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In order to propose high effective simulation using finite element method (FEM) for predicting deformation and residual stress generated by one pass butt welding, a series of numerical analyses were carried out. By idealizing the movement of heat source (the instantaneous heat input method), the tendency of welding out-of-plane deformation and the residual stress distribution could be predicted. The computing time was around 9% of that by the precise model with considering the movement of heat source. On the other hand, applicability of two dimensional shell elements instead of generally used three dimensional solid elements was examined. The heat input model with considering the temperature distribution in the thickness direction was proposed for the simulation by using the shell elements. It was confirmed that the welding out-of-plane deformation and residual stress could be predicted with high accuracy by the model with shell elements and the distributed heat input methods. The computing time was around 8% of that by the precise model with solid elements.

In constructing steel structures, welding is generally used for joining and assembling members. Then, welding deformation and residual stress are inevitably generated due to expansion and shrinkage of welded parts caused by local heating/cooling. Welding deformation and residual stress influence the accuracy of manufacturing, load carrying capacity and fatigue strength of members [

For predicting welding deformation and residual stress generated in structural steel members, numerical si- mulation by thermal elasto-plastic analysis based on FEM is an effective method [

In this study, two calculation methods are examined by which the simulation of welding deformation and re- sidual stress becomes more effective. One is to idealize the movement of heat source which requires many cal- culation steps and the other is to apply the two dimensional elements instead of three dimensional elements which enlarge the numbers of the nodes and elements of models.

A butt welding of thin steel plates [

An analysis model in this study is one pass butt welding of thin steel plates.

The heat input of welding, ^{3}) by

One pass butt welding model

FE analysis model by 8-nodes solid elements

Equation (2) is given into the heat input elements as a body heat flux. The heating time per each heat input ele- ment is decided by dividing the length of each heat input element,

A heat transfer from the surface of model is considered as thermal boundary conditions. A rigid body dis- placement is fixed as mechanical boundary conditions.

Here,

^{3}), and

Non-steady thermal conduction analysis was carried out for the butt welding model.

In the thermal elasto-plastic analysis, the temperature data obtained by the non-steady thermal conduction analysis is used as input data for the thermal elasto-plastic stress analysis. Therefore, it is indispensable that the temperature data are simulated with high accuracy.

By using the obtained thermal conduction analysis results, thermal elasto-plastic stress analysis was carried out.

The results indicated that the welding deformation and residual stress could be simulated with high accuracy by the precisely modeled analysis in which the movement of heat source was considered and three dimensional solid elements were used. When using a general personal computer (CPU 2.93 GHz), the computing time of this

Temperature histories by precise analysis model

Results of precise analysis model. (a) Out-of-plane deformation; (b) Residual stress

model was 4416 seconds (around 74 minutes).

As shown in Chapter 2, many calculation steps are required for considering the movement of heat source in welding. The longer the weld line becomes, the more calculation steps are necessary. Therefore, it is examined to idealize the movement of heart source in welding. That is, the total heat energy of welding is given into the weld line at one time. This method is well known as instantaneous heat source model [

In the case of instantaneous heat source model, the heat energy, ^{3}) by Equation (3) is given into the all heat input elements in one second. The calculation step for heat input is only one time. And also, making the complicated analysis modeling becomes relatively simple and easy.

Temperature histories obtained by instantaneous heat source model. (a) Heat efficiency; (b) Heat efficiency

rose rapidly just after the heat input. On the other hand, the temperature at the center of the weld line rose just after the heat source passes that section in the case of the moving heat source model. For comparing with the moving heat source model, the welding start time of the instantaneous heat source model was shifted.

Even though the total heat energy was the same, the maximum temperature of the instantaneous heat source model was lower than that of the moving heat source model. This was because the temperature of the instanta- neous heat source model rose in the short time and decreased after that. On the other hand, the temperature of the moving heat source model gradually rose with the passage of the heart source during the relatively long time.

In order to simulate the temperature histories by the instantaneous heat source model as close to those by the moving heat source model as possible, the heat efficiency,

By using the temperature data in the case that the heat efficiency,

In order to investigate the reason why the magnitude of welding out-of-plane deformation of the instantaneous heat source model was smaller than that of the moving heat source model, the generation histories of the weld- ing out-of-plane deformation of both models are shown in

In the case of the moving heat source model, the out-of-plane deformation at the center of the weld line occurred when the heat source passed that section (the time was 30 s). Because of the V-shaped groove, the heat input at the upper side was larger than that at the lower side in the thickness direction. Therefore, the shrinkage in the direction perpendicular to the weld line was larger at the upper side rather than at the lower side. As a re- sult, V-shaped out-of-plane deformation occurred [

The computing time of the instantaneous heat source model was 387 seconds (around 6.5 minutes). It was around 9% of that of the moving heat source model.

