Numerical Simulation of Temperature Field and Stress Field in Medium-High Carbon Steel Weld Overlay Before and After Heat Source Removal

Literature Overview

This study employs finite element numerical simulation to analyse the transient thermal and mechanical behaviour of medium-high carbon steel weld overlay layers, with particular focus on the critical transient period immediately following heat source removal. The research addresses a widely recognised gap in welding process understanding: while the thermal cycle during active welding is well characterised, the post-weld cooling and stress evolution phase—which governs residual stress distribution, distortion, and cracking susceptibility—has received comparatively limited attention. The study utilises coupled thermo-mechanical finite element analysis (FEA) with sequentially coupled temperature-stress solution algorithms to capture the complex material behaviour of medium-high carbon steel during the full welding and cooling cycle.

Core Technical Content

Simulation Methodology and Material Models

The numerical model employed a three-dimensional solid element mesh with a total of 185,000 elements and 210,000 nodes, using an 8-node hexahedral element formulation with reduced integration. The welding heat source was modelled using a double-ellipsoidal heat source distribution, which more accurately represents the asymmetric temperature distribution of a moving arc than the simpler Gaussian model. The heat source parameters were calibrated against experimental thermocouple readings taken at predefined locations on the overlay layer surface and at the base metal surface.

The material model incorporated the following temperature-dependent properties for the medium-high carbon steel (45 steel, 0.45%C, 0.65%Mn):

The plastic constitutive model adopted a von Mises yield criterion with isotropic hardening, incorporating temperature-dependent yield strength data obtained from high-temperature tensile testing. The phase transformation effects on residual stress were accounted for using the Koistinen-Marburger equation to predict the volume fraction of martensite formed during cooling through the martensite start (Ms) temperature of approximately 320 degrees Celsius for the 45 steel base material.

Temperature Field Analysis

The transient temperature distribution during and after welding revealed several important features. During active welding, the peak temperature at the fusion boundary reached approximately 1450-1520 degrees Celsius, with a thermal gradient of 50-80 degC/mm in the direction perpendicular to the weld axis. The cooling rate at the fusion boundary was calculated to be 12-18 degC/s for a single-pass overlay and 8-12 degC/s for a multi-pass overlay, depending on the interpass temperature.

The most critical finding from the temperature field analysis was the characterisation of the post-heat-source-removal cooling phase. Immediately after the heat source passes a given location, the temperature drops rapidly from the peak value, but the rate of cooling decreases significantly as the thermal energy redistributes through the workpiece. The study identified a "critical cooling window" occurring approximately 3-8 seconds after heat source passage, during which the temperature traverses the range of 800-400 degrees Celsius. This window is particularly significant for medium-high carbon steel because it encompasses the temperature range where phase transformations (austenite to bainite/martensite) occur and where hydrogen embrittlement susceptibility is maximised.

Stress Field Evolution

The residual stress distribution revealed a complex three-dimensional pattern that varied significantly between the active welding phase and the post-weld cooling phase. During welding, the material immediately ahead of the heat source experienced compressive stresses due to thermal expansion, while the material behind the heat source underwent tensile stresses as the molten pool solidified and contracted. After heat source removal, the stress field underwent substantial redistribution as the entire workpiece cooled uniformly.

The following table summarises the peak residual stress values at key locations:

The transition from compressive to tensile residual stresses upon cooling is a direct consequence of the differential thermal contraction between the overlay layer and the base metal. The overlay layer, having experienced the full thermal cycle from ambient to peak welding temperature and back, contracts more than the surrounding base metal, which experienced a lower peak temperature. This differential contraction generates tensile residual stresses in the overlay layer and compressive stresses in the adjacent base metal.

Phase Transformation Effects on Residual Stress

Martensitic Transformation Stress

For medium-high carbon steel base materials, the phase transformation from austenite to martensite during cooling introduces additional volumetric expansion that partially offsets the thermal contraction. The Koistinen-Marburger model predicted that approximately 75-85% of the austenite transforms to martensite between the Ms temperature (320 degC) and room temperature, resulting in a volumetric expansion of approximately 2-3%. This transformation-induced expansion generates compressive stresses that can partially or fully counteract the thermally induced tensile residual stresses.

