脆性/韧性断裂机理与判据及裂尖变形理论研究
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摘要
大量实验研究表明,对于岩土工程实践中的大部分宏观裂纹问题,线弹性断裂力学仍然具有广泛的适用性。线弹性断裂力学将奇异性引入裂尖断裂过程,对复杂的应力与应变场进行了线性求解。在小范围屈服条件下,脆性断裂和韧性断裂过程中裂尖附近弹性区内的应力与应变场仍可以采用线弹性断裂理论描述。而弹塑性断裂力学的研究目前仍主要局限于理论探讨。对于脆性和韧性断裂过程的开裂机理,目前仍缺乏合理的描述,尚不能合理地解释韧性断裂试验试验结果。本文针对脆性断裂和韧性断裂特性和机理,在下列方面进行了比较深入而系统的理论分析和数值计算。
1.通过分析断裂的宏观和细微观行为,探讨了宏观与微观断裂之间的相互关系。裂尖处断裂过程区内的微损伤形貌对于裂尖开裂演化特征尤其是韧性断裂具有显著的影响。根据对脆性、韧性断裂过程的裂尖开裂形式与裂纹的载荷模式之间关系的探讨,首先明确了载荷模式与裂纹开裂类形式间的区别及其相互关系;重新阐明了载荷类型和断裂形式及不同载荷模式下的应力强度因子和不同断裂形式的断裂韧度等概念,澄清了传统断裂力学中对裂纹的起裂点(启裂点)和起裂方向之间关系的不同认识。
2.基于上述认识,从另一个新的角度提出并阐述了脆性断裂和韧性断裂的裂纹开裂扩展机理。根据脆性断裂与韧性断裂过程中裂纹不同的开裂形式和机理,对裂纹尖端处进行了不同形式的简化,分别建立了适用于脆性断裂和韧性断裂过程分析的裂尖简化断裂模型。
3.对于脆性断裂过程,根据所建立的脆性断裂裂尖简化模型,利用通用有限元分析软件ABAQUS和通用分析工具软件MATLAB详细地分析了Ⅰ型、Ⅱ型及Ⅰ-Ⅱ复合型载荷作用下的裂尖处应力分布。根据所提出的断裂机理,建立了裂尖径向平面最大应力准则MSRP(MSRP: the Maximum Stress on Radial Plane),给出了Ⅰ-Ⅱ复合型载荷模式下发生脆性断裂的复合判据。首次通过分析建立了Ⅰ-Ⅱ复合型载荷模式下两类应力强度因子K_Ⅰ和K_Ⅱ之间的理论关系及复合型断裂的应力强度因子K_Ⅰ-K_Ⅱ相互作用包络曲线,对不同应力复合比情况下裂纹开裂角进行了理论预测,通过与脆性断裂试验结果的对比,论证了所提出的脆性断裂理论的合理性。进而利用MATLAB对K_Ⅰ-K_Ⅱ的包络线进行了数值拟合,得到了Ⅰ-Ⅱ复合型断裂的经验判据。
4.由于对韧性断裂机理尚缺乏深入的认识,目前主要停留在探索性的定性分析。韧性断裂的演化过程非常复杂,且具有一定的随机性,通过韧性断裂实验所
The linear elastic fracture mechanics has been widely used in the analysis of the stress field at the neighborhood of crack-tip while the singularity around the crack-tip is considered. It is indicated by fracture experimental tests that the theory of linear elastic mechanics is still applicable in the analysis of problems of macroscopic fracture. Under condition of small-scale yield, the distribution of stress and strain at the region of crack-tip can be described by theory of the linear elastic fracture mechanics. On the other hand, the studies and application of the elasto-plastic fracture theory are limited due to the sophistication of the elasto-plastic fracture problem. The experimental data for ductile fracture can not be well interpreted at present. In this thesis, a comprehensive study on the crack mechanisms and fracture criterions for both brittle fracture and ductile fracture are made. The main work includes the following parts.1. Based on the investigations on fracture behavior in both macroscopic scale and microscopic scale, the relationship between both scales of fracture is examined. It is indicated that the micro damage patterns of crack-tip in the fracture process have significant effects on the crack evolution and feature behaviour of crack-tip especially on the ductile fracture process. Based on the analysis of the relationship between the cracking types and the loading modes at the region of crack-tip in the brittle fracture and ductile fracture process, the difference between load mode and crack type is clarified, and the crack type and the stress intensity factors and fracture toughness under various loading modes are reclassified and redefined. The ambiguous recognition on the relationship of the azimuth angle of crack initiation point and the crack initiation direction, which are taken as identical in the traditional fracture mechanics, is clarified.2. Two fracture mechanisms for the brittle fracture and the ductile fracture are developed respectively. According to the different fracture mechanisms, the crack-tip is simplified and corresponding crack-tip fracture models are developed.3. For brittle fracture process, based on the simplified crack-tip brittle fracture model, the universal software of FEM, ABAQUS, and the universal tool software of analysis, MATLAB are used to analyze the distributions of stresses at the neighborhood of crack-tip under loading of I-mode and H-mode and the mixed-mode. According to the fracture mechanism and simplified crack-tip model proposed in the thesis, the criterion based on the maximum stress on the radial plane (MSRP) of crack-tip is presented for brittle fracture. The theoretical expression of the MSRP criterion for brittle fracture under mixed-mode loading and the formulae for prediction of the crack initiation angles are given. The curve of predicted crack initiation angles and the envelope curve of stress intensity factors of K_I-K_II under various conditions with different stress compound stress ratios are given. Through the comparison with the brittle fracture experimental data, the rationality of the proposed brittle fracture mechanism and the MSRP criterion are illustrated. By curve-fitting for the envelope curve of K_I-K_II computed, the empirical relation of the fracture criterion for crack-tip under mixed-mode loading is given. .4. Although many theoretical analyses and experimental investigations have been made for the ductile or elasto-plastic fracture problem, it seems that the theories and
experiments which have been achieved cannot be directly used in engineering practice. Therefore, deep understanding on behavior of ductile fracture is required. The theories of elasto-plastic fracture developed cannot well match with the experimental data which display a certain randomness and discreteness. The discreteness between theoretical predictions and experimental observations is usually attributed to the inaccuracies due to non-homogeneity of materials around crack-tip and the random errors generated in the experimental tests and observations of ductile fracture. In order to well interpret the experimental data, an alternating mechanism of ductile fracture is proposed based on examination of elasto-plastic stress distributions of the crack-tip. It is shown by analyzing the fracture process and plastic zone of the crack-tip that the orientation of crack initiation is not the same as initial cracking orientation of the crack. For the condition in which the plastic deformation at the crack-tip has minor influence on the stress distributions of the crack-tip, a simplified model of the crack-tip for ductile fracture is developed. By examining the effect of Poisson's ratio of materials on the stress field of the crack-tip in the high stress zone, it is found that the stresses of three directions in the crack-tip play a significant role in the evolution of the crack. The maximum Mises stress at the crack-tip will control the propagation of the crack when the Poisson's ratio is equal to 0.5. Based on these analyses, the MMSRP criterion of ductile fracture is proposed. The criterion is based on the maximum Mises stress on radial plane at the crack-tip. The theoretical expressions for the proposed criterion and cracking angle of crack are given. The proposed criterion is compared with other conventional criteria of ductile fracture and related experimental data and the rationality and reliability of the proposed criterion are illustrated.5. By examining the experimental data of ductile fracture, it is shown that two types of crack initiation and evolution exist in the ductile fracture process. For these two types of crack development, the main controlling factor will be different. When the plastic deformations or displacements are induced in the crack-tip zone, the deformation analyses of the crack-tip is performed by the universal FEM software, ABAQUS based on the proposed mechanism of ductile fracture. The deformation crack-tip model for ductile fracture of the crack-tip is developed to consider the effect of the deformation of the crack-tip. Through the analyses of the deformation process of the crack-tip under different modes of loading, the transformation interrelation of the coordinates between the configurations before and after deformation is established. The ratio of the action radius of stresses in the neighborhood of the crack-tip respectively before and after deformation is defined as the polar radius deformation multiple which is used to modify the stresses and deformations which take account the deformation effect of the crack-tip according to the stresses and deformations before cracking.6. Based on the proposed deformation crack-tip theory, the strain factor kd is proposed to express the nonlinear effect induced by the micro-distortion and plastic deformation. Furthermore based on the elastic theory of fracture mechanics, the I-mode ductile-brittle fracture and II-mode ductile plastic fracture are analyzed. The experimental data can be well matched by using MATLAB through properly choosing the strain factor. The cracking direction angle predicted by the proposed theory can well agree with the experimental observations. It is shown that the numerical analyses by using the proposed method can reasonably describe the stress distribution of the crack-tip in ductile fracture process and can interpret the ductile fracture behavior of different types. It is concluded that the maximum circumferential tensile stress of the
