X80管线钢韧性断裂研究与有限元模拟
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摘要
西气东输工程是我国石油天然气工业的里程碑,其管道安全是与社会经济、政治、人民生命安全密切相关的重大问题。西气东输工程的设计思想采用的是夏比冲击功和DWTT断面纤维率控制方法,而作为衡量材料韧性断裂指标的JIC和CTOD因X80钢具有高韧性而导致测试无效,而广泛应用的传统断裂失效评定图存在参数确定问题。本文主要针对TMCP工艺生产的X80钢,采用具有物理意义的细观孔洞扩展模型来描述其韧性断裂特性,寻找表征X80钢韧性断裂的可靠方法。
应用不同颈缩程度的拉伸试验,通过金相观察和微细观测量,探明了X80钢中孔洞萌生的机理,第一阶段孔洞的形核是围绕钙处理硫化物,在颈缩初期即开始了;第二阶段属高应变量阶段,此时孔洞是通过MA岛/基体界面脱离形核。测定了钙处理硫化物/基体界面强度和MA岛/基体界面强度。
结合裂纹体断口观察,建立了体胞模型,对X80钢孔洞扩张进行了数值分析,对比分析了细观损伤理论中RT模型、Gurson模型、GTN模型和王自强模型的适用范围,获得了不同应力状态下孔洞扩张演化规律。针对先期形核孔洞聚合阶段的特点,分析了MA岛形核的可能性。体胞分析结果说明,在应力三轴度高于2时,完全可以不用考虑MA岛/基体界面脱离形核孔洞对断裂过程的影响。而在低应力三轴度(小于等于1)下,存在MA岛/基体界面脱离的条件,由于MA岛的含量远大于钙处理硫化物的含量,因此充分考虑二次形核对断裂过程的作用是十分必要的。
当夹杂物形态趋于球化,在不同应力状态,不同应力三轴度下,对应的体胞承载能力接近一致;而扁平椭球体孔洞则显示了较低的承载能力。微孔洞密度增加,导致孔洞扩张加快,降低材料的韧性。
考虑断裂过程区应力状态分布特点,有限元模拟得到与试验极其近似的裂纹扩展形貌,并获得了与试验记录的载荷-位移曲线高度吻合的预测曲线,使微观结构与宏观力学性能的联系有了真实的物理基础,提高了数值分析的可靠度。通过区域积分方法,获得了表征X80韧性断裂的特征值。
测定了X80钢疲劳裂纹扩展速率,采用有限元分析了X80钢管道在役运行条件下表面裂纹疲劳扩展特性,得到了不同初始形态的表面裂纹穿透过程的变化规律。运用已获得的细观力学模型对亚临界穿透裂纹疲劳扩展进行了分析,结合BS7910规范构造了先漏后破准则(即LBB)安全评定图。
Natural gas transporting project from the West to the East is a milestone in China's oil and gas industry, pipeline safety is a major issue closely related to its social, economic, political, people's lives and safety . Fracture control methods used in the project are Charpy impact energy and fiber rate in DWTT cross-section. For high toughness X80 steel , JIC and CTOD as indicators to measure fracture toughness have invalid test results , and determination of basic fracture toughness parameters in widely applied traditional Failure assessment diagram is a exist problem. This dissertation focused on charactering ductile fracture of TMCP X80 steel using micro-porous dilational model to describe the process of ductile fracture properties, looking for reliable method to characterize fracture toughness of X80 steel.
Appling a serials of tensile test of different necking degrees, by metallographic observation and micro observations, the mechanism of void nucleation in X80 steel was proved that, the first stage of voids nucleation occurs around the composite calcium sulfide inclusions, in the early necking stage; the second stage of nucleation of voids occurs at the MA island sites, in a deep necking stage, it begins voids nucleation by MA island / matrix interface decohesion. the strength of calcium sulfide/ matrix interface and the MA island / matrix interface are measured. Numerical analysis of voids growth in X80 steel had performed by cell models, Combining observation of crack body fracture surface and identifying microstructure parameters. Comparative analysis of the meso-damage theorys such as RT model, Gurson model, GTN model and Wang Ziqiang model had made, the applied scopes of them were distinguished. The void evolution laws under various stress states were obtained by finite element calculations. Voids nucleation through MA islands was discussed, and found that suffering high stress triaxiality(>2), stress at MA/matrix interfaces is not enough to take them apart from matrix, while in low stress triaxiality(≤1), interface stress is so higher to make voids nucleation. Load carry capacities of micro voids trending to spheric are near to each other, at the same stress triaxiality. But oblate micro voids show low load carry capacities, decreasing fracture toughness of X80 steel.
Considering stress distribution in the fracture process zone, prediction of crack growth in X80 specimens by finite element analysis was approximated to experimental results, and the predicted load - displacement curves were consistent to the experimental results. Well predictions of macroscopic mechanical properties using the micromechanical parameters by cell model calculations were shown, which can improve the reliability of the numerical analysis. Through domain integration, we obtained a characterization value of fracture toughness of X80.
Fatigue crack growth rates of X80 steel was tested, propagation process through the wall thickness of the surface crack in X80 pipeline under operating conditions had been performed with different initial surface crack shape using finite element analysis. Fatigue growth analysis of sub-critical breakthrough crack in pipeline had also performed using meso-mechanics model. Leak-before-break criteria (LBB) safety assessment diagram was constructed according to BS7910 specification.
应用不同颈缩程度的拉伸试验,通过金相观察和微细观测量,探明了X80钢中孔洞萌生的机理,第一阶段孔洞的形核是围绕钙处理硫化物,在颈缩初期即开始了;第二阶段属高应变量阶段,此时孔洞是通过MA岛/基体界面脱离形核。测定了钙处理硫化物/基体界面强度和MA岛/基体界面强度。
结合裂纹体断口观察,建立了体胞模型,对X80钢孔洞扩张进行了数值分析,对比分析了细观损伤理论中RT模型、Gurson模型、GTN模型和王自强模型的适用范围,获得了不同应力状态下孔洞扩张演化规律。针对先期形核孔洞聚合阶段的特点,分析了MA岛形核的可能性。体胞分析结果说明,在应力三轴度高于2时,完全可以不用考虑MA岛/基体界面脱离形核孔洞对断裂过程的影响。而在低应力三轴度(小于等于1)下,存在MA岛/基体界面脱离的条件,由于MA岛的含量远大于钙处理硫化物的含量,因此充分考虑二次形核对断裂过程的作用是十分必要的。
当夹杂物形态趋于球化,在不同应力状态,不同应力三轴度下,对应的体胞承载能力接近一致;而扁平椭球体孔洞则显示了较低的承载能力。微孔洞密度增加,导致孔洞扩张加快,降低材料的韧性。
考虑断裂过程区应力状态分布特点,有限元模拟得到与试验极其近似的裂纹扩展形貌,并获得了与试验记录的载荷-位移曲线高度吻合的预测曲线,使微观结构与宏观力学性能的联系有了真实的物理基础,提高了数值分析的可靠度。通过区域积分方法,获得了表征X80韧性断裂的特征值。
测定了X80钢疲劳裂纹扩展速率,采用有限元分析了X80钢管道在役运行条件下表面裂纹疲劳扩展特性,得到了不同初始形态的表面裂纹穿透过程的变化规律。运用已获得的细观力学模型对亚临界穿透裂纹疲劳扩展进行了分析,结合BS7910规范构造了先漏后破准则(即LBB)安全评定图。
Natural gas transporting project from the West to the East is a milestone in China's oil and gas industry, pipeline safety is a major issue closely related to its social, economic, political, people's lives and safety . Fracture control methods used in the project are Charpy impact energy and fiber rate in DWTT cross-section. For high toughness X80 steel , JIC and CTOD as indicators to measure fracture toughness have invalid test results , and determination of basic fracture toughness parameters in widely applied traditional Failure assessment diagram is a exist problem. This dissertation focused on charactering ductile fracture of TMCP X80 steel using micro-porous dilational model to describe the process of ductile fracture properties, looking for reliable method to characterize fracture toughness of X80 steel.
