Finite Element Analysis of TIG Welding Temperature Field

Literature Overview

The paper by Cai Hongneng and Tang Muyao from Xi'an Jiaotong University (1996), published in the Journal of Mechanical Engineering, presents a finite element method (FEM) analysis of the temperature field generated during gas tungsten arc welding (GTAW/TIG). This foundational computational study was among the earlier applications of FEM to welding thermal analysis in China and established methodologies that continue to influence modern welding simulation practice.

Core Technical Methodology

The authors developed a three-dimensional finite element model to simulate the transient temperature distribution during TIG welding of carbon steel plates. The model accounts for the moving heat source, material property variations with temperature, heat loss through convection and radiation, and the phase change associated with melting and solidification.

The heat source is modeled as a conical double-ellipse distribution that characterizes the asymmetric energy deposition typical of TIG arcs:

• Front ellipse: represents the keyhole region with concentrated energy deposition ahead of the arc center
• Rear ellipse: represents the broader heat dissipation zone behind the arc center
• Peak temperature: approximately 1350 °C at the arc center for typical parameters (150-200 A, 12-16 V, 200-400 mm/min)

The governing equation is the three-dimensional transient heat conduction equation:

ρCp(∂T/∂t) = ∂/∂x(k ∂T/∂x) + ∂/∂y(k ∂T/∂y) + ∂/∂z(k ∂T/∂z) + Q(x,y,z,t)

where Q represents the volumetric heat source distribution, and material properties k, Cp, and ρ are functions of local temperature.

Results and Validation

The FEM predictions were validated against experimental thermocouple measurements taken at multiple locations on the plate surface and through-thickness. The comparison shows excellent agreement in the peak temperature region (within ±50 °C) and good agreement in the HAZ temperature gradients (within ±100 °C for temperatures above 500 °C).

Key findings from the simulation include:

• The maximum temperature at the weld pool surface reaches approximately 1350 °C, while the pool depth extends 2.5-3.5 mm for typical plate thicknesses of 6-10 mm
• The HAZ width (defined as the region experiencing temperatures above the Ac3 temperature of approximately 900 °C) measures 4-6 mm for the parameters studied
• The cooling rate at the fusion line varies from 10-50 °C/s depending on distance from the weld centerline
• The temperature field exhibits pronounced asymmetry in the direction of travel, with the leading edge being significantly hotter than the trailing edge
• Through-thickness temperature gradients are steepest near the surface and diminish rapidly with depth

The authors also investigate the effect of welding speed on the temperature field distribution, showing that doubling the travel speed from 200 to 400 mm/min reduces the maximum temperature by approximately 100 °C and narrows the HAZ by 30-40 percent while increasing the cooling rate at the fusion line by a factor of 2-3.

Engineering Practice Applications

The temperature field analysis directly informs several critical aspects of welding engineering practice:

1. Microstructure prediction: Cooling rates above 100 °C/s in carbon and low-alloy steels promote martensite formation, which increases hardness and crack susceptibility. The FEM model allows prediction of regions where such microstructures will develop.
2. Residual stress estimation: The non-uniform temperature distribution generates thermal strains that are partially relaxed upon cooling. Regions experiencing the steepest temperature gradients develop the highest residual stresses, typically approaching the yield strength at elevated temperatures.
3. Weld procedure optimization: By simulating different parameter combinations, engineers can identify the optimal balance between penetration, HAZ width, and cooling rate for a given application.
4. Crack susceptibility assessment: For cladding applications on pressure vessels, the cooling rate at the cladding-base metal interface determines whether brittle phases or cracks will form in the dilution zone.

For bimetallic pressure vessel fabrication, this type of analysis is particularly valuable when designing weld overlay procedures where the thermal cycling must be carefully controlled to prevent cracking at the dissimilar metal interface. The FEM approach allows virtual prototyping of welding sequences to minimize thermal distortion and residual stress before committing to physical trials.

Study Insights and Reflections

While the computational methods employed in this 1996 study are now considered rudimentary compared to modern welding simulation software, the fundamental approach remains valid and continues to be used as a pedagogical tool. The paper demonstrates that even relatively simple FEM models can provide engineering-grade predictions of welding thermal behavior when calibrated against experimental data.

The study also highlights an important limitation: the accuracy of thermal predictions depends critically on the heat source model. The double-ellipse model used here, while widely adopted, has known limitations in representing the true three-dimensional energy distribution of the TIG arc, particularly the keyhole effect at higher current densities. Modern implementations employ more sophisticated heat source models including Gaussian, Gaussian-Gaussian, and Goldak-ak models that better represent the arc physics.

For cladding engineers, the temperature field analysis provides the foundation for understanding dilution behavior at the overlay interface. The depth and duration of thermal exposure determine how much base metal is melted and incorporated into the weld metal, directly affecting the final composition of the cladding layer. This is particularly critical for nickel-based alloy overlays on carbon steel, where dilution must be controlled to maintain the corrosion resistance properties of the overlay alloy.