含肩部穿透裂纹接管安全评定
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摘要
接管焊缝处容易出现裂纹,这对压力容器及管道安全运行带来巨大的隐患,定量研究裂纹应力强度因子和结构极限载荷对缺陷结构安全评定具有重要的意义。应力强度因子反映裂纹尖端附近区域应力场强度,是接管在相贯线焊缝处裂纹的安全评定中的关键物理量。极限载荷分析相对于常规分析更能反映出接管受力状态的本质,在缺陷接管的安全评定和强度设计中是重要的物理量。
运用断裂力学理论,采用三维线弹性有限元分析方法,研究内压和弯矩下含肩部穿透裂纹接管的应力强度因子；运用弹塑性力学理论,采用三维弹塑性有限元方法,对此结构塑性极限载荷进行了计算和分析。提出了两个载荷下含缺陷结构的安全评定方法。
主要研究内容及结论如下：
(1)建立了轴向穿透裂纹管道有限元模型,并验证了模型求解应力强度因子和极限载荷的正确性。建立了含肩部穿透裂纹接管有限元模型,通过ANSYS提供的参数化编程语言(APDL)建立了参数化模型、加载和后处理宏程序。
(2)通过第一型应力强度因子、内压下极限载荷p和弯矩下极限载荷m来衡量接管的安全水平。确定了接管无量纲化参数裂纹长度a,接管管径比do／di,容器管径比Do／Di和接管与容器径比di／Di。
(3)仅受内压下,在不同的结构尺寸下,应力强度因子KIP与内压P都呈线性关系。裂纹长度越大,KIP越大,极限内压p越小。接管和容器的壁厚增加,KIP减少,p增大。当接管和容器的管径比都大于1.1时,继续增大厚度,KIP减少不明显。容器开孔越大,KIP越大,p越小。在容器和接管管径比大于1.1时给出KIP的拟合式,在管径比小于1.1时给出KIP、p与a、d0/di、D0/Di和di／Di的关系表,并给出内压下接管安全评定步骤。
(4)仅受弯矩下,在不同的结构尺寸下,应力强度因子KIM与弯矩M都呈线性关系。裂纹长度越大,KIM越大,极限弯矩m越小。接管和容器的壁厚增加,KIM减少,m增大。当接管和容器的管径比都大于1.1时,继续增大厚度,KIM减少不明显。容器开孔越大,KIM越小,m越大。在容器和接管管径比大于1.1时给出KIM的拟合式,在管径比小于1.1时给出KIM、m与a.d0/dt.D0/Di和di／Di关系表,并给出弯矩下接管安全评定步骤。
(5)在受内压和弯矩的联合作用下,裂纹应力强度因子为仅受内压下应力强度因子与仅受弯矩下应力强度因子线性加和,KIS=P.KIP+M-KIM。接管极限内压与极限弯矩的关系符合线性方程,mB.P+pA·M-mB·pA=0。提出在联合作用下含肩部穿透裂纹接管安全评定的所用参数断裂比Kr=KIS/Kp+ρ,载荷比并给出内压和弯矩下接管安全评定步骤。
Cracks that tend to appear in weld joint between vessel and nozzle are bearing enormous risk to nozzle safety, thus quantitative investigations into stress intensity factor and limit load are of great significance to the safety rating of pressure vessel containing defects. Stress intensity factor, reflecting the stress field intensity near the tip zone of the crack, is one of the key parameters in the safety rating of weld joint cracks. And the limit load is another important parameter, the analysis of which can reveal a more authentic state of stress than conventional analysis.
Based upon the theory of fracture mechanics,3D linear elastic FEA is adopted to study the stress intensity factor of nozzles with through-wall crack at the shoulder under the conditions of various internal pressure and moment. In the application of the elastic-plastic mechanics theory,3D elastic-plastic FEA is used to calculate and analyse the limit plastic load of the same structure. It is proposed the safety assessment method for vessels containing defects under two loads.
The main contents and the corresponding conclusions are as follows:
(1) The finite element model of piping containing axial wall-though crack is estabished then validated by calculating the stress intensity factor and limit load. APDL provided by ANSYS is applied to establish the parameterization model, loading and post-processing macro-programs, composing the finite element model of nozzle with through-wall crack at the shoulder.
(2) KI (the type I stress intensity factor),p (limit load under pressure) and m (limit load under moment) are applied to rate the nozzle safety. Dimensionless numbers such as crack length a, diameter ratio of nozzle do/di, diameter ratio of vessel Do/Di and diameter ratio of nozzle and vessel di/Di are determined.
