三维复合型脆性断裂行为的数值计算与实验研究
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摘要
三维复合型断裂问题由于其复杂性，许多问题迄今仍然没有得到一致的结论，有待进一步研究。本文参考以往的研究成果，运用改进的AFM（all fracture modes）试样对三维复合型脆性断裂这一复杂的问题进行深入的数值计算、实验研究和理论探讨，其理论意义和工程应用价值是十分明显的。
本文介绍了Richard提出的CTS（compact tension shear）、AFM试样及其加载装置的特点，在其基础上设计出了改进的AFM试样及其加载装置，并论述了采用该试样及其夹具进行三维断裂实验的原理。
通过限定单边缺口拉伸（single edge notched tension，简称SENT）试样边界条件将三维断裂问题转化为平面应变问题，利用虚拟裂纹闭合（virtual crack closure，简称VCC）法和等效积分区域（equivalent domain integral，简称EDI）法对SENT试样进行了数值分析，计算了平面应变状态下裂纹前缘的无量纲应力强度因子。并与二维解析解进行比较，发现VCC法计算精确且简便，适合对三维复合型断裂问题进行数值分析。
采用VCC法对三种不同厚度比的AFM试样进行了I型、II型、III型加载模式下的断裂行为数值计算。研究了试样厚度比对试样裂纹前缘无量纲应力强度因子分布的影响。研究表明，II型加载导致裂纹前缘诱发产生局部的III型载荷；III型加载导致裂纹前缘诱发产生II型载荷。且III型加载诱发裂纹前缘产生的II型应力为强耦合效应。为了尽可能减小此种耦合效应，本文选择出了合适的试样厚度。
对选定厚度的AFM试样模型，采用VCC法计算了I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下裂纹前缘的无量纲应力强度因子，并且根据Richard准则计算得到了I型、II型、III型、I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下裂纹前缘的无量纲等效应力强度因子，预测了各种类型载荷下的裂纹启裂点。
选择透光率高的有机玻璃作为试样材料，运用改进的AFM试样及其夹具，进行了I型、II型、III型、I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下的三维断裂试验，观测了各种加载模式下裂纹启裂、不稳定扩展直至断裂破坏的全过程。结果表明，采用VCC法和Richard准则进行数值计算所得启裂点的预测结果，与实验观察到的现象是一致的，验证了数值计算结果的正确。
将不同复合比载荷下实验测得的启裂角和临界载荷与经典的断裂准则——最大周向应力准则（或MTS准则）、最小应变能密度因子准则（S准则）、最大应变能释放率准则（G准则），以及现有的Pook准则和Richard准则进行了分析比较，发现了Richard准则结果与断裂实验结果吻合得最好，说明了Richard准则能很好地表征三维脆性断裂行为。
本文采用改进的AFM试样，进行了各种复合型加载下三维脆性断裂行为的数值分析及实验研究，得到了很好的三维断裂结果，丰富了三维脆性断裂的研究。
Due to the complexity of three dimensional (3D) mixed mode fracture problem, thecorresponding issue is not yet well understood and needs further investigation. Based onprevious relative studies, the3D mixed mode brittle fracture was investigated on modified allfracture modes (AFM) specimen by numerical calculation, experimental study, and theoreticaldiscussion. The corresponding theoretical meaning and engineering application value isdistinct.
The compact tension shear (CTS) specimen and the AFM specimen in combination withtheir special loading devices were introduced. Based on their advantages, the modified AFMspecimen and its special loading device were proposed, and the corresponding principle of3Dfracture experiment was discussed.
By suppressing corresponding boundary conditions (BCs), the plane strain conditionswere enforced on3D-model of the single edge notched tension (SENT) specimen.Non-dimensional stress intensity factors (SIFs) were calculated by virtual crack closure (VCC)method and equivalent domain integral (EDI) method respectively along the crack front. Bycomparing the numerical results with the corresponding2D reference analytical value, theVCC method was found to be so numerically accurate and handy that it can be fitful fornumerically analyzing3D mixed mode fracture problem.
The fracture behavior was computationally investigated by the VCC method on AFMspecimens with three thickness ratios, under mode I, mode II, and mode III loading conditionsrespectively. The influence of thickness ratio was investigated on the distribution ofnon-dimensional SIFs along the crack front. It was obtained that although the specimen isglobally subjected to the mode II loading, the mode III fracture behavior is induced locallyalong the crack front, and vice versa. In particular, it is strong coupling effect that mode IIstresses are induced by mode III loading along the crack front. In order to reduce this couplingeffect as far as possible, the specimen with appropriate thickness was proposed in this paper.
For the AFM model with the given thickness, the non-dimensional SIFs along the crackfront were calculated by the VCC method, under mixed mode I+II, mixed mode I+III, mixedmode II+III, and mixed mode I+II+III loading conditions. Based on the previous non-dimensional SIFs data, a series of non-dimensional equivalent SIFs and initial breakpointsalong the crack front were calculated by employing the Richard criterion, for pure mode I, puremode II, pure mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixedmode I+II+III.
Based on the proposed AFM specimen made of transparent material–PMMA and therelated loading device, a series of3D experimental investigations were performed under modeI, mode II, mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixed modeI+II+III loading conditions. Correspondingly, the complete process was observed from crackinitial break, unstable propagate to final fracture. It was shown that the initial breakpointassessments by the VCC method and the Richard criterion were in agreement withcorresponding experimental findings, and the validity of the computational results wasdemonstrated.
Critical loads and initiation angles, which were gained by different mixed mode loadingexperiment, were compared with three classical criterion––the maximum tangential stresscriterion (or MTS criterion), the strain energy density criterion (S criterion), and themaximum energy release rate criterion (G criterion), and recently developed3D fracturecriteria––Pook criterion and Richard criterion. It was found that the prediction by Richardcriterion agrees well with the results by fracture experiment. Therefore, Richard criterion isapplicable for predicting3D brittle fracture behavior.
In this paper, with the proposed AFM specimen,3D numerical calculations andexperimental investigation were achieved for mode I, mode II, mode III, mixed mode I+II,mixed mode I+III, mixed mode II+III, and mixed mode I+II+III loading conditions. Thepromising3D fracture results can make contribution to3D brittle fracture investigation.
