岩石动态断裂韧性测试方法研究
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摘要
本文基于分离式霍普金森压杆(SHPB)试验技术,借助平台人字形切槽巴西圆盘型试件(CCNBD),详细研究了取自3个深度下同一岩性(玄武岩)的岩石动态断裂韧性的测试方法。研究发现,在满足动态力平衡的条件下,可将准静态断裂韧性计算公式推广到动态断裂韧性测试中；提出了用最小应力强度因子以及最大外载荷作为动态断裂失稳判据来判定断裂韧性的方法；运用LS-DYNA程序,分析了测试系统在满足SHPB两个基本假定(一维应力波假定和应力均匀化假定)前提下的能量耗散；在此基础上,进行了岩石动态断裂韧性测试,得到了动态断裂韧性随着加载率增大而增大的规律,并进一步应用应力场多轴化对该现象进行了解释；结合岩石的静态力学性质,讨论了影响断裂韧性的主要因素,研究发现岩石内部微裂纹的开裂、扩展、贯通主要由拉应力控制,且岩石的拉伸强度对断裂韧性起着决定性影响。
Based on Split Hopkinson Pressure Bar (SHPB) testing system, and using Flattened Cracked Chevron Notched Brazilian Disc (CCNBD) specimen, this paper researches the dynamic fracture toughness test method of the same basalt with three different depths. It can extend the quasi-static fracture toughness testing equation into dynamic fracture toughness method, only if the dynamic force balance was satisfied. And it has proposed a dynamic failure criterion to determine the critical value of the stress intensity factor, i.e. the minimum dimensionless stress intensity factor and the maximum stress corresponded. The LS-DYNA program has been adopted to analyze the energy release of the testing system, and verified the two fundamental assumptions (one dimension stress wave and stress equalization). It has obtained that the dynamic fracture toughness increases with the loading rate, and illuminated it from the point of multi-axial stress field at the crack tip. It has discussed the influence factor of the fracture toughness, combined with rock static tensile strength. It provides estimation of rock failure from the micro crack growth, propagation and coalescence induced by tensile strength.
Based on Split Hopkinson Pressure Bar (SHPB) testing system, and using Flattened Cracked Chevron Notched Brazilian Disc (CCNBD) specimen, this paper researches the dynamic fracture toughness test method of the same basalt with three different depths. It can extend the quasi-static fracture toughness testing equation into dynamic fracture toughness method, only if the dynamic force balance was satisfied. And it has proposed a dynamic failure criterion to determine the critical value of the stress intensity factor, i.e. the minimum dimensionless stress intensity factor and the maximum stress corresponded. The LS-DYNA program has been adopted to analyze the energy release of the testing system, and verified the two fundamental assumptions (one dimension stress wave and stress equalization). It has obtained that the dynamic fracture toughness increases with the loading rate, and illuminated it from the point of multi-axial stress field at the crack tip. It has discussed the influence factor of the fracture toughness, combined with rock static tensile strength. It provides estimation of rock failure from the micro crack growth, propagation and coalescence induced by tensile strength.
引文
[1]谢和平,陈忠辉.岩石力学[M] 北京：科学出版社2004.
[2]周宏伟,谢和平,左建平.深部高地应力下岩石力学行为研究进展[J].力学进展,2005,35(1),91-99
[3]谢和平,彭苏萍,何满潮.深部开采-基础理论与工程实践[M].北京：科学出版社2006
[4]谢和平.深部高应力下的资源开采—现状、基础科学问题与展望.见：香山科学会议编.科学前沿与未来.北京：中国环境科学出版社,2002,179-191
[5]王驹,陈伟明,苏锐等.高放废物地质处置及其若干关键科学问题[J].岩石力学与工程学报,2006,25(4),801-812.
[6]王礼立.应力波基础[M] 北京：国防工业出版社2005.
[7]庄茁,蒋持平.工程断裂与损失[M] 北京：机械工业出版社2004.
[8]李夕兵,古德生.岩石冲击动力学[M] 长沙：中南工业大学出版社1994.
[9]Melvin F. Kanninen and Carl H. Popelar. Advanced Fracture Mechanics.高等断裂力学[M] 洪其麟 郑光华 郑祺选 饶寿期 李石 戴羿 译.北京：北京航空学院出版社发行,1987
[10]Rolfe S.T.and Barsom J. M.. Fracture And Fatigue Control in Structures—— Applications of Fracture Mechanics结构中的断裂与疲劳控制——断裂力学的应用[M]刘文珽 仇仲翼 黄乃人 张诚文 译1985.
[11]高庆.工程断裂力学[M] 重庆：重庆大学出版社1986.
[12]袁懋昶.断裂力学理论及其工程应用第一卷线弹性断裂力学(上册)[M] 重庆：重庆大学出版社1989.
[13]袁懋昶.断裂力学理论及其工程应用第一卷线弹性断裂力学(下册)[M] 重庆：重庆大学出版社1989.
[14]范天佑.断裂动力学原理与应用[M] 北京：北京理工大学出版社2006.
[15]Standard method for notch bar impact testing of metallic materials. E23 Annual Book of ASTM,1984, (Philadelphia):210
[16]Kalthoff J F. et al. Evaluating material properties by dynamic testing. ESIS Publication.1996(20):25-35
[17]Bohme W. and Kalthoff J F. The behavior of notched bend specimen in impact testing. International Journal of Fracture.1982,20(1):139-143
[18]ISRM Testing Commission. Suggested method for determining the fracture toughness of rock[J].1988.
[19]Xu C. Fracture Mechanics and Its Application in Rock Excavation Engineering [D]. Press:The University of Leeds.1993.
[20]Fowell RJ, Xu C. The use of the cracked Brazilian disc geometry for rock fracture investigation [J]. Int J Rock Mech Min Sci Geomech Abstr,1994,31:571-579P.
[21]Fowell RJ, Xu C. et al. An update on the fracture toughness testing methods related to the cracked chevron notched brazilian disk specimen[J]. Pure and Applied Geophysics,2006,13:1047-1057P.
[22]ISRM Testing Commission. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc(CCNBD) specimens[J]. Int J Rock Mech Min Sci Geomech Abstr,1995,32:57-64P.
[23]Tang C A and Xu X H. A new method for measuring dynamic fracture toughness of rock[J]. Engineering Fracture Mechanics,1990,35:783-791P.
[24]Kalthoff J F. On the measurement of dynamic fracture toughness-a review of recent work[J]. Int J Fract,1985,27:277-298P.
[25]Nakamura T, Shih C F and Freund L B. Elastic-plastic analysis of a dynamically loaded circumferentially notched round bar[J]. Engng Fract Mech,1985, 22(3):437-452P.
