Numerical Simulation of Stress of Pipeline in Mountain Areas with Large Slopes

LIU Congyue; BU Mingzhe; ZHANG Jie; NIU Shengyuan; LIU Yiming; HAN Bin

doi:10.7512/j.issn.1001-2303.2024.08.15

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Numerical Simulation of Stress of Pipeline in Mountain Areas with Large Slopes
- role： First author 第一作者
- Affiliation：
  School of Materials Science and Engineering, China University of Petroleum, Qingdao 266580, China
- Introduction：刘聪月（2001—），女，硕士研究生，主要从事材料焊接新技术的研究。
LIU Congyue
1 ,
- Affiliation：
  School of Materials Science and Engineering, China University of Petroleum, Qingdao 266580, China
  PipeChina Engineering Technology Innovation Co., Ltd., Tianjin 300450, China
BU Mingzhe
1 2 ,
- Affiliation：
  Aotai Electric Co., Ltd., Jinan 250101, China
ZHANG Jie
3 ,
- Affiliation：
  School of Materials Science and Engineering, China University of Petroleum, Qingdao 266580, China
NIU Shengyuan
1 ,
- Affiliation：
  School of Materials Science and Engineering, China University of Petroleum, Qingdao 266580, China
LIU Yiming
1 ,
- role： Corresponding author 通讯作者
- Affiliation：
  School of Materials Science and Engineering, China University of Petroleum, Qingdao 266580, China
- Email： hbzhjh@upc.edu.cn
- Introduction：韩　彬（1973—），男，博士，教授，主要从事新材料焊接和表面工程的研究。E-mail：hbzhjh@upc.edu.cn。
HAN Bin
1
Vol. 54, Issue 8, Pages: 108-117(2024)
Published： 25 August 2024 ，
DOI： 10.7512/j.issn.1001-2303.2024.08.15
Accepted：

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刘聪月，卜明哲，张杰，等.大坡度山区管道焊接接头应力数值模拟研究［J］.电焊机，2024，54（8）：108-117.

LIU Congyue, BU Mingzhe, ZHANG Jie, et al.Numerical Simulation of Stress of Pipeline in Mountain Areas with Large Slopes[J].Electric Welding Machine, 2024, 54(8): 108-117.
刘聪月，卜明哲，张杰，等.大坡度山区管道焊接接头应力数值模拟研究［J］.电焊机，2024，54（8）：108-117. DOI： 10.7512/j.issn.1001-2303.2024.08.15.

LIU Congyue, BU Mingzhe, ZHANG Jie, et al.Numerical Simulation of Stress of Pipeline in Mountain Areas with Large Slopes[J].Electric Welding Machine, 2024, 54(8): 108-117. DOI： 10.7512/j.issn.1001-2303.2024.08.15.

Numerical Simulation of Stress of Pipeline in Mountain Areas with Large Slopes

LIU Congyue ; BU Mingzhe ; ZHANG Jie ; NIU Shengyuan ; LIU Yiming ; HAN Bin ;

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Abstract

The long-distance pipeline passes through mountains and hills, and the laying and welding process sometimes needs to be carried out at a 5°~45° slope. The pipeline in mountain areas with large slopes often fails due to excessive tensile stress, so its stress distribution becomes a necessary research topic. In this paper, the stress distribution of welded joints of X70 steel with a slope of 25° using automatic welding is studied. Based on the Thermal-Metallurgic-Mechanical theory, the finite element model of the welded joints of pipelines in mountainous areas with high slopes is established, and the actual heat source model and construction environment are taken as the boundary conditions. The welded joints are uniquely divided into higher and lower sides, and finally, the stress distribution is obtained, which fills the gap in the study of the stress distribution of welded joints in mountainous areas with large slopes. The hole-drilling method and the coercive method are used to measure the stress level of the inner and outer surfaces of the pipeline to verify the accuracy of the stress simulation. The welded joints are subjected to axial stress along the pipe due to gravity and supporting force. So the stress distribution of welded joints of pipelines in mountain areas with large slopes is different from that of pipelines without slope. The average width of the coarse-grained zone of the root welding layer of the higher side is 27 μm wider than that of the lower side. The average width of the coarse-grained zone of the hot welding layer of the higher side is 21 μm wider than that of the lower side. The tensile stress of the root welding layer of the higher side is 135 MPa higher than that of the lower side, and the high tensile stress zone of the root welding layer of the higher side is 1.6 mm wider than that of the lower side.

