混凝土Ⅰ型、Ⅱ型断裂参数确定的研究
|
摘要
由于混凝土材料内部缺陷和施工阶段以及使用阶段各种因素的作用，混凝土结构尤其是大体积混凝土结构不可避免出现裂缝。因此，正确评估裂缝的稳定性、安全性，进而对混凝土结构进行合理的维修和加固，以及提高混凝土材料和大体积混凝土结构设计水平，一直是工程界和学术界极为关注的问题。而在混凝土建筑物设计阶段对混凝土拌和物设计和结构选型的抗裂设计，以及对已建混凝土建筑物出现的裂缝进行评估时，首先均需测定混凝土断裂韧度参数。基于此，本文结合水电水利行业标准DL/T5332-2005《水工混凝土断裂试验规程》(以下简称为《规程》)的制定和国家自然科学基金项目“基于粘聚力的混凝土Ⅱ型与复合型双K断裂准则及其参数确定(50178015)”，对混凝土Ⅰ型、Ⅱ型断裂参数确定开展了如下的研究工作：
1．混凝土起裂荷载的确定、断裂韧度的尺寸效应和形状效应是《规程》制定过程中的重要问题。为了对《规程》的制定提供更充足的基础数据，受编制组委托，分析了最大尺寸为S×D×B=2200×550×240 mm~3的三点弯曲梁试件和最大尺寸为2H×D×B=1200×1200×250mm~3的楔入劈拉试件共140个不同级配及湿筛法大坝混凝土试件的断裂试验。结果表明：电阻应变片法测定起裂荷载的方法可行；三点弯曲梁法所测得的混凝土双K断裂韧度值无明显的尺寸效应；采用《规程》规定的楔入劈拉加载方式所测得的混凝土断裂韧度值表现出一定程度的尺寸效应；在相同配合比、相同高度条件下，两种试件测定的双K断裂韧度值无明显的差异。
2．分析了《规程》规定的楔入劈拉加载方式所测得的混凝土断裂韧度值表现出一定程度的尺寸效应的原因是竖向分荷载P_V引起的附加力矩M_V对试件裂缝端部应力场和断裂参数计算具有影响，提出了在试件宽度1／4处施加楔入荷载以消除此影响从而测得混凝土真实断裂参数的新的试验方法——楔入式紧凑拉伸断裂试验方法。
3．使用双K断裂模型韧度三参数定律确定混凝土起裂韧度时，韧度增值K_(Ic)~c的计算无论是积分计算方法还是简化计算方法都较复杂。为了《规程》在工程界的推广使用，提出了韧度增值K_(Ic)~c的二元拉格朗日插值计算方法。通过与积分和简化计算方法比较，表明此插值计算方法具有很高的精度，计算过程得到进一步的简化，使用计算器即可实现，非常便于工程人员实际使用。
4．采用国际上新近提出的两端切口Ⅱ型断裂试件开展了混凝土Ⅱ型断裂试验，分析研究了试件的破坏机理。试验观测到裂缝起裂角θ_0约为0(?)，且沿着韧带方向扩展；裂缝尖端韧带出现具有典型剪切特征的混凝土碎片，表明发生了剪切破坏模式。由试验测定的曲线上的特征点确定临界荷载，进而由此试件几何相应的应力强度因子公式计算出混凝土Ⅱ型断裂韧度。试验表明，两端切口Ⅱ型断裂试件是进行混凝土Ⅱ型断裂试验及测试混凝土K_(Ⅱc)合适的试件形式。
5．基于课题组近年研究的基础上，提出了一种进行混凝土Ⅱ型断裂试验的初始无切口半边对称加载新的试件形式及其应力强度因子解析公式。此试件由于剪切应力集中在名义韧带端部区域形成剪切微裂区；当微裂区尖端Ⅱ型应力强度因子达到混凝土Ⅱ型断裂韧度时，试件发生Ⅱ型断裂破坏。因此，初始无切口半边对称加载试件断裂破坏机理与两端切口半边对称加载试件破坏机理本质上是相同的。
6．试验观察到混凝土Ⅱ型断裂过程可分为三个明显的阶段：裂缝起裂、稳定扩展、失稳破坏，本文引入起裂断裂韧度K_(Ⅱc)~(ini)和失稳断裂韧度K_(Ⅱc)~(un)两个断裂参数来描述混凝土结构Ⅱ型断裂裂缝起裂、稳定扩展、失稳破坏全过程，建立了判定混凝土结构Ⅱ型断裂破坏的Ⅱ型断裂双K断裂准则，即：K_Ⅱ=K_(Ⅱc)~(ini)时，裂缝起裂；K_(Ⅱc)~(ini)Due to inherent defects of concrete materials and various influences from construction and operation periods of structures, concrete is inevitable to crack, especially for mass concrete structures. Thus the appropriate appraisal of crack stability, safety and consequent maintenance and reinforcement of concrete structures, and the improvement of concrete materials and mass concrete structure design have always been the issues of concern in the engineering and academic fields. For crack-resistance design during concrete mixing stages and structure pattern choices, together with the evaluation of cracks occurring in existing concrete buildings, the first thing is to determine the concrete fracture toughness. Considering these facts, the author carried out the researches on determination of modeⅠand modeⅡfracture parameters for concrete shown as follows. And this research is part of the professional standard of water conservancy and hydro power profession: Norm for Fracture Test of Hydraulic Concrete (DL/T5332-2005) and National Nature Science Foundation project "The modeⅡand mixed mode double-K fracture criterion and the determination of the corresponding double-K fracture parameters of concrete based on the cohesive force (50178015)" .
1. The determination of crack initiation load, the size effect of fracture toughness as well as geometry influence are key issues in the norm. To provide sufficient test data for the norm, a total of 140 specimens were tested on three-point bending beams and wedge-splitting specimen fabricated with various grading aggregates and wet-screened components of dam concrete. The maximum size for three-point bending beams isS×D×B = 2200×550×240mm~3 , and wedge-splitting specimens with 2H×D×S = 1200×1200×250mm~3. The results show that its is feasible to use electric resistance strain gauges to determine the crack initiation load; no apparent size effect is observed in the double-K fracture toughness from three-point bending beams, while the double-K fracture toughness from wedge-splitting testing according to the norm shows a certain size effect; and the double-K fracture toughness from these geometries are almost of the same magnitude for the same aggregate grading and same specimen height.
2. The size effect in the fracture toughness from wedge-splitting tests could be attributed to the influence of vertical component of load P_v and additional moment M_v on the stress field around the crack tip. Accordingly, a novel wedge-splitting test on compact tension specimen for true fracture parameters is proposed where the load is imposed at quarter-point of the specimen width to counteract the above-mentioned influences.
3. In three-parameter law of fracture toughness for quasi-brittle materials, the cohesive force-induced fracture toughness K_(Ic)~c is difficult to be obtained whether by using integration or simplified method. For practical applications of the norm, an alternative determining method for K_(Ic)~c is put forward using a bivariate Lagrange interpolation function. By comparison withthe simplified method, the interpolation method is shown to have a higher accuracy. And still this much more simple calculating procedure can be achieved on a pocket calculator and it is very convenient for practical use.
4. Failure mechanism for concrete is explored based on experiments on double-edge notched specimens. The measured initiation fracture angle is approximately O~(-|o) and the crack propagates along the ligament line. The presence of concrete fragments typical of shear fracture at the crack tip shows that the specimen is experiencing modeⅡfracture. Feature points on the experimental curve could be used to determine the critical load, and in turn the fracture toughness K_(IIc) is calculated by using the corresponding stress intensity factorformula for the given specimen. The proposed method is shown to be robust and applicable to predict modeⅡfracture.
5. Based on the author's recent research, a symmetrically non-notched specimen is recommended to conduct modeⅡfracture tests of concrete and its stress intensity factor analytical formula is presented. A mirco-shear zone is developed in the front of the nominal ligament as a result of high stress concentration. As the modeⅡstress intensity factor in the tip of mirco-shear zone reaches the modeⅡfracture toughness, the specimen will fail in modeⅡfracture. Consequently, failure mechanism for this specimen is essentially the same with double-edge notched specimens
6. ModeⅡfracture process for concrete could be described by three observable stages: crack initiation, stable propagation and unstable failure. The initiation fracture toughness K_(IIc)~(ini) and unstable fracture toughness K_(IIc)~(un) are introduced here to differentiate these three stages. Thus a modeⅡfracture double-K fracture criterion for concrete is established, i.e., when K_(II) = K_(IIc)~(ini) the preformed crack begins to crack initially; when K_(IIc)~(ini)< K_(II) < K_(IIc)~(un) thepropagating crack develops steadily; when K_(II)≥K_(IIc)~(un) the crack propagates unsteadily.
1．混凝土起裂荷载的确定、断裂韧度的尺寸效应和形状效应是《规程》制定过程中的重要问题。为了对《规程》的制定提供更充足的基础数据，受编制组委托，分析了最大尺寸为S×D×B=2200×550×240 mm~3的三点弯曲梁试件和最大尺寸为2H×D×B=1200×1200×250mm~3的楔入劈拉试件共140个不同级配及湿筛法大坝混凝土试件的断裂试验。结果表明：电阻应变片法测定起裂荷载的方法可行；三点弯曲梁法所测得的混凝土双K断裂韧度值无明显的尺寸效应；采用《规程》规定的楔入劈拉加载方式所测得的混凝土断裂韧度值表现出一定程度的尺寸效应；在相同配合比、相同高度条件下，两种试件测定的双K断裂韧度值无明显的差异。
2．分析了《规程》规定的楔入劈拉加载方式所测得的混凝土断裂韧度值表现出一定程度的尺寸效应的原因是竖向分荷载P_V引起的附加力矩M_V对试件裂缝端部应力场和断裂参数计算具有影响，提出了在试件宽度1／4处施加楔入荷载以消除此影响从而测得混凝土真实断裂参数的新的试验方法——楔入式紧凑拉伸断裂试验方法。
3．使用双K断裂模型韧度三参数定律确定混凝土起裂韧度时，韧度增值K_(Ic)~c的计算无论是积分计算方法还是简化计算方法都较复杂。为了《规程》在工程界的推广使用，提出了韧度增值K_(Ic)~c的二元拉格朗日插值计算方法。通过与积分和简化计算方法比较，表明此插值计算方法具有很高的精度，计算过程得到进一步的简化，使用计算器即可实现，非常便于工程人员实际使用。
4．采用国际上新近提出的两端切口Ⅱ型断裂试件开展了混凝土Ⅱ型断裂试验，分析研究了试件的破坏机理。试验观测到裂缝起裂角θ_0约为0(?)，且沿着韧带方向扩展；裂缝尖端韧带出现具有典型剪切特征的混凝土碎片，表明发生了剪切破坏模式。由试验测定的曲线上的特征点确定临界荷载，进而由此试件几何相应的应力强度因子公式计算出混凝土Ⅱ型断裂韧度。试验表明，两端切口Ⅱ型断裂试件是进行混凝土Ⅱ型断裂试验及测试混凝土K_(Ⅱc)合适的试件形式。
5．基于课题组近年研究的基础上，提出了一种进行混凝土Ⅱ型断裂试验的初始无切口半边对称加载新的试件形式及其应力强度因子解析公式。此试件由于剪切应力集中在名义韧带端部区域形成剪切微裂区；当微裂区尖端Ⅱ型应力强度因子达到混凝土Ⅱ型断裂韧度时，试件发生Ⅱ型断裂破坏。因此，初始无切口半边对称加载试件断裂破坏机理与两端切口半边对称加载试件破坏机理本质上是相同的。
6．试验观察到混凝土Ⅱ型断裂过程可分为三个明显的阶段：裂缝起裂、稳定扩展、失稳破坏，本文引入起裂断裂韧度K_(Ⅱc)~(ini)和失稳断裂韧度K_(Ⅱc)~(un)两个断裂参数来描述混凝土结构Ⅱ型断裂裂缝起裂、稳定扩展、失稳破坏全过程，建立了判定混凝土结构Ⅱ型断裂破坏的Ⅱ型断裂双K断裂准则，即：K_Ⅱ=K_(Ⅱc)~(ini)时，裂缝起裂；K_(Ⅱc)~(ini)
1. The determination of crack initiation load, the size effect of fracture toughness as well as geometry influence are key issues in the norm. To provide sufficient test data for the norm, a total of 140 specimens were tested on three-point bending beams and wedge-splitting specimen fabricated with various grading aggregates and wet-screened components of dam concrete. The maximum size for three-point bending beams isS×D×B = 2200×550×240mm~3 , and wedge-splitting specimens with 2H×D×S = 1200×1200×250mm~3. The results show that its is feasible to use electric resistance strain gauges to determine the crack initiation load; no apparent size effect is observed in the double-K fracture toughness from three-point bending beams, while the double-K fracture toughness from wedge-splitting testing according to the norm shows a certain size effect; and the double-K fracture toughness from these geometries are almost of the same magnitude for the same aggregate grading and same specimen height.