[26]Wada H. Determination of dynamic fracture toughness for PMMA [J]. Engng Fract Mech,1992,41:821-831P.
[27]Wada H. Seika M and Kennedy T C. et al. Investigation of loading rate and plate thickness effects on dynamic fracture toughness of PMMA [J]. Engng Fract Mech, 1996,54:805-811P.
[28]Rittle D. The influence of temperature on dynamic failure mode transitions [J]. Mech Mater,1998,30:217-227P.
[29]Rittle D., Levin R. Mode-mixity and dynamic failure mode transitions in polycarbonate [J]. Mech Mater,1998,30:197-216P.
[30]Rittle D.,Maigre H. An investigation of dynamic crack initiation in PMMA [J]. Mech Mater,1996,23:229-239P.
[31]Rittle D.,Maigre H. A study of mixed mode dynamic crack initiation in PMMA [J]. Mech Research Communications,1996,23:475-481P.
[32]R. Chen, K. Xia, F. Dai, et al. Determination of dynamic fracture parameters using a semi-circular bend technique in split Hopkinson pressure bar testing [J]. Engineering Fracture Mechanics,2009,76:1268-1276.
[33]Feng Dai, K. Xia, Lizhong Tang. Rate dependence of the.flexural tensile strength of Laurentian granite [J]. Int J Rock Mech Min Sci,2009, Article in press.
[34]王启智,贾学明.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第一部分：解析和数值结果[J] 岩石力学与工程学报,2002,21[9]：1285-1289.
[35]王启智,吴礼舟.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第二部分：试验结果[J] 岩石力学与工程学报,2004,23[2]：199-204.
[36]贾学明,王启智.标定ISRM岩石断裂韧度新型试样CCNBD的应力强度因子[J] 岩石力学与工程学报,2003,22[8]：1227-1233.
[37]张盛,王启智.采用中心圆孔裂缝平台圆盘确定岩石的动态断裂韧度[J] 岩土工程学报,2006,28[6]：723-728.
[38]王礼立,王永刚.应力波在用SHPB研究材料动态本构特性中的重要作用[J] 爆炸与冲击,2005,25[1]：17-25.
[39]Han Zhao, Gerard Gary. On the use of SHPB techniques to determine the dynamic behavior of materials in the range of small strains [J]. Int J Solids Structures, 1996,23:3363-3375P.
[40]陶俊林,陈裕泽,田常津等.SHPB系统圆柱型试件的惯性效应分析[J]固体力学学报, 2005,26[1]：107-110.
[41]陈刚,陶俊林,黄西成等.SHPB的径向惯性效应修正[J]西南科技大学学报,2008,23[2]：15-18.
[42]陶俊林.SHPB试验中几个问题的讨论[J]西南科技大学学报,2009,24[3]：27-35.
[43]张晓欣,刘瑞堂,邹广平.动态断裂韧度测试过程中的惯性效应分析[J]中国力学学会学术大会2005(CCTAM2005)
[44]类维生苏燕董建令等.动态断裂过程的惯性效应[J]理化检验-物理分册,1996,32[4]：32-34.
[45]李存剑,李少华,翁宇庆.动态断裂韧性测试中的惯性效应分析[J]理化检验-物理分册,2000,36[11]：483-485.
[46]陶俊林,田常津,陈裕泽等.SHPB系统试件恒应变率加载实验方法研究[J]爆炸与冲击,2004,24[5]：413-418.
[47]X. B. Li, T S Lok and J. Zhao. Dynamic characteristics of granite subjected to intermediate loading rate [J]. Rock Mechanics and Rock Engineering,2005, 38(1):21-39P.
[48]Richard J Wasley. Stress Wave Propagation in Solids-An introduction [M] New York:Marcel Dekker, Inc.1973.
[49]J D Achenbach. Wave Propagation in Elastic Solids [M] New York:North Holland Publishing Company Amsterdam London. American Elsevier Publishing Company, INC.1973.
[50]Ch Zhang and D Gross. On Wave Propagation in Elastic Solids with Cracks [M] Southampton UK, Boston USA:Computational Mechanics Publications.1998.
[51]Z X Zhang, S Q Kou, J Yu, et al. Effects of loading rate on rock fracture [J]. Int J Rock Mech Min Sci,1999,36:597-611.
[52]Kumar A. The effect of stress rate and temperature on the strength of basalt and granite[J]. Geophysics,1968,33(3):501-510
[53]Hakailehto K 0. The behaviour of rock under impulse loads-A study using the Hopkinson split bar method[Doctor Thesis][D]. Otaniemi-Heisinki:Technical University,1969
[54]Cristensen R J, Swanson S R, Brown W S. Split-Hopkinson bar tests on rock under confining pressure[J]. Experimental Mechanics,1972,12(11):508-513
[55]段祝平,孙琦清,扬大光等.高应变率下金属动力学性能的实验与理论研究[J].力学进展,1981,11(1)：1-15
[56]李夕兵.冲击荷载下岩石能耗及破碎力学性质的研究[硕士学位论文][D].长沙：中南工业大学,1986
[57]唐志平,王礼立.SHPB实验的电脑化数据处理系统[J].爆炸与冲击,1986,6(4)：320-327
[58]刘剑飞,胡时胜,王道荣.用于脆性材料的Hopkinson压杆动态实验新方法[J].实验力学,2001,16(3)：283-290
[59]Frantz C. E. Follansbe P. S. and Wright W. J. New experimental techniques with the split Hopkinson pressure bar[C]. Proceeding of the 8th International Conference on High Energy Rate Fabrication, Pressure Vessel and Piping Division. New York: ASME,1984,229-236
[60]Nemat-Nasser S Isaacs J B and Starrett J E. Hopkinson techniques for dynamic recovery experiments[C]. Proceeding of the Royal Society of London, Series A, 1991,534(1894):371-391
[61]Wu X J and Gorham D A. Stress equilibrium in the split Hopkinson pressure bar test[J]. J. Physic. in France,1997,7(3):91-96
[62]Frew D J, Forrestal M J and Chen W. Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar[J]. Experimental Mechanics,2002, 42(1):93-106
[63]卢芳云,Chen W. and Frew D. J.软材料的SHPB实验设计[J],爆炸与冲击,2002,22(1)：15-20
[64]徐明利,张若棋,张光莹.SHPB实验中试件内早期应力平衡分析[J].爆炸与冲击,2003,23(3)：235-241
[65]胡金生,唐德高,陈向欣等.提高大直径SHPB装置精度的方法[J].解放军理工大学学报,2003,14(1)：71-74
[66]赵习金、卢芳云、王悟等.入射波整形技术的实验和理论研究[J].高压物理学报,2004,18(3)：231-236
[67]王鲁明,赵坚,华安增等.脆性材料SHPB实验技术的研究[J].岩石力学与工程学报,2003,22(11)：1798-1802
[68]Ellwood S, Griffiths L J, and Parry D J. Materials testing at high constant strain rates[J]. Journal of Physics E:Scientific Instruments.1982,15(3):280-282
[69]李夕兵,刘德顺,古德生.消除岩石动态实验曲线振荡的有效途径[J].中南工业大学学报,1995,26(4)：457-460
[70]李夕兵,古德生.冲击载荷下岩石动态应力应变全图测试中的合理加载波形[J],爆炸与冲击.1993,13(2)：125-131
[71]Li X B Lok T S and Zhao J. Dynamic characteristics of granite subjected to intermediate loading rate[J]. Rock Mechanics and Rock Engineering,2005, 38(1):21-39
[72]刘德顺,李夕兵.冲击机械系统动力学[M].北京：科学出版社,1999
[73]李夕兵.矿岩中应力波的传输效应和能量耗散规律的研究[博士学位论文][D].长沙： 中南工业大学,1992
[74]Bazant Z P. Instability, ductility, and size effect in strain-softening concrete [J]. Journal of the Engineering Mechanics Division, ASCE,1976,102(2): 331-344.
