crack propagation and crack branching[J]. International Journal of Fracture. Vol.26,1984: 141-154
[18]K.Ravi-Chandar and W.G.Knauss.An experimental investigation into dynamic fracture:Ⅳ.On the interaction of stress waves with propagating cracks [J]. International Journal of Fracture. Vol. 26,1984:189-200
[1]LS-DYNA Keyword user's manual, March 2001 version 960, Livermore Software Technology Corporation
[2]工程材料实用手册,结构钢、不锈钢[M],中国标准出版社,1988
[3]汤铁钢、李庆忠、陈永涛,等。实现材料高应变率拉伸加载的爆炸膨胀环技术[J],爆炸与冲击,2009,Vol.29(5)：546-549
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