1.通过分析断裂的宏观和细微观行为,探讨了宏观与微观断裂之间的相互关系。裂尖处断裂过程区内的微损伤形貌对于裂尖开裂演化特征尤其是韧性断裂具有显著的影响。根据对脆性、韧性断裂过程的裂尖开裂形式与裂纹的载荷模式之间关系的探讨,首先明确了载荷模式与裂纹开裂类形式间的区别及其相互关系;重新阐明了载荷类型和断裂形式及不同载荷模式下的应力强度因子和不同断裂形式的断裂韧度等概念,澄清了传统断裂力学中对裂纹的起裂点(启裂点)和起裂方向之间关系的不同认识。
2.基于上述认识,从另一个新的角度提出并阐述了脆性断裂和韧性断裂的裂纹开裂扩展机理。根据脆性断裂与韧性断裂过程中裂纹不同的开裂形式和机理,对裂纹尖端处进行了不同形式的简化,分别建立了适用于脆性断裂和韧性断裂过程分析的裂尖简化断裂模型。
3.对于脆性断裂过程,根据所建立的脆性断裂裂尖简化模型,利用通用有限元分析软件ABAQUS和通用分析工具软件MATLAB详细地分析了Ⅰ型、Ⅱ型及Ⅰ-Ⅱ复合型载荷作用下的裂尖处应力分布。根据所提出的断裂机理,建立了裂尖径向平面最大应力准则MSRP(MSRP: the Maximum Stress on Radial Plane),给出了Ⅰ-Ⅱ复合型载荷模式下发生脆性断裂的复合判据。首次通过分析建立了Ⅰ-Ⅱ复合型载荷模式下两类应力强度因子K_Ⅰ和K_Ⅱ之间的理论关系及复合型断裂的应力强度因子K_Ⅰ-K_Ⅱ相互作用包络曲线,对不同应力复合比情况下裂纹开裂角进行了理论预测,通过与脆性断裂试验结果的对比,论证了所提出的脆性断裂理论的合理性。进而利用MATLAB对K_Ⅰ-K_Ⅱ的包络线进行了数值拟合,得到了Ⅰ-Ⅱ复合型断裂的经验判据。
4.由于对韧性断裂机理尚缺乏深入的认识,目前主要停留在探索性的定性分析。韧性断裂的演化过程非常复杂,且具有一定的随机性,通过韧性断裂实验所
The linear elastic fracture mechanics has been widely used in the analysis of the stress field at the neighborhood of crack-tip while the singularity around the crack-tip is considered. It is indicated by fracture experimental tests that the theory of linear elastic mechanics is still applicable in the analysis of problems of macroscopic fracture. Under condition of small-scale yield, the distribution of stress and strain at the region of crack-tip can be described by theory of the linear elastic fracture mechanics. On the other hand, the studies and application of the elasto-plastic fracture theory are limited due to the sophistication of the elasto-plastic fracture problem. The experimental data for ductile fracture can not be well interpreted at present. In this thesis, a comprehensive study on the crack mechanisms and fracture criterions for both brittle fracture and ductile fracture are made. The main work includes the following parts.1. Based on the investigations on fracture behavior in both macroscopic scale and microscopic scale, the relationship between both scales of fracture is examined. It is indicated that the micro damage patterns of crack-tip in the fracture process have significant effects on the crack evolution and feature behaviour of crack-tip especially on the ductile fracture process. Based on the analysis of the relationship between the cracking types and the loading modes at the region of crack-tip in the brittle fracture and ductile fracture process, the difference between load mode and crack type is clarified, and the crack type and the stress intensity factors and fracture toughness under various loading modes are reclassified and redefined. The ambiguous recognition on the relationship of the azimuth angle of crack initiation point and the crack initiation direction, which are taken as identical in the traditional fracture mechanics, is clarified.2. Two fracture mechanisms for the brittle fracture and the ductile fracture are developed respectively. According to the different fracture mechanisms, the crack-tip is simplified and corresponding crack-tip fracture models are developed.3. For brittle fracture process, based on the simplified crack-tip brittle fracture model, the universal software of FEM, ABAQUS, and the universal tool software of analysis, MATLAB are used to analyze the distributions of stresses at the neighborhood of crack-tip under loading of I-mode and H-mode and the mixed-mode. According to the fracture mechanism and simplified crack-tip model proposed in the thesis, the criterion based on the maximum stress on the radial plane (MSRP) of crack-tip is presented for brittle fracture. The theoretical expression of the MSRP criterion for brittle fracture under mixed-mode loading and the formulae for prediction of the crack initiation angles are given. The curve of predicted crack initiation angles and the envelope curve of stress intensity factors of K_I-K_II under various conditions with different stress compound stress ratios are given. Through the comparison with the brittle fracture experimental data, the rationality of the proposed brittle fracture mechanism and the MSRP criterion are illustrated. By curve-fitting for the envelope curve of K_I-K_II computed, the empirical relation of the fracture criterion for crack-tip under mixed-mode loading is given. .4. Although many theoretical analyses and experimental investigations have been made for the ductile or elasto-plastic fracture problem, it seems that the theories and
experiments which have been achieved cannot be directly used in engineering practice. Therefore, deep understanding on behavior of ductile fracture is required. The theories of elasto-plastic fracture developed cannot well match with the experimental data which display a certain randomness and discreteness. The discreteness between theoretical predictions and experimental observations is usually attributed to the inaccuracies due to non-homogeneity of materials around crack-tip and the random errors generated in the experimental tests and observations of ductile fracture. In order to well interpret the experimental data, an alternating mechanism of ductile fracture is proposed based on examination of elasto-plastic stress distributions of the crack-tip. It is shown by analyzing the fracture process and plastic zone of the crack-tip that the orientation of crack initiation is not the same as initial cracking orientation of the crack. For the condition in which the plastic deformation at the crack-tip has minor influence on the stress distributions of the crack-tip, a simplified model of the crack-tip for ductile fracture is developed. By examining the effect of Poisson's ratio of materials on the stress field of the crack-tip in the high stress zone, it is found that the stresses of three directions in the crack-tip play a significant role in the evolution of the crack. The maximum Mises stress at the crack-tip will control the propagation of the crack when the Poisson's ratio is equal to 0.5. Based on these analyses, the MMSRP criterion of ductile fracture is proposed. The criterion is based on the maximum Mises stress on radial plane at the crack-tip. The theoretical expressions for the proposed criterion and cracking angle of crack are given. The proposed criterion is compared with other conventional criteria of ductile fracture and related experimental data and the rationality and reliability of the proposed criterion are illustrated.5. By examining the experimental data of ductile fracture, it is shown that two types of crack initiation and evolution exist in the ductile fracture process. For these two types of crack development, the main controlling factor will be different. When the plastic deformations or displacements are induced in the crack-tip zone, the deformation analyses of the crack-tip is performed by the universal FEM software, ABAQUS based on the proposed mechanism of ductile fracture. The deformation crack-tip model for ductile fracture of the crack-tip is developed to consider the effect of the deformation of the crack-tip. Through the analyses of the deformation process of the crack-tip under different modes of loading, the transformation interrelation of the coordinates between the configurations before and after deformation is established. The ratio of the action radius of stresses in the neighborhood of the crack-tip respectively before and after deformation is defined as the polar radius deformation multiple which is used to modify the stresses and deformations which take account the deformation effect of the crack-tip according to the stresses and deformations before cracking.6. Based on the proposed deformation crack-tip theory, the strain factor kd is proposed to express the nonlinear effect induced by the micro-distortion and plastic deformation. Furthermore based on the elastic theory of fracture mechanics, the I-mode ductile-brittle fracture and II-mode ductile plastic fracture are analyzed. The experimental data can be well matched by using MATLAB through properly choosing the strain factor. The cracking direction angle predicted by the proposed theory can well agree with the experimental observations. It is shown that the numerical analyses by using the proposed method can reasonably describe the stress distribution of the crack-tip in ductile fracture process and can interpret the ductile fracture behavior of different types. It is concluded that the maximum circumferential tensile stress of the
引文
[1] 何庆芝,郦正能.工程断裂力学[M].北京:北京航空航天大学出版社,1993.