2. The size effect in the fracture toughness from wedge-splitting tests could be attributed to the influence of vertical component of load P_v and additional moment M_v on the stress field around the crack tip. Accordingly, a novel wedge-splitting test on compact tension specimen for true fracture parameters is proposed where the load is imposed at quarter-point of the specimen width to counteract the above-mentioned influences.
3. In three-parameter law of fracture toughness for quasi-brittle materials, the cohesive force-induced fracture toughness K_(Ic)~c is difficult to be obtained whether by using integration or simplified method. For practical applications of the norm, an alternative determining method for K_(Ic)~c is put forward using a bivariate Lagrange interpolation function. By comparison withthe simplified method, the interpolation method is shown to have a higher accuracy. And still this much more simple calculating procedure can be achieved on a pocket calculator and it is very convenient for practical use.
4. Failure mechanism for concrete is explored based on experiments on double-edge notched specimens. The measured initiation fracture angle is approximately O~(-|o) and the crack propagates along the ligament line. The presence of concrete fragments typical of shear fracture at the crack tip shows that the specimen is experiencing modeⅡfracture. Feature points on the experimental curve could be used to determine the critical load, and in turn the fracture toughness K_(IIc) is calculated by using the corresponding stress intensity factorformula for the given specimen. The proposed method is shown to be robust and applicable to predict modeⅡfracture.
5. Based on the author's recent research, a symmetrically non-notched specimen is recommended to conduct modeⅡfracture tests of concrete and its stress intensity factor analytical formula is presented. A mirco-shear zone is developed in the front of the nominal ligament as a result of high stress concentration. As the modeⅡstress intensity factor in the tip of mirco-shear zone reaches the modeⅡfracture toughness, the specimen will fail in modeⅡfracture. Consequently, failure mechanism for this specimen is essentially the same with double-edge notched specimens
6. ModeⅡfracture process for concrete could be described by three observable stages: crack initiation, stable propagation and unstable failure. The initiation fracture toughness K_(IIc)~(ini) and unstable fracture toughness K_(IIc)~(un) are introduced here to differentiate these three stages. Thus a modeⅡfracture double-K fracture criterion for concrete is established, i.e., when K_(II) = K_(IIc)~(ini) the preformed crack begins to crack initially; when K_(IIc)~(ini)< K_(II) < K_(IIc)~(un) thepropagating crack develops steadily; when K_(II)≥K_(IIc)~(un) the crack propagates unsteadily.
引文
[1] ACI Committee 446. State-of-Art Report. American Concrete Institute, Detroit, ACI SpecialPublication. 1989.
[2] Mindess S. Fracture Process Zone Detection. Fracture Mechanics Test Method for Concrete, Reportof Technical Committee 89-FMT,1991 RILEM, Chapman and Hall.
[3] 徐世娘，赵国藩．光弹性贴片法研究混凝土裂缝扩展过程．水力发电学报，1991，10(3)：8-18．
[4] 徐世娘，赵国藩．混凝土裂缝的稳定扩展过程与临界裂缝尖端张开位移．水利学报，1989，20(4)： 33-44．
[5] Hillerborg A, Modeer M and Petersson P E. Analysis of crack formation and crack growth inconcrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976,6: 773-782.
[6] Petersson PE. Crack growth and development of fracture zones in plain concrete and similarmaterials. Division of Building Materials, Lund Institute of Technology, Report TVBM-1006,1981.
[7] Reinhardt H W, Cornelissen H A W and Hordijk D A. Tensile tests and failure analysis of concrete.Journal of Structural Engineering, 1986,112(11): 2462-2477.
[8] Gopalaratnam V S and Shah S P. Softening response of plain concrete in direct tension. ACI Journal,1985, 82(3): 310-323.
[9] Bazant Z P and Oh B H. Crack Band Theory for Fracture of Concrete. Materials and Structures,1983,16(93): 155-177.
[10] Jenq YS and Shah SP. Two Parameter Fracture Model for Concrete. Journal of EngineeringMechanics, 1985,111(10): 1227-1241.
[11] Jenq, YS and Shah SP. A fracture toughness criterion for concrete. Engineering Fracture Mechanics,1985, 21(5): 1055-1069.
[12] Swartz SE and Go CG. Validity of compliance calibration to cracked concrete beams in bending.Experimental Mechanics, 1984, 24(2): 129-134.
[13] Swartz SE and Refai TME. Influence of size on opening mode fracture parameters for precrackedconcrete beams in bending. Proceedings of SEM-RILEM International Conference on Fracture ofConcrete and Rock. Houston, Texas, 1987: 242-254.
[14] Nallathambi P and Karihaloo BL. Determination of specimen-size independent fracture toughness ofplain concrete. Magazine of Concrete Research, 1986, 38(135): 67-76.
[15] Karihaloo BL and Nallathambi P. An improved effective crack model for the determination offracture toughness of concrete. Cement and Concrete Research, 1989, 19: 603-610
[16] Karihaloo BL and Nallathambi P. Effective Crack Model for the Determination of FractureToughness (K_(Ic)~s) of Concrete. Engineering Fracture Mechanics, 1990: 35(4/5): 637-645.
[17] Bazant ZP, Kim JK and Pfeiffer PA. Determination of Fracture Properties from Size Effect Tests.Journal of Structural Engineering (ASCE), 1986, 112(2): 289-307.
[18] Bazant ZP and Kazemi MT. Determination of fracture energy, process zone length and brittlenessnumber from size effect, with application to rock and concrete. International Journal of Fracture,1990,(44): 111-131.
[19] Zhimin Wu, Shutong Yang, Xiaozhi Hu and Jianjun Zheng. An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams. Engineering Fracture Mechanics, 2006, 73: 2166-2191.
[20] 吴智敏，杨树桐，郑建军．混凝土等效断裂韧度的解析方法及其尺寸效应．水利学报，2006， 37(7)： 795-800．
[21] 徐世娘，赵国藩．混凝土结构裂缝扩展的双K断裂准则．土木工程学报，1992，25(2)：32-38．
[22] Xu Shilang and Reinhardt Hans W. Determination of double-K criterion for crack propagation inquasi-brittle fracture, Part Ⅰ: Experimental investigation of crack propagation. International Journalof Fracture, 1999, 98(2): 111-149.
[23] Xu Shilang and Reinhardt Hans W. Determination of double-K criterion for crack propagation inquasi-brittle fracture, Part Ⅱ: Analytical evaluating and practical measuring methods for three-pointbending notched beams. International Journal of Fracture, 1999,98(2): 151-177.
[24] Xu Shilang and Reinhardt Hans W. Determination of double-K criterion for crack propagation inquasi-brittle fracture, Part Ⅲ: Compact tension specimens and wedge splitting specimens.International Journal of Fracture, 1999,98(2): 179-193.
[25] Xu Shilang and Reinhardt Hans W. A simplified method for determining double-K fractureparameters for three-point bending tests. International Journal of Fracture, 2000,104:181-208.
[26] Xu Shilang and Reinhardt Hans W. Crack extension resistance and fracture properties ofquasi-brittle softening materials like concrete based on the complete process of fracture.International Journal of Fracture, 1998, 92: 71-99.
[27] Reinhardt Hans W and Xu Shilang. Crack extension resistance based on the cohesive force inconcrete. Engineering Fracture Mechanics, 1999,64:563-587.
[28] 赵艳华．混凝土断裂过程中的能量分析研究： (博士学位论文)．大连：大连理工大学，2002．
[29] 赵艳华，徐世娘，吴智敏．混凝土结构裂缝扩展的双G准则．土木工程学报，2004，37(10)： 13-18．
[30] RILEM Technical Committee 50-FMC. Determination of the Fracture Energy of Mortar andConcrete by Means of Three-Point Bend Tests of Notched Beams, Proposed RILEM DraftRecommendations. Materials and Structures. 1985,18(106): 285-296.
[31] Nordtest Method, NT BUILD 491, Concrete and Mortar, Hardened: Fracture Energy (Model Ⅰ) -Three-point bend tests on notched beams. 1999.
[32] JCI-TC 992. Test method for fracture energy of plain concrete (Draft). 2001.
[33] CEB-Comite Euro-International du Beton-CEB-FIP Model Code 1990, Bulletin D'Information No.213/214, Lausanne. 1993.
[34] RILEM Technical Committee 89-FMT. Determination of fracture parameters (K_(Ic)~s and CTODc) ofplain concrete using three-point bend tests, Proposed RILEM Draft Recommendations. Materials and Structures, 1990, 23(138): 457-460.
[35] RILEM Technical Committee 89-FMT. Size-Effect Method for Determining Fracture Energy and Process Zone Size of Concrete, Proposed RILEM Draft Recommendations. Materials and Structures, 1990,23(138): 461-465.
[36] 中华人民共和国电力行业标准．DL／T5332-2005水工混凝土断裂试验规程．北京：中国电力出 版社，2006．
[37] 于骁中，张彦秋，曹建国等．混凝土复合型(Ⅰ、Ⅱ型)裂纹断裂准则的计算和试验研究．水利学 报，1982，13(6)：27-37．
[38] 徐道远，梁正平，王德峻等．混凝土Ⅰ、Ⅱ复合裂纹断裂判据的探讨．水利学报，1982，13(6)： 57-61．
[39] Jenq Y and Shah S. Mixed mode fracture parameters of concrete. International Journal of Fracture, 1988, 38:123-142.
[40] 陈玉泉．混凝土复合断裂准则的试验研究：(硕士学位论文)．大连：大连理工大学，1988．
[41] 胡蓓雷，赵国藩．混凝土Ⅰ-Ⅱ复合型裂纹有效断裂准则．大连理工大学学报，1996，36(6)： 776-781．
[42] 高泉．混凝土断裂参数的测试方法及复合型裂纹断裂判据的试验研究： (博士学位论文)．大 连：大连理工大学，1992．
[43] 赵艳华，徐世烺．Ⅰ-Ⅱ复合型裂纹脆性断裂的最小J_2准则．工程力学，2002，19(4)：94-98．
[44] Cramer Steven M and Pugel Anton D. Compacted shear specimen for wood mode Ⅱ fractureinvestigation. International Journal of Fracture, 1987, 35(3): 163-174.
[45] Bazant ZP. Concepts Models and Determination of Material Properties, Fracture Mechanics ofConcrete Structures, Elsevier Applied Science, State-of-Art Report by ACI Committee 446, Londonand New York, 1992.
[46] Kaplan MF. Crack propagation and fracture of concrete. Journal of the American Concrete Institute,1961,58(5): 591-610.
[47] Saouma VE, Natekar D and Hansen E. Cohesive stresses and size effects in elasto-plastic andquasi-brittle materials. International Journal of Fracture, 2003,119: 287-298.