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Keywords

large slopes; automatic welding; numerical simulation; higher and lower sides; stress distribution

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0 引言

长输管道因其运量大、安全性高等独特优势获得了广泛的应用^［

1］。近年来，我国长输管道敷设长度共达50万公里^{［Reference 2

Baidu Scholar

2］}。由于长输管道敷设距离长且地势多山区丘陵，管道敷设及焊接过程需经过5°~45°的坡度地形^{［Reference 3

Baidu Scholar

3］}。其中，坡度小于25°的管道焊接工艺基于无坡度管道焊接工艺制定，而坡度25°及以上的管道焊接工艺基于坡度为25°的管道焊接工艺制定^{［Reference 4-5

4-5］}。因此称坡度在25°及以上的山区管道为大坡度山区管道，且坡度为25°的管道焊接工艺为大坡度山区管道焊接工艺的基准^{［Reference 6-7

6-7］}。由于坡度的影响，管道焊接过程中对焊机的爬坡能力、焊接效率等有着极高的要求^{［Reference 8

Baidu Scholar

8］}。全自动焊外根焊工艺因其焊机易于爬坡、焊接效率高等优点成为大坡度山区管道主流的焊接工艺^{［Reference 9-10

9-10］}。

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相较无坡度管道而言，大坡度山区管道常出现因冷裂纹导致的焊接接头断裂失效问题^［

11］。据国家管网西南管道局统计，大坡度山区管道全自动焊焊接接头出现冷裂纹的情况中有82%为拉应力水平过大导致^{［Reference 12

Baidu Scholar

12］}，因此掌握大坡度山区管道焊接接头应力分布成为控制冷裂纹的重要环节。目前，管道应力测量方法主要有盲孔法、中子衍射法、X射线法等^{［Reference 13-16

13-16］}，但由于独特的施工环境、破坏性试验及大型精密仪器无法直接使用等问题导致应力测量困难。Ma^{［Reference 17

Baidu Scholar

17］}及Eva S V^{［Reference 18

Baidu Scholar

18］}等学者曾提出坡度将改变管道焊接接头应力状态的理论，随后Sisan A^{［Reference 19

Baidu Scholar

19］}等人预测了大坡度山区管道焊接接头应力分布结果，但其研究方法为在无坡度管道上添加坡度进行应力分析，导致计算精度较低。随着有限元技术的兴起，因其具有效率高、经济性好等优点，已成为研究管道焊接应力的主流方法。Sabra A^{［Reference 20

Baidu Scholar

20］}等人根据试验建立了TMM（Thermal-Metallurgic-Mechanical）理论并将其应用到应力的有限元模拟过程中。随后Sarvanis^{［Reference 21

Baidu Scholar

21］}等学者使用TMM理论模型对管道焊接应力进行模拟且结果准确，使得TMM理论模型成为管道焊接应力模拟的主流理论模型。Sharma^{［Reference 22

Baidu Scholar

22］}等人基于TMM理论使用有限元法对大坡度管道焊接接头进行应力分析，但其未充分考虑坡度因素。Martin^{［Reference 23

Baidu Scholar

23］}等人使用管道立焊热源模型代替大坡度管道焊接热源模型进行应力分析，但其精度较低。总体来说，针对大坡度管道焊接接头应力的研究方法不明确，至今并未有文献明确指出大坡度山区管道焊接接头应力的分布规律^{［Reference 24-25

24-25］}。

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目前有关大坡度山区管道焊接接头应力分布的研究非常少，为此本文针对X70钢坡度为25°全自动焊外根焊工艺下山区管道焊接接头应力分布规律进行了研究。基于TMM理论对其应力分布进行有限元模拟并进行试验验证，最终得出其应力分布规律。

