NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION

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1 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 15 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION M. Slováček 1, V. Diviš 1, L. Junek 1, V. Ochodek 2 1 Institute of Applied Mechanics Brno Ltd., 2 Technical University Ostrava (Czech Republic) ABSTRACT The paper presents the results of our recent developments. Studies for detailed understanding of the behaviour of a steel structure during welding operations have been carried out. Mainly the distortion of the steel structure has been observed. Several welding experiments have been prepared and carried out. The results from the welding experiments have been used as the input and output parameters during the numerical simulations. Measurements were also carried out on the material properties needed for numerical analysis. Numerical simulations have been made according to experiments. The calculated results were compared with the measured results. Based on the comparison parameters have been determined, which have an influence on the final distortion of the steel structure. The following input parameters have been observed: model of the temperature source, constraint condition, and material models. A good correlation has been obtained for temperature (mainly for shape and size of the molten zone) as well as distortion prediction between experimental and numerical approaches. The double ellipsoid heat source model has been used and modified to fit the measured parameters. The modified double ellipsoid heat source was used for MMAW and GTAW welding technology. IIW-Thesaurus keywords: Mathematical models; MMA welding; Arc welding; GTA welding; Gas shielded arc welding; EB welding; Radiation welding; Distortion; Deformation; Residual stresses; Welding power sources; Process equipment; Comparisons; Mechanical properties; Prediction; Plastic deformation; Thermal properties; Physical properties. 1 INTRODUCTION Welding is the most prevalent metal joining process. The absorbed heat input during the welding process creates residual stresses as well as distortion in the steel components. The type and extent of distortion and the residual stresses are influenced by a number of different factors such as the clamping condition, mechanical and thermal properties, type and size of the heat source, welding parameters, weld joints design, temperature of surroundings, etc. Residual tensile stresses also have a negative influence on the structure lifetime and its brittle fracture resistance. Residual stresses create a balanced system of inner forces, which exists even under no external loading. The numerical simulation of the welding process is one way to determine the level of the residual stresses and distortion. The calculated residual stresses are used for prediction of the lifetime including influence of the welding process or finding possibilities of the defect initiation and defect growth under service condition. Residual stresses are created mainly in cases when the steel structure is very stiff. On the Doc. IIW (ex-doc. X ) recommended for publication by Commission X Structural performances of welded joints - Fracture avoidance. other hand, when the structure is free, or the movement of some components of the steel structure is allowed, the residual stresses have a lower level than for fixed cases but the distortions are still created. The control of distortion is very important due to manufacturing tolerances for follow-up machining and assembly processes. It is clear that the compromise between fully fixed and absolutely free construction needs to be found. The main aim of the current project has been to predict the distortion, which is the basis of the numerical simulation for the real steel structures. First, several welding experiments have been completed. Several input and output parameters have been measured, which have been used during numerical simulations. The material properties of the steel were also measured. Second, the numerical simulations of the experiments have been completed. The calculated and measured parameters have been compared (mainly temperature cycle and distortion). The set of input parameters have been found for which the calculated and measured distortions have been in correlation. The relation between the input parameters (mainly size and shape of the heat source, input welding parameters and welding technology, and efficiency of the welding process) and the output parameters (distortion) has been calculated. The aim of the development has been to find the input parameters and Welding in the World, Vol. 49, n 11/12, 2005