本文介绍了Richard提出的CTS（compact tension shear）、AFM试样及其加载装置的特点，在其基础上设计出了改进的AFM试样及其加载装置，并论述了采用该试样及其夹具进行三维断裂实验的原理。
通过限定单边缺口拉伸（single edge notched tension，简称SENT）试样边界条件将三维断裂问题转化为平面应变问题，利用虚拟裂纹闭合（virtual crack closure，简称VCC）法和等效积分区域（equivalent domain integral，简称EDI）法对SENT试样进行了数值分析，计算了平面应变状态下裂纹前缘的无量纲应力强度因子。并与二维解析解进行比较，发现VCC法计算精确且简便，适合对三维复合型断裂问题进行数值分析。
采用VCC法对三种不同厚度比的AFM试样进行了I型、II型、III型加载模式下的断裂行为数值计算。研究了试样厚度比对试样裂纹前缘无量纲应力强度因子分布的影响。研究表明，II型加载导致裂纹前缘诱发产生局部的III型载荷；III型加载导致裂纹前缘诱发产生II型载荷。且III型加载诱发裂纹前缘产生的II型应力为强耦合效应。为了尽可能减小此种耦合效应，本文选择出了合适的试样厚度。
对选定厚度的AFM试样模型，采用VCC法计算了I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下裂纹前缘的无量纲应力强度因子，并且根据Richard准则计算得到了I型、II型、III型、I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下裂纹前缘的无量纲等效应力强度因子，预测了各种类型载荷下的裂纹启裂点。
选择透光率高的有机玻璃作为试样材料，运用改进的AFM试样及其夹具，进行了I型、II型、III型、I+II复合型、I+III复合型、II+III复合型、I+II+III复合型加载下的三维断裂试验，观测了各种加载模式下裂纹启裂、不稳定扩展直至断裂破坏的全过程。结果表明，采用VCC法和Richard准则进行数值计算所得启裂点的预测结果，与实验观察到的现象是一致的，验证了数值计算结果的正确。
将不同复合比载荷下实验测得的启裂角和临界载荷与经典的断裂准则——最大周向应力准则（或MTS准则）、最小应变能密度因子准则（S准则）、最大应变能释放率准则（G准则），以及现有的Pook准则和Richard准则进行了分析比较，发现了Richard准则结果与断裂实验结果吻合得最好，说明了Richard准则能很好地表征三维脆性断裂行为。
本文采用改进的AFM试样，进行了各种复合型加载下三维脆性断裂行为的数值分析及实验研究，得到了很好的三维断裂结果，丰富了三维脆性断裂的研究。
Due to the complexity of three dimensional (3D) mixed mode fracture problem, thecorresponding issue is not yet well understood and needs further investigation. Based onprevious relative studies, the3D mixed mode brittle fracture was investigated on modified allfracture modes (AFM) specimen by numerical calculation, experimental study, and theoreticaldiscussion. The corresponding theoretical meaning and engineering application value isdistinct.
The compact tension shear (CTS) specimen and the AFM specimen in combination withtheir special loading devices were introduced. Based on their advantages, the modified AFMspecimen and its special loading device were proposed, and the corresponding principle of3Dfracture experiment was discussed.
By suppressing corresponding boundary conditions (BCs), the plane strain conditionswere enforced on3D-model of the single edge notched tension (SENT) specimen.Non-dimensional stress intensity factors (SIFs) were calculated by virtual crack closure (VCC)method and equivalent domain integral (EDI) method respectively along the crack front. Bycomparing the numerical results with the corresponding2D reference analytical value, theVCC method was found to be so numerically accurate and handy that it can be fitful fornumerically analyzing3D mixed mode fracture problem.
The fracture behavior was computationally investigated by the VCC method on AFMspecimens with three thickness ratios, under mode I, mode II, and mode III loading conditionsrespectively. The influence of thickness ratio was investigated on the distribution ofnon-dimensional SIFs along the crack front. It was obtained that although the specimen isglobally subjected to the mode II loading, the mode III fracture behavior is induced locallyalong the crack front, and vice versa. In particular, it is strong coupling effect that mode IIstresses are induced by mode III loading along the crack front. In order to reduce this couplingeffect as far as possible, the specimen with appropriate thickness was proposed in this paper.
For the AFM model with the given thickness, the non-dimensional SIFs along the crackfront were calculated by the VCC method, under mixed mode I+II, mixed mode I+III, mixedmode II+III, and mixed mode I+II+III loading conditions. Based on the previous non-dimensional SIFs data, a series of non-dimensional equivalent SIFs and initial breakpointsalong the crack front were calculated by employing the Richard criterion, for pure mode I, puremode II, pure mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixedmode I+II+III.
Based on the proposed AFM specimen made of transparent material–PMMA and therelated loading device, a series of3D experimental investigations were performed under modeI, mode II, mode III, mixed mode I+II, mixed mode I+III, mixed mode II+III, and mixed modeI+II+III loading conditions. Correspondingly, the complete process was observed from crackinitial break, unstable propagate to final fracture. It was shown that the initial breakpointassessments by the VCC method and the Richard criterion were in agreement withcorresponding experimental findings, and the validity of the computational results wasdemonstrated.
Critical loads and initiation angles, which were gained by different mixed mode loadingexperiment, were compared with three classical criterion––the maximum tangential stresscriterion (or MTS criterion), the strain energy density criterion (S criterion), and themaximum energy release rate criterion (G criterion), and recently developed3D fracturecriteria––Pook criterion and Richard criterion. It was found that the prediction by Richardcriterion agrees well with the results by fracture experiment. Therefore, Richard criterion isapplicable for predicting3D brittle fracture behavior.
In this paper, with the proposed AFM specimen,3D numerical calculations andexperimental investigation were achieved for mode I, mode II, mode III, mixed mode I+II,mixed mode I+III, mixed mode II+III, and mixed mode I+II+III loading conditions. Thepromising3D fracture results can make contribution to3D brittle fracture investigation.
引文
[1]郦正能.应用断裂力学.北京航空航天大学出版社,2012:1-112页
[2]李庆芬.断裂力学及其工程应用.第1版.哈尔滨工程大学,2004:4-105页
[3]龙述尧.弹性力学问题的局部petrov-Galerkin方法.力学学报.2001,33(4):508-517页
[4]王自强,陈少华.高等断裂力学.科学出版社.2009:1-4页
[5] Chen Z. Z., Tokaji K.. Effects of particle size on fatigue crack initiation and smallcrack growth in SiC particulate-reinforced aluminum alloy composites. MaterialsLetters.2004,58:2314-2321P