[48] ACI Committee 446. ACI Committee 446 Minutes. Toronto, 2000.
[49] Barrett JD and Foschi RO. Mode Ⅱ stress-intensity factors for cracked wood beams. EngineeringFractures Mechanics, 1977,9(2): 371-378.
[50] Giare GS. Fracture toughness of unidirectional fibre reinforced composites in Mode Ⅱ. EngineeringFracture Mechanics, 1984, 20(1): 11-22.
[51] Russell AJ and Street KN. Moisture and temperature effects on the mixed-mode delaminationfracture of unidirectional graphite/epoxy. ASTM STP 876: 349 - 370, 1985.
[52] Gillespie Jr JM, Carlsson LA, Pipes RB. Finite element analysis of the end notched flexurespecimen for measuring mode Ⅱ fracture toughness. Compos Sci Technol, 1986, 27: 177 - 197.
[53] Salpekar SA, Raju IS, OBrien TK. Strain energy release rate analysis of the end notched flexurespecimen using the finite element method. J Compos Technol Res, 1988,10: 133 - 139.
[54] He MY, Evans AG. Finite element analysis of beam specimens used to measure the delaminationresistance of composites. J Compos Technol Res, 1992,14: 235 - 40.
[55] Carlsson LA, Gillespie JW and Pipes RB. On the analysis and design of the end notched flexure(ENF) specimen for mode Ⅱ testing. J. Compos. Mater., 1986, 20: 594 - 604.
[56] Mall S, Vozzola RP and Zawada LP. Characterization of fracture in fiber-reinforced ceramiccomposites under shear loading. J. Am. Ceram. Soc. 19619,72:1175-1178.
[57] Mall S and Mol JH. Mode Ⅱ fracture toughness testing of a fiber-reinforced ceramic composite.Engineering Fracture Mechanics, 1991,38(1): 55-69.
[58] Mall S and Truskowski JW. Characterization of mode Ⅱ fracture behavior in fiber-reinforcedceramic composite utilizing laser interferometry. Experimental Mechanics, 1992,32(3): 234-239.
[59] Wang Y and Williams JG. Corrections for Mode Ⅱ fracture toughness specimens of compositesmaterials. Composites Science and Technology, 1992, 43(3): 251-256.
[60] Corleto CR and Hogan HA. Energy release rates for thu ENF specimen using a beam on an elasticfoundation. J Compos Mater, 1995,29:1420 - 1436.
[61] Sankar BV and Sharma SK. Mode Ⅱ delamination toughness of stitched graphite/epoxy textilecomposites. Composites Science and Technology, 1997,57(7): 729-737
[62] Ding W and Kortschot MT. A simplified beam analysis of the end notched flexure mode Ⅱdelamination specimen. Compos Struct, 1999,45: 271 - 278.
[63] Wang Jialai, Qiao Pizhong. Novel beam analysis of end notched flexure specimen for mode-Ⅱfracture. Engineering Fracture Mechanics, 2004,71(2): 219-231.
[64] de Morais AB, Rebelo CC, de Castro PMST, Marques AT and Davies P. Interlaminar fracturestudies in Portugal: past, present and future. Fatigue & Fracture of Engineering Materials&Structures, 2004,27(9), 767-773.
[65] de Moura MFSF, Silva MAL, de Morais AB, Morais JJL. Equivalent crack based mode Ⅱ fracturecharacterization of wood. Engineering Fracture Mechanics, 2006,73: 978 - 993.
[66] Kageyama K, Kikuchi M and Yanagisawa N. Stabilized end notched flexure test: characterization ofmode II interlaminar crack growth. ASTM STP 1110: 210-225,1991.
[67] Kiyoshi Tanaka, Kazuro Kageyama and Masaki Hojo. Prestandardization study on mode Ⅱinterlaminar fracture toughness test for CFRP in Japan. Composites, 1995,26(4): 257-267.
[68] Hiroshi Yoshihara and Masamitsu Ohta. Measurement of mode Ⅱ fracture toughness of wood by theend-notched flexure test. J Wood Sci, 2000,46: 273-278.
[69] Qiao P, Wang J and Davalos JF. Analysis of tapered ENF specimen and characterization of bondedinterface fracture under mode Ⅱ loading. Int. J. Solids Struct., 2003, 40:1865 - 1884.
[70] Paul Robinson. A concept for experimentally evaluating the effect of friction in the 4-ENFinterlaminar toughness test. International Journal of Fracture, 2001,110: L37-L42.
[71] Yoshiara H. Mode Ⅱ R-curve of wood measured by 4-ENF test. Engineering Fracture Mechanics,2004,71: 2065-2077.
[72] Vanderkley PS. Mode Ⅰ-Mode Ⅱ Delamination Fracture Toughness of a Unidirectional Graphite/Epoxy Composite. Master of Science Thesis, Texas A & M University, 1981.
[73] Wang H, Vu-Khanh T and Le VN. Effects of large deflection on Mode Ⅱ fracture test of compositematerials. Journal of Composite Materials, 1995, 29(6): 833-849.
[74] Wang H and Vu-Khanh T. Use of end-loaded-split (ELS) test to study stable fracture behaviour ofcomposites under mode Ⅱ loading. Composite Structures, 1995, 36: 71-79.
[75] Davies P, Blackman BRK and Brunner AJ. Mode II delamination. In: Moore DR, Pavan A, Williams JG, editors. Fracture mechanics testing methods for polymers adhesives and composites. Amsterdam, London, New York: Elsevier; 2001, 307 - 334.
[76] Blackman BRK, Kinloch AJ and Paraschi M. The determination of the mode II adhesive fracture resistance, G_(iic), of structural adhesive joints: an effective crack length approach. Engineering Fracture Mechanics, 2005,72 (6): 877-897.
[77] Murphy JF. Strength of Wood Beams with End Splits. Forest Products, Madison, USA, U.S. Department of Agriculture, Forest Product Research Laboratory, Report 347,1979.
[78] Murphy JF. Mode II wood test specimen: Beam with center slit. Journal of Testing and Evaluation, 1988, 16(4): 364-368.
[79] Iosipescu N. New Accurate Procedure For Single Shear Testing of Metals. Journal of Materials, 1967, 2(3): 537-566.
[80] Hiroshi Yoshihara, Hisashi Ohsaki and Masamitsu Ohta. Applicability of the Iosipescu shear test on the measurement of the shear properties of wood. J Wood Sci, 1999, 45: 24-29.
[81] Yoshitaka Kubojima, Hixoshi Yoshihara, Hisashi Ohsaki and Masamitsu Ohta. Accuracy of shear properties of wood obtained by simplified Iosipescu shear test. J Wood Sci, 2000,46:279-283.
[82] Liu JY. Effects of shear coupling on shear properties of wood. Wood Fiber Sci, 2000, 32(4): 458-465.
[83] Xavier JC, Garrido NM, Oliveira M, Morais JL, Camanho PP and Pierron F. A comparison between the Iosipescu and off-axis shear test methods for the characterization of Pinus Pinaster Ait. Composites: Part A, 2004, 35: 827-840.
[84] Xu LR, Sengupta S and Kuai H. An experimental and numerical investigation of adhesive bonding strengths of polymer materials. International Journal of Adhesion & Adhesives, 2004, 24: 455-460.
[85] Kwon HJ, Jar P-YB. Fracture toughness of polymers in shear mode. Polymer, 2005, 46(26), 12480-12492.
[86] Walrath DE, Adams DF. The Iosipescu shear test as applied to composite materials. Exp. Mech., 1983, 23(1): 105-110.
[87] Adams DF, Walrath DE. Further developments of the Iosipescu shear test method. Exp. Mech., 1987, 27(2): 113-119.
[88] ASTM, "Standard test method for shear properties of composite materials by the V-Notched beam method", D5379/D5379M-98, American Society for Testing and Materials, West Conshohocken, Pennsylvania, PA, 1998.
[89] ASTM, "Shear strength of continuous fiber-reinforced advanced ceramics at ambient temperatures", in Annual Book of ASTM Standards, Practice No. C1292-95a, American Society for Testing and Materials, West Conshohocken, PA, 1995.
[90] Pierron F, Vautrin A, Harris B. The Iosipescu in-plane shear test: validation on an isotropic material. Exp Mech, 1995, 35(2): 130-136.
[91] Pierron F. Saint-Venant effects in the Iosipescu specimen. Journal of Composite Materials, 1998, 32(22): 1986-2015.
[92] Pierron F, Vautrin A. Measurement of the in-plane shear strength of unidirectional composites with the Iosipescu test. Compos Sci Technol, 1997, 57(12): 1653-1660.
[93] Pierron F, Vautrin A. New ideas on the measurement of the in-plane shear strength of unidirectionalcomposites. J Compos Mater, 1997,31(9): 1989-1997.
[94] Jai-Sug Hawong, Dong-Chul Shin, Un-Cheol Baek. Validation of pure shear test device using finiteelement method and experimental methods. Engineering Fracture Mechanics, 2004, 71 (2): 233-243.
[95] Arrea M, Ingraffea AR. Mixed-mode crack propagation in mortar and concrete. Dept. of StructuralEngineering. Report 81-13, Cornell University, 1981.
[96] Ingraffea AR and Panthaki, MJ. Analysis of 'Shear Fracture' Tests of Concrete Beams. FiniteElement Analysis of Reinforced Concrete Structures, ASCE, Tokyo, 151-173.1985.
[97] Bazant ZP and Pfeiffer PA. Shear fracture tests of concrete. Materials and Structures, 1986,19(110):111-121.
[98] Barr B. The fracture characteristics of FRC materials in shear. Fibre reinforced concrete Propertiesand application (Edited by Shah and Baston),. ACI special publication, 1987:27-53.
[99] Barr B, Hasso A and Khalifa SP. A study of Mode Ⅱ notched beam, cylinders and cores.International conference on fracture of concrete and rock (Edited by Shah and Swartz), USA,SEM-RILEM, Houston, 1987.
[100] Swartz SE, Lu LW, Tang LD and Refai TME. Mode Ⅱ fracture-parameter estimates for concretefrom beam specimens. Experimental Mechanics, 1988, 28(2): 146-153.
[101] Swartz SE and Taha NM. Mixed mode crack propagation and fracture in concrete. EngineeringFracture Mechanics, 1990, 35(1/2/3): 137-144.
[102] Swartz SE and Taha NM. Crack propagation and fracture of plain concrete beams subjected to shearand compression. ACI Structural Journal, 1991, 88(2): 169-177.
[103] Ballatore E, Carpinteri A, Ferrara G and Melchorri G. Mixed mode fracture energy of concrete.Engineering Fracture Mechanics, 1990,35(1/2/3): 145-157.
[104] Carpinteri A, Valente S, Ferrara G and Melchorri G. Is mode Ⅱ fracture energy a real materialproperty? Computer and Structures, 1993,48(3): 397-412'.
[105] Kumosa M. and Hull D. Mixed-mode fracture of composites using Iosipescu shear test. InternationalJournal of Fracture, 1987, 35(2): 83-102.
[106] Rots Jan G and Borst Rene de. Analysis of mixed-mode Fracture in concrete. Journal of EngineeringMechanics, 1987,113(11): 1739-1758.
[107] Bansal A and Kumosa M. Experimental and analytical studies of failure modes in Iosipescuspecimens under biaxial loadings. Journal of Composite Materials, 1995, 29(3): 334-358.
[108] Bansal A and Kumosa M. Analysis of double-cracked Iosipescu specimens under biaxial loadings.Engineering Fracture Mechanics, 1998,59(1): 89-100.
