Y.P. Yang and F.W. Brust
Battelle, 505 King Avenue
Columbus, Ohio, 43201, USA
TWI, Granta Park
Cambridge CB1 6AL, UK
BAE Systems, 1048 Govan Road
Glasgow Scotland, G51 4XP, UK
Paper presented at PVP 2004, ASME Pressure Vessels and Piping Conference 25-29 July 2004, San Diego, CA., USA
Virtual fabrication technology (VFT) weld modeling software has been mainly used in thick-structure welding simulation. Recently both U. S. and European shipyards have shown strong interests in using the software to predict and control welding distortion of thin-plate ship panels. It is more complicated to simulate the welding of thin structures than thick structures because buckling distortion often occurs during the welding of thin structures. To evaluate the effectiveness of VFT for predicting distortion in thin structures, a bead-on-plate specimen, a butt joint of two large plates, and a long T stiffener were analyzed with VFT welding modeling software. By comparing the predicted distortions with those obtained by measurement, it was found that VFT can accurately predict welding-induced distortions of thin structures. Sensitivity studies show that pre-deformation induced by upstream fabrication processes and heat input are important factors influencing predicted distortions. Both distortion trends and magnitudes for thin structures are influenced by pre-deformation and heat input.
Lightweight structures are being increasingly used in recent years in both U. S. shipyards and European shipyards. From 1990 to 2000, the production ratio of thin steel (10mm or less) to plate structures for certain specific vessels has risen to over 90% by weight.  Severe distortions have been observed in the building of large thin ship panels. To understand the distortion mechanism and propose suitable methods to control distortion, shipbuilders urgently need a distortion prediction tool which is able to be used to assist the building of the thin ship panels.
Many researchers [2-6] have tried to develop modeling methodologies to simulate the welding process, but the modeling techniques that have been developed have often been too complex, inaccurate, or too labor intensive to be applied industrially. Although significant progress has been made in finite-element modeling of welding processes in recent years, many of the modeling techniques are still far short of being used successfully for the control of residual stress and distortion in actual structures.  Michaleris  developed a shrinkage force method to predict the distortions of thin structures. He estimated a shrinkage force for each weld by performing a two-dimensional (2D) finite element analysis of a weld cross section. Then, the estimated shrinkage forces are applied to a three-dimensional (3D) model to predict buckling distortion. Nonlinear interactions between welds are ignored and the residual stress information in the structures cannot be obtained by this method. Brust [7-8] , Dong [9-10] and Yang [11-12] performed residual stress analysis on an actual structure and then used the predicted residual stress distribution to form the stress-stiffening matrix in the instability analysis. More recently, a major initiative was funded by the U. S. Navy to perform a comprehensive assessment of lightweight panel fabrication technology. A series of large test panels were used to quantify dimensional variations through the fabrication processes in the current production environment. The transient thermal tensioning and reverse arching techniques have been developed to control buckling distortion of large thin test ship panels. Some modeling methodologies of buckling distortion were developed in the project. 
Since 1996, Battelle and Caterpillar have been working together to develop an industrial-use methodology and user-friendly software for predicting weld residual stress and distortion in large and complicated structures. A large amount of manpower and equipment was invested for model development, program coding, and validation. Finally, Virtual Fabrication Technology (VFT) a weld modeling computer tool was developed based on Battelle's weld modeling experience(which spans more than 20 years), and deep understanding of welding processes. [7-15] VFT is a state-of-the-art cutting and welding simulation tool that allows rapid solutions for large, complex metallic structures containing both single-pass and multi-pass welds and allows the user to consider or input all critical variables. It can be used in product design stages to help in weld design and in the manufacturing stage to determine the optimal weld processes to minimize welding-induced distortion. But weld modeling procedures developed for thick structures may not be directly used to predict buckling distortion in a thin structure. Further developments for weld modeling of thin structures are presented in this paper so the distortion mechanism and predictions may be accurately accounted for.
VFT weld software
The procedure for simulating the arc welding processes with VFT is illustrated in Fig.1. Three kinds of modeling procedures: a local weld residual stress analysis procedure, moving-arc analysis procedure, and a lump-pass analysis procedure are included in the software. The Local weld residual stress analysis procedure has been widely used in predicting and mitigating weld residual stresses in pressure vessels [10,16] and nuclear piping system.  The moving-arc analysis procedure was developed for predicting distortion in large and complicated welded structures. It has been widely used in many applications such as earthmoving equipment design [8,18] , thermal cutting induced distortion prediction  , and weld hot cracking mitigations.  The lump-pass modeling procedure was recently developed for the maritime industry to predict distortion on extremely large ship structures. 