Appling a serials of tensile test of different necking degrees, by metallographic observation and micro observations, the mechanism of void nucleation in X80 steel was proved that, the first stage of voids nucleation occurs around the composite calcium sulfide inclusions, in the early necking stage; the second stage of nucleation of voids occurs at the MA island sites, in a deep necking stage, it begins voids nucleation by MA island / matrix interface decohesion. the strength of calcium sulfide/ matrix interface and the MA island / matrix interface are measured. Numerical analysis of voids growth in X80 steel had performed by cell models, Combining observation of crack body fracture surface and identifying microstructure parameters. Comparative analysis of the meso-damage theorys such as RT model, Gurson model, GTN model and Wang Ziqiang model had made, the applied scopes of them were distinguished. The void evolution laws under various stress states were obtained by finite element calculations. Voids nucleation through MA islands was discussed, and found that suffering high stress triaxiality(>2), stress at MA/matrix interfaces is not enough to take them apart from matrix, while in low stress triaxiality(≤1), interface stress is so higher to make voids nucleation. Load carry capacities of micro voids trending to spheric are near to each other, at the same stress triaxiality. But oblate micro voids show low load carry capacities, decreasing fracture toughness of X80 steel.
Considering stress distribution in the fracture process zone, prediction of crack growth in X80 specimens by finite element analysis was approximated to experimental results, and the predicted load - displacement curves were consistent to the experimental results. Well predictions of macroscopic mechanical properties using the micromechanical parameters by cell model calculations were shown, which can improve the reliability of the numerical analysis. Through domain integration, we obtained a characterization value of fracture toughness of X80.
Fatigue crack growth rates of X80 steel was tested, propagation process through the wall thickness of the surface crack in X80 pipeline under operating conditions had been performed with different initial surface crack shape using finite element analysis. Fatigue growth analysis of sub-critical breakthrough crack in pipeline had also performed using meso-mechanics model. Leak-before-break criteria (LBB) safety assessment diagram was constructed according to BS7910 specification.
引文
[1]潘家华.中国天然气工业的发展前景[J].油气储运. 2005, 24(6): 1-3.
[2]李鹤林.天然气输送钢管研究与应用中的几个热点问题[J].中国机械工程. 2001, 13(12): 349-352.
[3] N Sanderson R O M J. Study of X100 line pipe costs point to potential savings[J]. Oil and Gas Journal. 1999, 97(1): 54-57.
[4] Ag Glover D H D D. High-strength steel becomes standard on Alberta gas system[J]. Oil and Gas Journal. 1999, 97(1): 44-50.
[5] Mk Graf H H C H. High-strength large diameter pipe for long-distance high-pressure gas pipelines[J]. International Journal of Offshore and Polar Engineering. 2004, 14(1): 69-74.
[6]王仪康.高压输气管线材料和相关问题[J].焊管. 2000, 23(3): 89-93.
[7]王仪康.高压输气管线用钢[J].焊管. 2002, 25(1): 1-10.
[8] Makino H, Kubo T, Shiwaku T, et al. Prediction for crack propagation and arrest of shear fracture in ultra-high pressure natural gas pipelines[J]. ISIJ international. 2001, 41(4): 381-388.
[9] Maxey W A, Kiefner J F, Eiber R J. Ductile fracture arrest in gas pipelines[R]. American Gas Association, Arlington, VA, 1976.
[10] Poynton W. Design and Application of Shear Fracture Propagation Studies[J]. ASME Publication No. 74-Mat-10, American Society of Mechanical Engineers, United Engineering Center, 345 E. 47 th St., New York, N. Y. 10017. 1974.
[11]帅健陈福来.输气管道延性断裂的止裂结构及韧性确定方法[J].压力容器. 2006, 23(7): 39-43.
[12]冯耀荣马秋荣霍春勇.管线断裂控制参量的研究[J].焊管. 2002, 25(4): 15-20.
[1] Timoshenko S. History of Strength of Materials[M]. New York: McGraw-Hill, 1953.
[2] Yu M. Advances in strength theories for materials under complex stress state in the 20th Century[J]. Appl. Mech. Rev. 2002, 55(3): 169-218.
[3] Shield R. On Coulomb’s law of failure in soils[J]. J. Mech. Phys. Solids. 1955, 4(1): 10-16.
[4] Paul B. A modification of the Coulomb-Mohr theory of fracture[J]. ASME J. Appl. Mech. 1961, 28(2): 259-268.
[5] Harkness R. An essay on Mohr-Coulomb[M]. Stress-Strain Behaviour of Soils, Parry R, Foulis Co., 1971, 212-219.
[6] Pankaj M K. Benchmark tests in Mohr-Coulomb elastoplasticity[M]. Computational Mechanics, Yk Cheung H L A A, Rotterdam:Balkema, 1991, 753-759.
[7] Heyman J. Coulomb’s Menoir on Statics[M]. London: Imperial College Press, 1997.
[8] Schajer G. Mohr-Coulomb criterion expressed in terms of stress invariants[J]. ASME J. Appl. Mech. 1998,65(7): 1066-1068.
[9] Griffith A A. The Phenomena of Rupture and Flow in Solids[J]. Philosophical Transactions of the Royal Society of London. Series A. 1920, 221: 163-198.
[10] Orowan E. Discussion in Symposium on Internal Stresses in Metals and Alloys[C]. Lodon: Institute of Metals, 1948.
[11] Irwin G R. Fracturing of Metals[M]. Ohio: American Society for metals, 1948: 147-166.
[12] Irwing G R. Analysis of stresses and strains near the end of a crack traversing a plate[J]. J. Appl. Mech. 1957, 24: 361-364.
[13] Dugdale D S. Yielding of Steel Sheets Containing Slits[J]. J. Mech. Phys. Solids. 1960, 8(2): 100-104.
[14] Barenblatt G I. The Mathematical Theory of Equilibrium Cracks in Brittle Fracture[J]. Advances in applied mechanics. 1962, 7: 55-129.
[15] Wells A A. Application of fracture mechanics at and beyond general yielding[J]. British Welding Journal. 1963, 10: 563-570.
[16] Rice J R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks[J]. J. Appl. Mech. 1968, 35(2): 379-386.
[17] Hutchinson J W. Singular behaviour at the end of a tensile crack in a hardening material[J]. J Mech Phys Solids. 1968, 16(1): 13-31.
[18] Rice J R, Rosengren G F. Plane strain deformation near a crack tip in a power law hardening material[J]. J Mech Phys Solids. 1968, 16(1): 1-12.
[19] Begley J A, Landes J D. The J integral as a fracture criterion[C]. Part II,ASTM STP-514: American Society for Testing and Materials, 1972.
[20] Zener C. A Theoretical Criterion for the Initiation of Slip Bands[J]. Physical Review. 1946, 69(3-4): 128-129.
[21] Stroh A N. The formation of cracks as a result of plastic flow[J]. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1954, 223(1154): 404-414.
[22] Cottrell A H. Theory of brittle fracture in steel and similar metals[J]. Trans. Met. Soc. AIME. 1958, 212: 192-203.
[23] Cottrell A H. Dislocations and plastic flow in crystals[J]. American Journal of Physics. 1954, 22: 242-243.
[24] Jr. C. J M, Cohen M. Initiation of cleavage in polycrystalline iron[J]. Acta Metallurgica. 1965, 13(6): 591-604.
[25] Smith E. Physical Basis of Yield and Fracture[C]. Institute of Physics and Physical Society,Oxford, United Kingdom: 1966.
[26] Wilshaw T R, Rau C A, Tetelman A S. A general model to predict the elastic-plastic stress distribution and fracture strength of notched bars in plane strain bending[J]. Engineering Fracture Mechanics. 1968, 1(1): 191-211.
[27] Tetelman A S, Wilshaw T R, Rau C A. The critical tensile stress criterion for cleavage[J]. International Journal of Fracture. 1968, 4(2): 147-156.