(3) When subjected to internal pressure solely, KIP is proportional to P in conditions of different structure sizes. Longer crack, bigger hole and thinner wall make a larger KIp and a smaller p. When both do/di and Do/Di are larger than 1.1, KIP decreases unobviously with the increase of the thickness of nozzle and the thickness of vessel. The fitting equation is obtained when both do/di and Do/Di is larger than 1.1. The relationship table of KI, p, a, do/di, Do/Di and di/Di are presented when diameter ratio of vessel and diameter ratio of nozzle is smaller than 1.1, and safety assessment is made under internal pressure.
(4) When subjected to internal pressure solely, KIM is proportional to M in conditions of different structure sizes. Longer crack, smaller hole and thinner wall make a larger KIM and a smaller m. When both do/di and Do/Di are larger than 1.1, KIM decreases unobviously with the increase of the thickness of nozzle and the thickness of vessel. The fitting equation is obtained when both do/di and Do/Di is larger than 1.1. The relationship table of KIM, m, a, do/di Do/Di and di/Di are presented when diameter ratio of vessel and diameter ratio of nozzle is smaller than 1.1, and safety assessment is made under moment.
(5) When subjected to the combination of internal pressure and moment, stress intensity factor is simply the summation of the stress intensity factors that are subjected to internal pressure and moment respectively, KIS= P·KIP+M·KIM. The relation between limit pressure and limit moment fits the linearity equation, mB·P+pA·M-mB·pA= 0. And the fracture ratio and load ratio used to safety assessment under internal pressure and moment are given, which are And safety assessment is made under internal pressure and moment.
运用断裂力学理论,采用三维线弹性有限元分析方法,研究内压和弯矩下含肩部穿透裂纹接管的应力强度因子；运用弹塑性力学理论,采用三维弹塑性有限元方法,对此结构塑性极限载荷进行了计算和分析。提出了两个载荷下含缺陷结构的安全评定方法。
主要研究内容及结论如下：
(1)建立了轴向穿透裂纹管道有限元模型,并验证了模型求解应力强度因子和极限载荷的正确性。建立了含肩部穿透裂纹接管有限元模型,通过ANSYS提供的参数化编程语言(APDL)建立了参数化模型、加载和后处理宏程序。
(2)通过第一型应力强度因子、内压下极限载荷p和弯矩下极限载荷m来衡量接管的安全水平。确定了接管无量纲化参数裂纹长度a,接管管径比do／di,容器管径比Do／Di和接管与容器径比di／Di。
(3)仅受内压下,在不同的结构尺寸下,应力强度因子KIP与内压P都呈线性关系。裂纹长度越大,KIP越大,极限内压p越小。接管和容器的壁厚增加,KIP减少,p增大。当接管和容器的管径比都大于1.1时,继续增大厚度,KIP减少不明显。容器开孔越大,KIP越大,p越小。在容器和接管管径比大于1.1时给出KIP的拟合式,在管径比小于1.1时给出KIP、p与a、d0/di、D0/Di和di／Di的关系表,并给出内压下接管安全评定步骤。
(4)仅受弯矩下,在不同的结构尺寸下,应力强度因子KIM与弯矩M都呈线性关系。裂纹长度越大,KIM越大,极限弯矩m越小。接管和容器的壁厚增加,KIM减少,m增大。当接管和容器的管径比都大于1.1时,继续增大厚度,KIM减少不明显。容器开孔越大,KIM越小,m越大。在容器和接管管径比大于1.1时给出KIM的拟合式,在管径比小于1.1时给出KIM、m与a.d0/dt.D0/Di和di／Di关系表,并给出弯矩下接管安全评定步骤。
(5)在受内压和弯矩的联合作用下,裂纹应力强度因子为仅受内压下应力强度因子与仅受弯矩下应力强度因子线性加和,KIS=P.KIP+M-KIM。接管极限内压与极限弯矩的关系符合线性方程,mB.P+pA·M-mB·pA=0。提出在联合作用下含肩部穿透裂纹接管安全评定的所用参数断裂比Kr=KIS/Kp+ρ,载荷比并给出内压和弯矩下接管安全评定步骤。
Cracks that tend to appear in weld joint between vessel and nozzle are bearing enormous risk to nozzle safety, thus quantitative investigations into stress intensity factor and limit load are of great significance to the safety rating of pressure vessel containing defects. Stress intensity factor, reflecting the stress field intensity near the tip zone of the crack, is one of the key parameters in the safety rating of weld joint cracks. And the limit load is another important parameter, the analysis of which can reveal a more authentic state of stress than conventional analysis.
