Scholarly article on topic 'Residual Stresses in Girth Welded Joint of Layered-to-Solid Cylindrical Vessels: A Finite Element Model'

Residual Stresses in Girth Welded Joint of Layered-to-Solid Cylindrical Vessels: A Finite Element Model Academic research paper on "Materials engineering"

CC BY-NC-ND
0
0
Share paper
Academic journal
Procedia Engineering
OECD Field of science
Keywords
{"Residual stress" / "girth welding joint" / "layered-to-solid cylindrical vessel" / "finite element method"}

Abstract of research paper on Materials engineering, author of scientific article — R.C. Wei, S.G. Xu, C. Wang, X.D. Chen

Abstract Layered cylindrical vessels are used widely in process industries. During the girth welding of layered-to-layered sections, residual stresses are generated and influence the structure integrity. In this paper, the Finite Element Method (FEM) was used to predict the residual stresses in a layered-to-layered joint. The results of numerical calculation show that large residual stresses are generated in the weld and Heat Affect Zone (HAZ). Due to the material mismatching between inner stainless steel layer and outer low alloy steel layer, discontinuous stress distributions occurred. The gap between discrete layers has a great effect on the residual stress in HAZ. Through the whole vessel thickness of multi-layers, the stress distributions in layers are not continuous.

Academic research paper on topic "Residual Stresses in Girth Welded Joint of Layered-to-Solid Cylindrical Vessels: A Finite Element Model"

CrossMark

Available online at www.sciencedirect.com

ScienceDirect

Procedía Engineering 130 (2015) 560 - 570

Procedía Engineering

www.elsevier.com/locate/procedia

14th International Conference on Pressure Vessel Technology

Residual Stresses in Girth Welded Joint of Layered-to-Solid Cylindrical Vessels: A Finite Element Model

R.C. Weiab, S.G. Xua'*, C. Wanga, X.D. Chenab

aCollege of Chemical Engineering, China University of Petroleum (Huadong), Qingdao 266580, China bHefei General Machinery Research Institute, Hefei 230031, China

Abstract

Layered cylindrical vessels are used widely in process industries. During the girth welding of layered-to-layered sections, residual stresses are generated and influence the structure integrity. In this paper, the Finite Element Method (FEM) was used to predict the residual stresses in a layered-to-layered joint. The results of numerical calculation show that large residual stresses are generated in the weld and Heat Affect Zone (HAZ). Due to the material mismatching between inner stainless steel layer and outer low alloy steel layer, discontinuous stress distributions occurred. The gap between discrete layers has a great effect on the residual stress in HAZ. Through the whole vessel thickness of multi-layers, the stress distributions in layers are not continuous. ©2015 The Authors.Published byElsevierLtd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPVT-14

Keywords:Residual stress; girth weldingjoint; layered-to-solid cylindrical vessel; finite element method

1. Introduction

The layered cylindrical vessel has wide engineering applications. Examples of such vessels include layered high pressure cylindrical vessel in process industries, safety chambers for proof testing of small pressure vessels, andhydrogen tanks. It can be divided into several categories depending on the layered vessel type, such as concentric wrapped shell, coil wound, shrink fit, and spiral wrapped. For better performance of such a cylindrical vessel, the design rule is as recommended by ASME VIII-1[1]. The joint of layered-to-solid section is circumferentially welded together. Crack development in the girth welding region of a layered-to-solid joint is a

* Corresponding author. Tel.: +86-532-86983482; fax: +86-532-86983480. E-mail address:xsgl23@163.com

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICPVT-14

doi: 10.1016/j.proeng.2015.12.267

common problem because of the complicated geometry [2]. The presence of weld-induced residual stresses can be a major concern in the structural integrity assessment of the welded parts. These stresses, especially tensile stresses within and near the weld area generally have adverse effects, increasing the susceptibility to fatigue damage, stress corrosion cracking and brittle fracture [3]. Thus, in addition to paying more attention to mechanical and thermal stress, good prediction and an efficient evaluation of the welding residual stress are necessary [4].

In general, welding residual stress field depends on several main factors including material properties, structural dimensions and external constraint condition, welding process parameters such as heat input, welding pass number and sequence, preheating temperature and inter-pass temperature. The approaches to the welding residual stress are including experimental methods, numerical methods, and theoretical methods. Experimental methods, such as X-ray [5], hole-drilling [6], and neutron diffraction [7] are used to measure the welding residual stress in engineering. With the development of computer technology, the finite element method (FEM) has proved to be a powerful tool to predict the residual stress [8-10]. FEM is now being more frequently applied to predict residual stresses in welded components for assessment purposes [11]. An evaluation combined with FEM and experiment to determine the as-welded residual stress field has become a trend.

