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Finite element analysis of residual stress in 2.25Cr-1Mo steel pipe during welding and heat treatment process
Journal of Manufacturing Processes 47 (2019) 110–118
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Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Finite element analysis of residual stress in 2.25Cr-1Mo steel pipe during welding and heat treatment process
T
⁎
Sendong Rena,b, Suo Lia, Yifeng Wanga, Dean Denga, , Ninshu Mab a b
College of Material Science and Engineering, Chongqing University, Shazhengjie, Shapingba, Chongqing, 400044, China Joining and Welding Research Institute, Osaka University, Mihogaoka, Ibaraki, Osaka, 567-0047, Japan
A R T I C LE I N FO
A B S T R A C T
Keywords: Numerical simulation Solid-state phase transformation Tempering effect Creep
The circumferential butt-welded pipe was fabricated using 2.25Cr-1Mo steel and then subjected to local postweld heat treatment (LPWHT) for releasing residual stress after multi-pass welding. The sectioning method was employed to measure residual stress. Based on SYSWELD software, a thermo-metallurgical-mechanical coupled computational approach was developed to analyses the residual stress distribution on 2.25Cr-1Mo welded pipe. A three-dimensional finite element model and moving heat source model were employed in simulation. The effects of solid-state phase transformation (SSPT), tempering as well as creep were considered simultaneously. The effectivity of computational approach was verified by experimental measurement. The simulation results showed that SSPT could induce an undulating stress profile and large stress gradient in welded zone. The stress gradient could be reduced during LPWHT while there were stress peaks at the edges of heated region. Tempering effect could decrease the residual stress at high-stress region by material softening and yielding. Creep caused a global transformation from elastic strain to plastic strain, which led to a macro-scale stress relaxation. It is necessary to consider SSTP, tempering as well as creep in material model for more accurate simulation results.
1. Introduction 2.25Cr-1Mo steel is an important structural material in nuclear power plants and ultra-supercritical (USC) power plants. With an excellent resistance to both creep and corrosion at high temperature as well as low thermal expansion coefficient, it is widely used to fabricate steam pipes and turbine rotors [1]. Such large equipment is always assembled by multi-pass welding, its safe operation and service life are mainly determined by the quality of welded joints. During welding process, the nonhomogeneous temperature distribution can introduce residual stress, which is detrimental to the mechanical property of welded joints [2]. Therefore, large welded structures are subjected to post-weld heat treatment in order to mitigate residual stress. As an important indicator of welding quality, residual stress distribution is difficult to measure. Withers et al. [3] compared the capabilities and shortcomings of various stress measurement techniques, they believed it was still a challenge to measure residual stress in the depths of large structure, especially when the equipment was in operation. Therefore, it is valuable to track stress evolution during welding and PWHT process and predict its distribution by numerical simulation method. With special metallurgical character, the solid-state phase transformation (SSPT) will present in Cr-Mo steels during welding and
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PWHT process. Deng et al. proposed that SSPT could introduce volume change, yield strength variation and transformation-induced plasticity (TRIP), which had significant influences on welding residual stress [4]. Tsai et al. investigated the microstructural evolution in 2.25Cr-1Mo steel. Both martensite and bainite existed during high temperature exposure [5]. Nitschke-Pagel and Wohlfahrt reported that bainite and martensite transformation had distinct influences on welding residual stress [6]. Meanwhile, tempering effect and creep could also affect the residual stress in PWHT and service process. Deng and Murakawa [7] investigated the residual stress in multi-pass welded joints, the reduction of residual stress was attributed to tempering and material softening. Holzapfel et al. [8] discussed the stress relaxation behaviors in 40CrMo4. They presented cyclic creep effects could cause an obvious stress relaxation in high temperature. In order to obtain accurate simulation results, all of the above factors should be considered in numerical model. Heretofore, some finite element models have been proposed to study the residual stress in welded pipes. Deng and Murakawa [7] presented that the volume change and yield strength variation induced by martensite transformation had remarkable effect on welding residual stress in 9Cr-1Mo steel. Their investigation about stress distribution in 2.25Cr-1Mo pipe suggested that the phase-dependent material
Corresponding author. E-mail address: [email protected] (D. Deng).
https://doi.org/10.1016/j.jmapro.2019.09.019 Received 17 June 2019; Received in revised form 10 August 2019; Accepted 23 September 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Journal of Manufacturing Processes 47 (2019) 110–118
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properties were necessary for a precise prediction [9]. Yaghi et al. [10] demonstrated the residual stress profiles on P91 multi-pass welded pipe, the undulating contours reflected the effect of volumetric change during martensite transformation. The relationship between pipe diameter and residual stress was also clarified. In thick-walled finite element model, welding stress on surfaces was independent to the pipe diameter, while the state in thin-walled model was different [11]. Katsareas and Youtsos [12] predicted the residual stress field in a dissimilar metal welded pipe based on ANSYS. The “birth and death of elements” technique was applied to consider the successive material depositing in practical production. Their researches shown material model should be specific enough to consider all metallurgical factors and mechanical behaviours as much as possible in order to obtain accurate simulation results. A detail finite element mesh which could realize the actual shape and dimensions of structure was also important. Besides, a 3-D model was established to investigate the feature of stress profiles in SUS304 stainless steel pipe, the results showed that residual stress distributed homogenously along circumferential direction except for weld start-end region [13]. Sattari-Far and Farahani reported the relationship between weld pass number and residual stresses in buttwelded pipes, a large axial tensile stress would appear on the inner surface of thick-wall welded pipe with increasing pass number [14]. Duranton et al. believed 3-D model had advantage to reflect the actual constraint conditions so that the simulation result would be more realistic [15]. However, there are few reports considering both 3-D model and complex metallurgical behaviors simultaneously in welding and LPWHT simulation procedure. In the present study, a full-scale finite element model was established to research the stress distribution on 2.25Cr-1Mo welded pipe. Moving heat source was employed to describe the welding heat input. Welding parameters were identical to practical production. Both diffusive and displacive phase transformation were considered in material model. Tempering effect and creep were taken into account as crucial phenomena during LPWHT. The simulation results were verified by the sectioning method.
Table 1 Chemical composition of base metal and filler metals (wt.%).
