Heat Transfer Model of MIG Spot Welding During Spray Transfer

Literature Overview

This foundational study by Wu Chuansong, Wu Lin, and Chen Dinghua from Harbin Institute of Technology was published in the Welding Journal in 1991. Despite its age, this research remains highly relevant as it establishes the fundamental heat transfer modeling framework for MIG welding under spray transfer conditions. The work provides the theoretical basis for understanding how heat is distributed within the weld pool, which directly governs solidification behavior, residual stress development, and microstructural evolution.

The study specifically addresses spot welding applications where the welding process is interrupted at regular intervals, creating unique thermal cycling conditions that differ from continuous welding. Understanding heat transfer in this discontinuous mode is essential for predicting weld quality in applications such as spot weld strengthening of clad plates, repair welding of pressure vessels, and localized overlay deposition.

Theoretical Framework

Governing Equations

The heat transfer model is based on the three-dimensional transient heat conduction equation with source terms representing the welding heat input:

∂T/∂t = α(∂²T/∂x² + ∂²T/∂y² + ∂²T/∂z²) + Q/(ρ·c)

Where T is temperature, t is time, α is thermal diffusivity, Q is the heat source intensity, ρ is density, and c is specific heat. The heat source is modeled as a moving Gaussian distribution for the spray transfer regime, with the peak heat flux located at the arc root and the distribution width determined by the arc spot size.

For spray transfer conditions, the heat source parameters are characterized by:

Heat Distribution Pattern

The model predicts a characteristic heat distribution with the highest temperatures concentrated in a small region near the arc root, with rapid temperature gradients extending radially outward. The peak temperature at the pool surface reaches approximately 2300–2800°C for steel, while the pool boundary is defined by the solidus temperature contour (approximately 1450–1500°C for carbon steel).

The depth of the weld pool is governed by the balance between heat input rate and heat dissipation through conduction to the surrounding material. For spray transfer MIG welding of carbon steel plates, the typical pool dimensions are:

• Pool length (along travel direction): 8–15 mm
• Pool width (transverse): 4–8 mm
• Pool depth (penetration): 2–5 mm
• Pool volume: 50–200 mm³

Spot Welding Thermal Characteristics

Thermal Cycling in Discontinuous Welding

In spot welding applications, the heat input is applied intermittently, creating a unique thermal history for the material. Between successive spots, the material cools by conduction and convection, partially recovering from the thermal damage of the previous spot. The degree of recovery depends on the inter-spot interval (time between successive welds) and the thermal conductivity of the material.

The study establishes that for carbon steel, a cooling interval of 15–30 seconds between spots allows the surface temperature to drop from approximately 400–500°C (immediately after welding) to below 150°C, which is below the threshold for significant microstructural change. This enables the deposition of multiple spots without cumulative thermal damage.

Heat Accumulation Effects

When the inter-spot interval is insufficient, heat accumulates in the material, leading to progressive widening of the HAZ and potential softening of previously welded regions. The study quantifies this effect by showing that with intervals below 10 seconds, the HAZ width increases by 20–40% for each successive spot. This heat accumulation effect is particularly critical in clad plate applications where the base metal must not be excessively softened by repeated thermal cycles.

Model Validation and Practical Applications

Validation Against Experimental Data

The model predictions were validated against thermocouple measurements and infrared thermography data obtained from actual welding experiments. The agreement between predicted and measured temperature distributions was within ±15% for temperatures above 200°C, with larger discrepancies at lower temperatures due to the difficulty of accurately modeling heat losses through convection and radiation.

The model accurately predicts the pool dimensions and the HAZ boundary temperature contours, making it suitable for use in weld design and process planning. However, it does not account for fluid flow within the pool, which affects the local temperature distribution and solidification pattern. For detailed microstructure prediction, the model should be coupled with a fluid dynamics model.

Applications to Cladding and Overlay

The heat transfer model has direct applications to cladding and overlay welding, where the thermal cycle governs the dilution ratio, the microstructure of the overlay, and the bond strength between the overlay and the base metal. For example, in electroslag welding overlay of stainless steel on carbon steel, the model can predict the dilution ratio based on the heat input and the travel speed. The dilution ratio (DR) can be estimated as:

DR = f(Q, v, t, ρ, c, α)

Where t is plate thickness. Higher heat inputs and lower travel speeds increase dilution, while thicker plates reduce dilution by providing more thermal mass.

For laser cladding applications, the model can be adapted by replacing the Gaussian heat source with a more concentrated laser heat source, typically modeled as a double-ellipsoidal distribution. The fundamental principles of heat transfer remain the same, but the much higher energy density of the laser creates steeper temperature gradients and shallower pools with faster cooling rates.

Engineering Practice Integration

Process Parameter Selection

The heat transfer model provides a quantitative basis for selecting welding parameters to achieve specific weld pool dimensions and thermal cycles. For example, if a narrow HAZ is required to minimize softening of a high-strength base metal, the model can be used to determine the maximum allowable heat input for a given travel speed and plate thickness.

For overlay welding of nickel-based alloys on carbon steel, the model helps predict the dilution ratio, which must be controlled to ensure the overlay maintains its corrosion resistance. A dilution ratio above 30–40% can compromise the alloy's resistance to pitting and crevice corrosion. The model enables engineers to select parameters that limit dilution while maintaining adequate bond strength.

Residual Stress Prediction

The thermal model can be extended to predict residual stress distributions by incorporating thermal expansion coefficients and elastic-plastic material behavior. The residual stresses in MIG welded joints are primarily tensile in the weld and compressive in the surrounding HAZ, with magnitudes approaching the yield strength of the material. Understanding these stress distributions is critical for predicting distortion, fatigue life, and susceptibility to stress corrosion cracking.

Study Reflection and Modern Relevance

Although published in 1991, this research established modeling principles that remain fundamental to modern welding simulation and process design. The Gaussian heat source model, while simplified, provides surprisingly accurate predictions of temperature distributions for spray transfer welding conditions. Modern finite element models use more sophisticated heat source representations, but the fundamental physics described in this study remains unchanged.

For engineers working on cladding and overlay applications today, the key insight from this research is that heat input control is the primary lever for managing dilution, HAZ width, and residual stress. The quantitative relationships established here enable rational process design rather than purely empirical trial-and-error approaches. The model also highlights the importance of considering thermal history in multi-pass or multi-spot welding operations, where cumulative thermal effects can significantly impact final joint quality. This foundational understanding continues to inform modern process development for bimetallic products and clad pressure vessels.