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1 材料和试验步骤

1.1 试验材料

试验管道外径为813 mm，壁厚17.5 mm。母材及焊材化学成分如表1所示，力学性能如表2所示。全自动焊焊接参数如表3所示。

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表1 母材及焊材化学成分（质量分数，%）

Table 1 Chemical composition of base material and welding materials （wt.%）

材料	C	Mn	P	S	Si	Cr
X70	0.100	1.510	0.008	0.003	0.180	0.025
ACL-X52M	0.069	1.070	0.006	0.003	0.190	0.020
AFR-85K2	0.065	1.150	0.009	0.003	0.009	0.020

Download: CSV

Download: Table Images

表2 母材及焊材机械性能

Table 2 Mechanical properties of base metal and welding materials

材料	屈服强度/MPa	拉伸强度/MPa	延伸率/%
X70	520	580	27
ACL-X52M	453	528	30
AFR-85K2	584	649	26

Download: CSV

Download: Table Images

表3 焊接工艺参数

Table 3 Welding parameters

道次	电流/A	电压/V	焊速 /（mm·s^-1）	热输入 /（kJ·mm^-1）	摆宽 /mm
根焊	120~200	16~22	5~8	0.40~5.05	1~2
热焊	180~230	20~26	31~41	0.90~1.46	3~5
填充焊	180~230	20~26	23~36	0.93~1.97	6~11
盖面焊	180~230	20~26	23~33	0.55~1.45	12~15

Download: CSV

Download: Table Images

1.2 试验步骤

采用SYSWELD有限元软件（SYSWELD2008）进行温度场、微观组织和应力场分布模拟。温度场结果使用热电偶测温仪HPDJ8125进行测量验证。使用4%硝酸酒精腐蚀焊接接头后，使用光学显微镜Leica DM2500 M进行微观组织验证。采用盲孔应力测量仪HP-MK1以及矫顽力应力测量仪NOVOTEST KRC-M2验证应力结果。

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2 大坡度山区管道焊接接头有限元模型的建立

基于TMM理论对大坡度山区管道焊接接头应力进行数值模拟。根据实际焊接接头建立有限元模型，加载热源并设置边界条件。

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2.1 有限元模型

为兼顾计算效率及准确性，模拟过程使用二维旋转有限元模型计算，三维实体有限元模型验证的方法进行研究。大量研究表明，使用二维模型代替三维模型已经广泛应用于管道应力计算中^［

26-29］。为保证计算效率，二维有限元模型网格数自焊缝向其两侧逐渐减少。该模型单边长度为500 mm，最小网格为0.5 mm×0.3 mm。由于大坡度山区管道铺设、焊接及服役过程始终处于一定坡度上，为体现其独特性，本文将大坡度山区管道定义为上下坡口。如图1所示，同一管段较高位置为上坡口，较低位置为下坡口。与无坡度管道不同，大坡度山区管道研究均需区分上下坡口。

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图1 二维有限元模型与三维有限元模型上下坡口示意

Fig.1 Schematic diagram of the higher and lower sides of 2D finite element model and 3D finite element model

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2.2 热源模型

大量文献表明，双椭球热源模型可以用来很好地描述熔化极气体保护焊^［

30-32］。因此，本文使用如式（1）所示的双椭球热源模型，且管道内壁、外壁与空气之间均为对流换热^{［Reference 33

Baidu Scholar

33］}。

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q_{f} (x, y, z) = \frac{12 \sqrt[]{3} η U I}{(a_{f} + a_{r}) b_{h} c_{h} π \sqrt[]{π}} e x p (- \frac{3 x^{2}}{a_{f}} - \frac{3 y^{2}}{b_{h}^{2}} - \frac{3 z^{2}}{c_{h}^{2}}), x \geq 0

q_{r} (x, y, z) = \frac{12 \sqrt[]{3} η U I}{(a_{f} + a_{r}) b_{h} c_{h} π \sqrt[]{π}} e x p (- \frac{3 x^{2}}{a_{r}} - \frac{3 y^{2}}{b_{h}^{2}} - \frac{3 z^{2}}{c_{h}^{2}}), x \geq 0

