Keywords

1 Introduction

Welding process is a key process in the manufacture and production of nuclear power pressure equipment, in the nuclear power plant primary circuit system, there are many nozzle safety ends, mainly including the hot section and cold section on the reactor pressure vessel to take over the safety end, the fluctuating tube on the regulator to take over the safety end, etc., the corresponding geometry, materials, welding processes are generally similar [1,2,3]. It has been observed that the coupling of residual stress formed after welding and service load will accelerate the stress corrosion phenomenon of components, promote the germination and propagation of cracks, and thus threaten the safe operation of nuclear power plants. Therefore, it is necessary to pay close attention to the residual stress changes of the welded joint [4, 5].

In the current research, there are few three-dimensional overall simulations of welded joints at the safety end of the pipe. In the process of welding temperature field calculation, the correct selection of heat source model is an important guarantee for the accuracy of the calculation results [6, 7]. Based on ANSYS APDL, this paper simulates the welding safety end of the joint by using ellipsoid heat source and body heat rate heat source model, and analyzes the changes of welding temperature field and stress field.

2 Geometry and Meshing

The object studied in this paper is the model of welded joints of the safety end of the pressure vessel of the primary circuit reactor of nuclear power plants, with a total length of 1628.7 mm, an inner and outer radius of 417.3 mm and 500.3 mm, respectively, and a single-sided V-shaped groove with an angle of 15°. In addition, considering the calculation of the three-dimensional model, it is necessary to simplify the weld part reasonably, and relevant studies have shown that for the simulation of multi-pass welding problems, the intermediate process has little effect on the residual stress, therefore, under comprehensive consideration, the total weld area is divided into 11 layers, and the thickness of the weld in the cover welding stage at the end of the welding is 11.5 mm, and the rest are 8 mm, as shown in Fig. 1. In this paper, the thermal–mechanical indirect coupling is used for simulation, the solid70 unit is selected for thermal analysis, and the structural analysis is converted to the solid185 unit by etchg, tts command. The meshing adopts a combination of mapping surface mesh and sweep mesh, which is easier to obtain a good quality hexahedral mesh, the weld and heat affected zone are the places with the highest degree of mesh fineness, and the base metal area can be properly coarseened for computational efficiency, as shown in Fig. 2.

Fig. 1
A diagram. A rectangle diagram that is divided into 5 parts. The parts are the nozzle, overlaying, welding, butt welding, and safety end. The layer of overlaying is found below the part of the nozzle.

Cross-sectional view of the welded joint at the safety end of the reactor receiver

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Fig. 2
A 3 D mess model of welded joints. The whole surface is covered with square mesh.

Finite element model of welded joint at the safety end of a reactor takeover

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3 Welding Process and Heat Source Model

According to the welding process of nuclear power equipment, for the welding joint of the safety end of the pipe with isolation layer, the preheating treatment is generally not done before welding, and the temperature between the welding layers is controlled at 100–200 °C, and the excessive interlayer temperature will adversely affect the nickel-based alloy. In this simulation, the welding speed is set to 20 mm/s, the current is set to 630 A, and the voltage is set to 35 V. The main driving factor for the welding process to proceed is determined by the welding heat source, which causes phase changes, thermal strains, thermal stresses. For welding engineering applications, Gaussian surface heat source, double ellipsoidal heat source, bulk heat rate model, conical heat source, and strip heat source are commonly used [8, 9]. For large cylindrical models, the double ellipsoidal heat source model and the bulk heat rate model are usually used in the numerical simulation of welding, and the expression is as follows. The shape parameters of the double ellipsoid heat source have a great influence on the temperature field, and it is necessary to obtain the ideal parameters through repeated experiments [10], and \({a}_{f}\) = 8 mm, \({a}_{r}\) = 12 mm, b = 10 mm, c = 11.5 mm are used in this paper.

$$ q\left( {x,y,z} \right) = \frac{{6\sqrt 3 f_{f} \eta UI}}{{aba_{f} \pi^{3/2} }}{\text{exp}}\left( {\frac{{ - 3x^{2} }}{{a_{f}^{2} }}} \right){\text{exp}}\left( {\frac{{ - 3y^{2} }}{{b^{2} }}} \right) \cdot {\text{exp}}\left( {\frac{{ - 3z^{2} }}{{c^{2} }}} \right) $$
(1)
$$ q\left( {x,y,z} \right) = \frac{{6\sqrt 3 f_{r} \eta UI}}{{aba_{r} \pi^{3/2} }}{\text{exp}}\left( {\frac{{ - 3x^{2} }}{{a_{r}^{2} }}} \right){\text{exp}}\left( {\frac{{ - 3y^{2} }}{{b^{2} }}} \right) \cdot {\text{exp}}\left( {\frac{{ - 3z^{2} }}{{c^{2} }}} \right) $$
(2)
$$HGEN=\frac{K*U*I}{A*V*DT}$$
(3)

In Eqs. (1) and (2), q is the heat generation rate, w m-3; af, ar, b, c are the shape parameters of the double ellipsoidal heat source, m; ff and fr are the energy distribution coefficients before and after the heat source model, where HGEN represents the bulk heat generation rate (w/m3), K represents the welding efficiency, A represents the weld cross-sectional area (m2), V represents the welding speed (m/s), and DT represents the time step size of each substep (s).