[28] Ritchie R O, Knott J F, Rice R. On the relationship between critical tensile stress and fracture stress in mild steels[J]. J Mech Phys Solids. 1973, 21(3): 395-410.
[29] Curry D. Comparison between two models of cleavage fracture[J]. Met. Sci. 1980, 14(2): 78-80.
[30] Argon A S, Im J, Safoglu R. Cavity formation from inclusions in ductile fracture[J]. Metall. Trans. A. 1975, 6(4): 825-837.
[31] Goods S H, Brown L M. The nucleation of cavities by plastic deformation[J]. Acta Metall. 1979, 27(1): 1-15.
[32] Edelson B I, Baldwin J W. The effect of second phases on the mechanical properties of alloys[J]. Trans.ASM. 1962, 55: 230-250.
[33] Becker R, Smelser R, Richmond O, et al. The effect of void shape on void growth and ductility in axisymmetric tension tests[J]. Metallurgical and Materials Transactions A. 1989, 20(5): 853-861.
[34] Kwon D, Asaro R J. A study of void nucleation, growth, and coalescence in spheroidized 1518 steel[J]. Metallurgical and Materials Transactions A. 1990, 21(1): 117-134.
[35] Thompson A W. Modeling of local strains in ductile fracture[J]. Metallurgical and Materials Transactions A. 1987, 18(11): 1877-1886.
[36] Thomason P. A View on Ductile-Fracture Modelling[J]. Fatigue & Fracture of Engineering Materials & Structures. 1998, 21: 1105-1122.
[37] Kwon D. Interfacial decohesion around spheroidal carbide particles[J]. Scripta metallurgica. 1988, 22(7): 1161-1164.
[38] Leroy G, Embury J, Edwards G, et al. A model of ductile fracture based on the nucleation and growth of voids[J]. Acta Metallurgica. 1981, 29(8): 1509-1520.
[39] Mcclintock F A. A criterion for ductile fracture by the growth of holes[J]. J. appl. Mech. 1968, 35: 363-371.
[40] Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. J Mech Phys Solids. 1969, 17(3): 201-217.
[41] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part I-yield criteria and flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology. 1977, 99(1): 2-15.
[42] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta Metall. 1984, 32(1): 157-169.
[43] Chu C C, Needleman A. Void nucleation effects in biaxially stretched sheets[J]. Journal of Engineering Materials and Technology. 1980, 102(3): 249-256.
[44] Kuna M, Sun D Z. Three-dimensional cell model analyses of void growth in ductile materials[J]. International Journal of Fracture. 1996, 81(3): 235-258.
[45] Pardoen T, Doghri I, Delannay F. Experimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars[J]. Acta Materialia. 1998, 46(2): 541-552.
[46] Jie W, Yonggang H, Keh-Chih H. The void-size effect on plastic flow localization in the Gurson model[J]. Acta Mechanica Sinica. 2004, 20(4): 393-399.
[47] Liu B, Huang Y, Li M, et al. A study of the void size effect based on the Taylor dislocation model[J]. International Journal of Plasticity. 2005, 21(11): 2107-2122.
[48] Pardoen T, Hutchinson J W. An extended model for void growth and coalescence[J]. Journal of the Mechanics and Physics of Solids. 2000, 48(12): 2467-2512.
[49] Perrin G, Leblond J B. Accelerated void growth in porous ductile solids containing two populations of cavities[J]. International Journal of Plasticity. 2000, 16(1): 91-120.
[50] Ristinmaa M. Void growth in cyclic loaded porous plastic solid[J]. Mechanics of Materials. 1997, 26(4): 227-245.
[51] Thomson C, Worswick M J, Pilkey A, et al. Modeling void nucleation and growth within periodic clusters of particles[J]. Journal of the Mechanics and Physics of Solids. 1998, 47(1): 1-26.
[52] Wen J, Huang Y, Hwang K C, et al. The modified Gurson model accounting for the void size effect[J]. International Journal of Plasticity. 2005, 21(2): 381-395.
[53] Zhang K S, Bai J B, Fran D. Numerical analysis of the influence of the Lode parameter on void growth[J]. International Journal of Solids and Structures. 2001, 38(32-33): 5847-5856.
[54] Zhang Z L. A SENSITIVITY ANALYSIS OF MATERIAL PARAMETERS FOR THE GURSONCONSTITUTIVE MODEL[J]. Fatigue & Fracture of Engineering Materials & Structures. 1996, 19(5): 561-570.
[55] Thomason P F. Three-dimensional model for ductile fracture by the growth and coalescence of microvoids.[J]. ACTA METALLURG. 1985, 33(6): 1087-1095.
[56] Weck A, Wilkinson D S, Maire E, et al. Visualization by X-ray tomography of void growth and coalescence leading to fracture in model materials[J]. Acta Materialia. 2008, 56(12): 2919-2928.
[57] Cox T B, Low J R. An investigation of the plastic fracture of AISI 4340 and 18 Nickel-200 grade maraging steels[J]. Metallurgical and Materials Transactions B. 1974, 5(6): 1457-1470.
[58] Thomason P F. Ductile fracture of metals[M]. Oxfood: Pergamon Press, 1990: 219.
[59] Thomason P F. Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids.[J]. ACTA METALLURG. 1985, 33(6): 1079-1085.
[60] Lemaitre J. How to use damage mechanics[J]. Nuclear Engineering and Design. 1984, 80(3): 233-245.
[61] Latham D J, Cockcroft M G. A simple criterion of fracture for ductile metals[J]. UK National Engineering Laboratory Report. 1966, 240.
[62]于忠奇.基于LEMAITRE损伤理论的韧性断裂准则建立及板料成形极限预测[D].哈尔滨工业大学, 2003.
[63]郑长卿.延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.
[64] Shichun W U, Hua L. A kinetic equation for ductile damage at large plastic strain[J]. Journal of materials processing technology. 1990, 21(3): 295-302.
[65] Clift S E, Hartley P, Sturgess C E, et al. Fracture prediction in plastic deformation processes[J]. International journal of mechanical sciences. 1990, 32(1): 1-17.
[66] Irwin G R. Fracture of pressure vessels[J]. Materials for Missiles and Spacecraft. 1963: 204-229.
[67] Hood J E. Fracture of steel pipelines[J]. International Journal of Pressure Vessels and Piping. 1974, 2(3): 165-178.
[68] Duffy A R, Mcclure G M, Eiber R J, et al. Fracture design practices for pressure piping[J]. Fracture. 1969, 5: 159-232.
[69] Sharples J K, Clayton A M. A leak-before-break assessment method for pressure vessels and some current unresolved issues[J]. International Journal of Pressure Vessels and Piping. 1990, 43(1-3): 317-327.
[1] Qiu H, Mori H, Enoki M, et al. Evaluation of ductile fracture of structural steels by microvoid model[J]. ISIJ international. 1999, 39(4): 358-364.
[2] Poruks P, Yakubtsov I, Boyd J D. Martensite–ferrite interface strength in a low-carbon bainitic steel[J]. Scripta Materialia. 2006, 54(1): 41-45.
[3]翁宇庆等.超细晶钢——钢的组织细化理论与控制技术[M].北京:冶金工业出版社, 2003.
[4] Smith Y E, Coldren A P, Cryderman R L. Toward Improved Ductility and Toughness, Climax Molybdenum Co[J]. Ann Arbor, MI. 1971, 119.
[5]李鹤林,郭生武,冯耀荣.高强度微合金管线钢显微组织分析与鉴别图谱[M].北京:石油工业出版社, 2001.
[6] Ramberg W O W R. Description of stress-strain curves by three parameters[R]. Washington DC: National Advisory Committee For Aeronautics, 1943.
[7] Bridgeman P W. Studies in Large Plastic Flow and Fracture[M]. New York: McGraw-Hill, 1952.
[8] Zhang Z L, Hauge M, Qdegard J, et al. Determining material true stress-strain curve from tensile specimens with rectangular cross-section[J]. International Journal of Solids and Structures. 1999, 36(23): 3497-3516.
