Numerical simulation research on welded residual stress and distortion of aero-engine afterburner lobe mixer with different welding sequences

Most thin-walled parts of aero-engines with intricate surfaces, such as lobe mixer, are welded using tungsten inert gas (TIG), which will certainly induce stress and distortion, causing a serious influence on assembly accuracy. The objective of this study was to establish a finite element model to optimize TIG wire filler welding sequence for an aero-engine lobe mixer composed of GH3044 nickel–based superalloy at the thickness of 2 mm. A new method for optimizing residual stress and distortion in the welding of large-size components was proposed. We carried out a 2-mm-thickness plate TIG wire filler welding experiment to obtain the ideal process parameters and validate the heat source model and thermal boundary condition, and also designed a set of frock clamp. The stress and distortion of the lobed mixer were analyzed under various welding sequences based on the established finite element model. The results showed that the peak residual stress difference of the lobe mixer is smaller using such a fixture. But different welding sequences affected the stress uniformity throughout the structural member. Only the symmetrical welding of single weld was a better process, with a peak distortion of 0.54 mm and more uniform stress distribution.


Introduction
The lobe mixer is commonly employed in aeroengines because it not only speeds up the mixing of internal-external duct gases and improves the engine's thrust-weight ratio, but it also reduces engine exhaust noise and infrared radiation [1]. However, a lobe mixer must be utilized for an extended period of time in a harsh environment with high temperatures and pressures, which results in the materials used are almost all nickel-based superalloys.
In recent years, many academics have been concentrating on the process-texture -property studies of various welding methods based on nickel-based superalloys. Sivaprasad et al. [2] studied the effects of three TIG welding processes including continuous current, pulse, and swing on the fatigue properties of Inconel 718 superalloy welded joints. Hong et al. [3] carried out laser welding experiments of Inconel 718 superalloy with different grain sizes of 5-mm thickness. Tucker et al. [4] investigated the effect of velocity and defocus distance on the porosity of laser-welded joints in Inconel 690 superalloy. They established the relationship between porosity, weld depth, welding velocity, and defocus through a large number of experiments. Ola et al. [5] used the laser-TIG hybrid process to weld Inconel 738 superalloy plates with a thickness of 10 mm, and obtained high-quality welded joints with good textures and no cracks. Wang et al. [6] used pulse laser welding technology to complete c-276 superalloy sheet welding with a thickness of only 0.381 mm and analyzed the weld texture, element segregation, and mechanical properties. Arash et al. [7] conducted electron beam welding experiments on ZHS6U superalloy sheets for aero-engine blades with a thickness of 3 mm to study the effect of pre-weld heat treatment on the joint structure. A few scholars concerned about the residual stress and distortion analysis of welded joint. Chen et al. [8] evaluated the residual stress state at the weldment surface in the radial and hoop directions of a single crystal nickel-base superalloy using the focused ion beam-digital image correlation (FIB-DIC) micro-ring-core method. Vishvesha et al. [9] utilized the inherent strain method is proposed here to predict distortion in an outer ring of GBC (guide blade carrier) of a steam turbine.
Although laser beam and electron beam welding methods are gradually being used in a wide range of industries [10][11][12][13], the tungsten inert gas (TIG) welding is a joining method that is frequently used to aerospace parts, such as rotating blades, pressure vessel [14], vanes, and gas turbine disc [15]. It has advantages such as stable arc and easier adjustment of heat input. A full lobe mixer must be obtained by welding multiple lobes owing to its intricate surfaces, and it is inevitable to produce residual stress and distortion using TIG process. However, due to the large size of the components and the number of welds, there are challenges of long lead times and high costs in optimizing the welding process using a purely experimental approach. Therefore, if the residual stress and distortion of the whole component can be predicted by numerical simulation, it will be of great help to control the welding quality of a whole structural part.
At present, the finite element (FE) method has become a reliable approach to predict welding stress and distortion. Taraphdar et al. [16] established different 3D and 2D FE models to evaluate their competence in predicting residual stress distribution in an SA516 Gr. 70 multipass butt-welded joint by comparing their accuracy and total required computational time. They concluded that 3D model can provide a better veracity of residual stresses distributed across the weld cross-section. Pandey et al. [17] developed a threedimensional finite element model to predict the residual stress distribution of different filler materials in P91 steel. With the advancement of high-performance computers, many researchers have concentrated their attention on the study of residual stress and deformation in large-scale and sophisticated components [18]. Song et al. [19] established a three-dimensional finite element model for electron beam welding of aero-engine combustion chamber components and calculated the stress distribution in each region by use of the inverse characteristic strain method. Guo et al. [20] optimized the TIG welding parameters and sequences of the T-joint on an aero-engine ring part by comparing the residual stress and distortion, which was based on the finite element analysis and have important guiding significance in the actual welding process. Zhao et al. [21] adopted the inherent strain model (ISM), the large heat source model (LHM), and the moving heat source model (MHM) to simulate the welding distortions and residual stresses in a large welded structure of underframe. Liu et al. [22,23] used the finite element method to project the residual stress and deformation during the spot welding of the automobile wall panels, and the simulated were consistent with the experimental results.
In this paper, a new method for optimizing residual stress and distortion in welding of large-size parts combining experiment and simulation was proposed. We performed a 2-mm-thick flat TIG wire filler welding experiment to verify the combined heat source involved of a dual ellipsoid and a cylindrical and thermal boundary condition, and also designed a set of frock clamp. Then, a three-dimensional finite element model of the lobe mixer in an aero-engine lobe mixer was established to analyze the stress and distortion during the TIG welding. Finally, the effects of different welding sequences on the residual stress and distortion for the weld seams of the lobe mixer were discussed. The most appropriate welding sequence was discovered.