[2] 孙广忠.岩体结构力学[M].北京:科学出版社,1988.
[3] 杨卫.宏微观断裂力学[M].北京:国防工业出版社,1995.
[4] Erdogan F, Sih G C. On the crack extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering, 1963, 85(4): 519-527.
[5] Paris P C, Sih G C. Fracture toughness testing and its applications[M]. American Society for Testing and Materials, Philadelphia, 1965, 60.
[6] Inglis C E. Stresses in a plate due to the presence of cracks and sharp comers[J]. Transactions of the Institute of Naval Architects, 1913, 55:219-241.
[7] Griffith A A. The phenomena of rupture and flow in solids[J]. Phil. Trans., Ser. A, 1920, 221: 163-198.
[8] Griffith A A. The theory of rupture[A]. Proceeding of the First International Conference. on Application Mechanics[C], Delft, 1924, 55-63.
[9] Irwin G R. Onset of fast crack propagation in high strength steel and aluminum alloys[A]. Sagamore Research Conference Proceedings[C], 1956, 2:289-305.
[10] Orowan E. Fracture and strength of solids[R]. Reports on Progress in Physics, 1948, Ⅻ: 185.
[11] Irwin G R. Analysis of stresses and strains near the end of a crack transversing a plate[J]. Appl. Mech., 1957, 24:361-364.
[12] Irwin G R. Plastic zone near a crack and fracture toughness[A]. Sagamore Research Conference Proceedings[C], 1961, 4.
[13] Tada H, Paris P C, Irwin G R. The stress analysis of cracks handbook (2nd Edition)[M]. St. Louis: Pads Productions Inc., 1985.
[14] Wells A A. Application of fracture mechanics at and beyond general yielding[J]. British Welding Journal. 1963, 10:563-570.
[15] Dugdale D S. Yielding in steel sheets containing slits[J]. Mech. Phys. Solids, 1960, 8:100-108.
[16] Barenblatt G I. The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech., New York: Academic Press, 1962, 7:55-129.
[17] Cottrell A H. Mechanisms of fracture[M], the 1963 Tewksbury lecture, Tewksbury Symposium on Fracture[C], 1963, 1-27.
[18] Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks[J]. Appl. Mech., 1968, 35: 379-386.
[19] Rice J R, Rosengren G F. Plane strain deformation near a crack tip in power-law hardening material[J]. Mech. Phys. Solids, 1968, 16: 1-12.
[20] Hutchinson J W. Singular behavior at the end of a tensile crack tip in a hardening material[J]. Mech. Phys. Solids, 1968, 16: 13-31.
[21] Begley J A, Landes J D. The J-Intergral as a fracture criterion[A]. ASTM STP 514, American Society for Testing and Materials[C], Philadelphia, 1972, 1-20.
[22] Rice J R, Thomson R. Ductile versus brittle behaviour of crystals[J]. Philosophical Magazine, 1974, 29:97.
[23] 黄克智,肖纪美.材料的损伤断裂机理和宏微观力学理论[M].北京:清华大学出版社,1999.
[24] 宿彦京,王燕斌,褚武扬.吸附促进位错发射、运动导致脆性裂纹形核[J].中国科学(E辑),1997,27(5):397-403.
[25] 陈奇志,褚武扬,肖纪美.薄膜中纳米裂纹在无位错区中的形核、钝化或扩展[J].自然科学进展—国家重点实验室通讯,1995,5(6):743-753.
[26] 张琼,周海芳.单晶硅裂纹尖端的位错发射行为[J].中国有色金属学报,2001,11(5):815-818.
[27] 钱才富,乔利杰,褚武扬.钝裂纹发射位错后的应力分布及有效应力强度因子[J].中国科学(E辑),2000,30(6):497-504.
[28] 钱才富,姜忠军.裂纹尖端塑性区和无位错区的微观模拟[J].金属学报,2004,40(2):159-162.
[29] 钱才富.位错和位错偶沿单一滑移系从裂纹尖端的发射[J].金属学报,1999,35(5):546-550.
[30] 余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997.
[31] 尹双增.断裂、损伤理论及应用[M].北京:清华大学出版社,1992.
[32] 杨晓翔,范家齐,匡震邦.求解混合型裂纹应力强度因子的围线积分法[J].计算结构力学及其应用,1996,13(1):84-89.
[33] 栾茂田,Ugai Keizo.岩土工程研究中若干基本力学问题的思考[J].大连理工大学学报,1999,39(2):309-317.
[34] Zienkiewicz O C. The Finite Element Method[M]. London, McGraw-Hill,1977.
[35] 王泳嘉.边界元法有岩石力学中的应用[J].岩石力学与工程学报,1986,5(2):205-222.
[36] 应隆安.无限元方法[M].北京:北京大学出版社,1992.
[37] 王泳嘉.拉格朗日元法及其在岩土力学中的应用[A].第二届全国青年岩土力学与工程学术会议论文集《岩土力学与工程》[C].大连:大连理工大学出版社,1995,22-33.
[38] Kawai T. New discrete structural models and generalization of the method of limit analysis[J], Finite Elements in Nonlinear Mechanics, NIT, Tronheim, 1977, 885-909.
[39] Cundall P A. A computer model for simulating progressive, large-scale movements in blocky rock systems[A]. Proceeding of the International Symposium on Rock Fracture[C], Nancy, France, 1971.
[40] Shi G H. Discontinuous deformation analysis: A new numerical model for the static and dynamics of block systems[D]. A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy, Berkeley: University of California, 1988.
[41] 寇晓东.无单元法及其在岩土工程中的应用[J].岩土工程学报,1998,20(1):6-9.
[42] Shi G H. Numerical manifold method[A]. Proceedings of the First International Conference on Analysis of Discontinuous Deformation (ICADD-1) (Edited by Li J C, Wang C-Y and Sheng J)[C], Chungli, Taiwan, 1995, 187-222,
[43] Chang C C. Computational simulation of progressive fracture in fiber composites[J]. Journal of Composite Materials, 1987, 21: 834-855.
[44] 汤安民,刘泽明.铝合金材料断裂形式变化规律的试验分析[J].西安理工大学学报,2003,19(3):226-229.
[45] 杨卫.细观力学和细观损伤力学[J].力学进展,1992,22(1):1-9.
