球形储罐局部消应力热处理的机理与效果评价研究
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摘要
球形储罐是应用广泛的大型压力容器。使用中发现裂纹等缺陷后通常需要进行补焊和局部消应力热处理。目前各国标准中均未给出有效的关于球形储罐局部热处理的规定。公开报道的案例表明,对局部热处理远未达到有效控制水平。
本文采用有限元数值模拟和试验相结合的方法对球形储罐局部热处理问题进行了研究。研究中提出了考察区域的概念以及以此为基础的局部加热过程热跟踪的算法,建立了球形储罐多层多道补焊过程数值模拟模型和三种局部加热过程分析模型,并开发出了对应的运算程序。为分析局部热处理的效果,提出了补焊区域表面平均残余应力、熔敷金属平均残余应力和结构最大残余应力三种评价方法。通过大规模系列运算,得出了许多有价值的结论。
研究发现,若采用小面积集中加热,局部加热过程本身会带来足以引起材料屈服的残余热应力。虽然残余热应力在冷却过程中产生,但造成残余热应力的真正原因是加热、恒温过程形成的塑性应变和蠕变应变,而冷却速度对残余热应力基本无影响。当同时考虑焊接残余应力时,局部加热过程本身带来的热应力仍是影响热处理效果的主要控制因素。增加加热面积可以有效降低局部加热带来的残余热应力,提高残余应力消除率。
分析表明,在球形容器局部热处理中,焊接残余应力的消除机制包括高温屈服和高温蠕变。材料的高温蠕变起到两个相反的作用,它有利于焊接残余应力的消除,但会增加局部热处理过程本身带来的残余热应力。在材料屈服、蠕变和温度梯度共同作用下,局部热处理存在最优的恒温温度和恒温时间。
对十种可能的影响因素进行了逐一分析,表明球形储罐体积、壁厚、加热区域弧长半径和恒温温度是影响局部热处理效果的主要因素;环形保温带宽、加热升温速度、恒温时间和考察区域尺寸对热处理效果影响不显著,为次要因素;冷却速度(包括加速冷却)和加热面布置对补焊残余应力消除效果几乎没有影响。
基于合于使用的原则,得出球形储罐局部热处理加热区域弧长半径的推荐准则为R_(heat)≥3.4(R_it)~(1/2)。这时,可以将考察区域的残余应力平均值控制在30%σ_s左右,最大残余应力可控制在50%σ_s左右,对应的焊接残余应力消除率可分别达到75%和67%。
Spherical tanks are widely used large-scale pressure vessels. Repair welding and local stress-relief heat treatment (LSRHT) is usually employed in case defects such as cracks are found. Effective specifications on LSRHT are not yet given in the standards presently available. It shows from the analysis on the published cases that the LSRHT is far away from effectively controlling.
Researches on LSRHT of spherical tanks are performed in this paper based on the methodology of combination of numerical simulation and experiments. The concept of observed region and based on that, the arithmetic for the thermal tracing of LSRHT process are put forward. A model simulating the multi-layer multi-bead repair welding process and three models for the LSRHT process are founded, and the corresponding programs are developed in which especially the thermal tracing program is included. In order to analysis the efficiency of LSRHT, three evaluation methods are employed, viz. the maximum residual stress, the average residual stresses on the weld surface and in the deposit metal. Through large-scale series analysis, many valuable conclusions are obtained.
It is found that the LSRHT process itself does cause obvious residual thermal stress that is high enough to cause yield when concentrated heating on small region is adopted. The residual thermal stress is formed phenomenally in the cooling period, however, the plastic and creep strain formed in the heating and holding periods are found to be the real reason, and the cooling rate can hardly affect the final stress. In the analysis in which the weld residual stress is included, the thermal stress induced by local heating is still the main control factor. Sufficiently enlarged heated region can lower effectively the residual thermal stresses, and also results in desirable relief efficiency of weld residual stress.