[6] Pirondi A., Collini L.. Analysis of crack propagation resistance of Al-Al2O3particulate-reinforced composite friction stir welded butt joints. International Journal ofFatigue.2009,31:111-121P
[7]郑健龙,周志刚,张起森.沥青路面抗裂设计理论与方法.北京:人民交通出版社,2000
[8]李灏,陈树坚.断裂理论基础.成都:四川人民出版社,1983:37页
[9]吴望周.化工设备断裂失效分析基础.南京:东南大学出版社,1991:60-61页
[10]董蕙茹,郭万林.三维复合型断裂的试验方法探讨.实验力学.2002,17(4):497-499页
[11] Lazarus V., Buchholz F.-G., Fulland M., Wiebesiek J.. Comparison of predictions bymode II or mode III criteria on crack front twisting in three or four point bendingexperiments. International Journal of Fracture.2008,153(2):141-151P
[12] Vijayakumar K., Atluri S. N.. An embedded elliptical flaw in a infinite solid subject toan arbitrary crack face traction. ASME J. Appl. Mech..1981,49:88-98P
[13]刘勇,陈世健,高鑫,康兴无.基于统一强度理论的断裂准则.现代机械.2009,5:88页
[14] Jun Chang, Jin-quan Xu, Yoshiharu Mutoh. A general mixed-mode brittle fracturecriterion for cracked materials. Engineering Fracture Mechanics.2006,73(9):1249-1263P
[15]张永元.三维裂纹应力强度因子计算综述--Ⅱ、数值计算法.力学进展.1981,1:37-52页
[16]樊鸿,张盛,王启智.复合型三维裂纹应力强度因子计算方法的研究.四川大学学报(工程科学版).2009,41(4):48-52页
[17]郭彦双.脆性材料中三维裂隙断裂试验、理论与数值模拟研究.山东大学博士学位论文.2007:7-72页
[18] Liebowitz H., Sandhu J.S., Lee J. D., Menandro F.C.M.. Computational fracturemechanics: research and application. Engineering Fracture Mechanics.1995,50:653-670P
[19] Tracey D. M.. Finite elements for three-dimensional elastic crack analysis. NuclearEngineering and Design.1974,26:282-290P
[20] Barsoum R. S.. On the use of isoparametric finite elements in linear fracture mechanics.International Journal Numerical Methods in Engineering.1976,10(1)：25-37P
[21] Rajus I. S., Newman Jr. J. C.. Stress-intensity factor for a wide range of semi-ellipticalsurface cracks in finite-thickness plates. Engineering Fracture Mechanics.1979,11:817-829P
[22]栾茂田, Ugai Keizo.岩土工程研究中若干基本力学问题的思考.大连理工大学学报.1999,39(2):309-317P
[23]王泳嘉.边界元法有岩石力学中的应用.岩石力学与工程学报.1986,5(2):205-222P
[24] Aliabadi M. H.. Boundary element formulations in fracture mechanics: a review.Computer Aided Assessment and Control of Localized Damage-Proceedings of theInternational Conference, Localized Damage IV.1996:3-19P
[25] Portela A. The dual BEM: effective implementation for crack problem. Int J forNumerical Methods in engineering.1992,33:269-287P
[26]顾克秋,钱林方,袁人枢.基于边界元法的疲劳裂纹扩展模拟.南京理工大学学报.1995,19(6):517-520P
[27]寇晓东.无单元法及其在岩土工程中的应用.岩土工程学报,1998,20(1):6-9P
[28] Xu Y., Saigal. S.. Element free galerkin study of steady quasi-static crack growth inplane strain tension in elastic-plastic materials. Computational Mechanics.1998,22:255-265P
[29] Tabbara M. R., Stone C. M.. A computational method for quasi-static fracture.Computational Mechanics.1998,22:203-210P
[30]应隆安.无限元方法.北京:北京大学出版社,1992
[31] Xu Y.; Yuan H.. Computational analysis of mixed-mode fatigue crack growth inquasi-brittle materials using extended finite element methods, Engng. Fract. Mech..2009,76(2):165-181P
[32] Shi G. H.. Numerical manifold method. Li J. C., Wang C-Y, Sheng J.. Proceedings ofFirst International Conference on Analysis of Discontinuous Deformation (ICADD-1),Taiwan,1995:187-222P
[33] Shi G. H.. Manifold method. Proceedings of the First International Forum on DDA andSimulation of Discontinuous Media. Berkeley.1996:52-204P
[34] Alriabadi M. H.. A new generation of boundary element formulations for crackproblems in fracture mechanics. Int. J. Fracture.1997,86(l):91-125P
[35] Nishioka, Toshihisa. State of the art in computational dynamic fracture mechanic.JSME International Journal, Series A.1994,37(4):313-333P
[36] Hagedorn, Karl Edgar. Some aspects of fracture mechanics researeh during the last25years. Steel Research.1998,69:206-213P
[37]王铎,杜善义,袁祖培等.断裂力学.哈尔滨工业大学出版社.1989:1-48页
[38]何正嘉,陈雪峰,李兵等.小波有限元理论及其工程应用.北京:科学出版社.2006:78-96页
[39]李明宝.基于有限元理论的木材机械性能建模与仿真研究.东北林业大学博士学位论文.2007:15页
[40]李慧芳.裂纹扩展机理研究及管板开裂的数值模拟.北京化工大学博士学位论文.2009:6-44页
[41]沈成康.断裂力学.上海:同济大学出版社,1996:80-95页
[42]程靳,赵树山.断裂力学.北京:科学出版社,2006:42-59页
[43]孙宗颀,饶秋华,王桂尧.剪切断裂韧度(KIIC)确定的研究.岩石力学与工程学报.2002,21(2):199-203P
[44]张对红,刘错,张静.裂纹尖端附近区域的应力应变场分析.油气储运.2002,20(9):13-19页
[45]陈梦成,宋功河.复合型裂纹应力与应力强度因子分析的位移间断法.华东交通大学学报.1997,14(l):43-47页
[46] Parks D. M.. A stiff ness derivative finite element technique for determination of cracktip stress intensity factors. International Journal of Fracture.1974,10:487P
[47] Hellen T. K.. On the method of virtual crack extensions. International Journal ForNumerical Methods In Engineering.1975,9:187P
[48]黄志鹏,朱可善,郭映忠.岩石裂纹小范围屈服时声发射总数与应力强度因子关系的研究.重庆建筑大学学报.1995,20(2):41-46页
[49]马开平,柳春图.计算平面I、II型复合应力强度因子的半权函数法.机械强度.2003,25(5):576-579页
[50] Richard H. A.. Specimens for investigating biaxial fracture and fatigue processes.Biaxial and Multiaxial Fatigue.1989:217-229P
[51]王自强.高等断裂力学.第1版.科学出版社，2009:105-107页
[52] Richard H. A.. A new compact shear specimen. International Journal of Fracture.1981,17(5):105-107P
[53] Erdogan F., Sih G. C.. On the crack extention in plates under loading and transverseshear trans. A. S. M. E. Journal of Basic Engineering.1963,85(4):519-527P
[54] Sih G. C.. Strain energy density faetor applied to mixed mode crack problems.International Journal of Fracture.1974,10(3):305-321P
[55] Yoda M.. The J-integral fracture criterion under opening and tearing modes andunloading effects. Engineering Fracture Mechanics.1979,13:647-656P
[56] Pook L. P. Comments on fatigue crack growth under mixed modes I and III and puremode III loading. K. J. Miller, M. W. Brown. In Multiaxial Fatigue, Philadelphia,1985.Philadelphia: ASTM STP853,1985:249-263P
[57] Suresh S., Tschegg E. K.. Combined mode I-mode III fracture fatigue-precrackedAlumina. Journal of the American Ceramic Society.1987,70:726-733P
[58] Tschegg E. K., Stanzl S. E., Mayer H. R., Czegley M.. Crack face interactions andnear-threshold fatigue crack growth. Fatigue and Fracture of Engineering Materials andStructures.1992,16:71-83P