Based upon the theory of fracture mechanics,3D linear elastic FEA is adopted to study the stress intensity factor of nozzles with through-wall crack at the shoulder under the conditions of various internal pressure and moment. In the application of the elastic-plastic mechanics theory,3D elastic-plastic FEA is used to calculate and analyse the limit plastic load of the same structure. It is proposed the safety assessment method for vessels containing defects under two loads.
The main contents and the corresponding conclusions are as follows:
(1) The finite element model of piping containing axial wall-though crack is estabished then validated by calculating the stress intensity factor and limit load. APDL provided by ANSYS is applied to establish the parameterization model, loading and post-processing macro-programs, composing the finite element model of nozzle with through-wall crack at the shoulder.
(2) KI (the type I stress intensity factor),p (limit load under pressure) and m (limit load under moment) are applied to rate the nozzle safety. Dimensionless numbers such as crack length a, diameter ratio of nozzle do/di, diameter ratio of vessel Do/Di and diameter ratio of nozzle and vessel di/Di are determined.
(3) When subjected to internal pressure solely, KIP is proportional to P in conditions of different structure sizes. Longer crack, bigger hole and thinner wall make a larger KIp and a smaller p. When both do/di and Do/Di are larger than 1.1, KIP decreases unobviously with the increase of the thickness of nozzle and the thickness of vessel. The fitting equation is obtained when both do/di and Do/Di is larger than 1.1. The relationship table of KI, p, a, do/di, Do/Di and di/Di are presented when diameter ratio of vessel and diameter ratio of nozzle is smaller than 1.1, and safety assessment is made under internal pressure.
(4) When subjected to internal pressure solely, KIM is proportional to M in conditions of different structure sizes. Longer crack, smaller hole and thinner wall make a larger KIM and a smaller m. When both do/di and Do/Di are larger than 1.1, KIM decreases unobviously with the increase of the thickness of nozzle and the thickness of vessel. The fitting equation is obtained when both do/di and Do/Di is larger than 1.1. The relationship table of KIM, m, a, do/di Do/Di and di/Di are presented when diameter ratio of vessel and diameter ratio of nozzle is smaller than 1.1, and safety assessment is made under moment.
(5) When subjected to the combination of internal pressure and moment, stress intensity factor is simply the summation of the stress intensity factors that are subjected to internal pressure and moment respectively, KIS= P·KIP+M·KIM. The relation between limit pressure and limit moment fits the linearity equation, mB·P+pA·M-mB·pA= 0. And the fracture ratio and load ratio used to safety assessment under internal pressure and moment are given, which are And safety assessment is made under internal pressure and moment.
引文
[1]兰州石油机械研究所.压力容器设计知识[M].化学工业出版社,2005
[2]国家质检总局办公厅.2008年全国特种设备安全状况.国家质检总局,2009http://tzsbaqjcj. aqsiq. gov. cn/tzwj/zjwh/200904/t20090429_112899. htm
[3]Tada,H.,Paris, P. C., etal. The Stress Analysis of Crack Handbook[M]. Del. Res. Corp. Hellertown, Pa,1973
[4]Rice, I. R. A path independent integral and approximate analysis of strain concentrations by notches and cracks[J]. Journal of Applied Mechanics,1968,35 (2):379-386
[5]Hutchinson. J. W. Singular behavior at the end of a tensile tip in a hardening material [J]. J. Mech. Phys. Dolids,1968,16:1-2
[6]Electric Power Research Institute. Ductile Fracture Handbook (three volumes) [M].1989,6
[7]Wells, A. A. Application of fracture mechanics at and beyond general yielding[J]. British Welding J,1963,10:563-570
[8]Newman, J. C., Booth. B. C., Shivakumar. K. N. An elasitic-plastic finite-element analysis of the J-resistance curve using a CTOD criterion[C]. ASTM STP 1988,945:665-685