2 16 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION model for numerical simulation to correspond with reality. The researchers from the Institute of Applied Mechanics have a lot of experience with numerical simulation of the welding process. During last 10 years the validation of the method has been done mainly for residual stresses. The numerical simulations have been used for prediction of the level of the residual stresses and consequent lifetime assessment. Now the development projects concern the distortion prediction. From the literature it can be seen that the computer simulations are widely used for welding research and for prediction of the structure behaviour during welding operations. The finite element numerical simulation is a very strong tool and can also decrease the number of premanufacturing experiments, time for development or innovation of the products and, of course, decreasing the cost. The commercial finite elements code SYSWELD has been used for numerical simulation. 2 NUMERICAL SIMULATION OF WELDING-THEORETICAL BACKROUND The numerical simulation of welding can be divided into two methods. The first one is the classical transient method, which means that the numerical analyses are done step by step. The all-welding process is numerically simulated without any time simplification. The nonstationary temperature fields are solved at each time interval. The temperature fields are taken as a loading condition for structural analysis. The structural analysis (strains, stresses, and distortion) is made at the same time intervals as in the temperature analysis. The numerical solutions are done for each welding pass. It is evident that the method is very slow and needs a lot of time and steps for finishing the numerical simulation. A very large construction part cannot be solved. The classical transient method can be applied very successfully for prediction of residual stresses, strains, and distortion on very simple construction parts with a low number of passes or with using some simplification (analysis on the 2D models). The classical transient method has also been named the local approach. The big structures with a lot of welding operations and kilometres of welded joints can be numerically solved with the help of the new methodology, local-global approach. There is a connection between the results from the classical transient local approach of the welding and global elastic analysis. The results from local-global approach are only distortion. 2.1 Transient method of welding numerical simulation The numerical modelling of the classical transient method by the SYSWELD code [1] consists of three stages. 1. During the first stage a complete diagram of anisothermic decomposition (CCT diagram) is entered by a special pre-process module. The results of this stage are coefficients describing the kinetic of transformation process depending on cooling rate in individual areas of the heat-affected zone. The coefficients depend on the temperature and on the metallurgical phase of the particular material and are used as direct input to the second phase. 2. The second stage is a thermo metallurgical solution. This part needs complete thermo physical and thermo metallurgical material properties. A classical equation of the heat conduction, extended with the transformation of latent heat during change of phase and during melting of material, is applied. Coupling between phase transformation and heat conductivity is used. The results of the first stage are the following: Non-stationary temperature fields; percentage distribution of individual phases; size of primary austenitic grain; hardness, special module: hardness is calculated on the base of empirical expressions. The temperature analysis is a transient calculation in each time interval. The all-welding passes must be simulated. 3. The results of the second stage (mainly non-stationary temperature fields) are applied as a loading condition in the third stages (the structural analysis). The complete mechanical properties are needed. The mechanical properties (thermal expansion, yield stress, hardness, Young modulus, etc.) depend on the temperature and individual phases. The resulting mechanical properties in the weld joint and heat-affected zone are calculated on the basis of individual phases distribution and their mechanical properties. The transformation plasticity is considered during change of the metallurgical phases. The results of the second stage are: Total deformation: consist of elastic part, thermal part, convectional plastic part, transformation plasticity; residual stresses; distortion Model of the heat source The model of the thermal source is one of the most important input parameters. The computation model is loaded only with non-stationary temperature fields. Thermal load represents the thermal energy flow into the material during the welding process. The results (distortion, residual stresses) depend very much on finding the correct model of the thermal source and appropriate temperature distributions. The total input power is defined by equation (1) and depends on the welding input parameters and welding technology. The model of the heat source is applied during the classical transient analysis. Q = U I η (1) where Q is the total input power [W] U is the voltage [V]