式中　 $q_{f}$ 、 $q_{r}$ 为热源能量； $η$ 为电弧效率； $U$ 为焊接电压（单位：V）； $I$ 为焊接电流（单位：A）； $a_{f}$ 、 $a_{r}$ 、 $b_{h}$ 、 $c_{h}$ 为双椭球热源参数。

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2.3 冶金与力学模型

本文主要使用扩散及切变模型来描述大坡度山区管道焊接接头固态相变。其扩散及切变模型为Leblond模型及Koistinen-Marburger模型^［

34］，如式（2）所示，Leblond模型主要控制奥氏体-珠光体、奥氏体-贝氏体及奥氏体-铁素体转变。如式（3）所示，切变Koistinen-Marburger模型主要控制奥氏体-马氏体转变。

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\frac{d P (T)}{d t} = f (\dot{T}) \times \frac{P_{e q} (T) - P (T)}{τ (T)}

（2）

式中　 $p$ 为相比例； $t$ 为时间（单位：s）； $\dot{T}$ 为加热或冷却速率； $P_{e q}$ 为相平衡比例； $τ$ 为温度函数。

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P (T) = 1 - e x p (- b (M_{s} - T))

（3）

式中　 $p$ 为马氏体相比例； $T$ 为温度（单位：K）； $M_{s}$ 为马氏体开始转变温度； $b$ 为相变参数（管线钢一般为0.018）。

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Von Mises应力因三向应力考虑全面，常被用来评价应力水平。因此，本文使用Von Mises应力进行应力水平评价，其公式如下所示。

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a_{V o n} = \sqrt[]{((a_{1} - a_{2})^{2} + (a_{2} - a_{3})^{2} + (a_{3} - a_{1})^{2}) / 3}

（4）

式中　 $a_{1}$ 、 $a_{2}$ 、 $a_{3}$ 为三向应力水平。此外，本研究中泊松比始终为0.33。

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2.4 边界条件建立

如图2所示，与无坡度管道焊接接头不同，大坡度山区管道在坡度地形上施工导致其受到重力的影响。由于同时受到地面的支持力，焊接接头受到重力的影响并非竖直向下而是延管道轴向。这个力成为了坡度对山区管道独特的影响因素，同时也成为了其应力模拟计中独特的边界条件。

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图2 大坡度山区管道受力方式

Fig.2 Stress mode of pipelines in mountainous area with large slopes

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3 模拟结果分析

在有限元模型、热源模型及边界条件建立后，通过有限元模拟计算得到温度场、组织分布及应力场。

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3.1 温度场分析

如图3所示，模拟所得整体焊缝形貌与实际基本相同，同时峰值温度及t_8/5数值也基本相同，证明了模拟热源加载的准确性。

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图3 温度场分布

Fig.3 Temperature distribution

3.2 组织分布分析

温度场决定了焊接接头组织的分布情况，模拟所得焊接接头组织分布如图4所示，焊缝区以贝氏体组织为主。上下坡口热影响区组织均为贝氏体及铁素体组织。通过光镜对焊接接头组织的拍摄也验证了模拟所得的结论。但与无坡度管道焊接接头组织分布基本对称不同，根焊及热焊层粗晶区上下坡口不对称。根焊层上坡口粗晶区平均宽度较下坡口宽27 μm。热焊层上坡口粗晶区平均宽度较下坡口宽21 μm。

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图4 组织对比

Fig.4 Microstructure comparison

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3.3 应力场分析

基于温度场及组织场的分析最终得到大坡度山区管道焊接接头应力分布规律，应力分布云图如图5所示。与无坡度管道焊接接头轴向应力水平对称的现象不同，受到坡度的影响，大坡度山区管道焊接接头出现了上下坡口轴向应力水平不对称，上坡口拉应力水平较高，且高拉应力区较宽的现象。根焊层上坡口高应力区较下坡口宽2.2 mm。Von Mises应力水平也出现了同样的现象，根焊层上坡口Von Mises高拉应力区较下坡口高拉应力区宽1.6 mm。

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图5 应力分布

Fig.5 Stress distribution

通过云图可以发现，受坡度影响，大坡度山区管道焊接接头根焊层及热焊层呈现上下坡口应力水平不对称，上坡口拉应力水平高且高拉应力区宽的现象。但云图只能定性表征应力分布情况。为准确表征大坡度山区管道焊接接头应力状态，根据图6对不同焊层进行应力分析。

