Welding Deformation Simulation of Center Overlay Plates Under Different Constraints - Technical Study Note

Research Context and Motivation

Welding deformation is one of the most persistent challenges in cladding plate manufacturing and bimetal pressure vessel fabrication. When an overlay weld is deposited on a thick backing plate, the asymmetric thermal input generates complex residual stress fields that cause angular distortion, longitudinal shrinkage, and transverse bowing. These deformations directly affect the dimensional accuracy of the finished product, the quality of subsequent machining operations, and the structural integrity of pressure vessel components. This study examines finite element analysis (FEA) simulations of welding deformation for test plates with center overlay welds under varying constraint conditions, providing insights that are directly transferable to industrial cladding plate production and vessel fabrication.

Numerical Simulation Methodology

The simulation typically employs a coupled thermo-mechanical approach, where the thermal field is solved first using a moving heat source model (commonly the double-ellipsoidal Goldak model or a Gaussian distribution), and the resulting temperature history is then mapped onto a structural model for mechanical analysis. The material behavior is modeled with an elastic-plastic constitutive law that incorporates temperature-dependent yield strength, thermal expansion coefficient, and thermal conductivity.

The key modeling parameters include:

Analysis of Constraint Effects on Deformation

The study compares three constraint scenarios: (1) a completely free plate with no boundary restrictions, (2) a plate clamped at all four edges, and (3) a plate with fixture supports at selected locations. The results demonstrate that the constraint condition has a profound influence on both the magnitude and the distribution of welding deformation.

In the free-edge condition, the plate undergoes significant angular distortion with the overlay side deflecting upward (away from the weld). The maximum out-of-plane displacement can reach 15 to 25 mm for a 30 mm thick plate with a 6 mm overlay layer, depending on heat input. The longitudinal shrinkage is typically 0.2 to 0.5 mm per 100 mm of weld length.

Under full edge clamping, the angular distortion is significantly suppressed, but the residual stresses in the clamped regions increase substantially, creating a risk of cracking in the HAZ and near the weld toe. The stress concentration at the clamped edges can reach 300 to 450 MPa, exceeding the yield strength of common structural steels.

The fixture-supported condition represents a practical compromise: strategic placement of stiffeners or backing plates at 200 to 400 mm intervals can reduce angular distortion by 40 to 60 percent while avoiding the excessive stress concentrations associated with full clamping. This finding has direct implications for the design of welding fixtures in cladding plate production lines.

Residual Stress Distribution

The residual stress analysis reveals that the maximum tensile stress in the overlay layer is approximately 200 to 350 MPa, concentrated near the weld centerline and the overlay/base metal interface. The compressive stress in the base plate can reach -150 to -250 MPa in the region directly beneath the weld. These residual stresses are of critical concern for pressure vessel applications, as they contribute to fatigue crack initiation at the overlay surface and can promote intergranular stress corrosion cracking (IGSCC) in sensitized stainless steel overlays.

Engineering Practice Implications

The simulation results provide actionable guidance for reducing welding deformation in cladding plate manufacturing. First, the use of back-step welding (welding from the center outward in both directions) is recommended to reduce longitudinal shrinkage by up to 30 percent. Second, pre-deformation (reverse bowing) of the plate before welding can compensate for the expected angular distortion, achieving final flatness within ±1 mm over a 2000 mm plate length. Third, the selection of appropriate heat input is essential: excessive heat input increases both deformation and the risk of microstructural degradation in the overlay layer.

For bimetal pressure vessel fabrication, where cladding plate flatness and overlay layer integrity are paramount, the simulation insights support the adoption of low-heat-input multi-pass overlay strategies with controlled interpass temperatures. The residual stress data also informs the design of post-weld stress relief procedures, indicating that a PWHT at 580 to 620 degrees Celsius for 2 hours per 25 mm of thickness is generally sufficient to reduce residual stresses below 100 MPa.

Key Questions and Reflections

A significant question arising from this study is the accuracy of the constraint modeling in representing real-world welding fixtures. The idealized boundary conditions in FEA may not fully capture the compliance of actual clamping hardware, which introduces nonlinear contact behavior and frictional effects. Future work should incorporate more realistic constraint models using contact algorithms and experimental validation through digital image correlation (DIC) measurements.

Summary and Conclusions

The FEA simulation of welding deformation under different constraint conditions provides a powerful tool for optimizing cladding plate fabrication processes. The results clearly demonstrate that constraint design is a critical factor in controlling both deformation and residual stress. Engineers should leverage simulation-based analysis to design welding fixtures, select welding sequences, and establish thermal management protocols that minimize deformation while maintaining overlay layer integrity. The integration of numerical simulation with experimental validation and process optimization represents a robust methodology for improving the quality and efficiency of bimetal product manufacturing.