3 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 17 I is the current [A] η is the efficiency [-] The parameters U and I are clear and are determined during the welding process. The parameter η is not known and should be found in the literature or measured. It is possible to find the value of the parameter η in the literature [2, 3], but it has a very wide range for the various types of the technology. Because of it, it is needed to make some checking measurements of temperature cycles, and the shape and size of the heataffected zone to obtain and indirectedly verify the correct value of the parameter η. The convective movements of the fluid in the pool are not computed (fluid dynamics). The SYSWELD code does not predict the shape and the size of the bead, molten zone, and heat-affected zone (all factors depend on welding parameters, weld geometry design etc.) and these parameters should be determined by means of experiments. The Institute of Applied Mechanics Brno has paid attention to find the correct model of the heat source for each welding technology. The special heat source models for the MMAW and GTAW technology have been developed. The double ellipsoidal heat source model [4, 5] has been used as a basis and this model has been modified. The model is shown in Figure 1 and is described with equation (2). This equation has two different variants, the first one describing the heat source in front of the wire and the second one describing the heat source behind the wire. The differences are only in parameters c and coefficient f. q (x, y, z, t) = 3.x 2 3.y 2 3.z f. Q. e a 2. e b 2. e c 2 (2) a. b. c. π. π where q is the heat flux [W/mm 2 ] f is a coefficient [-] Q is the total input power [W] a, b, c, d are the sizes of the melted area [mm] Figure 1 Double ellipsoidal model of heat source The value Q is calculated according to equation (1), parameters a, b, c, and d are measured on the macrograph, and f is found based on the experiments or from the literature. The best value of f for the model on the basis [6] of heat source appears as f 1 = 0,6, f 2 = 1,4. The double ellipsoidal model has been modified and adjusted for the technology corresponding with the welding conditions utilized. The modifications have been done according to measurement of the temperature cycles, and the shape and size of the melted areas. 2.2 Local global approach The local global approach is a new methodology for determination of distortion of large structures during the welding assembly process. The distortion of numerical simulation by the local global approach is done in the four following stages: 1. The first stage is a classical transient numerical analysis of the welding. Typical welded joints on the structure and simulated by classical transient method are chosen. These procedures are named local modelling and local approach. 2. In the second stage, the global model representing the structure (in our case, vessel, ribs, flexible housings, supports etc.) is created. 3. The total plastic deformation solved on the local models is transferred to the global model. The global model is loaded with total plastic deformation, which has been solved on the local model. 4. The fourth stage consists of the structural elastic analysis including each welded joint. The results give distortion during and at the end of the assembly process. 3 MATERIAL PROPERTIES The material properties are very important input parameters and can be taken from measurement or the literature. The material properties are very strongly dependent on the temperature and also on the metallurgical phases. The accuracy of the numerical simulation of the welding process depends on several factors. One factor represents the correct input material properties. IAM Brno has got its own internal database with measured input material properties for 15 various steel materials. The IAM Brno cooperates with several research material and welding institutes and universities and can measure the complete needed material properties for numerical analysis. At present, the best combination is that the mechanical material properties are measured and thermo-physical material properties are taken from literature. The mechanical material properties (thermal expansion, yield stress, and strain hardening) are measured up to 800 o C and also for each metallurgical phase alone. The following input material properties are needed for the numerical simulation of the welding process: 1. Thermo metallurgical solution a) CCT diagram (measurement).

4 18 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION b) Thermal conduction (literature). c) Specific heat (literature). d) Density (literature). e) Heat transfer (literature). 2. Mechanical analysis a) Thermal expansion (measurement). b) Youngs modulus (measurement). c) Yield stress (measurement). d) Strain hardening (measurement.) e) Viscoplastic parameters (measurement). 4 EXPERIMENTS An experimental program has been prepared which contains the following experiments [7]: 1. Welding of 3 mm thick plates, MMAW technology. 2. Welding of 3 mm thick plates, GTAW technology. 3. Welding of 10 mm thick plates, MMAW technology. 4. Welding of 10 mm thick plates, GTAW technology. 5. Welding of 20 mm thick plates, GTAW technology. 6. Welding of 20 mm thick plates, back welding technology, combination of MMAW and GTAW technology. 7. Welding of 10 mm plates, MMAW technology, T joints, two variants. 8. Electron beam welding, flexible housing components, 20 mm thick plate. 9. Check welding for determination of input parameters for the heat source model, MMAW, GTAW, and EB technology. Two types of the constraint condition were applied. The first type of experiment was welded so that one plate was fixed and the other plate was free. The second type of experiment was welded in the frame. Both plates were fixed, and one plate was released after finishing the welding process. The main aim of the experimental program was to prepare and find the input parameters for the numerical simulations and to prepare the examples for the verification of the solution method. The complete measurement of the output parameters during the welding experiment was performed. The following parameters were measured: 1. Temperature cycles with thermocouples and digital thermometers. 2. Distortion and shrinkage with inductive gauges. 3. Surface stress with strain gauges. 4. Internal forces in the fixed places. 5. Residual stresses using the hole drilling method. 6. Size and shape of the melting area and heat-affected zone. 7. Input parameters of power source (voltage, current, and welding velocity. The results have been used for the determination of the size and shape of the heat source, the efficiency of the welding technology employed, the size of the distortion and the level of the residual stresses. All the experiments have been simulated and measured parameters have been compared with the calculated results. If the comparison is correct then it is possible to make the conclusion that the chosen solution method suits the real numerical simulation. The austenitic material 316L has been used for all the experiments. One part of the experimental program was the determination of the input material properties. The material properties were found from the three following sources. EFDA [8] and ENEA Bologna [8] supplied the results of the measurement. The other measurements were made by the Technical University Ostrava and Vitkovice Material Research Institute [8]. Based on the measured results, the input material properties of material 316L were prepared. The detailed descriptions and results of all the welding experiments are in reference [7]. Two experiments were chosen and presented in the following chapters mm thick plate, MMAW technology, free plate Seven inductive sensors of displacement were used. Temperature cycles were scanned with eight thermocouples. One plate was fixed and the other one was free. The vertical distortion was measured on the free plate. (See Figures 2 to 7 and Table 1). Table 1 Welding parameters Bead No. Ø wire I U v [mm] [A] [V] [cm/min.] 1. 2, ,1 2. 3, ,8 3. 3, ,1 Figure 2 Treatment of weld area Figure 3 Process of welding beads