[9]Dugdale, D. S., Yielding of steel sheets containing Slits[J].J. Mech. Phys. Solids,1960, 8:100-108
[10]赵耀.拉载下周向壁穿裂纹圆柱壳的弹塑性解析解[J].固体力学学报,1992,20(1)：82-89
[11]张正国.Dugdale模型解法研究[J].哈尔滨工程大学学报,1998,19(1)：83-93
[12]张正国,杨国义,邹广平.Dugdale模型权函数法一般公式[J].哈尔滨工程大学学报,2000,21(1)：34-36
[13]Lam, k. Y. Tay, T. E. and Wang W., The Dugdale solution for crack at the edge of an elliptical hole in an infinite plate[J]. Engineering Fracture Mechanics,1996,53 (1):97-106
[14]范天佑.断裂理论基础[M].科学出版社,2003
[15]Ainsworth, R. A. Assessment of the integrity of structure containing defect British Energy Generation Ltd[J]. Amendment,2001
[16]徐秉业.塑性力学[M].北京：高等教育出版社,1988
[17]马晓士.工程塑性力学[M].北京：高等教育出版社，1983
[18]徐秉业,陈森灿.塑性理论简明教程[M].北京：清华大学出版社,1981
[19]M. Save. Experimental Verification of Plastic Limit Analysis of Torispherical and Toriconical Heads[S]. Pressure Vessel and Piping Design and Analysis I, ASME, 1972:382-416
[20]ASME Boiler and Pressure Vessel Code. Section Ⅲ and Ⅷ-2,1986 Version[S]
[21]章为民,陆明万,张如一.确定实际极限载荷的零曲率准则[J].固体力学学报,1989(2)：152-159
[22]Bouchard, P. J. Practical Application of the R6 Leak-Before-Break Procedure[J]. Paper 10, Specialist Meeting on Leak before Break in Reactor Piping and Vessels. Lyon, France: October,1995
[23]Kumar, V., German, M., and Wilkening, W., Andrews, W.. Advance in Elastic-Plastic Fracture Analyses[J]. ERPI Final Report NP-3067, Electric Power Research Institute, Pab A lto, CA, August 1984
[24]Zahoor, A. Fracture of Circumferentially Cracked Pipes [J]. ASME J. of Pressure Vessel Technology,1987, Vol.108:529-531
[25]Zahoor, A. J-Integral Analysis for Notched Round Bar in Tension [J]. ASME J. of Pressure Vessel Technology,1987, Vol.109:155-158
[26]Zahoor, A. Evaluation of J-Integral Estimation Scheme for Flawed Through-wall Pipes [J]. Nuclear Engineering and Design,1987, Vol.100:1-9
[27]V.Kumar etc.. Estimation Technique for the Prediction of Elastic-plastic Fracture of Structural Components of Nuclear systems[J].5th and 6th Semiannual Report to EPRI, Feb.1981-Jan.1982
[28]胡正民,王威强,李培宁等.EPRI全塑性解估算长屈服平台钢含缺陷结构的J积分[J].石油化工设备,1992,21(3)：10-13.
[29]Schroeder J. Analysis of test date on branch-pipe connections exposed to internal pressure and/or external couples[J]. WRC 200,1974:1～53
[30]Ellyin F. An experimental study of elasto-plastic response of branch-pipe tee connections subjected to internal pressure, external couples and combined loadings [J]. WRC 230,1977:1～43
[31]Schroeder J. Limit intersection of external couples and internal pressure for branch-pipe lateral and tee connections part I:upper bounds to in-plane and out-of-plane limit couples applied to the branch for branch-pipe diameter ratio smaller than 0.8[J]. Int. Conf. Pres. Ves. Tech., Part 1, New York,1973:456～478
[32]Tabone C J. Pressure-plus-moment limit load analysis for a cylindrical shell nozzle[J]. ASME Journal of Pressure Vessel Technology,1987,109 (1):297～301
[33]Nadarajah C, Mackenzie D. Limit and shakedown analysis of nozzle/cylinder intersection under internal pressure and in-plane moment loading [J]. Int. J. Pres. Ves.&Piping, 1996,68 (3):261-272
[34]Moffat D G, Mistry H. Interaction of external moment loads and internal pressure on a variety of branch pipe intersections [J]. Proc. Sixth Int. Conf. on Press. Vess. Tech. Beijing:Vol.1, Design and Analysis, Oxford:Pergamon Press,1988.533～549
[35]Yahiaoui K, Moffat D G, Moreton D N. Plastic loads of cracked forged piping branch junctions:experimental results and comparison with numerical data[J]. Int. J. of Pre. Vessels&Piping,2000,77 (6):249～260
[36]Xuan F Z. An engineering analysis approach for plastic limit load of pressurized piping branch junctions[Ph D Thesis][J]. Shanghai:East China University of Science and Technology,2002
[37]Wichman, K. R. et al. Local Stresses In Spherical and Cylindrical Shells Due to External Loadings[J]. WRC Bulletion 107.1979.