[75]Auertini C, Cadoni E and Labibes K. Dynamic mechanical behavior of large concrete specimens by means of Hopkinson bar bundle[C]. Proc.2nd ISIE'96. Beijing: Chinese Journal of Mechanics Press,1996,214-219
[76]Ouchterlony F. A core based specimen with chevron edge notch for fracture toughness measurement [C]. Rock Mechanics-Key to Energy Production,27th US Symposium on Rock Mechanics, Jostens Publications.1986
[77]Ouchterlony F. On the background to the formulae and accuracy of rock fracture toughness measurements using ISRM standard core specimens [J]. Int J Rock Mech. Min. Sci.& Geomech. Abstr,1989,26(1):13-23
[78]Pook L P. The effect of crack angle on fracture toughness [J]. Engineering Fracture Mechanics,1971,3(3):205-218
[79]Chen J F. The development of the Cracked Chevron Notched Brazilian Disc Method for rock fracture toughness measurement and tunneling machine performance prediction. [D] Ph. D Thesis. The University of Newcastle uponTyne.1989
[80]Timoshenko S P and Goodier J N. Theory of Elasticity.3rd ed. [M] New York, McGraw-Hill,1970
[81]Sneddon I N. The distribution of stress in the neighborhood of a crack in a elastic solid [J]. Proc. Roy. Soc,1946, A-187:229-260
[82]Sneddon I N and Lowengrub M. Crack problems in the classical theory of elasticity [M].1969
[83]Frocht M M. Photo elasticity [M].1948
[84]Munz D G et al.Compliance and stress intensity coefficients for short bar specimens with chevron notches [J]. International Journal of Fracture,1980, 16(4):359-374
[85]Munz D G and Shannon J L. Fracture toughness calculation from maximum load in four point bend tests of Chevron Notch Specimens [J]. International Journal of Fracture,1980,16:137-141
[86]Bluhm J I. Slice synthesis of a three dimensional work of fracture specimen [J]. Engineering Fracture Mechanics,1975,7:593-604
[87]李战鲁.分离式霍普金森压杆加载下岩石动态断裂韧度测定的实验研究[D].四川大学硕士学位论文,2006.
[88]宋小林.大理岩动态劈裂拉伸强度和裂纹起裂扩展特性[D].四川大学硕士学位论文,2005.
[89]李伟.大理岩动态力学性能的分离式霍普金森杆实验研究[D].四川大学硕士学位论文,2005.
[90]董世明,王清远,舒尚文.扁平巴西圆盘试件的应力强度因子分析[J] 结构强度研究.
[91]Dalley J W and Barker D B. Dynamic measurement of initiation toughness at high loading rates[J]. Experimental Mechanics.1988,9:298-303P.
[92]吕俊波.Hopkinson杆动态断裂韧度测试技术研究[D].哈尔滨工程大学硕士学位论文,2005.
[93]董新龙,王礼立,王悟,等40CrNiMoA钢的动态剪切断裂行为研究[J].爆炸与冲击,1999,19[3]：222-228.
[94]Conque H and Lankford J. Influence of loading rate on fracture properties of heavy metals. Institute of Physics Conference.1989, Bristol,102:89-97P.
[95]曹效昂,韩小平,朱西平.冲击载荷下复合材料层板断裂韧性的实验研究[J].西北工业大学学报,2007.25[1]：65-68.
[96]宫能平弹塑性材料动态断裂韧性的理论与实验研究——表征与测试[D].中国科学技术大学博士学位论文,2001.
[97]金属手册第八卷：金属力学试验.第九版.1986：1-50,322-361P
[98]Kalthoff J W. In handbook on experimental mech. Ed. A S Kobayashi.1986,11-35P.
[99]Rubio L, ed. Determination of dynamic fracture initiation toughness using three-point bending tests in a modified Hopkinson Pressure Bar. Experimental Mechanics.2003,43(4):379-386P.
[100]Weisbrod G and Rittel D. A method for dynamic fracture toughness determination using short beams. International Journal of Fracture.2000,104:89-103P.
[101]郝瑞漳.Ⅰ型动态弹塑性裂尖场及动态起裂韧性测试技术研究[D].西北工业大学硕士学位论文.1996.
[102]楼一珊,陈勉,史明义,等.岩石Ⅰ、Ⅱ型断裂韧性的测试及其影响因素分析[J].中国石油大学学报,2007,31[4]：85-89.
[103]黎立云,宁海龙,许风光,等.Ⅲ型裂纹断裂韧性测试及数值分析[J].岩石力学与工程学报,2006,25[12]：2523-2528.
[104]朱丽慧,赵钦新,顾海澄,等.10Cr9M01VNbN耐热钢的动态断裂韧度研究[J].西安交通大学学报,1999,33[2]：41-45.
[105]李存剑,李少华,翁宇庆.HQ785C钢示波冲击试验韧脆断裂转变特性研究[J].机械工程材料,1999,23[1]：12-14.
[106]王洪山.KId实用测量法[J].理化检验-物理分册,2002,38[3]：107-110.
[107]韩海军,于荣莉.TC4合金静动态断裂韧性KIc、KId相关性研究[J].科学技术与工程,2006,6[15]：2339-2341.
[108]姜风春,刘瑞堂,刘殿魁.动态弹塑性断裂韧性测试方法的比较研究[J].实验力学,1992,14[2]：267-272.