5 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 19 Figure 4 Measured temperature cycles Figure 5 Measured vertical distortion

6 20 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION Figure 6 Experiments Figure 7 Distortion after welding mm thick plate, MMAW technology, fixed plates Two inductive sensors of displacement were used. Temperature cycles were measured with the eight thermocouples. One dynamometer was used to measure the inner force in fixed condition. The both plates were Table 2 Welding parameters Bead No. Ø wire I U v [mm] [A] [V] [cm/min.] 1. 2, , ,9 3. 2, ,4 4. 3, ,5 fixed and after welding one plate was released. (See Figures 8 to 13 and Table 2). 5 NUMERICAL SIMULATION OF WELDING PROCESS The numerical simulations are divided into several groups as follows [8]: 1. Numerical simulation of welding experiments. 2. Preparation of the various local models and their numerical simulation for the verification of the localglobal approach. 3. Numerical simulation of the global models (distortion prediction). Figure 8 Treatment of weld area Figure 9 Process of welding beads Figure 10 Measured temperature cycles

7 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 21 Figure 11 Experiments, after welding Figure 12 Vertical distortion after welding process and releasing transferred to the global models. The following numerical simulation have been done: a) MMAW technology, 10 mm thick plate Fixed constraint condition and release. Model with the stiffness constraint condition. Numerical simulation on the 2D model. b) GTAW technology, 10 mm thick plate Fixed condition and release. c) GTAW technology, 60 mm thick plate 2D model, fixed constraint condition and release. The models, simulated in group 1, have also been taken as the local models for the analysis with the assembly module. The third group contains numerical simulation by means of the assembly module (local-global approach). The calculated distortions of the assembly module are compared with the distortion calculated on the local models. Figure 13 Measured vertical distortion after welding process The first group represents the numerical simulation of the welding experiment. The following numerical simulations of the experiments have been done: a) MMAW technology, 10 mm thick plate. b) GTAW technology, 10 mm thick plate. c) GTAW technology, 20 mm thick plate. Several variants have been done (different sequences of welding passes). There was also the optimization of the welding process before the welding experiment. d) EB technology, 20 mm thick plate, flexible housing components. The numerical simulations for finding the correct input parameters (mainly parameters that determine the heat source model) have been done in parallel with the numerical simulation of the welding experiments. There are very close relations between the experiments and all numerical simulations in this stage. The second group contains various types of the local models. The calculated total plastic strains have been 5.1 Numerical simulation of the welding experiment Several numerical simulations have been done according to experiments. The following results have been compared between the measurements and numerical calculations: 1. Temperature cycle. 2. Maximum reached temperature. 3. Shape and size of the melting area. 4. Distortion during the welding process and at the end of the welding process. All the stated parameters have been compared with each numerical analysis MMAW technology, 10 mm thick free plate The numerical simulation of 10 mm thick plates with MMAW technology has been done [8]. The 10 mm thick plates were welded with 3 beads according to an experiment using MMAW technology. The first results have confirmed that this numerical simulation is very suitable for the verification of the solution method.