Welding materials
In this study, base metal is nickel-based superalloy GH3044, which is a typical solid solution strengthened nickel-based anti-oxidation alloy that has high plasticity and medium thermal strength below 900 °C [24]. The size in the experiment is 100 × 50 × 2 mm 3 . The filler wire is HGH3044 with a diameter of 1.5 mm. The base metal and filler wire have the same chemical composition, as shown in Table 1 [25].

Apparatus and welding process
The ZX7-315STG DC argon arc welder produced by China Shandong AoTai Electric Co. Ltd. was used to weld GH3044 alloy plates. This welding machine adopted contact and high-frequency arc starting mode, which can adjust striking current separately, and had good arc starting performance. Considering the safety problem, the welding machine was also equipped with temperature protection, overcurrent protection, short circuit protection, and other safety protection functions. Figure 1a is the schematic diagram of the actual plate welding clamping process.
The welding voltage and the speed were set as 10 V and 3.2 mm·s −1 respectively according to the "Welding Handbook" [26]. The welding power and heat input were controlled by changing the current. There were six groups of welding experiments in this study, as shown in Table 2. The line energy, namely heat input, is obtained by multiplying the current by the voltage and dividing by the velocity. In the TIG welding process, the argon with a purity of 99.99% was used as protective gas with a flow of 10 L·min −1 and the arc efficiency was 75%. The wire filling TIG process is shown in Fig. 1b. Figure 2 shows the macroscopic morphology of each weld cross-section, which numbers a to f correspond to Nos. 1 to 6 in Table 2, respectively. There are obvious incomplete penetration defects in the first and second groups. The samples in the third to sixth groups all fulfill the fundamental specifications of the joint. However, there is an obvious asymmetry in the welding seam for the fifth and sixth groups. The depth and width of the molten pool were measured to study the influence of the welding parameters on the macroscopic appearance characteristics of the weld crosssection. The weld penetration is the distance from the highest of reinforcement to the lowest at the bottom and the weld width is the distance between the farthest two points Fig. 1 The schematic diagram of a actual plate welding clamping process and b TIG wire filler welding process of the fusion line, as show in Fig. 3c. The measured results are shown in the bar graph in Fig. 3a. Moreover, the aspect ratio (K 1 = depth/width) was calculated and then plotted on Fig. 3b. The most crucial parameter of flat butt joints is penetration. It can be seen from Fig. 3a that the weld depth gradually increases with the welding current. The weld depth is greatest when the current is 105 A, reaching 3.46 mm, which is larger than the thickness of the plate. However, the weld width for all welding processes is between 5 and 6 mm, which in the widest is 5.90 mm and narrowest is 5.25 mm. It demonstrates that while all other welding parameters are constant, the welding current has minimal influence on penetration breadth but has a significant effect on penetration depth. The aspect ratio of experiments are between 0.3 and 0.7, as depicted in Fig. 3b, which steadily rises as the current increases, reaching a maximum value of 0.63. Interestingly, when the welding current is 95A and 100A, their welding seam aspect ratio is the same, both are 0.54.