4 Results and Discussions

4.1 Comparison of Welding Temperature Field Analysis Results

Two different heat source models are used as heat load inputs and analyzed using Ansys apdl. Because of the large number of weld layers, Only the temperature field distribution of the first and last welds are captured in this paper, the results are shown in the Figs. 3 and 4. From the temperature field analysis results, it can be seen that the welding heat source center moves continuously along the circumferential direction of the weld. The temperature is the highest from the welding heat source center and the heat gradient is distributed in an ellipsoidal shape. The welding time of each weld is set to 157 s, and the cooling time of 10,000 s is set after welding is completed to cool it to room temperature.

Fig. 3
A heatmap presents the distribution of the temperature field of the joint. Most of the parts of the specimen have temperatures between 25 and 197.602 units. The middle part has temperatures between 1060.61 and 1405.81 units.

Temperature field distribution of the first weld under the action of body heat generation rate heat source

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Fig. 4
A heatmap presents the distribution of the temperature field of the joint. Most of the parts of the specimen have a temperature of 25 units. The middle part has temperatures between 1017.3 and 1340.07 units.

Temperature field distribution of the first weld under the action of double ellipsoidal heat source

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Comparing the instantaneous temperature field of the two bulk heat source models at the same time, the temperature field distribution trend is basically the same. Due to the combined effect of heat conduction and heat source movement, the temperature field of the high temperature zone of the bulk heat rate model is also ellipsoidal, so the shape of the two molten pools is basically similar. From the temperature field of the first weld, the highest temperature under the action of the body heat rate model is 1595 °C, the highest temperature under the action of the double ellipsoidal heat source is 1513 °C. The maximum temperature in the high temperature area is about 60 °C higher than that of the double ellipsoid heat source because the energy of the body heat rate heat source is more concentrated. This is shown in Figs. 5 and 6, from the temperature field of the last weld, the maximum temperature is reduced due to the reduction of the interlayer temperature during the welding process, and the effect of the double ellipsoid heat source is more obvious from the figure.

Fig. 5
A heatmap presents the distribution of the temperature field of the joint. Most of the parts of the specimen have temperatures between 25.0032 and 194.061 units. The middle part has temperatures between 194.061 and 532.177 units.

Temperature field distribution of final weld under the action of body heat generation rate heat source

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Fig. 6
A heatmap presents the distribution of the temperature field of the joint. Most of the parts of the specimen have temperatures between 25.002 and 177.208 units. The middle part has temperatures between 177.208 and 481.619 units.

Temperature field distribution of final weld under the action of double ellipsoid heat source

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4.2 Analysis and Comparison of Welding Stress Field Results

When performing stress field analysis, it is necessary to fix constraints on both ends of the welded joint, otherwise there will be a situation where the calculation does not converge. The calculation results of the temperature field of the two are taken as the thermal load, that is, read the.rth file, and the *do cycle statement is also used to apply it one by one, and finally obtain the welding residual stress after the cooling of the two. As shown in the Figs. 7 and 8, the overall welding residual stress size when using double ellipsoid heat source is 395 MPa, and the welding residual stress size when using bulk heat rate heat source is 417 MPa, the difference between the two is about 20 MPa, indicating that the use of different heat sources has a certain impact on the welding residual stress field, but the residual stress distribution of the two is basically the same. The stress at the weld and the heat-affected zone is large, and the stress influence at the base metal away from the weld is small. Select the 0° direction as the path to observe the distribution of welding residual stress after the cooling of the entire welded joint. As can be seen from Fig. 9, the peak residual stress after cooling is located at the junction of the weld and the base metal, and the stress gradually decreases far from the weld.

Fig. 7
A 3 D titled heatmap presents the distribution of the residual stress field of the joint. The upper part of the specimen has residual stress fields between 0.446 E plus 07 and 0.503 E plus 08 units. The lower part has residual stress fields between 0.503 E plus 08 and 0.142 E plus 09.

Distribution of residual stress field after welding under the action of bulk heat generation rate heat source

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Fig. 8
A 3 D titled heatmap presents the distribution of the residual stress field of the joint. The upper part of the specimen has residual stress fields between 0.364 E plus 07 and 0.471 E plus 08 units. The lower part has residual stress fields between 0.471 E plus 08 and 0.134 E plus 09.

Distribution of residual stress field after welding under the action of double ellipsoid heat source

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Fig. 9
A multiline graph of von Mises stress versus distance. It presents the variations in bulk heat rate heat source, and double ellipsoid heat source. The curves fluctuate with the change in time. The double ellipsoid heat source first increases, then increases vertically, then gives a sharp peak.

Distribution of residual stress under the action of two heat sources

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5 Conclusion

Based on the results and discussions presented above, the conclusions are obtained as below:

  1. (1)

    The double ellipsoid heat source model needs to determine the shape parameters according to the actual situation of the molten pool, while the body heat rate heat source model is more efficient.

  2. (2)

    The shape of the molten pool of the double ellipsoid heat source and the body heat rate heat source is ellipsoid and the size is basically the same. The overall stress field under the action of body heat rate heat is about 20 MPa higher than that of the double ellipsoid heat source, and the stress field distribution law of the two is the same.

  3. (3)

    Double ellipsoidal heat source and bulk heat rate heat source have advantages and disadvantages when simulating the welding process of the safety end. More heat source models can be tried for comparative analysis and better heat source models can be selected.