Base metal TGS-2CM MGT-2CM
C
Si
Mn
P
S
Cr
Mo
Cu
Al
Ni
0.12 0.09 0.08
0.21 0.32 0.34
0.51 0.71 0.76
0.004 0.007 0.007
0.002 0.005 0.005
2.26 2.26 2.29
0.98 1.04 0.98
0.15 0.13 0.13
0.007 0.015 0.015
0.19 0.17 0.17
Table 2 Welding parameters. Bead No.
Method
Current (A)
Voltage (V)
Welding speed (mm min−1)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
TIG TIG TIG MIG MIG MIG MIG MIG MIG MIG MIG MIG MIG MIG
105 180 180 150 150 250 250 250 250 250 250 250 250 250
11 11 11 19 19 27 27 27 27 27 27 27 27 27
61 107 94 212 207 279 282 265 282 273 295 265 271 277
during TIG and MIG process, respectively. The pre-heat temperature was 150 °C, and the inter-pass temperature was about 180–200 °C. After welding process, local post-weld heat treatment (LPWHT) was applied to the pipe. Lu et al. [16] investigated the mechanical behavior of tubular joint during LPWHT and recommended a criterion to calculate the optimum heated band width. In this study, LPWHT area was 220 mm wide. Local material was heated to 680 °C, preserved for 1 h then cooled slowly. The heating and cooling rates were about 100 °C/h and 50 °C/h, respectively.
2. Experimental procedure
2.2. Residual stress measurement
2.1. Pipe geometry and fabrication process
In present work, the sectioning method was employed to measure residual stress after welding and LPWHT process. It was originally proposed by Kalakoutsky [17] to gauge the residual stress in bar. The principle of sectioning method is shown in Fig.2. Once a small piece is cut from structure, it will deform under the influence of internal stress, and then reflect tensile or compressive strain which can be measured. When applying in plate or cylinder structures, the residual stresses are calculated by following equations:
The 2.25Cr-1Mo circumferential butt-welded pipe was normalized at 930 °C and tempered at 730 °C then fabricated by multi-pass welding. Over dimension as well as welding sequence are shown in Fig. 1. Weld passes 1 to 3 were deposited by tungsten inert gas (TIG) welding using TGS-2CM wire as filler metal. The remaining passes were performed by metal inert gas (MIG) welding depositing MGT-2CM wire. The chemical composition (wt.%) of base metal and filler metals are given in Table 1. The welding parameters are listed in Table 2. 99% Ar and 95% Ar + 5% CO2 were employed to shield the weld zone from atmospheric gases
E (εx + vεy ) 1 − v2 E σy = − (εy + vεx ) 1 − v2 σx = −
(1)
where, E and v are Young’s modulus [GPa] and Poisson’s ratio, respectively. Fig. 3 shows the measuring positions on both inner and outer surfaces of welded pipe. In order to avoid the influence of stress fluctuation, they were far away from the welding start-end location. 3. Numerical simulation 3.1. Material properties and finite element model The temperature profile and residual stress distribution of 2.25Cr1Mo pipe were investigated numerically based on SYSWELD software. The thermo-metallurgical-mechanical coupled process was solved simultaneously. During welding and LPWHT process, the thermophysical
Fig. 1. Welded pipe over dimension and welding sequence. 111
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Fig. 2. Principle of the sectioning method.
properties, mechanical properties and metallurgical characteristics of material are changed with temperature varying. The temperature-dependent material properties of 2.25Cr-1Mo are shown in Figs. 4 and 5 [9]. Meanwhile, a three-dimensional finite element model was established referring to the real dimensions of welded pipe, as shown in Fig. 6. For the equilibrium between calculation efficiency and simulation accuracy, elements in beads and vicinity were refined, then mesh transition technology was employed to decline element quantity. The model included 63,600 cubic elements and 70,500 structural nodes. Two different numerical simulation schemes were employed to clarify the influence of tempering and creep on residual stress during LPWHT process, as shown in Table 3. 3.2. Thermal analysis Kiyoshima et al. [18] reported the influence of heat source models on welding residual stress distribution and distortion. Their research indicated that moving heat source performed well in computational accuracy. In current work, the double ellipsoidal heat source [19] was employed to describe the heat input of moving welding arc. The transient heat conduction could be described by following equation:
ρcp
∂q ∂T = ∇ (λ∇T ) + arc ∂t ∂t
Fig. 4. Temperature-dependent thermophysical properties of 2.25Cr-1Mo.
[J⋅mm-1⋅s-1⋅K-1], respectively, ∇ is the spatial gradient operator, qarc is the energy density of the heat source [J⋅mm-3 ]. The heat transfer between model and environment was defined by convection Newton's law and radiation Stefan-Boltzmann's law, respectively:
(2)
where ρ , cp , T, t and λ are density [g⋅mm−3 ], specific heat capacity [J⋅g -1⋅K-1], temperature [K], time [s] and thermal conductivity
qc = ac (T − T0)
Fig. 3. Measuring positions of residual stress. 112
(3)
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Leblond equation [20]:
Peq (T ) − P (T ) dP (T ) = f (T˙ )⋅ τ (T ) dt
(5)
where Peq presents the proportion of austenite at a current temperature T. P is proportion of austenite in equilibrium state. The value of parameter Peq for austenite is zero at A1 and linearly increases to 1 at A3 . τ /f is equivalent to a “time delay”. The parameter τ is related with temperature and f is decided by heating rate. Their values are adjusted carefully in order to fit the continuous heating transformation diagram. For the 2.25Cr-1Mo steel, A1 and A3 were assumed to be 773 °C and 881 °C [9], respectively. 3.3.2. Bainite transformation Austenite can transform into pearlite, bainite as well as martensite successively during continuous cooling. Compared with martensite, bainite forms at a higher temperature range. Bainite transformation is diffusive and it was also described by the Leblond equation in numerical model. Kunitake and Okada [21] proposed the following formula to calculate the start temperature of Bainite (Bs):
Fig. 5. Temperature-dependent mechanical properties of 2.25Cr-1Mo.