The analysis shows that the relief mechanism of weld residual stress includes high temperature yield and creep. In the LSRHT process of spherical tank, the creep mechanism has two opposite effects, it is helpful for the relief of weld residual stress, but can enlarge the residual thermal stress induced by LSRHT process itself. Under the combination effect of yield, creep and thermal gradient, best holding temperature and holding time exist.
It can be found through one by one analysis on ten factors which are possibly influential on stress relief ratio, arc radius of heated region, holding temperature, volume and wall thickness of spherical tanks are primary effective factors. Band width of annular insulated region, heating rate, holding time and the size of observed region are secondary factors. Heating pattern and cooling rate (include accelerated cooling) can hardly affect the relief ratio of weld residual stress.
Based on the principle of“Fitness for Purpose”, the recommended criterion about arc radius of heated region is R heat≥3.4Rit. In this case, the average residual stress in observed region can be controlled approximately at 30%σs, and the maximum residual stress at 50%σ_s, the corresponding relief ratios of weld residual stress are 75% and 67%, respectively.
本文采用有限元数值模拟和试验相结合的方法对球形储罐局部热处理问题进行了研究。研究中提出了考察区域的概念以及以此为基础的局部加热过程热跟踪的算法,建立了球形储罐多层多道补焊过程数值模拟模型和三种局部加热过程分析模型,并开发出了对应的运算程序。为分析局部热处理的效果,提出了补焊区域表面平均残余应力、熔敷金属平均残余应力和结构最大残余应力三种评价方法。通过大规模系列运算,得出了许多有价值的结论。
研究发现,若采用小面积集中加热,局部加热过程本身会带来足以引起材料屈服的残余热应力。虽然残余热应力在冷却过程中产生,但造成残余热应力的真正原因是加热、恒温过程形成的塑性应变和蠕变应变,而冷却速度对残余热应力基本无影响。当同时考虑焊接残余应力时,局部加热过程本身带来的热应力仍是影响热处理效果的主要控制因素。增加加热面积可以有效降低局部加热带来的残余热应力,提高残余应力消除率。
分析表明,在球形容器局部热处理中,焊接残余应力的消除机制包括高温屈服和高温蠕变。材料的高温蠕变起到两个相反的作用,它有利于焊接残余应力的消除,但会增加局部热处理过程本身带来的残余热应力。在材料屈服、蠕变和温度梯度共同作用下,局部热处理存在最优的恒温温度和恒温时间。
对十种可能的影响因素进行了逐一分析,表明球形储罐体积、壁厚、加热区域弧长半径和恒温温度是影响局部热处理效果的主要因素;环形保温带宽、加热升温速度、恒温时间和考察区域尺寸对热处理效果影响不显著,为次要因素;冷却速度(包括加速冷却)和加热面布置对补焊残余应力消除效果几乎没有影响。
基于合于使用的原则,得出球形储罐局部热处理加热区域弧长半径的推荐准则为R_(heat)≥3.4(R_it)~(1/2)。这时,可以将考察区域的残余应力平均值控制在30%σ_s左右,最大残余应力可控制在50%σ_s左右,对应的焊接残余应力消除率可分别达到75%和67%。
Spherical tanks are widely used large-scale pressure vessels. Repair welding and local stress-relief heat treatment (LSRHT) is usually employed in case defects such as cracks are found. Effective specifications on LSRHT are not yet given in the standards presently available. It shows from the analysis on the published cases that the LSRHT is far away from effectively controlling.
Researches on LSRHT of spherical tanks are performed in this paper based on the methodology of combination of numerical simulation and experiments. The concept of observed region and based on that, the arithmetic for the thermal tracing of LSRHT process are put forward. A model simulating the multi-layer multi-bead repair welding process and three models for the LSRHT process are founded, and the corresponding programs are developed in which especially the thermal tracing program is included. In order to analysis the efficiency of LSRHT, three evaluation methods are employed, viz. the maximum residual stress, the average residual stresses on the weld surface and in the deposit metal. Through large-scale series analysis, many valuable conclusions are obtained.
