Unified Finite Element Model of TIG Welding Arc and Molten Pool

Literature Overview

This 2006 publication from Shanghai Jiao Tong University's Institute of Welding Engineering, authored by Lu Fenggui, Tang Xinhua, Li Shaoqing, Yao Shun, and Lou Songnian, presents a unified mathematical model coupling the TIG welding arc plasma with the molten pool dynamics. Published in Materials for Mechanical Engineering, this work represents a significant advancement in welding process modeling that bridges the gap between arc physics and weld pool behavior.

Theoretical Framework

Governing Equations

The unified model couples the following physical phenomena through a single computational domain:

Arc plasma region:

• Navier-Stokes equations for plasma flow
• Maxwell's equations for electromagnetic field
• Energy equation with radiation and heat conduction terms
• Species transport equations for ionization equilibrium

Molten pool region:

• Navier-Stokes equations with surface tension gradient (Marangoni effect)
• Energy equation with phase change (SOLV/enthalpy method)
• Momentum equation with electromagnetic body force (Lorentz force)
• Surface tension boundary condition with temperature dependence

Key Assumptions and Simplifications

Model Validation and Results

Temperature Distribution Comparison

The model demonstrates excellent agreement with experimental measurements, with maximum deviation of 3.1% in the pool center region. This level of accuracy is achieved through careful calibration of the arc force coefficient and the surface tension temperature gradient parameter.

Flow Pattern Analysis

The unified model reveals a complex three-dimensional flow pattern in the molten pool that differs significantly from simplified two-dimensional predictions:

1. Central depression: A deep central crater forms due to the combined action of arc pressure and electromagnetic pinch force, with depth reaching 1.2–1.8 mm for typical parameters.
2. Peripheral flow: Liquid metal flows outward from the pool center along the surface, driven by surface tension gradients (Marangoni convection) that reverse direction at temperatures below the surface tension inflection point (~1600°C for steel).
3. Bottom circulation: A reverse flow occurs at the pool bottom, driven by buoyancy forces and electromagnetic body force, creating a recirculation zone that significantly affects weld geometry.

Engineering Applications

Weld Geometry Prediction

The model successfully predicts weld penetration depth, width, and reinforcement height within ±15% of experimental values for various material combinations:

Process Optimization

The model enables systematic parameter optimization for cladding applications:

• Heat input control: By predicting the thermal field, the model identifies optimal current-speed combinations that maintain the dilution ratio within specified limits (typically 10–20% for overlay welding).
• Bond line quality: The predicted flow pattern identifies regions of potential lack of fusion, enabling process parameter adjustment before physical welding.
• Residual stress prediction: Coupled thermal-mechanical analysis provides residual stress distributions critical for pressure vessel design.

Key Reflections

This unified modeling approach represents a paradigm shift from the traditional practice of treating the arc and pool as separate phenomena. The coupling reveals feedback mechanisms—such as how pool surface deformation affects arc constriction, which in turn modifies heat input distribution—that are invisible in decoupled models. For engineers involved in bimetal pressure vessel fabrication, this type of modeling provides the quantitative foundation needed to establish welding procedure specifications (WPS) with confidence, reducing reliance on costly trial welds and enabling virtual qualification of new material combinations.