[109]唐春安.岩石破裂过程中的灾变[M] 北京：煤炭工业出版社1991.
[110]郭伟国,李玉龙,索涛.应力波基础简明教程[M] 西安：西北工业大学出版社2007.
[111]赵海鸥编著,LS-DYNA动力分析指南,兵器工业出版社,2003：14-26.
[112]Hallquist John 0. LS-DYNA Theoretical manual. Livermore Software Technology Corporation,1998.
[113]鲍亦冈,刘振锋等著.北京地质百年研究：北京地区基础地质研究的历史与最新成果.北京：地质出版社,2001
[114]杨荣丰等.北京地区岩浆岩和火山碎屑岩的特征及其对窑坡煤系的影响.煤田地质与勘探,2003,31,8-10
[115]白志民,葛世炜,鲍亦冈.燕山造山带中生代火山喷发及岩浆演化.地质论评,1999,45(增),534-539
[116]冯宝华.京西门头沟南大岭组玄武岩古风化壳及变质作用.煤田地质与勘探,1988,85,4-5
[117]S.S.澳古士梯蒂斯(S. S. Augustithis)著,路凤香等译.玄武岩结构图册及其成因意义.北京：地质出版社,1983
[118]刘粤惠,刘平安编著.X射线衍射分析原理与应用.北京：化学工业出版社,2003
[119]中华人民共和国国家标准.GB／T 50266-99.工程岩体试验方法标准[S].北京：建设部标准定额研究所,1999.
[120]Shan Renliang, Jiang Yusheng, Li Baoqiang. Obtaining dynamic complete stress-strain curves for rock using the Split Hopkinson Pressure Bar technique. International Journal of Rock Mechanics and Mining Sciences.2000,37:983-992P.
[121]沙桂英.应力波载荷作用下金属断裂动态分析方法研究[D].哈尔滨工程大学博士学位论文.2001
[122]郑州大学化工实验中心过程装备与控制工程实验室.过程装备与控制工程专业实验指导书[M].2007.
[123]卢敏,李万昌,傅秋卫.示波器数据采集与管理系统[J].高能量密度物理,2007,4：161-164.
[124]周君,汪洋,夏渊明.有机玻璃纯Ⅰ型和纯Ⅱ型动态断裂行为的实验研究[J] 高分子材料科学与工程,2008,24[2]：10-18.
[125]Jun Zhou, Yang Wang, Yuanming Xia. Mode I fracture toughness of PMMA at high loading rates [J] J Mater Sci,2006,41:8363-8366.
[126]Deng H and Nemat-Nasser S. Dynamic damage evolution in brittle solids[J]. Mechanics of Materials.1992,14:83-103P.
[127]Nemat-Nasser S and Deng H. Strain rate effect on brittle failure in compression[J]. Acta metal mater.1994,42:1013-1024P.
[128]Golshani, Aliakbar, Okui Yoshiaki, Oda Masanobu, Takemura Takato. A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite[J]. Mechanics of Materials,2006,38:287-303P.
[129]Li H B, Zhao J, Li T J. Micromechanical modeling of the mechanical properties of a granite under dynamic uniaxial compressive loads[J]. International journal of rock mechanics and mining sciences,2000,37:923-935P.
[130]Golshani, Aliakbar, Oda Masanobu, Okui Yoshiaki, Takemura Takato, Munkhtogoo E. Numerical simulation of the excavation damaged zone around an opening in brittle rock[J]. International journal of rock mechanics and mining sciences, 2007,44:835-845P.
[131]Li H B, Zhao J, Li T J. Triaxial compression tests on a granite at different strain rates and confining pressures[J]. International journal of rock mechanics and mining sciences,1999,36:1057-1063P.
[132]刘彩平.岩石动态裂纹扩展的不稳定性及其物理机制研究[D].中国矿业大学(北京)博士学位论文.2005
[133]M S Paterson.实验岩石形变-脆性域[M].张崇寿等译.北京：地质出版社,1979
[134]李江腾,古德生,曹平等.岩石断裂韧度与抗压强度的相关规律[J].中南大学学报(自然科学版),2009,40[6]：1695-1699.
[135]Yu Yong, Zhang Jianxun, Zhang Jichun. A modified brazilian disk tension test [J]. International journal of rock mechanics and mining sciences,2009,46: 421-425P.
[136]Whittaker BN, Singh RN, Sun G. Rock fracture mechanics:principles, design and applications. Amsterdam:Elsevier,1992.
[137]Zhang ZX. An empirical relation between mode I fracture toughness and the tensile strength of rock [J]. International journal of rock mechanics and mining sciences,2002,39:401-406P.
[138]Wang J. J., Zhu J. G., Chiu C. F., and Zhang H. Experimental study on fracture toughness and tensile strength of a clay[J]. Engineering Geology.2007,94: 65-75P.
[139]Zhang ZX, Kou SQ, Yu J, Yu Y, Jiang LG, Lindqvist PA. Effects of loading rate on rock fracture. Int J Rock Mech Min 1999;36(5):597-611.
[140]Zhang ZX, Kou SQ, Jiang LG, Lindqvist PA. Effects of loading rate on rock fracture:fracture characteristics and energy partitioning. Int J Rock Mech Min 2000; 37 (5):745-62.
[141]Nemat-Nasser S and Horii H. Brittle failure in compression:splitting, faulting and brittle-ductile transition[J]. Philosophical transactions of the royal society of London. Series A, Mathematical and Physical Sciences.1986,319: 337-374P.
[142]Horii H and Nemat-Nasser S. Elastic fields of interacting inhomogeneities[J]. Int J Solids Structures.1985,21:731-745P.
[143]Horii H and Nemat-Nasser S. Overall moduli of solids with micro cracks: load-induced anisotropy[J]. J. Mech. Phys. Solids.1983,31:155-171P.
[144]Nemat-Nasser S and Horii H. Rock failure in compression[J]. Int J Engng Sci. 1984,22:999-1011P.
[145]徐纪成,刘大安,孙宗颀等.岩石断裂韧度的国际联合试验研究[J].中南工业大学学报,1995,26[3]：310-313.
[146]崔振东,刘大安,安光明等.岩石Ⅰ型断裂韧度测试方法研究进展[J].测试技术学报,2009,23[3]：189-196.
[147]黎振兹,张静宜,刘大安等.岩石断裂力学测试与理论研究[J].中国有色金属学报, 1994,4[4]：18-21.
[148]徐纪成,刘大安,张静宜等.岩石断裂韧度测试技术研究[J].中南工业大学学报,1997,28[3]：216-218.
[149]GAOWenjiao, SHAN Renliang, WANG Gongcheng. Constitutive relation of Yunjialing Anthracite under medium strain rate[J]. Journal of China University of Mining and Technology,2007,17[1]:126-132.