It is found that the LSRHT process itself does cause obvious residual thermal stress that is high enough to cause yield when concentrated heating on small region is adopted. The residual thermal stress is formed phenomenally in the cooling period, however, the plastic and creep strain formed in the heating and holding periods are found to be the real reason, and the cooling rate can hardly affect the final stress. In the analysis in which the weld residual stress is included, the thermal stress induced by local heating is still the main control factor. Sufficiently enlarged heated region can lower effectively the residual thermal stresses, and also results in desirable relief efficiency of weld residual stress.
The analysis shows that the relief mechanism of weld residual stress includes high temperature yield and creep. In the LSRHT process of spherical tank, the creep mechanism has two opposite effects, it is helpful for the relief of weld residual stress, but can enlarge the residual thermal stress induced by LSRHT process itself. Under the combination effect of yield, creep and thermal gradient, best holding temperature and holding time exist.
It can be found through one by one analysis on ten factors which are possibly influential on stress relief ratio, arc radius of heated region, holding temperature, volume and wall thickness of spherical tanks are primary effective factors. Band width of annular insulated region, heating rate, holding time and the size of observed region are secondary factors. Heating pattern and cooling rate (include accelerated cooling) can hardly affect the relief ratio of weld residual stress.
Based on the principle of“Fitness for Purpose”, the recommended criterion about arc radius of heated region is R heat≥3.4Rit. In this case, the average residual stress in observed region can be controlled approximately at 30%σs, and the maximum residual stress at 50%σ_s, the corresponding relief ratios of weld residual stress are 75% and 67%, respectively.
引文
[1] 韩伟基,中国球形容器建设回顾与展望,石油工程建设,1999 年第 1 期:2～5
[2] 国家质量技术监督局,GB12337-1998 钢制球形储罐,中华人民共和国国家标准,北京:中国标准出版社,1999
[3] 李友,杨成刚,球形储罐焊后热处理,金属热处理,2002,27(3):42～44
[4] 陈志华,涂善东,王正东,反射板对球罐整体热处理内部流场的影响,石油化工设备,2004,33(6):13～16
[5] 陈志华,涂善东,王正东,大型球罐整体热处理改进方法与数值模拟,金属热处理,2004,29(3):43～45
[6] 国家质检总局特种设备事故调查处理中心,特种设备典型事故案例集,北京:航空工业出版社,2005
[7] 中华人民共和国国务院令第 373 号,特种设备安全监察条例,2003-03
[8] 中华人民共和国机械工业部,JB4732-95 钢制压力容器——分析设计标准,中华人民共和国行业标准,北京:机械工业出版社,1995
[9] 王泽军,萧艳彤,黄长河等,液化石油气球罐裂纹成因分析与讨论,化工机械,2005,32(4):237～240,242