Analysis of tensile properties of joints
Tensile specimens were prepared using a super CNC wire cutting machine, as detailed in Fig. 4a, followed by a grinding machine to smooth out the weld reinforcement. The electronic universal testing machine whose model was CMT 5105 that the maximum tension was 100 KN, and the experimental force and displacement were within ± 0.1% of the indicated error was conducted on each group of specimens to measure the tensile the properties. The elongation and tensile strength after break of GH3044 base metal and welded joints under different process parameters were obtained in Fig. 4b and c.
We found that all elongation and tensile strength of the joint were lower than that of the base material and all welded joints fracture location were in the vicinity of the weld, indicating that the weld seams became the weakest position of the mechanical properties. Figure 4c made clear that parent alloy had the best mechanical properties with a tensile strength of 892.31 MPa and an elongation of 54.84%. The #1 specimens had the lowest tensile properties, with an elongation after break of just 8.39% and a tensile strength of 566.21 MPa, equivalent to only 63.45% of the tensile strength of the base metal. In all welded joints, #4 specimen had the best tensile performance with an elongation of 37.10% and a tensile strength of 874.17 MPa, which was 97.97% of the base metal.
Based on the studies of morphological features and tensile properties including elongation and tensile strength of different welded joints, the fourth set of welding parameters had the best forming, namely the welding current was 95 A.

Model assumptions
The thermo-elastoplastic calculation theory is established under the condition of a series of basic assumptions on the elastoplastic behavior of materials: (1) The materials studied in this paper are isotropic.
(2) The material obeys the Von Mises yield criterion when it yields.

Material properties
Material properties include thermophysical and mechanical parameters, which include density, specific heat capacity, and thermal conductivity in the former and the coefficient of thermal expansion, Young's modulus, yield strength, and Poisson's ratio in the latter.
The temperature-dependent material property parameters of GH3044 are shown in Fig. 5. These data below 1300 K are come from China Superlloys Handbook-Vol. 1 [27], and those above 1300 K are calculated through JmatPro 7.0 software according to the chemical composition in Table 1, and the influence of latent heat of phase change on the material parameters is considered in this process. Figure 5a, b, c, and d show the specific heat, density, thermal conductivity, Young modulus, yield strength, thermal expansion, and Poisson's ratio of GH3044 at different temperatures, respectively. Specifically, the yield strength and Young's modulus not exist in theory when the temperature is higher than the melting point. However, both parameters are set to a small value to meet the convergence requirement of finite element calculation in this paper.

Geometry and mesh modeling
We can obtain the lobe mixer geometric model as shown in Fig. 6 by simplifying the SwALN, which in the parameters is shown in Table 3 [28,29]. Figure 6a and b show the primary view and side view, respectively. Figure 6c and d depict the dimensions corresponding to the geometric parameters in Table 3, respectively. This lobe mixer is connected by 12 lobes of identical size through TIG welding, so there are 12 welds in the whole component.
The mesh model of the lobe mixer is shown in Fig. 7a. A 4:2 quantity ratio is used in the grid transition method, as depicted in Fig. 7b. The grid size is about 0.85 mm for all weld seams and its vicinity, as shown in Fig. 7c. The other areas are relatively large with a size of about 4.26 mm, as displayed in Fig. 7d. The total number of grids is 109,344. And the number of nodes is 196,860.