[46] 邢永明,戴福隆,杨卫.准解理微裂纹裂尖纳观变形场的实验研究[J].中国科学(A辑),2000,30(8):721-726.
[47] 洪其麟译.高等断裂力学[M].北京:北京航空学出版社,1987.
[48] 匡震邦,马法尚.裂纹端部场[M].西安:西安交通大学出版社,2002.
[49] 杨连生,杨卫.强韧化材料的细观力学设计[J].力学进展,1997,27(2):177-184.
[50] 孙宗颀,饶秋华,王桂尧.剪切断裂韧度(K_(Ⅱc))确定的研究[J].岩石力学与工程学报,2002,21(2):199-203.
[51] 张对红,刘错,张静.裂纹尖端附近区域的应力应变场分析[J].油气储运,2002,20(9):13-19.
[52] 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[J].华东交通大学学报,1997,14(1):54.
[53] 郑传超,刘元镛.微观裂纹尺寸l_0的确定及其对门槛应力强度因子的影响[J].西安公路交通大学学报,1995,15(2):12-17.
[54] 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[J].重庆建筑大学学报,1998,20(2):41-46.
[55] 庞之恒.平面弹性断裂问题各阶应力强度因子的直接积分表达[J].贵州师范大学学报(自然科学版),2001,19(4):57-64.
[56] 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[J].机械强度,2003,25(5):576-579.
[57] 尹奇志,肖金生,吕运冰,李格升.孔边应力集中和裂纹尖端应力强度因子的有限元分析[J].武汉理工大学学报(交通科学与工程版),2002,26(1):47-50.
[58] Masazumi Amagai. Investigation of stress singularity field and stress intensity factors for cracks[J]. Finite Elements in Analysis and Design, 1998, 30:97-124.
[59] 朱平,沙江波,邓增杰.J-积分断裂准则在弹塑性Ⅰ-Ⅱ复合型加载下的应用探讨[J].西安交通大学学报,1994,28(2):43-48.
[60] 沙江波,朱平.Ⅰ+Ⅱ型弹塑性断裂的宏观与微观过程[J].西安交通大学学报,1996,30(12):87-94.
[61] 万建松,岳珠峰.金属韧性断裂的细观研究[J].计算力学学报,2002,19(3):320-323.
[62] Klapper H. Generation and propagation of dislocations during crystal growth[J]. Materials Chemistry and Physics, 2000, 66:101-109.
[63] 郑长卿.韧性断裂细观力学的初步研究及其应用[M].西安:西北工业大学出版社,1988,8-19.
[64] 郭田福,杨卫.平面应变脆性损伤裂纹场分析[J].固体力学学报,1995,16(2):132-139.
[65] 杨连生,杨卫.断裂过程的有限元模拟[J].计算力学学报,1997,14(4):407-412.
[66] 杨卫,郭田福,傅增力.裂尖超钝化:实验、理论与数值模拟[J].力学学报,1993,25(4):468-478.
[67] Moran B, Oritz M, Shih C F. Formulation of implicit finite elements methods for multiplicative finite deformation plasticity[J]. International Journal of Numerical Metal Engineering, 1990, 29:483-514.
[68] Guo T F, Yang W. Crack tip profiles generated by anisotropic damage[J]. International Journal of Damage Mechanics, 1993, 2:364-384.
[69] Rao Q H, Sun Z Q, Stephansson O, LI C L, Stillborg B. Shear fracture (mode Ⅱ) of brittle rock[J]. International Journal of Rock Mechanics Mining Sciences, 2003, 40:355-375.
[70] 包亦望,孙立.脆性材料在双向应力下的断裂和失效研究[J].无机材料学报,1998,13(6):847-852.
[71] 张志呈.岩石爆破裂纹的起裂、扩展、分岔与止裂[J].爆破,1999,16(4):21-24.
[72] 黎立云,黎振兹,孙宗颀.岩石的复合型断裂实验及分析[J].岩石力学与工程学报,1994,13(2):134-140.
[73] 余天堂.岩土材料固有各向异性的模拟[J].岩石力学与工程学报,2004,23(10):1604-1607.
[74] 朱子龙,李建林,王康平.三峡工程岩石拉剪蠕变断裂试验研究[J].武汉水利电力大学(宜昌)学报,1998,20(3):16-19.
[75] 徐平,夏熙伦.三峡工程花岗岩蠕变断裂与Ⅰ-Ⅱ型断裂试验研究[J].长江科学院院报,1995,12(3):31-36.
[76] 朱子龙,李建林,王康平.三峡工程岩石拉剪断裂试验研究[J].武汉水利电力大学(宜昌)学报,1998,20(1):1-6.
[77] 何伟,郑恒祥.脆性材料复合裂纹断裂判据研究[J].郑州大学学报(理学版),2003,35(2):92-94.
[78] 俞树荣,严志刚,曹睿,陈剑虹.钝化预裂纹尖端开裂对应力应变分布的影响[J].兰州理工大学学报,2004,30(1):1-4.
[79] 徐平,夏熙伦.花岗岩Ⅰ-Ⅱ复合型断裂试验及断裂数值分析[J].岩石力学与工程学报,1996,15(1):62-70.
[80] 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[J].机械强度,2003,25(3):347-351.
[81] 许斌,江见鲸.混凝土Ⅰ-Ⅱ复合型断裂判据研究[J].工程力学,1995,12(2):13-21.
[82] 胡海平,苏玉堂,常俐俐,李志潭.轴承钢GCr15混合型(Ⅰ+Ⅱ)断裂试验研究[J].太原重型机械学院学报,1994,15(1):50-56.
[83] 汤安民,师俊平.复杂应力状态断裂判据的讨论[J].西安理工大学学报,2000,16(1):47-73.
[84] 陈增涛,王铎.复合型裂纹的混合开裂准则[J].哈尔滨工业大学学报,1994,26(4):127-131.
[85] 赵艳华,徐世烺.Ⅰ-Ⅱ复合型裂纹脆性断裂的最小J_2准则[J].工程力学,2002,19(4):94-98.
[86] 李术才,朱维申.复杂应力状态下断续节理岩体断裂损伤机理研究及其应用[J].岩石力 学与工程学报,1999,18(2):142-146.
[87] 丁卫华,仵彦卿,蒲毅彬.低应变率下岩石内部裂纹演化的X射线CT方法[J].岩石力学与工程学报,2003,22(11):1793-1797.
[88] 丁卫华,仵彦卿,蒲毅彬.基于X射线CT的岩石内部裂纹宽度测量[J].岩石力学与工程学报,2003,22(9):1421-1425.
[89] Palaniswamy K, Knauss W G. On the problem of crack extension in britte solids under general loading[R]. Report SM 74-8, Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, 1974.
[90] Hussain M A, Pu S L, Underwood J H. In "Fracture Analysis, ASTM STP 560" ASTM[R], Philadelphia, 1974, 2-28.
[91] 张淳源.论非线性断裂力学的基本平衡定律(Ⅱ)—非局部理论(主要结果简介)[J].湘潭大学自然科学学报,1995,17(1):28-32.
[92] 俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998.
[93] 汤安民,张瑞平,王忠民.最大主应力与形状改变比能对断裂的影响[J].西安理工大学学报,1999,15(3):59-63.
[94] 汤安民,朱文艺,卢智先.韧性材料的几种断裂形式及判据讨论[J].机械强度,2002,24(4):566-570.
[95] 汤安民,王忠民.断裂力学判据存在的一个问题及讨论[J].机械强度,2001,23(2):222-224.
[96] 汤安民,师俊平,卢智先.韧性材料复合型断裂启裂点与开裂方向的讨论[J].机械强度,2002,24(2):266-269.
[97] 汤安民,王静.几种金属材料断裂形式变化规律的试验分析[J].实验力学,2003,18(4):440-444.