[9]陈篪.金属断裂研究文集[M].冶金工业出版社, 1978.
[10]叶裕恭.基于偏析线的圆棒颈缩分析[J].力学学报. 1986, 18(1): 46-56.
[11]刘瑞堂,姜风春.单轴拉伸试样的颈缩过程及形变强化特性的影响[J].物理测试. 1998, 10(5): 5-8.
[12]王心美,岳珠峰.正交各向异性材料拉伸圆棒的颈缩研究[J].燃气涡轮试验与研究. 2004, 17(002): 33-35.
[13] Zhang K S. Fracture prediction and necking analysis[J]. Engineering Fracture Mechanics. 1995, 52(3): 575-582.
[14] Argon A S, Im J, Safoglu R. Cavity formation from inclusions in ductile fracture[J]. Metall. Trans. A. 1975, 6(4): 825-837.
[15] Beremin F. Cavity formation from inclusions in ductile fracture of A508 steel[J]. Metallurgical and Materials Transactions A. 1981, 12(5): 723-731.
[16] Wang C, Wu X, Liu J, et al. Study on M/A islands in pipeline steel X70[J]. Journal of University of Science and Technology Beijing. 2005, 12(1): 43-47.
[17] Shanmugam S, Misra R D K, Hartmann J, et al. Microstructure of high strength niobium-containing pipeline steel[J]. Materials Science and Engineering A. 2006, 441: 215-229.
[18] Leroy G, Embury J, Edwards G, et al. A model of ductile fracture based on the nucleation and growth of voids[J]. Acta Metallurgica. 1981, 29(8): 1509-1520.
[19] Kwon D. Interfacial decohesion around spheroidal carbide particles[J]. Scripta metallurgica. 1988, 22(7): 1161-1164.
[1]郑长卿.延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.
[2] Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. J Mech Phys Solids. 1969, 17(3): 201-217.
[3] Higham D J, Higham N J. MATLAB guide[M]. Society for Industrial Mathematics, 2005.
[4] Mcclintock F A. A criterion for ductile fracture by the growth of holes[J]. J. appl. Mech. 1968, 35: 363-371.
[5] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part I-yield criteria and flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology. 1977, 99(1): 2-15.
[6] Budiansky B, Hutchinson J W, Slutsky S. Void growth and collapse in viscous solids[J]. Mechanics of Solids. 1982: 13-45.
[7] Lee B J, Mear M E. Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids[J]. Journal of the Mechanics and Physics of Solids. 1992, 40(8): 1805-1836.
[8] Yee K C, Mear M E. Effect of void shape on the macroscopic response of non-linear porous solids[J]. International journal of plasticity. 1996, 12(1): 45-68.
[9] Gologanu M, Leblond J B, Devaux J. Approximate models for ductile metals containing nonspherical voids—case of axisymmetric oblate ellipsoidal cavities[J]. Journal of Engineering Materials and Technology. 1994, 116: 290.
[10] Tvergaard V. On localization in ductile materials containing spherical voids[J]. International Journal of Fracture. 1982, 18(4): 237-252.
[11] Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions[J]. InternationalJournal of Fracture. 1981, 17(4): 389-407.
[12] Hom C L, Mcmeeking R M. Void growth in elastic-plastic materials[J]. Journal of Applied Mechanics. 1989, 56: 309.
[13] ABAQUS Theory Manual Version 6.8, Hibbitt, Karlsson & Sorensen Inc, 2008.
[14]王自强,秦嘉亮.含空洞非线性材料的本构势和空洞扩展率[J].固体力学学报. 1989, 10(002): 127-142.
[15] Thomason P F. Three-dimensional model for ductile fracture by the growth and coalescence of microvoids.[J]. ACTA METALLURG. 1985, 33(6): 1087-1095.
[16] Thomason P F. Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids.[J]. ACTA METALLURG. 1985, 33(6): 1079-1085.
[17] Clift S E, Hartley P, Sturgess C E, et al. Fracture prediction in plastic deformation processes[J]. International journal of mechanical sciences. 1990, 32(1): 1-17.
[18] Thomason P. A View on Ductile-Fracture Modelling[J]. Fatigue & Fracture of Engineering Materials & Structures. 1998, 21: 1105-1122.
[19] Ragab A R. A model for ductile fracture based on internal necking of spheroidal voids[J]. Acta Materialia. 2004, 52(13): 3997-4009.
[20] Benzerga A A. Micromechanics of coalescence in ductile fracture[J]. Journal of the Mechanics and Physics of Solids. 2002, 50(6): 1331-1362.
[21] Needleman A, Tvergaard V. Analysis of ductile rupture in notched bars.[J]. J. MECH. PHYS. SOL. 1984, 32(6): 461-490.
[22] Zhang Z L, Niemi E. A new failure criterion for the Gurson-Tvergaard dilational constitutive model[J]. International Journal of Fracture. 1994, 70(4): 321-334.
[23] Sun D Z, Sester M, Schmitt W. Development and Application of Micromechanical Material Models for the Characterization of Materials[J]. JOURNAL DE PHYSIQUE 4. 1996, 6(6): 431-439.
[24] Redanz P, Fleck N A, Mcmeeking R M. Failure of a Porous Solid from a Deep Notch[J]. International Journal of Fracture. 1997, 88(2): 187-202.
[25] P C P. Fracture modelling of WC-Co hardmetals using crystal plasticity theory and the Gurson model[J]. Fatigue & Fracture of Engineering Materials & Structures. 1999, 22(1): 77-86.
[26] Pardoen T, Doghri I, Delannay F. Experimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars[J]. Acta Materialia. 1998, 46(2): 541-552.
[27] Becker R, Needleman A, Richmond O, et al. Void growth and failure in notched bars[J]. Journal of the Mechanics and Physics of Solids. 1988, 36(3): 317-351.
[28] Koplik J, Needleman A. Void growth and coalescence in porous plastic solids[J]. Int. J. Solids Struct. 1988, 24(8): 835-853.
[29] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta Metall. 1984, 32(1): 157-169.
[30] Schmitt W, Sun D Z, Kienzler R. Application of micro-mechanical models to the prediction of ductile fracture[J]. Localized Damage Computer-Aided Assessment and Control. 1990, 1: 349-359.
[31] Xia L, Shih C F, Hutchinson J W. A computational approach to ductile crack growth under large scale yielding conditions[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(3): 389-413.
[32] Tvergaard V. Studies of void growth in a thin ductile layer between ceramics[J]. Computational Mechanics. 1997, 20(1): 186-191.
[33] Leroy G, Embury J, Edwards G, et al. A model of ductile fracture based on the nucleation and growth of voids[J]. Acta Metallurgica. 1981, 29(8): 1509-1520.
[34] Kwon D. Interfacial decohesion around spheroidal carbide particles[J]. Scripta metallurgica. 1988, 22(7): 1161-1164.
[1]罗金恒,赵新伟,李新华,等. X80管线钢断裂韧性研究[J].压力容器. 2007, 24(008): 6-9.
[2] Sun D Z, Sester M, Schmitt W. Development and Application of Micromechanical Material Models for the Characterization of Materials[J]. JOURNAL DE PHYSIQUE 4. 1996, 6(6): 431-439.
[3] Brocks W, Sun D Z, Nig H. Verification of the transferability of micromechanical parameters by cell model calculations with visco-plastic materials[J]. International Journal of Plasticity. 1995, 11(8): 971-989.
[4] Bauvineau L, Burlet H, Eripret C, et al. Modelling Ductile Stable Crack Growth in a C-Mn Steel with Local Approaches[J]. Journal de Physique(France) IV(France). 1996, 6(6): 33-42.
[5] Gao X, Faleskog J, Shih C F. Cell model for nonlinear fracture analysis-II. Fracture-process calibration and verification[J]. International Journal of Fracture. 1998, 89(4): 375-398.
[6] Hachez F, Atkins A G, Dodds R H, et al. MICROMECHANICS-BASED MODELLING OF DUCTILE TEARING IN THIN PLATES[C]. KTH, Stockholm, Sweden: 2004.