[59] Davenport J. C. W., Smith D. J.. A study of superimposed fracture modes I, II and IIIon PMMA. Fatigue and Fracture of Engineering Materials and Structures.1993,16:1125-1133P
[60] Xu D., Reinhardt H. W.. Softening of concrete under torsional loading. S. Shah, S. E.Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments, London,1989. London: Elsevier Applied Science,1989:39-50P
[61] Yacoub-Tokatly Z., Barr B.. Mode III fracture--a tentative test geometry. S. Shah, S. E.Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments, London,1989. London: Elsevier Applied Science,1989:596-604P
[62] Keuser W., Walraven J.. Fracture of plain concrete under mixed mode conditions. S.Shah, S. E. Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments.London,1989. London: Elsevier Applied Science,1989:625-634P
[63] Luong M. P.. Fracture behaviour of concrete and rock under mode II and mode IIIshear loading. S. Shah, S. E. Swartz, B. Barr. In Fracture of Concrete and Rock: RecentDevelopments. London,1989. London: Elsevier Applied Science,1989:18-26P
[64] Sarkar S.. The behaviour and failure of plain concrete under the action of combinedcompression and torsion. S. Shah, S. E. Swartz, B. Barr. In Fracture of Concrete andRock: Recent Developments. London,1989. London: Elsevier Applied Science,1989:475-493P
[65] Pook L. P.. A finite element analysis of the angle crack specimen. H. P. Rossmanith andK. J. Miller MEP. In Mixed Mode Fatigue and Fracture, London,1993. London: ESIS,1993:285-302P
[66] Kamat S. V., Srinivas M., Rama R. P.. Mixed mode I/III fracture toughness of armcoiron. Acta Materialia.1998,46:4985-4992P
[67] Ueda Y., Ikeda K., Yao T., Aoki M.. Characteristics of brittle fracture under generalcombined modes including those under bi-axial tensile loads. Engineering FractureMechanics.1983,18:1131-1158P
[68] Farshad M., Flueler P.. Investigation of mode III fracture toughness using ananti-clastic plate bending method. Engineering Fracture Mechanics.1998,60:597-603P
[69] Pook, L. P.. The fatigue crack direction and threshold behaviour of mild steel undermixed mode I and III loading. International Journal of Fatigue.1985,7:21-30P
[70] Tohgo K., Otsuka A., Yoshida M.. Fatigue behaviour of a surface crack under mixedmode loading. H. Kitagawa, T. Tanaka. In Fatigue’90Proceedings of the FourthInternational Conference on Fatigue and Fatigue Thresholds, U.K.:1990. U.K.:Materials and Component Engineering Publications.1990,1:567-572P
[71] Ueda Y., Ikeda K., Yao T., Aoki M.. Characteristics of brittle fracture under generalcombined modes including those under bi-axial tensile loads. Engineering FractureMechanics.1983,18:1131-1158P
[72] Yoda M. The J-integral fracture criterion under opening and tearing modes andunloading effects. Engineering Fracture Mechanics.1979,13:647-656P
[73] Rosenfield A. R., Duckworth W. H.. Combined tension/transverse-shear fracture ofglass. International Journal of Fracture.1987,32:59-62P
[74] Keuser W., Walraven J.. Fracture of plain concrete under mixed mode conditions. S.Shah, S. E. Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments,London: Elsevier Applied Science,1989:625-634P
[75] Suresh S., Tschegg E. K.. Combined mode I-mode III fracture of fatigue-precrackedalumina. Journal of the American Ceramic Society.1987,70:726-733P
[76] Kumar A. M., Hirth J. P., Hoagland R., Feng X.. A suggested test procedure to measuremixed mode I-III fracture toughness of brittle materials. Journal of Testing andEvaluation, JTEVA.1994,22:327-334P
[77]陈增涛,王铎.复合型裂纹的混合开裂准则.哈尔滨工业大学学报.1994,26(4):127-131页
[78]杨新辉,栾茂田,杨庆.基于简化裂尖断裂模型的脆性断裂机理及复合型断裂判据.大连理工大学学报,2005,45(5):712-716页
[79]蒋玉川,王启智.形状改变比能密度因子断裂准则.工程力学.2005,22(5):31-35页
[80]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页
[81]龚俊,朗福元,王珉.基于统一强度理论的复合型裂纹断裂准则.机械强度.2003，25(3):347-351页
[82]赵艳华,徐世娘. I-II复合型裂纹脆性断裂的最小J2准则.工程力学.2002,19(4):94-98页
[83]汤安民,师俊平.复杂应力状态断裂判据的讨论.西安理工大学学报.2000,16(l):47-73页
[84]许斌,江见鲸.混凝土I-II复合型断裂判据研究.工程力学.1995,12(2):13-21页
[85] Jun Chang, Jin-quan Xu, Yoshiharu Mutoh.. A general mixed-mode brittle fracturecriterion for cracked materials. Engineering Fracture Mechanics.2006,73:1249-1263P
[86] Ayatollahi M. R., Aliha M. R. M.. Cracked Brazilian disc specimen subjected to modeII deformation. Engineering Fracture Mechanics.2005,72:493-503P
[87] Murrell S A F. The theory of the propagation of elliptical cracks under variousconditions of plane strain or plane stress, Part I. British Journal of Applied Physics.1964,15:1195-1220P
[88] Rao Q H, Sun Z Q, Stephansson O.. Shear fracture (mode II) of brittle rock.International Journal of Rock Mechanics and Mining Science.2003,40(3):355-375P
[89] Shen B, Stephansson O.. Modification of the G criterion for crack propogationsubjected to compression. Engineering Fracture Mechanics,1994,47(2):177-189P
[90] Sun Zongqi. Is crack branching under shear loading caused by shear fracture?—Acritical review on maximum circumferential stress theory. Transactions of NonferrousMetals Society of China.2001,11(2):287-292P
[91]栾茂田,杨新辉,杨庆.考虑三向应力效应复合型最大Mises应力断裂判据.岩土力学.2006,27(6):1647-1652页
[92] Irwin G. R.. Analysis of stresses and strains near the end of a crack traversing a plate.Journal of Applied Mechanics.1957,24:361-364P
[93] Palnaiswmay K., Kauss W. G.. On the problem of crack extension in britte solids undergeneral lodaing. Report SM74-8, Graduate Aeronautical Laboratories, CaliforniaInstitute of Technology, Pasadena,1974
[94] Palnaiswmay K., Kauss W. G.. Propagation of a crack under general in plane tension.International Journal of Fracture Mechanics.1972,8:114-117P
[95] Nuismer R.J.. An energy release rate criterion for mixed mode fracture. Int. Jour.. Fract.Mech.1975,11(2):245-250P