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图6 应力分析路径

Fig.6 Stress analysis path

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轴向应力分布如图7所示。与无坡度管道焊接接头应力分布对称的现象不同，受坡度影响，根焊层上下坡口应力水平不同，上坡口拉应力水平高，最高拉应力为628 MPa，位于上坡口热影响区，下坡口相同位置处应力为453 MPa。热焊层也出现了上下坡口应力不对称的现象。

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图7 轴向应力分布

Fig.7 Axial stress distribution

环向应力分布如图8所示。环向应力分布与轴向应力分布不同。因大坡度山区管道主要受到重力及支持力导致的轴向应力的影响，因此环向应力仍保持焊缝两侧应力水平对称分布的情况。

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图8 环向应力分布

Fig.8 Hoop stress distribution

焊接接头Von Mises应力分布如图9所示。受坡度影响，根焊层上下坡口应力水平不对称，上坡口拉应力水平较高，最高拉应力为639 MPa，出现在上坡口热影响区，下坡口相同位置应力为504 MPa。热焊层最大拉应力为625 MPa，出现在上坡口热影响区，下坡口相同位置处应力为507 MPa。

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图9 Von Mises应力分布

Fig.9 Von Mises stress distribution

为验证应力模拟结果准确，通过盲孔法及矫顽力法对管道内表面及外表面应力水平进行测量。如图10所示，模拟值与测量值误差在10%以内。实际测量同样表明，根焊层轴向应力呈现上下坡口应力水平不对称，上坡口拉应力水平高且高应力区宽的现象。

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图10 模拟与试验对比

Fig.10 Comparison between simulation and experiment

4 结论

本文针对坡度为25°全自动焊外根焊工艺下的大坡度山区管道焊接接头（X70钢）应力分布规律进行了深入研究。基于TMM理论，通过有限元模拟和试验验证，得出以下结论：

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（1）与无坡度管道焊接接头不同，大坡度山区管道受到重力与地面支持力的共同作用，最终其焊接接头受到延管道轴向应力的影响。

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（2）与无坡度管道不同，受到坡度影响，大坡度山区管道根焊层上坡口粗晶区平均宽度较下坡口宽27 μm，热焊层上坡口粗晶区平均宽度较下坡口宽21 μm。

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（3）受到沿管道轴向应力的影响，与无坡度管道焊接接头应力分布状态不同，大坡度山区管道焊接接头根焊层及热焊层均出现上下坡口应力水平不对称，上坡口拉应力水平较高且高拉应力区较宽的现象。根焊层上坡口拉应力较下坡口高135 MPa；高拉应力区较下坡口宽2 mm。

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摘要

长输管道经过的地势多山区丘陵，管道敷设及焊接过程有时需在5°~45°坡度情况下进行。大坡度山区管道常出现因过大的拉应力导致失效的现象，因此其应力分布成为必要的研究课题。文中就坡度为25°的X70钢全自动焊外根焊工艺下山区管道焊接接头应力分布规律进行研究。基于TMM理论，根据实际焊接接头建立大坡度山区管道焊接接头有限元模型，将实际热源模型及施工环境作为边界条件，独特将焊接接头分为上下坡口，最终得到其应力分布规律，填补了大坡度山区管道焊接接头应力分布研究的空白。通过盲孔法及矫顽力法对管道内外表面应力水平进行测量，验证应力模拟结果准确性。通过模拟与实际测量得到结论，由于重力及支持力的作用，焊接接头受到沿管道轴向的应力，导致大坡度山区管道焊接接头应力分布与无坡度管道不同。其根焊层上坡口粗晶区平均宽度较下坡口宽27 μm，热焊层上坡口粗晶区平均宽度较下坡口宽21 μm。根焊层上坡口拉应力较下坡口高135 MPa，高拉应力区较下坡口宽1.6 mm。