Bs = 732 − 202C + 216Si − 85Mn − 37Ni − 47Cr − 39Mo
(in weight percent)
(6)
considering the minor difference in composition of base material and filler metals, the Bs of 2.25Cr-1Mo was assumed to be 570 °C [5]. 3.3.3. Martensite transformation As the temperature descends to martensite start temperature (Ms), austenite will transform into martensite rather than bainite. This process is displacive and it can be described by the Koistinen-Marburger relationship [22]:
fm = (1 − fd ){1 − exp[−b (Ms − T )]} (T ≤ Ms )
where, fm is the fraction of welded martensite, fd is the total fraction of bainite and ferrite. b characterizes the evolution of martensitic transformation with temperature, and its value depends to the chemical composition of material. For most carbon steel and low alloy steel, the value of b is 0.011. In present study, the Ms of 2.25Cr-1Mo steel were assumed to be 410 °C [9].
Fig. 6. FE model of pipe and meshes near the weld zone. Table 3 Numerical simulation schemes.
Case-A Case-B
SSPT
Tempering
Creep
Yes Yes
Yes Yes
No Yes
qr = εC0 (T 4 − T04 )
(7)
3.3.4. Tempering process When the as-welded microstructure is re-heated into a certain temperature range, it will be tempered. Gil Mur et al. [23] realized tempered phase generated depending on temperature and time. It was described by Leblond equation as a diffusive process in the material model. However, the parameters of tempering are difficult to test by experiment. In this study, only the relationship between temperature and phase proportion was considered in tempering process, the influence of time was weakened. Since the base metal of 2.25Cr-1Mo steel was in tempered condition, as-welded phase was supposed to alter into base metal when be tempered. The tempering process was assumed to start at 650 °C and end at 780 °C [24].
(4)
where ac = 2.5 × 10−5J⋅mm2⋅s-1⋅K-1 is the convective heat transfer coefficient, ε = 0.8 is the absorption of steel, C0 = 5.67 × 10−14J⋅mm-2⋅s-1⋅K-4 is the Stefan-Boltzmann constant, T0 is the ambient temperature [K]. Besides, thermal cycle curve was employed to control temperature variation during LPWHT process.
3.3. Metallurgical analysis
3.4. Mechanical analysis
3.3.1. Austenitizing process Once a steel is heated above the cementite disappearance temperature ( A1), ferrite phase will transform into austenite as the cementite dissolves in the matrix. Such a transition will finish at the α -ferrite disappearance temperature ( A3 ). During this process, the structural transition from body-centered cubic (bcc) to face-centered cubic (fcc) can lead to an obvious volume shrinkage. The austenitizing process is diffusive and it was described by the
During multi-pass welding and LPWHT process, the thermal effect and SSPT lead to an additional volumetric strain, which can be divided into some independent components: (8)
ε˙ = ε˙ e + ε˙ cp + ε˙ th + ε˙ v + ε˙ tp
εe
ε cp
ε th
is conventional plastic strain, is thermal Where is elastic strain, strain induced by thermal effect, ε v and ε tp are volume change and transformation plasticity respectively, which are related to SSPT. 113
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Fig. 8. The relationship between minimum strain rate and stress of 2.25Cr1Mo.
Fig. 7. Yield stress of 2.25Cr-1Mo.
Furthermore, the discrepancy in yield strength between various microstructures can influence the residual stress obviously. Fig. 7 demonstrates the yield strengths variation of base metal and as-welded metal. It should be mentioned that martensite and bainite were not distinguished in this property. The detail proportion of bainite and martensite as well as its influence on stress was not considered in present research. In SYSWELD, a weighted average algorithm is employed to calculate the yield strength of mixed phase according to the proportions of individual microstructures. Leblond et al. [25] proposed that SSPT could relieve the accumulated plastic strain partly. Therefore, strain hardening in 2.25Cr-1Mo steel is not as obvious as in stainless steel and a perfect plasticity model was adopted in current work. 3.5. Viscoplasticity analysis As a kind of viscoplastic strain, creep can lead to a relaxation of residual stress, especially in a high temperature environment. Therefore, it is necessary to consider creep factor in LPWHT simulation to ensure the computational accuracy. Besseling presented that the creep process could be differentiated into three periods [26]. The current work paid more attention to the stationary creep, which is known as the secondary creep. The Norton’s law was employed to describe the secondary creep process [27], as follows:
ε˙ cr =
3 S A (σ )n 2 σ
Fig. 9. Peak temperature distribution in (a) 0° and (b) 180° sections.
(9)
where ε˙ cr is the creep strain rate, σ is equivalent stress, S is the deviatoric stress, A and n are temperature-dependent material constants, which can be obtained from the creep test result as shown in Fig. 8. 4. Result and discussion 4.1. Temperature filed and microstructure profile The peak temperature distribution in distinct sections were shown in Fig. 9. Although the beads arrangement and meshes are symmetric in FE model, the peak temperature profiles were still asymmetric due to the difference of welding heat input and welding velocity. Compared to the middle of beads, the cooling condition of start-end location was better, thus the profile in 0° section was narrower. Overall, all deposited material in groove was heated above melting temperature, which was conformed to the actual condition. The tempered phase distribution is presented in Fig. 10. Since the
Fig. 10. Tempered phase distribution after (a) welding and (b) LPWHT process.
raw material was normalized then tempered before welding process, the tempered phase proportion in base metal was almost 100%. Its value in welding zone and HAZ was far less because this part of tempered phase was transformed from as-welded phase. Tempered phase could generate during the re-heating stage of multi-pass welding. But it 114
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Fig. 12. Evolution of hoop residual stress. (a–e are the stress profiles when the 1st, 5th, 9th,11th, 14th bead was deposited). Fig. 11. Distribution of hoop residual stress in (a) whole pipe, (b) 0° section and (c) 180° section.
would be eliminated once the temperature was higher than A1. Thus, there was less than 20% tempered phase preserved after welding process, as shown in Fig. 10(a). While in Fig. 10(b), more than 40% tempered phase was accumulated during LPWHT process for a longer hold time and suitable temperature.