[96] Sih G. C., Barthelemy B. M.. Mixed mode fatigue crack growth predictions.Engineering Fracture Mechanics.1980,13:439-451P
[97]田常海,任明法,陈浩然.复合型裂纹脆断主应变因子准则.大连理工大学学报.2003,41(3):139页
[98] Amestoy M., Bui H. D., Dang-Van K.. Analytic asymptotic solution of the kinkedcrack problem. Advances in Fracture Research.1981:107-113P
[99] Hussain M. A., Pu S. I., Underwood J. H.. Strain energy release rate for a crack undercombined mode I and mode II. In Fracture Analysis, ASTM STP560. AmericanSociety for Testing and Materials, Philadelphia.1974:2-28P
[100]杨新辉.脆性/韧性断裂机理与判据及裂尖变形理论研究.大连理工大学博士学位论文.2005:2页
[101] Pook L. P.. Thin sheet and micromechanism problems. Fracture and Fatige:Elasto-plasticity.1980:143-153P
[102] Pook L. P.. American society for testing and materials. Multiaxial Fatigues, ASTM853.1985:249-263P
[103] Pook L. P.. On the fatigue crack paths. Int. J. Fatigue.1995,17(1):5-13P
[104] Richard H. A., Buchholz F.-G, Kullmer G., Schoullmann M..2D-and3D-mixed modefracture criteria. Key Engng Mater.2003:257P
[105] Richard H. A., Fulland M., Buchholz F.-G, Schoullmann M..3D fracture criteria forStructures with Cracks. Steel Reasearch.2003,74:491-497P
[106] Sander M., Richard H. A.. Experimental and numerical investigations on the influenceof the loading direction on the fatigue crack growth. International Journal of Fatigue.2006,28(5-6):583-591P
[107] Rikard R., Buchholz F. G., Wang H., et al.. Investigation of mixed mode I/IIinterlaminar fracture toughness of laminated composites by using a CTS type specimen.Engineering Fracture Mechanics.1998,61:325-342P
[108] Rikards R.. Interlaminar fracture behavior of laminated composites. Coumputers&Structures.2000,76:11-18P
[109] Richard H. A., Kuna M.. Theoretical and experimental study of superimposed fractureMode I, II, III. Engineering Fracture Mechanics.1990,35(6):949-960P
[110] Wu Hengyi, Ma Gang, Xia Yuanming. Experimental study of tensile properties ofPMMA at intermediate strain rate. Materials Letters.2004,58(29):3681-3685P
[111]中华人民共和国国家标准.金属材料室温拉伸试验方法. GB/T228-2002
[112]中华人民共和国国家标准.金属材料弹性模量和泊松比试验方法. GB/T22315-2008
[113]邹广平.材料力学实验基础.第1版.哈尔滨工程大学出版社,2010:13-176页
[114]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用.第1版.科学出版社,2009:1-35页
[115] Irwin G. R.. One set of fast crack propagation in high strength steel and aluminumalloys. Sagamore Researsh Conference Proceedings.1956,2:289-305P
[116] Irwin G. R.. Crack-extension force for a part-through crack in a plate. J Appl Mech.1962,29:651-654P
[117] Rybicki E. F., Kanninen M. F.. A finite element calculation of stress intensity factors bya modified crack closure integral. Engineeing Fracture Mechanics.1977,9(4):931-938P
[118] Raju I. S.. Calculation of strain-energy release rates with high-order and singularfinite-elements. Engineering Fracture Mechanics.1987,28:251-274P
[119]张允涛,黄其青,殷之平.虚拟裂纹闭合法在MSC.Patran中的二次开发.航空计算技术.2009,39(2):41-45页
[120] Fawaz S. A.. Application of the virtual crack closure technique to calculate stressintersity factors for through cracks with an elliptical crack front. Engineering FractureMechanics.1998,3:327-342P
[121] Rice J. R.. A path independent integral and the approximate analysis o strainconcentration by notches and cracks. Journal of Appled Mechanics.1968,35:379-386P
[122]赵建生.断裂力学及断裂物理.第1版.华中科技大学出版社,2003:161-162,197-198页
[123] Moura B., Shih C. F.. A treatment of crack tip contour integrals. International Journalof Fracture.1987,35:295-310P
[124] Shivakumar K. N., Raju I. S.. An equivalent domain integral method forthree-dimensional mixed-mode fracture problem. Engineering Fracture Mechanics.1992,42:935-959P
[125] Murakami Y.. Stress intensity factors handbook. Vol.1. Pergamon Press, Oxford,1978:94-96P
[126]中华人民共和国国家标准.金属材料平面应变断裂韧度KIC试验方法. GB/T4161-2007
[127]王新敏,李义强,许宏伟. ANSYS结构分析单元与应用.第1版.人民交通出版社，2011:237-239页
[128] Cao J. J., Yang G. J., Parker J. A, et al. Crack modeling in FE analysis of circulartubular joints. Engineering Fracture Mechanics.1998,61(5-6):537-553P
[129]曾攀,雷丽萍,方刚.结构的建模与分析.第1版.机械工业出版社,2011:300-303页
[130] Benthem J. P.. States of stress at the vertex of a quarter-infinite crack in a half-space.International Journal Solids and Structures.1977,13(5):479-492P
[131] Bazant Z. P., Estenssoro L. F.. Surface singularity and crack propagation. InternationalJournal Solids and Structures.1979,15:405-426P
[132] Pook L. P.. A finite element analysis of the angle crack specimen. Mixed mode fatigueand fracture.1993:285-302P
[133] Buchholz F.-G., Chergui A., Richard H. A.. Fracture analyses and experimentalresults of crack growth under general mixed mode loading conditions. EngineeringFracture Mechanics.2004,71:455-468P
[134] Zhu Li, Li Qing-fen, Buchholz F.-G.. Computational fracture analysis of anAFM-Specimen under mixed mode loading conditions. Journal of Marine Science andApplication.2011,10(1):105-112P
[135] Li Qing-fen, Zhu Li, Zhu Shi-fan, Buchholz F.-G.. Fracture behavior inAFM-Specimen with single crack under different loading conditions. StructuralDurability and Health Monitoring.2010,6(3-4):273-288P
[136] Buchholz. F.-G., Chergui A., Richard H. A.. Fracture analyses and experimental resultsof crack growth under general mixed mode loading conditions. Engineering FracutreMechanics.2004,71:455-468P
[137]余启明,何晓鸣,刘泽宇,夏磊,姜曼,李尚松. Q370qE高强度钢板试件的疲劳裂纹预制试验研究.第十三届中国科协年会第19分会场-公路在综合交通运输体系中的地位和作用研讨会论文集,中国天津,2011
[138] Ayatollahi M. R., Aliha M. R. M., Hasani M. M. Mixed mode brittle fracture in PMMA--an experimental study using SCB specimens. Materials Science and Engineering A.2006,417(1-2):348-356P
[139] Bhattacharjee D., Knott J. F. Effect of mixed mode I and II loading on the fracturesurface of polymethyl methacrylate (PMMA). Int J Fracture.1995,72:359-381P.
