缺陷介质爆生裂纹扩展规律的动态焦散线试验研究
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摘要
利用动态焦散线测试系统,采用模型试验,研究了爆炸载荷下缺陷介质应力波传播过程、裂纹扩展机制；多节理裂隙的贯通机制；边界缺陷板条中应力波作用机理、边界缺陷端部裂纹扩展行为；并结合Det.-准则对动载下裂纹起始扩展的条件和方向进行预测分析。研究结果表明：(1)不同缺陷介质裂纹的扩展规律有很大的区别,裂隙缺陷方向、位置是影响裂纹扩展的主要因素,闭合节理和充填节理相对更助于裂纹的扩展,裂纹尖端动态能量释放率对裂纹扩展具有驱动作用；(2)爆炸载荷下多节理裂纹贯通模式多为复合破坏模式,倾斜节理组更有助于节理裂隙的贯通,更有利于提高定向断裂控制爆破的效果；(3)板条试件边界斜裂纹和切口尖端拉应力场是造成裂纹和切口起裂、扩展的主要原因；(4)动态焦散线和Det.-准则相结合是描述裂纹起始扩展的有效途径,在动态断裂力学研究中具有广泛的使用价值。
The model experiment was carried out by dynamic caustics test system. The stress wave propagation and crack expand mechanism in material containing flaws were studied under blast loading; the coalescence mechanism of multi-joints was investigated; the dynamic behavior of artificially flawed strips was researched; the direction and the critical condition of the crack initiation were analysed by uniting Det.-Criterion with caustics. The results show that (1) the crack propagation laws are different in different flawed media; the direction and position of flaws play a main role in crack advance process; the closed joints and filled joints are relatively conduce to crack running; dynamic energy release rate drives crack extension; (2) the coalescence mode of multi-joints are most mixed breakage subject to blast loading; slant joints sets help to joint flaw coalescence and are propitious to the effect of direction fracture controlling blasting; (3) the tensile stress filed at the tip of oblique edge-crack and slant notch in strips is the main cause initiating and running of crack and notch; (4) uniting Det.-Criterion with caustics is an effective method expressing crack initiation and propagation and has wide-ranging use in the study of dynamic fracture mechanics.
The model experiment was carried out by dynamic caustics test system. The stress wave propagation and crack expand mechanism in material containing flaws were studied under blast loading; the coalescence mechanism of multi-joints was investigated; the dynamic behavior of artificially flawed strips was researched; the direction and the critical condition of the crack initiation were analysed by uniting Det.-Criterion with caustics. The results show that (1) the crack propagation laws are different in different flawed media; the direction and position of flaws play a main role in crack advance process; the closed joints and filled joints are relatively conduce to crack running; dynamic energy release rate drives crack extension; (2) the coalescence mode of multi-joints are most mixed breakage subject to blast loading; slant joints sets help to joint flaw coalescence and are propitious to the effect of direction fracture controlling blasting; (3) the tensile stress filed at the tip of oblique edge-crack and slant notch in strips is the main cause initiating and running of crack and notch; (4) uniting Det.-Criterion with caustics is an effective method expressing crack initiation and propagation and has wide-ranging use in the study of dynamic fracture mechanics.
引文
1. 邵鹏.断续节理岩体中弹性波动力效应研究[M].徐州：中国矿业大学出版社,2005：1-2
2. 刘再华,解德,王元汉,等.工程断裂动力学[M].武汉：华中理工大学出版社,1996：281-300
3. Belland, L. Structure as a control in Rock Fragmentation-Coral Lake Iron Ove Deposit. CIMM BULL.1959:321-328
4. Gnirk P K.9th Symp. On Rock Mechanics. Colorado School of Mines,1968:321-345
5. Larson W C, Pugleisec J M.U.S. BMRI 7863,1974
6. Singh D P, etal. Proc. lth Int. Symp.On Rock Frag, By Blasting. Lulea, Sweden,1983:533-559 7. Ferdyce D L, Fourney W L节理对应力波传播的影响.第四届国际岩石爆破破碎学术会议论文集.北京：冶金工业出版社,1995：212-223
8. Daniel IM, Row lands R E. On Wave and Fracture Propagation in Rock Media[J]. Experimental Mechanics, 1975,15(12):449-457
9. Shukla A, Singh R. Explosively Generated Pulse Propagation Through Particles Containing Natural Cracks[J].Mechanics of Materials,1996,23:255-270
10. Yang Z G, Rustan A. 1th Int. Symp. On Rock Frag. By Blasting. Lulea, Sweden,1983:581-603
11.何思为.裂隙岩体爆破破碎的理论与应用研究[D].北京：中国地质大学,1992
12.张奇.结构面影响应力波传播的几个特征.岩土力学与工程学报,西安：陕西科技出版社,1994
13.郭文章.节理岩体爆破数值模型及其实验研究[D].北京：中国矿业大学,1997
14. Einert J and Kalthoff J F. Experimental Determination of Dynamic Stress Intensity Factors by Shadow Patterns in Exp Evaluation of Stress Concentration and Intensity Factors ed Sih G C Chaper5[M]. USA:Nartinus Nijhoff Publichers,1981:281-330
15. Kalthoff, J F., Beinert, J. and Winkler, S.. Fast fracture and crack arrest[J]. ASTM STP628,1977:161-176
16. Kalthoff, J F. Beinert, J. and Winkler, S. and Klemm, W. Experimental analysis of dynamic effects in different crack arrest test specimens[J]. ASTM STP711,1980:109-127
17. Kalthoff, J F. Milios. The influence of dynamic effects in impact loading[J]. International Journal of Fracture, 1981,17:217-230
18. Kalthoff, J F. Milios, J. Experimental Determination of Dynamic Stress Intensity Factors by Shadow Patterns[J]. Int. J. Mech. Sci.,1981,23:423-436