[150]JU Yang, SUDAK Les, XIE Heping. Study on stress wave propagation in fractured rocks with fractal joint surfaces[J]. International Journal of Solids and Structures,2007,44:4256-4271.
[151]王鲁明,赵坚,华安增等.脆性材料SHPB试验技术的研究[J].岩石力学与工程学报,2003,22[11]：1798-1802.
[152]刘剑飞,胡时胜,王道荣.用于脆性材料的Hopkinson压杆动态试验新方法[J].实验力学,2001,16[3]：283-290.
[153]宫能平,夏渊明.一种弹塑性材料动态起裂韧度的J表征和测试方法[J].固体力学学报,2003,24[2]：185-191.
[154]Cook N G W. The failure of rock [J], International journal of rock mechanics and mining sciences,1965,2(3):389-403P.
[155]潘岳,王志强,张勇.突变理论在岩体系统动力失稳中的应用[M]北京：科学出版社2008.
[156]张黎明,王在泉,张晓娟等.岩体动力失稳的折迭突变模型[J].岩土工程学报,2009,31(4),552-557.
[157]潘岳.岩石破坏过程的折迭突变模型[J].岩土工程学报,1999,21(3),552-557.
[158]张明,李仲奎.准脆性材料破裂过程失稳的尖点突变模型[J].岩石力学与工程学报,2006,25(6),1233-1239.
[159]凌复华.突变理论—历史、现状和展望[J].力学进展,1984,14(4),389-404.
[2]周宏伟,谢和平,左建平.深部高地应力下岩石力学行为研究进展[J].力学进展,2005,35(1),91-99
[3]谢和平,彭苏萍,何满潮.深部开采-基础理论与工程实践[M].北京：科学出版社2006
[4]谢和平.深部高应力下的资源开采—现状、基础科学问题与展望.见：香山科学会议编.科学前沿与未来.北京：中国环境科学出版社,2002,179-191
[5]王驹,陈伟明,苏锐等.高放废物地质处置及其若干关键科学问题[J].岩石力学与工程学报,2006,25(4),801-812.
[6]王礼立.应力波基础[M] 北京：国防工业出版社2005.
[7]庄茁,蒋持平.工程断裂与损失[M] 北京：机械工业出版社2004.
[8]李夕兵,古德生.岩石冲击动力学[M] 长沙：中南工业大学出版社1994.
[9]Melvin F. Kanninen and Carl H. Popelar. Advanced Fracture Mechanics.高等断裂力学[M] 洪其麟 郑光华 郑祺选 饶寿期 李石 戴羿 译.北京：北京航空学院出版社发行,1987
[10]Rolfe S.T.and Barsom J. M.. Fracture And Fatigue Control in Structures—— Applications of Fracture Mechanics结构中的断裂与疲劳控制——断裂力学的应用[M]刘文珽 仇仲翼 黄乃人 张诚文 译1985.
[11]高庆.工程断裂力学[M] 重庆：重庆大学出版社1986.
[12]袁懋昶.断裂力学理论及其工程应用第一卷线弹性断裂力学(上册)[M] 重庆：重庆大学出版社1989.
[13]袁懋昶.断裂力学理论及其工程应用第一卷线弹性断裂力学(下册)[M] 重庆：重庆大学出版社1989.
[14]范天佑.断裂动力学原理与应用[M] 北京：北京理工大学出版社2006.
[15]Standard method for notch bar impact testing of metallic materials. E23 Annual Book of ASTM,1984, (Philadelphia):210
[16]Kalthoff J F. et al. Evaluating material properties by dynamic testing. ESIS Publication.1996(20):25-35
[17]Bohme W. and Kalthoff J F. The behavior of notched bend specimen in impact testing. International Journal of Fracture.1982,20(1):139-143
[18]ISRM Testing Commission. Suggested method for determining the fracture toughness of rock[J].1988.
[19]Xu C. Fracture Mechanics and Its Application in Rock Excavation Engineering [D]. Press:The University of Leeds.1993.
[20]Fowell RJ, Xu C. The use of the cracked Brazilian disc geometry for rock fracture investigation [J]. Int J Rock Mech Min Sci Geomech Abstr,1994,31:571-579P.
[21]Fowell RJ, Xu C. et al. An update on the fracture toughness testing methods related to the cracked chevron notched brazilian disk specimen[J]. Pure and Applied Geophysics,2006,13:1047-1057P.
[22]ISRM Testing Commission. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc(CCNBD) specimens[J]. Int J Rock Mech Min Sci Geomech Abstr,1995,32:57-64P.
[23]Tang C A and Xu X H. A new method for measuring dynamic fracture toughness of rock[J]. Engineering Fracture Mechanics,1990,35:783-791P.
[24]Kalthoff J F. On the measurement of dynamic fracture toughness-a review of recent work[J]. Int J Fract,1985,27:277-298P.
[25]Nakamura T, Shih C F and Freund L B. Elastic-plastic analysis of a dynamically loaded circumferentially notched round bar[J]. Engng Fract Mech,1985, 22(3):437-452P.
[26]Wada H. Determination of dynamic fracture toughness for PMMA [J]. Engng Fract Mech,1992,41:821-831P.
[27]Wada H. Seika M and Kennedy T C. et al. Investigation of loading rate and plate thickness effects on dynamic fracture toughness of PMMA [J]. Engng Fract Mech, 1996,54:805-811P.
[28]Rittle D. The influence of temperature on dynamic failure mode transitions [J]. Mech Mater,1998,30:217-227P.
[29]Rittle D., Levin R. Mode-mixity and dynamic failure mode transitions in polycarbonate [J]. Mech Mater,1998,30:197-216P.
[30]Rittle D.,Maigre H. An investigation of dynamic crack initiation in PMMA [J]. Mech Mater,1996,23:229-239P.
[31]Rittle D.,Maigre H. A study of mixed mode dynamic crack initiation in PMMA [J]. Mech Research Communications,1996,23:475-481P.
[32]R. Chen, K. Xia, F. Dai, et al. Determination of dynamic fracture parameters using a semi-circular bend technique in split Hopkinson pressure bar testing [J]. Engineering Fracture Mechanics,2009,76:1268-1276.
[33]Feng Dai, K. Xia, Lizhong Tang. Rate dependence of the.flexural tensile strength of Laurentian granite [J]. Int J Rock Mech Min Sci,2009, Article in press.
[34]王启智,贾学明.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第一部分：解析和数值结果[J] 岩石力学与工程学报,2002,21[9]：1285-1289.