In the past, a number of FEM models have been proposed and employed to predict welding residuals stress in welded structures. Xu, et al [12] used the Finite Element Method (FEM) to predict the residual stresses in a tube to tube sheet weld. The effect of heat input, preheating temperature, and gap between the tube and tube hole on residual stresses was also investigated by numerical simulation. Jiang, et al [13] developed a sequential coupling finite element procedure to predict residual stresses and deformations in the butt welding of an ultra-thick tube-sheet in a large scale reactor by the finite element method. Yaghi, et al [14] reported the FE simulation of residual stresses, due to the arc-welding of a P92 steel pipe mainly using a nickel-based alloy (In625) as a dissimilar weld material. The structural analysis part of the FE method of determining the residual stress field in the welded pipe was described and the results were presented and discussed. Deng [15] has compared the simulated results of both the temperature field and the welding residual stress field with experimental measurements for the SUS304 stainless steel pipe. The research showed that a 2D axi-symmetric model can also give a reasonable prediction for both the temperature field and the residual stress field in stainless steel pipe except for the welding start-finish location.

The mechanical stress due to inner pressure in girth welded joint of a layered-to-solid cylindrical vessel has been investigated by Zhang [16]. However, the welding residual stress was not taken into consideration. Therefore, it is not clear what the residual stress distribution in weld and HAZ of a layered-to-solidjoint with multi-pass welding is. It is also not clear whether the gaps between layers have any effect on residual stress or not and it is discussed in this paper, with the aim to provide a reference for optimizing the layered-to-solid weld for the cylindrical vessels.

This paper focuses on the residual stress distributions in girth-welded joint of layered-to-solid cylindrical vessel through the numerical investigation that involved a sequentially coupled 2-D thermo-mechanical FE analysis. An axi-symmetric thermal and mechanical model was established and validated by the experimental data in the literature.

2. FE analysis of the residual stress

A sequential coupling thermal-structural analysis procedure combined with the element birth and death technology was used to calculate the welding temperature and residual stress by FE software ABAQUS. The thermal analysis was first carried out to obtain the welding temperature field, and then the temperature results were incrementally applied to the structural model to calculate the residual stress.

2.1. Geometrical model and meshing

The finite element model was simplified for the reason that the layered-to-solid welding geometry and the welding process were very complex. As shown in Fig. 1, the geometrical model of a layered-to-solid welded joint was built with an 8mm thickness of a liner. The total thickness of the strength layers (layer 2-9) without the liner taking into consideration are 62 mm. The interlayer gap is inevitable in the layered cylindrical shell. The real gap ishard to obtain, and thus, a 360 degree uniform interlayer gap of 0.1mm was established for convenience of calculation [17]. Although real welding is a 3D procedure, it is often considered sufficient to represent a

circumferential weld with an axi-symmetric FE model [15]. 2-D simulations are much faster and easier to perform which can also give a reasonable prediction for both temperature field and the residual stress field. Therefore, the methodology described here is based on an axi-symmetric model.

As shown in Fig. 1, the whole welding consists of weld zones 1 and 2. Zone 1 and zone 2 are the weld metal on both sides. Zone 1 has 3 weld layers, and Zone 2 has 12 weld layers. The welding sequence and the weld passes of the welded joint are shown in Fig. 2. There are 42 welding passes in total for welding deposit, and the weld metal is deposited from 1 to 42. For welding layer 1 through layer 4, each layer has one pass, for welding layer 5 through layer 8; each layer has two passes, while the rest of the layers each have three passes. A 2D axi-symmetric model was established and the FE meshing of welded joint is shown in Fig. 3. In total, 4,263 nodes with 3,843 associated elements were meshed. The element type used in heat transfer model is DCAX4 (a 4-node linear axisymmetric heat transfer quadrilateral element), while CAX4R (a 4-node bilinear axisymmetric quadrilateral reduced integration element) in stress model.

Unit: mm

t.1 „

r-TT- a,

Zone 2 ;/ :

7oneI " ' ™ ¿Miei y^jV,

Fig. 1. The geometrical model oflayered-to-solid weldedjoint.

Fig. 2.Welding sequence and passes.