[140] Smith D. J., Ayatollahi M. R., Pavier M. J.. On the consequences of T-stress in elasticbrittle fracture. Proc Roy Soc A.2006,462:2415-2437P
[141] Tada H., Paris P. C., Irwin G. R.. The stress analysis of creak handbook. Del. ReseacrhCopr. Hellertown Pa,1973
[142] Sih G. C.. Handbook of stress intensity factor of researchers and engineers. LehighUniv. Bethehem Pa,1973
[143] Rooks D. P., Cartwright D. J.. Compendium of stress intensity factors. London,HerMajesty’s Stationary Office,1976
[144]中国航空院研究院报编.应力强度因子手册.科学出版社,1981
[2]李庆芬.断裂力学及其工程应用.第1版.哈尔滨工程大学,2004:4-105页
[3]龙述尧.弹性力学问题的局部petrov-Galerkin方法.力学学报.2001,33(4):508-517页
[4]王自强,陈少华.高等断裂力学.科学出版社.2009:1-4页
[5] Chen Z. Z., Tokaji K.. Effects of particle size on fatigue crack initiation and smallcrack growth in SiC particulate-reinforced aluminum alloy composites. MaterialsLetters.2004,58:2314-2321P
[6] Pirondi A., Collini L.. Analysis of crack propagation resistance of Al-Al2O3particulate-reinforced composite friction stir welded butt joints. International Journal ofFatigue.2009,31:111-121P
[7]郑健龙,周志刚,张起森.沥青路面抗裂设计理论与方法.北京:人民交通出版社,2000
[8]李灏,陈树坚.断裂理论基础.成都:四川人民出版社,1983:37页
[9]吴望周.化工设备断裂失效分析基础.南京:东南大学出版社,1991:60-61页
[10]董蕙茹,郭万林.三维复合型断裂的试验方法探讨.实验力学.2002,17(4):497-499页
[11] Lazarus V., Buchholz F.-G., Fulland M., Wiebesiek J.. Comparison of predictions bymode II or mode III criteria on crack front twisting in three or four point bendingexperiments. International Journal of Fracture.2008,153(2):141-151P
[12] Vijayakumar K., Atluri S. N.. An embedded elliptical flaw in a infinite solid subject toan arbitrary crack face traction. ASME J. Appl. Mech..1981,49:88-98P
[13]刘勇,陈世健,高鑫,康兴无.基于统一强度理论的断裂准则.现代机械.2009,5:88页
[14] Jun Chang, Jin-quan Xu, Yoshiharu Mutoh. A general mixed-mode brittle fracturecriterion for cracked materials. Engineering Fracture Mechanics.2006,73(9):1249-1263P
[15]张永元.三维裂纹应力强度因子计算综述--Ⅱ、数值计算法.力学进展.1981,1:37-52页
[16]樊鸿,张盛,王启智.复合型三维裂纹应力强度因子计算方法的研究.四川大学学报(工程科学版).2009,41(4):48-52页
[17]郭彦双.脆性材料中三维裂隙断裂试验、理论与数值模拟研究.山东大学博士学位论文.2007:7-72页
[18] Liebowitz H., Sandhu J.S., Lee J. D., Menandro F.C.M.. Computational fracturemechanics: research and application. Engineering Fracture Mechanics.1995,50:653-670P
[19] Tracey D. M.. Finite elements for three-dimensional elastic crack analysis. NuclearEngineering and Design.1974,26:282-290P
[20] Barsoum R. S.. On the use of isoparametric finite elements in linear fracture mechanics.International Journal Numerical Methods in Engineering.1976,10(1)：25-37P
[21] Rajus I. S., Newman Jr. J. C.. Stress-intensity factor for a wide range of semi-ellipticalsurface cracks in finite-thickness plates. Engineering Fracture Mechanics.1979,11:817-829P
[22]栾茂田, Ugai Keizo.岩土工程研究中若干基本力学问题的思考.大连理工大学学报.1999,39(2):309-317P
[23]王泳嘉.边界元法有岩石力学中的应用.岩石力学与工程学报.1986,5(2):205-222P
[24] Aliabadi M. H.. Boundary element formulations in fracture mechanics: a review.Computer Aided Assessment and Control of Localized Damage-Proceedings of theInternational Conference, Localized Damage IV.1996:3-19P
[25] Portela A. The dual BEM: effective implementation for crack problem. Int J forNumerical Methods in engineering.1992,33:269-287P
[26]顾克秋,钱林方,袁人枢.基于边界元法的疲劳裂纹扩展模拟.南京理工大学学报.1995,19(6):517-520P
[27]寇晓东.无单元法及其在岩土工程中的应用.岩土工程学报,1998,20(1):6-9P
[28] Xu Y., Saigal. S.. Element free galerkin study of steady quasi-static crack growth inplane strain tension in elastic-plastic materials. Computational Mechanics.1998,22:255-265P
[29] Tabbara M. R., Stone C. M.. A computational method for quasi-static fracture.Computational Mechanics.1998,22:203-210P
[30]应隆安.无限元方法.北京:北京大学出版社,1992
[31] Xu Y.; Yuan H.. Computational analysis of mixed-mode fatigue crack growth inquasi-brittle materials using extended finite element methods, Engng. Fract. Mech..2009,76(2):165-181P
[32] Shi G. H.. Numerical manifold method. Li J. C., Wang C-Y, Sheng J.. Proceedings ofFirst International Conference on Analysis of Discontinuous Deformation (ICADD-1),Taiwan,1995:187-222P
[33] Shi G. H.. Manifold method. Proceedings of the First International Forum on DDA andSimulation of Discontinuous Media. Berkeley.1996:52-204P
[34] Alriabadi M. H.. A new generation of boundary element formulations for crackproblems in fracture mechanics. Int. J. Fracture.1997,86(l):91-125P
[35] Nishioka, Toshihisa. State of the art in computational dynamic fracture mechanic.JSME International Journal, Series A.1994,37(4):313-333P
[36] Hagedorn, Karl Edgar. Some aspects of fracture mechanics researeh during the last25years. Steel Research.1998,69:206-213P
[37]王铎,杜善义,袁祖培等.断裂力学.哈尔滨工业大学出版社.1989:1-48页
[38]何正嘉,陈雪峰,李兵等.小波有限元理论及其工程应用.北京:科学出版社.2006:78-96页
[39]李明宝.基于有限元理论的木材机械性能建模与仿真研究.东北林业大学博士学位论文.2007:15页
[40]李慧芳.裂纹扩展机理研究及管板开裂的数值模拟.北京化工大学博士学位论文.2009:6-44页
[41]沈成康.断裂力学.上海:同济大学出版社,1996:80-95页
[42]程靳,赵树山.断裂力学.北京:科学出版社,2006:42-59页
[43]孙宗颀,饶秋华,王桂尧.剪切断裂韧度(KIIC)确定的研究.岩石力学与工程学报.2002,21(2):199-203P
[44]张对红,刘错,张静.裂纹尖端附近区域的应力应变场分析.油气储运.2002,20(9):13-19页
[45]陈梦成,宋功河.复合型裂纹应力与应力强度因子分析的位移间断法.华东交通大学学报.1997,14(l):43-47页
[46] Parks D. M.. A stiff ness derivative finite element technique for determination of cracktip stress intensity factors. International Journal of Fracture.1974,10:487P
[47] Hellen T. K.. On the method of virtual crack extensions. International Journal ForNumerical Methods In Engineering.1975,9:187P
[48]黄志鹏,朱可善,郭映忠.岩石裂纹小范围屈服时声发射总数与应力强度因子关系的研究.重庆建筑大学学报.1995,20(2):41-46页
[49]马开平,柳春图.计算平面I、II型复合应力强度因子的半权函数法.机械强度.2003,25(5):576-579页
[50] Richard H. A.. Specimens for investigating biaxial fracture and fatigue processes.Biaxial and Multiaxial Fatigue.1989:217-229P
[51]王自强.高等断裂力学.第1版.科学出版社，2009:105-107页
[52] Richard H. A.. A new compact shear specimen. International Journal of Fracture.1981,17(5):105-107P
[53] Erdogan F., Sih G. C.. On the crack extention in plates under loading and transverseshear trans. A. S. M. E. Journal of Basic Engineering.1963,85(4):519-527P
[54] Sih G. C.. Strain energy density faetor applied to mixed mode crack problems.International Journal of Fracture.1974,10(3):305-321P
[55] Yoda M.. The J-integral fracture criterion under opening and tearing modes andunloading effects. Engineering Fracture Mechanics.1979,13:647-656P