[38]杜护军等.钢制对焊无缝管件和承插焊管件的检验[J].第一届全国管道学术会议交流会议论文集,1997：140-144
[39]张庆江.宝钢自备电厂1#炉汽包下降管管座焊缝缺陷对寿命影响的评价[J].上海发电设备成套设计研究所,1986,10
[40]Kobayashi, A. S. et al.. Corner Crack at a Nozzle, Third International Conference on Pressure Vessel Technology[J]. Part 2, Materials and Fabrication,1977:507～515
[41]Mohamed, M. A. and Schroeder. Stress Intensity Factor Solution for Crotch-Corner Cracks of Tee-Intersections of Cylindrical Shells[J]. Int. J. of Fracture,14 (6) 1978:605～ 621
[42]Kobayashi, A. S. et al. Embedded Elliptical Crack at a Corner[J]. Pres. Ves. Tech. 1978,100:28～33
[43]Friedman, E. and Jones, D. P. The Effect of Flaw Shape on the Fracture Propensity of Nozzle Corner Flaws [J]. Pres. Ves. Tech.1988,110:59-63
[44]A. Th. Diamantoudis and G. N. Labeas. Stress intensity factors of semi-elliptical surface cracks inpressure vessels by global-local finite element methodology[J]. Engineering Fracture Mechanics 72,2005:1299～1312
[45]杨宁祥.焊制异径三通肩部轴向穿透裂纹弹塑性有限元分析[D].大连理工大学硕士毕业论文.2006,12
[46]Lynch M A, Moffat D G and Moretem D N. Limit load for cracked piping branch junctions under pressure and branch out-of-plane bending[J]. Int J of Pres Ves&Piping,2000,77 (5):185-194
[47]Miller, A. G. Review of Limit Loads of Structures Containing Defects[J]. Int. J. Pres. Ves&Piping Vol.32,1988:197-327
[48]Lind, N. C.. Approximate Stress-Concentration Analysis for Pressurized Branch Pipe Connections [J]. ASME Paper67,1967:951～958
[49]Meng, Q.. Plastic Limit Analysis of Pressure Vessels with Defects[J]. PhD Thesis UMIST,1984.
[50]Plancq, D. Berton, M. N.. Limit Analysis Based on Elastic Compensation Method of Branch[J].
[51]Xuan Fuzhen, Liu Changjun, Hui Hu, et al. Plastic limit pressure of equal-diameter piping branch junctions with axial crack[J]. Chinese Journal of Petroleum Machinery,2001,29 (7):11-14,25
[52]轩福贞,李培宁,孙亮.管道三通塑性极限压力及其影响因素分析[J].油气储运,2000,19(10)：26～31
[53]Folias E S. An axial crack in a pressurized cylindrical shell[J]. Int. J. Fract. Mech.,1965,1:104-113
[54]李培宁等.含轴向裂纹等径焊制三通的塑性极限载荷[J].石油机械,2001,29(7)：11～14,25
[55]李培宁等.含环向裂纹等径焊制三通极限压力(Ⅰ)——有限元分析[J].石油化工设备,2001,30(4)：16～20
[56]李培宁等.含环向裂纹等径焊制三通极限压力(Ⅱ)——工程估算方法[J].石油化工设备,2001,30(5)：28～30
[57]Yahiaoui K, Moffat D G and Moretem D N. Plastic loads of cracked piping branch junctions: experimental results and comparison with numerical data[J]. Int J of Pres Ves&Piping,2000,77 (6):249～260
[58]Grebner. H. et al.. Experimental and Calculation on Crack Opening and Leak Rate of a Pipe Branch Within the HDR-Program [J]. Nuclear Engineering and Design, Vol.147, 1993:79-84
[59]Fuzhen Xuan, Chen Wang, Peining Li. Experimental investigation of the limit load of the ANSI B16.9 tees with and without cracks under internal pressure[J]. Engineering Failure Analysis,2005,12:453～464
[60]GB／T 19624-2004“在用含缺陷压力容器安全评定”[S]
[61]EPRI Research Project 1757-69, Ductile Fracture Handbook. VOLUME 2.1990,6.1-1[S]
[62]中国国家标准化管理委员会.GB／T 8163-2008输送流体用无缝钢管[S].中国标准出版社,2008
[63]喻健良,闫兴清.加强筋对含裂纹平板的止裂性能研究[J].石油化工设备,2008.9(5)：12-16
[64]轩福贞,李培宁,涂善东.复杂载荷下管道三通的塑性极限载荷[J].机械强度,2003,25(6)：646-650
[65]刘彩霞.焊制三通管件塑性极限载荷的有限元分析[D].北京化工大学硕士学位论文.2003
[66]贾慧灵.受外载作用焊接三通塑性极限载荷的有限元分析[D].北京化工大学硕士学位论文2004
[67]徐谦.典型承压结构的塑性极限载荷分析[D].北京化工大学硕士学位论文.2006
[68]闫兴清.加强筋止裂性能研究及管件极限载荷计算[D].大连理工大学硕士学位论文.2006