4.2. Welding residual stress distribution The distribution of hoop residual stress is shown in Fig. 11. It is noteworthy that both tensile and compressive stress were lower in 0° section, as well as the start-end location. Deng and Kiyoshima [28] realized the distinctive stress distribution related to the distinguished constraint conditions and temperature histories. Fig. 12 gives the evolution of hoop stress. Due to the influence of SSPT, there was compressive stress in each bead and its HAZ, tensile stress formed in surrounding area. Therefore, the hoop stress distribution appeared an undulating feature after multi-pass welding. For the previous deposited materials, they were re-heated above yield temperature repeatedly. The accumulated plastic strain led to a high tensile stress at room temperature, whose peak value could approach to the yield strength of as-welded metal. As a result of stress equilibrium, there was compressive stress located in a narrow region at weld root as well as the outside of HAZ. Besides, the compressive stress in base metal was larger at the inside of pipe since the circumferential constraint here is stronger. Figs. 13 and 14 show the distribution and evolution of axial stress, respectively. Its profile in welding start-end location was also distinct. The peak value of axial stress was lower than hoop stress for a weaker axial constraint. Unlike hoop stress, the axial stress could only be equilibrated along thickness direction so that the tensile and compressive stress shown an alternate distribution by layers. Finally, there was a narrow region with large tensile stress in weld root, compressive stress appeared at the outer face of pipe. The simulation and measurement results of residual stress after
Fig. 13. Distribution of axial residual stress in (a) whole pipe, (b) 0° section and (c) 180° section.
welding process are compared in Fig. 15. The sectioning method reflects an average stress near the measured positions while the stress gradient is large in weld seam and HAZ. Although measurement error, personality error as well as assumption and simplification of welding model induce a deviation between simulation and measurement results, the tendencies are consistent. It demonstrates that the developed computational approach is effective to simulate welding residual stress 115
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Fig. 14. Evolution of axial residual stress. (a–e are the stress profiles when the 1st, 5th, 9th,11th, 14th bead was deposited).
Fig. 16. Profiles of (a) hoop and (b) axial stress in 180° section after LPWHT process.
Fig. 15. Comparison of simulation and measurement results of welding residual stress. 116
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Fig. 17. Comparison of simulation and measurement results of LPWHT residual stress.
B, the region with high tensile or compressive stress diminished obviously, stress peak values also shown a clear decline. Fig. 17 presents the simulation and measurement results of residual stress after LPWHT process. Under the influence of local heating, plastic strain was easy to accumulate during heating stage, which induced to larger elastic strain and tensile stress after cooling. Hence, there were stress peaks near to the edges of heated area, which were more obvious in hoop direction as the result of stronger constraint. The simulation results of Case-B shown a better agreement with measurement results in stress changing trend. It also suggested that creep could not be neglected in the numerical simulation of LPWHT process for the accuracy of numerical simulation.
in 2.25Cr-1Mo steel. 4.3. LPWHT residual stress distribution Residual stress profiles in 180° section after LPWHT process are shown in Fig. 16. During LPWHT process, both tempering and creep can reduce the residual stress with distinct principles, while the stress distribution feature was almost unchanged. Tensile stress appeared at the center of welded zone, while compressive stress located in the surrounding region as the result of stress equilibrium. By comparing Case-A and CaseB, the significant stress variation demonstrated that creep could not be neglected in numerical simulation. Residual stress is determined by elastic strain, Young’s modulus as well as yield strength of material. During welding and LPWHT process, the tempering effect is accompanied with phase transformation and material softening. Once the yield strength of mixed phase is lower than local stress, the material will yield and elastic strain changes into plastic strain. Finally, there will be a lower residual stress. Such phenomenon is more obvious at the position with high original stress. As for the region with low-level stress, residual stress will redistribute because of the global stress balance. Creep leads to a permanent deformation of solid metal, the increasing plastic strain and decreasing elastic strain will result in stress relaxation. Different with tempering, the strain variation is independent with material properties changing. Especially, creep can occur with a stress which is still below the yield strength of material, so that the strain variation and stress relaxation can appear in a wide zone. In Case-
5. Conclusion In present work, a computational approach was developed based on SYSWELD to investigate the residual stress in 2.25Cr-1Mo circumferential butt-welded pipe during welding and LPWHT process. 3-D full scale FE model and moving heat source were employed in the simulation. The effect of solid-state phase transformation, tempering and creep were considered numerically. Meanwhile, the sectioning method was employed to measure the residual stress after welding and LPWHT process. The following conclusions can be summarized: (1) The experiment measurements and simulation results show good consistency with each other, which confirms the effectiveness of the developed computational approach. (2) The simulation results show that solid-state phase transformation 117
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leads to undulating stress distribution and large stress gradient in welded zone. Hoop stress is larger than axial stress generally, which is induced by stronger constraint. (3) Tempering effect can decrease the yield strength of mixed phase. Original high stresses are decreased with material softening and yielding. The variation of low-level stresses is induced by global stress equilibrium. (4) Creep causes a permanent deformation of solid metal. The transformation from elastic strain to plastic strain leads to a large-scale stress relaxation, which is independent with the variation of material mechanical properties. (5) According to the comparison of simulation and measurement results, it is necessary to consider tempering effect and creep simultaneously in LPWHT simulation in order to obtain an accuracy result.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This work is supported by the National Natural Science Foundation of China [Grant No.51875063 and No.51275544]. References [1] Laha K, Bhanu Sankara Rao K, Mannan SL. Creep behaviour of post-weld heattreated 2.25 Cr-1Mo ferritic steel base, weld metal and weldments. Mater Sci Eng A 1990;129(2):183–95. [2] Liang W, Murakawa H, Deng D. Investigation of welding residual stress distribution in a thick-plate joint with an emphasis on the features near weld end-start. Mater Des 2015;67:303–12. [3] Withers PJ, Turski M, Edwards L, Bouchard PJ, Buttle DJ. Recent advances in residual stress measurement. Int J Press Vessel Pip 2008;85(3):118–27. [4] Deng D, Zhang Y, Li S, Tong Y. Influence of solid-state phase transfor-mation on residual stress in P92 steel welded joint. Acta Metall Sin 2016;52(4):394–402. [5] Tsai M, Chiou C, Yang J. Microstructural evolution of simulated heat-affected zone in modified 2.25 Cr-1Mo steel during high temperature exposure. J Mater Sci 2003;38(11):2373–91. [6] Nitschke-Pagel T, Wohlfahrt H. Residual stresses in welded joints – sources and consequences. Mater Sci Forum 2002;404–407:215–26.