[109]张琦，过镇海．砼抗剪强度和剪切变形的研究．建筑结构学报，1992，13(5)：17-24．
[110]徐道远，付赣清．压剪复合应力强度因子和混凝土压剪断裂判据．河海大学学报，1988，16(1)： 97-104．
[111]胡蓓雷，赵国藩，宋玉普等．混凝土复合型断裂试件试验的试件形式及试验装置系统．大连理 工大学学报，1997，37(1)：38-44．
[112]罗章，李夕兵，赵伏军，吴宪平．Ⅱ型荷载下混凝土剪切断裂的测试研究．实验力学，2002， 17(4)：444-451．
[113]郝圣旺，李慧剑，黎振兹等．混凝土四点剪切(Ⅱ型)断裂的数值研究．燕山大学学报，2002， 26(1)：67-70．
[114]郝圣旺，李慧剑，黎振兹等．紧凑四点剪切砼Ⅱ型断裂实验研究与数值分析．工程力学，2003， 20(2)：138-141．
[115]董宇光，李慧剑，严小丽．四点剪切加载下混凝土裂纹扩展路径研究．固体力学学报，2004， 25(2)：198-202．
[116]徐道远，冯伯林，郭建中．混凝土Ⅱ型断裂的FCM和断裂能．河海大学学报，1990，18(3)：8-14．
[117]王桂尧，黎立云，孙宗颀．岩石Ⅱ型裂纹扩展的一般规律．中南矿冶学院学报，1994，25(4)： 450-454．
[118]黎立云，黎振兹，孙宗颀．岩石的复合型断裂实验及分析．岩石力学与工程学报，1994，13(2)： 134-140．
[119]徐平，夏熙伦．花岗岩Ⅰ-Ⅱ复合型断裂试验及断裂数值分析．岩石力学与工程学报，1996，15(1)： 62-70．
[120]王桂尧，孙宗颀，徐纪成．纯剪载荷作用下的岩石断裂．中国有色金属学报，1996，6(1)：17-21．
[121]刘大安，黎立云，马孝春．岩石Ⅱ型裂纹初裂及后继破坏机理研究．岩石力学与工程学报，1998， 17(3)：286-291．
[122] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Effect of specimen thicknesson Mode Ⅱ fracture toughness of rock. Journal of Central South University of Technology, 2001,8(2): 114-119.
[123] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Microscope characteristics ofdifferent fracture modes of little rock. Journal Central South University of Technology, 2001, 8(3):175-179.
[124] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Effect of loading pointposition on fracture mode of rock. Transactions of Nonferrous Metals Society of China, 2001,11(5):764-767.
[125] Davies J, So KW. Further development of fracture test in mode Ⅱ. International Journal of Fracture,1986, 31(1): R19-R21.
[126] Barr B and Derradj M. Numerical study of a shear (Mode Ⅱ) type test specimen geometry.Engineering Fracture Mechanics, 1990, 35(1/2/3): 171-180.
[127] Mattock AH and Hawkins NM. Shear transfer in reinforced concrete-recent research. PCI Journal,1972,17(2): 55-75.
[128] Williams JG. and Birch MW. Mixed mode fracture in anisotropy media in cracks and fracture.ASTM STP610,1976: 125-137.
[129] Markham MF and D Dawson. Interlaminar Shear Strength of Fiber-Reinforced Composites.Composites, 1975, 6: 173.
[130] Dadras P and McDowell JS. Analytical and Experimental Evaluation of Double-notched ShearSpecimens of Orthotropic Materials. Experimental Mechanics, 1990, 30: 184.
[131] (?)nal (?) and Bansal NP. In-plane and interlaminar shear strength of a unidirectional hi-nicalonfiber-reinforced celsian matrix composite. NASA/TM-2000-210608.http://gltrs.grc.nasa.gov/GLTRS (NASA)
[132] ASTM, "In-Plane Shear Strength of Reinforced Plastics;," in Annual Book of ASTM Standards,Practice No. D3846-85, American Society for Testing and Materials, West Conshohocken, PA,1995.
[133] Barr BIG, Liu KLW. Compact shear test specimen. Journal of Materials Science Letters, 1983, 2(11):663-666.
[134] Watkins J and Liu KLW. A finite element study of the short beam test specimen under Mode IIloading. The International Journal of Cement and Lightweight Concrete, 1985, 7(1): 39-47.
[135] Liu K, Barr BIG and Watkins J. Mode II fracture of fiber reinforced concrete materials. TheInternational Journal of Cement and Lightweight Concrete, 1985, 7(2): 93-101.
[136] Barr BIG, Hasso A and Liu KLW. Shear strength of FRC materials. Composites, 1985, 16(4):320-334.
[137] Barr BIG. Compact shear test specimen for FRC materials. Composites, 1987,18(1): 54-60.
[138] Hsu TC, Mau ST and Chen B. Theory of shear transfer strength of reinforced concrete. ACIStructural Journal, 1987, 84(2): 149-160.
[139] Valle M, and Buyukozturk O. Behavior of fiber reinforced high-strength concrete under direct shear.ACI Materials Journal, 1993, 90(2): 122-133.
[140] Khaloo AR and Nakseok K. Influence of concrete and fiber characteristics on behavior of steel fiberreinforced concrete under direct shear. ACI Materials Journal, 1997, 94(6): 592-601.
[141]金初阳，余冬生，张秉友．AS高强混凝土抗剪强度的试验研究．水利学报，1992，23(11)： 75-80．(还使用了冲穿剪切)
[142]中国工程建设标准化协会标准．CECS13：89钢纤维混凝土试验方法．北京：中国计划出版社， 1996．
[143] JSCE-SF6 Method of test for shear strength and toughness tests of steel fiber-reinforced concrete.Japan Society of Civil Engineers, Tokyo, 1990.
[144] Amir A. Mirsayah and Nemkumar Banthia. Shear strength of steel fiber-reinforced concrete. ACIMaterials Journal, 2002, 99(5): 473-479.
[145]高丹盈，朱海堂，汤寄予．纤维高强混凝土抗剪强度的试验研究．建筑科学，2004，20(5)：69-73．
[146]中华人民共和国电力行业标准．DL/T5150-2001水工混凝土试验规程．北京：中国电力出版社， 2002．
[147]赵志方，赵国藩，黄承逵．新老混凝土粘结的抗剪性能研究．建筑结构学报，1999，20(6)：26-31．
[148]王桂尧，孙宗颀，徐纪成，曹平．岩石纯剪断裂的新：型实验方法．中南工业大学学报，1995， 26(3)：314-318．
[149] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Mode 11 fracture mechanismof direct shearing specimen with guiding grooves of rock. Transactions of Nonferrous MetalsSociety of China, 2001,11(4): 613-616.
[150] Pellicane PJ. Ultimate Tensile Strength Analysis of Wood. Ph. D. thesis, Department of Forest andWood Science, Colorado State University , FortCollins, Colorado, USA, 1980.
[151] American Society for Testing and Materials. The annual book of ASTM standards, Section 4.Construction Volume 04.09: Wood. Philadelphia, Pennsylvania, 1985.
[152] Richard HA. A New Compact Shear Specimen. International Journal of Fracture, 1981, 17(5): R105-107.
[153] Richard HA and Kuna M. Theoretical and experimental study of superimposed fracture Mode I, II, III. Engineering Fracture Mechanics, 1990, 35(6): 949-960.
[154] Banks-Sills L and Arcan M. An Edge-cracked Mode II Fracture Specimen. Experimental Mechanics, 1983, 23(3): 257-261.
[155] Banks-Sills L and Arcan M. Toward a pure shear specimen for K_(IIC) determination. International Journal of Fracture, 1983,22(1): R9-R14.
[156] Lo KW, Gong YB, Tamilselvan T and Lai MO. A proposed specimen for K_(IIC) testing. International Journal of Fracture, 2003,124(3/4): 127-137.
[157] Jones DL and Chisholm DB. An Investigation of the Edge-sliding Mode II in Fracture Mechanics. Engineering Fracture Mechanics, 1975, 7(2): 261-270.
[158] Chisholm DB and Jones DL. An analytical and experimental stress analysis of a practical Mode II fracture test specimen. Experimental Mechanics, 1977,17(1): 7-13.
[159] Jones DL and Chisholm DB. Further parametric and boundary condition studies of the compact shear specimen. Proceedings of third International conference on numerical methods in fracture mechanics, Swansea, Penerdge Press LTD., 1984: 697-709.
[160] Boontanjai C. The fracture toughness properties of pinus radiate, Maser's thesis. University of Aukland, New Zealand, 1979.
[161] Mall S, Murphy JF and Shottafer JE. Criterion for mixed mode fracture in wood. Journal of Engineering Mechanics, ASCE, 1983,109(3): 680-690.
[162] Watkins J. Fracture toughness test for soil-cement samples in mode II. International Journal of Fracture, 1983, 23(4): R135-R138.
[163] Bochenek A and Prokopski G. The investigation of aggregate grain size on fracture toughness of ordinary concrete structures. International Journal of Fracture, 1989, 41(4): 197-205.
[164] Brandt AM and Prokopski G. Critical values of stress intensity factor in mode II fracture of cementitious composites. Journal of Materials Science, 1990, 25(8): 3605-3610.
[165] Brandt AM and Prokopski G. On the fractal dimension of fracture surfaces of concrete elements. Journal of Materials Science, 1993, 28(17): 4762-4766.
[166] Prokopski G. Effect of coarse aggregate quantity on Fracture toughness of concretes. Journal of Materials Science 1993, 28(21): 5717-5721.
[167] Prokopski G, Halbiniak J and Langier B. The examination of the fracture toughness of concretes with diverse structure. Journal of Materials Science, 1998, 33(7): 1819-1825.
[168] Takeda J, Komoto H and Tanikawa T. Rate effects on cracked extension in Mode II specimens of mortar. International workshop on fracture toughness and fracture energy/SEDAI/12-14. 1988.
[169] Davies J, Morgan TG and Yim CWA. The finite element analysis of a punch-through shear specimen in mode II. International Journal of Fracture, 1985, 28(6): R47-R48.
[170] Davies J, Yim CWA and Morgan TG. Determination of fracture parameters of a punch-through shear specimen. The International Journal of Cement and Lightweight Concrete, 1987, 9(1): 33-41.
[171] Davies J. Numerical study of punch-through shear specimen in mode II testing for cementitious materials. The International Journal of Cement and Lightweight Concrete, 1988, 10(1): 3-14.
[172] Davies J. Study of Shear Fracture in Mortar Specimens, Cement and Concrete Research, 1995, 25(5):1031-1042.
[173] Davies J. Experimental study of crack propagation in the modified punch-through shear specimen inmixed-mode loading. Fracture Mechanics of Concrete: Structures, Proceedings FRAMCOS-3, ed.Mihashi H and Rokugo K, Aedificatio Publishers, Freiburg, Germany, 1998: 761-771.
[174] Tschegg EK, Humer K and Weber H. Mode Ⅱ fracture tests on fiber-reinforced plastics. Journal ofMaterials Science, 1995,30(5): 1251-1258.
[175] Luong MP. Tensile and Shear Strengths of Concrete and Rock. Engineering Fracture Mechanics,1990,35(1/2/3): 127-135.
[176] Backers T, Stephansson O, Rybacki E. Rock fracture roughness testing in Mode Ⅱ-punch-throughshear test. International Journal of Rock Mechanics & Mining Sciences, 2002,39(6): 755-769.
[177] Backers T, Dresen G, Rybacki E and Stephansson O. New data on mode Ⅱ fracture toughness ofrock from the punch through shear test. Int. J. Rock Mech. Min. Sci, 2004, 41(3): 1-6, ,SINOROCK2004 Symposium.
[178] Jeoungseok Yoon and Seokwon Jeon. Experimental verification of a PTS mode Ⅱ test for rock. Int. J.Rock Mech. Min. Sci, 2004,41(3): 1-7, SINOROCK2004 Symposium.