[56] Pook L. P. Comments on fatigue crack growth under mixed modes I and III and puremode III loading. K. J. Miller, M. W. Brown. In Multiaxial Fatigue, Philadelphia,1985.Philadelphia: ASTM STP853,1985:249-263P
[57] Suresh S., Tschegg E. K.. Combined mode I-mode III fracture fatigue-precrackedAlumina. Journal of the American Ceramic Society.1987,70:726-733P
[58] Tschegg E. K., Stanzl S. E., Mayer H. R., Czegley M.. Crack face interactions andnear-threshold fatigue crack growth. Fatigue and Fracture of Engineering Materials andStructures.1992,16:71-83P
[59] Davenport J. C. W., Smith D. J.. A study of superimposed fracture modes I, II and IIIon PMMA. Fatigue and Fracture of Engineering Materials and Structures.1993,16:1125-1133P
[60] Xu D., Reinhardt H. W.. Softening of concrete under torsional loading. S. Shah, S. E.Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments, London,1989. London: Elsevier Applied Science,1989:39-50P
[61] Yacoub-Tokatly Z., Barr B.. Mode III fracture--a tentative test geometry. S. Shah, S. E.Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments, London,1989. London: Elsevier Applied Science,1989:596-604P
[62] Keuser W., Walraven J.. Fracture of plain concrete under mixed mode conditions. S.Shah, S. E. Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments.London,1989. London: Elsevier Applied Science,1989:625-634P
[63] Luong M. P.. Fracture behaviour of concrete and rock under mode II and mode IIIshear loading. S. Shah, S. E. Swartz, B. Barr. In Fracture of Concrete and Rock: RecentDevelopments. London,1989. London: Elsevier Applied Science,1989:18-26P
[64] Sarkar S.. The behaviour and failure of plain concrete under the action of combinedcompression and torsion. S. Shah, S. E. Swartz, B. Barr. In Fracture of Concrete andRock: Recent Developments. London,1989. London: Elsevier Applied Science,1989:475-493P
[65] Pook L. P.. A finite element analysis of the angle crack specimen. H. P. Rossmanith andK. J. Miller MEP. In Mixed Mode Fatigue and Fracture, London,1993. London: ESIS,1993:285-302P
[66] Kamat S. V., Srinivas M., Rama R. P.. Mixed mode I/III fracture toughness of armcoiron. Acta Materialia.1998,46:4985-4992P
[67] Ueda Y., Ikeda K., Yao T., Aoki M.. Characteristics of brittle fracture under generalcombined modes including those under bi-axial tensile loads. Engineering FractureMechanics.1983,18:1131-1158P
[68] Farshad M., Flueler P.. Investigation of mode III fracture toughness using ananti-clastic plate bending method. Engineering Fracture Mechanics.1998,60:597-603P
[69] Pook, L. P.. The fatigue crack direction and threshold behaviour of mild steel undermixed mode I and III loading. International Journal of Fatigue.1985,7:21-30P
[70] Tohgo K., Otsuka A., Yoshida M.. Fatigue behaviour of a surface crack under mixedmode loading. H. Kitagawa, T. Tanaka. In Fatigue’90Proceedings of the FourthInternational Conference on Fatigue and Fatigue Thresholds, U.K.:1990. U.K.:Materials and Component Engineering Publications.1990,1:567-572P
[71] Ueda Y., Ikeda K., Yao T., Aoki M.. Characteristics of brittle fracture under generalcombined modes including those under bi-axial tensile loads. Engineering FractureMechanics.1983,18:1131-1158P
[72] Yoda M. The J-integral fracture criterion under opening and tearing modes andunloading effects. Engineering Fracture Mechanics.1979,13:647-656P
[73] Rosenfield A. R., Duckworth W. H.. Combined tension/transverse-shear fracture ofglass. International Journal of Fracture.1987,32:59-62P
[74] Keuser W., Walraven J.. Fracture of plain concrete under mixed mode conditions. S.Shah, S. E. Swartz, B. Barr. In Fracture of Concrete and Rock: Recent Developments,London: Elsevier Applied Science,1989:625-634P
[75] Suresh S., Tschegg E. K.. Combined mode I-mode III fracture of fatigue-precrackedalumina. Journal of the American Ceramic Society.1987,70:726-733P
[76] Kumar A. M., Hirth J. P., Hoagland R., Feng X.. A suggested test procedure to measuremixed mode I-III fracture toughness of brittle materials. Journal of Testing andEvaluation, JTEVA.1994,22:327-334P
[77]陈增涛,王铎.复合型裂纹的混合开裂准则.哈尔滨工业大学学报.1994,26(4):127-131页
[78]杨新辉,栾茂田,杨庆.基于简化裂尖断裂模型的脆性断裂机理及复合型断裂判据.大连理工大学学报,2005,45(5):712-716页
[79]蒋玉川,王启智.形状改变比能密度因子断裂准则.工程力学.2005,22(5):31-35页
[80]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页
[81]龚俊,朗福元,王珉.基于统一强度理论的复合型裂纹断裂准则.机械强度.2003，25(3):347-351页
[82]赵艳华,徐世娘. I-II复合型裂纹脆性断裂的最小J2准则.工程力学.2002,19(4):94-98页
[83]汤安民,师俊平.复杂应力状态断裂判据的讨论.西安理工大学学报.2000,16(l):47-73页
[84]许斌,江见鲸.混凝土I-II复合型断裂判据研究.工程力学.1995,12(2):13-21页
[85] Jun Chang, Jin-quan Xu, Yoshiharu Mutoh.. A general mixed-mode brittle fracturecriterion for cracked materials. Engineering Fracture Mechanics.2006,73:1249-1263P
[86] Ayatollahi M. R., Aliha M. R. M.. Cracked Brazilian disc specimen subjected to modeII deformation. Engineering Fracture Mechanics.2005,72:493-503P
[87] Murrell S A F. The theory of the propagation of elliptical cracks under variousconditions of plane strain or plane stress, Part I. British Journal of Applied Physics.1964,15:1195-1220P
[88] Rao Q H, Sun Z Q, Stephansson O.. Shear fracture (mode II) of brittle rock.International Journal of Rock Mechanics and Mining Science.2003,40(3):355-375P
[89] Shen B, Stephansson O.. Modification of the G criterion for crack propogationsubjected to compression. Engineering Fracture Mechanics,1994,47(2):177-189P
[90] Sun Zongqi. Is crack branching under shear loading caused by shear fracture?—Acritical review on maximum circumferential stress theory. Transactions of NonferrousMetals Society of China.2001,11(2):287-292P
[91]栾茂田,杨新辉,杨庆.考虑三向应力效应复合型最大Mises应力断裂判据.岩土力学.2006,27(6):1647-1652页
[92] Irwin G. R.. Analysis of stresses and strains near the end of a crack traversing a plate.Journal of Applied Mechanics.1957,24:361-364P
[93] Palnaiswmay K., Kauss W. G.. On the problem of crack extension in britte solids undergeneral lodaing. Report SM74-8, Graduate Aeronautical Laboratories, CaliforniaInstitute of Technology, Pasadena,1974
[94] Palnaiswmay K., Kauss W. G.. Propagation of a crack under general in plane tension.International Journal of Fracture Mechanics.1972,8:114-117P
[95] Nuismer R.J.. An energy release rate criterion for mixed mode fracture. Int. Jour.. Fract.Mech.1975,11(2):245-250P
