Examples of the calculated transient temperature and stress fields during welding are shown in Fig. 4(a) and (b). As shown in Fig. 4(a), the transient temperature field due to the moving welding heat source is well demonstrated. The welding induced residual stress is in the magnitude of the yield strength of the material (around 450 MPa). This predicted residual stress magnitude is reasonable and comparable with those reported in literature.

Fig. 4: (a) calculated temperature field and (b) calculated stress field.

In the welding simulation, the clamping locations were assumed to be fixed in the welding model. The reaction forces on weld fixture at various pre-cambering locations during and after welding are shown in Fig. 5. As stated in previous sections, the reaction forces during welding in this case study were the combination of the mechanical force from pre-cambering and the thermal induced force from welding. The mechanical forces due to pre-cambering are shown at time zero in Fig. 5, where the welding process was not yet started. The values of the mechanical forces at various locations depend on the magnitudes and directions of pre-cambering at the corresponding positions.

Fig. 5: The reaction forces at various clamping locations during welding process

From Fig. 5, it can be observed that the reaction forces varied significantly during the welding and subsequent cooling stage. Such variations resulted from welding induced thermal stress. It can be seen that the reaction forces at some locations were almost doubled due to welding induced thermal reaction forces. For example, the reaction at location 4 before welding (time=0) was around -85 kN and its value reached -153 kN after welding. Therefore, the fixture would have been significantly under-designed without considering the thermal induced reaction force.

2.3.3 Fixture Stiffness Analysis

The stiffness of weld fixture was examined through linear static analysis, in which the reaction forces at the final cooling stage from the welding simulation were applied to the fixture FEA model. This is because the maximum reaction forces at most of the pre-cambering locations were reached at the final cooling stage, as shown in Fig. 5. The results from the structural analysis show that the fixture would be significantly deformed, as shown in Fig. 6(a), and the maximum

Fig. 6: (a) Deformation of weld fixture and (b) Stress distribution in weld fixture.

2

stress in the "hot" spot in the model is 518 MPa, as shown in Fig. 6(b), which is much higher than the yield strength of the material. This implies that the original fixture was under-designed. During welding experiments, it was also observed that some clamps for pre-cambering were broken during welding due to significant thermal induced reaction forces. The failure of the clamps in the fixture and its global deformation would deviate the defined pre-cambering scheme and thus affected the flatness of the bottom plate after welding.

Based on the results of the fixture structure analysis, the weld fixture was modified to increase the stiffness in order to account for welding induced additional reaction forces. The deformation and stress distribution in the modified weld fixture is shown in Fig. 7 (a) and (b), respectively. Compared to that in original fixture, the deformation in the modified fixture was significantly reduced. Also, the stress in the modified fixture model was reduced to 298 MPa. Therefore the modified weld fixture is strong enough to withstand the combination reaction forces and maintain the pre-cambering scheme.

Fig. 7: (a) Deformation of weld fixture and (b) Stress distribution in the modified weld fixture.

2.3.4 Effect of weld fixture stiffness on product flatness

The distortions at critical points on the bottom plate of the welded parts were measured after the parts were cooled to room temperature and released from the fixture. The flatness check was

Fig. 8: Distortions in weld products using original and modified weld fixtures
(Parts 1-3 used original fixture and parts 4-7 used modified fixture)

made for seven weld parts, of which three were welded using the original weld fixture and four were welded using the modified weld fixture. The degree of flatness in these weld parts are compared in Fig. 8. It can be observed that the distortions in the three parts using the original fixture were much larger than the flatness tolerance (1.5 mm). As mentioned previously, this is primarily due to the failure of the parts in the fixture (clamps) and the global deformation of the fixture during welding. In contrast, the distortions were significantly reduced after using the modified weld fixture that was stiff enough to support the pre-cambering scheme. Almost all four parts meet the flatness requirement.