[69]郑津洋,董其伍,桑芝富.过程装备设计[M].化学工业出版社.2001
[70]喻健良,闫兴清.含轴向内表面裂纹管道极限载荷有限元计算[J].管道技术与设备,2008(2)：4-10
[71]EPRI Research Project 1757-69, Ductile Fracture Handbook. VOLUME 2.1990,6.3-1[S]
[72]栾春远.压力容器ANSYS分析与强度计算[M].北京：中国水利水电出版社,2008
[73]何家胜.圆柱形薄壁压力容器大开孔接管部位的安定性分析[J].武汉：武汉化工学院学报,1997，9：65-67.
[2]国家质检总局办公厅.2008年全国特种设备安全状况.国家质检总局,2009http://tzsbaqjcj. aqsiq. gov. cn/tzwj/zjwh/200904/t20090429_112899. htm
[3]Tada,H.,Paris, P. C., etal. The Stress Analysis of Crack Handbook[M]. Del. Res. Corp. Hellertown, Pa,1973
[4]Rice, I. R. A path independent integral and approximate analysis of strain concentrations by notches and cracks[J]. Journal of Applied Mechanics,1968,35 (2):379-386
[5]Hutchinson. J. W. Singular behavior at the end of a tensile tip in a hardening material [J]. J. Mech. Phys. Dolids,1968,16:1-2
[6]Electric Power Research Institute. Ductile Fracture Handbook (three volumes) [M].1989,6
[7]Wells, A. A. Application of fracture mechanics at and beyond general yielding[J]. British Welding J,1963,10:563-570
[8]Newman, J. C., Booth. B. C., Shivakumar. K. N. An elasitic-plastic finite-element analysis of the J-resistance curve using a CTOD criterion[C]. ASTM STP 1988,945:665-685
[9]Dugdale, D. S., Yielding of steel sheets containing Slits[J].J. Mech. Phys. Solids,1960, 8:100-108
[10]赵耀.拉载下周向壁穿裂纹圆柱壳的弹塑性解析解[J].固体力学学报,1992,20(1)：82-89
[11]张正国.Dugdale模型解法研究[J].哈尔滨工程大学学报,1998,19(1)：83-93
[12]张正国,杨国义,邹广平.Dugdale模型权函数法一般公式[J].哈尔滨工程大学学报,2000,21(1)：34-36
[13]Lam, k. Y. Tay, T. E. and Wang W., The Dugdale solution for crack at the edge of an elliptical hole in an infinite plate[J]. Engineering Fracture Mechanics,1996,53 (1):97-106
[14]范天佑.断裂理论基础[M].科学出版社,2003
[15]Ainsworth, R. A. Assessment of the integrity of structure containing defect British Energy Generation Ltd[J]. Amendment,2001
[16]徐秉业.塑性力学[M].北京：高等教育出版社,1988
[17]马晓士.工程塑性力学[M].北京：高等教育出版社，1983
[18]徐秉业,陈森灿.塑性理论简明教程[M].北京：清华大学出版社,1981
[19]M. Save. Experimental Verification of Plastic Limit Analysis of Torispherical and Toriconical Heads[S]. Pressure Vessel and Piping Design and Analysis I, ASME, 1972:382-416
[20]ASME Boiler and Pressure Vessel Code. Section Ⅲ and Ⅷ-2,1986 Version[S]
[21]章为民,陆明万,张如一.确定实际极限载荷的零曲率准则[J].固体力学学报,1989(2)：152-159
[22]Bouchard, P. J. Practical Application of the R6 Leak-Before-Break Procedure[J]. Paper 10, Specialist Meeting on Leak before Break in Reactor Piping and Vessels. Lyon, France: October,1995
[23]Kumar, V., German, M., and Wilkening, W., Andrews, W.. Advance in Elastic-Plastic Fracture Analyses[J]. ERPI Final Report NP-3067, Electric Power Research Institute, Pab A lto, CA, August 1984
[24]Zahoor, A. Fracture of Circumferentially Cracked Pipes [J]. ASME J. of Pressure Vessel Technology,1987, Vol.108:529-531
[25]Zahoor, A. J-Integral Analysis for Notched Round Bar in Tension [J]. ASME J. of Pressure Vessel Technology,1987, Vol.109:155-158
[26]Zahoor, A. Evaluation of J-Integral Estimation Scheme for Flawed Through-wall Pipes [J]. Nuclear Engineering and Design,1987, Vol.100:1-9
[27]V.Kumar etc.. Estimation Technique for the Prediction of Elastic-plastic Fracture of Structural Components of Nuclear systems[J].5th and 6th Semiannual Report to EPRI, Feb.1981-Jan.1982
[28]胡正民,王威强,李培宁等.EPRI全塑性解估算长屈服平台钢含缺陷结构的J积分[J].石油化工设备,1992,21(3)：10-13.
