Three-Dimensional Dynamic Simulation of Overlay Weld Temperature Field

Literature Overview

This paper presents a comprehensive three-dimensional dynamic numerical simulation of the temperature field during weld overlay (cladding) operations, advancing beyond the simplifications of two-dimensional steady-state or quasi-steady-state models. The study captures the transient thermal behavior associated with the progressive deposition of overlay material, including the effects of heat input variation, material property changes with temperature, and the complex thermal interactions between successive overlay passes. For engineers involved in overlay procedure development and pressure vessel fabrication, this work provides a powerful analytical tool for predicting thermal cycles, residual stresses, and microstructural transformations.

Core Technical Content

Numerical Model Development

The paper describes a finite element-based three-dimensional transient thermal analysis that models the complete overlay welding sequence, including substrate preheating, multiple overlay passes, interpass cooling, and post-weld heat treatment. The model incorporates temperature-dependent material properties for both the base metal and overlay material, including thermal conductivity, specific heat capacity, and thermal expansion coefficient, which vary significantly with temperature and phase composition.

A key innovation of the model is the dynamic meshing technique that progressively adds material elements as each overlay pass is deposited. This approach accurately represents the changing geometry and thermal boundary conditions during multi-pass overlay welding, which conventional fixed-mesh models cannot capture. The mesh refinement strategy ensures adequate resolution in the heat-affected zone (HAZ) and fusion zone (FZ) while maintaining computational efficiency for the larger substrate volume.

Thermal Cycle Characterization

The simulation results provide detailed thermal cycle predictions for various locations within the overlay deposit and base metal, including peak temperature, cooling rate (800-500 degrees C), time above critical temperatures, and temperature distribution profiles. The paper demonstrates that the three-dimensional model predicts thermal cycles that differ significantly from two-dimensional steady-state models, particularly in the first and last passes where the thermal boundary conditions are most asymmetric.

The cooling rate predictions from the three-dimensional model show that the maximum cooling rate occurs in the first overlay pass, typically reaching 10-50 degrees C per second depending on heat input and substrate preheat. Subsequent passes experience progressively lower cooling rates due to the thermal mass of previously deposited material, with the final pass often exhibiting cooling rates 30-50 percent lower than the first pass. This progressive reduction in cooling rate has direct implications for microstructural evolution, with the first pass potentially developing a harder, more martensitic microstructure compared to subsequent passes.

Residual Stress Prediction

The paper extends the thermal analysis to include thermo-elastic-plastic deformation analysis, predicting residual stress distributions in the overlay deposit and adjacent base metal. The results demonstrate that residual stresses develop primarily in the longitudinal direction (along the weld travel direction), with compressive stresses in the overlay material and tensile stresses in the base metal adjacent to the fusion line. The magnitude of residual stresses depends on the mismatch in thermal expansion coefficients between the overlay and base metals, the constraint provided by the base metal, and the sequence of pass deposition.

For a typical stainless steel overlay on carbon steel substrate, the predicted residual stresses range from -150 to -300 MPa (compressive) in the overlay layer and +100 to +250 MPa (tensile) in the base metal HAZ. These predictions are in reasonable agreement with experimental measurements obtained through X-ray diffraction and hole-drilling methods, validating the model's predictive capability for engineering applications.

Process Parameter Effects

Heat Input Influence on Thermal Field

The paper systematically investigates the effects of heat input on the overlay temperature field, demonstrating that heat input directly controls the peak temperature, cooling rate, and thermal gradient magnitude. Higher heat inputs result in broader thermal affected zones, lower cooling rates, and reduced thermal gradients, which generally favor slower microstructural transformations and reduced residual stresses. However, excessive heat input can lead to undesirable grain growth, softening of the base metal HAZ, and increased distortion.

The optimal heat input range for most overlay applications is identified as 15-30 kJ/cm for submerged arc welding (SAW) overlay and 8-20 kJ/cm for gas metal arc welding (GMAW) overlay, with specific values depending on the material system, overlay thickness, and service requirements. The paper provides parametric studies that enable engineers to predict thermal cycle characteristics for specific process parameter combinations without extensive experimental trials.

Multi-Pass Sequence Optimization

The three-dimensional simulation reveals that the sequence of overlay pass deposition significantly influences the final thermal field and residual stress distribution. The paper compares several pass sequencing strategies, including sequential (pass 1 to pass N), alternating (odd passes followed by even passes), and symmetric (deposited from the center outward) approaches, demonstrating that the optimal sequence depends on the specific application requirements.