[10] Beom No Lee, Effect of residual stresses on fracture behavior of weldments, Dissertation for the Degree of Philosophy in the Graduate School of the Ohio University, 2001
[11] 王泽军,吴海,陆金明等,CF62 钢制丙烯球罐的检验与分析,中国锅炉压力容器安全 2000,16(1):25～28
[12] 天津市特种设备监督检验技术研究院,在用压力容器检验报告书,津容定检2004-1654 号,2005 年 3 月 4 日
[13] 天津市特种设备监督检验技术研究院,压力容器全面检验报告,津容定检2005-0678 号,2005 年 6 月 8 日
[14] 张悦,查玉辉,顾春兰等,低温球罐焊缝返修产生延迟裂纹的修复,石油化工设备,2003,32(4):25～26
[15] 中华人民共和国国家质量监督检验检疫总局,TSG R7001-2004 在用压力容器定期检验规则,特种设备安全技术规范,北京:中国计量出版社,2004-08
[16] 陈伯蠡,焊接工程缺欠分析与对策,北京:机械工业出版社,1998
[17] 国家质量技术监督局,压力容器安全技术监察规程,北京:中国劳动社会保障出版社,1999
[18] 中华人民共和国劳动部,蒸汽锅炉安全技术监察规程,北京:劳动部中国锅炉压力容器安全杂志社,1996
[19] 国家质量技术监督局,GB150-1998 钢制压力容器,中华人民共和国国家标准,北京:中国标准出版社,1998
[20] ASME Code for Pressure Piping, B31.1-2001 Power Piping, An American national standard, American Society of Mechanical Engineers, New York, 2001
[21] ASME Code for Pressure Piping, B31.3-2002 Process Piping, An American national standard, American Society of Mechanical Engineers, New York, 2002
[22] ASME Boiler and Pressure Vessel Code, Rules for Construction of Pressure Vessels, Section VIII, Division 1, UW-40, American Society of Mechanical Engineers, New York, 2001
[23] ASME Boiler and Pressure Vessel Code, Rules for Construction of Pressure Vessels: Alternative Rules, Section VIII, Division 2, Part AF, American Society of Mechanical Engineers, New York, 2001
[24] ASME Boiler and Pressure Vessel Code, Rules for Construction of Pressure Vessels: Alternative Rules for Construction of High Pressure Vessels, Section VIII, Division 3, Part KF, American Society of Mechanical Engineers, New York, 2001
[25] 张亦良,徐学东,程咏梅,2000m3在役压力容器应力状况分析,实验力学,2001,16(3):276～282
[26] 张亦良,徐学东,王泽军,1500m3液化石油气球罐残余应力分析,石油化工设备,2004,33(6):9～12
[27] 王泽军,牛卫飞,球形容器局部热处理效果评价——现状与解决思路,特种设备安全国际论坛文集境内论文选集(二),北京:中国标准出版社,2006,725～729
[28] 袁相启,徐世忠,赵有明等,ATK901 球罐焊接修复中的局部热处理,焊接,1987(8):17～20
[29] 许强,江平,方国爱等. 压力容器局部焊后热处理试验研究. 焊接技术,1989(6):31～33
[30] 汪建华,陆皓,局部焊后热处理最佳加热条件的研究(一)一种基于粘弹塑性有限元分析的直接评定方法,压力容器,1999,16(1):14～17
[31] 汪建华,陆皓,局部焊后热处理最佳加热条件的研究(二)临界加热宽度的确定准则,压力容器,1999,16(2):8～11
[32] 汪建华,陆皓,村川英一,局部焊后热处理加热宽度的直接评定方法,焊接学报,2000,21(2):39～42
[33] Jianhua Wang, Hao LU, Hidekazu MURAKAWA, Mechanical behavior in local post weld heat treatment (Report I) – Visco-Elastic-Plastic FEM analysis of local PWHT, Trans. JWRI, 1998, 27 (1): 24~29
[34] Hidekazu MURAKAWA, Hao LU, Jianhua Wang, Mechanical behavior in local post weld heat treatment (Report II) - Determination of critical heated band during local PWHT, Trans. JWRI, 1998, 27 (1): 20~26
[35] 陆皓,汪建华,村川英一,三维管接头焊后局部热处理加热宽度准则,焊接学报,2001,22(1):11～14