[35]王启智,吴礼舟.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第二部分：试验结果[J] 岩石力学与工程学报,2004,23[2]：199-204.
[36]贾学明,王启智.标定ISRM岩石断裂韧度新型试样CCNBD的应力强度因子[J] 岩石力学与工程学报,2003,22[8]：1227-1233.
[37]张盛,王启智.采用中心圆孔裂缝平台圆盘确定岩石的动态断裂韧度[J] 岩土工程学报,2006,28[6]：723-728.
[38]王礼立,王永刚.应力波在用SHPB研究材料动态本构特性中的重要作用[J] 爆炸与冲击,2005,25[1]：17-25.
[39]Han Zhao, Gerard Gary. On the use of SHPB techniques to determine the dynamic behavior of materials in the range of small strains [J]. Int J Solids Structures, 1996,23:3363-3375P.
[40]陶俊林,陈裕泽,田常津等.SHPB系统圆柱型试件的惯性效应分析[J]固体力学学报, 2005,26[1]：107-110.
[41]陈刚,陶俊林,黄西成等.SHPB的径向惯性效应修正[J]西南科技大学学报,2008,23[2]：15-18.
[42]陶俊林.SHPB试验中几个问题的讨论[J]西南科技大学学报,2009,24[3]：27-35.
[43]张晓欣,刘瑞堂,邹广平.动态断裂韧度测试过程中的惯性效应分析[J]中国力学学会学术大会2005(CCTAM2005)
[44]类维生苏燕董建令等.动态断裂过程的惯性效应[J]理化检验-物理分册,1996,32[4]：32-34.
[45]李存剑,李少华,翁宇庆.动态断裂韧性测试中的惯性效应分析[J]理化检验-物理分册,2000,36[11]：483-485.
[46]陶俊林,田常津,陈裕泽等.SHPB系统试件恒应变率加载实验方法研究[J]爆炸与冲击,2004,24[5]：413-418.
[47]X. B. Li, T S Lok and J. Zhao. Dynamic characteristics of granite subjected to intermediate loading rate [J]. Rock Mechanics and Rock Engineering,2005, 38(1):21-39P.
[48]Richard J Wasley. Stress Wave Propagation in Solids-An introduction [M] New York:Marcel Dekker, Inc.1973.
[49]J D Achenbach. Wave Propagation in Elastic Solids [M] New York:North Holland Publishing Company Amsterdam London. American Elsevier Publishing Company, INC.1973.
[50]Ch Zhang and D Gross. On Wave Propagation in Elastic Solids with Cracks [M] Southampton UK, Boston USA:Computational Mechanics Publications.1998.
[51]Z X Zhang, S Q Kou, J Yu, et al. Effects of loading rate on rock fracture [J]. Int J Rock Mech Min Sci,1999,36:597-611.
[52]Kumar A. The effect of stress rate and temperature on the strength of basalt and granite[J]. Geophysics,1968,33(3):501-510
[53]Hakailehto K 0. The behaviour of rock under impulse loads-A study using the Hopkinson split bar method[Doctor Thesis][D]. Otaniemi-Heisinki:Technical University,1969
[54]Cristensen R J, Swanson S R, Brown W S. Split-Hopkinson bar tests on rock under confining pressure[J]. Experimental Mechanics,1972,12(11):508-513
[55]段祝平,孙琦清,扬大光等.高应变率下金属动力学性能的实验与理论研究[J].力学进展,1981,11(1)：1-15
[56]李夕兵.冲击荷载下岩石能耗及破碎力学性质的研究[硕士学位论文][D].长沙：中南工业大学,1986
[57]唐志平,王礼立.SHPB实验的电脑化数据处理系统[J].爆炸与冲击,1986,6(4)：320-327
[58]刘剑飞,胡时胜,王道荣.用于脆性材料的Hopkinson压杆动态实验新方法[J].实验力学,2001,16(3)：283-290
[59]Frantz C. E. Follansbe P. S. and Wright W. J. New experimental techniques with the split Hopkinson pressure bar[C]. Proceeding of the 8th International Conference on High Energy Rate Fabrication, Pressure Vessel and Piping Division. New York: ASME,1984,229-236
[60]Nemat-Nasser S Isaacs J B and Starrett J E. Hopkinson techniques for dynamic recovery experiments[C]. Proceeding of the Royal Society of London, Series A, 1991,534(1894):371-391
[61]Wu X J and Gorham D A. Stress equilibrium in the split Hopkinson pressure bar test[J]. J. Physic. in France,1997,7(3):91-96
[62]Frew D J, Forrestal M J and Chen W. Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar[J]. Experimental Mechanics,2002, 42(1):93-106
[63]卢芳云,Chen W. and Frew D. J.软材料的SHPB实验设计[J],爆炸与冲击,2002,22(1)：15-20
[64]徐明利,张若棋,张光莹.SHPB实验中试件内早期应力平衡分析[J].爆炸与冲击,2003,23(3)：235-241
[65]胡金生,唐德高,陈向欣等.提高大直径SHPB装置精度的方法[J].解放军理工大学学报,2003,14(1)：71-74
[66]赵习金、卢芳云、王悟等.入射波整形技术的实验和理论研究[J].高压物理学报,2004,18(3)：231-236
[67]王鲁明,赵坚,华安增等.脆性材料SHPB实验技术的研究[J].岩石力学与工程学报,2003,22(11)：1798-1802
[68]Ellwood S, Griffiths L J, and Parry D J. Materials testing at high constant strain rates[J]. Journal of Physics E:Scientific Instruments.1982,15(3):280-282
[69]李夕兵,刘德顺,古德生.消除岩石动态实验曲线振荡的有效途径[J].中南工业大学学报,1995,26(4)：457-460
[70]李夕兵,古德生.冲击载荷下岩石动态应力应变全图测试中的合理加载波形[J],爆炸与冲击.1993,13(2)：125-131
[71]Li X B Lok T S and Zhao J. Dynamic characteristics of granite subjected to intermediate loading rate[J]. Rock Mechanics and Rock Engineering,2005, 38(1):21-39
[72]刘德顺,李夕兵.冲击机械系统动力学[M].北京：科学出版社,1999
[73]李夕兵.矿岩中应力波的传输效应和能量耗散规律的研究[博士学位论文][D].长沙： 中南工业大学,1992
[74]Bazant Z P. Instability, ductility, and size effect in strain-softening concrete [J]. Journal of the Engineering Mechanics Division, ASCE,1976,102(2): 331-344.