8 22 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION Figure 14 Finite element model and constraint condition Figure 15 Constraint condition during the experiment The finite element model and the constraint condition are shown in Figures 14 and 15. One side of the plate was fixed and the other side was free. The distortion was determined on the free side of the plate. Several numerical analyses have been done with different types of input parameters for the model of the heat source, efficiency of the arc, and shape and size of the melting area and the heat-affected zone. The best input parameters based on the calculated results have been chosen and these parameters have been used for the analysis of the real welding process. First, the numerical simulation of the welding process with parameters obtained from measurements was done. The double ellipsoidal heat source model with 0,7 efficiency was used. The parameters of calculated and measured results have been compared: temperature cycle, peak temperatures, shape and size of the molten zone, and vertical distortion. A discrepancy between the calculated and measured results was found, mainly in the shape and size of the molten zone, temperature cycle, and vertical distortion. Table 3 presents the comparison between the calculated and measured vertical distortion. The arc efficiency is a very important parameter. The arc efficiency influenced the amount of the heat source power. Since arc efficiency ranges from 0,6 to 0,85 for MMAW and cannot be directly measured from experiments, sensitivity analyses for the arc efficiency were performed. The aim of these analyses was to determine the influence of various values of the efficiency on the result of temperature (mainly on the shape and size of the molten zone) and vertical distortion. Table 4 presents the calculated results of the vertical distortions, obtained using the different levels of efficiency for the double ellipsoidal heat source model. The level of the chosen efficiency influenced the final distortion. The differences between the maximum and minimum distortions after welding was 20 %. The correct heat input (level of efficiency) should be determined when based on the measured temperature cycle. However, the efficiency is not the only parameter that influenced the shape and size of the molten zone and the final distortion. The shape of the molten zone depends on the chosen model of the heat source. The sensitivity analyses for various parameters of the double ellipsoidal heat source model and level of the efficiency were done. Numerical simulations of one bead in the groove were carried out. Three different parameters for the double ellipsoidal model were applied. The first model of the heat source was applied to the double ellipsoidal model directly without any modification and other models were used according to the following equations (3 and 4). All the same welding parameters and material properties were used except the model of the heat source. The results of these analyses are shown in Table 5. Figures 16 to 18 present the different shape and size of the molten zone for each type of the heat source model. Bead No. Table 3 Distortion comparison Vertical distortion [mm] Calculated Measured 1. 7,51 2, ,6 7, ,6 13,3 Bead No. Table 4 Distortion comparison Calculated vertical distortion [mm] Efficiency Efficiency Efficiency Efficiency 0,85 0,8 0,7 0,6 Measured distortion [mm] 1. 5,86 6,78 7,51 7,98 2,6 2. 8,20 7,51 10,64 11,68 7, ,23 16,62 17,60 18,18 13,3

9 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 23 Efficiency Table 5 Distortion comparison Heat source model Double Double Double ellipsoidal model ellipsoidal ellipsoidal model Variant 1 model Variant 2 Vertical distortion [mm] 0,5 4,56 4,62 4,64 0,6 4,48 4,33 4,34 0,7 4,45 3,8 3,83 0,8 4,3 3,24 3,27 0,9 4,1 2,54 2,62 1 3,87 1,89 1,96 Figure 16 Double ellipsoidal model Figure 17 Double ellipsoidal model, Variant 1 Figure 18 Double ellipsoidal model, Variant 2 2.x 2 2.y 2 2.(z v.(τ t)) 2 q (x, y, z) = f f. Q. e a 2. e b 2. e c 2 (3) a. b. c. π. π (Variant 1) 1.x 2 1.y 2 1.(z v.(τ t)) 2 q (x, y, z) = f f. Q. e a 2. e b 2. e c 2 (4) a. b. c. π. π (Variant 2) It is clear from the table and figures that the shape and size of the molten zone (temperature fields) are very important parameters. Each model of the heat source has caused a different shape and size of the molten zone (it means also different temperature fields). The temperature gradient through the thickness has the main influence on the vertical distortion. If the accuracy between the calculated and measured results were good the molten and heat-affected zone should be modelled very precisely. The double ellipsoidal heat source model cannot be used there as the general model for all-welding processes. The double ellipsoidal heat source model should be modified for each process used. Several numerical simulations were carried out with the aim to find appropriate parameters of the double ellipsoidal model. The shape and size of the molten zone and vertical distortion were controlled. The heat source for the first bead was simulated with the non-modified double ellipsoidal model. The second bead was simulated with the modified double ellipsoidal model according to equation (5) and the third bead was simulated with the modified double ellipsoidal model according to equation (6). 1.x 2 1.y 2 3.z f. Q q(x, y, z, t) =. e a 2. e b 2. e c 2 (5) a. b. c. π. π 8.x y 2 3.z f. Q q(x, y, z, t) =. e a 2. e b 2. e c 2 (6) a. b. c. π. π