[7] Simonsen B C, T R. Experimental and numerical modelling of ductile crack propagation in large-scale shell structures[J]. Marine Structures. 2004, 17(1): 1-27.
[8] Feucht M, Sun D Z, Erhart T, et al. Recent Development and Applications of the Gurson Model[J]. Proceedings to the Fifth LS-DYNA Anwenderforum, Ulm, Germany. 2006.
[9] Xia L, Shih C F. Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(2): 233-259.
[10] Xia L, Shih C F. Ductile crack growth-II. Void nucleation and geometry effects on macroscopic fracture behavior[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(12): 1953-1981.
[11] Xia L, Shih C F, Hutchinson J W. A computational approach to ductile crack growth under large scale yielding conditions[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(3): 389-413.
[12] Liu Y, Murakami S, Kanagawa Y. Mesh-dependence and stress singularity in finite element analysis of creep crack growth by continuum damage mechanics approach[J]. European journal of mechanics. A. Solids. 1994, 13(3): 395-418.
[13] Matos P P, Mcmeeking R M, Charalambides P G, et al. A method for calculating stress intensities in bimaterial fracture[J]. International Journal of Fracture. 1989, 40(4): 235-254.
[14] Stolk J, Verdonschot N, Mann K A, et al. Prevention of mesh-dependent damage growth in finite element simulations of crack formation in acrylic bone cement[J]. Journal of biomechanics. 2003, 36(6): 861-871.
[15] Tvergaard V, Hutchinson J W. Two mechanisms of ductile fracture: void by void growth versus multiple void interaction[J]. International Journal of Solids and Structures. 2002, 39(13-14): 3581-3597.
[16] Knott J F. Micromechanisms of fibrous crack extension in engineering alloys[J]. Metal Science. 1980, 14(9): 327-336.
[17] Landes J D. The blunting line in elastic-plastic fracture[J]. Fatigue & Fracture of Engineering Materials &Structures. 1995, 18(11): 1289-1297.
[18] Needleman A, Tvergaard V. Analysis of ductile rupture in notched bars.[J]. J. MECH. PHYS. SOL. 1984, 32(6): 461-490.
[19] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta Metall. 1984, 32(1): 157-169.
[20]马法尚,匡震邦.韧性断裂的微观模型及其在约束断裂中的应用.[J].力学学报. 1995, 27(S1): 120-124.
[21]汤安民,师俊平.几种金属材料宏观断裂形式的试验研究[J].应用力学学报. 2004, 21(003): 142-144.
[22] Khan S, Khraisheh M K. Analysis of mixed mode crack initiation angles under various loading conditions[J]. Engineering Fracture Mechanics. 2000, 67(5): 397-419.
[23]孙国有,魏志刚,王晓春,等.空穴机理在45钢剪切型断裂过程中的作用[J].机械科学与技术. 2001, 20(z1): 66-70.
[24]黄克智,余寿文.弹塑性断裂力学[M].北京:清华大学出版社, 1985.
[25]王波,杨卫,黄克智.基于非J控制扩展的安全评定方法[J].力学学报. 1992, 24(003): 339-349.
[26] Rice J R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks[J]. J. Appl. Mech. 1968, 35(2): 379-386.
[1] Ukadgaonker V G, Babu R S. Review of work related to " leak-before-break " assessment[J]. International Journal of Pressure Vessels and Piping. 1996, 69(2): 135-148.
[2] Bsi. Guide to methods for assessing the acceptability of flaws in metallic structures[S]. BS 7910-2005.
[3] Paris P, Erdogan F. A critical analysis of crack propagation laws[J]. Journal of Basic Engineering. 1963, 85(4): 528-534.
[4] Newman J C, Raju I S. An empirical stress-intensity factor equation for the surface crack[J]. Engineering Fracture Mechanics. 1981, 15(1): 185-192.
[5]邱保文,袁泽喜,周桂峰.油气管线裂纹型缺陷的疲劳寿命预测[J].武汉科技大学学报:自然科学版. 2009, 32(003): 247-250.
[6] Lin X B, Smith R A. Numerical analysis of fatigue growth of external surface cracks in pressurized cylinders[J]. International Journal of Pressure Vessels and Piping. 1997, 71(4): 293-300.
[7]李云龙,庄传晶,冯耀荣,等.油气输送管道疲劳寿命分析及预测[J].油气储运. 2004, 23(12): 41-43.
[8]赵新伟,罗金恒,董保胜,等.西气东输管道安全评价[J].理化检验:物理分册. 2005, 41(1): 82-88.
[9] Kiefner J F, Maxey W A, Eiber R J, et al. Failure stress levels of flaws in pressurized cylinders[J]. ASTM special technical publication. 1973(536): 461-481.
[10]冯耀荣,霍春勇,高惠临,等.长输管道稳态气体泄漏率的计算[J].油气储运. 2002, 21(8): 11-15.
[11]王占山,张化光,冯健,等.长距离流体输送管道泄漏检测与定位技术的现状与展望[J].化工自动化及仪表. 2003, 30(5): 5-10.
[2]李鹤林.天然气输送钢管研究与应用中的几个热点问题[J].中国机械工程. 2001, 13(12): 349-352.
[3] N Sanderson R O M J. Study of X100 line pipe costs point to potential savings[J]. Oil and Gas Journal. 1999, 97(1): 54-57.
[4] Ag Glover D H D D. High-strength steel becomes standard on Alberta gas system[J]. Oil and Gas Journal. 1999, 97(1): 44-50.
[5] Mk Graf H H C H. High-strength large diameter pipe for long-distance high-pressure gas pipelines[J]. International Journal of Offshore and Polar Engineering. 2004, 14(1): 69-74.
[6]王仪康.高压输气管线材料和相关问题[J].焊管. 2000, 23(3): 89-93.
[7]王仪康.高压输气管线用钢[J].焊管. 2002, 25(1): 1-10.
[8] Makino H, Kubo T, Shiwaku T, et al. Prediction for crack propagation and arrest of shear fracture in ultra-high pressure natural gas pipelines[J]. ISIJ international. 2001, 41(4): 381-388.
[9] Maxey W A, Kiefner J F, Eiber R J. Ductile fracture arrest in gas pipelines[R]. American Gas Association, Arlington, VA, 1976.
[10] Poynton W. Design and Application of Shear Fracture Propagation Studies[J]. ASME Publication No. 74-Mat-10, American Society of Mechanical Engineers, United Engineering Center, 345 E. 47 th St., New York, N. Y. 10017. 1974.
[11]帅健陈福来.输气管道延性断裂的止裂结构及韧性确定方法[J].压力容器. 2006, 23(7): 39-43.
[12]冯耀荣马秋荣霍春勇.管线断裂控制参量的研究[J].焊管. 2002, 25(4): 15-20.
[1] Timoshenko S. History of Strength of Materials[M]. New York: McGraw-Hill, 1953.
[2] Yu M. Advances in strength theories for materials under complex stress state in the 20th Century[J]. Appl. Mech. Rev. 2002, 55(3): 169-218.
[3] Shield R. On Coulomb’s law of failure in soils[J]. J. Mech. Phys. Solids. 1955, 4(1): 10-16.
[4] Paul B. A modification of the Coulomb-Mohr theory of fracture[J]. ASME J. Appl. Mech. 1961, 28(2): 259-268.
[5] Harkness R. An essay on Mohr-Coulomb[M]. Stress-Strain Behaviour of Soils, Parry R, Foulis Co., 1971, 212-219.
[6] Pankaj M K. Benchmark tests in Mohr-Coulomb elastoplasticity[M]. Computational Mechanics, Yk Cheung H L A A, Rotterdam:Balkema, 1991, 753-759.
[7] Heyman J. Coulomb’s Menoir on Statics[M]. London: Imperial College Press, 1997.
[8] Schajer G. Mohr-Coulomb criterion expressed in terms of stress invariants[J]. ASME J. Appl. Mech. 1998,65(7): 1066-1068.