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Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Finite element analysis of residual stress in 2.25Cr-1Mo steel pipe during welding and heat treatment process
T
⁎
Sendong Rena,b, Suo Lia, Yifeng Wanga, Dean Denga, , Ninshu Mab a b
College of Material Science and Engineering, Chongqing University, Shazhengjie, Shapingba, Chongqing, 400044, China Joining and Welding Research Institute, Osaka University, Mihogaoka, Ibaraki, Osaka, 567-0047, Japan
A R T I C LE I N FO
A B S T R A C T
Keywords: Numerical simulation Solid-state phase transformation Tempering effect Creep
The circumferential butt-welded pipe was fabricated using 2.25Cr-1Mo steel and then subjected to local postweld heat treatment (LPWHT) for releasing residual stress after multi-pass welding. The sectioning method was employed to measure residual stress. Based on SYSWELD software, a thermo-metallurgical-mechanical coupled computational approach was developed to analyses the residual stress distribution on 2.25Cr-1Mo welded pipe. A three-dimensional finite element model and moving heat source model were employed in simulation. The effects of solid-state phase transformation (SSPT), tempering as well as creep were considered simultaneously. The effectivity of computational approach was verified by experimental measurement. The simulation results showed that SSPT could induce an undulating stress profile and large stress gradient in welded zone. The stress gradient could be reduced during LPWHT while there were stress peaks at the edges of heated region. Tempering effect could decrease the residual stress at high-stress region by material softening and yielding. Creep caused a global transformation from elastic strain to plastic strain, which led to a macro-scale stress relaxation. It is necessary to consider SSTP, tempering as well as creep in material model for more accurate simulation results.
1. Introduction 2.25Cr-1Mo steel is an important structural material in nuclear power plants and ultra-supercritical (USC) power plants. With an excellent resistance to both creep and corrosion at high temperature as well as low thermal expansion coefficient, it is widely used to fabricate steam pipes and turbine rotors [1]. Such large equipment is always assembled by multi-pass welding, its safe operation and service life are mainly determined by the quality of welded joints. During welding process, the nonhomogeneous temperature distribution can introduce residual stress, which is detrimental to the mechanical property of welded joints [2]. Therefore, large welded structures are subjected to post-weld heat treatment in order to mitigate residual stress. As an important indicator of welding quality, residual stress distribution is difficult to measure. Withers et al. [3] compared the capabilities and shortcomings of various stress measurement techniques, they believed it was still a challenge to measure residual stress in the depths of large structure, especially when the equipment was in operation. Therefore, it is valuable to track stress evolution during welding and PWHT process and predict its distribution by numerical simulation method. With special metallurgical character, the solid-state phase transformation (SSPT) will present in Cr-Mo steels during welding and
⁎
PWHT process. Deng et al. proposed that SSPT could introduce volume change, yield strength variation and transformation-induced plasticity (TRIP), which had significant influences on welding residual stress [4]. Tsai et al. investigated the microstructural evolution in 2.25Cr-1Mo steel. Both martensite and bainite existed during high temperature exposure [5]. Nitschke-Pagel and Wohlfahrt reported that bainite and martensite transformation had distinct influences on welding residual stress [6]. Meanwhile, tempering effect and creep could also affect the residual stress in PWHT and service process. Deng and Murakawa [7] investigated the residual stress in multi-pass welded joints, the reduction of residual stress was attributed to tempering and material softening. Holzapfel et al. [8] discussed the stress relaxation behaviors in 40CrMo4. They presented cyclic creep effects could cause an obvious stress relaxation in high temperature. In order to obtain accurate simulation results, all of the above factors should be considered in numerical model. Heretofore, some finite element models have been proposed to study the residual stress in welded pipes. Deng and Murakawa [7] presented that the volume change and yield strength variation induced by martensite transformation had remarkable effect on welding residual stress in 9Cr-1Mo steel. Their investigation about stress distribution in 2.25Cr-1Mo pipe suggested that the phase-dependent material
Corresponding author. E-mail address: [email protected] (D. Deng).
https://doi.org/10.1016/j.jmapro.2019.09.019 Received 17 June 2019; Received in revised form 10 August 2019; Accepted 23 September 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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properties were necessary for a precise prediction [9]. Yaghi et al. [10] demonstrated the residual stress profiles on P91 multi-pass welded pipe, the undulating contours reflected the effect of volumetric change during martensite transformation. The relationship between pipe diameter and residual stress was also clarified. In thick-walled finite element model, welding stress on surfaces was independent to the pipe diameter, while the state in thin-walled model was different [11]. Katsareas and Youtsos [12] predicted the residual stress field in a dissimilar metal welded pipe based on ANSYS. The “birth and death of elements” technique was applied to consider the successive material depositing in practical production. Their researches shown material model should be specific enough to consider all metallurgical factors and mechanical behaviours as much as possible in order to obtain accurate simulation results. A detail finite element mesh which could realize the actual shape and dimensions of structure was also important. Besides, a 3-D model was established to investigate the feature of stress profiles in SUS304 stainless steel pipe, the results showed that residual stress distributed homogenously along circumferential direction except for weld start-end region [13]. Sattari-Far and Farahani reported the relationship between weld pass number and residual stresses in buttwelded pipes, a large axial tensile stress would appear on the inner surface of thick-wall welded pipe with increasing pass number [14]. Duranton et al. believed 3-D model had advantage to reflect the actual constraint conditions so that the simulation result would be more realistic [15]. However, there are few reports considering both 3-D model and complex metallurgical behaviors simultaneously in welding and LPWHT simulation procedure. In the present study, a full-scale finite element model was established to research the stress distribution on 2.25Cr-1Mo welded pipe. Moving heat source was employed to describe the welding heat input. Welding parameters were identical to practical production. Both diffusive and displacive phase transformation were considered in material model. Tempering effect and creep were taken into account as crucial phenomena during LPWHT. The simulation results were verified by the sectioning method.
Table 1 Chemical composition of base metal and filler metals (wt.%).