10 24 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION Figure 19 Residual stress (equivalent MISE stress) at the end of the 3 beads Figure 20 Vertical distortion at the end of each bead Figure 19 represents the equivalent Mise stress at the end of the welding process. The results are shown on the deformed model. The distortions are 2-times enlarged. Figure 20 shows a vertical distortion at the end of each bead. Table 6 shows the comparison between the calculated and the measured vertical distortion. It is evident that the agreement between the calculated and measured results is very good. The main aim has been obtained; that is, the very good agreement of the distortion during and at the end of the welding process. The influence of the input parameters on the final distortion and sensitivity of the distortion on the input parameters has been found. Now, we know which parameters should be changed or adjusted to obtain the correct distortion GTAW technology, 10 mm thick free plate The 10 mm thick plates were welded with 10 beads using GTAW technology. The example also is very suitable for the verification of the input parameters for the numerical simulations. The heat source model for the GTAW technology has been validated. The finite element model and the constraint conditions are shown in Figures 21 and 22. One side of the plate was fixed and the other side was free. The distortions have been determined on the free side of the plate. In this case the appropriate heat source model has been found for GTAW technology and welding parameters used. The applied model of the source is as follows: q(x, y, z, t) = 1.y 2 1.z f. Q. e b 2. e c 2 (7) a. b. c. π. π Figure 21 Constraint condition Table 6 Comparison between calculated and measured vertical distortion Bead No. Vertical distortion [mm] Measured Calculated 1. 2,45 2, ,26 6, ,33 12,64 Figure 22 Constraint condition during experiment

11 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 25 Figure 23 Residual stress (equivalent MISE stress) at the end of the 10 beads Table 7 Comparison between calculated and measured vertical distortion Bead No. Vertical distortion [mm] Measured Calculated 1. 0,74 0, ,37 2, ,22 5, ,7 10, ,9 15, ,6 20, ,35 26, , ,9 36, ,1 43,8 Figure 24 Vertical distortion at the end of the 5 th and 10 th beads The vertical distortions were measured during the welding experiments. The value of the measured vertical distortion is 0,2 mm and the calculated value is 0,18 mm. There is evidently a very good agreement between the calculated and measured vertical distortion. Figure 23 represents the equivalent Mise stress at the end of the welding process. The figures include the distortion of the plate. The distortions are 1-times enlarged. Figure 24 shows a vertical distortion at the end of the 5 th and last beads. Table 7 shows the comparison between the calculated and measured vertical distortion. Figure 25 Finite element model Numerical simulation of the EB welding technology An experiment for electron beam welding to correspond with some components during the welding of the fusion reactor has been proposed. The flexible housing components will be welded by electron beam welding technology. The welding experiment was done and the numerical simulation was carried out according to experiments. The finite element model is shown in Figure 25. The non-modified conical heat source model was used. The residual equivalent MISE stresses at the end of the welding process are shown in Figure 26. The final vertical distortions at the end of the welding process are shown in Figure 27. Figure 26 Residual MISE stress at the end of the welding process