[98] 刘艳红.等W线上最大环向拉应力理论求解Ⅰ-Ⅱ复合型裂纹断裂角[J].贵州工业大学学报(自然科学版),2003,32(1):4-6.
[99] 蒋玉川,王启智.复合型裂纹扩展的形状改变比能准则[J].四川大学学报(工程科学版),2004,36(3):20-23.
[100] 杨伯源,胡宗陵.线弹簧模型柔度与裂纹开裂角之间的关系[J].合肥工业大学学报(自然科学版),1998,21(3):25-30.
[101] 朱维申,陈卫忠,申晋.雁形裂纹扩展的模型试验及断裂力学机制研究[J].固体力学学报,1998,19(4):355-360.
[102] 朱维申,张强勇,李术才.三维脆弹塑性断裂损伤模型在裂隙岩体工程中的应用[J],固体力学学报,1999,20(2):164-170.
[103] 黄明利,唐春安,朱万成.岩石破裂过程的数值模拟研究[J].岩石力学与工程学报,2000,19(4):468-471.
[104] 沈珠江.岩土破损力学:理想脆弹塑性模型[J].岩土工程学报,2003,25(3):253-257.
[105] 马君峰,吕国志.一种基于裂尖损伤区的裂纹扩展模型[J].机械科学与技术,1999,18(5):701-703.
[106] 赵爱红,虞吉林.准脆性材料的细观损伤演化模型[J].清华大学学报(自然科学版),2000,40(5):88-91.
[107] 王新友,吴科如.准脆性类材料的等效裂纹断裂模型[J].大连理工大学学报,1997, 37(1):821-824.
[108] 左宏,郑长卿.Ⅰ-Ⅱ复合型韧断特征及机理的实验研究[J].机械强度,1973,19(1):62-65.
[109] 左宏,陈宜亨,郑长卿.复合型韧性断裂实验和控制参数[J].力学学报,1999,31(5):534-541.
[110] 刘元镛,徐绯,葛东云.弹塑性裂纹扩展的裂尖参数研究[J].西北工业大学学报,2000,18(1):5-10.
[111] 荣伟,张德驺,马茂元.金属断裂韧性与微观参量的关系[J].哈尔滨船舶工程学院学报,1994,15(2):31-39.
[112] 汤安民,师俊平.铝合金材料剪切断裂实验分析[J].力学季刊,2002,23(1):82-86.
[113] 万玲,许江.压应力作用下预制裂纹脆性材料的断裂特性[J].重庆大学学报,1994,17(6):78-82.
[114] 董新龙,王礼立,虞吉林.两种类型的剪切断裂韧性及其裂纹扩展[J].宁波大学学报(理工版),2000,13(1):21-25.
[115] Zheng M, Niemi E, Zheng X. An energetic approach to predict fatigue crack initiation life of LY12CZ aluminum and 16Mn Steel[J]. Theoretical and Applied Fracture Mechanics, 1997, 26:23-28.
[116] Li-Chun Bian, Kwang Soo Kim. The minimum plastic zone radius criterion for crack initiation direction applied to surface cracks and through-cracks under mixed mode loading[J]. International Journal of Fatigue, 2004, 26:1169-1178.
[117] 董蕙茹,郭万林.三维复合型断裂的试验方法探讨[J].实验力学,2002,17(4):497-503.
[118] 程侠,于克萍,邰卫华.金属板材中裂纹尖端区的损伤分析[J].长安大学学报(建筑与环境科学版),2003,20(1):61-64.
[119] 杨楠,佟景伟,舒庆琏.裂纹纹尖弹塑性应力应变场的实验研究和数值分析[J].实验力学,2003,18(3):338-342.
[120] Newman J C Jr., Dawicke D S, Sutton M A, Bigelow C A. A fracture criterion for widespread cracking in thin-sheet aluminum alloys[A]. ICAF 17 International Committee on Aeronautical Fatigue[C], 1993, 443-468.
[121] 孙国有,薛继良,兰清生,李贵军.空洞扩张与Ⅰ-Ⅱ复合型裂纹的断裂参量[J].浙江大学学报(自然科学版),1994,28(1):1-8.
[122] 李晓红,张克实.延性材料损伤演化及材料软化的孔洞尺寸影响[J].机械强度,2003,25(1):081-084.
[123] 切列帕诺夫,黄克智译,脆性断裂力学[M].1974,北京:科学出版社,1990.
[124] 周小平,张永兴.压剪应力作用下复杂形状多裂纹应力强度因子[J].上海交通大学学报,2003,37(12):1905-1909.
[125] 李振环,匡震邦,张克实.三轴应力场中不同形状孔洞的长大及其新模型[J].计算力学学报,2000,17(4):447-455.
[126] Biner S B. Fatigue crack growth studies under mixed-mode loading[J]. International Journal of Fatigue, 2003, 23: S259-S263.
[127] Kong X M, Schluter N, Dahl W. Effect of triaxial stress on mixed-mode fracture[J]. Engineering Fracture Mechanics, 1995, 52(2):379-388.
[128] Kienzler R, Herrmann G Fracture criteria based on local properties of the Eshelby tensor[J]. Mechanics Research Communications, 2002, 29:521-527.
[129] Samal M K, Dutta B K, Kushawaha H S. A study on ductile fracture initiation in the PHT piping material of an Indian PHWR using local approach[J]. International Journal of Pressure Vessels and Piping, 1999, 76:319-330.
[130] IsaKsson P, Stahle P. A directional crack path criterion for crack growth in ductile materials subjected to shear and compressive loading under plane strain conditions[J]. International Journal of Solids and Structures, 2003, 40:3523-3536.
[131] Sutton M A, Boone M L, Ma F H, Helm J D. A combined modeling-experimental study of the crack opening displacement fracture criterion for characterization of stable crack growth under mixed mode Ⅰ/Ⅱ loading in thin sheet materials[J]. Engineering Fracture Mechanics, 2000, 66:171-185.
[132] Lee S, Ravichandran G. Crack initiation in brittle solids under multiaxial compression[J]. Engineering Fracture Mechanics, 2003, 70:1645-1658.
[133] Pardoen T, Hachez F, Marchioni B, Blyth P H, Atkins A G. Mode I fracture of sheet metal[J]. Journal of the Mechanics and Physics of Solids, 2004, 52:423-452.
[134] Simonsen B C, Tornqvist R. Experimental and numerical modeling of ductile crack propagation in large-scale shell structures[J]. Marine Structure, 2004, 17:1-27.
[135] Imad A, Wilsius J, Nait Abdelaziz M, Mesmacque G. Experiments and numerical approaches to ductile tearing in an 2024-T351 aluminum alloy[J]. International Journal of Mechanical Sciences, 2003, 45:1849-1861.
[136] Wall O. Numerical modeling of fracture initiation in large steel specimens at impact[J]. Engineering Fracture Mechanics, 2002, 69:851-863.
[137] Negre P, Steglich D, Brocks D, Kocak M. Numerical simulation of crack extension in aluminum welds[J]. Computational Materials Science, 2003, 28:723-731.
[138] Liu S, Yuh C J, Zhu X K. Tensile-shear transition in mixed-mode Ⅰ/Ⅲ fracture[J]. International Journal of Solids and Structures, 2004, 41:6147-6172.
[139] Dhar S, Dixit P M, Sethuraman J. A continuum damage mechanics model for ductile fracture[J]. International Journal of Pressure Vessels and Piping, 2000, 77: 335-344.
[140] Belytschko T, Liu Y, Gu L. Element free Galerkin method[J]. International Journal of Numerical Methods in Engineering, 1994, 37:229-256.
[141] 王水林,葛修润.流形元方法在模拟裂纹扩展中的应用[J].岩石力学与工程学报,1997,16(5):405-410.