Fig. 3.FE mesh ofthe weldedjoint.

2.2. Material properties

In the layered section, the material of the liner (layer 1) is austenitic stainless steellCrl8Ni9, a Chinese steel grade, which is equivalent to Type 304, and used for corrosion resistance, while the material of dummy layer and strength layers is low alloy steel Q345R, which is a Chinese grade. The welding metal of layer 2-3 are assumed to have the same material properties as the liner that is lCrl8Ni9 steel, while the rest are assumed to have the same material properties as Q345R steel. In the solid section, the clad metal is lCrl8Ni9 steel, and the base metal is lCrl8Ni9 steel. For thermal and mechanical analysis, temperature-dependent thermo-physical and mechanical properties of the materials are incorporated, and the properties of the materials are assumed to keep constant when temperature arise a high level (up to melting temperature), as shown in Table.l.

Table 1. Temperature-dependent thermo-physical and mechanical properties.

Temperature (°C) 20 200 400 600 800

Young's modulus (GPa) 199 180 166 150 125

Yield strength (MPa) 206 153 108 82 69

Poisson's ratio 0.28 0.28 0.28 0.28 0.28

lCrl8Ni9 Density (kg/m3) 8010 7931 7840 7755 7667

Thermal expasion(l/oC*10~6) 16.0 17.2 18.2 18.6 19.5

Thermal conductivity (W/m °C) 15.26 17.6 20.2 22.8 25.4

Specific heat(J/kg °C) 500 544.3 582 634 686

Young's modulus (GPa) 200 183 160 150 125

Yield strength (MPa) 345 310 280 210 160

Poisson's ratio 0.3 0.3 0.3 0.3 0.3

Q345 Density (kg/m3) 7850 7840 7830 7820 7810

Thermal expasion(l/oC*10~6) 14.0 14.2 16.0 16.6 18

Thermal conductivity (W/m °C) 53.17 47.73 39.57 36.01 33

Specific heat(J/kg °C) 461 523 607 678 700

2.3. Temperature field analysis

Temperature field used as the primary input data for the structure analysis should be calculated first. The arc heat is modelled with corresponding heat source functions in the FE model. The simulation of weld metal deposition is achieved by "Element birth and death" technology. To achieve the "element death" effect, the ABAQUS program does not actually remove "killed" elements. Instead, it deactivates them by multiplying their stiffness (or conductivity, or other analogous quantity) by a severe reduction factor. Before welding, the weld metal elements are killed. Once the welding starts, the welded pass is alive and heated, then it is cooled down until the next weld pass cycle begins.

The distributed heat flux, DFLUX, is given by

DFLUX =-(1)

The net line energy is given by

Q = —- (2)

where U is the voltage, I is the current, ^ is the arc efficiency, which were 24V, 200 A and 0.7, respectively. The weld pass volume V, which is a 3-D parameter, is related to the duration t that is equal to the time taken by the weld electrode to move around volume V, causing it to melt, as it travels around the circumference at speed v (3mm/s). The value of V related to the effective volume of the weld material is directly influenced by the heat generation in the axi-symmetric simulation, so it can only be estimated. As a guideline, a fraction of the circumference equal to 1/16-1/2 of a radian can be used to estimate V. In this simulation, the value 1/8 was set at this study. The reasonable molten zone size is achieved when the melting temperature (1340-1390°C) is reached in all the elements that are included in the particular weld pass [18-19].

Heat losses are inevitably during the heating cycle process which should be taken into calculation for highly accuracy. Thermal radiation losses and convection losses are two portions of the total heat losses. Radiation losses are dominant for higher temperatures in and around the weld zone while convection losses for lower temperatures away from the weld zone. As for the boundary conditions applied to the thermal model, their combined effect is represented in the following two equations for the temperature-dependent heat transfer coefficient, h [18]:

2.4. Residual stress analysis

Temperature distribution obtained from thermal analysis was used as input data to calculate the residual stress.The element birth and death technique has also been used in stress analysis. The subsequent thermal-mechanical analysis involves the use of temperature histories computed by the previous heat transfer analysis for each time increment as an input (thermal loading) for the calculation of transient and residual thermal stress distributions. The incremental form of total strain {df} can be described as [20]

where {de6}, {dep} and {deth} is the elastic strain, plastic and thermal strain increment, respectively [20].In residual stress analysis, the elastic strain is modeledusing the isotropic Hooke's rule with temperature-dependentYoung's modulus. The thermal strain is considered using thermalexpansion coefficient of thermal expansion. For the plastic behavior, a rate-independentplastic model is employed with Von Misesyield surface, temperature-dependent mechanical properties and linearisotropic hardening law.