[9] Griffith A A. The Phenomena of Rupture and Flow in Solids[J]. Philosophical Transactions of the Royal Society of London. Series A. 1920, 221: 163-198.
[10] Orowan E. Discussion in Symposium on Internal Stresses in Metals and Alloys[C]. Lodon: Institute of Metals, 1948.
[11] Irwin G R. Fracturing of Metals[M]. Ohio: American Society for metals, 1948: 147-166.
[12] Irwing G R. Analysis of stresses and strains near the end of a crack traversing a plate[J]. J. Appl. Mech. 1957, 24: 361-364.
[13] Dugdale D S. Yielding of Steel Sheets Containing Slits[J]. J. Mech. Phys. Solids. 1960, 8(2): 100-104.
[14] Barenblatt G I. The Mathematical Theory of Equilibrium Cracks in Brittle Fracture[J]. Advances in applied mechanics. 1962, 7: 55-129.
[15] Wells A A. Application of fracture mechanics at and beyond general yielding[J]. British Welding Journal. 1963, 10: 563-570.
[16] Rice J R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks[J]. J. Appl. Mech. 1968, 35(2): 379-386.
[17] Hutchinson J W. Singular behaviour at the end of a tensile crack in a hardening material[J]. J Mech Phys Solids. 1968, 16(1): 13-31.
[18] Rice J R, Rosengren G F. Plane strain deformation near a crack tip in a power law hardening material[J]. J Mech Phys Solids. 1968, 16(1): 1-12.
[19] Begley J A, Landes J D. The J integral as a fracture criterion[C]. Part II,ASTM STP-514: American Society for Testing and Materials, 1972.
[20] Zener C. A Theoretical Criterion for the Initiation of Slip Bands[J]. Physical Review. 1946, 69(3-4): 128-129.
[21] Stroh A N. The formation of cracks as a result of plastic flow[J]. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1954, 223(1154): 404-414.
[22] Cottrell A H. Theory of brittle fracture in steel and similar metals[J]. Trans. Met. Soc. AIME. 1958, 212: 192-203.
[23] Cottrell A H. Dislocations and plastic flow in crystals[J]. American Journal of Physics. 1954, 22: 242-243.
[24] Jr. C. J M, Cohen M. Initiation of cleavage in polycrystalline iron[J]. Acta Metallurgica. 1965, 13(6): 591-604.
[25] Smith E. Physical Basis of Yield and Fracture[C]. Institute of Physics and Physical Society,Oxford, United Kingdom: 1966.
[26] Wilshaw T R, Rau C A, Tetelman A S. A general model to predict the elastic-plastic stress distribution and fracture strength of notched bars in plane strain bending[J]. Engineering Fracture Mechanics. 1968, 1(1): 191-211.
[27] Tetelman A S, Wilshaw T R, Rau C A. The critical tensile stress criterion for cleavage[J]. International Journal of Fracture. 1968, 4(2): 147-156.
[28] Ritchie R O, Knott J F, Rice R. On the relationship between critical tensile stress and fracture stress in mild steels[J]. J Mech Phys Solids. 1973, 21(3): 395-410.
[29] Curry D. Comparison between two models of cleavage fracture[J]. Met. Sci. 1980, 14(2): 78-80.
[30] Argon A S, Im J, Safoglu R. Cavity formation from inclusions in ductile fracture[J]. Metall. Trans. A. 1975, 6(4): 825-837.
[31] Goods S H, Brown L M. The nucleation of cavities by plastic deformation[J]. Acta Metall. 1979, 27(1): 1-15.
[32] Edelson B I, Baldwin J W. The effect of second phases on the mechanical properties of alloys[J]. Trans.ASM. 1962, 55: 230-250.
[33] Becker R, Smelser R, Richmond O, et al. The effect of void shape on void growth and ductility in axisymmetric tension tests[J]. Metallurgical and Materials Transactions A. 1989, 20(5): 853-861.
[34] Kwon D, Asaro R J. A study of void nucleation, growth, and coalescence in spheroidized 1518 steel[J]. Metallurgical and Materials Transactions A. 1990, 21(1): 117-134.
[35] Thompson A W. Modeling of local strains in ductile fracture[J]. Metallurgical and Materials Transactions A. 1987, 18(11): 1877-1886.
[36] Thomason P. A View on Ductile-Fracture Modelling[J]. Fatigue & Fracture of Engineering Materials & Structures. 1998, 21: 1105-1122.
[37] Kwon D. Interfacial decohesion around spheroidal carbide particles[J]. Scripta metallurgica. 1988, 22(7): 1161-1164.
[38] Leroy G, Embury J, Edwards G, et al. A model of ductile fracture based on the nucleation and growth of voids[J]. Acta Metallurgica. 1981, 29(8): 1509-1520.
[39] Mcclintock F A. A criterion for ductile fracture by the growth of holes[J]. J. appl. Mech. 1968, 35: 363-371.
[40] Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. J Mech Phys Solids. 1969, 17(3): 201-217.
[41] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part I-yield criteria and flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology. 1977, 99(1): 2-15.
[42] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta Metall. 1984, 32(1): 157-169.
[43] Chu C C, Needleman A. Void nucleation effects in biaxially stretched sheets[J]. Journal of Engineering Materials and Technology. 1980, 102(3): 249-256.
[44] Kuna M, Sun D Z. Three-dimensional cell model analyses of void growth in ductile materials[J]. International Journal of Fracture. 1996, 81(3): 235-258.
[45] Pardoen T, Doghri I, Delannay F. Experimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars[J]. Acta Materialia. 1998, 46(2): 541-552.
[46] Jie W, Yonggang H, Keh-Chih H. The void-size effect on plastic flow localization in the Gurson model[J]. Acta Mechanica Sinica. 2004, 20(4): 393-399.
[47] Liu B, Huang Y, Li M, et al. A study of the void size effect based on the Taylor dislocation model[J]. International Journal of Plasticity. 2005, 21(11): 2107-2122.
[48] Pardoen T, Hutchinson J W. An extended model for void growth and coalescence[J]. Journal of the Mechanics and Physics of Solids. 2000, 48(12): 2467-2512.
[49] Perrin G, Leblond J B. Accelerated void growth in porous ductile solids containing two populations of cavities[J]. International Journal of Plasticity. 2000, 16(1): 91-120.
[50] Ristinmaa M. Void growth in cyclic loaded porous plastic solid[J]. Mechanics of Materials. 1997, 26(4): 227-245.
[51] Thomson C, Worswick M J, Pilkey A, et al. Modeling void nucleation and growth within periodic clusters of particles[J]. Journal of the Mechanics and Physics of Solids. 1998, 47(1): 1-26.
[52] Wen J, Huang Y, Hwang K C, et al. The modified Gurson model accounting for the void size effect[J]. International Journal of Plasticity. 2005, 21(2): 381-395.
[53] Zhang K S, Bai J B, Fran D. Numerical analysis of the influence of the Lode parameter on void growth[J]. International Journal of Solids and Structures. 2001, 38(32-33): 5847-5856.
[54] Zhang Z L. A SENSITIVITY ANALYSIS OF MATERIAL PARAMETERS FOR THE GURSONCONSTITUTIVE MODEL[J]. Fatigue & Fracture of Engineering Materials & Structures. 1996, 19(5): 561-570.
[55] Thomason P F. Three-dimensional model for ductile fracture by the growth and coalescence of microvoids.[J]. ACTA METALLURG. 1985, 33(6): 1087-1095.
[56] Weck A, Wilkinson D S, Maire E, et al. Visualization by X-ray tomography of void growth and coalescence leading to fracture in model materials[J]. Acta Materialia. 2008, 56(12): 2919-2928.
[57] Cox T B, Low J R. An investigation of the plastic fracture of AISI 4340 and 18 Nickel-200 grade maraging steels[J]. Metallurgical and Materials Transactions B. 1974, 5(6): 1457-1470.
[58] Thomason P F. Ductile fracture of metals[M]. Oxfood: Pergamon Press, 1990: 219.