[179]王桂尧，孙宗颀，徐纪成．岩石压剪断裂机理及强度准则的探讨．岩土工程学报，1996，18(4)： 68-74．
[180]王桂尧，孙宗颀，徐纪成．岩石Ⅱ型断裂韧度的实验方法．中国有色金属学报，1999，9(1)： 175-179．
[181]饶秋华，孙宗颀，Li Chunlin，B．Stillborg．剪切盒加载下岩石剪切(Ⅱ型)断裂韧度K_(Ⅱc)的测定． 中南工业大学学报，2001，32(6)：563-567．
[182] Sun Zongqi. Is crack branching under shear loading caused by shear fracture? A critical review on maximum circumferential stress theory. Trans. Nonferrous Met. Soc. China, 2001,11(2): 287-292.
[183]孙宗颀，饶秋华，王桂尧．剪切断裂韧度(K_(Ⅱc))确定的研究．岩石力学与工程学报，2002，21(2)： 199-203．
[184]孙宗颀．如何判断在各种加载条件下的断裂模式：Ⅰ型还是Ⅱ型．全国第八届岩石、混凝土断 裂、损伤和强度学术会议，烟台，2003．
[185] Rao Qiuhua, Sun Zongqi, Li Chunlin, O. Stephansson and B. Stillborg. Shear fracture (Mode Ⅱ) of brittle rock. International Journal of Rock Mechanics and Mining Sciences, 2003, 40(3): 355-375.
[186] Xu Shilang, Reinhardt HW and Murat Gappoev. Mode Ⅱ fracture testing method for highly orthotropic materials like wood. International Journal of Fracture, 1996,75(2): 185-214.
[187] Reinhardt HW, Ozbolt Josko, Xu Shilang and Dinku A. Shear of structural concrete members and pure mode Ⅱ testing. Advanced Cement Based Materials, 1997, 5(3-4): 75-85.
[188] Reinhardt HW, Xu Shilang. Experimental determination of K_(Ⅱc) of normal strength concrete.Materials and Structures, 1998, 31(209): 296-302.
[189] Tada H, Paris P and Irwin G. The Stress Analysis of Cracks Handbook (second edition). ParisProductions Incorporated, St. Louis, 1985.
[190] Keer LM. Stress Analysis for Bonded Layers. Journal of Applied Mechanics, 1974, 41(3): 679-683.
[191] Yahsi OS. and Gocmen AE. Contact Problem for Two Perfectly Bonded Dissimilar Infinite Strips.International Journal of Fracture, 1987,34(3): 161-177.
[192] Keer LM. and Guo Q. Stress Analysis for symmetrically loaded bonded layers. International Journalof Fracture, 1990,43(1): 69-81.
[193] Radaj D. and Zhang S. Stress Intensity Factors for Spot Welds between Plates of Unequal Thickness.Engineering Fracture Mechanics, 1991,39(2): 391-413.
[194] Reinhardt Hans W, Xu Shilang. A practical testing approach to determine mode Ⅱ fracture energyfor concrete. International Journal of Fracture, 2000,105(2): 107-125.
[195]姜娟．混凝土Ⅱ型断裂数值模拟： (硕士学位论文)．大连：大连理工大学，2003．
[196]徐世娘，赵艳华．混凝土Ⅱ型断裂与破坏过程的三维非线性有限元数值模拟．水力发电学报， 2004，23(5)：15-21．
[197] Wu EM. Application of Fracture Mechanics to Anisotropy Plates. Journal of Applied Mechanics,1967: 967-974.
[198] Desayi P. Fracture of concrete in compression. Materials and Structure, 1977,10(57): 139-144.
[199] Liu C, Huang Y, Lovato ML and Stout MG. Measurement of the fracture toughness of a fiber-reinforced composite using the Brazilian disk geometry. International Journal of Fracture, 1997, 87:241-263.
[200] Liu C, Huang Y and Stout MG. Enhanced mode-Ⅱ fracture toughness of an epoxy resin due to shearbanding. Acta mater, 1998, 46(16): 5647-5661.
[201] Ayatollahi MR, Aliha MRM. Cracked Brazilian disc specimen subjected to mode Ⅱ deformation.Engineering Fracture Mechanics, 2005,72: 493-503.
[202] Jia Z, Castro-Montero A and Shah SP. Observation of mixed mode fracture with center notched diskspecimens. Cement and Concrete Research, 1996, 26(1): 125-137.
[203] Chen Feng, Cao Ping, Rao Qiuhua, Sun Zongqi. Use of double edge-cracked Brazilian diskgeometry for compression-shear fracture investigation of rock. Journal of Central South Universityof Technology, 2003,10(3): 211-215.
[204] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅰ: studies on specimens of some new geometries. Journal of Structural Engineering(Madras), 1999, 26(1): 11-18.
[205] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅱ: fracture toughness of cement paste, mortar, concrete and no-fines concrete. Journalof Structural Engineering (Madras), 1999,26(1): 19-27.
[206] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅲ: studies on shear strength and slip of cement paste, mortar, concrete and no-finesconcrete. Journal of Structural Engineering (Madras), 1999, 26(2): 91-97.
[207] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅳ: fracture toughness, shear strength and slip of fiber reinforced cement mortar andconcrete. Journal of Structural Engineering (Madras), 2000, 26(4): 267-273.
[208]中华人民共和国国家标准．GB4161-84金属材料平面应变断裂韧度K_(Ⅰc)试验方法．北京：中国 标准出版社，1997．
[209] Hillemeier B, Hilsdorf HK. Fracture Mechanics Studies on Concrete Compounds. Cement andConcrete Research, 1977, 7:523-536.
[210] Brühwiler E and Wittmann FH. The wedge splitting test, a new method of Performing stable fracturemechanics tests. Engineering Fracture Mechanics, 1990, 35(1/2/3): 117-125.
[211]卜丹．楔入式紧凑拉伸断裂试验研究： (硕士学位论文)．大连：大连理工大学，2006．
[212]徐世烺，卜丹，张秀芳．不同尺寸楔入式紧凑拉伸试件双K断裂参数的试验测定．土木工程 学报，2008，41(2)：70-76．
[213]徐世烺，卜丹，张秀芳．楔入式紧凑拉伸法确定混凝土的断裂能．水利学报，2007，38(6)：47-53．
[214]陈篪，蔡其巩，王仁智等．工程断裂力学(上册)．北京：国防工业出版社，1979：139．
[215]徐世烺，吴智敏，丁生根．砼双K断裂参数的实用解析方法．工程力学，2003，20(3)：54-61．
[216]吴智敏，徐世烺，王金来．三点弯曲梁法研究砼双K断裂参数及其尺寸效应．水力发电学报， 2000，19(4)：16-24．
[217] Ozbolt J, Reinhardt HW and Xu Shilang. Numerical studies on the double-edge notched mode Ⅱgeometry. In: Mihashi H and Rokugo K, ed. Fracture Mechanics of Concrete Structures. ProceedingsFRAMCOS-3, Freiburg, Germany: Aedificatio Publishers, 1998: 773-782.
[218] Cedolin L, Bisi G and Narodello P. Sulla determinazione sperimentale dell'energia di fracttura inmodo Ⅱ per il calcestruzzo. Studie e Ricerche. 1997,18.
[219] Cedolin L, Bisi G and Narodello P. On the detection of crack propagation in Reinhardt'sdouble-edge concrete testing specimen for mode Ⅱ. Dipartmento di Ingegneria Strutturale,Politecnico di Milano, 1998.
[220] Prisco M and Ferrara L. On the evaluation of mode Ⅱ fracture energy in high stength concrete. In: deBorst, R. Bicanic, N. Mang and G. Meschke, ed. Computational Modelling of Concrete Structures.Rotterdam: Balkema, 1998: 409-418.
[221]孙雅珍，余天庆．混凝土破坏的断裂和损伤耦合分析．全国第九届岩石、混凝土断裂、损伤和 强度学术会议，贵阳，2005．
[2] Mindess S. Fracture Process Zone Detection. Fracture Mechanics Test Method for Concrete, Reportof Technical Committee 89-FMT,1991 RILEM, Chapman and Hall.
[3] 徐世娘，赵国藩．光弹性贴片法研究混凝土裂缝扩展过程．水力发电学报，1991，10(3)：8-18．
[4] 徐世娘，赵国藩．混凝土裂缝的稳定扩展过程与临界裂缝尖端张开位移．水利学报，1989，20(4)： 33-44．
[5] Hillerborg A, Modeer M and Petersson P E. Analysis of crack formation and crack growth inconcrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976,6: 773-782.
[6] Petersson PE. Crack growth and development of fracture zones in plain concrete and similarmaterials. Division of Building Materials, Lund Institute of Technology, Report TVBM-1006,1981.
[7] Reinhardt H W, Cornelissen H A W and Hordijk D A. Tensile tests and failure analysis of concrete.Journal of Structural Engineering, 1986,112(11): 2462-2477.
[8] Gopalaratnam V S and Shah S P. Softening response of plain concrete in direct tension. ACI Journal,1985, 82(3): 310-323.
[9] Bazant Z P and Oh B H. Crack Band Theory for Fracture of Concrete. Materials and Structures,1983,16(93): 155-177.
[10] Jenq YS and Shah SP. Two Parameter Fracture Model for Concrete. Journal of EngineeringMechanics, 1985,111(10): 1227-1241.
[11] Jenq, YS and Shah SP. A fracture toughness criterion for concrete. Engineering Fracture Mechanics,1985, 21(5): 1055-1069.
[12] Swartz SE and Go CG. Validity of compliance calibration to cracked concrete beams in bending.Experimental Mechanics, 1984, 24(2): 129-134.
[13] Swartz SE and Refai TME. Influence of size on opening mode fracture parameters for precrackedconcrete beams in bending. Proceedings of SEM-RILEM International Conference on Fracture ofConcrete and Rock. Houston, Texas, 1987: 242-254.
[14] Nallathambi P and Karihaloo BL. Determination of specimen-size independent fracture toughness ofplain concrete. Magazine of Concrete Research, 1986, 38(135): 67-76.
[15] Karihaloo BL and Nallathambi P. An improved effective crack model for the determination offracture toughness of concrete. Cement and Concrete Research, 1989, 19: 603-610
[16] Karihaloo BL and Nallathambi P. Effective Crack Model for the Determination of FractureToughness (K_(Ic)~s) of Concrete. Engineering Fracture Mechanics, 1990: 35(4/5): 637-645.
[17] Bazant ZP, Kim JK and Pfeiffer PA. Determination of Fracture Properties from Size Effect Tests.Journal of Structural Engineering (ASCE), 1986, 112(2): 289-307.
[18] Bazant ZP and Kazemi MT. Determination of fracture energy, process zone length and brittlenessnumber from size effect, with application to rock and concrete. International Journal of Fracture,1990,(44): 111-131.
[19] Zhimin Wu, Shutong Yang, Xiaozhi Hu and Jianjun Zheng. An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams. Engineering Fracture Mechanics, 2006, 73: 2166-2191.
[20] 吴智敏，杨树桐，郑建军．混凝土等效断裂韧度的解析方法及其尺寸效应．水利学报，2006， 37(7)： 795-800．
[21] 徐世娘，赵国藩．混凝土结构裂缝扩展的双K断裂准则．土木工程学报，1992，25(2)：32-38．
[22] Xu Shilang and Reinhardt Hans W. Determination of double-K criterion for crack propagation inquasi-brittle fracture, Part Ⅰ: Experimental investigation of crack propagation. International Journalof Fracture, 1999, 98(2): 111-149.
[23] Xu Shilang and Reinhardt Hans W. Determination of double-K criterion for crack propagation inquasi-brittle fracture, Part Ⅱ: Analytical evaluating and practical measuring methods for three-pointbending notched beams. International Journal of Fracture, 1999,98(2): 151-177.
[24] Xu Shilang and Reinhardt Hans W. Determination of double-K criterion for crack propagation inquasi-brittle fracture, Part Ⅲ: Compact tension specimens and wedge splitting specimens.International Journal of Fracture, 1999,98(2): 179-193.