Abstract

The long-distance pipeline passes through mountains and hills

and the laying and welding process sometimes needs to be carried out at a 5°~45° slope. The pipeline in mountain areas with large slopes often fails due to excessive tensile stress

so its stress distribution becomes a necessary research topic. In this paper

the stress distribution of welded joints of X70 steel with a slope of 25° using automatic welding is studied. Based on the Thermal-Metallurgic-Mechanical theory

the finite element model of the welded joints of pipelines in mountainous areas with high slopes is established

and the actual heat source model and construction environment are taken as the boundary conditions. The welded joints are uniquely divided into higher and lower sides

and finally

the stress distribution is obtained

which fills the gap in the study of the stress distribution of welded joints in mountainous areas with large slopes. The hole-drilling method and the coercive method are used to measure the stress level of the inner and outer surfaces of the pipeline to verify the accuracy of the stress simulation. The welded joints are subjected to axial stress along the pipe due to gravity and supporting force. So the stress distribution of welded joints of pipelines in mountain areas with large slopes is different from that of pipelines without slope. The average width of the coarse-grained zone of the root welding layer of the higher side is 27 μm wider than that of the lower side. The average width of the coarse-grained zone of the hot welding layer of the higher side is 21 μm wider than that of the lower side. The tensile stress of the root welding layer of the higher side is 135 MPa higher than that of the lower side

and the high tensile stress zone of the root welding layer of the higher side is 1.6 mm wider than that of the lower side.

关键词

管道全自动焊接数值模拟上下坡口应力分布

Keywords

large slopesautomatic weldingnumerical simulationhigher and lower sidesstress distribution

references

CAPEK J，TROJAN K，KEC J，et al. On the Weldability of Thick P355NL1 Pressure Vessel Steel Plates Using Laser Welding［J］. Materials （Basel），2020，14（1）： 131.

CHUN Y S，PARK K-T，LEE C S. Delayed static failure of twinning-induced plasticity steels［J］. Scripta Materialia，2012，66（12）：960-965.

GAO X，SHAO Y，XIE L，et al. Prediction of Corrosive Fatigue Life of Submarine Pipelines of API 5L X56 Steel Materials［J］.Materials（Basel），2019，12（7）：1031.

GOU R，ZHANG Y，XU X，et al. Residual stress measurement of new and in-service X70 pipelines by X-ray diffraction method［J］. NDT & E International， 2011，44（5）：387-393.

LE J，TIAN Y，MENDES J，et al. Deep learning for radial SMS myocardial perfusion reconstruction using the 3D residual booster U-net［J］. Magnetic Resonance Imaging，2021，83：178-188.

MARQUES E S V，SILVA F J G，PEREIRA A B. Comparison of Finite Element Methods in Fusion Welding Processes—A Review［J］. Metals，2020，10（1）：75.

MIRZAEE-SISAN A，WU G. Residual stress in pipeline girth welds- A review of recent data and modelling ［J］. International Journal of Pressure Vessels and Piping，2019，169：142-152.

SABRA ATIA M K，JAIN M K. A parametric study of FE modeling of die-less clinching of AA7075 aluminum sheets［J］. Thin-Walled Structures， 2018， 132：717-728.

SARVANIS G C，CHATZOPOULOU G，FAPPAS D，et al. Bending response of lap welded steel pipeline joints ［J］. Thin-Walled Structures，2020，157：107065.

SHARMA S K，MAHESHWARI S. A review on welding of high strength oil and gas pipeline steels［J］. Journal of Natural Gas Science and Engineering，2017，38：203-217.

WALD F，VILD M，KUŘíKOVá M，et al. Finite‐Element‐Bemessung von Stahlverbindungen basierend auf der Komponentenmethode［J］. Stahlbau，2020，89（5）：482-495.

XU K，QIAO G Y，SHI X B，et al. Effect of stress-relief annealing on the fatigue properties of X80 welded pipes［J］. Materials Science and Engineering： A，2021，807：140854.

REN X B，ZHANG Z L，NYHUS B. Effect of residual stresses on ductile crack growth resistance［J］. Engineering Fracture Mechanics，2010，77（8）：1325-1337.

RONG Y，XU J，HUANG Y，et al. Review on finite element analysis of welding deformation and residual stress［J］. Science and Technology of Welding and Joining，2017，23（3）：198-208.

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