19. Theocaris, P.S. and Papadopoulos, GA.. Elastodynamic forms of caustics for running cracks under constant velocity[J]. Engineering Fracture Mech.,1980,13:683-689
20. P. S. Theocaris, G. A.Papadopoulos.The dynamic behavior of an oblique edge-crack under impact loading[J]. J. Mech. Phys. Solids,1984,32(4):281-300
21. Katsamanis, F., Raftopoulos, D. and Theocaris, P.S..Static and dynamic stress intensity factors by the mothod of transmitted caustics. Journal of Engineering Math. Technology,1977,99:105-109
22. Theocaris, P.S.. Dynamic propagation and arrest measurements by the method of caustics on overlapping skew-parallel cracks[J]. International Journal of Solids Structure,1978,14:639-653
23. Goldsmith, W. and Katsamanis, F.. Fracture of notched polymeric beams due to central impact[J]. Experimental Mechanics,1979,18:235-244
24. Rosakis, A.J.. Analysis of the optical method of caustics for dynamic crack propagation[J]. Eng. Fracture Mech.,1980,13:331-347
25. Krishnaswamy, S. and Rosakis, A.J.. On the extent of dominance of asymptotic elastic dynamic crack-tip fields[J]. J. App. Mech.,1991,58(1):87-94
26. Theocaris, P. S. and Ioakimidis, N. O.. The Equations of Caustics for Crack and Other Dynamic Plane Elasticity Problems[J]. Engng Fract Mech,1979,12:613-615
27. Osakis, A. I., Zehnder, A. T.. On the Method of Caustics:an Exact Analysis Based on Geometrical Optics[J]. J. of Elasticity,1985,15:347-367
28. Theocaris, P.S. Milios, J.. Dynamic crack propagation in composites. Int. J. of Fracture,1980,16:31-51
29. Theocaris, P.S. Milios, J. Crack propagation velocities in bi-phase plates under static and dynamic loading[J]. Engineering Fracture Mechanics.1980,13:599-609
30. P. S. Theocaris, A. A. Serafetinides, Propagation of a slant crack under impact studied by caustics[J]. Int. J. Impact Engng.,1984,2(3):251-261
31. P. S. Theocaris, G A.Papadopoulos, J. Milios. Crack interaction in bending due to impact[J]. Int. J. Impact Engng,1984,2(2):131-149
32. F. Katsamanis, D. Raftopoulos, P. S. Theocaris. The dependence of crack velocity on the critical stress in fracture. Experimental Mechanics[J],1977,17:128-132
33. P. S. Theocaris. The reflected caustics method for the evaluation of the mode III stress intensity factor[J]. Int. J. Mech. Sci.1981,23:105-117
34. Freund, L.B. and Rosakis, A.J.. The structure of the near tip field during transient elastic dynamic crack growth[J]. J. Mech. Phys. Solids,1992,40(3):699-719
35. Chen Liu and Rosakis, A.J.. The interpretation of optical caustics in the presence of dynamic non-uniform crack-tip motion histories[J].1993,30(7):875-897
36. Ravi-Chandar, K. and Knauss, W.G. Dynamic crack-tip stress under stress wave loading[J]. Int. J. Fracture, 1984,25:237-262
37. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅰ Crack initiation and arrest[J]. Int. J. of Fract.1984,25:247-262
38. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅱ Microstructural aspects[J]. Int. J. of Fract.1984,26:247-262
39. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅲ On steady-state crack propagation and crack branching[J].1984,26:141-154
40. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅳ. On the interaction of stress waves with propagating cracks[J]. International Journal of Fracture,1984,26:189-200
41. G.A. Papadopoulos, M. Konsta-Gdoutos. Edge-cracked stiffened panels analyzed by caustics[J]. Theoretical and Applied Fracture Mechannics,2005,43:115-120
42. Yuichi Kawagishi, Masayuki Shozu, Yukio Hirose. Experimental evaluation of stress field around crack tip by caustics method[J]. Mechanics of Materials,2001,33:741-757
43. Theocaris, P. S.. Interaction of cracks with other cracks or boundaries[J]. Int. J. of Fracture Mech.,1972,8(1): 37-47
44. Theocaris, P.S.. Complex stress intensity factors of bifurcation cracks[J]. J. of the Mech. and Phys. of Solids, 1972,20:265-279
45. Theocaris, P.S.. Dynamiccrack propagation in composites[J]. ACTA Mechanica. Sinica,1976,24:99-115
46. I. V. Rokach. On the Influence of One-point-bend Impact Test Parameters on Dynamic Stress Intensity Factor Variation[J]. Materials Science and Engineering,1997, A234-236:838-841
47. Herrmann, K., F. Ferber. Failure Mechanics in Thermally Loaded Models of Fibrous Composites with a Brittle Matrix[C]. Proc. Int. Symposium on Composite Materials and Structures, Peking, China, June, 1988:483-488
48. G. A. Papadopoulos. Dynamic Caustics and its Application[J]. Optics and Lasers in Engineering 1990, (52): 583-597
49. G. A. Papadopoulos, Theocaris, P. S. The variation of the dynamic modulus on crack propagation modes[J]. Int. J. Fracture,1987, (35):195-219
50.杨槐堂.动态阴影法与断裂时表面波的测量[C].第五届全国实验力学学术会议论文集.南京：1987：OC18