[36] 陆皓,汪建华,村川英一,Cr-Mo 钢管子局部焊后热处理加热宽度准则的确定,焊接学报,2006,27(3):5～8
[37] McEnerney J W. Recommended Practices for Local Heating of Weld in Pipe and Tubing. ANSI/AWS D10.10, 1998
[38] 汪建华,陆皓,魏良武等,局部焊后热处理两类评定准则的研究,机械工程学报,2001,37(6):24～28
[39] 陆皓,汪建华,村川英一,基于粘弹塑性理论局部焊后热处理评定准则,上海交通大学学报,2001,35(3):427～430
[40] 杨世铭,陶文铨,传热学,北京:高等教育出版社,1998
[41] 上海材料研究所,机械工业常用材料性能数据手册(第一册),1987-12
[42] 潘家祯,压力容器材料实用手册——碳钢及合金钢,北京:化学工业出版社,2000
[43] 国家技术监督局,GB6654-1996 压力容器用钢板,中华人民共和国国家标准,北京:中国标准出版社,1996-04
[44] Lars-Erik Lindgren, Henrik Alberg, Konstantin Domkin, Constitutive modeling and parameter optimization, Paper of VII International Conference on Computational Plasticity (COMPLAS 2003), CIMNE, Barcelona, 2003
[45] H. Alberg, D. Berglund, Comparison of plastic, viscoplastic and creep models when modeling welding and stress relief heat treatment, Comput. Methods Appl. Mech. Engrg. 2003, 192: 5189-5208
[46] Henrik Alberg, Simulation of Welding and Heat Treatment: Modeling and Validation, Doctoral thesis, Lule? University of Technology, 2005
[47] 陈钢,含凹坑压力容器极限与安定性数值分析,博士学位论文,清华大学,1994
[48] 张翼,边缘应力区局部减薄强度特征的研究,硕士学位论文,天津大学,2006
[49] 倪红芳,凌祥,涂善东,多道焊三维残余应力场有限元模拟,机械强度,2004,26(2):218～222
[50] 董俊慧,霍立兴,张玉凤,环焊缝管道焊接应力应变三维有限元分析,机械工程学报,2001,37(12),86～89
[51] 陈翠欣,李午申,王庆鹏等,焊接温度场的三维动态有限元模拟,天津大学学报,2005,38(5):466～470
[52] P. Duranton, J. Devaux, V. Robin et al, 3D modelling of multipass welding of a 316L stainless steel pipe, Journal of Materials Processing Technology 2004, 153–154: 457～463
[53] 朱援祥,张小飞,杨兵等,基于有限元的多次补焊焊接残余应力的数值模拟,焊接学报,2002,23(1):65～68
[54] JAHM Software, MPDB (demo) version 6.51, http://www.jahm.com
[55] B. Brickstad, B. L. Josefson, A parametric study of residual stresses in multi-pass butt-welded stainless steel pipes, International journal of pressure vessels and piping, 1998, 75: 11~25
[56] 贾法勇,不锈钢与铝合金焊接接头疲劳评定的热点应力方法及局部法研究,博士学位论文,天津大学,2004
[57] ANSYS Inc, ANSYS Release 8.0 documentation
[58] 梁晓燕,中厚板多道焊焊接过程中温度场和应力场的三维数值模拟,硕士学位论文,华中科技大学,2004
[59] Thomas H. Courtney, Mechanical behavior of materials, 北京:机械工业出版社(Mc Graw Hill 公司授权原版影印),2004
[60] 国家技术监督局,GB7704-87 X 射线应力测定方法,北京:中国标准出版社,1987
[61] 国家技术监督局,GB/T4338-1995 金属材料 高温拉伸试验,北京:中国标准出版社,1995
[62] OriginLab Corporation, Origin Reference version 7
[63] 穆霞英,蠕变力学,西安:西安交通大学出版社,1990
[64] 国家技术监督局,GB/T2039-1997 金属拉伸蠕变及持久试验方法,北京:中国标准出版社,1997
[2] 国家质量技术监督局,GB12337-1998 钢制球形储罐,中华人民共和国国家标准,北京:中国标准出版社,1999
[3] 李友,杨成刚,球形储罐焊后热处理,金属热处理,2002,27(3):42～44
[4] 陈志华,涂善东,王正东,反射板对球罐整体热处理内部流场的影响,石油化工设备,2004,33(6):13～16
[5] 陈志华,涂善东,王正东,大型球罐整体热处理改进方法与数值模拟,金属热处理,2004,29(3):43～45