[59] Thomason P F. Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids.[J]. ACTA METALLURG. 1985, 33(6): 1079-1085.
[60] Lemaitre J. How to use damage mechanics[J]. Nuclear Engineering and Design. 1984, 80(3): 233-245.
[61] Latham D J, Cockcroft M G. A simple criterion of fracture for ductile metals[J]. UK National Engineering Laboratory Report. 1966, 240.
[62]于忠奇.基于LEMAITRE损伤理论的韧性断裂准则建立及板料成形极限预测[D].哈尔滨工业大学, 2003.
[63]郑长卿.延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.
[64] Shichun W U, Hua L. A kinetic equation for ductile damage at large plastic strain[J]. Journal of materials processing technology. 1990, 21(3): 295-302.
[65] Clift S E, Hartley P, Sturgess C E, et al. Fracture prediction in plastic deformation processes[J]. International journal of mechanical sciences. 1990, 32(1): 1-17.
[66] Irwin G R. Fracture of pressure vessels[J]. Materials for Missiles and Spacecraft. 1963: 204-229.
[67] Hood J E. Fracture of steel pipelines[J]. International Journal of Pressure Vessels and Piping. 1974, 2(3): 165-178.
[68] Duffy A R, Mcclure G M, Eiber R J, et al. Fracture design practices for pressure piping[J]. Fracture. 1969, 5: 159-232.
[69] Sharples J K, Clayton A M. A leak-before-break assessment method for pressure vessels and some current unresolved issues[J]. International Journal of Pressure Vessels and Piping. 1990, 43(1-3): 317-327.
[1] Qiu H, Mori H, Enoki M, et al. Evaluation of ductile fracture of structural steels by microvoid model[J]. ISIJ international. 1999, 39(4): 358-364.
[2] Poruks P, Yakubtsov I, Boyd J D. Martensite–ferrite interface strength in a low-carbon bainitic steel[J]. Scripta Materialia. 2006, 54(1): 41-45.
[3]翁宇庆等.超细晶钢——钢的组织细化理论与控制技术[M].北京:冶金工业出版社, 2003.
[4] Smith Y E, Coldren A P, Cryderman R L. Toward Improved Ductility and Toughness, Climax Molybdenum Co[J]. Ann Arbor, MI. 1971, 119.
[5]李鹤林,郭生武,冯耀荣.高强度微合金管线钢显微组织分析与鉴别图谱[M].北京:石油工业出版社, 2001.
[6] Ramberg W O W R. Description of stress-strain curves by three parameters[R]. Washington DC: National Advisory Committee For Aeronautics, 1943.
[7] Bridgeman P W. Studies in Large Plastic Flow and Fracture[M]. New York: McGraw-Hill, 1952.
[8] Zhang Z L, Hauge M, Qdegard J, et al. Determining material true stress-strain curve from tensile specimens with rectangular cross-section[J]. International Journal of Solids and Structures. 1999, 36(23): 3497-3516.
[9]陈篪.金属断裂研究文集[M].冶金工业出版社, 1978.
[10]叶裕恭.基于偏析线的圆棒颈缩分析[J].力学学报. 1986, 18(1): 46-56.
[11]刘瑞堂,姜风春.单轴拉伸试样的颈缩过程及形变强化特性的影响[J].物理测试. 1998, 10(5): 5-8.
[12]王心美,岳珠峰.正交各向异性材料拉伸圆棒的颈缩研究[J].燃气涡轮试验与研究. 2004, 17(002): 33-35.
[13] Zhang K S. Fracture prediction and necking analysis[J]. Engineering Fracture Mechanics. 1995, 52(3): 575-582.
[14] Argon A S, Im J, Safoglu R. Cavity formation from inclusions in ductile fracture[J]. Metall. Trans. A. 1975, 6(4): 825-837.
[15] Beremin F. Cavity formation from inclusions in ductile fracture of A508 steel[J]. Metallurgical and Materials Transactions A. 1981, 12(5): 723-731.
[16] Wang C, Wu X, Liu J, et al. Study on M/A islands in pipeline steel X70[J]. Journal of University of Science and Technology Beijing. 2005, 12(1): 43-47.
[17] Shanmugam S, Misra R D K, Hartmann J, et al. Microstructure of high strength niobium-containing pipeline steel[J]. Materials Science and Engineering A. 2006, 441: 215-229.
[18] Leroy G, Embury J, Edwards G, et al. A model of ductile fracture based on the nucleation and growth of voids[J]. Acta Metallurgica. 1981, 29(8): 1509-1520.
[19] Kwon D. Interfacial decohesion around spheroidal carbide particles[J]. Scripta metallurgica. 1988, 22(7): 1161-1164.
[1]郑长卿.延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.
[2] Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. J Mech Phys Solids. 1969, 17(3): 201-217.
[3] Higham D J, Higham N J. MATLAB guide[M]. Society for Industrial Mathematics, 2005.
[4] Mcclintock F A. A criterion for ductile fracture by the growth of holes[J]. J. appl. Mech. 1968, 35: 363-371.
[5] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part I-yield criteria and flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology. 1977, 99(1): 2-15.
[6] Budiansky B, Hutchinson J W, Slutsky S. Void growth and collapse in viscous solids[J]. Mechanics of Solids. 1982: 13-45.
[7] Lee B J, Mear M E. Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids[J]. Journal of the Mechanics and Physics of Solids. 1992, 40(8): 1805-1836.
[8] Yee K C, Mear M E. Effect of void shape on the macroscopic response of non-linear porous solids[J]. International journal of plasticity. 1996, 12(1): 45-68.
[9] Gologanu M, Leblond J B, Devaux J. Approximate models for ductile metals containing nonspherical voids—case of axisymmetric oblate ellipsoidal cavities[J]. Journal of Engineering Materials and Technology. 1994, 116: 290.
[10] Tvergaard V. On localization in ductile materials containing spherical voids[J]. International Journal of Fracture. 1982, 18(4): 237-252.
[11] Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions[J]. InternationalJournal of Fracture. 1981, 17(4): 389-407.
[12] Hom C L, Mcmeeking R M. Void growth in elastic-plastic materials[J]. Journal of Applied Mechanics. 1989, 56: 309.
[13] ABAQUS Theory Manual Version 6.8, Hibbitt, Karlsson & Sorensen Inc, 2008.
[14]王自强,秦嘉亮.含空洞非线性材料的本构势和空洞扩展率[J].固体力学学报. 1989, 10(002): 127-142.
[15] Thomason P F. Three-dimensional model for ductile fracture by the growth and coalescence of microvoids.[J]. ACTA METALLURG. 1985, 33(6): 1087-1095.
[16] Thomason P F. Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids.[J]. ACTA METALLURG. 1985, 33(6): 1079-1085.
[17] Clift S E, Hartley P, Sturgess C E, et al. Fracture prediction in plastic deformation processes[J]. International journal of mechanical sciences. 1990, 32(1): 1-17.
[18] Thomason P. A View on Ductile-Fracture Modelling[J]. Fatigue & Fracture of Engineering Materials & Structures. 1998, 21: 1105-1122.
[19] Ragab A R. A model for ductile fracture based on internal necking of spheroidal voids[J]. Acta Materialia. 2004, 52(13): 3997-4009.
[20] Benzerga A A. Micromechanics of coalescence in ductile fracture[J]. Journal of the Mechanics and Physics of Solids. 2002, 50(6): 1331-1362.
[21] Needleman A, Tvergaard V. Analysis of ductile rupture in notched bars.[J]. J. MECH. PHYS. SOL. 1984, 32(6): 461-490.
[22] Zhang Z L, Niemi E. A new failure criterion for the Gurson-Tvergaard dilational constitutive model[J]. International Journal of Fracture. 1994, 70(4): 321-334.
[23] Sun D Z, Sester M, Schmitt W. Development and Application of Micromechanical Material Models for the Characterization of Materials[J]. JOURNAL DE PHYSIQUE 4. 1996, 6(6): 431-439.