51.苏先基,刘承.动态焦散线实验中的几个基本问题研究[C].第五届全国实验力学学术会议论文集.南京：1987：OC1
52.苏先基,刘承.用动态焦散线法研究圆环在冲击载荷作用下的破坏机理[C].第五届全国实验力学学术会议论文集.南京：1987：OC2
53.苏先基,刘承.动态断裂过程中的动力因素对用焦散线法测量K1的影响[C].第五届全国实验力学学术会议论文集.南京：1987：OC3
54.苏先基,雷志辉.动态焦散线实验方法及其在断裂力学中的初步应用[J].力学学报,1987,19(4)：357-365
55.杨槐堂.同时采用光弹性法和焦散线法测量裂纹传播时动态应力强度因子的尝试[C].第六届全国实验力学学术会议论文集.北京：北京大学出版社,1 989：914-917
56.李承奇.匀速运动裂纹动态焦散线研究[C].第六届全国实验力学学术会议论文集.北京：北京大学出版社,1989：1333-1337
57.陈东伟.用伪焦散线方法研究轮轨接触应力问题[D].北京工业大学,1990
58.赵亚溥,方竞,苏先基.高阶应力渐近场下Ⅱ型动态裂纹的焦散线分析[C].第七届全国实验力学学术会议论文集.北京：北京大学出版社,1992：701-704
59.励争.轮轨动态接触问题及动光弹性主应力分离的研究[D].北京大学,1992
60.姚学锋,方竞.冲击下含偏置裂纹三点弯曲梁的断裂机理研究[C].第八届全国实验力学学术会议论文集.哈尔滨：哈尔滨工业大学出版社,1995：322-325
61.姚学锋.动态断裂力学中若干重要问题的实验研究[D].北京大学,1996
62.姚学锋,方竞.冲击载荷下扩展裂纹尖端动态能量释放率分布的焦散线分析[J].爆炸与冲击,1996,16(2)：111-116
63.姚学锋,倪受庸,赵亚溥.含裂纹三点弯曲梁起始扩展的动态分析[J].应用力学学报,1996,13(4)：122-126
64.姚学锋,倪受庸,方竞.关于瞬态应力强度因子和裂纹扩展加速度之间的关系探讨[J].工程力学,1996,13(3)：33-39
65.姚学锋,熊春阳,方竞.含偏置裂纹三点弯曲梁的动态断裂行为研究[J].力学学报,1996，28(6)：661-669
66.姚学锋,许尉,徐曼琼,等.集中荷载作用下正交复合材料板奇异应力场的焦散线模拟实验[J].实验力学,2003,18(3)：349-354
67.姚学锋,刘宁,金观昌.编织复合材料的横向冲击力学行为研究[J].高科技纤维与应用,2001,26(5)：29-34
68.刘宁,姚学锋,金观昌,等.编织复合材料的冲击损伤与断裂行为研究[J].实验力学,2002,17(2)：184-190
69.段自立.裂纹失稳扩展轨迹焦散线和伪焦散线实验研究[J].固体力学学报,1995,16(3)：269-273
70.段自立.平面角裂纹失稳扩展轨迹的焦散线法实验研究[J].华中理工大学学报,1995,23(3)：94-99
71.许昭永,杨润海.加载破裂和卸载破裂的焦散阴影区动态特征的实验研究[J].地震学报,2002,24(2)：186-195
72.马宇平,李桃香.直升机某接头模拟裂纹K1的光焦散线法测量[C].第五届全国实验力学学术会论文摘要汇编,南京：实验应力分析专业委员会,1987：oc5
73.段自力,罗明,陈荣清,等.光弹法和焦散线法研究联结零件接触应力[J].华中理工大学学报,1994,(1)：170-173
74.马建，韦疑男.透射焦散线法研究甲板开口边缘Ⅰ型裂纹的应力强度因子[J].上海交通大学学报,1998，(11)：58-61
75.张忠平.确定应力强度因子的光弹性法与焦散线法[J].应用力学学报,2001,18(3)：100-104
76.张忠平.焦散线法确定应力强度因子的一种简便方法[J].纺织高校基础科学学报,1998,11(2)：110-114
77.张忠平,雷洪利,王锋会,等.焦散线法确定应力强度因子的条件[J].力学季刊,2001,22(3)：359-362
78.虞吉林,吴汉琨.斜入射透射焦散线测量误差的数值分析[J].实验力学,1997,12(2)：209-215
79. X.F. Yao, W. Xu, K. Arakawa, et al. Dynamic optical visualization on the interaction between propagating crack and stationary crack[J]. Optics and Lasers in Engineering,2005,43(2):195-207
80. X.F. Yao, W. Xu, M.Q. Xu, et al. Experimental study of dynamic fracture behavior of PMMA with overlapping offset-parallel cracks[J]. Polymer Testing,2003,22 (6):663-670
81. Theocaris, P. S.. Reflected shadow method for the study of constrained zones in cracked plates[J]. Applied Optics,1971,10(10):2240-2247
82.苏先基,励争.用反射式动态焦散线法测定金属材料的动态断裂性能[C].第六届全国实验力学学术会议论文集.北京：北京大学出版社，1989：1318-1323
83.薛慧.反射式焦散线法及其在测量应力强度因子中的应用[D].天津：天津大学,1986
84.薛慧等.第五届全国实验力学学术会论文摘要汇编[C].南京：实验应力分析专业委员会,1987：0oc
85.薛慧,宋锦良.环氧树脂涂层焦散想法及用于测定应力强度因子[J].实验力学,1987,2(3)：105-110
86.涂卫真,管大椿.第五届全国实验力学学术会论文摘要汇编[C].南京：实验应力分析专业委员会,1987：oc5
87.苏先基,刘承.用反射式动态焦散线法测定金属材料的动态断裂性能[C].第六届全国实验力学学术会论文摘要汇编.上海：北京大学出版社,1989：1318-1322
88.励争,苏先基,傅缤.水泥石动态断裂韧性的实验研究[J].力学与实践,1999,1：41-44
89.黄镇屏,张讯.焦散线方法测定脆性材料的断裂韧度[C]第六届全国实验力学学术会论文摘要汇编.上海：北京大学出版社,1989：1324-1328
90.王锋会,党进宝.焦散线方法在铝合金材料弹塑性断裂中的应用研究[C].第七届全国实验力学学术会论文摘要汇编,北京：北京大学出版社，1992：678-681
91.段自力.金属试样裂纹尖端COD的焦散法测定[J].华中理工大学学报,1995,5：117-122
92.段自力.确定裂纹尖端形状及张开位移的焦散线-伪焦散线法实验研究[J].实验力学,1995,02：145-149
93.段自力,周文华,匡健.测量裂纹尖端形状和张开位移的实验研究[J].力学与实践,1995,(05)：38-41
94.段自立.裂纹失稳扩展轨迹焦散线和伪焦散线实验研究[J].固体力学学报,1995,16(3)：269-273
95.段自立.平面角裂纹失稳扩展轨迹的焦散线法实验研究[J].华中理工大学学报,1995,23(3)：94-99
96.励争,苏先基,傅缤.水泥石动态断裂韧性的实验研究[J].力学与实践,1999,21(1)：41-44
97. Xuefeng Yao, Junda Chen, Guangchang Jin, et al. Caustics analysis of singularities in orthotropic composite materials with mode-Ⅰ crack[J]. Composites Science and Technology,2004,64:917-924
98. X.F. Yao, W. Xu, M.Q. Xu, et al. Caustics study on stress singularities in laminated composites under concentrated loads[J]. International Journal of Solids and Structures,2004,41:3383-3393
99. X.F. Yao, W. Xu, S.L. Bai, et al. Caustics analysis of the crack initiation and propagation of graded materials[J]. Composites and Technology,2007,1:1-10
100. Yang Renshu, Yue zhongwen, Xiao Tongshe, et al. Experimental Research on the Dynamic Fracture Behavior of Rock Under Impact Load Using the Caustics Method[J]. Mining Science and Technology, 2009,15(1):23-29
101.肖同社.岩石动态裂纹扩展焦散线试验研究[D].北京：中国矿业大学(北京),2006
102.商厚胜.节理岩体爆破裂纹扩展机理的动焦散实验研究[D].北京：中国矿业大学(北京),1999
103.李清,杨仁树.节理介质中爆炸裂纹扩展的细观行为研究[J].中国矿业大学学报,2002,3l(3)：271-274
104.李清,杨仁树.爆炸载荷裂纹扩展的应力强度因子及其断裂行为[J].煤炭学报,2002,27(3)：290-293
105.杨仁树.岩石炮孔定向断裂控制爆破机理动焦散实验研究[D].北京：中国矿业大学北京校区,1997
106. Song Junsheng, Yang Renshu. Theory Analysis and Experiment Study on The Fracture Propagation Under Blasting Load. Journal of Coal Science and Engineering [J].1998,2:64-67
107.庄金钊,杨仁树,刘继敏,等.掏槽控制爆破动焦散实验研究[J].中国矿业大学学报.2003,3：255-258
108.姚雪峰,方竟,熊春阳.爆炸应力波作用下裂纹与孔洞的动态焦散分析[J].爆炸与冲击,1998,(03)：231-236
109. Papadopoulos GA. Fracture mechanics, in:The Experimental Method of Caustics and the Det.-Criterion of Fracture, Springer-Verlag, Berlin, Heidelberg, New York,1992,211-222
110. Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear[J]. J Basic Engng Trans ASME Ser D,1963,85:519-527