[25] Xu Shilang and Reinhardt Hans W. A simplified method for determining double-K fractureparameters for three-point bending tests. International Journal of Fracture, 2000,104:181-208.
[26] Xu Shilang and Reinhardt Hans W. Crack extension resistance and fracture properties ofquasi-brittle softening materials like concrete based on the complete process of fracture.International Journal of Fracture, 1998, 92: 71-99.
[27] Reinhardt Hans W and Xu Shilang. Crack extension resistance based on the cohesive force inconcrete. Engineering Fracture Mechanics, 1999,64:563-587.
[28] 赵艳华．混凝土断裂过程中的能量分析研究： (博士学位论文)．大连：大连理工大学，2002．
[29] 赵艳华，徐世娘，吴智敏．混凝土结构裂缝扩展的双G准则．土木工程学报，2004，37(10)： 13-18．
[30] RILEM Technical Committee 50-FMC. Determination of the Fracture Energy of Mortar andConcrete by Means of Three-Point Bend Tests of Notched Beams, Proposed RILEM DraftRecommendations. Materials and Structures. 1985,18(106): 285-296.
[31] Nordtest Method, NT BUILD 491, Concrete and Mortar, Hardened: Fracture Energy (Model Ⅰ) -Three-point bend tests on notched beams. 1999.
[32] JCI-TC 992. Test method for fracture energy of plain concrete (Draft). 2001.
[33] CEB-Comite Euro-International du Beton-CEB-FIP Model Code 1990, Bulletin D'Information No.213/214, Lausanne. 1993.
[34] RILEM Technical Committee 89-FMT. Determination of fracture parameters (K_(Ic)~s and CTODc) ofplain concrete using three-point bend tests, Proposed RILEM Draft Recommendations. Materials and Structures, 1990, 23(138): 457-460.
[35] RILEM Technical Committee 89-FMT. Size-Effect Method for Determining Fracture Energy and Process Zone Size of Concrete, Proposed RILEM Draft Recommendations. Materials and Structures, 1990,23(138): 461-465.
[36] 中华人民共和国电力行业标准．DL／T5332-2005水工混凝土断裂试验规程．北京：中国电力出 版社，2006．
[37] 于骁中，张彦秋，曹建国等．混凝土复合型(Ⅰ、Ⅱ型)裂纹断裂准则的计算和试验研究．水利学 报，1982，13(6)：27-37．
[38] 徐道远，梁正平，王德峻等．混凝土Ⅰ、Ⅱ复合裂纹断裂判据的探讨．水利学报，1982，13(6)： 57-61．
[39] Jenq Y and Shah S. Mixed mode fracture parameters of concrete. International Journal of Fracture, 1988, 38:123-142.
[40] 陈玉泉．混凝土复合断裂准则的试验研究：(硕士学位论文)．大连：大连理工大学，1988．
[41] 胡蓓雷，赵国藩．混凝土Ⅰ-Ⅱ复合型裂纹有效断裂准则．大连理工大学学报，1996，36(6)： 776-781．
[42] 高泉．混凝土断裂参数的测试方法及复合型裂纹断裂判据的试验研究： (博士学位论文)．大 连：大连理工大学，1992．
[43] 赵艳华，徐世烺．Ⅰ-Ⅱ复合型裂纹脆性断裂的最小J_2准则．工程力学，2002，19(4)：94-98．
[44] Cramer Steven M and Pugel Anton D. Compacted shear specimen for wood mode Ⅱ fractureinvestigation. International Journal of Fracture, 1987, 35(3): 163-174.
[45] Bazant ZP. Concepts Models and Determination of Material Properties, Fracture Mechanics ofConcrete Structures, Elsevier Applied Science, State-of-Art Report by ACI Committee 446, Londonand New York, 1992.
[46] Kaplan MF. Crack propagation and fracture of concrete. Journal of the American Concrete Institute,1961,58(5): 591-610.
[47] Saouma VE, Natekar D and Hansen E. Cohesive stresses and size effects in elasto-plastic andquasi-brittle materials. International Journal of Fracture, 2003,119: 287-298.
[48] ACI Committee 446. ACI Committee 446 Minutes. Toronto, 2000.
[49] Barrett JD and Foschi RO. Mode Ⅱ stress-intensity factors for cracked wood beams. EngineeringFractures Mechanics, 1977,9(2): 371-378.
[50] Giare GS. Fracture toughness of unidirectional fibre reinforced composites in Mode Ⅱ. EngineeringFracture Mechanics, 1984, 20(1): 11-22.
[51] Russell AJ and Street KN. Moisture and temperature effects on the mixed-mode delaminationfracture of unidirectional graphite/epoxy. ASTM STP 876: 349 - 370, 1985.
[52] Gillespie Jr JM, Carlsson LA, Pipes RB. Finite element analysis of the end notched flexurespecimen for measuring mode Ⅱ fracture toughness. Compos Sci Technol, 1986, 27: 177 - 197.
[53] Salpekar SA, Raju IS, OBrien TK. Strain energy release rate analysis of the end notched flexurespecimen using the finite element method. J Compos Technol Res, 1988,10: 133 - 139.
[54] He MY, Evans AG. Finite element analysis of beam specimens used to measure the delaminationresistance of composites. J Compos Technol Res, 1992,14: 235 - 40.
[55] Carlsson LA, Gillespie JW and Pipes RB. On the analysis and design of the end notched flexure(ENF) specimen for mode Ⅱ testing. J. Compos. Mater., 1986, 20: 594 - 604.
[56] Mall S, Vozzola RP and Zawada LP. Characterization of fracture in fiber-reinforced ceramiccomposites under shear loading. J. Am. Ceram. Soc. 19619,72:1175-1178.
[57] Mall S and Mol JH. Mode Ⅱ fracture toughness testing of a fiber-reinforced ceramic composite.Engineering Fracture Mechanics, 1991,38(1): 55-69.
[58] Mall S and Truskowski JW. Characterization of mode Ⅱ fracture behavior in fiber-reinforcedceramic composite utilizing laser interferometry. Experimental Mechanics, 1992,32(3): 234-239.
[59] Wang Y and Williams JG. Corrections for Mode Ⅱ fracture toughness specimens of compositesmaterials. Composites Science and Technology, 1992, 43(3): 251-256.
[60] Corleto CR and Hogan HA. Energy release rates for thu ENF specimen using a beam on an elasticfoundation. J Compos Mater, 1995,29:1420 - 1436.
[61] Sankar BV and Sharma SK. Mode Ⅱ delamination toughness of stitched graphite/epoxy textilecomposites. Composites Science and Technology, 1997,57(7): 729-737
[62] Ding W and Kortschot MT. A simplified beam analysis of the end notched flexure mode Ⅱdelamination specimen. Compos Struct, 1999,45: 271 - 278.
[63] Wang Jialai, Qiao Pizhong. Novel beam analysis of end notched flexure specimen for mode-Ⅱfracture. Engineering Fracture Mechanics, 2004,71(2): 219-231.
[64] de Morais AB, Rebelo CC, de Castro PMST, Marques AT and Davies P. Interlaminar fracturestudies in Portugal: past, present and future. Fatigue & Fracture of Engineering Materials&Structures, 2004,27(9), 767-773.
[65] de Moura MFSF, Silva MAL, de Morais AB, Morais JJL. Equivalent crack based mode Ⅱ fracturecharacterization of wood. Engineering Fracture Mechanics, 2006,73: 978 - 993.
[66] Kageyama K, Kikuchi M and Yanagisawa N. Stabilized end notched flexure test: characterization ofmode II interlaminar crack growth. ASTM STP 1110: 210-225,1991.
[67] Kiyoshi Tanaka, Kazuro Kageyama and Masaki Hojo. Prestandardization study on mode Ⅱinterlaminar fracture toughness test for CFRP in Japan. Composites, 1995,26(4): 257-267.
[68] Hiroshi Yoshihara and Masamitsu Ohta. Measurement of mode Ⅱ fracture toughness of wood by theend-notched flexure test. J Wood Sci, 2000,46: 273-278.
[69] Qiao P, Wang J and Davalos JF. Analysis of tapered ENF specimen and characterization of bondedinterface fracture under mode Ⅱ loading. Int. J. Solids Struct., 2003, 40:1865 - 1884.
[70] Paul Robinson. A concept for experimentally evaluating the effect of friction in the 4-ENFinterlaminar toughness test. International Journal of Fracture, 2001,110: L37-L42.
[71] Yoshiara H. Mode Ⅱ R-curve of wood measured by 4-ENF test. Engineering Fracture Mechanics,2004,71: 2065-2077.
[72] Vanderkley PS. Mode Ⅰ-Mode Ⅱ Delamination Fracture Toughness of a Unidirectional Graphite/Epoxy Composite. Master of Science Thesis, Texas A & M University, 1981.
[73] Wang H, Vu-Khanh T and Le VN. Effects of large deflection on Mode Ⅱ fracture test of compositematerials. Journal of Composite Materials, 1995, 29(6): 833-849.
[74] Wang H and Vu-Khanh T. Use of end-loaded-split (ELS) test to study stable fracture behaviour ofcomposites under mode Ⅱ loading. Composite Structures, 1995, 36: 71-79.
[75] Davies P, Blackman BRK and Brunner AJ. Mode II delamination. In: Moore DR, Pavan A, Williams JG, editors. Fracture mechanics testing methods for polymers adhesives and composites. Amsterdam, London, New York: Elsevier; 2001, 307 - 334.
[76] Blackman BRK, Kinloch AJ and Paraschi M. The determination of the mode II adhesive fracture resistance, G_(iic), of structural adhesive joints: an effective crack length approach. Engineering Fracture Mechanics, 2005,72 (6): 877-897.
[77] Murphy JF. Strength of Wood Beams with End Splits. Forest Products, Madison, USA, U.S. Department of Agriculture, Forest Product Research Laboratory, Report 347,1979.
[78] Murphy JF. Mode II wood test specimen: Beam with center slit. Journal of Testing and Evaluation, 1988, 16(4): 364-368.
[79] Iosipescu N. New Accurate Procedure For Single Shear Testing of Metals. Journal of Materials, 1967, 2(3): 537-566.
[80] Hiroshi Yoshihara, Hisashi Ohsaki and Masamitsu Ohta. Applicability of the Iosipescu shear test on the measurement of the shear properties of wood. J Wood Sci, 1999, 45: 24-29.
[81] Yoshitaka Kubojima, Hixoshi Yoshihara, Hisashi Ohsaki and Masamitsu Ohta. Accuracy of shear properties of wood obtained by simplified Iosipescu shear test. J Wood Sci, 2000,46:279-283.
[82] Liu JY. Effects of shear coupling on shear properties of wood. Wood Fiber Sci, 2000, 32(4): 458-465.
[83] Xavier JC, Garrido NM, Oliveira M, Morais JL, Camanho PP and Pierron F. A comparison between the Iosipescu and off-axis shear test methods for the characterization of Pinus Pinaster Ait. Composites: Part A, 2004, 35: 827-840.
[84] Xu LR, Sengupta S and Kuai H. An experimental and numerical investigation of adhesive bonding strengths of polymer materials. International Journal of Adhesion & Adhesives, 2004, 24: 455-460.
[85] Kwon HJ, Jar P-YB. Fracture toughness of polymers in shear mode. Polymer, 2005, 46(26), 12480-12492.
[86] Walrath DE, Adams DF. The Iosipescu shear test as applied to composite materials. Exp. Mech., 1983, 23(1): 105-110.
[87] Adams DF, Walrath DE. Further developments of the Iosipescu shear test method. Exp. Mech., 1987, 27(2): 113-119.
[88] ASTM, "Standard test method for shear properties of composite materials by the V-Notched beam method", D5379/D5379M-98, American Society for Testing and Materials, West Conshohocken, Pennsylvania, PA, 1998.