12 26 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION Figure 27 Vertical distortion at the end of the welding process Figure 28 Finite element model Numerical simulation of the fixed plates experiments The research program concerning the distortion is still continuing. The releasing process after welding is widely used for the welding assembly process. The process of releasing of the clamping condition causes the change of the size and shape of the steel components and often the manufacturing tolerances are not kept. The industry requirement is to predict the distortion after releasing the clamping condition after the welding process and the optimization of the welding parameters, sequence or supports stiffness to obtain the very close manufacturing tolerances. Two types of the experiments have been carried out. The first one with 10 mm thick plate welded with MMAW method and the second one with 20 mm thick plate welded with the back welding processes (combination of MMAW and GTAW method). First, the numerical simulation of the MMAW technology has been carried out. This experiment has been chosen because the numerical simulation of the 10 mm thick plate with four beads needs a short calculation time. The first 2D numerical simulation has been carried out. The calculated and measured results showed a big discrepancy. The sensitivity analyses has been performed and the influence of the input material parameters (mainly thermal expansion coefficient), heat source model and fixed condition (mainly its stiffness), has been revealed. It has been suggested that the main influence on the final distortion after the welding process and releasing needs a more correct model of the fixed condition and heat source model. The correct stiffness of the fixed condition should be considered. The real 3D model includes the plates and fixed frame condition for modelling. The finite elements model is shown in Figure 28. The two models have been considered, the frame is modelled with 3D linear elements or alternatively with shell elements. The sensitivity analyses have also been performed with different stiffness of the frame. The set of the numerical simulations has been completed. The calculated ver- Figure 29 Equivalent MISE stress after welding tical distortion is still smaller than that measured. The main influence on the final distortion after releasing is the stiffness of the frame. Figures 29 to 32 present the results of one of the variants of the numerical simulation. Figure 30 Equivalent MISE stress after welding and releasing

13 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 27 Figure 31 Vertical distortion after welding Based on the measured and calculated results, it is evident that the frame is not very stiff. The frame was distorted during welding. Part of the distortion was transferred to the frame. Based on the calculation, a requirement of another experiment with a much stiffer frame is evident. The project is still under investigation and the summary of this part of the project will be presented in a future paper. 5.2 Numerical simulation of the global models, local-global approach The local-global approach is a new methodology for the determination of the distortion during an assembly process. The distortion on the large construction parts can be determined and the optimization of the welding technology can be made. All the previous works have also been done to prepare the input data (local models) for the local-global approach. The transfer of totally plastic deformation from local models to global models has been verified. The comparison between distortions calculated for the local and global models were done. The method of the solution for the local-global approach has been validated and a set of input parameters has been found, which will be used during the real numerical simulation. The following examples (variants) for the validation of the method have been prepared: mm thick plate, MMAW, free constraint condition mm thick plate, GTAW, free constraint condition mm thick plate, GTAW, free constraint condition, distortion prediction without experiment mm thick plate, MMAW, totally fixed constraint condition and release mm thick plate, MMAW, various stiffness were implemented on one side of the plate. The transfer and the numerical analysis have been checked for: A. 3D local model to a 3D global model. Figure 32 Vertical distortion after welding and releasing B. 3D local model to a combined 3D/Shell global model. C. 2D local model to a 3D global model. The following figures (Figures 33 to 37) present the comparison of the calculated results and the distortion calculated for the local and global models. Table 8 shows the complete comparison of the distortions for each calculated variants. The aim was to validate in the following way the numerical simulation. The local model should be 2D. The advantages of the 2D model give a shorter solution time than the 3D model. Therefore, more variants of the local models can be simulated. The global model can be created as a combination of 3D, shell, and bead elements. The calculation time and requirement for the internal computer memory is smaller for the model created with the combination of 3D and shell elements than for the model created only with the 3D elements. The 3D elements will be used for the weld and close surroundings and shell elements will be used for parts as ribs, supports, inner and outer shell, etc. Figure 33 Comparison of distortions between local and global models, Variant 1A (10 mm thick plate, MMAW technology, free constraint condition)

14 28 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION Figure 34 Distortion of the global models (coupling 3D-shell elements), Variant 1B (10 mm thick plate, MMAW technology, free constraint condition) Figure 35 Distortion comparison between local and global models, Variant 1A (20 mm thick plate, technology MMAW, free constraint condition) Figure 36 Distortion of the local models, variant 5A, 10 mm thick plate, MMAW technology, stiffness on one side of the plate Figure 37 Distortion of the global models, variant 5A, 10 mm thick plate, MMAW technology, stiffness on one side of the plate Table 8 Distortion comparison Variant Vertical distortion [mm] Local model Global model 3D analysis 2D analysis 3D analysis Coupling 3D/shell analysis 1A, 1B 12,1 12,9 13,7 1C 15,35 15,31 (14,36)* 2A, 2B 42 43,2 45,7 3A 95, ,7546 4A 0,5 0,48 5A 1,048 0,988 (1,032)** * Two models with different mesh have been prepared and analysed. The first model (vertical distortion 15,31) is finer than the second one (vertical distortion 14,36). ** The various types of the transfer tool of the totally plastic deformation from the local model to the global model have been applied.