Boundary conditions should be applied to prevent the rigid body motion during the structural analysis. Owing to the axi-symmetry of the FE model, B1 through B9 are constrained in the Y-direction, and B10 is constrained in the X-direction, as shown in Fig. 4.

In order to analyze the results, 5reference paths named PI throughP5are defined as shown in Fig. 4. PI is along the weld centerline (WCL). P2 and P3 are along the inner and outer surfaces of weld and HAZ, respectively. P4and P5 are along the HAZ in the solid section and layered section, through the whole thickness of cylindrical wall, respectively, as shown in Fig. 4.

3. Verification of the FE modeling

To verify the accuracy of the FEM method, a 2D axi-symmetric model of the pipe welding joint with the same geometrical, material and welding parameters as those used in the Lee's paper was generated. The temperature-dependent mechanical and thermal propertied of the material were the same as in literature [21]. The comparisons of the residual stress calculated by FEM and the Lee's experimental measurements by Lee, et al were presented in Ref [22]. The results of comparison indicated that the predicted results from the FE analysis were in reasonably good agreement with the experimental measurements. Therefore, the FE procedure used in Ref [22] can be utilized in the layered-to-solid welded joint in this study.

0.0668T whenO < T < 500° C 0.23 IT - 82.1 whenT > 500° C

Fig. 4. Location ofreference paths andboundary conditions.

4. Results and discussion

4.1. Residual stress distribution contour

The stress contours of radial stress (Sll), axial stress (S22), hoop stress (S33) and von Mises stress are shown in Fig. 5. The peak stresses of radial stress, axial stress and hoop stress are 65.2MPa, 478MPa and 465MPa, respectively. Radial stress (Sll) is very small in the weld and will not be discussed in the following. The peak hoop stress is located on the weld metal, and the peak axial stress is located on HAZ, as shown in Fig. 5. The peak von Mises stress is located on the weld metal near the interface between layer 2 and layer 3. It also can be seen that the stress in the zone near layer 1 and layer 2 is not continuous. This is because the yield strength of layer 1 is smaller than layer 2. The mismatching of yield strength between layer 1 and layer 2 causes an unbalanced distribution of residual stresses.

4.2. Residual stress distribution along WCL

Figure 6 shows the stress distribution along the reference path PI. PI is the center line of the weld metal. The weld metal in this zone is deposited from welding pass 1 to welding pass 42. In the stainless steel side, it is shown that S22 increases from the inner surface to the center, reaching a maximum tensile stress of 350MPa at the interface between stainless steel and low alloy steel. In the low alloy steel zone, the S22 first decreases from the interface between stainless steel and low alloy steel, reaching a tensile stress of 197.5MPa, and then it sharply increases and reaches a maximum tensile stress of 393.2MPa. The S22 again decreases gradually in the rest thickness. The S22 in the interface between stainless steel and low alloy steel is discontinuous. This is because the yield strength of stainless steel is smaller than low alloy steel. The mismatching of yield strength caused an unbalanced distribution of residual stresses.

S33 is tensile stress along the reference path PI. It has the similar varying trend to the S22 in the stainless steel side. In the low alloy side, it is shown that S33 increases gradually, reaching a maximum tensile stress of 456.5MPa at the thickness 5=51mm. From Fig. 6, it can be seen that the maximum compressive hoop stress S33 is located on the starting point of PI, and then increases gradually through the thickness and changes into a maximum tensile stress.

S, S11 (Avg: 100%) - +6.52e+07

--+2.08e+07

--+1.19e+07

--+3.03e+06

-5.84e+06

---1.47e+07

---2.36e+07

■ -3.25e+07

■ -4.13e+07

■ -5.02e+07 ---5.91e+07

■ -6.80e+07

---7.68e+07

---8.57e+07

---9.46e+07

S, S22 (Avg: 100%) r +4.78e+08

Fig. 5. The residual stress contour (a)radial stress; (b) axial stress; (c) hoop stress; (d)von Mises stress.

Stainless stee Low alloy steel

—y......

-■-S33 —•—S99

Radial distance from inner surface(mm]

Fig. 6. Residual stress distributions along WCL (PI).