Fig.1. An integrated arc welding simulation process
Local weld residual stress analysis procedure
This analysis procedure is mainly used to calculate weld residual stress on the local level of a welded structure. As shown in Fig.1, 2D cross section models (generalized plane strain or axis-symmetric models) are normally used for the local weld residual stress analysis. VFT-DFLUX subroutine is recommended for accurate modeling of heat input and prediction of temperature field and history. To effectively use this DFLUX subroutine, a FEA model should be generated based upon the weld cross section profile or at least the closest estimation of a weld cross section area. Tacks welds should be included in FEA models. In some situations, surface contacts and proper boundary conditions may be used to simulate constraint from the welding fixture. The Global-to-local modeling procedure could be used if a significant 3D effect exists.
Moving-arc analysis procedure
This analysis procedure is mainly used in the distortion analysis of large and complicated structures. A 3D shell model was specially developed to accurately predict distortion for single-pass welding. [20,21] A 3D solid model was developed to simulate pass by pass depositions for multiple pass welding. The CTSP (Comprehensive Thermal Solution Procedure) is commonly used for moving-arc thermal analysis for both 3D shell and solid models. It is based on analytical solutions and is therefore extremely fast when compared with finite element based thermal solutions. CTSP also works with complex structures not traditionally handled with analytical solutions.
Lump-pass analysis procedure
The lump-pass analysis procedure was recently developed for shipbuilding and ship repair applications. Typically ship structures are large with many weld passes and with extremely long weld lengths. The computer time required for CTSP thermal solution solver is time-wise acceptable. However, the ABAQUS structural solution with UMAT requires considerable time. Therefore, Lump-pass simulation technology for 3D solid models was developed to aid in the prediction of weld-induced distortion of ship structures.
Fig.2. VFT welding simulation flow
The thermal analysis could be performed using CTSP lump-pass code or an FE based thermal code. Until recently, lump-pass analysis could only be applied to 3D solid models. However, if all passes are lumped into one pass, it is possible to use a shell model just like a single-pass welding simulation. Currently the shell-model lump-pass analysis procedure is being further developed.
VFT Simulation process flow
The overall VFT simulation process flow is shown in Fig.2. The first step, which is not mandatory, is to develop a solid model of the part or structure that is to be welded. This could, for instance, be a Pro/E solid model that is passed on from the design department. By importing this solid model into a meshing generation tool, such as I-DEAS, FEMAP, or CUBIT, a finite element model can be developed. Note that CUBIT was specially developed for weld simulation by Sandia National Laboratory and Caterpillar. The next step is to transform the finite element model into the VFT-GUI to define weld parameters, weld passes, and welding sequences. The output from the VFT-GUI is a thermal input file. Three alternative methods of thermal analysis are shown in Fig.1. Choosing the most appropriate method is based on the user's analysis intension and structure size or weld length.
After the thermal analysis is performed, the temperature versus time histories are then written to a file in a format that can be automatically read by UMAT-WELD and related weld utility subroutines along with ABAQUS. It is important to note that the temperature file size is automatically controlled by CTSP since temperatures only need to be calculated near the current and prior weld locations. These specially written utility routines automate the weld modeling process and account for many features of weld modeling such as melting/re-melting, history annihilation, etc., which are not properly accounted for in commercial FE packages. The simulation results are outputted as residual stress and distortion.
Thin plate bead-on-plate analysis
A bead-on-plate specimen was designed for developing shell modeling procedures for thin structures. In order to validate these results, a 3D solid model analysis, which is known to produce accurate results, was carried out.
Welding test specimen
Fig.3 shows the experimental setup. A plate with dimensions 10" long and 12" wide sits on three points (two rest pins and one roller bearing). Robotic MIG welding was used to create the bead-on-plate with the weld placed along the middle of the plate as shown. The Plate was made of low carbon steel with a thickness of 3mm. The welding parameters used were a current of 261 amps, a voltage of 22.4 volts, and a travel speed of 16.93 mm/s. Displacement monitoring sensors (10 LVDTs) were set up on the plate to measure out-of-plate and in-plane distortions. Ten sets of experiments were conducted under similar conditions and welding-induced distortions measured in each case.