Thermal analysis
The welding heat source model is used to describe the heat flux distribution of the workpiece during the welding process, and its accuracy directly affects the numerical simulation results of the welding temperature field. In the process of filler wire TIG welding, the heat that forms the molten pool comes from two aspects: one is from the heat generated by the tungsten arc, and the other is from the metal droplets formed after the welding wire is melted. Therefore, a combined heat source model, as shown in Fig. 8c, consisting of a double ellipsoid and a cylindrical heat source is employed to serve as moving heat source during filler wire TIG welding [30]. The double ellipsoidal heat source model is used to describe the heat input of the TIG arc, as shown in Fig. 8a. It can be expressed by Eqs. 1 and 2 [31].
where q 1 (x, y, z) and q 2 (x, y, z) represent the heat flow distribution of the two-quarter ellipsoids before and after the heat source model respectively. The parameters of a 1 and a 2 are the front and rear semi-axial lengths of the heat source  respectively. The parameter b represents the half-width of the heat source, and c is the penetration depth of the heat source. f 1 and f 2 represent the energy distribution coefficient before and after the ellipsoid respectively, furthermore, f 1 + f 2 = 2 and f 1 = 2a 2 ∕(a 1 +a 2 ) and f 2 = 2a 1 ∕ a 1 + a 2 .
A cylindrical heat source model with uniform heat flux is adopted to describe the distribution of droplet enthalpy on the workpiece, as shown in Fig. 8b. The energy is evenly distributed in a cylinder, which can be expressed by Eq. 3.
where q(x, y, z) represents the heat flux distribution of molten drop on the workpiece and r 0 is the effective radius of action of the heat source. The parameters of z m and z n represent the coordinate values in the depth direction of the columnar heat source respectively.
The double ellipsoidal and the coupled heat source are used to simulate the fourth set of experimental parameters respectively. The morphologies of the two molten pools are compared with the experimental results respectively, as shown in Fig. 9. The left is the simulative result and the right is the experimental. The melting temperature of GH3044 nickel-based superalloy is between 1352 and 1375 °C from the Ref.
[27], the higher than 1360 °C is regarded as the molten zone in this paper according to the Sect. 3.2.
The simulated molten pool profile is basically consistent with the experimental results. There is only a small difference in the molten width from Fig. 9a. That is because the flow of liquid metal in the molten pool is not considered in the finite element calculation. As can be seen from Fig. 9b, both the molten width and the fusion line are greatly different from the experiment. It can be inferred that the finite element simulation of TIG wire filler welding using the combination heat source mode is completely reasonable.

Residual stress analysis
In this study, the blind hole method was used to measure the equivalent residual stress after welding, and the equipment used were a HP-MK4 tester by Nanjing Hepple Technology Co. Ltd and the BX120-3CA resistance strain gauges. Figure 10a represents the locations of the four points for the stress measurement and also the extraction path of the simulated values. Figure 10b shows the experimental measurement apparatus including a drilling apparatus and a blind hole method stress tester. Figure 10c plots the results of the experimental and simulated residual stresses.
The simulated stress curve in Fig. 10c uncovers the residual stress of the weld seam is between 270 and 330 MPa and is approximately symmetrical distribution on the tested path. The experimental results agree with the simulated results in terms of stress variation trends, and although there are errors between the measured and simulated residual stresses at four points, none of them exceed 10%, which is sufficient to verify the accuracy of the finite element model.

The initial and boundary conditions
For thermal-structural analysis, the initial conditions include the initial temperature and mechanics of the workpiece. Since the butt experiment of the GH3044 nickel-based superalloy plate is completed at room temperature and the workpiece is not preheated, the initial temperature in the finite element model is set as 25 °C in this paper. Also, assuming that the component is artificially aged to release the stress, so the initial stress is zero.
The lobe mixer has a large number of continuously curved surfaces, large size, complex structure, and thin wall thickness. Therefore, the assembly device as shown in Fig. 11 is designed to prevent large distortion. It is mainly composed of an upper top plate, a lower top plate, a support plate, and a center positioning tube, as show in Fig. 11a and b, respectively. The upper surface, the lower surface, and the inner surfaces of the external duct of the mixer are in contact with the fixture as shown in Fig. 12a and b. These surfaces are mainly heated conduction with a high heat transfer coefficient of 600 W·m −2 ·K −1 . The remaining surfaces are in direct contact with the air, and mainly heat transfer ways are convection and radiation. The heat transfer coefficient is set as 60 W·m −2 ·K −1 considering these two heat transfer modes.
The axial and circumferential displacement of the lobe mixer is restricted under the upper and lower top plates from Fig. 12. Moreover, the support plate is close to the inner walls of the external ducts, which restricts the deformation of the external ducts.

Numerical simulation schemes designing
The finite element model of the lobe mixer is established by the commercial finite element software MSC. Marc. Then, the fourth group of experiments is numerically simulated. The simulation-process parameters are shown in Table 4.
TIG welding on the lobe mixer is divided into three distinct steps: welding, cooling, and releasing fixtures. In this study, six simulation schemes are designed to investigate the influences of different welding sequences on the residual stress and distortion, as detailed in Fig. 13. The  As illustrated in Fig. 12a, all models adopt the welding direction from the gas out to the inlet and the release order of releasing the top fixture first followed by the lower clamp. Figure 14 shows the simulative residual stress results of different welding sequences after welding. They are highly similar in stress maximum and distribution areas. Residual stress is mainly concentrated in the weld zone, and there are only small differences in other local areas. The peak stresses of different welding sequences are all between 240 and 244 MPa. Besides, the residual stress of case 1 is the highest, which is 244.00 MPa. The case 3, which is 240.11 MPa, is the lowest among all schemes. In addition, it is obvious that the peak stress point of each scheme occurs at the edge of the air inlet, namely the arc closure point.