111. Palaniswanmy K, Knauss WG Propagation of a crack under general in-plane tension[J]. Int J Fract Mech, 1972,8:114-117
112. Hussain MA, Pu SL, Underwood J. Strain energy release rate for a crack under combined mode I and Ⅱ[J].ASTM STP,1974,560:2-28
113. Sih GC. Some basic problems in fracture mechanics and new concepts[J]. Engng Fract Mech,1973, 5:365-377
114. Theocaris PS, Papadopoulos GA. The distribution of the elastic strain-energy density at the crack tip for fracture modes Ⅰ and Ⅱ [J]. Int J Fract,1982,18:81-112
115. Theocaris PS, Andrianopoulos NP. A Modified strain-energy density criterion applied to crack propagation[J]. J Appl Mech,1982,81-86
116. Wang M-H. A Modified S Theory[J]. Engng Fract Mech,1985,22:579-584
117. Theocaris PS, Andrianopoulos NP. The Mises elastic-plastic boundary as the core region in fracture criterion[J]. Engng Fract Mech,1982,16:425-432
118. Theocaris PS, Andrianopoulos NP.The T-criterion applied to ductile fracture[J]. Int J Fract,1982,20:125-130
119. Yehia NAB. On the use of the T-criterion in fracture mechanics[J]. Engng Fract Mech,1985,22:189-199
120. Papadopoulos GA. The stationary value of the third stress invariant as a local fracture parameter(Det-criterion)[J]. Engng Fract Mech,1987,27:643-652
121. Papadopoulos GA. New concepts on the Det-criterion[J]. Engng Fract Mech,1989,33:283-293
122. Papadopoulos GA. The influence of geometry of edge-cracked plates on crack initiation[J]. Engng Fract Mech,1987,26:945-954
123. Papadopoulos GA. Crack initiation under biaxial loading[J]. Engng Fract Mech,1988,29:585-598
124. Papadopoulos GA. Dynamic crack-bifurcation by the Det-criterion[J]. Engng Fract Mech,1988,31:887-893
125. Papadopoulos GA, Poniridis PI. Crack initiation from blunt notches under biaxial loading[J]. Engng Fract Mech,1988,31:65-78
126. Papadopoulos GA, Poniridis PI. The influence of geometry of edge-blunt-notched plates on crack initiation[J]. Engng Fract Mech,1988,31:271-287
127. Papadopoulos GA, Poniridis PI. Crack initiation under biaxial loading with higher-order approximation[J]. Engng Fract Mech,1989,32:351-360
128. Ramulu, M., Kobayshi, A. S. Dynamic crack curving-A photoelastic evaluation[J]. Experimental mechanics,1983,23(3):1-9
129. J.S. Hawong, A.S. Kobay, M.S. Dadkhah, B.S., et al. Dynamic crack curving and branching under biaxial loading[J]. Experimental mechanics,1987,7:146-153
130. M. Remulu, A.S Kobayashi. Mechanics of curving and branchong ---a dynamic fracture analysis[J]. International Journal of Fracture,1985,27:187-201
131.NABIL A.B. YEHIA, MARK S. SHEPHARD. Automatic crack growth tracking of biomaterial interface cracks[J]. International Journal of Fracture,1988,37:123-135
132. P. ISAKSSON, P.STAHLE. Prediction of shear crack growth direction under compressive loading and plane strain condition[J]. International Journal of Fracture,2002,113:175-194
133. S.K. MAITI, R.A. SMITH. Comparison of the criteria for mixed mode brittle fracture based on the pre-instability stress-strain field. Part I:Slit and elliptical cracks under uniaxial tensile loading[J]. International Journal of Fracture,1983,23:281-295
134. S.K. MAITI, R.A. SMITH. Comparison of the criteria for mixed mode brittle fracture based on the pre-instability stress-strain field. Part Ⅱ:Pure shear under uniaxial compressive loading[J]. International Journal of Fracture,1984,24:5-22
135. Lifeng MA, Alexander M. KORSUNSKY. On the use of vector J-integral in crack growth criteria for brittle solids[J]. International Journal of Fracture,2005,133:39-46
136.计欣华,邓宗白,鲁阳等.工程实验力学[M].北京：机械工业出版社,2005,1:258-259
137. Sneddon, I. N., Lowengrub, M.. Crack problems in the classical theory of elastlcity[M], Wiley, New Yuwk, 1969:17-18
138. Eringen, A. C., Suhubi, E. S.. Elastodynamic[M], Linear Theory Academic press, NY 1975,2:565-573
139.杨仁树,桂来保.焦散线方法及其应用[M].北京：中国矿业大学出版社,1997,7：82-88
140. Theocaris, P.S., Petrou, L.. Inside and outside bounds of validity of the method of caustics in elasticity. Eng. Fracture Mech.,1986,23(4):681-693
141. K. Takahashi, K. Arakawa, Experimental mechanics, dependence of crack acceleration on the dynamic stress intensity factor in polymers, Exp. Mech,1987,27:195-217
142.边亚东.含多裂纹三点弯曲梁动焦散研究[D].北京：中国矿业大学(北京),2005,5
143. Ferund L. B. Dynamic fracture mechanics [M]. Edinburgh:Cambridge University Press,1990
144. Nema-tNasser S, Horii H. Compression-induced nonPlanar crack extension with application to splitting,exfoliation and rockburst. J Geophys Res,1982,87(BS):6805-6821
145. Huang J F, Chen G L, Zhao Y H etal. An experimental study of the strain field development Prior to of a marble Plate under comperssion. Tectonophysics,1990,175:269-284
146. Wong R H C, Chau K T. Crack coalescence in a rock-like material containing tow craks.Int J Rock Mech Min Sci,1998,35(2):147-164