Fig.3. Baseline bead-on-plate coupon
Finite element model
Fig.4b shows the weld cross section of the test specimen. Fig.4a and Fig.4c show the predicted temperature distribution. Due to the symmetry of structure, half of the plate was used to generate the finite element model. The 6" long weld is located in the middle of the plate with a very fine mesh.
Fig.4. Temperature distribution on 3D solid model
A 3D shell model was generated to simulate the welding distortion with the consideration of weld bead thickness as shown in Fig.5. In the shell model, the plate thickness is 3mm and the thickness of bead position is 5.2 mm which is more than 70% larger than that of the plate thickness. The boundary conditions were used to simulate the constrain conditions.
Fig.5. Shell model generation and boundary conditions
Thermal flow analysis
The thermal solutions were performed using the rapid thermal solution code.  In order to validate the temperature predictions, four thermocouples were mounted on the top of the plate to record the temperature history. Fig.6 shows the temperature comparison between the experiment and the 3D shell-model prediction, which shows that the thermal history was accurately predicted.
Fig.6. Temperature comparison between experiment and prediction
The mechanical analyses were conducted using ABAQUS with a material subroutine.  The predicted temperature history was read into ABAQUS with a specially developed data-interface subroutine. Fig.7 shows the distortion comparison between the 3D shell model and the 3D solid model. Similar distortion shapes were predicted by the 3D solid mode and the shell model. Fig.8 shows the distortion-history comparison between the prediction and experiment at LVDT 22-30. The LVDT locations are shown in Fig.3. Both out-of-plane distortion ( Figures 8a, 8b, and 8c) and in-plane distortion ( Figures 8d, 8e, and 8f) were reasonably predicted by both the 3D solid model and 3D shell model. Note that each figure in Fig.8 contains 10 sets of welding experiment. There are large variations in the experimental results, especially in Fig.8b and Fig.8c. This is because each plate is different and has an initial imperfection. The initial imperfection has a significant impact on welding-induced distortion magnitudes and shapes, which has been discussed in detail in Ref.  .
Fig.7. Overall distortion shape of 3D shell and solid model
Fig.8. Distortion comparisons between prediction and experiment
Note that the analysis of the 3D shell model took much less CPU time than that of the 3D solid model and the 3D shell model was much easier to create. For a large and complex structure, this work suggests that it will be beneficial to choose a 3D shell model for predicting welding-induced distortions.
Thin plate butt joint analysis
The modeling procedures for thin plate butt joints are similar to those for bead-on-plate except that VFT users may need to map the initial plate displacements onto the weld model before welding analysis. This pre-deformation could be induced by tack welding or upstream processes. The flux core arc welding process (FCAW) was used to weld the butt joint.
Effect of heat input on distortion
The amount of heat input can have a large effect on the distortion for thin structures. Based on the American Welding Society (AWS) welding handbook, arc efficiency is 66% to 85% for both shield metal arc welding (SMAW) and gasmetal arc welding (GMAW). FCAW is a process between SMAW and GMAW. Therefore, the arc efficiency for FCAW should also be between 66% and 85%. The arc efficiency is defined as the ratio of the energy actually transferred into the workpiece to the energy generated by the power source. Since we usually don't include the slag formed from the flux in the weld model, we need to subtract the energy to melt the flux from the energy transferred into the workpiece. Assuming 10% of arc efficiency is used to melt the flux, the FCAW arc efficiency used for weld modeling input should be 56% to 75%.
Fig.9 and Fig.10 show the effect of heat input on temperature distribution locally and globally. Three kinds of heat input were obtained by adjusting the arc efficiency of FCAW. When the arc efficiency is 45%, the weld profile is under predicted compared with the weld profiles as shown in Fig.9d. When the arc efficiency is 75%, the weld profile is over predicted. The weld profile is most closely predicted using an arc efficiency of 60%. Fig.10 shows the effect of the amount of heat input on the final distortion. As can be seen in the figure, using arc efficiencies of 45% and 75% result in opposite directions of the distortion. Therefore, the correct heat input is very important for a thin structure. For a thick structure, the heat input will affect the magnitude of the final distortion without changing the distortion trend.
Fig.9. Heat input effect on temperature distribution
Fig.10. Heat input effect on welding-induced deformation
Pre-deformed shape mapping procedures
Fig.11 shows the tack weld locations in a test specimen. Two plates with dimensions, 450 mm long, 900 mm wide, and 5 mm thick, were tacked together from the back side with FCAW. After tack welding, the specimen was significantly distorted as shown in Fig. 12a due to low rigidity of the structure. The tack-weld induced distortions were measured with a special device, and then mapped to the weld model with using a VFT mapping code. Fig.12b shows the mapped pre-deformed distortion shape. (In Fig.12a - legend needs mm).
