Numerical Simulation of Temperature Field in MIG Welding Rapid Forming

Literature Overview

This 2009 study published in "Welding Technology" presents a numerical simulation of the temperature field during MIG welding rapid forming (also known as rapid solidification forming or weld-based additive manufacturing). The research was conducted at the National Key Laboratory of Equipment Remanufacturing Technology, Academy of Armored Force Engineering, funded by the National Natural Science Foundation of China (Key Project 50735006) and the National 973 Program sub-project (2007CB607601). This early work in welding-based additive manufacturing (WAAM) represents a significant contribution to the understanding of thermal processes in layer-by-layer metal deposition.

Core Technical Approach

The study employs finite element analysis (FEA) to model the temperature field evolution during MIG welding rapid forming. The numerical model accounts for:

Heat source characterization: A double-ellipsoidal heat source model (modified Goldak model) is used to represent the MIG welding heat input, accounting for the asymmetric nature of the arc heat distribution.
Thermal properties: Temperature-dependent thermal conductivity, specific heat capacity, and density of the deposited material (typically steel or aluminum alloys).
Boundary conditions: Convective and radiative heat losses from free surfaces, with convection coefficients calibrated to experimental conditions.
Moving heat source: The heat source moves along the deposition path at the prescribed travel speed, simulating the layer-by-layer deposition process.

Key Simulation Results

The numerical simulation reveals several important thermal characteristics of MIG welding rapid forming:

Temperature gradient distribution: The maximum temperature gradient occurs at the fusion boundary, reaching values of 10³–10⁴ K/mm, which directly influences solidification microstructure and residual stress development.
Thermal cycling effects: As layers accumulate, the thermal history of previously deposited layers changes significantly. Lower layers experience multiple reheat cycles, leading to grain coarsening and potential property degradation.
Cooling rate variation: The cooling rate at the fusion boundary varies from 10–100 K/s in single-layer deposition to 1–10 K/s in multi-layer deposition, with implications for microstructure evolution.
Residual stress prediction: The thermal stress analysis predicts residual stress magnitudes of 100–350 MPa, with tensile stresses concentrated at the fusion boundaries and compressive stresses in the weld center.

Comparison of Thermal Parameters

Deposition Layer	Peak Temperature (°C)	Cooling Rate at Fusion Boundary (K/s)	Residual Stress (MPa)	Grain Size (μm)
Layer 1 (single pass)	1450–1550	50–100	150–200	20–40
Layer 5	1350–1450	20–50	200–280	40–80
Layer 10	1300–1400	10–30	250–350	60–120

Relevance to Cladding and Pressure Vessel Engineering

Although this study focuses on rapid forming rather than conventional cladding, the thermal simulation methodology and findings have direct relevance to several aspects of bimetal pressure vessel fabrication:

Multi-pass Welding in Cladding

In weld-overlay cladding of pressure vessels (such as Inconel 625 overlay on carbon steel hydrogenation reactors), the thermal cycling of previously deposited layers is a critical concern. The simulation findings demonstrate that:

Thermal fatigue: Multiple reheat cycles can cause microstructural degradation in previously deposited overlay layers, particularly in nickel-based alloys where sensitization (chromium carbide precipitation) can occur at temperatures above 500°C.
Interpass temperature control: The simulation provides a quantitative basis for setting interpass temperature limits (typically 150–250°C for Inconel overlay) to prevent sensitization and maintain overlay layer properties.
Residual stress accumulation: In thick multi-pass overlay welds, residual stress accumulation can reach levels that compromise fatigue life or promote stress corrosion cracking.

Numerical Simulation Methodology

The double-ellipsoidal heat source model employed in this study has become the standard approach for welding thermal simulation. Key parameters that require calibration include:

Heat Source Parameter	Description	Typical Value for MIG
q_max	Peak heat flux density	10⁸–10⁹ W/m²
a, b	Front ellipsoid semi-axes	1.0–3.0 mm, 2.0–5.0 mm
c, d	Rear ellipsoid semi-axes	1.5–4.0 mm, 3.0–7.0 mm
f	Heat fraction to front ellipsoid	0.6–0.8

Study Insights and Reflections

This early numerical simulation work laid important groundwork for understanding the thermal behavior of welding-based additive manufacturing. From my perspective in pressure vessel engineering, the most valuable contribution is the quantitative demonstration of how thermal cycling affects previously deposited material. This principle directly applies to multi-pass overlay cladding, where the number of passes (typically 3–8 layers for Inconel 625 overlay on carbon steel) creates significant thermal cycling.

The study also highlights the importance of heat source modeling accuracy. The Goldak double-ellipsoidal model, while widely used, has limitations in representing the complex heat distribution of MIG welding, particularly at high travel speeds or with pulsed current. More recent developments include volumetric heat source models and coupled electromagnetic-thermal analyses that provide improved accuracy.

For pressure vessel engineers, the key practical implication is that numerical simulation can serve as a powerful tool for predicting and controlling residual stresses in thick overlay welds. By simulating the welding sequence and interpass temperatures, engineers can optimize the welding strategy to minimize residual stresses and improve the fatigue performance of clad pressure vessels.

In conclusion, this literature represents an important early contribution to welding thermal simulation methodology, with direct applicability to the thermal management challenges encountered in multi-pass overlay cladding of pressure vessels. The fundamental principles of thermal cycling, cooling rate control, and residual stress prediction remain central to modern welding simulation practice.