147. Wong R H C, Chau K T, Tang C A, etal. Analysis of crack coalescence in rock-like materials containing three flaws-Part Ⅰ:experimental approach. Int J Rock Mech Min Sci,2001,38:909-924
148. Gehle C, Kutter H K. Breakage and shear behaviour of intermittent rock joins.Int J Rock Mech Min Sci, 2003,40:687-700
149.黄明利.岩石多裂纹相互作用破坏机制的研究[J].岩石力学与工程学报,2001,20(3)：423-423
150.刘远明,夏才初.共面闭合非贯通节理岩体贯通机制和破坏强度准则研究[J].岩石力学与工程学报,2006,10(25)：2086-2090
151.朱维申,陈卫忠,申晋.雁形裂纹扩展的模型试验及断裂力学机制研究[J]固体力学学报,1998,19(4)：356-360
152.王忠昶,赵德深,王怀亮.裂纹岩体贯通机制的数值模拟研究[J]大连大学学报,2007,28(6)：32-36
153.黄明利,唐春安,梁正召.岩石裂纹相互作用的应力场分析[J]东北大学学报(自然科学版),2001,22(4)：446-449
154.黄明利,冯夏庭，王水林.多裂纹在不同岩石介质中的扩展贯通机制分析[J].岩十力学,2002, 23(2)：142-146
155.刘刚,龙景奎,王照华.断续节理相互作用的数值模拟[J].采矿与安全工程学报,2007,24(2)：155-158
156.张平.裂隙介质静动应力条件下的破坏模式与局部化渐进破损模型研究[D],2004,10
157. Theocaris PS, Papadopoulos GA. The dynamic behaviour of sharp V-notches under impact loading[J]. Int J Solids Structures,1987,23:1581-1600
158. Theocaris PS, Katsamnis F. Response of cracks to impact by caustics[J].Engng Fract Mech,1978,10: 197-210
159. Hill R. The mathematical theory of plasticity[M]. Clarendon Press, Oxford,1964
160. Sih GC, Cha CK. A fracture criterion for three-dimensional crack problem[J].Engng Fract Mech,1974, 6:699-723
161. Theocaris PS, Papadopoulos GA. The influence of biaxiality of loading on the form of caustics in cracked plates[J]. Acta Mechanich,1982,44:201-222
162.苏先基,励争.固体力学动态测试技术[M].北京：高等教育出版社,1997,7
2. 刘再华,解德,王元汉,等.工程断裂动力学[M].武汉：华中理工大学出版社,1996：281-300
3. Belland, L. Structure as a control in Rock Fragmentation-Coral Lake Iron Ove Deposit. CIMM BULL.1959:321-328
4. Gnirk P K.9th Symp. On Rock Mechanics. Colorado School of Mines,1968:321-345
5. Larson W C, Pugleisec J M.U.S. BMRI 7863,1974
6. Singh D P, etal. Proc. lth Int. Symp.On Rock Frag, By Blasting. Lulea, Sweden,1983:533-559 7. Ferdyce D L, Fourney W L节理对应力波传播的影响.第四届国际岩石爆破破碎学术会议论文集.北京：冶金工业出版社,1995：212-223
8. Daniel IM, Row lands R E. On Wave and Fracture Propagation in Rock Media[J]. Experimental Mechanics, 1975,15(12):449-457
9. Shukla A, Singh R. Explosively Generated Pulse Propagation Through Particles Containing Natural Cracks[J].Mechanics of Materials,1996,23:255-270
10. Yang Z G, Rustan A. 1th Int. Symp. On Rock Frag. By Blasting. Lulea, Sweden,1983:581-603
11.何思为.裂隙岩体爆破破碎的理论与应用研究[D].北京：中国地质大学,1992
12.张奇.结构面影响应力波传播的几个特征.岩土力学与工程学报,西安：陕西科技出版社,1994
13.郭文章.节理岩体爆破数值模型及其实验研究[D].北京：中国矿业大学,1997
14. Einert J and Kalthoff J F. Experimental Determination of Dynamic Stress Intensity Factors by Shadow Patterns in Exp Evaluation of Stress Concentration and Intensity Factors ed Sih G C Chaper5[M]. USA:Nartinus Nijhoff Publichers,1981:281-330
15. Kalthoff, J F., Beinert, J. and Winkler, S.. Fast fracture and crack arrest[J]. ASTM STP628,1977:161-176
16. Kalthoff, J F. Beinert, J. and Winkler, S. and Klemm, W. Experimental analysis of dynamic effects in different crack arrest test specimens[J]. ASTM STP711,1980:109-127
17. Kalthoff, J F. Milios. The influence of dynamic effects in impact loading[J]. International Journal of Fracture, 1981,17:217-230
18. Kalthoff, J F. Milios, J. Experimental Determination of Dynamic Stress Intensity Factors by Shadow Patterns[J]. Int. J. Mech. Sci.,1981,23:423-436
19. Theocaris, P.S. and Papadopoulos, GA.. Elastodynamic forms of caustics for running cracks under constant velocity[J]. Engineering Fracture Mech.,1980,13:683-689
20. P. S. Theocaris, G. A.Papadopoulos.The dynamic behavior of an oblique edge-crack under impact loading[J]. J. Mech. Phys. Solids,1984,32(4):281-300
21. Katsamanis, F., Raftopoulos, D. and Theocaris, P.S..Static and dynamic stress intensity factors by the mothod of transmitted caustics. Journal of Engineering Math. Technology,1977,99:105-109
22. Theocaris, P.S.. Dynamic propagation and arrest measurements by the method of caustics on overlapping skew-parallel cracks[J]. International Journal of Solids Structure,1978,14:639-653
23. Goldsmith, W. and Katsamanis, F.. Fracture of notched polymeric beams due to central impact[J]. Experimental Mechanics,1979,18:235-244
24. Rosakis, A.J.. Analysis of the optical method of caustics for dynamic crack propagation[J]. Eng. Fracture Mech.,1980,13:331-347
25. Krishnaswamy, S. and Rosakis, A.J.. On the extent of dominance of asymptotic elastic dynamic crack-tip fields[J]. J. App. Mech.,1991,58(1):87-94
26. Theocaris, P. S. and Ioakimidis, N. O.. The Equations of Caustics for Crack and Other Dynamic Plane Elasticity Problems[J]. Engng Fract Mech,1979,12:613-615
27. Osakis, A. I., Zehnder, A. T.. On the Method of Caustics:an Exact Analysis Based on Geometrical Optics[J]. J. of Elasticity,1985,15:347-367
28. Theocaris, P.S. Milios, J.. Dynamic crack propagation in composites. Int. J. of Fracture,1980,16:31-51