[96] Sih G. C., Barthelemy B. M.. Mixed mode fatigue crack growth predictions.Engineering Fracture Mechanics.1980,13:439-451P
[97]田常海,任明法,陈浩然.复合型裂纹脆断主应变因子准则.大连理工大学学报.2003,41(3):139页
[98] Amestoy M., Bui H. D., Dang-Van K.. Analytic asymptotic solution of the kinkedcrack problem. Advances in Fracture Research.1981:107-113P
[99] Hussain M. A., Pu S. I., Underwood J. H.. Strain energy release rate for a crack undercombined mode I and mode II. In Fracture Analysis, ASTM STP560. AmericanSociety for Testing and Materials, Philadelphia.1974:2-28P
[100]杨新辉.脆性/韧性断裂机理与判据及裂尖变形理论研究.大连理工大学博士学位论文.2005:2页
[101] Pook L. P.. Thin sheet and micromechanism problems. Fracture and Fatige:Elasto-plasticity.1980:143-153P
[102] Pook L. P.. American society for testing and materials. Multiaxial Fatigues, ASTM853.1985:249-263P
[103] Pook L. P.. On the fatigue crack paths. Int. J. Fatigue.1995,17(1):5-13P
[104] Richard H. A., Buchholz F.-G, Kullmer G., Schoullmann M..2D-and3D-mixed modefracture criteria. Key Engng Mater.2003:257P
[105] Richard H. A., Fulland M., Buchholz F.-G, Schoullmann M..3D fracture criteria forStructures with Cracks. Steel Reasearch.2003,74:491-497P
[106] Sander M., Richard H. A.. Experimental and numerical investigations on the influenceof the loading direction on the fatigue crack growth. International Journal of Fatigue.2006,28(5-6):583-591P
[107] Rikard R., Buchholz F. G., Wang H., et al.. Investigation of mixed mode I/IIinterlaminar fracture toughness of laminated composites by using a CTS type specimen.Engineering Fracture Mechanics.1998,61:325-342P
[108] Rikards R.. Interlaminar fracture behavior of laminated composites. Coumputers&Structures.2000,76:11-18P
[109] Richard H. A., Kuna M.. Theoretical and experimental study of superimposed fractureMode I, II, III. Engineering Fracture Mechanics.1990,35(6):949-960P
[110] Wu Hengyi, Ma Gang, Xia Yuanming. Experimental study of tensile properties ofPMMA at intermediate strain rate. Materials Letters.2004,58(29):3681-3685P
[111]中华人民共和国国家标准.金属材料室温拉伸试验方法. GB/T228-2002
[112]中华人民共和国国家标准.金属材料弹性模量和泊松比试验方法. GB/T22315-2008
[113]邹广平.材料力学实验基础.第1版.哈尔滨工程大学出版社,2010:13-176页
[114]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用.第1版.科学出版社,2009:1-35页
[115] Irwin G. R.. One set of fast crack propagation in high strength steel and aluminumalloys. Sagamore Researsh Conference Proceedings.1956,2:289-305P
[116] Irwin G. R.. Crack-extension force for a part-through crack in a plate. J Appl Mech.1962,29:651-654P
[117] Rybicki E. F., Kanninen M. F.. A finite element calculation of stress intensity factors bya modified crack closure integral. Engineeing Fracture Mechanics.1977,9(4):931-938P
[118] Raju I. S.. Calculation of strain-energy release rates with high-order and singularfinite-elements. Engineering Fracture Mechanics.1987,28:251-274P
[119]张允涛,黄其青,殷之平.虚拟裂纹闭合法在MSC.Patran中的二次开发.航空计算技术.2009,39(2):41-45页
[120] Fawaz S. A.. Application of the virtual crack closure technique to calculate stressintersity factors for through cracks with an elliptical crack front. Engineering FractureMechanics.1998,3:327-342P
[121] Rice J. R.. A path independent integral and the approximate analysis o strainconcentration by notches and cracks. Journal of Appled Mechanics.1968,35:379-386P
[122]赵建生.断裂力学及断裂物理.第1版.华中科技大学出版社,2003:161-162,197-198页
[123] Moura B., Shih C. F.. A treatment of crack tip contour integrals. International Journalof Fracture.1987,35:295-310P
[124] Shivakumar K. N., Raju I. S.. An equivalent domain integral method forthree-dimensional mixed-mode fracture problem. Engineering Fracture Mechanics.1992,42:935-959P
[125] Murakami Y.. Stress intensity factors handbook. Vol.1. Pergamon Press, Oxford,1978:94-96P
[126]中华人民共和国国家标准.金属材料平面应变断裂韧度KIC试验方法. GB/T4161-2007
[127]王新敏,李义强,许宏伟. ANSYS结构分析单元与应用.第1版.人民交通出版社，2011:237-239页
[128] Cao J. J., Yang G. J., Parker J. A, et al. Crack modeling in FE analysis of circulartubular joints. Engineering Fracture Mechanics.1998,61(5-6):537-553P
[129]曾攀,雷丽萍,方刚.结构的建模与分析.第1版.机械工业出版社,2011:300-303页
[130] Benthem J. P.. States of stress at the vertex of a quarter-infinite crack in a half-space.International Journal Solids and Structures.1977,13(5):479-492P
[131] Bazant Z. P., Estenssoro L. F.. Surface singularity and crack propagation. InternationalJournal Solids and Structures.1979,15:405-426P
[132] Pook L. P.. A finite element analysis of the angle crack specimen. Mixed mode fatigueand fracture.1993:285-302P
[133] Buchholz F.-G., Chergui A., Richard H. A.. Fracture analyses and experimentalresults of crack growth under general mixed mode loading conditions. EngineeringFracture Mechanics.2004,71:455-468P
[134] Zhu Li, Li Qing-fen, Buchholz F.-G.. Computational fracture analysis of anAFM-Specimen under mixed mode loading conditions. Journal of Marine Science andApplication.2011,10(1):105-112P
[135] Li Qing-fen, Zhu Li, Zhu Shi-fan, Buchholz F.-G.. Fracture behavior inAFM-Specimen with single crack under different loading conditions. StructuralDurability and Health Monitoring.2010,6(3-4):273-288P
[136] Buchholz. F.-G., Chergui A., Richard H. A.. Fracture analyses and experimental resultsof crack growth under general mixed mode loading conditions. Engineering FracutreMechanics.2004,71:455-468P
[137]余启明,何晓鸣,刘泽宇,夏磊,姜曼,李尚松. Q370qE高强度钢板试件的疲劳裂纹预制试验研究.第十三届中国科协年会第19分会场-公路在综合交通运输体系中的地位和作用研讨会论文集,中国天津,2011
[138] Ayatollahi M. R., Aliha M. R. M., Hasani M. M. Mixed mode brittle fracture in PMMA--an experimental study using SCB specimens. Materials Science and Engineering A.2006,417(1-2):348-356P
[139] Bhattacharjee D., Knott J. F. Effect of mixed mode I and II loading on the fracturesurface of polymethyl methacrylate (PMMA). Int J Fracture.1995,72:359-381P.
[140] Smith D. J., Ayatollahi M. R., Pavier M. J.. On the consequences of T-stress in elasticbrittle fracture. Proc Roy Soc A.2006,462:2415-2437P
[141] Tada H., Paris P. C., Irwin G. R.. The stress analysis of creak handbook. Del. ReseacrhCopr. Hellertown Pa,1973
[142] Sih G. C.. Handbook of stress intensity factor of researchers and engineers. LehighUniv. Bethehem Pa,1973
[143] Rooks D. P., Cartwright D. J.. Compendium of stress intensity factors. London,HerMajesty’s Stationary Office,1976
[144]中国航空院研究院报编.应力强度因子手册.科学出版社,1981
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