15 NUMERICAL SIMULATION OF THE WELDING PROCESS - DISTORTION AND RESIDUAL STRESS PREDICTION, HEAT SOURCE MODEL DETERMINATION 29 6 CONCLUSION The main objects of this work have been to find the methodology of the numerical simulation of welding, mainly for the prediction of distortion. The experimental program has been prepared. The measured results during the experiments have been used as input parameters (welding power, shape and size of the molten area) for the numerical simulations and also for the comparison of calculated and measured results (temperature cycles, distortion). The following conclusions can be drawn: 1. The appropriate heat source models for welding GTAW and MMAW technology and used welding parameters have been found. The relation between the quantity of input heat flux to material, shape and size of the molten zone and distortion have also been found. 2. Classical numerical simulations according to the welding experiments have been carried out. The calculated and measured distortions have been compared and the agreement was very good. 3. Several local models have been simulated with different constraint conditions. These models have been used for the verification of the methodology local-global approach. The calculated total plastic deformations of the models with a different constraint condition have been transferred to the global models. The process of transferring the total plastic deformations has been validated. 4. Global analyses have been done and the final distortions have been compared between the global and local models. A very good agreement exists between the results calculated for the local and global models. 5. The local-global method has been validated and this method can be used for the prediction of the distortion during the welding assembly process. 6. The main influence for the angular distortion shows the temperature gradient through the thickness of the plate. The high temperature gradient through the plate thickness causes great angular distortion. If the whole plate thickness is melted, the angular distortion is not as high as in the cases when only a part of the thickness is melted. However, the distortion also depends on the stiffness of the welded structure. All stated facts show that the accuracy of the heat source modelling has a very high influence on the distortion prediction. All the research projects have only one main aim to find the solution method and input parameters so that the numerical simulation of the welding process can be compared to reality. The IAM Brno used numerical simulations of welding for real cases in industries and based on the calculated results, various improvements and changes of the technology or prediction of the lifetime, etc. have been implemented. Examples of the application of the numerical simulation in industry are stated in [9]. REFERENCES [1] ESI Group: SYSWELD reference manual, Digital form SYSWELD version [2] Kou S.: Welding metallurgy, University of the Wisconsin, a Wiley-Interscience publication, August [3] Hrivňák I., Štembera V., Mráz L., Király F.: Diagramy rozpadu austenitu vývojových čs.konstrukčných ocelí a zvarových kovov, Výzkumný ústav zváračský, leden [4] Goldak J., Bibby M., Moore J., House R., Patel B.: Computer modeling of heat flow in welds, Metallurgical transaction B, Volume 17 B, September [5] Goldak J., Chakravarti A., Bibby M.: A new finite element model for welding heat source, Metallurgical transactions B, Volume 15 B, June [6] Dong P.: Residual stresses and distortion in welded structures: What we know today and beyond, IIW/IIS Doc.XII-X/XIII/XV-RSDP-89-03, Based on keynote lecture presented at the 6 th International conference of trends in welding research, April 15-16, 2002, Pine Mountain, Georgia, USA. [7] Diviš V., Slováček M., Ochodek V., Floryan J.: Evaluation of welding distortion of VV polodial segmant, validation of method, experiments, Zpráva ÚAM Brno 3616/04, Brno, October [8] Slováček M., Diviš V.: Evaluation of welding distortion of VV polodial segmant, validation of method, Zpráva ÚAM Brno, Brno 3586/04, October [9] Slováček M., Diviš V.: Technická podpora v oblasti svařování, Workshop Svařování konstrukcí (welding of the constructions), Czech Welding Society, February 2005.