29. Theocaris, P.S. Milios, J. Crack propagation velocities in bi-phase plates under static and dynamic loading[J]. Engineering Fracture Mechanics.1980,13:599-609
30. P. S. Theocaris, A. A. Serafetinides, Propagation of a slant crack under impact studied by caustics[J]. Int. J. Impact Engng.,1984,2(3):251-261
31. P. S. Theocaris, G A.Papadopoulos, J. Milios. Crack interaction in bending due to impact[J]. Int. J. Impact Engng,1984,2(2):131-149
32. F. Katsamanis, D. Raftopoulos, P. S. Theocaris. The dependence of crack velocity on the critical stress in fracture. Experimental Mechanics[J],1977,17:128-132
33. P. S. Theocaris. The reflected caustics method for the evaluation of the mode III stress intensity factor[J]. Int. J. Mech. Sci.1981,23:105-117
34. Freund, L.B. and Rosakis, A.J.. The structure of the near tip field during transient elastic dynamic crack growth[J]. J. Mech. Phys. Solids,1992,40(3):699-719
35. Chen Liu and Rosakis, A.J.. The interpretation of optical caustics in the presence of dynamic non-uniform crack-tip motion histories[J].1993,30(7):875-897
36. Ravi-Chandar, K. and Knauss, W.G. Dynamic crack-tip stress under stress wave loading[J]. Int. J. Fracture, 1984,25:237-262
37. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅰ Crack initiation and arrest[J]. Int. J. of Fract.1984,25:247-262
38. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅱ Microstructural aspects[J]. Int. J. of Fract.1984,26:247-262
39. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅲ On steady-state crack propagation and crack branching[J].1984,26:141-154
40. K. Ravi-chandar, W. G Knauss. An experimental investigation into dynamic fracture:Ⅳ. On the interaction of stress waves with propagating cracks[J]. International Journal of Fracture,1984,26:189-200
41. G.A. Papadopoulos, M. Konsta-Gdoutos. Edge-cracked stiffened panels analyzed by caustics[J]. Theoretical and Applied Fracture Mechannics,2005,43:115-120
42. Yuichi Kawagishi, Masayuki Shozu, Yukio Hirose. Experimental evaluation of stress field around crack tip by caustics method[J]. Mechanics of Materials,2001,33:741-757
43. Theocaris, P. S.. Interaction of cracks with other cracks or boundaries[J]. Int. J. of Fracture Mech.,1972,8(1): 37-47
44. Theocaris, P.S.. Complex stress intensity factors of bifurcation cracks[J]. J. of the Mech. and Phys. of Solids, 1972,20:265-279
45. Theocaris, P.S.. Dynamiccrack propagation in composites[J]. ACTA Mechanica. Sinica,1976,24:99-115
46. I. V. Rokach. On the Influence of One-point-bend Impact Test Parameters on Dynamic Stress Intensity Factor Variation[J]. Materials Science and Engineering,1997, A234-236:838-841
47. Herrmann, K., F. Ferber. Failure Mechanics in Thermally Loaded Models of Fibrous Composites with a Brittle Matrix[C]. Proc. Int. Symposium on Composite Materials and Structures, Peking, China, June, 1988:483-488
48. G. A. Papadopoulos. Dynamic Caustics and its Application[J]. Optics and Lasers in Engineering 1990, (52): 583-597
49. G. A. Papadopoulos, Theocaris, P. S. The variation of the dynamic modulus on crack propagation modes[J]. Int. J. Fracture,1987, (35):195-219
50.杨槐堂.动态阴影法与断裂时表面波的测量[C].第五届全国实验力学学术会议论文集.南京：1987：OC18
51.苏先基,刘承.动态焦散线实验中的几个基本问题研究[C].第五届全国实验力学学术会议论文集.南京：1987：OC1
52.苏先基,刘承.用动态焦散线法研究圆环在冲击载荷作用下的破坏机理[C].第五届全国实验力学学术会议论文集.南京：1987：OC2
53.苏先基,刘承.动态断裂过程中的动力因素对用焦散线法测量K1的影响[C].第五届全国实验力学学术会议论文集.南京：1987：OC3
54.苏先基,雷志辉.动态焦散线实验方法及其在断裂力学中的初步应用[J].力学学报,1987,19(4)：357-365
55.杨槐堂.同时采用光弹性法和焦散线法测量裂纹传播时动态应力强度因子的尝试[C].第六届全国实验力学学术会议论文集.北京：北京大学出版社,1 989：914-917
56.李承奇.匀速运动裂纹动态焦散线研究[C].第六届全国实验力学学术会议论文集.北京：北京大学出版社,1989：1333-1337
57.陈东伟.用伪焦散线方法研究轮轨接触应力问题[D].北京工业大学,1990
58.赵亚溥,方竞,苏先基.高阶应力渐近场下Ⅱ型动态裂纹的焦散线分析[C].第七届全国实验力学学术会议论文集.北京：北京大学出版社,1992：701-704
59.励争.轮轨动态接触问题及动光弹性主应力分离的研究[D].北京大学,1992
60.姚学锋,方竞.冲击下含偏置裂纹三点弯曲梁的断裂机理研究[C].第八届全国实验力学学术会议论文集.哈尔滨：哈尔滨工业大学出版社,1995：322-325
61.姚学锋.动态断裂力学中若干重要问题的实验研究[D].北京大学,1996
62.姚学锋,方竞.冲击载荷下扩展裂纹尖端动态能量释放率分布的焦散线分析[J].爆炸与冲击,1996,16(2)：111-116
63.姚学锋,倪受庸,赵亚溥.含裂纹三点弯曲梁起始扩展的动态分析[J].应用力学学报,1996,13(4)：122-126
64.姚学锋,倪受庸,方竞.关于瞬态应力强度因子和裂纹扩展加速度之间的关系探讨[J].工程力学,1996,13(3)：33-39
65.姚学锋,熊春阳,方竞.含偏置裂纹三点弯曲梁的动态断裂行为研究[J].力学学报,1996，28(6)：661-669
66.姚学锋,许尉,徐曼琼,等.集中荷载作用下正交复合材料板奇异应力场的焦散线模拟实验[J].实验力学,2003,18(3)：349-354
67.姚学锋,刘宁,金观昌.编织复合材料的横向冲击力学行为研究[J].高科技纤维与应用,2001,26(5)：29-34
68.刘宁,姚学锋,金观昌,等.编织复合材料的冲击损伤与断裂行为研究[J].实验力学,2002,17(2)：184-190
69.段自立.裂纹失稳扩展轨迹焦散线和伪焦散线实验研究[J].固体力学学报,1995,16(3)：269-273
70.段自立.平面角裂纹失稳扩展轨迹的焦散线法实验研究[J].华中理工大学学报,1995,23(3)：94-99
71.许昭永,杨润海.加载破裂和卸载破裂的焦散阴影区动态特征的实验研究[J].地震学报,2002,24(2)：186-195
72.马宇平,李桃香.直升机某接头模拟裂纹K1的光焦散线法测量[C].第五届全国实验力学学术会论文摘要汇编,南京：实验应力分析专业委员会,1987：oc5
73.段自力,罗明,陈荣清,等.光弹法和焦散线法研究联结零件接触应力[J].华中理工大学学报,1994,(1)：170-173
74.马建，韦疑男.透射焦散线法研究甲板开口边缘Ⅰ型裂纹的应力强度因子[J].上海交通大学学报,1998，(11)：58-61
75.张忠平.确定应力强度因子的光弹性法与焦散线法[J].应用力学学报,2001,18(3)：100-104