Base metal TGS-2CM MGT-2CM
C
Si
Mn
P
S
Cr
Mo
Cu
Al
Ni
0.12 0.09 0.08
0.21 0.32 0.34
0.51 0.71 0.76
0.004 0.007 0.007
0.002 0.005 0.005
2.26 2.26 2.29
0.98 1.04 0.98
0.15 0.13 0.13
0.007 0.015 0.015
0.19 0.17 0.17
Table 2 Welding parameters. Bead No.
Method
Current (A)
Voltage (V)
Welding speed (mm min−1)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
TIG TIG TIG MIG MIG MIG MIG MIG MIG MIG MIG MIG MIG MIG
105 180 180 150 150 250 250 250 250 250 250 250 250 250
11 11 11 19 19 27 27 27 27 27 27 27 27 27
61 107 94 212 207 279 282 265 282 273 295 265 271 277
during TIG and MIG process, respectively. The pre-heat temperature was 150 °C, and the inter-pass temperature was about 180–200 °C. After welding process, local post-weld heat treatment (LPWHT) was applied to the pipe. Lu et al. [16] investigated the mechanical behavior of tubular joint during LPWHT and recommended a criterion to calculate the optimum heated band width. In this study, LPWHT area was 220 mm wide. Local material was heated to 680 °C, preserved for 1 h then cooled slowly. The heating and cooling rates were about 100 °C/h and 50 °C/h, respectively.
2. Experimental procedure
2.2. Residual stress measurement
2.1. Pipe geometry and fabrication process
In present work, the sectioning method was employed to measure residual stress after welding and LPWHT process. It was originally proposed by Kalakoutsky [17] to gauge the residual stress in bar. The principle of sectioning method is shown in Fig.2. Once a small piece is cut from structure, it will deform under the influence of internal stress, and then reflect tensile or compressive strain which can be measured. When applying in plate or cylinder structures, the residual stresses are calculated by following equations:
The 2.25Cr-1Mo circumferential butt-welded pipe was normalized at 930 °C and tempered at 730 °C then fabricated by multi-pass welding. Over dimension as well as welding sequence are shown in Fig. 1. Weld passes 1 to 3 were deposited by tungsten inert gas (TIG) welding using TGS-2CM wire as filler metal. The remaining passes were performed by metal inert gas (MIG) welding depositing MGT-2CM wire. The chemical composition (wt.%) of base metal and filler metals are given in Table 1. The welding parameters are listed in Table 2. 99% Ar and 95% Ar + 5% CO2 were employed to shield the weld zone from atmospheric gases
E (εx + vεy ) 1 − v2 E σy = − (εy + vεx ) 1 − v2 σx = −
(1)
where, E and v are Young’s modulus [GPa] and Poisson’s ratio, respectively. Fig. 3 shows the measuring positions on both inner and outer surfaces of welded pipe. In order to avoid the influence of stress fluctuation, they were far away from the welding start-end location. 3. Numerical simulation 3.1. Material properties and finite element model The temperature profile and residual stress distribution of 2.25Cr1Mo pipe were investigated numerically based on SYSWELD software. The thermo-metallurgical-mechanical coupled process was solved simultaneously. During welding and LPWHT process, the thermophysical
Fig. 1. Welded pipe over dimension and welding sequence. 111
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Fig. 2. Principle of the sectioning method.
properties, mechanical properties and metallurgical characteristics of material are changed with temperature varying. The temperature-dependent material properties of 2.25Cr-1Mo are shown in Figs. 4 and 5 [9]. Meanwhile, a three-dimensional finite element model was established referring to the real dimensions of welded pipe, as shown in Fig. 6. For the equilibrium between calculation efficiency and simulation accuracy, elements in beads and vicinity were refined, then mesh transition technology was employed to decline element quantity. The model included 63,600 cubic elements and 70,500 structural nodes. Two different numerical simulation schemes were employed to clarify the influence of tempering and creep on residual stress during LPWHT process, as shown in Table 3. 3.2. Thermal analysis Kiyoshima et al. [18] reported the influence of heat source models on welding residual stress distribution and distortion. Their research indicated that moving heat source performed well in computational accuracy. In current work, the double ellipsoidal heat source [19] was employed to describe the heat input of moving welding arc. The transient heat conduction could be described by following equation:
ρcp
∂q ∂T = ∇ (λ∇T ) + arc ∂t ∂t
Fig. 4. Temperature-dependent thermophysical properties of 2.25Cr-1Mo.
[J⋅mm-1⋅s-1⋅K-1], respectively, ∇ is the spatial gradient operator, qarc is the energy density of the heat source [J⋅mm-3 ]. The heat transfer between model and environment was defined by convection Newton's law and radiation Stefan-Boltzmann's law, respectively:
(2)
where ρ , cp , T, t and λ are density [g⋅mm−3 ], specific heat capacity [J⋅g -1⋅K-1], temperature [K], time [s] and thermal conductivity
qc = ac (T − T0)
Fig. 3. Measuring positions of residual stress. 112
(3)
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Leblond equation [20]:
Peq (T ) − P (T ) dP (T ) = f (T˙ )⋅ τ (T ) dt
(5)
where Peq presents the proportion of austenite at a current temperature T. P is proportion of austenite in equilibrium state. The value of parameter Peq for austenite is zero at A1 and linearly increases to 1 at A3 . τ /f is equivalent to a “time delay”. The parameter τ is related with temperature and f is decided by heating rate. Their values are adjusted carefully in order to fit the continuous heating transformation diagram. For the 2.25Cr-1Mo steel, A1 and A3 were assumed to be 773 °C and 881 °C [9], respectively. 3.3.2. Bainite transformation Austenite can transform into pearlite, bainite as well as martensite successively during continuous cooling. Compared with martensite, bainite forms at a higher temperature range. Bainite transformation is diffusive and it was also described by the Leblond equation in numerical model. Kunitake and Okada [21] proposed the following formula to calculate the start temperature of Bainite (Bs):
Fig. 5. Temperature-dependent mechanical properties of 2.25Cr-1Mo.