[142] 李卧东,王元汉,陈晓波.模拟裂纹传播的新方法-无网格伽辽金法[J].岩土力学,2001,22(4):33-36.
[143] 王芝银,王思敬,杨志法.岩石大变形分析的流形方法[J].岩石力学与工程学报,1997,16(5):399-404.
[144] 莫海鸿,陈尤雯.流形法在岩石力学研究中的应用[J].华南理工大学学报(自然科学版),1998,26(9):48-53.
[145] Liu G R, Gu Y T. A point interpolation method for two-dimensional solid[J]. International Journal of Numerical Mathematical Engineering, 2001, 50:937-951.
[146] Luan M T, Tian R, Yang Q. A new mesh-free method - Finite-cover element-free method[A].
[2] 孙广忠.岩体结构力学[M].北京:科学出版社,1988.
[3] 杨卫.宏微观断裂力学[M].北京:国防工业出版社,1995.
[4] Erdogan F, Sih G C. On the crack extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering, 1963, 85(4): 519-527.
[5] Paris P C, Sih G C. Fracture toughness testing and its applications[M]. American Society for Testing and Materials, Philadelphia, 1965, 60.
[6] Inglis C E. Stresses in a plate due to the presence of cracks and sharp comers[J]. Transactions of the Institute of Naval Architects, 1913, 55:219-241.
[7] Griffith A A. The phenomena of rupture and flow in solids[J]. Phil. Trans., Ser. A, 1920, 221: 163-198.
[8] Griffith A A. The theory of rupture[A]. Proceeding of the First International Conference. on Application Mechanics[C], Delft, 1924, 55-63.
[9] Irwin G R. Onset of fast crack propagation in high strength steel and aluminum alloys[A]. Sagamore Research Conference Proceedings[C], 1956, 2:289-305.
[10] Orowan E. Fracture and strength of solids[R]. Reports on Progress in Physics, 1948, Ⅻ: 185.
[11] Irwin G R. Analysis of stresses and strains near the end of a crack transversing a plate[J]. Appl. Mech., 1957, 24:361-364.
[12] Irwin G R. Plastic zone near a crack and fracture toughness[A]. Sagamore Research Conference Proceedings[C], 1961, 4.
[13] Tada H, Paris P C, Irwin G R. The stress analysis of cracks handbook (2nd Edition)[M]. St. Louis: Pads Productions Inc., 1985.
[14] Wells A A. Application of fracture mechanics at and beyond general yielding[J]. British Welding Journal. 1963, 10:563-570.
[15] Dugdale D S. Yielding in steel sheets containing slits[J]. Mech. Phys. Solids, 1960, 8:100-108.
[16] Barenblatt G I. The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech., New York: Academic Press, 1962, 7:55-129.
[17] Cottrell A H. Mechanisms of fracture[M], the 1963 Tewksbury lecture, Tewksbury Symposium on Fracture[C], 1963, 1-27.
[18] Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks[J]. Appl. Mech., 1968, 35: 379-386.
[19] Rice J R, Rosengren G F. Plane strain deformation near a crack tip in power-law hardening material[J]. Mech. Phys. Solids, 1968, 16: 1-12.
[20] Hutchinson J W. Singular behavior at the end of a tensile crack tip in a hardening material[J]. Mech. Phys. Solids, 1968, 16: 13-31.
[21] Begley J A, Landes J D. The J-Intergral as a fracture criterion[A]. ASTM STP 514, American Society for Testing and Materials[C], Philadelphia, 1972, 1-20.
[22] Rice J R, Thomson R. Ductile versus brittle behaviour of crystals[J]. Philosophical Magazine, 1974, 29:97.
[23] 黄克智,肖纪美.材料的损伤断裂机理和宏微观力学理论[M].北京:清华大学出版社,1999.
[24] 宿彦京,王燕斌,褚武扬.吸附促进位错发射、运动导致脆性裂纹形核[J].中国科学(E辑),1997,27(5):397-403.
[25] 陈奇志,褚武扬,肖纪美.薄膜中纳米裂纹在无位错区中的形核、钝化或扩展[J].自然科学进展—国家重点实验室通讯,1995,5(6):743-753.
[26] 张琼,周海芳.单晶硅裂纹尖端的位错发射行为[J].中国有色金属学报,2001,11(5):815-818.
[27] 钱才富,乔利杰,褚武扬.钝裂纹发射位错后的应力分布及有效应力强度因子[J].中国科学(E辑),2000,30(6):497-504.
[28] 钱才富,姜忠军.裂纹尖端塑性区和无位错区的微观模拟[J].金属学报,2004,40(2):159-162.
[29] 钱才富.位错和位错偶沿单一滑移系从裂纹尖端的发射[J].金属学报,1999,35(5):546-550.
[30] 余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997.
[31] 尹双增.断裂、损伤理论及应用[M].北京:清华大学出版社,1992.
[32] 杨晓翔,范家齐,匡震邦.求解混合型裂纹应力强度因子的围线积分法[J].计算结构力学及其应用,1996,13(1):84-89.
[33] 栾茂田,Ugai Keizo.岩土工程研究中若干基本力学问题的思考[J].大连理工大学学报,1999,39(2):309-317.
[34] Zienkiewicz O C. The Finite Element Method[M]. London, McGraw-Hill,1977.
[35] 王泳嘉.边界元法有岩石力学中的应用[J].岩石力学与工程学报,1986,5(2):205-222.
[36] 应隆安.无限元方法[M].北京:北京大学出版社,1992.
[37] 王泳嘉.拉格朗日元法及其在岩土力学中的应用[A].第二届全国青年岩土力学与工程学术会议论文集《岩土力学与工程》[C].大连:大连理工大学出版社,1995,22-33.
[38] Kawai T. New discrete structural models and generalization of the method of limit analysis[J], Finite Elements in Nonlinear Mechanics, NIT, Tronheim, 1977, 885-909.
[39] Cundall P A. A computer model for simulating progressive, large-scale movements in blocky rock systems[A]. Proceeding of the International Symposium on Rock Fracture[C], Nancy, France, 1971.
[40] Shi G H. Discontinuous deformation analysis: A new numerical model for the static and dynamics of block systems[D]. A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy, Berkeley: University of California, 1988.
[41] 寇晓东.无单元法及其在岩土工程中的应用[J].岩土工程学报,1998,20(1):6-9.
[42] Shi G H. Numerical manifold method[A]. Proceedings of the First International Conference on Analysis of Discontinuous Deformation (ICADD-1) (Edited by Li J C, Wang C-Y and Sheng J)[C], Chungli, Taiwan, 1995, 187-222,
[43] Chang C C. Computational simulation of progressive fracture in fiber composites[J]. Journal of Composite Materials, 1987, 21: 834-855.
[44] 汤安民,刘泽明.铝合金材料断裂形式变化规律的试验分析[J].西安理工大学学报,2003,19(3):226-229.
[45] 杨卫.细观力学和细观损伤力学[J].力学进展,1992,22(1):1-9.
[46] 邢永明,戴福隆,杨卫.准解理微裂纹裂尖纳观变形场的实验研究[J].中国科学(A辑),2000,30(8):721-726.
[47] 洪其麟译.高等断裂力学[M].北京:北京航空学出版社,1987.
[48] 匡震邦,马法尚.裂纹端部场[M].西安:西安交通大学出版社,2002.
[49] 杨连生,杨卫.强韧化材料的细观力学设计[J].力学进展,1997,27(2):177-184.
[50] 孙宗颀,饶秋华,王桂尧.剪切断裂韧度(K_(Ⅱc))确定的研究[J].岩石力学与工程学报,2002,21(2):199-203.
[51] 张对红,刘错,张静.裂纹尖端附近区域的应力应变场分析[J].油气储运,2002,20(9):13-19.