76.张忠平.焦散线法确定应力强度因子的一种简便方法[J].纺织高校基础科学学报,1998,11(2)：110-114
77.张忠平,雷洪利,王锋会,等.焦散线法确定应力强度因子的条件[J].力学季刊,2001,22(3)：359-362
78.虞吉林,吴汉琨.斜入射透射焦散线测量误差的数值分析[J].实验力学,1997,12(2)：209-215
79. X.F. Yao, W. Xu, K. Arakawa, et al. Dynamic optical visualization on the interaction between propagating crack and stationary crack[J]. Optics and Lasers in Engineering,2005,43(2):195-207
80. X.F. Yao, W. Xu, M.Q. Xu, et al. Experimental study of dynamic fracture behavior of PMMA with overlapping offset-parallel cracks[J]. Polymer Testing,2003,22 (6):663-670
81. Theocaris, P. S.. Reflected shadow method for the study of constrained zones in cracked plates[J]. Applied Optics,1971,10(10):2240-2247
82.苏先基,励争.用反射式动态焦散线法测定金属材料的动态断裂性能[C].第六届全国实验力学学术会议论文集.北京：北京大学出版社，1989：1318-1323
83.薛慧.反射式焦散线法及其在测量应力强度因子中的应用[D].天津：天津大学,1986
84.薛慧等.第五届全国实验力学学术会论文摘要汇编[C].南京：实验应力分析专业委员会,1987：0oc
85.薛慧,宋锦良.环氧树脂涂层焦散想法及用于测定应力强度因子[J].实验力学,1987,2(3)：105-110
86.涂卫真,管大椿.第五届全国实验力学学术会论文摘要汇编[C].南京：实验应力分析专业委员会,1987：oc5
87.苏先基,刘承.用反射式动态焦散线法测定金属材料的动态断裂性能[C].第六届全国实验力学学术会论文摘要汇编.上海：北京大学出版社,1989：1318-1322
88.励争,苏先基,傅缤.水泥石动态断裂韧性的实验研究[J].力学与实践,1999,1：41-44
89.黄镇屏,张讯.焦散线方法测定脆性材料的断裂韧度[C]第六届全国实验力学学术会论文摘要汇编.上海：北京大学出版社,1989：1324-1328
90.王锋会,党进宝.焦散线方法在铝合金材料弹塑性断裂中的应用研究[C].第七届全国实验力学学术会论文摘要汇编,北京：北京大学出版社，1992：678-681
91.段自力.金属试样裂纹尖端COD的焦散法测定[J].华中理工大学学报,1995,5：117-122
92.段自力.确定裂纹尖端形状及张开位移的焦散线-伪焦散线法实验研究[J].实验力学,1995,02：145-149
93.段自力,周文华,匡健.测量裂纹尖端形状和张开位移的实验研究[J].力学与实践,1995,(05)：38-41
94.段自立.裂纹失稳扩展轨迹焦散线和伪焦散线实验研究[J].固体力学学报,1995,16(3)：269-273
95.段自立.平面角裂纹失稳扩展轨迹的焦散线法实验研究[J].华中理工大学学报,1995,23(3)：94-99
96.励争,苏先基,傅缤.水泥石动态断裂韧性的实验研究[J].力学与实践,1999,21(1)：41-44
97. Xuefeng Yao, Junda Chen, Guangchang Jin, et al. Caustics analysis of singularities in orthotropic composite materials with mode-Ⅰ crack[J]. Composites Science and Technology,2004,64:917-924
98. X.F. Yao, W. Xu, M.Q. Xu, et al. Caustics study on stress singularities in laminated composites under concentrated loads[J]. International Journal of Solids and Structures,2004,41:3383-3393
99. X.F. Yao, W. Xu, S.L. Bai, et al. Caustics analysis of the crack initiation and propagation of graded materials[J]. Composites and Technology,2007,1:1-10
100. Yang Renshu, Yue zhongwen, Xiao Tongshe, et al. Experimental Research on the Dynamic Fracture Behavior of Rock Under Impact Load Using the Caustics Method[J]. Mining Science and Technology, 2009,15(1):23-29
101.肖同社.岩石动态裂纹扩展焦散线试验研究[D].北京：中国矿业大学(北京),2006
102.商厚胜.节理岩体爆破裂纹扩展机理的动焦散实验研究[D].北京：中国矿业大学(北京),1999
103.李清,杨仁树.节理介质中爆炸裂纹扩展的细观行为研究[J].中国矿业大学学报,2002,3l(3)：271-274
104.李清,杨仁树.爆炸载荷裂纹扩展的应力强度因子及其断裂行为[J].煤炭学报,2002,27(3)：290-293
105.杨仁树.岩石炮孔定向断裂控制爆破机理动焦散实验研究[D].北京：中国矿业大学北京校区,1997
106. Song Junsheng, Yang Renshu. Theory Analysis and Experiment Study on The Fracture Propagation Under Blasting Load. Journal of Coal Science and Engineering [J].1998,2:64-67
107.庄金钊,杨仁树,刘继敏,等.掏槽控制爆破动焦散实验研究[J].中国矿业大学学报.2003,3：255-258
108.姚雪峰,方竟,熊春阳.爆炸应力波作用下裂纹与孔洞的动态焦散分析[J].爆炸与冲击,1998,(03)：231-236
109. Papadopoulos GA. Fracture mechanics, in:The Experimental Method of Caustics and the Det.-Criterion of Fracture, Springer-Verlag, Berlin, Heidelberg, New York,1992,211-222
110. Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear[J]. J Basic Engng Trans ASME Ser D,1963,85:519-527
111. Palaniswanmy K, Knauss WG Propagation of a crack under general in-plane tension[J]. Int J Fract Mech, 1972,8:114-117
112. Hussain MA, Pu SL, Underwood J. Strain energy release rate for a crack under combined mode I and Ⅱ[J].ASTM STP,1974,560:2-28
113. Sih GC. Some basic problems in fracture mechanics and new concepts[J]. Engng Fract Mech,1973, 5:365-377
114. Theocaris PS, Papadopoulos GA. The distribution of the elastic strain-energy density at the crack tip for fracture modes Ⅰ and Ⅱ [J]. Int J Fract,1982,18:81-112
115. Theocaris PS, Andrianopoulos NP. A Modified strain-energy density criterion applied to crack propagation[J]. J Appl Mech,1982,81-86
116. Wang M-H. A Modified S Theory[J]. Engng Fract Mech,1985,22:579-584
117. Theocaris PS, Andrianopoulos NP. The Mises elastic-plastic boundary as the core region in fracture criterion[J]. Engng Fract Mech,1982,16:425-432
118. Theocaris PS, Andrianopoulos NP.The T-criterion applied to ductile fracture[J]. Int J Fract,1982,20:125-130
119. Yehia NAB. On the use of the T-criterion in fracture mechanics[J]. Engng Fract Mech,1985,22:189-199
120. Papadopoulos GA. The stationary value of the third stress invariant as a local fracture parameter(Det-criterion)[J]. Engng Fract Mech,1987,27:643-652
121. Papadopoulos GA. New concepts on the Det-criterion[J]. Engng Fract Mech,1989,33:283-293
122. Papadopoulos GA. The influence of geometry of edge-cracked plates on crack initiation[J]. Engng Fract Mech,1987,26:945-954
123. Papadopoulos GA. Crack initiation under biaxial loading[J]. Engng Fract Mech,1988,29:585-598