[6] 国家质检总局特种设备事故调查处理中心,特种设备典型事故案例集,北京:航空工业出版社,2005
[7] 中华人民共和国国务院令第 373 号,特种设备安全监察条例,2003-03
[8] 中华人民共和国机械工业部,JB4732-95 钢制压力容器——分析设计标准,中华人民共和国行业标准,北京:机械工业出版社,1995
[9] 王泽军,萧艳彤,黄长河等,液化石油气球罐裂纹成因分析与讨论,化工机械,2005,32(4):237～240,242
[10] Beom No Lee, Effect of residual stresses on fracture behavior of weldments, Dissertation for the Degree of Philosophy in the Graduate School of the Ohio University, 2001
[11] 王泽军,吴海,陆金明等,CF62 钢制丙烯球罐的检验与分析,中国锅炉压力容器安全 2000,16(1):25～28
[12] 天津市特种设备监督检验技术研究院,在用压力容器检验报告书,津容定检2004-1654 号,2005 年 3 月 4 日
[13] 天津市特种设备监督检验技术研究院,压力容器全面检验报告,津容定检2005-0678 号,2005 年 6 月 8 日
[14] 张悦,查玉辉,顾春兰等,低温球罐焊缝返修产生延迟裂纹的修复,石油化工设备,2003,32(4):25～26
[15] 中华人民共和国国家质量监督检验检疫总局,TSG R7001-2004 在用压力容器定期检验规则,特种设备安全技术规范,北京:中国计量出版社,2004-08
[16] 陈伯蠡,焊接工程缺欠分析与对策,北京:机械工业出版社,1998
[17] 国家质量技术监督局,压力容器安全技术监察规程,北京:中国劳动社会保障出版社,1999
[18] 中华人民共和国劳动部,蒸汽锅炉安全技术监察规程,北京:劳动部中国锅炉压力容器安全杂志社,1996
[19] 国家质量技术监督局,GB150-1998 钢制压力容器,中华人民共和国国家标准,北京:中国标准出版社,1998
[20] ASME Code for Pressure Piping, B31.1-2001 Power Piping, An American national standard, American Society of Mechanical Engineers, New York, 2001
[21] ASME Code for Pressure Piping, B31.3-2002 Process Piping, An American national standard, American Society of Mechanical Engineers, New York, 2002
[22] ASME Boiler and Pressure Vessel Code, Rules for Construction of Pressure Vessels, Section VIII, Division 1, UW-40, American Society of Mechanical Engineers, New York, 2001
[23] ASME Boiler and Pressure Vessel Code, Rules for Construction of Pressure Vessels: Alternative Rules, Section VIII, Division 2, Part AF, American Society of Mechanical Engineers, New York, 2001
[24] ASME Boiler and Pressure Vessel Code, Rules for Construction of Pressure Vessels: Alternative Rules for Construction of High Pressure Vessels, Section VIII, Division 3, Part KF, American Society of Mechanical Engineers, New York, 2001
[25] 张亦良,徐学东,程咏梅,2000m3在役压力容器应力状况分析,实验力学,2001,16(3):276～282
[26] 张亦良,徐学东,王泽军,1500m3液化石油气球罐残余应力分析,石油化工设备,2004,33(6):9～12
[27] 王泽军,牛卫飞,球形容器局部热处理效果评价——现状与解决思路,特种设备安全国际论坛文集境内论文选集(二),北京:中国标准出版社,2006,725～729
[28] 袁相启,徐世忠,赵有明等,ATK901 球罐焊接修复中的局部热处理,焊接,1987(8):17～20
[29] 许强,江平,方国爱等. 压力容器局部焊后热处理试验研究. 焊接技术,1989(6):31～33
[30] 汪建华,陆皓,局部焊后热处理最佳加热条件的研究(一)一种基于粘弹塑性有限元分析的直接评定方法,压力容器,1999,16(1):14～17
[31] 汪建华,陆皓,局部焊后热处理最佳加热条件的研究(二)临界加热宽度的确定准则,压力容器,1999,16(2):8～11
[32] 汪建华,陆皓,村川英一,局部焊后热处理加热宽度的直接评定方法,焊接学报,2000,21(2):39～42
[33] Jianhua Wang, Hao LU, Hidekazu MURAKAWA, Mechanical behavior in local post weld heat treatment (Report I) – Visco-Elastic-Plastic FEM analysis of local PWHT, Trans. JWRI, 1998, 27 (1): 24~29