Fig.11. Tack weld configuration
Fig.12. Mapping pre-deformation to the weld model
It should be pointed out that tack-weld induced distortions can be predicted using VFT. This way, users don't need to map the pre-deformed shape to the weld model. The disadvantage is that the distortion before tack welding, i.e. the initial plate shape, is not included in the weld model.
A pre-deformed shape can have a great impact on the resistance of the structure to buckling distortion. It reduces the buckling strength of the structure. If buckling happens, the pre-deformed shape will determine the distortion direction. Therefore, if the simulation does not include the pre-deformation, the predicted distortions could be in the opposite direction to the actual distortions. As such the predicted distortion magnitude could be smaller than the experimental results.
A thermo-elastic-plastic-based buckling analysis procedure has been well developed as described in Refs. [1, 11 and 23] . Three steps are included in this procedure: weld residual stress analysis, buckling analysis including weld residual stress, and buckling distortion prediction including identified buckling mode or the pre-deformed shape on the structure.
Fig.13 shows a final-distortion comparison between experiment and prediction. The distortion in the weld area increases from 2.5 mm to 7mm. The overall distortion shape (W shape) is similar to the pre-deformed shape as shown in Fig.12. A good agreement was achieved between the prediction and the experiment.
Fig.13. Deformation after welding
Fig.14 shows the predicted deformation induced by welding only. The predicted distortion shape looks like a V, which is different with the experimental results as shown in Fig.13a. The actual specimen became a W shape after welding. Therefore, it is important to include the pre-deformation in the weld model for predicting distortion accurately.
Fig.14. Predicted deformation induced by welding only
Thin plate tee joint analysis
Thin ship panels have been increasingly used in both U. S. shipyards and European shipyards. T-stiffeners are a main component in the ship panels to increase the panel stiffness. Due to the low-rigidity nature of thin structures, large distortions have been observed and viewed as a major obstacle in the fabrication of thin ship panels. Many factors contribute to the thin-panel distortions such as welding heat input, weld sizes, and the pre-deformations due to material handling as well as operations before welding. It is too costly to build many test panels to investigate distortion mitigation methods. Therefore, both U. S. shipyards and European shipyards are keen to identify distortion-prediction software to assist in the building of thin ship panels. Currently, VFT has been evaluated in both U.S. shipyards and European shipyards for this purpose.
To demonstrate the effectiveness of VFT in predicting the distortion of thin ship panels, a simple T-stiffener model was designed as shown in Fig.15. Note that the dimensions: 2286x127x6.35' are arbitrary and not based on any ship designs. The double-sided fillets shown in Fig.15 were created by considering the penetration of GMAW processes. The tack welds, 1 inch long per 10 inch skip, were simulated. The material is DH36, which is a commonly used material in shipyards.
Fig.15. A double T-fillet model
By performing the thermal and structural analyses as described in the above bead-on-plate example, the longitudinal stress distribution and distortions were predicted as shown in Fig.16. The residual stress predictions are reasonable based on past experience. Because the neutral axis of the structure is near the horizontal plate, the structure bends up in the middle section. It should be pointed out that the heat input and weld size were estimated based on current welding experience. Therefore, the predictions cannot be directly compared with any measurements.
Fig.16. Longitudinal residual stress and deformation
This example demonstrates that VFT can be used to predict residual stress and distortion of a simple T stiffener. Since the ship panels are built by many T stiffeners, VFT should be able to simulate the welding process for entire panels. Computer simulation run times are relatively low as VFT was designed for high-speed welding simulations.
This paper has reviewed the overall modeling procedures available in VFT weld simulation software. The moving arc modeling procedure was used to analyze the welding of a bead-on-plate specimen, a butt-joint, and a Tee stiffener. Pre-deformation before welding, heat input, and weld size greatly contribute to buckling distortions. It is therefore suggested that, they should be included in any simulation exercise to accurately predict welding-induced distortions, particularly of thin structures. The T-stiffener analysis shows that VFT software is suitable for predicting distortion of large ship panels. More results will be published in the near future.
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The authors would like to acknowledge Tower Automotive for supporting this study. Adam Fisher, Robert Broman and Raj Thakkar participated in the experimental work of the bead-on-plate welding test. BAE Systems Naval Ships and the University of Newcastle provided the measurement results of the butt joint welding test. TWI coordinated the study of the butt joint.