The net effect of phase transformation on residual stress depends critically on the cooling rate. At slow cooling rates (below 5 degC/s), the austenite has time to transform to pearlite and bainite, which involve minimal volumetric change, and the residual stresses remain predominantly tensile. At fast cooling rates (above 15 degC/s), the austenite transforms to martensite with significant volumetric expansion, potentially reducing tensile residual stresses or even producing compressive residual stresses at the fusion boundary.

Simulation Validation

The numerical simulation results were validated against experimental measurements obtained using the contour method and the hole-drilling strain gauge method. The contour method, applied to a sectioned overlay weld, provided through-thickness residual stress profiles with an accuracy of ±15 MPa. The simulation-prediction agreement was within ±25 MPa for the majority of the measured profile, with the largest deviations occurring at the fusion boundary where the steep stress gradients exceeded the resolution of the experimental measurement technique.

Engineering Practice Implications

Cracking Susceptibility Assessment

The combined thermal and mechanical analysis provides a comprehensive basis for assessing cracking susceptibility in medium-high carbon steel weld overlay applications. The critical cracking window occurs during the post-weld cooling phase when three conditions coincide: (1) the temperature is in the range of 200-400 degrees Celsius where hydrogen embrittlement is most effective, (2) the tensile residual stresses are at their peak values, and (3) the microstructure is transitioning through the brittle martensite formation stage.

For medium-high carbon steel overlay applications, the following countermeasures are recommended based on the simulation findings:

1. Preheating to 200-300 degrees Celsius to reduce the peak cooling rate and minimise martensite formation
2. Interpass temperature control maintained at 150-250 degrees Celsius to prevent excessive cooling between passes
3. Post-weld stress relief treatment at 550-650 degrees Celsius for 1 hour per 25 mm of thickness to reduce residual stresses by 60-80%
4. Use of low-hydrogen consumables with moisture content below 0.5% and controlled arc length to minimise hydrogen pickup
5. Consideration of mechanical stress relief (peening or shot blasting) as a supplementary measure to reduce surface tensile stresses

Process Parameter Optimisation

The simulation results identified the following process parameter sensitivities:

• Welding current: Increasing current by 20% increases peak temperature by approximately 80 degrees Celsius and reduces cooling rate by 25%, but also increases dilution and base metal heat input
• Travel speed: Reducing travel speed by 30% increases heat input per unit length by approximately 45%, significantly increasing the affected zone width and residual stress magnitude
• Heat source power density: Higher power density (as achieved with laser or plasma processes) produces narrower heat-affected zones but steeper thermal gradients, resulting in higher localised residual stresses
• Number of passes: Multi-pass welding with lower heat input per pass produces lower peak temperatures but more thermal cycles, potentially leading to grain coarsening in the heat-affected zone

Study Insights and Conclusions

The numerical simulation of temperature and stress fields in medium-high carbon steel weld overlay provides a powerful analytical tool for understanding and predicting welding-induced defects. The most significant finding is that the post-heat-source-removal cooling phase, rather than the active welding phase, governs the final residual stress state and cracking susceptibility. This insight has direct implications for process optimisation: rather than focusing solely on welding parameters that control the peak temperature and cooling rate during active welding, engineers should also consider the thermal management of the cooling phase, including controlled cooling rates, post-weld heat treatment, and mechanical stress relief. The coupled thermo-mechanical simulation approach demonstrated in this study should be adopted as a standard design tool for weld overlay process qualification, particularly for applications involving high-strength or high-carbon base materials where cracking susceptibility is a critical concern. The simulation results provide a quantitative basis for setting process parameter limits, defining inspection requirements, and evaluating the effectiveness of countermeasures against welding-induced cracking.