[89] ASTM, "Shear strength of continuous fiber-reinforced advanced ceramics at ambient temperatures", in Annual Book of ASTM Standards, Practice No. C1292-95a, American Society for Testing and Materials, West Conshohocken, PA, 1995.
[90] Pierron F, Vautrin A, Harris B. The Iosipescu in-plane shear test: validation on an isotropic material. Exp Mech, 1995, 35(2): 130-136.
[91] Pierron F. Saint-Venant effects in the Iosipescu specimen. Journal of Composite Materials, 1998, 32(22): 1986-2015.
[92] Pierron F, Vautrin A. Measurement of the in-plane shear strength of unidirectional composites with the Iosipescu test. Compos Sci Technol, 1997, 57(12): 1653-1660.
[93] Pierron F, Vautrin A. New ideas on the measurement of the in-plane shear strength of unidirectionalcomposites. J Compos Mater, 1997,31(9): 1989-1997.
[94] Jai-Sug Hawong, Dong-Chul Shin, Un-Cheol Baek. Validation of pure shear test device using finiteelement method and experimental methods. Engineering Fracture Mechanics, 2004, 71 (2): 233-243.
[95] Arrea M, Ingraffea AR. Mixed-mode crack propagation in mortar and concrete. Dept. of StructuralEngineering. Report 81-13, Cornell University, 1981.
[96] Ingraffea AR and Panthaki, MJ. Analysis of 'Shear Fracture' Tests of Concrete Beams. FiniteElement Analysis of Reinforced Concrete Structures, ASCE, Tokyo, 151-173.1985.
[97] Bazant ZP and Pfeiffer PA. Shear fracture tests of concrete. Materials and Structures, 1986,19(110):111-121.
[98] Barr B. The fracture characteristics of FRC materials in shear. Fibre reinforced concrete Propertiesand application (Edited by Shah and Baston),. ACI special publication, 1987:27-53.
[99] Barr B, Hasso A and Khalifa SP. A study of Mode Ⅱ notched beam, cylinders and cores.International conference on fracture of concrete and rock (Edited by Shah and Swartz), USA,SEM-RILEM, Houston, 1987.
[100] Swartz SE, Lu LW, Tang LD and Refai TME. Mode Ⅱ fracture-parameter estimates for concretefrom beam specimens. Experimental Mechanics, 1988, 28(2): 146-153.
[101] Swartz SE and Taha NM. Mixed mode crack propagation and fracture in concrete. EngineeringFracture Mechanics, 1990, 35(1/2/3): 137-144.
[102] Swartz SE and Taha NM. Crack propagation and fracture of plain concrete beams subjected to shearand compression. ACI Structural Journal, 1991, 88(2): 169-177.
[103] Ballatore E, Carpinteri A, Ferrara G and Melchorri G. Mixed mode fracture energy of concrete.Engineering Fracture Mechanics, 1990,35(1/2/3): 145-157.
[104] Carpinteri A, Valente S, Ferrara G and Melchorri G. Is mode Ⅱ fracture energy a real materialproperty? Computer and Structures, 1993,48(3): 397-412'.
[105] Kumosa M. and Hull D. Mixed-mode fracture of composites using Iosipescu shear test. InternationalJournal of Fracture, 1987, 35(2): 83-102.
[106] Rots Jan G and Borst Rene de. Analysis of mixed-mode Fracture in concrete. Journal of EngineeringMechanics, 1987,113(11): 1739-1758.
[107] Bansal A and Kumosa M. Experimental and analytical studies of failure modes in Iosipescuspecimens under biaxial loadings. Journal of Composite Materials, 1995, 29(3): 334-358.
[108] Bansal A and Kumosa M. Analysis of double-cracked Iosipescu specimens under biaxial loadings.Engineering Fracture Mechanics, 1998,59(1): 89-100.
[109]张琦，过镇海．砼抗剪强度和剪切变形的研究．建筑结构学报，1992，13(5)：17-24．
[110]徐道远，付赣清．压剪复合应力强度因子和混凝土压剪断裂判据．河海大学学报，1988，16(1)： 97-104．
[111]胡蓓雷，赵国藩，宋玉普等．混凝土复合型断裂试件试验的试件形式及试验装置系统．大连理 工大学学报，1997，37(1)：38-44．
[112]罗章，李夕兵，赵伏军，吴宪平．Ⅱ型荷载下混凝土剪切断裂的测试研究．实验力学，2002， 17(4)：444-451．
[113]郝圣旺，李慧剑，黎振兹等．混凝土四点剪切(Ⅱ型)断裂的数值研究．燕山大学学报，2002， 26(1)：67-70．
[114]郝圣旺，李慧剑，黎振兹等．紧凑四点剪切砼Ⅱ型断裂实验研究与数值分析．工程力学，2003， 20(2)：138-141．
[115]董宇光，李慧剑，严小丽．四点剪切加载下混凝土裂纹扩展路径研究．固体力学学报，2004， 25(2)：198-202．
[116]徐道远，冯伯林，郭建中．混凝土Ⅱ型断裂的FCM和断裂能．河海大学学报，1990，18(3)：8-14．
[117]王桂尧，黎立云，孙宗颀．岩石Ⅱ型裂纹扩展的一般规律．中南矿冶学院学报，1994，25(4)： 450-454．
[118]黎立云，黎振兹，孙宗颀．岩石的复合型断裂实验及分析．岩石力学与工程学报，1994，13(2)： 134-140．
[119]徐平，夏熙伦．花岗岩Ⅰ-Ⅱ复合型断裂试验及断裂数值分析．岩石力学与工程学报，1996，15(1)： 62-70．
[120]王桂尧，孙宗颀，徐纪成．纯剪载荷作用下的岩石断裂．中国有色金属学报，1996，6(1)：17-21．
[121]刘大安，黎立云，马孝春．岩石Ⅱ型裂纹初裂及后继破坏机理研究．岩石力学与工程学报，1998， 17(3)：286-291．
[122] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Effect of specimen thicknesson Mode Ⅱ fracture toughness of rock. Journal of Central South University of Technology, 2001,8(2): 114-119.
[123] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Microscope characteristics ofdifferent fracture modes of little rock. Journal Central South University of Technology, 2001, 8(3):175-179.
[124] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Effect of loading pointposition on fracture mode of rock. Transactions of Nonferrous Metals Society of China, 2001,11(5):764-767.
[125] Davies J, So KW. Further development of fracture test in mode Ⅱ. International Journal of Fracture,1986, 31(1): R19-R21.
[126] Barr B and Derradj M. Numerical study of a shear (Mode Ⅱ) type test specimen geometry.Engineering Fracture Mechanics, 1990, 35(1/2/3): 171-180.
[127] Mattock AH and Hawkins NM. Shear transfer in reinforced concrete-recent research. PCI Journal,1972,17(2): 55-75.
[128] Williams JG. and Birch MW. Mixed mode fracture in anisotropy media in cracks and fracture.ASTM STP610,1976: 125-137.
[129] Markham MF and D Dawson. Interlaminar Shear Strength of Fiber-Reinforced Composites.Composites, 1975, 6: 173.
[130] Dadras P and McDowell JS. Analytical and Experimental Evaluation of Double-notched ShearSpecimens of Orthotropic Materials. Experimental Mechanics, 1990, 30: 184.
[131] (?)nal (?) and Bansal NP. In-plane and interlaminar shear strength of a unidirectional hi-nicalonfiber-reinforced celsian matrix composite. NASA/TM-2000-210608.http://gltrs.grc.nasa.gov/GLTRS (NASA)
[132] ASTM, "In-Plane Shear Strength of Reinforced Plastics;," in Annual Book of ASTM Standards,Practice No. D3846-85, American Society for Testing and Materials, West Conshohocken, PA,1995.
[133] Barr BIG, Liu KLW. Compact shear test specimen. Journal of Materials Science Letters, 1983, 2(11):663-666.
[134] Watkins J and Liu KLW. A finite element study of the short beam test specimen under Mode IIloading. The International Journal of Cement and Lightweight Concrete, 1985, 7(1): 39-47.
[135] Liu K, Barr BIG and Watkins J. Mode II fracture of fiber reinforced concrete materials. TheInternational Journal of Cement and Lightweight Concrete, 1985, 7(2): 93-101.
[136] Barr BIG, Hasso A and Liu KLW. Shear strength of FRC materials. Composites, 1985, 16(4):320-334.
[137] Barr BIG. Compact shear test specimen for FRC materials. Composites, 1987,18(1): 54-60.
[138] Hsu TC, Mau ST and Chen B. Theory of shear transfer strength of reinforced concrete. ACIStructural Journal, 1987, 84(2): 149-160.
[139] Valle M, and Buyukozturk O. Behavior of fiber reinforced high-strength concrete under direct shear.ACI Materials Journal, 1993, 90(2): 122-133.
[140] Khaloo AR and Nakseok K. Influence of concrete and fiber characteristics on behavior of steel fiberreinforced concrete under direct shear. ACI Materials Journal, 1997, 94(6): 592-601.
[141]金初阳，余冬生，张秉友．AS高强混凝土抗剪强度的试验研究．水利学报，1992，23(11)： 75-80．(还使用了冲穿剪切)
[142]中国工程建设标准化协会标准．CECS13：89钢纤维混凝土试验方法．北京：中国计划出版社， 1996．
[143] JSCE-SF6 Method of test for shear strength and toughness tests of steel fiber-reinforced concrete.Japan Society of Civil Engineers, Tokyo, 1990.
[144] Amir A. Mirsayah and Nemkumar Banthia. Shear strength of steel fiber-reinforced concrete. ACIMaterials Journal, 2002, 99(5): 473-479.
[145]高丹盈，朱海堂，汤寄予．纤维高强混凝土抗剪强度的试验研究．建筑科学，2004，20(5)：69-73．
[146]中华人民共和国电力行业标准．DL/T5150-2001水工混凝土试验规程．北京：中国电力出版社， 2002．
[147]赵志方，赵国藩，黄承逵．新老混凝土粘结的抗剪性能研究．建筑结构学报，1999，20(6)：26-31．
[148]王桂尧，孙宗颀，徐纪成，曹平．岩石纯剪断裂的新：型实验方法．中南工业大学学报，1995， 26(3)：314-318．
[149] Rao Qiuhua, Sun Zongqi, Wang Guirao, Xu Jicheng and Zhang Jingyi. Mode 11 fracture mechanismof direct shearing specimen with guiding grooves of rock. Transactions of Nonferrous MetalsSociety of China, 2001,11(4): 613-616.
[150] Pellicane PJ. Ultimate Tensile Strength Analysis of Wood. Ph. D. thesis, Department of Forest andWood Science, Colorado State University , FortCollins, Colorado, USA, 1980.
[151] American Society for Testing and Materials. The annual book of ASTM standards, Section 4.Construction Volume 04.09: Wood. Philadelphia, Pennsylvania, 1985.
[152] Richard HA. A New Compact Shear Specimen. International Journal of Fracture, 1981, 17(5): R105-107.
[153] Richard HA and Kuna M. Theoretical and experimental study of superimposed fracture Mode I, II, III. Engineering Fracture Mechanics, 1990, 35(6): 949-960.
[154] Banks-Sills L and Arcan M. An Edge-cracked Mode II Fracture Specimen. Experimental Mechanics, 1983, 23(3): 257-261.
[155] Banks-Sills L and Arcan M. Toward a pure shear specimen for K_(IIC) determination. International Journal of Fracture, 1983,22(1): R9-R14.
[156] Lo KW, Gong YB, Tamilselvan T and Lai MO. A proposed specimen for K_(IIC) testing. International Journal of Fracture, 2003,124(3/4): 127-137.
[157] Jones DL and Chisholm DB. An Investigation of the Edge-sliding Mode II in Fracture Mechanics. Engineering Fracture Mechanics, 1975, 7(2): 261-270.
[158] Chisholm DB and Jones DL. An analytical and experimental stress analysis of a practical Mode II fracture test specimen. Experimental Mechanics, 1977,17(1): 7-13.