Residual stress analysis
The average residual stress of each weld, as seen in Fig. 15, has great differences in different welding sequences. The average residual stress in the first weld, which is close to 85 MPa, is higher than all welds and in the twelfth weld is close to 72 MPa for different welding sequences. The reason for the large stress difference between the first and last welds is that in all welding sequences, the first weld is completed first and the twelfth weld is completed last. Because the two welds are neighboring, the first weld undergoes more thermal cycles than the twelfth weld, resulting in a higher residual stress in the first weld. Figure 15a plots the average stress of each weld under the three welding sequences including case 1, case 2, and case 3. For case 1, namely skip welding with 0°, the average stress of each weld decreases steadily, making the stress difference between adjacent welds smaller. For the skip welding of 60° with a single weld (case 2), the average stress curve of the weld has a saw tooth form and the stress variation between neighboring welds is substantial. Additionally, it is discovered that the even-numbered welds completed later than the odd-numbered welds have higher residual stresses. For the symmetrical welding of single weld (case 3), the average residual stress declines linearly from the first to the sixth welds, but it abruptly jumped to 84 MPa in the seventh weld, which is comparable to the stress in the first weld, before progressively declining to 72.3 MPa at the end. It is also discovered that the stresses in the symmetrical welds are extremely near to one another. For instance, the second weld's average stress is 81.6 MPa, and the eighth weld's is 80.6 MPa; the average stresses of the third and ninth welds are 77.7 MPa and 76.8 MPa, respectively. Figure 15b shows the average stress of each weld from case 4 to case 6. For the skip welding of 90° with two adjacent welds (case 4), the mean stress curve demonstrates a quasi-periodic fluctuation with three periods, and each period consists of four weld seams. The greatest residual stress fell from 84.8 MPa in the first cycle to 82.4 MPa in the second cycle, and then to 79.9 MPa in the third cycle. The average stress of the eleventh weld in this process is 72.1 MPa. For the symmetrical welding of two adjacent welds (case 5), it is obvious that the weld's average stress curve also follows a quasi-periodic law. The stress curve is separated into three phases in a single period, i.e., six welds. The two neighboring continuous welded seams constitute a phase in two cycles. Taking a the first period as an example, the first phase includes the first and second welds, the second phase is consisted of the third and fourth welds. In addition, the fifth weld, which has a value of 71.5 MPa, is the one Fig. 12 The assembly of the lobe mixer: a primary view and b top view with the lowest average residual stress. For the symmetrical welding of three adjacent welds (case 6), the green curve reveals that the average residual stress of the weld seam performed first is greater than that of the weld finished later. For example, the first, second, and third welds all have higher average mean stress than that of the fourth, fifth, and sixth. The mean stresses of the tenth, eleventh, and twelfth welds are very close, and the eleventh weld has the lowest value, which is 72.5 MPa. The column graph depicts the stress differential between neighboring welds for various welding sequences, as illustrated in Fig. 16. These data are calculated by subtracting the stress values for the lower weld numbers by those for the larger weld numbers, and then taking the absolute value of the difference. For example, the parameter "1|2" represents the value of the second weld less the value of the first weld. The abscissa denotes the number of adjacent weld seams.
Excessive stress difference causes unequal stress distribution on the lobe mixer, which will affect the stability of the whole component. The histogram clearly illustrates that the welding sequence has a significant impact on the Fig. 13 Schemes for six different welding sequences residual stress of nearby welds. The first set of data, weld '1|2 ', demonstrates that the residual stress differential between the first and second welds is rather considerable in the skip welding of 60° with a single weld (case 2), reaching 11.38 MPa, while stress differential below the symmetrical welding of three adjacent welds (case 6) is the smallest, at only 1.61 MPa. Other processes have a stress differential of less than 3.5 MPa. For the weld '2|3 ', it is noticeable that the stress differential in the skip welding of 90° with two adjacent welds (case 4) is the greatest, reaching 10.13 MPa, followed by 9.96 MPa in case 2, and the process with skip welding with 0° (case 1) has the smallest value with 2.15 MPa. For the weld '3|4 ', case 2 has the greatest stress differential, at 10.81 MPa, followed by case 6, which is 7.88 MPa. Case 4 has the smallest stress differential, at just 0.46 MPa. For the weld '4|5 ', case 2 and case 4 welding sequences cause a stress difference with 9.48 MPa and 10.03 MPa, respectively. In addition, the stress difference of case 6 is the smallest, only 0.18 MPa. For the weld '5|6', only case 2 results in a stress difference of 9.62 MPa, while the others are less than 2 MPa. For the weld '6|7', except for case 1, where the stress difference is 0.64 MPa, the other welding processes cause the stress differential to exceed 8 MPa, with the greatest value reaching 12.93 MPa of case 3. For the weld '7|8', the stress difference is only 0.04 MPa when using the welding sequence of case 4, and case 2 has the largest stress difference, which is 8.37 MPa. For the weld '8|9', case 4 has the highest stress difference at 7.33 MPa, followed by case 2 at 7.00 MPa. Case 1 has the smallest value at only 0.84 MPa. For the weld '9|10', case 1 and case 5 (symmetrical welding of two adjacent welds) have extremely comparable stress differences, both approximately 1 MPa. Additionally, case  2 has the largest stress difference with 7.2 MPa. For the weld '10|11', the stress difference is just 0.17 MPa when using the case 6 welding sequence, and the maximum is 4.7 MPa when using the case 2 welding sequence. For the weld '11|12', the largest stress difference is 4.15 MPa in case 2, whereas the stress differences in the other five different welding sequences are all less than 1.5 MPa, which in the minimum is only 0.2 MPa. For the weld '11|1', the stress difference is all around 12 MPa under six different welding sequences. This is because the average stress of the first weld is quite high, surpassing 84 MPa, but that of the final weld, i.e., the twelfth weld, is lower, both below 73.5 MPa, which makes the stress difference of these two weld seams more significant.
The blue histogram displays the variance of average stress of the twelve welds in different welding sequences, as detailed in Fig. 17. As can be noticed, adopting the welding sequence of case 1 has the smallest variance of the weld stress, at 14.47, followed by case 6 with 22.08, while case 5 has the largest variance with 22.38. In addition, the variances of case 2, case 3, and case 4 with the welding sequence are 21.53, 21.88, and 22.04, respectively. The preceding data indicates that the welding sequence of case 1 can improve the uniformity of the weld stress distribution on the lobe mixer. Figure 18 displays the deformation contour for different welding sequences after welding. It can be seen that the deformed regions are mainly concentrated near the external ducts and the entrance of inner ducts for all welding processes. Besides, the maximum deformations are close, which them are all around 0.6 mm. Case 3 is the smallest with 0.54 mm, and the largest is case 1 with 0.62 mm. The maximum deformation of case 2, 4, 5, and 6 is 0.57 mm, 0.58 mm, 0.55 mm, and 0.56 mm, respectively. Therefore, it indicates that symmetrical welding of two or three adjacent welds has little effect on the maximum deformation. But they are inferior to the single weld symmetric welding in terms of controlling deformation. It can be also concluded that symmetric welding is better than skip welding.