[52] 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[J].华东交通大学学报,1997,14(1):54.
[53] 郑传超,刘元镛.微观裂纹尺寸l_0的确定及其对门槛应力强度因子的影响[J].西安公路交通大学学报,1995,15(2):12-17.
[54] 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[J].重庆建筑大学学报,1998,20(2):41-46.
[55] 庞之恒.平面弹性断裂问题各阶应力强度因子的直接积分表达[J].贵州师范大学学报(自然科学版),2001,19(4):57-64.
[56] 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[J].机械强度,2003,25(5):576-579.
[57] 尹奇志,肖金生,吕运冰,李格升.孔边应力集中和裂纹尖端应力强度因子的有限元分析[J].武汉理工大学学报(交通科学与工程版),2002,26(1):47-50.
[58] Masazumi Amagai. Investigation of stress singularity field and stress intensity factors for cracks[J]. Finite Elements in Analysis and Design, 1998, 30:97-124.
[59] 朱平,沙江波,邓增杰.J-积分断裂准则在弹塑性Ⅰ-Ⅱ复合型加载下的应用探讨[J].西安交通大学学报,1994,28(2):43-48.
[60] 沙江波,朱平.Ⅰ+Ⅱ型弹塑性断裂的宏观与微观过程[J].西安交通大学学报,1996,30(12):87-94.
[61] 万建松,岳珠峰.金属韧性断裂的细观研究[J].计算力学学报,2002,19(3):320-323.
[62] Klapper H. Generation and propagation of dislocations during crystal growth[J]. Materials Chemistry and Physics, 2000, 66:101-109.
[63] 郑长卿.韧性断裂细观力学的初步研究及其应用[M].西安:西北工业大学出版社,1988,8-19.
[64] 郭田福,杨卫.平面应变脆性损伤裂纹场分析[J].固体力学学报,1995,16(2):132-139.
[65] 杨连生,杨卫.断裂过程的有限元模拟[J].计算力学学报,1997,14(4):407-412.
[66] 杨卫,郭田福,傅增力.裂尖超钝化:实验、理论与数值模拟[J].力学学报,1993,25(4):468-478.
[67] Moran B, Oritz M, Shih C F. Formulation of implicit finite elements methods for multiplicative finite deformation plasticity[J]. International Journal of Numerical Metal Engineering, 1990, 29:483-514.
[68] Guo T F, Yang W. Crack tip profiles generated by anisotropic damage[J]. International Journal of Damage Mechanics, 1993, 2:364-384.
[69] Rao Q H, Sun Z Q, Stephansson O, LI C L, Stillborg B. Shear fracture (mode Ⅱ) of brittle rock[J]. International Journal of Rock Mechanics Mining Sciences, 2003, 40:355-375.
[70] 包亦望,孙立.脆性材料在双向应力下的断裂和失效研究[J].无机材料学报,1998,13(6):847-852.
[71] 张志呈.岩石爆破裂纹的起裂、扩展、分岔与止裂[J].爆破,1999,16(4):21-24.
[72] 黎立云,黎振兹,孙宗颀.岩石的复合型断裂实验及分析[J].岩石力学与工程学报,1994,13(2):134-140.
[73] 余天堂.岩土材料固有各向异性的模拟[J].岩石力学与工程学报,2004,23(10):1604-1607.
[74] 朱子龙,李建林,王康平.三峡工程岩石拉剪蠕变断裂试验研究[J].武汉水利电力大学(宜昌)学报,1998,20(3):16-19.
[75] 徐平,夏熙伦.三峡工程花岗岩蠕变断裂与Ⅰ-Ⅱ型断裂试验研究[J].长江科学院院报,1995,12(3):31-36.
[76] 朱子龙,李建林,王康平.三峡工程岩石拉剪断裂试验研究[J].武汉水利电力大学(宜昌)学报,1998,20(1):1-6.
[77] 何伟,郑恒祥.脆性材料复合裂纹断裂判据研究[J].郑州大学学报(理学版),2003,35(2):92-94.
[78] 俞树荣,严志刚,曹睿,陈剑虹.钝化预裂纹尖端开裂对应力应变分布的影响[J].兰州理工大学学报,2004,30(1):1-4.
[79] 徐平,夏熙伦.花岗岩Ⅰ-Ⅱ复合型断裂试验及断裂数值分析[J].岩石力学与工程学报,1996,15(1):62-70.
[80] 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[J].机械强度,2003,25(3):347-351.
[81] 许斌,江见鲸.混凝土Ⅰ-Ⅱ复合型断裂判据研究[J].工程力学,1995,12(2):13-21.
[82] 胡海平,苏玉堂,常俐俐,李志潭.轴承钢GCr15混合型(Ⅰ+Ⅱ)断裂试验研究[J].太原重型机械学院学报,1994,15(1):50-56.
[83] 汤安民,师俊平.复杂应力状态断裂判据的讨论[J].西安理工大学学报,2000,16(1):47-73.
[84] 陈增涛,王铎.复合型裂纹的混合开裂准则[J].哈尔滨工业大学学报,1994,26(4):127-131.
[85] 赵艳华,徐世烺.Ⅰ-Ⅱ复合型裂纹脆性断裂的最小J_2准则[J].工程力学,2002,19(4):94-98.
[86] 李术才,朱维申.复杂应力状态下断续节理岩体断裂损伤机理研究及其应用[J].岩石力 学与工程学报,1999,18(2):142-146.
[87] 丁卫华,仵彦卿,蒲毅彬.低应变率下岩石内部裂纹演化的X射线CT方法[J].岩石力学与工程学报,2003,22(11):1793-1797.
[88] 丁卫华,仵彦卿,蒲毅彬.基于X射线CT的岩石内部裂纹宽度测量[J].岩石力学与工程学报,2003,22(9):1421-1425.
[89] Palaniswamy K, Knauss W G. On the problem of crack extension in britte solids under general loading[R]. Report SM 74-8, Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, 1974.
[90] Hussain M A, Pu S L, Underwood J H. In "Fracture Analysis, ASTM STP 560" ASTM[R], Philadelphia, 1974, 2-28.
[91] 张淳源.论非线性断裂力学的基本平衡定律(Ⅱ)—非局部理论(主要结果简介)[J].湘潭大学自然科学学报,1995,17(1):28-32.
[92] 俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998.
[93] 汤安民,张瑞平,王忠民.最大主应力与形状改变比能对断裂的影响[J].西安理工大学学报,1999,15(3):59-63.
[94] 汤安民,朱文艺,卢智先.韧性材料的几种断裂形式及判据讨论[J].机械强度,2002,24(4):566-570.
[95] 汤安民,王忠民.断裂力学判据存在的一个问题及讨论[J].机械强度,2001,23(2):222-224.
[96] 汤安民,师俊平,卢智先.韧性材料复合型断裂启裂点与开裂方向的讨论[J].机械强度,2002,24(2):266-269.
[97] 汤安民,王静.几种金属材料断裂形式变化规律的试验分析[J].实验力学,2003,18(4):440-444.
[98] 刘艳红.等W线上最大环向拉应力理论求解Ⅰ-Ⅱ复合型裂纹断裂角[J].贵州工业大学学报(自然科学版),2003,32(1):4-6.
[99] 蒋玉川,王启智.复合型裂纹扩展的形状改变比能准则[J].四川大学学报(工程科学版),2004,36(3):20-23.
[100] 杨伯源,胡宗陵.线弹簧模型柔度与裂纹开裂角之间的关系[J].合肥工业大学学报(自然科学版),1998,21(3):25-30.
[101] 朱维申,陈卫忠,申晋.雁形裂纹扩展的模型试验及断裂力学机制研究[J].固体力学学报,1998,19(4):355-360.