[75]Auertini C, Cadoni E and Labibes K. Dynamic mechanical behavior of large concrete specimens by means of Hopkinson bar bundle[C]. Proc.2nd ISIE'96. Beijing: Chinese Journal of Mechanics Press,1996,214-219
[76]Ouchterlony F. A core based specimen with chevron edge notch for fracture toughness measurement [C]. Rock Mechanics-Key to Energy Production,27th US Symposium on Rock Mechanics, Jostens Publications.1986
[77]Ouchterlony F. On the background to the formulae and accuracy of rock fracture toughness measurements using ISRM standard core specimens [J]. Int J Rock Mech. Min. Sci.& Geomech. Abstr,1989,26(1):13-23
[78]Pook L P. The effect of crack angle on fracture toughness [J]. Engineering Fracture Mechanics,1971,3(3):205-218
[79]Chen J F. The development of the Cracked Chevron Notched Brazilian Disc Method for rock fracture toughness measurement and tunneling machine performance prediction. [D] Ph. D Thesis. The University of Newcastle uponTyne.1989
[80]Timoshenko S P and Goodier J N. Theory of Elasticity.3rd ed. [M] New York, McGraw-Hill,1970
[81]Sneddon I N. The distribution of stress in the neighborhood of a crack in a elastic solid [J]. Proc. Roy. Soc,1946, A-187:229-260
[82]Sneddon I N and Lowengrub M. Crack problems in the classical theory of elasticity [M].1969
[83]Frocht M M. Photo elasticity [M].1948
[84]Munz D G et al.Compliance and stress intensity coefficients for short bar specimens with chevron notches [J]. International Journal of Fracture,1980, 16(4):359-374
[85]Munz D G and Shannon J L. Fracture toughness calculation from maximum load in four point bend tests of Chevron Notch Specimens [J]. International Journal of Fracture,1980,16:137-141
[86]Bluhm J I. Slice synthesis of a three dimensional work of fracture specimen [J]. Engineering Fracture Mechanics,1975,7:593-604
[87]李战鲁.分离式霍普金森压杆加载下岩石动态断裂韧度测定的实验研究[D].四川大学硕士学位论文,2006.
[88]宋小林.大理岩动态劈裂拉伸强度和裂纹起裂扩展特性[D].四川大学硕士学位论文,2005.
[89]李伟.大理岩动态力学性能的分离式霍普金森杆实验研究[D].四川大学硕士学位论文,2005.
[90]董世明,王清远,舒尚文.扁平巴西圆盘试件的应力强度因子分析[J] 结构强度研究.
[91]Dalley J W and Barker D B. Dynamic measurement of initiation toughness at high loading rates[J]. Experimental Mechanics.1988,9:298-303P.
[92]吕俊波.Hopkinson杆动态断裂韧度测试技术研究[D].哈尔滨工程大学硕士学位论文,2005.
[93]董新龙,王礼立,王悟,等40CrNiMoA钢的动态剪切断裂行为研究[J].爆炸与冲击,1999,19[3]：222-228.
[94]Conque H and Lankford J. Influence of loading rate on fracture properties of heavy metals. Institute of Physics Conference.1989, Bristol,102:89-97P.
[95]曹效昂,韩小平,朱西平.冲击载荷下复合材料层板断裂韧性的实验研究[J].西北工业大学学报,2007.25[1]：65-68.
[96]宫能平弹塑性材料动态断裂韧性的理论与实验研究——表征与测试[D].中国科学技术大学博士学位论文,2001.
[97]金属手册第八卷：金属力学试验.第九版.1986：1-50,322-361P
[98]Kalthoff J W. In handbook on experimental mech. Ed. A S Kobayashi.1986,11-35P.
[99]Rubio L, ed. Determination of dynamic fracture initiation toughness using three-point bending tests in a modified Hopkinson Pressure Bar. Experimental Mechanics.2003,43(4):379-386P.
[100]Weisbrod G and Rittel D. A method for dynamic fracture toughness determination using short beams. International Journal of Fracture.2000,104:89-103P.
[101]郝瑞漳.Ⅰ型动态弹塑性裂尖场及动态起裂韧性测试技术研究[D].西北工业大学硕士学位论文.1996.
[102]楼一珊,陈勉,史明义,等.岩石Ⅰ、Ⅱ型断裂韧性的测试及其影响因素分析[J].中国石油大学学报,2007,31[4]：85-89.
[103]黎立云,宁海龙,许风光,等.Ⅲ型裂纹断裂韧性测试及数值分析[J].岩石力学与工程学报,2006,25[12]：2523-2528.
[104]朱丽慧,赵钦新,顾海澄,等.10Cr9M01VNbN耐热钢的动态断裂韧度研究[J].西安交通大学学报,1999,33[2]：41-45.
[105]李存剑,李少华,翁宇庆.HQ785C钢示波冲击试验韧脆断裂转变特性研究[J].机械工程材料,1999,23[1]：12-14.
[106]王洪山.KId实用测量法[J].理化检验-物理分册,2002,38[3]：107-110.
[107]韩海军,于荣莉.TC4合金静动态断裂韧性KIc、KId相关性研究[J].科学技术与工程,2006,6[15]：2339-2341.
[108]姜风春,刘瑞堂,刘殿魁.动态弹塑性断裂韧性测试方法的比较研究[J].实验力学,1992,14[2]：267-272.
[109]唐春安.岩石破裂过程中的灾变[M] 北京：煤炭工业出版社1991.
[110]郭伟国,李玉龙,索涛.应力波基础简明教程[M] 西安：西北工业大学出版社2007.
[111]赵海鸥编著,LS-DYNA动力分析指南,兵器工业出版社,2003：14-26.
[112]Hallquist John 0. LS-DYNA Theoretical manual. Livermore Software Technology Corporation,1998.
[113]鲍亦冈,刘振锋等著.北京地质百年研究：北京地区基础地质研究的历史与最新成果.北京：地质出版社,2001
[114]杨荣丰等.北京地区岩浆岩和火山碎屑岩的特征及其对窑坡煤系的影响.煤田地质与勘探,2003,31,8-10
[115]白志民,葛世炜,鲍亦冈.燕山造山带中生代火山喷发及岩浆演化.地质论评,1999,45(增),534-539
[116]冯宝华.京西门头沟南大岭组玄武岩古风化壳及变质作用.煤田地质与勘探,1988,85,4-5
[117]S.S.澳古士梯蒂斯(S. S. Augustithis)著,路凤香等译.玄武岩结构图册及其成因意义.北京：地质出版社,1983
[118]刘粤惠,刘平安编著.X射线衍射分析原理与应用.北京：化学工业出版社,2003
[119]中华人民共和国国家标准.GB／T 50266-99.工程岩体试验方法标准[S].北京：建设部标准定额研究所,1999.