[29]Schroeder J. Analysis of test date on branch-pipe connections exposed to internal pressure and/or external couples[J]. WRC 200,1974:1～53
[30]Ellyin F. An experimental study of elasto-plastic response of branch-pipe tee connections subjected to internal pressure, external couples and combined loadings [J]. WRC 230,1977:1～43
[31]Schroeder J. Limit intersection of external couples and internal pressure for branch-pipe lateral and tee connections part I:upper bounds to in-plane and out-of-plane limit couples applied to the branch for branch-pipe diameter ratio smaller than 0.8[J]. Int. Conf. Pres. Ves. Tech., Part 1, New York,1973:456～478
[32]Tabone C J. Pressure-plus-moment limit load analysis for a cylindrical shell nozzle[J]. ASME Journal of Pressure Vessel Technology,1987,109 (1):297～301
[33]Nadarajah C, Mackenzie D. Limit and shakedown analysis of nozzle/cylinder intersection under internal pressure and in-plane moment loading [J]. Int. J. Pres. Ves.&Piping, 1996,68 (3):261-272
[34]Moffat D G, Mistry H. Interaction of external moment loads and internal pressure on a variety of branch pipe intersections [J]. Proc. Sixth Int. Conf. on Press. Vess. Tech. Beijing:Vol.1, Design and Analysis, Oxford:Pergamon Press,1988.533～549
[35]Yahiaoui K, Moffat D G, Moreton D N. Plastic loads of cracked forged piping branch junctions:experimental results and comparison with numerical data[J]. Int. J. of Pre. Vessels&Piping,2000,77 (6):249～260
[36]Xuan F Z. An engineering analysis approach for plastic limit load of pressurized piping branch junctions[Ph D Thesis][J]. Shanghai:East China University of Science and Technology,2002
[37]Wichman, K. R. et al. Local Stresses In Spherical and Cylindrical Shells Due to External Loadings[J]. WRC Bulletion 107.1979.
[38]杜护军等.钢制对焊无缝管件和承插焊管件的检验[J].第一届全国管道学术会议交流会议论文集,1997：140-144
[39]张庆江.宝钢自备电厂1#炉汽包下降管管座焊缝缺陷对寿命影响的评价[J].上海发电设备成套设计研究所,1986,10
[40]Kobayashi, A. S. et al.. Corner Crack at a Nozzle, Third International Conference on Pressure Vessel Technology[J]. Part 2, Materials and Fabrication,1977:507～515
[41]Mohamed, M. A. and Schroeder. Stress Intensity Factor Solution for Crotch-Corner Cracks of Tee-Intersections of Cylindrical Shells[J]. Int. J. of Fracture,14 (6) 1978:605～ 621
[42]Kobayashi, A. S. et al. Embedded Elliptical Crack at a Corner[J]. Pres. Ves. Tech. 1978,100:28～33
[43]Friedman, E. and Jones, D. P. The Effect of Flaw Shape on the Fracture Propensity of Nozzle Corner Flaws [J]. Pres. Ves. Tech.1988,110:59-63
[44]A. Th. Diamantoudis and G. N. Labeas. Stress intensity factors of semi-elliptical surface cracks inpressure vessels by global-local finite element methodology[J]. Engineering Fracture Mechanics 72,2005:1299～1312
[45]杨宁祥.焊制异径三通肩部轴向穿透裂纹弹塑性有限元分析[D].大连理工大学硕士毕业论文.2006,12
[46]Lynch M A, Moffat D G and Moretem D N. Limit load for cracked piping branch junctions under pressure and branch out-of-plane bending[J]. Int J of Pres Ves&Piping,2000,77 (5):185-194
[47]Miller, A. G. Review of Limit Loads of Structures Containing Defects[J]. Int. J. Pres. Ves&Piping Vol.32,1988:197-327
[48]Lind, N. C.. Approximate Stress-Concentration Analysis for Pressurized Branch Pipe Connections [J]. ASME Paper67,1967:951～958
[49]Meng, Q.. Plastic Limit Analysis of Pressure Vessels with Defects[J]. PhD Thesis UMIST,1984.