Deformation analysis
The average deformations for different weld seams are calculated and illustrated in Fig. 19. It can be seen the welding sequence can significantly affect the average deformation of each weld from the fluctuation range of the curves.  Figure 19a describes the average deformation of each weld for the welding sequences of case 1, case 2 and case 3. For the skip welding with 0° (case 1), the average deformation of the weld grows initially, then reduces, and then increases from the first to the twelfth weld, which is completely different from the variation law of its stress. Additionally, the third weld has the greatest average distortion, measuring 0.31 mm, while the tenth weld has the least, measuring just 0.12 mm. It is worth noting that the first and twelfth welds have the same average deformation of 0.28 mm. For the skip welding of 60° with a single weld (case 2), the mean deformation curve is noticeably jagged. The fourth weld has the largest average deformation of 0.26 mm, followed by the fifth weld of 0.25 mm, and the ninth weld with the smallest of 0.14 mm. For the symmetrical welding of single weld (case 3), the dark blue curve clearly shows that the average distortion of all welds is about 0.2 mm. The maximum distortion is 0.23 mm of the six and twelfth weld seams, and the minimum is 0.18 mm of tenth and eleventh welds. Figure 19b depicts the average deformation of each weld for the welding sequences of case 4, case 5 and case 6. For the skip welding of 90° with two adjacent welds (case 4), the entire curve has a hump consisting of the third and fourth welds, and their average deformations are both 0.28 mm. Moreover, the average distortion of the remaining welds is less than 0.25 mm, with   19 The average deformation of each weld in different welding sequences: a From cases 1 to 3 and b from cases 4 to 6 the ninth weld having the least deformation of 0.14 mm. For the symmetrical welding of two adjacent welds (case 5) and the symmetrical welding of three adjacent welds (case 6), the average deformation curves' evolution law is similar in the two welding sequences, which is comparable to the mean stress curve variation law depicted in Fig. 15b. The curves also are smoother than in other welding sequences, and all welds had an average distortion of 0.17 to 0.24 mm.
The larger fluctuation, the greater difference of each weld is, which is not conducive to ensuring dimensional accuracy of lobe mixer. To directly reflect the degree of fluctuation of each curve, the variances of average deformation in different schemes are calculated, as shown in Fig. 20a. It is clearly that the average deformation variance is arranged from large to small in the following order: case 1 > case 4 > case 2 > case 6 > case 5 > case 3. Among these, case1 has a variance of 38.91 × 10 −4 , which is much larger than the average deformation variance of other welding sequences. In addition, with this welding sequence, the maximum deformation of the lobe mixer reached 0.62 mm. It is thereby inferred that adopting the welding sequence of a skip welding with 0° is unsuccessful for regulating the dimensional accuracy of the complete lobe mixer. Furthermore, using the welding sequence of the symmetrical welding of single weld (case 3) has the smallest variance with 3.31 × 10 −4 and peak deformation at 0.54 mm, which indicates that the deformation of the lobe mixer can be effectively controlled by using this.
The lobe mixer's gas input must be coupled to other components, the distortion requirements thus are considerable. Therefore, the maximum deformation at the entrance of the lobe mixer is measured as depicted in Fig. 20b. The peak deformation at the entrance of case 1 is the largest reaching 0.536 mm, followed by case 4 with 0.47 mm. Under the welding sequences of cases 5 and 6, the highest distortion of the entrance is 0.45 and 0.46 mm, respectively. However, the maximum distortions, which are 0.42 mm, are the same when utilizing the welding sequence of cases 2 and 3.