SUMMARY AND CONCLUSIONS

An integrated FEA based procedure for weld fixture design was proposed in the present study. The procedure was applied to examine the strength of an existing weld fixture by taking into account both the mechanical forces from pre-cambering and the welding induced thermal reaction forces. The following conclusions can be made based on the present study.

(1) Welding induced thermal reaction forces are significant and must be considered in weld fixture design, especially when the fabricated structure is large and the number/length of welds increases.

(2) Weld fixtures may deform or even break during welding if the reaction forces from thermal distortions are not considered. The deformation of the fixture itself will directly affect the pre-cambering process for distortion control.

(3) Welding simulation is critical in the integrated FEA based procedure for weld fixture design. The welding simulation tool used in this study has demonstrated the capability to effectively predict residual stress, distortion, and reaction forces, which are critical for weld fixture design.

REFERENCES

1. Cao, Z., Brust, F. W., Nanjundan, A., Dong, Y., and Jutla, T.: Advances in Computational Engineering and Sciences; Eds. S. N. Atluri and F. W. Brust, p. 630, Tech Science Press, 2000.

2. Cao, Z., Brust, F. W., Nanjundan, A., Dong, Y., and Jutla, T.: A Comprehensive Thermal Solution Procedures for Multiple Pass and Curved welds, 2000 ASME Pressure Vessels and Piping Conference, Seattle, Washington, July 23-27,2000.

3. User Manual for UMAT-CAT - A Welding Specific User Material Routine Interfaced with ABAQUS, Version 3.1, Caterpillar Inc., Peoria, IL, September 1999.

4. Brust, F. W., Dong, P., and Zhang, J.: Advances in Computational Engineering Science, Eds. S. N. Atluri, and G. Yagawa, p.51, Tech Science Press, 1997.

5. Brust, F. W., Yang, Y., Dong, Y., and T. Jutla: Advances in Computational Engineering and Sciences; Eds. S. N. Atluri and F. W. Brust, p. 714, Tech Science Press, 2000.

WELDING INDUCED DISTORTIONS MODELING OF LARGE PLATE STRUCTURES

R. D. Everhart*

ABSTRACT

A method for predicting the welding induced distortions of large plate structures is described. Predictive, three-dimensional modeling of large structures presents some special numerical challenges. As models become large (as required by accuracy considerations) demands on computer resources grow quickly. Run times can grow to days and weeks. Computer memory can be overrun quickly, and the simulation becomes impractical. To overcome some of these challenges, a method that is accurate and numerically efficient is detailed. The methodology is incorporated in a new computer program called EFFECT (Efficient, Fast First-principle's Engine for Combined Thermal-mechanical). EFFECT incorporates a very efficient thermal solver. Temperature distributions are generated "on the fly" to drive the mechanical solution. Finite element shell elements are used to model deformation of the plate structures. The BelytschkoTsay large displacement, geometrically non-linear shell element is employed. A selection of sophisticated plasticity models that accurately deal with material melting and solidification are available. Explicit time integration is used for the mechanical solution. The shell element that is used is computationally efficient, and the explicit time integration greatly reduces computer memory requirements. A novel time scaling technique is used to deal with the thermal and mechanical time scale differences. This method is especially useful for predicting the buckling and out-of-plane warping of large plate structures. Model results are compared with distortion test data from large steel test structures. The model is able to accurately predict buckling and warping behavior.

KEYWORDS

Welding, modeling, finite-element analysis, distortion, explicit time integration.

INTRODUCTION

A method for predicting the welding induced distortions of large plate structures is introduced in this paper. Some background on the problem will be given, the computational methods will be described, then two examples involving warping and buckling will be presented.

BACKGROUND

As pointed out by Brown and Song [1], accurate distortion modeling of large, complex structures requires three-dimensional models. Three-dimensional finite element models of these structures include many thousands of degrees of freedom. This presents a considerable computational resource challenge even for modern computers. It is not practical for an analyst to wait several days, or even weeks, for the results of an analysis. A reasonable goal for analysis turn-around time is for an analysis to run over-night. An analyst can submit an analysis before leaving work

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