[50]Plancq, D. Berton, M. N.. Limit Analysis Based on Elastic Compensation Method of Branch[J].
[51]Xuan Fuzhen, Liu Changjun, Hui Hu, et al. Plastic limit pressure of equal-diameter piping branch junctions with axial crack[J]. Chinese Journal of Petroleum Machinery,2001,29 (7):11-14,25
[52]轩福贞,李培宁,孙亮.管道三通塑性极限压力及其影响因素分析[J].油气储运,2000,19(10)：26～31
[53]Folias E S. An axial crack in a pressurized cylindrical shell[J]. Int. J. Fract. Mech.,1965,1:104-113
[54]李培宁等.含轴向裂纹等径焊制三通的塑性极限载荷[J].石油机械,2001,29(7)：11～14,25
[55]李培宁等.含环向裂纹等径焊制三通极限压力(Ⅰ)——有限元分析[J].石油化工设备,2001,30(4)：16～20
[56]李培宁等.含环向裂纹等径焊制三通极限压力(Ⅱ)——工程估算方法[J].石油化工设备,2001,30(5)：28～30
[57]Yahiaoui K, Moffat D G and Moretem D N. Plastic loads of cracked piping branch junctions: experimental results and comparison with numerical data[J]. Int J of Pres Ves&Piping,2000,77 (6):249～260
[58]Grebner. H. et al.. Experimental and Calculation on Crack Opening and Leak Rate of a Pipe Branch Within the HDR-Program [J]. Nuclear Engineering and Design, Vol.147, 1993:79-84
[59]Fuzhen Xuan, Chen Wang, Peining Li. Experimental investigation of the limit load of the ANSI B16.9 tees with and without cracks under internal pressure[J]. Engineering Failure Analysis,2005,12:453～464
[60]GB／T 19624-2004“在用含缺陷压力容器安全评定”[S]
[61]EPRI Research Project 1757-69, Ductile Fracture Handbook. VOLUME 2.1990,6.1-1[S]
[62]中国国家标准化管理委员会.GB／T 8163-2008输送流体用无缝钢管[S].中国标准出版社,2008
[63]喻健良,闫兴清.加强筋对含裂纹平板的止裂性能研究[J].石油化工设备,2008.9(5)：12-16
[64]轩福贞,李培宁,涂善东.复杂载荷下管道三通的塑性极限载荷[J].机械强度,2003,25(6)：646-650
[65]刘彩霞.焊制三通管件塑性极限载荷的有限元分析[D].北京化工大学硕士学位论文.2003
[66]贾慧灵.受外载作用焊接三通塑性极限载荷的有限元分析[D].北京化工大学硕士学位论文2004
[67]徐谦.典型承压结构的塑性极限载荷分析[D].北京化工大学硕士学位论文.2006
[68]闫兴清.加强筋止裂性能研究及管件极限载荷计算[D].大连理工大学硕士学位论文.2006
[69]郑津洋,董其伍,桑芝富.过程装备设计[M].化学工业出版社.2001
[70]喻健良,闫兴清.含轴向内表面裂纹管道极限载荷有限元计算[J].管道技术与设备,2008(2)：4-10
[71]EPRI Research Project 1757-69, Ductile Fracture Handbook. VOLUME 2.1990,6.3-1[S]
[72]栾春远.压力容器ANSYS分析与强度计算[M].北京：中国水利水电出版社,2008
[73]何家胜.圆柱形薄壁压力容器大开孔接管部位的安定性分析[J].武汉：武汉化工学院学报,1997，9：65-67.