[159] Jones DL and Chisholm DB. Further parametric and boundary condition studies of the compact shear specimen. Proceedings of third International conference on numerical methods in fracture mechanics, Swansea, Penerdge Press LTD., 1984: 697-709.
[160] Boontanjai C. The fracture toughness properties of pinus radiate, Maser's thesis. University of Aukland, New Zealand, 1979.
[161] Mall S, Murphy JF and Shottafer JE. Criterion for mixed mode fracture in wood. Journal of Engineering Mechanics, ASCE, 1983,109(3): 680-690.
[162] Watkins J. Fracture toughness test for soil-cement samples in mode II. International Journal of Fracture, 1983, 23(4): R135-R138.
[163] Bochenek A and Prokopski G. The investigation of aggregate grain size on fracture toughness of ordinary concrete structures. International Journal of Fracture, 1989, 41(4): 197-205.
[164] Brandt AM and Prokopski G. Critical values of stress intensity factor in mode II fracture of cementitious composites. Journal of Materials Science, 1990, 25(8): 3605-3610.
[165] Brandt AM and Prokopski G. On the fractal dimension of fracture surfaces of concrete elements. Journal of Materials Science, 1993, 28(17): 4762-4766.
[166] Prokopski G. Effect of coarse aggregate quantity on Fracture toughness of concretes. Journal of Materials Science 1993, 28(21): 5717-5721.
[167] Prokopski G, Halbiniak J and Langier B. The examination of the fracture toughness of concretes with diverse structure. Journal of Materials Science, 1998, 33(7): 1819-1825.
[168] Takeda J, Komoto H and Tanikawa T. Rate effects on cracked extension in Mode II specimens of mortar. International workshop on fracture toughness and fracture energy/SEDAI/12-14. 1988.
[169] Davies J, Morgan TG and Yim CWA. The finite element analysis of a punch-through shear specimen in mode II. International Journal of Fracture, 1985, 28(6): R47-R48.
[170] Davies J, Yim CWA and Morgan TG. Determination of fracture parameters of a punch-through shear specimen. The International Journal of Cement and Lightweight Concrete, 1987, 9(1): 33-41.
[171] Davies J. Numerical study of punch-through shear specimen in mode II testing for cementitious materials. The International Journal of Cement and Lightweight Concrete, 1988, 10(1): 3-14.
[172] Davies J. Study of Shear Fracture in Mortar Specimens, Cement and Concrete Research, 1995, 25(5):1031-1042.
[173] Davies J. Experimental study of crack propagation in the modified punch-through shear specimen inmixed-mode loading. Fracture Mechanics of Concrete: Structures, Proceedings FRAMCOS-3, ed.Mihashi H and Rokugo K, Aedificatio Publishers, Freiburg, Germany, 1998: 761-771.
[174] Tschegg EK, Humer K and Weber H. Mode Ⅱ fracture tests on fiber-reinforced plastics. Journal ofMaterials Science, 1995,30(5): 1251-1258.
[175] Luong MP. Tensile and Shear Strengths of Concrete and Rock. Engineering Fracture Mechanics,1990,35(1/2/3): 127-135.
[176] Backers T, Stephansson O, Rybacki E. Rock fracture roughness testing in Mode Ⅱ-punch-throughshear test. International Journal of Rock Mechanics & Mining Sciences, 2002,39(6): 755-769.
[177] Backers T, Dresen G, Rybacki E and Stephansson O. New data on mode Ⅱ fracture toughness ofrock from the punch through shear test. Int. J. Rock Mech. Min. Sci, 2004, 41(3): 1-6, ,SINOROCK2004 Symposium.
[178] Jeoungseok Yoon and Seokwon Jeon. Experimental verification of a PTS mode Ⅱ test for rock. Int. J.Rock Mech. Min. Sci, 2004,41(3): 1-7, SINOROCK2004 Symposium.
[179]王桂尧，孙宗颀，徐纪成．岩石压剪断裂机理及强度准则的探讨．岩土工程学报，1996，18(4)： 68-74．
[180]王桂尧，孙宗颀，徐纪成．岩石Ⅱ型断裂韧度的实验方法．中国有色金属学报，1999，9(1)： 175-179．
[181]饶秋华，孙宗颀，Li Chunlin，B．Stillborg．剪切盒加载下岩石剪切(Ⅱ型)断裂韧度K_(Ⅱc)的测定． 中南工业大学学报，2001，32(6)：563-567．
[182] Sun Zongqi. Is crack branching under shear loading caused by shear fracture? A critical review on maximum circumferential stress theory. Trans. Nonferrous Met. Soc. China, 2001,11(2): 287-292.
[183]孙宗颀，饶秋华，王桂尧．剪切断裂韧度(K_(Ⅱc))确定的研究．岩石力学与工程学报，2002，21(2)： 199-203．
[184]孙宗颀．如何判断在各种加载条件下的断裂模式：Ⅰ型还是Ⅱ型．全国第八届岩石、混凝土断 裂、损伤和强度学术会议，烟台，2003．
[185] Rao Qiuhua, Sun Zongqi, Li Chunlin, O. Stephansson and B. Stillborg. Shear fracture (Mode Ⅱ) of brittle rock. International Journal of Rock Mechanics and Mining Sciences, 2003, 40(3): 355-375.
[186] Xu Shilang, Reinhardt HW and Murat Gappoev. Mode Ⅱ fracture testing method for highly orthotropic materials like wood. International Journal of Fracture, 1996,75(2): 185-214.
[187] Reinhardt HW, Ozbolt Josko, Xu Shilang and Dinku A. Shear of structural concrete members and pure mode Ⅱ testing. Advanced Cement Based Materials, 1997, 5(3-4): 75-85.
[188] Reinhardt HW, Xu Shilang. Experimental determination of K_(Ⅱc) of normal strength concrete.Materials and Structures, 1998, 31(209): 296-302.
[189] Tada H, Paris P and Irwin G. The Stress Analysis of Cracks Handbook (second edition). ParisProductions Incorporated, St. Louis, 1985.
[190] Keer LM. Stress Analysis for Bonded Layers. Journal of Applied Mechanics, 1974, 41(3): 679-683.
[191] Yahsi OS. and Gocmen AE. Contact Problem for Two Perfectly Bonded Dissimilar Infinite Strips.International Journal of Fracture, 1987,34(3): 161-177.
[192] Keer LM. and Guo Q. Stress Analysis for symmetrically loaded bonded layers. International Journalof Fracture, 1990,43(1): 69-81.
[193] Radaj D. and Zhang S. Stress Intensity Factors for Spot Welds between Plates of Unequal Thickness.Engineering Fracture Mechanics, 1991,39(2): 391-413.
[194] Reinhardt Hans W, Xu Shilang. A practical testing approach to determine mode Ⅱ fracture energyfor concrete. International Journal of Fracture, 2000,105(2): 107-125.
[195]姜娟．混凝土Ⅱ型断裂数值模拟： (硕士学位论文)．大连：大连理工大学，2003．
[196]徐世娘，赵艳华．混凝土Ⅱ型断裂与破坏过程的三维非线性有限元数值模拟．水力发电学报， 2004，23(5)：15-21．
[197] Wu EM. Application of Fracture Mechanics to Anisotropy Plates. Journal of Applied Mechanics,1967: 967-974.
[198] Desayi P. Fracture of concrete in compression. Materials and Structure, 1977,10(57): 139-144.
[199] Liu C, Huang Y, Lovato ML and Stout MG. Measurement of the fracture toughness of a fiber-reinforced composite using the Brazilian disk geometry. International Journal of Fracture, 1997, 87:241-263.
[200] Liu C, Huang Y and Stout MG. Enhanced mode-Ⅱ fracture toughness of an epoxy resin due to shearbanding. Acta mater, 1998, 46(16): 5647-5661.
[201] Ayatollahi MR, Aliha MRM. Cracked Brazilian disc specimen subjected to mode Ⅱ deformation.Engineering Fracture Mechanics, 2005,72: 493-503.
[202] Jia Z, Castro-Montero A and Shah SP. Observation of mixed mode fracture with center notched diskspecimens. Cement and Concrete Research, 1996, 26(1): 125-137.
[203] Chen Feng, Cao Ping, Rao Qiuhua, Sun Zongqi. Use of double edge-cracked Brazilian diskgeometry for compression-shear fracture investigation of rock. Journal of Central South Universityof Technology, 2003,10(3): 211-215.
[204] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅰ: studies on specimens of some new geometries. Journal of Structural Engineering(Madras), 1999, 26(1): 11-18.
[205] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅱ: fracture toughness of cement paste, mortar, concrete and no-fines concrete. Journalof Structural Engineering (Madras), 1999,26(1): 19-27.
[206] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅲ: studies on shear strength and slip of cement paste, mortar, concrete and no-finesconcrete. Journal of Structural Engineering (Madras), 1999, 26(2): 91-97.
[207] Desayi Prakash, Raghuprasad B.K. and Bhaskar Desai V. Mode-Ⅱ fracture of cementitiousmaterials-Part Ⅳ: fracture toughness, shear strength and slip of fiber reinforced cement mortar andconcrete. Journal of Structural Engineering (Madras), 2000, 26(4): 267-273.
[208]中华人民共和国国家标准．GB4161-84金属材料平面应变断裂韧度K_(Ⅰc)试验方法．北京：中国 标准出版社，1997．
[209] Hillemeier B, Hilsdorf HK. Fracture Mechanics Studies on Concrete Compounds. Cement andConcrete Research, 1977, 7:523-536.
[210] Brühwiler E and Wittmann FH. The wedge splitting test, a new method of Performing stable fracturemechanics tests. Engineering Fracture Mechanics, 1990, 35(1/2/3): 117-125.
[211]卜丹．楔入式紧凑拉伸断裂试验研究： (硕士学位论文)．大连：大连理工大学，2006．
[212]徐世烺，卜丹，张秀芳．不同尺寸楔入式紧凑拉伸试件双K断裂参数的试验测定．土木工程 学报，2008，41(2)：70-76．
[213]徐世烺，卜丹，张秀芳．楔入式紧凑拉伸法确定混凝土的断裂能．水利学报，2007，38(6)：47-53．
[214]陈篪，蔡其巩，王仁智等．工程断裂力学(上册)．北京：国防工业出版社，1979：139．
[215]徐世烺，吴智敏，丁生根．砼双K断裂参数的实用解析方法．工程力学，2003，20(3)：54-61．
[216]吴智敏，徐世烺，王金来．三点弯曲梁法研究砼双K断裂参数及其尺寸效应．水力发电学报， 2000，19(4)：16-24．
[217] Ozbolt J, Reinhardt HW and Xu Shilang. Numerical studies on the double-edge notched mode Ⅱgeometry. In: Mihashi H and Rokugo K, ed. Fracture Mechanics of Concrete Structures. ProceedingsFRAMCOS-3, Freiburg, Germany: Aedificatio Publishers, 1998: 773-782.
[218] Cedolin L, Bisi G and Narodello P. Sulla determinazione sperimentale dell'energia di fracttura inmodo Ⅱ per il calcestruzzo. Studie e Ricerche. 1997,18.
[219] Cedolin L, Bisi G and Narodello P. On the detection of crack propagation in Reinhardt'sdouble-edge concrete testing specimen for mode Ⅱ. Dipartmento di Ingegneria Strutturale,Politecnico di Milano, 1998.
[220] Prisco M and Ferrara L. On the evaluation of mode Ⅱ fracture energy in high stength concrete. In: deBorst, R. Bicanic, N. Mang and G. Meschke, ed. Computational Modelling of Concrete Structures.Rotterdam: Balkema, 1998: 409-418.
[221]孙雅珍，余天庆．混凝土破坏的断裂和损伤耦合分析．全国第九届岩石、混凝土断裂、损伤和 强度学术会议，贵阳，2005．