Multi-Field Coupled Numerical Simulation of Submerged Arc Welding Overlay on Rolls

Background and Motivation

Roll surface overlay by submerged arc welding (SAW) is a widely used technique in the rolling mill industry to restore worn roll surfaces and improve roll performance through the introduction of alloyed overlay layers. The process involves the simultaneous action of thermal, mechanical, and metallurgical fields, making the prediction of residual stresses, microstructural evolution, and deformation extremely challenging. This literature presents a multi-field coupled numerical simulation methodology that integrates thermal analysis, mechanical (plastic) analysis, and phase transformation modeling to accurately predict the behavior of SAW overlay on rolls.

Methodology and Simulation Framework

The simulation framework is built upon a sequential coupled approach, where the thermal field is computed first, followed by the mechanical field with the temperature history as input, and finally the phase transformation field. This approach is computationally efficient and has been validated in numerous welding simulation studies. The key equations governing the thermal field include the transient heat conduction equation with moving heat source, while the mechanical field is governed by elasto-plastic constitutive relations incorporating thermal strains, plastic strains, and transformation-induced plasticity (TRIP) strains.

Simulation Module	Governing Equation	Key Parameters
Thermal field	Transient heat conduction with moving heat source	Heat input, weld speed, thermal conductivity, specific heat
Mechanical field	Elasto-plastic constitutive equation with thermal and TRIP strains	Yield strength, elastic modulus, Poisson's ratio, thermal expansion coefficient
Phase transformation	Koistinen-Marburger equation or similar	Transformation temperature, transformation rate, transformation strain
Residual stress	Integrated from mechanical field	Compressive and tensile residual stress distribution

The moving heat source is typically modeled using a double-elliptical or Gaussian distribution to account for the asymmetry of the weld bead in the direction of travel. The mesh is refined in the weld zone and heat-affected zone (HAZ) to capture steep temperature gradients, while a coarser mesh is used in the roll base material to reduce computational cost. Adaptive mesh refinement techniques may be employed to maintain accuracy near the weld pool boundary.

Key Results and Process Insights

The simulation results reveal several important process phenomena. First, the peak temperature in the weld zone can exceed 2000 °C, with rapid cooling rates in the range of 10–100 °C/s in the HAZ, which strongly influences the microstructural evolution of both the overlay metal and the base material. Second, the residual stress distribution shows a characteristic pattern of tensile stresses in the weld metal and compressive stresses in the adjacent base material, with magnitudes approaching the yield strength of the respective materials.

The TRIP effect is found to be significant in the HAZ, where the transformation of retained austenite to martensite during cooling contributes additional transformation strains that modify the residual stress state. This is particularly relevant for high-alloy overlay materials where the transformation temperature is depressed. The simulation also predicts the evolution of von Mises stress during the welding sequence, showing that stress accumulation over multiple passes can lead to stress levels exceeding the material's yield strength, which may result in cracking or distortion.

Defect Type	Primary Cause	Simulation Prediction	Countermeasure
Cracking in weld metal	High tensile residual stress combined with embrittlement	Stress concentration at weld root and toe	Preheating, post-weld heat treatment, filler selection
Distortion	Asymmetric thermal expansion and contraction	Transverse and longitudinal bowing of roll surface	Backing plate, clamping, multi-pass strategy
HAZ softening	Excessive grain growth at high peak temperatures	Reduced hardness in HAZ	Interpass temperature control, cooling rate management
Phase transformation defects	Retained austenite in HAZ	Mapped retained austenite fraction	Post-weld tempering, alloy composition adjustment

Engineering Practice and Process Optimization

The numerical simulation provides a powerful tool for process optimization before actual welding trials are conducted. By varying input parameters such as heat input, welding speed, interpass temperature, and preheating temperature, engineers can identify optimal process windows that minimize residual stress, prevent cracking, and ensure adequate bond strength between the overlay and the roll base material. This is particularly valuable for high-value roll components where trial-and-error approaches are costly and time-consuming.

The simulation also aids in the prediction of roll distortion during multi-pass overlay welding. By simulating the sequential deposition of multiple weld passes, the cumulative effect on roll geometry can be assessed, allowing for the design of appropriate compensation strategies. For example, the simulation can predict the amount of bowing that will occur, enabling the roll to be pre-bent in the opposite direction before welding to achieve a straight final profile.

Study Insights and Reflections

The most significant contribution of this study is the demonstration that a multi-field coupled simulation approach can provide reliable predictions of the thermal, mechanical, and metallurgical behavior of SAW overlay on rolls. This bridges the gap between empirical process development and physics-based process design. However, the accuracy of the simulation depends heavily on the quality of the input material data, including temperature-dependent mechanical properties, thermal properties, and phase transformation kinetics. Engineers must invest in obtaining accurate material data through thermomechanical analysis (TMA), differential scanning calorimetry (DSC), and mechanical testing at various temperatures.

I also note that while the sequential coupled approach is computationally efficient, it may not fully capture the feedback between phase transformation and mechanical deformation. For critical applications, a fully coupled approach may be necessary, although this comes at a significant increase in computational cost. The choice between sequential and fully coupled approaches should be guided by the specific engineering problem and the required level of accuracy.

This study reinforces the value of numerical simulation as an essential tool in modern welding engineering, complementing experimental work and accelerating the development of reliable, high-quality overlay welding processes for roll manufacturing.