124. Papadopoulos GA. Dynamic crack-bifurcation by the Det-criterion[J]. Engng Fract Mech,1988,31:887-893
125. Papadopoulos GA, Poniridis PI. Crack initiation from blunt notches under biaxial loading[J]. Engng Fract Mech,1988,31:65-78
126. Papadopoulos GA, Poniridis PI. The influence of geometry of edge-blunt-notched plates on crack initiation[J]. Engng Fract Mech,1988,31:271-287
127. Papadopoulos GA, Poniridis PI. Crack initiation under biaxial loading with higher-order approximation[J]. Engng Fract Mech,1989,32:351-360
128. Ramulu, M., Kobayshi, A. S. Dynamic crack curving-A photoelastic evaluation[J]. Experimental mechanics,1983,23(3):1-9
129. J.S. Hawong, A.S. Kobay, M.S. Dadkhah, B.S., et al. Dynamic crack curving and branching under biaxial loading[J]. Experimental mechanics,1987,7:146-153
130. M. Remulu, A.S Kobayashi. Mechanics of curving and branchong ---a dynamic fracture analysis[J]. International Journal of Fracture,1985,27:187-201
131.NABIL A.B. YEHIA, MARK S. SHEPHARD. Automatic crack growth tracking of biomaterial interface cracks[J]. International Journal of Fracture,1988,37:123-135
132. P. ISAKSSON, P.STAHLE. Prediction of shear crack growth direction under compressive loading and plane strain condition[J]. International Journal of Fracture,2002,113:175-194
133. S.K. MAITI, R.A. SMITH. Comparison of the criteria for mixed mode brittle fracture based on the pre-instability stress-strain field. Part I:Slit and elliptical cracks under uniaxial tensile loading[J]. International Journal of Fracture,1983,23:281-295
134. S.K. MAITI, R.A. SMITH. Comparison of the criteria for mixed mode brittle fracture based on the pre-instability stress-strain field. Part Ⅱ:Pure shear under uniaxial compressive loading[J]. International Journal of Fracture,1984,24:5-22
135. Lifeng MA, Alexander M. KORSUNSKY. On the use of vector J-integral in crack growth criteria for brittle solids[J]. International Journal of Fracture,2005,133:39-46
136.计欣华,邓宗白,鲁阳等.工程实验力学[M].北京：机械工业出版社,2005,1:258-259
137. Sneddon, I. N., Lowengrub, M.. Crack problems in the classical theory of elastlcity[M], Wiley, New Yuwk, 1969:17-18
138. Eringen, A. C., Suhubi, E. S.. Elastodynamic[M], Linear Theory Academic press, NY 1975,2:565-573
139.杨仁树,桂来保.焦散线方法及其应用[M].北京：中国矿业大学出版社,1997,7：82-88
140. Theocaris, P.S., Petrou, L.. Inside and outside bounds of validity of the method of caustics in elasticity. Eng. Fracture Mech.,1986,23(4):681-693
141. K. Takahashi, K. Arakawa, Experimental mechanics, dependence of crack acceleration on the dynamic stress intensity factor in polymers, Exp. Mech,1987,27:195-217
142.边亚东.含多裂纹三点弯曲梁动焦散研究[D].北京：中国矿业大学(北京),2005,5
143. Ferund L. B. Dynamic fracture mechanics [M]. Edinburgh:Cambridge University Press,1990
144. Nema-tNasser S, Horii H. Compression-induced nonPlanar crack extension with application to splitting,exfoliation and rockburst. J Geophys Res,1982,87(BS):6805-6821
145. Huang J F, Chen G L, Zhao Y H etal. An experimental study of the strain field development Prior to of a marble Plate under comperssion. Tectonophysics,1990,175:269-284
146. Wong R H C, Chau K T. Crack coalescence in a rock-like material containing tow craks.Int J Rock Mech Min Sci,1998,35(2):147-164
147. Wong R H C, Chau K T, Tang C A, etal. Analysis of crack coalescence in rock-like materials containing three flaws-Part Ⅰ:experimental approach. Int J Rock Mech Min Sci,2001,38:909-924
148. Gehle C, Kutter H K. Breakage and shear behaviour of intermittent rock joins.Int J Rock Mech Min Sci, 2003,40:687-700
149.黄明利.岩石多裂纹相互作用破坏机制的研究[J].岩石力学与工程学报,2001,20(3)：423-423
150.刘远明,夏才初.共面闭合非贯通节理岩体贯通机制和破坏强度准则研究[J].岩石力学与工程学报,2006,10(25)：2086-2090
151.朱维申,陈卫忠,申晋.雁形裂纹扩展的模型试验及断裂力学机制研究[J]固体力学学报,1998,19(4)：356-360
152.王忠昶,赵德深,王怀亮.裂纹岩体贯通机制的数值模拟研究[J]大连大学学报,2007,28(6)：32-36
153.黄明利,唐春安,梁正召.岩石裂纹相互作用的应力场分析[J]东北大学学报(自然科学版),2001,22(4)：446-449
154.黄明利,冯夏庭，王水林.多裂纹在不同岩石介质中的扩展贯通机制分析[J].岩十力学,2002, 23(2)：142-146
155.刘刚,龙景奎,王照华.断续节理相互作用的数值模拟[J].采矿与安全工程学报,2007,24(2)：155-158
156.张平.裂隙介质静动应力条件下的破坏模式与局部化渐进破损模型研究[D],2004,10
157. Theocaris PS, Papadopoulos GA. The dynamic behaviour of sharp V-notches under impact loading[J]. Int J Solids Structures,1987,23:1581-1600
158. Theocaris PS, Katsamnis F. Response of cracks to impact by caustics[J].Engng Fract Mech,1978,10: 197-210
159. Hill R. The mathematical theory of plasticity[M]. Clarendon Press, Oxford,1964
160. Sih GC, Cha CK. A fracture criterion for three-dimensional crack problem[J].Engng Fract Mech,1974, 6:699-723
161. Theocaris PS, Papadopoulos GA. The influence of biaxiality of loading on the form of caustics in cracked plates[J]. Acta Mechanich,1982,44:201-222
162.苏先基,励争.固体力学动态测试技术[M].北京：高等教育出版社,1997,7
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