Bs = 732 − 202C + 216Si − 85Mn − 37Ni − 47Cr − 39Mo
(in weight percent)
(6)
considering the minor difference in composition of base material and filler metals, the Bs of 2.25Cr-1Mo was assumed to be 570 °C [5]. 3.3.3. Martensite transformation As the temperature descends to martensite start temperature (Ms), austenite will transform into martensite rather than bainite. This process is displacive and it can be described by the Koistinen-Marburger relationship [22]:
fm = (1 − fd ){1 − exp[−b (Ms − T )]} (T ≤ Ms )
where, fm is the fraction of welded martensite, fd is the total fraction of bainite and ferrite. b characterizes the evolution of martensitic transformation with temperature, and its value depends to the chemical composition of material. For most carbon steel and low alloy steel, the value of b is 0.011. In present study, the Ms of 2.25Cr-1Mo steel were assumed to be 410 °C [9].
Fig. 6. FE model of pipe and meshes near the weld zone. Table 3 Numerical simulation schemes.
Case-A Case-B
SSPT
Tempering
Creep
Yes Yes
Yes Yes
No Yes
qr = εC0 (T 4 − T04 )
(7)
3.3.4. Tempering process When the as-welded microstructure is re-heated into a certain temperature range, it will be tempered. Gil Mur et al. [23] realized tempered phase generated depending on temperature and time. It was described by Leblond equation as a diffusive process in the material model. However, the parameters of tempering are difficult to test by experiment. In this study, only the relationship between temperature and phase proportion was considered in tempering process, the influence of time was weakened. Since the base metal of 2.25Cr-1Mo steel was in tempered condition, as-welded phase was supposed to alter into base metal when be tempered. The tempering process was assumed to start at 650 °C and end at 780 °C [24].
(4)
where ac = 2.5 × 10−5J⋅mm2⋅s-1⋅K-1 is the convective heat transfer coefficient, ε = 0.8 is the absorption of steel, C0 = 5.67 × 10−14J⋅mm-2⋅s-1⋅K-4 is the Stefan-Boltzmann constant, T0 is the ambient temperature [K]. Besides, thermal cycle curve was employed to control temperature variation during LPWHT process.
3.3. Metallurgical analysis
3.4. Mechanical analysis
3.3.1. Austenitizing process Once a steel is heated above the cementite disappearance temperature ( A1), ferrite phase will transform into austenite as the cementite dissolves in the matrix. Such a transition will finish at the α -ferrite disappearance temperature ( A3 ). During this process, the structural transition from body-centered cubic (bcc) to face-centered cubic (fcc) can lead to an obvious volume shrinkage. The austenitizing process is diffusive and it was described by the
During multi-pass welding and LPWHT process, the thermal effect and SSPT lead to an additional volumetric strain, which can be divided into some independent components: (8)
ε˙ = ε˙ e + ε˙ cp + ε˙ th + ε˙ v + ε˙ tp
εe
ε cp
ε th
is conventional plastic strain, is thermal Where is elastic strain, strain induced by thermal effect, ε v and ε tp are volume change and transformation plasticity respectively, which are related to SSPT. 113
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Fig. 8. The relationship between minimum strain rate and stress of 2.25Cr1Mo.
Fig. 7. Yield stress of 2.25Cr-1Mo.
Furthermore, the discrepancy in yield strength between various microstructures can influence the residual stress obviously. Fig. 7 demonstrates the yield strengths variation of base metal and as-welded metal. It should be mentioned that martensite and bainite were not distinguished in this property. The detail proportion of bainite and martensite as well as its influence on stress was not considered in present research. In SYSWELD, a weighted average algorithm is employed to calculate the yield strength of mixed phase according to the proportions of individual microstructures. Leblond et al. [25] proposed that SSPT could relieve the accumulated plastic strain partly. Therefore, strain hardening in 2.25Cr-1Mo steel is not as obvious as in stainless steel and a perfect plasticity model was adopted in current work. 3.5. Viscoplasticity analysis As a kind of viscoplastic strain, creep can lead to a relaxation of residual stress, especially in a high temperature environment. Therefore, it is necessary to consider creep factor in LPWHT simulation to ensure the computational accuracy. Besseling presented that the creep process could be differentiated into three periods [26]. The current work paid more attention to the stationary creep, which is known as the secondary creep. The Norton’s law was employed to describe the secondary creep process [27], as follows:
ε˙ cr =
3 S A (σ )n 2 σ
Fig. 9. Peak temperature distribution in (a) 0° and (b) 180° sections.
(9)
where ε˙ cr is the creep strain rate, σ is equivalent stress, S is the deviatoric stress, A and n are temperature-dependent material constants, which can be obtained from the creep test result as shown in Fig. 8. 4. Result and discussion 4.1. Temperature filed and microstructure profile The peak temperature distribution in distinct sections were shown in Fig. 9. Although the beads arrangement and meshes are symmetric in FE model, the peak temperature profiles were still asymmetric due to the difference of welding heat input and welding velocity. Compared to the middle of beads, the cooling condition of start-end location was better, thus the profile in 0° section was narrower. Overall, all deposited material in groove was heated above melting temperature, which was conformed to the actual condition. The tempered phase distribution is presented in Fig. 10. Since the
Fig. 10. Tempered phase distribution after (a) welding and (b) LPWHT process.
raw material was normalized then tempered before welding process, the tempered phase proportion in base metal was almost 100%. Its value in welding zone and HAZ was far less because this part of tempered phase was transformed from as-welded phase. Tempered phase could generate during the re-heating stage of multi-pass welding. But it 114
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Fig. 12. Evolution of hoop residual stress. (a–e are the stress profiles when the 1st, 5th, 9th,11th, 14th bead was deposited). Fig. 11. Distribution of hoop residual stress in (a) whole pipe, (b) 0° section and (c) 180° section.
would be eliminated once the temperature was higher than A1. Thus, there was less than 20% tempered phase preserved after welding process, as shown in Fig. 10(a). While in Fig. 10(b), more than 40% tempered phase was accumulated during LPWHT process for a longer hold time and suitable temperature.
