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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for the evening and have the results waiting the next morning. Run times of this order are the goal of the present development effort.

In order to meet the computational performance goals of this development effort, a paradigm shift was made in the solution strategy for these types of structures. Implicit time integration was discarded in favor of explicit time integration. Explicit time integration is used in such wellknown finite-element analysis codes such as LS-DYNA [2,3].

The use of explicit finite-element analysis techniques produces two benefits that are critical to the practical analysis of large structures. First, the in-core (RAM) memory requirement is vastly reduced. Explicit methods do not require the formation and storage of a stiffness matrix. Second, the explicit solution method is very efficient for large, highly non-linear problems. The implicit solution method convergence difficulties for highly non-linear material behavior are avoided.

This added performance comes at a cost however. Time scales must be carefully managed. The major inhibitor to the use of explicit time integration methods for these class of problems is that they are conditionally stable and are subject to the Courant condition [3]. The end result is that time steps are on the order of a fraction of a microsecond. It is easy to see that for welding simulations (typically several hundreds of seconds) many millions of time steps would be required for a simulation. This is clearly unacceptable. Therefore, time-scaling methods are employed to manage these time scale disparities. This technique and others are introduced in the computational methods section.

COMPUTATIONAL METHODS

The computational methods used for modeling welding induced distortions for large plate structures have been implemented in an analysis code called EFFECT (Efficient, Fast Firstprincipals Engine for Combined Thermal-mechanical). EFFECT can be thought of as a numerical test-bed for the consideration of explicit distortion analysis methods. In the following sections, some of the more critical numerical methods employed in EFFECT will be introduced.

There are two types of finite elements used. The plates that make up the structures are modeled with shell elements. The shell elements follow the formulation by Belytschko and Tsay [4]. A five-point numerical integration scheme is used in order to give good non-linear response performance. The weld beads are modeled explicitly with hexahedron continuum elements. They follow the formulation of Flanagan and Belytschko [5]. Both element types have a long history of successful application in such codes as LS DYNA [2,3].

The thermal solution is performed concurrently with the mechanical solution in the same explicit time integration loop. They are fully coupled. In order to deal with the disparity between time scales for the mechanical and thermal solutions (the stable time step for the thermal solution is much larger), the thermal solution uses sub-cycling. That is, several mechanical solution steps are performed for each thermal solution step. Using this strategy, the thermal solution time ends up being a small percentage of the total solution time.

The thermal solution algorithms used are similar to those developed by Liu and Belytschko [6]. The method is extended to hexahedron continuum elements and shell elements. The shell elements use a split integration technique. A two-dimensional transient heat conduction solution is performed in the plane of the element. A one-dimensional transient heat conduction solution is performed through the thickness of the element. This allows for full through-thickness effects to be included. This is important in weld zones.

The heat energy from welding is input to the system in two ways. First, the weld bead goes in "hot" (as it does in real life). The hexahedron elements that make up the weld bead are activated at a pre-determined temperature. Usually, this is the melting temperature of the material. The elements are activated according to the motion of the welding torch (speed and path). Second, welding energy is input to the base material to form the remainder of the heat affected zone. The Goldak (et. al.) double ellipsoidal heat source [7] is used to map the welding energy into the base metal.

Sophisticated material models are available for both hexahedron continuum elements and shell elements. Virtually all of the mechanical and thermal properties of the material may be input as a function of temperature. Phase changes are easily considered, so that melting and solidification are treated seamlessly in the analysis. To increase the flexibility of the models, information is input in a piece-wise linear fashion (tabular).

Proper time scale treatment is critical for application of explicit methods to welding simulations. The time scale differentials between the thermal and mechanical solutions are overcome using sub-cycling. There are several mechanical time steps for every thermal time step. Mass scaling is used to manage the mechanical solution time scale. This technique is common in metal stamping simulations for instance [8]. This technique takes advantage of the fact that the welding operation is a quasi-static process. Material velocities are vastly smaller than the sound speed of the material (on which the stable time step size is based). By artificially manipulating the masses, and thus the stable time step size, the time scale may be manipulated. This may only be reliably taken to the limit that material velocities remain at least a factor of 10 less than the artificial sound speed of the material. A check of this condition is made throughout the solution to insure compliance. This technique allows the character of the solution to be preserved while promoting computational economy in the solution.

These techniques form the core of the method. The method has been successfully applied to large plate structures, two of which are detailed in the following section.

RESULTS AND DISCUSSION

The explicit finite-element analysis methodology in EFFECT has been used to simulate the welding induced distortions in large plate structures. Two examples are presented in this paper. The first example involves out of plane warping, and the second example involves large scale buckling.

The out of plane warping of a steel plate structure with a welded tee joint (base plate 20"x20"x0.5") was analyzed with a full three-dimensional EFFECT analysis. A schematic of the