[120]Shan Renliang, Jiang Yusheng, Li Baoqiang. Obtaining dynamic complete stress-strain curves for rock using the Split Hopkinson Pressure Bar technique. International Journal of Rock Mechanics and Mining Sciences.2000,37:983-992P.
[121]沙桂英.应力波载荷作用下金属断裂动态分析方法研究[D].哈尔滨工程大学博士学位论文.2001
[122]郑州大学化工实验中心过程装备与控制工程实验室.过程装备与控制工程专业实验指导书[M].2007.
[123]卢敏,李万昌,傅秋卫.示波器数据采集与管理系统[J].高能量密度物理,2007,4：161-164.
[124]周君,汪洋,夏渊明.有机玻璃纯Ⅰ型和纯Ⅱ型动态断裂行为的实验研究[J] 高分子材料科学与工程,2008,24[2]：10-18.
[125]Jun Zhou, Yang Wang, Yuanming Xia. Mode I fracture toughness of PMMA at high loading rates [J] J Mater Sci,2006,41:8363-8366.
[126]Deng H and Nemat-Nasser S. Dynamic damage evolution in brittle solids[J]. Mechanics of Materials.1992,14:83-103P.
[127]Nemat-Nasser S and Deng H. Strain rate effect on brittle failure in compression[J]. Acta metal mater.1994,42:1013-1024P.
[128]Golshani, Aliakbar, Okui Yoshiaki, Oda Masanobu, Takemura Takato. A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite[J]. Mechanics of Materials,2006,38:287-303P.
[129]Li H B, Zhao J, Li T J. Micromechanical modeling of the mechanical properties of a granite under dynamic uniaxial compressive loads[J]. International journal of rock mechanics and mining sciences,2000,37:923-935P.
[130]Golshani, Aliakbar, Oda Masanobu, Okui Yoshiaki, Takemura Takato, Munkhtogoo E. Numerical simulation of the excavation damaged zone around an opening in brittle rock[J]. International journal of rock mechanics and mining sciences, 2007,44:835-845P.
[131]Li H B, Zhao J, Li T J. Triaxial compression tests on a granite at different strain rates and confining pressures[J]. International journal of rock mechanics and mining sciences,1999,36:1057-1063P.
[132]刘彩平.岩石动态裂纹扩展的不稳定性及其物理机制研究[D].中国矿业大学(北京)博士学位论文.2005
[133]M S Paterson.实验岩石形变-脆性域[M].张崇寿等译.北京：地质出版社,1979
[134]李江腾,古德生,曹平等.岩石断裂韧度与抗压强度的相关规律[J].中南大学学报(自然科学版),2009,40[6]：1695-1699.
[135]Yu Yong, Zhang Jianxun, Zhang Jichun. A modified brazilian disk tension test [J]. International journal of rock mechanics and mining sciences,2009,46: 421-425P.
[136]Whittaker BN, Singh RN, Sun G. Rock fracture mechanics:principles, design and applications. Amsterdam:Elsevier,1992.
[137]Zhang ZX. An empirical relation between mode I fracture toughness and the tensile strength of rock [J]. International journal of rock mechanics and mining sciences,2002,39:401-406P.
[138]Wang J. J., Zhu J. G., Chiu C. F., and Zhang H. Experimental study on fracture toughness and tensile strength of a clay[J]. Engineering Geology.2007,94: 65-75P.
[139]Zhang ZX, Kou SQ, Yu J, Yu Y, Jiang LG, Lindqvist PA. Effects of loading rate on rock fracture. Int J Rock Mech Min 1999;36(5):597-611.
[140]Zhang ZX, Kou SQ, Jiang LG, Lindqvist PA. Effects of loading rate on rock fracture:fracture characteristics and energy partitioning. Int J Rock Mech Min 2000; 37 (5):745-62.
[141]Nemat-Nasser S and Horii H. Brittle failure in compression:splitting, faulting and brittle-ductile transition[J]. Philosophical transactions of the royal society of London. Series A, Mathematical and Physical Sciences.1986,319: 337-374P.
[142]Horii H and Nemat-Nasser S. Elastic fields of interacting inhomogeneities[J]. Int J Solids Structures.1985,21:731-745P.
[143]Horii H and Nemat-Nasser S. Overall moduli of solids with micro cracks: load-induced anisotropy[J]. J. Mech. Phys. Solids.1983,31:155-171P.
[144]Nemat-Nasser S and Horii H. Rock failure in compression[J]. Int J Engng Sci. 1984,22:999-1011P.
[145]徐纪成,刘大安,孙宗颀等.岩石断裂韧度的国际联合试验研究[J].中南工业大学学报,1995,26[3]：310-313.
[146]崔振东,刘大安,安光明等.岩石Ⅰ型断裂韧度测试方法研究进展[J].测试技术学报,2009,23[3]：189-196.
[147]黎振兹,张静宜,刘大安等.岩石断裂力学测试与理论研究[J].中国有色金属学报, 1994,4[4]：18-21.
[148]徐纪成,刘大安,张静宜等.岩石断裂韧度测试技术研究[J].中南工业大学学报,1997,28[3]：216-218.
[149]GAOWenjiao, SHAN Renliang, WANG Gongcheng. Constitutive relation of Yunjialing Anthracite under medium strain rate[J]. Journal of China University of Mining and Technology,2007,17[1]:126-132.
[150]JU Yang, SUDAK Les, XIE Heping. Study on stress wave propagation in fractured rocks with fractal joint surfaces[J]. International Journal of Solids and Structures,2007,44:4256-4271.
[151]王鲁明,赵坚,华安增等.脆性材料SHPB试验技术的研究[J].岩石力学与工程学报,2003,22[11]：1798-1802.
[152]刘剑飞,胡时胜,王道荣.用于脆性材料的Hopkinson压杆动态试验新方法[J].实验力学,2001,16[3]：283-290.
[153]宫能平,夏渊明.一种弹塑性材料动态起裂韧度的J表征和测试方法[J].固体力学学报,2003,24[2]：185-191.
[154]Cook N G W. The failure of rock [J], International journal of rock mechanics and mining sciences,1965,2(3):389-403P.
[155]潘岳,王志强,张勇.突变理论在岩体系统动力失稳中的应用[M]北京：科学出版社2008.
[156]张黎明,王在泉,张晓娟等.岩体动力失稳的折迭突变模型[J].岩土工程学报,2009,31(4),552-557.
[157]潘岳.岩石破坏过程的折迭突变模型[J].岩土工程学报,1999,21(3),552-557.
[158]张明,李仲奎.准脆性材料破裂过程失稳的尖点突变模型[J].岩石力学与工程学报,2006,25(6),1233-1239.
[159]凌复华.突变理论—历史、现状和展望[J].力学进展,1984,14(4),389-404.
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