4.2. Welding residual stress distribution The distribution of hoop residual stress is shown in Fig. 11. It is noteworthy that both tensile and compressive stress were lower in 0° section, as well as the start-end location. Deng and Kiyoshima [28] realized the distinctive stress distribution related to the distinguished constraint conditions and temperature histories. Fig. 12 gives the evolution of hoop stress. Due to the influence of SSPT, there was compressive stress in each bead and its HAZ, tensile stress formed in surrounding area. Therefore, the hoop stress distribution appeared an undulating feature after multi-pass welding. For the previous deposited materials, they were re-heated above yield temperature repeatedly. The accumulated plastic strain led to a high tensile stress at room temperature, whose peak value could approach to the yield strength of as-welded metal. As a result of stress equilibrium, there was compressive stress located in a narrow region at weld root as well as the outside of HAZ. Besides, the compressive stress in base metal was larger at the inside of pipe since the circumferential constraint here is stronger. Figs. 13 and 14 show the distribution and evolution of axial stress, respectively. Its profile in welding start-end location was also distinct. The peak value of axial stress was lower than hoop stress for a weaker axial constraint. Unlike hoop stress, the axial stress could only be equilibrated along thickness direction so that the tensile and compressive stress shown an alternate distribution by layers. Finally, there was a narrow region with large tensile stress in weld root, compressive stress appeared at the outer face of pipe. The simulation and measurement results of residual stress after
Fig. 13. Distribution of axial residual stress in (a) whole pipe, (b) 0° section and (c) 180° section.
welding process are compared in Fig. 15. The sectioning method reflects an average stress near the measured positions while the stress gradient is large in weld seam and HAZ. Although measurement error, personality error as well as assumption and simplification of welding model induce a deviation between simulation and measurement results, the tendencies are consistent. It demonstrates that the developed computational approach is effective to simulate welding residual stress 115
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Fig. 14. Evolution of axial residual stress. (a–e are the stress profiles when the 1st, 5th, 9th,11th, 14th bead was deposited).
Fig. 16. Profiles of (a) hoop and (b) axial stress in 180° section after LPWHT process.
Fig. 15. Comparison of simulation and measurement results of welding residual stress. 116
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Fig. 17. Comparison of simulation and measurement results of LPWHT residual stress.
B, the region with high tensile or compressive stress diminished obviously, stress peak values also shown a clear decline. Fig. 17 presents the simulation and measurement results of residual stress after LPWHT process. Under the influence of local heating, plastic strain was easy to accumulate during heating stage, which induced to larger elastic strain and tensile stress after cooling. Hence, there were stress peaks near to the edges of heated area, which were more obvious in hoop direction as the result of stronger constraint. The simulation results of Case-B shown a better agreement with measurement results in stress changing trend. It also suggested that creep could not be neglected in the numerical simulation of LPWHT process for the accuracy of numerical simulation.
in 2.25Cr-1Mo steel. 4.3. LPWHT residual stress distribution Residual stress profiles in 180° section after LPWHT process are shown in Fig. 16. During LPWHT process, both tempering and creep can reduce the residual stress with distinct principles, while the stress distribution feature was almost unchanged. Tensile stress appeared at the center of welded zone, while compressive stress located in the surrounding region as the result of stress equilibrium. By comparing Case-A and CaseB, the significant stress variation demonstrated that creep could not be neglected in numerical simulation. Residual stress is determined by elastic strain, Young’s modulus as well as yield strength of material. During welding and LPWHT process, the tempering effect is accompanied with phase transformation and material softening. Once the yield strength of mixed phase is lower than local stress, the material will yield and elastic strain changes into plastic strain. Finally, there will be a lower residual stress. Such phenomenon is more obvious at the position with high original stress. As for the region with low-level stress, residual stress will redistribute because of the global stress balance. Creep leads to a permanent deformation of solid metal, the increasing plastic strain and decreasing elastic strain will result in stress relaxation. Different with tempering, the strain variation is independent with material properties changing. Especially, creep can occur with a stress which is still below the yield strength of material, so that the strain variation and stress relaxation can appear in a wide zone. In Case-
5. Conclusion In present work, a computational approach was developed based on SYSWELD to investigate the residual stress in 2.25Cr-1Mo circumferential butt-welded pipe during welding and LPWHT process. 3-D full scale FE model and moving heat source were employed in the simulation. The effect of solid-state phase transformation, tempering and creep were considered numerically. Meanwhile, the sectioning method was employed to measure the residual stress after welding and LPWHT process. The following conclusions can be summarized: (1) The experiment measurements and simulation results show good consistency with each other, which confirms the effectiveness of the developed computational approach. (2) The simulation results show that solid-state phase transformation 117
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leads to undulating stress distribution and large stress gradient in welded zone. Hoop stress is larger than axial stress generally, which is induced by stronger constraint. (3) Tempering effect can decrease the yield strength of mixed phase. Original high stresses are decreased with material softening and yielding. The variation of low-level stresses is induced by global stress equilibrium. (4) Creep causes a permanent deformation of solid metal. The transformation from elastic strain to plastic strain leads to a large-scale stress relaxation, which is independent with the variation of material mechanical properties. (5) According to the comparison of simulation and measurement results, it is necessary to consider tempering effect and creep simultaneously in LPWHT simulation in order to obtain an accuracy result.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This work is supported by the National Natural Science Foundation of China [Grant No.51875063 and No.51275544]. References [1] Laha K, Bhanu Sankara Rao K, Mannan SL. Creep behaviour of post-weld heattreated 2.25 Cr-1Mo ferritic steel base, weld metal and weldments. Mater Sci Eng A 1990;129(2):183–95. [2] Liang W, Murakawa H, Deng D. Investigation of welding residual stress distribution in a thick-plate joint with an emphasis on the features near weld end-start. Mater Des 2015;67:303–12. [3] Withers PJ, Turski M, Edwards L, Bouchard PJ, Buttle DJ. Recent advances in residual stress measurement. Int J Press Vessel Pip 2008;85(3):118–27. [4] Deng D, Zhang Y, Li S, Tong Y. Influence of solid-state phase transfor-mation on residual stress in P92 steel welded joint. Acta Metall Sin 2016;52(4):394–402. [5] Tsai M, Chiou C, Yang J. Microstructural evolution of simulated heat-affected zone in modified 2.25 Cr-1Mo steel during high temperature exposure. J Mater Sci 2003;38(11):2373–91. [6] Nitschke-Pagel T, Wohlfahrt H. Residual stresses in welded joints – sources and consequences. Mater Sci Forum 2002;404–407:215–26.
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