4.3. Residual stress distribution along the surface

Figure 7 shows the residual stress distributions along the inner surface. It can be seen that the axial stress S22 is tensile and the peak residual stress is 326MPa generated on the interface between weld and HAZ. The tensile hoop stress S33 is present on the weld and HAZ, and varied into compressive stress in the zone away from the weld metal and HAZ. The tensile peak S33 is 143MPa, while the compressive peak S33 is 91MPa.

Axial distance from WCL(mm)

Fig. 7. Residual stress distributions along inner surface (P2).

Figure 8 shows the residual stress distributions along the outer surface. It can be seen that tensile residual stresses are generated on the weld and HAZ. The peak of S22 is 493MPa, which is located in weld, while the peak of S33 is 419MPa presented in the interface between weld metal and HAZ. The residual hoop stresses S33 decreases, and varies into compressive stress in the zone away from the weld metal and HAZ. The compressive peak S33 is 67MPa.

Axial distance from WCL(mm)

Fig. 8. Residual stress distributions along outer surface (P3).

4.4. Residual stress distribution along the HAZ

Figure 9 shows the stress distribution along the reference path P4. It shows that S22 first increases from the inner surface, and then decreases to a constant value of 300MPa. The S22 increases near the outer surface, reaching a

tensile stress of 427MPa. The S33 increases sharply in zone near inner surface and then increases gradually, reaching a maximum tensile stress of 440MPa. The S33 decreases sharply near the outer surface, reaching a tensile stress of287MPa.

0 10 20 30 40 50 60 70

Radial distance from Inner surface(mm)

Fig. 9. Residual stress distributions along HAZ in solid section (P4).

The residual axial stresses along the HAZ in layered section are shown in Figure 10. It can be seen that the stress is discontinuous through whole thickness of cylindrical vessel wall. In each layer, the stress is continuous. The maximum tensile S22 is present on the inner surface of layer 1. The S22 in layer 8 and 9 is almost constant.

As shown in Fig. 11, in each layer, the S33 decreases from inner surface to outer surface. The maximum tensile S33 is present on the inner surface of layer 8, with a value of 450MPa. The discontinuous residual stress distribution in HAZ may be the significant difference between monobloc cylindrical vessel and layered cylindrical vessel.

- 1 2 3 4 5 6 7 8 9

f\ I \ \ \

- i \ \ I I I \ /■

: \ I • • \ i I • • \ • \

- I I «

0 10 20 30 40 50 60 70

Radial distance from inner surface(mm)

Fig. 10. Residual axial stress distribution along HAZ in layered section (P5).

Radial distance from inner surface(mm)

Fig. 11. Residual hoop stress distribution along HAZ in layered section (P5).

5. Conclusions

This study developed a sequential coupling finite element procedure to predict residual stresses in a layered-to-solid welded joint of the cylindrical vessels. The detailed 42 passes simulation with element birth and death was performed to demonstrate the evolution of the residual stress. Based on the obtained results, the following conclusions can be drawn:

(1) During the welding of the layered-to-solid section, large residual stresses are generated in the weld and HAZ, and the residual stresses gradually decrease away from the weld and HAZ. The residual stress distributions in the layered section and solid section are different due to the different geometry ofbase metals.

(2) Due to the material mismatching between inner stainless steel (zone 1) and low alloy steel (zone 2), a discontinuous stress distribution has been generated across the interface between stainless steel layer and low alloy steel layer, as shown in Fig. 8.

(3) The gap between discrete layers has a great effect on the residual stress in HAZ of layers. The residual stresses in each layer at the HAZ demonstrate a bending type distribution.

Acknowledgements

The authors wish to express their gratitude for the financial support by National Natural Science Foundation of China (Grant No.51404284) and Fundamental Research Funds for the Central Universities (Grant No.l5CX05011A).

References

[1] ASME. Boiler and Pressure Vessel Code,Sec. VIII-l.ASME; 2007.

[2] Weiqiang Wang, Aiju Li, Yanyong Zhu, Xiaojing Yao, Yan Liu, Zhonghe Chen, The explosion reason analysis of urea reactor of Pingyin, Eng. Fail. Anal. 16 (2009) 972-986.

[3] Taljat B, Radhakrishnan B, Zacharia T, Numerical analysis of GTA welding process with emphasis on post-solidification phase transformation effects on the residual stresses, Mater. Sci. Eng. A 246 (1998) 45-54.