[102] 朱维申,张强勇,李术才.三维脆弹塑性断裂损伤模型在裂隙岩体工程中的应用[J],固体力学学报,1999,20(2):164-170.
[103] 黄明利,唐春安,朱万成.岩石破裂过程的数值模拟研究[J].岩石力学与工程学报,2000,19(4):468-471.
[104] 沈珠江.岩土破损力学:理想脆弹塑性模型[J].岩土工程学报,2003,25(3):253-257.
[105] 马君峰,吕国志.一种基于裂尖损伤区的裂纹扩展模型[J].机械科学与技术,1999,18(5):701-703.
[106] 赵爱红,虞吉林.准脆性材料的细观损伤演化模型[J].清华大学学报(自然科学版),2000,40(5):88-91.
[107] 王新友,吴科如.准脆性类材料的等效裂纹断裂模型[J].大连理工大学学报,1997, 37(1):821-824.
[108] 左宏,郑长卿.Ⅰ-Ⅱ复合型韧断特征及机理的实验研究[J].机械强度,1973,19(1):62-65.
[109] 左宏,陈宜亨,郑长卿.复合型韧性断裂实验和控制参数[J].力学学报,1999,31(5):534-541.
[110] 刘元镛,徐绯,葛东云.弹塑性裂纹扩展的裂尖参数研究[J].西北工业大学学报,2000,18(1):5-10.
[111] 荣伟,张德驺,马茂元.金属断裂韧性与微观参量的关系[J].哈尔滨船舶工程学院学报,1994,15(2):31-39.
[112] 汤安民,师俊平.铝合金材料剪切断裂实验分析[J].力学季刊,2002,23(1):82-86.
[113] 万玲,许江.压应力作用下预制裂纹脆性材料的断裂特性[J].重庆大学学报,1994,17(6):78-82.
[114] 董新龙,王礼立,虞吉林.两种类型的剪切断裂韧性及其裂纹扩展[J].宁波大学学报(理工版),2000,13(1):21-25.
[115] Zheng M, Niemi E, Zheng X. An energetic approach to predict fatigue crack initiation life of LY12CZ aluminum and 16Mn Steel[J]. Theoretical and Applied Fracture Mechanics, 1997, 26:23-28.
[116] Li-Chun Bian, Kwang Soo Kim. The minimum plastic zone radius criterion for crack initiation direction applied to surface cracks and through-cracks under mixed mode loading[J]. International Journal of Fatigue, 2004, 26:1169-1178.
[117] 董蕙茹,郭万林.三维复合型断裂的试验方法探讨[J].实验力学,2002,17(4):497-503.
[118] 程侠,于克萍,邰卫华.金属板材中裂纹尖端区的损伤分析[J].长安大学学报(建筑与环境科学版),2003,20(1):61-64.
[119] 杨楠,佟景伟,舒庆琏.裂纹纹尖弹塑性应力应变场的实验研究和数值分析[J].实验力学,2003,18(3):338-342.
[120] Newman J C Jr., Dawicke D S, Sutton M A, Bigelow C A. A fracture criterion for widespread cracking in thin-sheet aluminum alloys[A]. ICAF 17 International Committee on Aeronautical Fatigue[C], 1993, 443-468.
[121] 孙国有,薛继良,兰清生,李贵军.空洞扩张与Ⅰ-Ⅱ复合型裂纹的断裂参量[J].浙江大学学报(自然科学版),1994,28(1):1-8.
[122] 李晓红,张克实.延性材料损伤演化及材料软化的孔洞尺寸影响[J].机械强度,2003,25(1):081-084.
[123] 切列帕诺夫,黄克智译,脆性断裂力学[M].1974,北京:科学出版社,1990.
[124] 周小平,张永兴.压剪应力作用下复杂形状多裂纹应力强度因子[J].上海交通大学学报,2003,37(12):1905-1909.
[125] 李振环,匡震邦,张克实.三轴应力场中不同形状孔洞的长大及其新模型[J].计算力学学报,2000,17(4):447-455.
[126] Biner S B. Fatigue crack growth studies under mixed-mode loading[J]. International Journal of Fatigue, 2003, 23: S259-S263.
[127] Kong X M, Schluter N, Dahl W. Effect of triaxial stress on mixed-mode fracture[J]. Engineering Fracture Mechanics, 1995, 52(2):379-388.
[128] Kienzler R, Herrmann G Fracture criteria based on local properties of the Eshelby tensor[J]. Mechanics Research Communications, 2002, 29:521-527.
[129] Samal M K, Dutta B K, Kushawaha H S. A study on ductile fracture initiation in the PHT piping material of an Indian PHWR using local approach[J]. International Journal of Pressure Vessels and Piping, 1999, 76:319-330.
[130] IsaKsson P, Stahle P. A directional crack path criterion for crack growth in ductile materials subjected to shear and compressive loading under plane strain conditions[J]. International Journal of Solids and Structures, 2003, 40:3523-3536.
[131] Sutton M A, Boone M L, Ma F H, Helm J D. A combined modeling-experimental study of the crack opening displacement fracture criterion for characterization of stable crack growth under mixed mode Ⅰ/Ⅱ loading in thin sheet materials[J]. Engineering Fracture Mechanics, 2000, 66:171-185.
[132] Lee S, Ravichandran G. Crack initiation in brittle solids under multiaxial compression[J]. Engineering Fracture Mechanics, 2003, 70:1645-1658.
[133] Pardoen T, Hachez F, Marchioni B, Blyth P H, Atkins A G. Mode I fracture of sheet metal[J]. Journal of the Mechanics and Physics of Solids, 2004, 52:423-452.
[134] Simonsen B C, Tornqvist R. Experimental and numerical modeling of ductile crack propagation in large-scale shell structures[J]. Marine Structure, 2004, 17:1-27.
[135] Imad A, Wilsius J, Nait Abdelaziz M, Mesmacque G. Experiments and numerical approaches to ductile tearing in an 2024-T351 aluminum alloy[J]. International Journal of Mechanical Sciences, 2003, 45:1849-1861.
[136] Wall O. Numerical modeling of fracture initiation in large steel specimens at impact[J]. Engineering Fracture Mechanics, 2002, 69:851-863.
[137] Negre P, Steglich D, Brocks D, Kocak M. Numerical simulation of crack extension in aluminum welds[J]. Computational Materials Science, 2003, 28:723-731.
[138] Liu S, Yuh C J, Zhu X K. Tensile-shear transition in mixed-mode Ⅰ/Ⅲ fracture[J]. International Journal of Solids and Structures, 2004, 41:6147-6172.
[139] Dhar S, Dixit P M, Sethuraman J. A continuum damage mechanics model for ductile fracture[J]. International Journal of Pressure Vessels and Piping, 2000, 77: 335-344.
[140] Belytschko T, Liu Y, Gu L. Element free Galerkin method[J]. International Journal of Numerical Methods in Engineering, 1994, 37:229-256.
[141] 王水林,葛修润.流形元方法在模拟裂纹扩展中的应用[J].岩石力学与工程学报,1997,16(5):405-410.
[142] 李卧东,王元汉,陈晓波.模拟裂纹传播的新方法-无网格伽辽金法[J].岩土力学,2001,22(4):33-36.
[143] 王芝银,王思敬,杨志法.岩石大变形分析的流形方法[J].岩石力学与工程学报,1997,16(5):399-404.
[144] 莫海鸿,陈尤雯.流形法在岩石力学研究中的应用[J].华南理工大学学报(自然科学版),1998,26(9):48-53.
[145] Liu G R, Gu Y T. A point interpolation method for two-dimensional solid[J]. International Journal of Numerical Mathematical Engineering, 2001, 50:937-951.
[146] Luan M T, Tian R, Yang Q. A new mesh-free method - Finite-cover element-free method[A].