[24] Redanz P, Fleck N A, Mcmeeking R M. Failure of a Porous Solid from a Deep Notch[J]. International Journal of Fracture. 1997, 88(2): 187-202.
[25] P C P. Fracture modelling of WC-Co hardmetals using crystal plasticity theory and the Gurson model[J]. Fatigue & Fracture of Engineering Materials & Structures. 1999, 22(1): 77-86.
[26] Pardoen T, Doghri I, Delannay F. Experimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars[J]. Acta Materialia. 1998, 46(2): 541-552.
[27] Becker R, Needleman A, Richmond O, et al. Void growth and failure in notched bars[J]. Journal of the Mechanics and Physics of Solids. 1988, 36(3): 317-351.
[28] Koplik J, Needleman A. Void growth and coalescence in porous plastic solids[J]. Int. J. Solids Struct. 1988, 24(8): 835-853.
[29] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta Metall. 1984, 32(1): 157-169.
[30] Schmitt W, Sun D Z, Kienzler R. Application of micro-mechanical models to the prediction of ductile fracture[J]. Localized Damage Computer-Aided Assessment and Control. 1990, 1: 349-359.
[31] Xia L, Shih C F, Hutchinson J W. A computational approach to ductile crack growth under large scale yielding conditions[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(3): 389-413.
[32] Tvergaard V. Studies of void growth in a thin ductile layer between ceramics[J]. Computational Mechanics. 1997, 20(1): 186-191.
[33] Leroy G, Embury J, Edwards G, et al. A model of ductile fracture based on the nucleation and growth of voids[J]. Acta Metallurgica. 1981, 29(8): 1509-1520.
[34] Kwon D. Interfacial decohesion around spheroidal carbide particles[J]. Scripta metallurgica. 1988, 22(7): 1161-1164.
[1]罗金恒,赵新伟,李新华,等. X80管线钢断裂韧性研究[J].压力容器. 2007, 24(008): 6-9.
[2] Sun D Z, Sester M, Schmitt W. Development and Application of Micromechanical Material Models for the Characterization of Materials[J]. JOURNAL DE PHYSIQUE 4. 1996, 6(6): 431-439.
[3] Brocks W, Sun D Z, Nig H. Verification of the transferability of micromechanical parameters by cell model calculations with visco-plastic materials[J]. International Journal of Plasticity. 1995, 11(8): 971-989.
[4] Bauvineau L, Burlet H, Eripret C, et al. Modelling Ductile Stable Crack Growth in a C-Mn Steel with Local Approaches[J]. Journal de Physique(France) IV(France). 1996, 6(6): 33-42.
[5] Gao X, Faleskog J, Shih C F. Cell model for nonlinear fracture analysis-II. Fracture-process calibration and verification[J]. International Journal of Fracture. 1998, 89(4): 375-398.
[6] Hachez F, Atkins A G, Dodds R H, et al. MICROMECHANICS-BASED MODELLING OF DUCTILE TEARING IN THIN PLATES[C]. KTH, Stockholm, Sweden: 2004.
[7] Simonsen B C, T R. Experimental and numerical modelling of ductile crack propagation in large-scale shell structures[J]. Marine Structures. 2004, 17(1): 1-27.
[8] Feucht M, Sun D Z, Erhart T, et al. Recent Development and Applications of the Gurson Model[J]. Proceedings to the Fifth LS-DYNA Anwenderforum, Ulm, Germany. 2006.
[9] Xia L, Shih C F. Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(2): 233-259.
[10] Xia L, Shih C F. Ductile crack growth-II. Void nucleation and geometry effects on macroscopic fracture behavior[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(12): 1953-1981.
[11] Xia L, Shih C F, Hutchinson J W. A computational approach to ductile crack growth under large scale yielding conditions[J]. Journal of the Mechanics and Physics of Solids. 1995, 43(3): 389-413.
[12] Liu Y, Murakami S, Kanagawa Y. Mesh-dependence and stress singularity in finite element analysis of creep crack growth by continuum damage mechanics approach[J]. European journal of mechanics. A. Solids. 1994, 13(3): 395-418.
[13] Matos P P, Mcmeeking R M, Charalambides P G, et al. A method for calculating stress intensities in bimaterial fracture[J]. International Journal of Fracture. 1989, 40(4): 235-254.
[14] Stolk J, Verdonschot N, Mann K A, et al. Prevention of mesh-dependent damage growth in finite element simulations of crack formation in acrylic bone cement[J]. Journal of biomechanics. 2003, 36(6): 861-871.
[15] Tvergaard V, Hutchinson J W. Two mechanisms of ductile fracture: void by void growth versus multiple void interaction[J]. International Journal of Solids and Structures. 2002, 39(13-14): 3581-3597.
[16] Knott J F. Micromechanisms of fibrous crack extension in engineering alloys[J]. Metal Science. 1980, 14(9): 327-336.
[17] Landes J D. The blunting line in elastic-plastic fracture[J]. Fatigue & Fracture of Engineering Materials &Structures. 1995, 18(11): 1289-1297.
[18] Needleman A, Tvergaard V. Analysis of ductile rupture in notched bars.[J]. J. MECH. PHYS. SOL. 1984, 32(6): 461-490.
[19] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. Acta Metall. 1984, 32(1): 157-169.
[20]马法尚,匡震邦.韧性断裂的微观模型及其在约束断裂中的应用.[J].力学学报. 1995, 27(S1): 120-124.
[21]汤安民,师俊平.几种金属材料宏观断裂形式的试验研究[J].应用力学学报. 2004, 21(003): 142-144.
[22] Khan S, Khraisheh M K. Analysis of mixed mode crack initiation angles under various loading conditions[J]. Engineering Fracture Mechanics. 2000, 67(5): 397-419.
[23]孙国有,魏志刚,王晓春,等.空穴机理在45钢剪切型断裂过程中的作用[J].机械科学与技术. 2001, 20(z1): 66-70.
[24]黄克智,余寿文.弹塑性断裂力学[M].北京:清华大学出版社, 1985.
[25]王波,杨卫,黄克智.基于非J控制扩展的安全评定方法[J].力学学报. 1992, 24(003): 339-349.
[26] Rice J R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks[J]. J. Appl. Mech. 1968, 35(2): 379-386.
[1] Ukadgaonker V G, Babu R S. Review of work related to " leak-before-break " assessment[J]. International Journal of Pressure Vessels and Piping. 1996, 69(2): 135-148.
[2] Bsi. Guide to methods for assessing the acceptability of flaws in metallic structures[S]. BS 7910-2005.
[3] Paris P, Erdogan F. A critical analysis of crack propagation laws[J]. Journal of Basic Engineering. 1963, 85(4): 528-534.
[4] Newman J C, Raju I S. An empirical stress-intensity factor equation for the surface crack[J]. Engineering Fracture Mechanics. 1981, 15(1): 185-192.
[5]邱保文,袁泽喜,周桂峰.油气管线裂纹型缺陷的疲劳寿命预测[J].武汉科技大学学报:自然科学版. 2009, 32(003): 247-250.
[6] Lin X B, Smith R A. Numerical analysis of fatigue growth of external surface cracks in pressurized cylinders[J]. International Journal of Pressure Vessels and Piping. 1997, 71(4): 293-300.
[7]李云龙,庄传晶,冯耀荣,等.油气输送管道疲劳寿命分析及预测[J].油气储运. 2004, 23(12): 41-43.
[8]赵新伟,罗金恒,董保胜,等.西气东输管道安全评价[J].理化检验:物理分册. 2005, 41(1): 82-88.
[9] Kiefner J F, Maxey W A, Eiber R J, et al. Failure stress levels of flaws in pressurized cylinders[J]. ASTM special technical publication. 1973(536): 461-481.
[10]冯耀荣,霍春勇,高惠临,等.长输管道稳态气体泄漏率的计算[J].油气储运. 2002, 21(8): 11-15.
[11]王占山,张化光,冯健,等.长距离流体输送管道泄漏检测与定位技术的现状与展望[J].化工自动化及仪表. 2003, 30(5): 5-10.