The generation mechanism of the out-of-plane-deformation of the instantaneous heat source model differed

Welding out-of-plane deformation and residual stress by instantaneous model. (a) Welding out-of-plane deformation; (b) Welding residual stress

Generation histories of welding out-of-plane deformation

from that of the moving heat source model. However, the tendency of the out-of-plane deformation could be predicted by the instantaneous heat source model even if the prediction accuracy of magnitude of out-of-plane deformation was not required so high. Furthermore, the welding residual stress distribution could be accurately predicted by the instantaneous heat source model. When the required accuracy of welding out-of-plane deforma- tion is not so high or when only the prediction of residual stress distribution is required, the instantaneous heat source model will be sufficiently available.

One of the reasons why the numerical simulation of welding by FEM takes a huge computing time is the use of three dimensional solid elements. For modeling the groove shape, solid elements should be used and some lay- ers should be made in the thickness direction even though the thickness of the plate is thin. Therefore, the num- bers of nodes and elements becomes large.

Here, application of two dimensional shell elements on the welding simulation is examined. By using the shell elements, the number of nodes and elements in the thickness direction can be decreased.

Here,

By the way, the out-of-plane deformation occurs due to a difference of temperature between upper and lower surfaces of plates in the case of one pass butt welding of thin steel plates with V-groove [

To solve this problem, a heat input method for the shell model shown in

Here,^{3}),

Image of shell model. (a) Solid model; (b) Shell model with uniform heat input; (c) Shell model with distributed heat input

Temperature histories obtained by shell models. (a) Results by uniform heat input; (b) Results by distributed heat input

compared with the solid model.

By considering the distribution of the heat energy in the thickness direction in the shell model, the welding out-of-plane deformation could be simulated with high accuracy. It could be said that the proposed heat input

Temperature differences between upper and lower surfaces

Welding out-of-plane deformation and residual stress by shell models. (a) Welding out-of-plane deformation; (b) Welding residual stress

method was valid. By the way, the computing time of the shell model with uniform heat input was 342 seconds (5.7 minutes). That with distributed heat input was 368 seconds (around 6.1 minutes). The computing times of the shell models were around 8% of that of the solid model.

In order to propose the effective calculation methods by FEM for predicting deformation and residual stress generated by one pass butt welding of thin steel plates, a series of numerical analyses were carried out.

The obtained main results are as follows.

The effect of idealizing the movement of heat source in welding (the instantaneous heat input model) was examined. It was confirmed that the generation mechanism of welding out-of-plane deformation by the instan- taneous heat input model differed from that by the precise model considering the movement of heat source.

Even though the tendency of out-of-plane deformation could be predicted, the magnitude of out-of-plane de- formation of the instantaneous heat source model was around 72% of that of the moving heat source model. On the other hand, the residual stress distribution of the instantaneous heat source model was almost the same as that of the moving heat source model.

The computing time by the instantaneous heat source model was around 9% of that of the moving heat source model. When the required accuracy of welding out-of-plane deformation is not so high or when only the predic- tion of residual stress distribution is required, the instantaneous heat source model will be sufficiently available.

Applicability of two dimensional shell elements instead of generally used three dimensional solid elements was examined. When the temperature distribution in the thickness direction was not considered, the welding out- of-plane deformation could not be simulated well. Therefore, the heat input method with considering the tem- perature distribution in the thickness direction was proposed for the simulation by using the shell elements.

It was confirmed that the welding out-of-plane deformation and residual stress could be predicted with high accuracy by the model with shell elements and the distributed heat input method. The difference of magnitude of the out-of-plane deformation between the shell model and the solid model was around 7%.

The computing time by the shell model was around 8% of that by the solid model.

The obvious effectiveness could be confirmed even in the simple analysis model in this study. The results in- dicated that the larger analysis models such as actual steel structures are simulated, the higher effectiveness by using the proposed simulation methods will be expected.

This research was partly supported by the Sasakawa Scientific Research Grant from the Japan Science Society.