[34] Hidekazu MURAKAWA, Hao LU, Jianhua Wang, Mechanical behavior in local post weld heat treatment (Report II) - Determination of critical heated band during local PWHT, Trans. JWRI, 1998, 27 (1): 20~26
[35] 陆皓,汪建华,村川英一,三维管接头焊后局部热处理加热宽度准则,焊接学报,2001,22(1):11～14
[36] 陆皓,汪建华,村川英一,Cr-Mo 钢管子局部焊后热处理加热宽度准则的确定,焊接学报,2006,27(3):5～8
[37] McEnerney J W. Recommended Practices for Local Heating of Weld in Pipe and Tubing. ANSI/AWS D10.10, 1998
[38] 汪建华,陆皓,魏良武等,局部焊后热处理两类评定准则的研究,机械工程学报,2001,37(6):24～28
[39] 陆皓,汪建华,村川英一,基于粘弹塑性理论局部焊后热处理评定准则,上海交通大学学报,2001,35(3):427～430
[40] 杨世铭,陶文铨,传热学,北京:高等教育出版社,1998
[41] 上海材料研究所,机械工业常用材料性能数据手册(第一册),1987-12
[42] 潘家祯,压力容器材料实用手册——碳钢及合金钢,北京:化学工业出版社,2000
[43] 国家技术监督局,GB6654-1996 压力容器用钢板,中华人民共和国国家标准,北京:中国标准出版社,1996-04
[44] Lars-Erik Lindgren, Henrik Alberg, Konstantin Domkin, Constitutive modeling and parameter optimization, Paper of VII International Conference on Computational Plasticity (COMPLAS 2003), CIMNE, Barcelona, 2003
[45] H. Alberg, D. Berglund, Comparison of plastic, viscoplastic and creep models when modeling welding and stress relief heat treatment, Comput. Methods Appl. Mech. Engrg. 2003, 192: 5189-5208
[46] Henrik Alberg, Simulation of Welding and Heat Treatment: Modeling and Validation, Doctoral thesis, Lule? University of Technology, 2005
[47] 陈钢,含凹坑压力容器极限与安定性数值分析,博士学位论文,清华大学,1994
[48] 张翼,边缘应力区局部减薄强度特征的研究,硕士学位论文,天津大学,2006
[49] 倪红芳,凌祥,涂善东,多道焊三维残余应力场有限元模拟,机械强度,2004,26(2):218～222
[50] 董俊慧,霍立兴,张玉凤,环焊缝管道焊接应力应变三维有限元分析,机械工程学报,2001,37(12),86～89
[51] 陈翠欣,李午申,王庆鹏等,焊接温度场的三维动态有限元模拟,天津大学学报,2005,38(5):466～470
[52] P. Duranton, J. Devaux, V. Robin et al, 3D modelling of multipass welding of a 316L stainless steel pipe, Journal of Materials Processing Technology 2004, 153–154: 457～463
[53] 朱援祥,张小飞,杨兵等,基于有限元的多次补焊焊接残余应力的数值模拟,焊接学报,2002,23(1):65～68
[54] JAHM Software, MPDB (demo) version 6.51, http://www.jahm.com
[55] B. Brickstad, B. L. Josefson, A parametric study of residual stresses in multi-pass butt-welded stainless steel pipes, International journal of pressure vessels and piping, 1998, 75: 11~25
[56] 贾法勇,不锈钢与铝合金焊接接头疲劳评定的热点应力方法及局部法研究,博士学位论文,天津大学,2004
[57] ANSYS Inc, ANSYS Release 8.0 documentation
[58] 梁晓燕,中厚板多道焊焊接过程中温度场和应力场的三维数值模拟,硕士学位论文,华中科技大学,2004
[59] Thomas H. Courtney, Mechanical behavior of materials, 北京:机械工业出版社(Mc Graw Hill 公司授权原版影印),2004
[60] 国家技术监督局,GB7704-87 X 射线应力测定方法,北京:中国标准出版社,1987
[61] 国家技术监督局,GB/T4338-1995 金属材料 高温拉伸试验,北京:中国标准出版社,1995
[62] OriginLab Corporation, Origin Reference version 7
[63] 穆霞英,蠕变力学,西安:西安交通大学出版社,1990
[64] 国家技术监督局,GB/T2039-1997 金属拉伸蠕变及持久试验方法,北京:中国标准出版社,1997