For overlay applications requiring uniform microstructure throughout the deposit thickness, the paper recommends a symmetric pass sequence that ensures similar thermal histories for all passes. For applications where maximum bond strength is the primary concern, a sequential sequence with the first pass deposited at the base metal interface provides the highest fusion zone quality due to the direct thermal interaction between the first pass and the base metal.

Substrate Preheat Effects

The paper quantifies the effects of substrate preheating on the overlay temperature field, demonstrating that preheating reduces peak temperatures in subsequent passes, lowers cooling rates, and decreases residual stress magnitudes. The recommended preheat temperature ranges from 150 to 400 degrees Celsius depending on the material system, with higher preheat temperatures required for materials with higher thermal conductivity (such as copper alloys) or higher carbon equivalent (such as low-alloy steels).

The simulation results show that preheating from ambient temperature to 200 degrees Celsius can reduce the maximum residual stress by approximately 20-30 percent and lower the cooling rate by 15-25 percent, significantly reducing the risk of hydrogen-induced cracking and improving the ductility of the overlay microstructure.

Engineering Practice Integration

Procedure Qualification and Optimization

The three-dimensional thermal simulation provides a powerful tool for overlay procedure qualification, enabling engineers to predict thermal cycles and residual stresses for proposed welding parameters without extensive trial welding. This capability is particularly valuable for novel material combinations or equipment configurations where experimental trials are costly or impractical. The paper demonstrates that the simulation can predict thermal cycles within +/-15 percent of experimental measurements, which is adequate for microstructural prediction and residual stress estimation.

For pressure vessel fabrication, the thermal simulation results can be used to verify compliance with code requirements for thermal cycles and cooling rates. For example, ASME VIII Division 2 requires control of cooling rates for certain materials, and the simulation can predict whether proposed welding parameters will meet these requirements. Similarly, the predicted residual stress distributions can be used to evaluate the need for post-weld stress relief and to optimize stress relief parameters.

Residual Stress Management

The paper's residual stress predictions provide a basis for residual stress management strategies in overlay fabrication. For applications where residual stresses are detrimental (such as stress corrosion cracking service or fatigue loading), the simulation can guide the selection of welding parameters, pass sequencing, and post-weld treatment to minimize residual stress magnitudes. The paper recommends a combination of moderate preheating, controlled interpass temperature, and post-weld stress relief at 600-650 degrees Celsius for 2-4 hours for most stainless steel overlay applications.

For applications where compressive residual stresses are beneficial (such as erosion-corrosion service), the simulation can identify parameter combinations that maximize compressive stresses in the overlay surface. The paper demonstrates that using lower heat inputs and higher travel speeds can increase compressive residual stresses in the overlay layer, potentially improving fatigue and erosion resistance.

Distortion Prediction and Control

The thermal simulation also predicts welding distortion, which is a critical concern for large overlay fabrication such as pressure vessel heads, shells, and heat exchanger tubesheets. The paper demonstrates that distortion is primarily driven by asymmetric thermal expansion and contraction, with the maximum distortion occurring at locations of maximum thermal gradient. The predicted distortion magnitudes (typically 0.1-0.5 percent of the component dimension) can be used to design fixtures, select welding sequences, and plan post-weld machining allowances.

Key Questions and Reflections

While the paper presents a sophisticated thermal simulation model, several limitations warrant consideration. The model assumes temperature-dependent material properties based on bulk material data, which may not accurately represent the properties of rapidly solidified weld metals or overlay deposits. The phase transformation behavior, which significantly influences residual stresses, is represented using simplified models that may not capture the full complexity of multi-phase transformations in multicomponent alloys.

The computational cost of three-dimensional transient analysis remains a practical limitation for routine engineering applications. While modern computational resources can handle models with millions of elements, the time required for simulation (typically several hours to several days depending on model size) may not be practical for every procedure qualification. The paper suggests that parametric studies using simplified models can identify critical parameters, followed by detailed three-dimensional analysis for the final procedure verification.

Study Insights and Implications

This paper represents a significant advancement in the analytical capabilities available to overlay welding engineers, providing a tool for predicting thermal cycles, residual stresses, and distortion with sufficient accuracy for engineering decision-making. The integration of thermal simulation into procedure development and qualification can reduce the number of trial welds required, accelerate procedure approval, and improve the predictability of overlay properties.

For bimetal pressure vessel fabrication, the thermal simulation approach enables a more systematic and rigorous approach to procedure qualification, moving beyond empirical parameter selection toward physics-based optimization. Engineers should incorporate thermal simulation into their procedure development workflow, using the simulation results to guide experimental trials and verify compliance with code requirements. The paper's methodology provides a framework for integrating simulation and experimentation in a complementary manner, leveraging the strengths of both approaches to achieve optimal overlay quality and performance.