[4] S.Ghosh, V. P. S. Rana, V. Kain, V. Mittal, S. K. Baveja, Role of residual stresses induced by industrial fabrication on stress corrosion cracking susceptibility ofaustenitic stainless steel, Mater. Des. 32 (2011) 3823-3831.

[10] [11] [12]

[20] [21] [22]

J. A. Martins, L. P. Cardoso, J. A. Fraymann, S. T. Button, Analyses of residual stresses on stamped valves by X-ray diffraction and finite elements method, J. Mater. Process. Tech. 179 (2006) 30-35.

P. J. Bouchard, D. George, J. R. Santisteban, G. Bruno, M. Dutta, L. Edwards, E. Kingston, D. J. Smith, Measurement of the residual stresses in a stainless steel pipe girth weld containing long and short repairs, Int. J. Pres. Ves. Pip. 82 (2005) 299-310. W. Woo, V. Em, C. R. Hubbard, H. J. Lee, K. S. Park, Residual stress determination in a dissimilar weld overlay pipe by neutron diffraction, Mat. Sci. Eng. A 528 (2011) 8021-8027.

W. Jiang, Y. Zhang, W. Woo, Using heat sink technology to decrease residual stress in 316L stainless steel welding joint: Finite element simulation, Int. J. Pres. Ves. Pip. 92 (2012) 56-62.

J. S. Kim, J. H. Seo, A study on welding residual stress analysis of a small bore nozzle with dissimilar metal welds, Int. J. Pres. Ves. Pip. 90-91 (2012) 69-76.

T.H. Hyde, R. Luo, A.A. Becker, Prediction of three-dimensional residual stresses at localized indentations in pipes, Int. J. Pres. Ves. Pip. 93-94(2012) 1-11.

M. Mochizuki, Control of welding residual stress for ensuring integrity against fatigue and stress-corrosion cracking. Nucl.Eng. Des. 237 (2007) 107-123.

S. Xu, W. Wang, Numerical investigation on weld residual stresses in tube to tube sheet joint of a heat exchanger, Int. J. Press. Vess.Pip. 101 (2013)37-44.

W. Jiang, J. M. Gong, W. Woo, Y. F. Wang, S. T. Tu. Control of welding residual stress and deformation of the butt welded ultrathick tube-sheet: effect of applied load. J. Press. Vess.-T. ASME 134(2012) 06140601-08.

A.H. Yaghi, T.H. Hyde, A.A. Becker, W. Sun, Finite element simulation of residual stresses induced by the dissimilar welding of a P92 steel pipe with weld metal IN625, Int. J. Press. Vess.Pip. 111-112 (2013) 173-186.

D. Deng, H. Murakawa, Numerical simulation of temperature field and residual stress in multi-pass welds in stainless steel pipe and comparison with experimental measurements, Comp. Mater. Sci. 37(2006) 269-277.

Y. Zhang, Y. Yang, J. Wang, P. Song, S. Li, M. Hu, X. Zhu. Finite element analysis of the stress conditions in the connection zone between the cylinder and the spherical head of an integrated multilayer wrapped high pressure vessel [J].Chemical machinery, 2010 (3): 319-323.

S. Xu, W. Wang, M. Song, M. Li, J. Tang, Modified formulation of layer stresses due to internal pressure of a layered vessel with interlayer gaps, J. Press. Vess.-T. ASME 132 (20105) 05120101-08.

Yaghi A, Hyde TH, Becker AA, Sun W, Williams J A. Residual stress simulation in thin and thick-walled stainless steel pipe welds including pipe diameter effects. Int J Pres Ves Pip 2006; 83(ll-12):864-874.

B. Brickstad, B.L. Josefson, A parametric study of residual stresses in multi-pass butt-welded stainless steel pipes, Int. J. Pres. Ves. Pip. 75(1998) 11-25.

Deng D, Kiyoshima S. FEM prediction of welding residual stresses in a SUS304 girth-welded pipe with emphasis on stress distribution near weld start/end location. Comp Mater Sci 2010; 50(2): 612-621.

C. H. Lee, K. H. Chang, Three-dimensional finite element simulation of residual stresses in circumferential welds of steel pipe including pipe diameter effects, Mat. Sci. Eng. A. 487 (2008) 210-218.

S. Xu, R. Wei, W. Wang, X. Chen. Residual stresses in the welding joint of the nozzle-to-head area of a layered high-pressure hydrogen storage tank. Int J Hydrogen Energ 39(2014): 11061-11070.