Conclusions
We firstly performed plate welding experiments to verify the reliability of the heat source model and thermal boundary conditions. Then, a large size three-dimensional finite element model for filler TIG welding of aero-engine afterburner lobe mixer was established based on the thermo-elastoplastic theory. Subsequently, the average residual stress and distortion of each weld under different welding sequences were calculated, and their variances were analyzed. Finally, the welding sequence was optimized in terms of residual stress and deformation uniformity between weld seams. Simple plate experiments are used to validate the welding process parameters, allowing for the optimization of various welding processes for large components. This method can save time and money by serving as a reference for structural design engineers and welding engineers. The main conclusions are as follows: (1) The hybrid heat source, namely the combination of double ellipsoidal and cylindrical heat source, has better reliability for the finite element modeling of GH3044 filler wire TIG welding. (2) A set of fixture is designed for flap mixer welding, which can effectively restrain the influence of different welding sequence on the peak stress of the whole component. (3) For various welding sequences, the residual stress in the first weld is close to 85 MPa, while the stress in the twelfth weld is only about 72 MPa. In addition, the welding sequence can result in an average stress difference of 13 MPa between the adjacent welds, which occurs in the sixth and seventh welds using the symmetrical welding of single weld (case 3) (4) The welding sequence has a great influence on the uniformity of the weld stress distribution on the afterburner lobe mixer, but less on the magnitude of the peak stress. Peak residual stress varies by less than 5 MPa while welding in various sequences. The maximum residual stress of the skip welding with 0° (case 1) is the highest with 244.00 MPa, and the symmetrical welding of single weld at 240.11 MPa is the lowest among all schemes. (5) The final peak distortion of the lobe mixer and the distortion-homogeneity between the welds are significantly influenced by the welding sequence. The maximum distortion of the whole lobe mixer is 0.54 mm adopting the symmetrical welding of single weld (case 3), which is the least among all welding schemes. The deformation variance is 3.31 × 10 −4 , assuring the component dimension stability. (6) The symmetrical welding of single weld is a welding sequence that may provide higher weld quality for aero-engine lobe mixer TIG wire filler welding with GH3044 from the point of view of residual stress and deformation uniformity between welds.