Welding Simulation in TEE joint requires a different modeling strategy from a conventional butt-welded plate. The intersecting plates create a three-dimensional heat-flow path, variable weld geometry, and strong thermal gradients around the joint intersection.
For a laser welding simulation in Abaqus, the most important modeling decisions are the heat-source coordinate system, laser travel path, Gaussian radius, absorbed power, mesh density, and temperature-dependent material properties.
This article presents a practical workflow for implementing a moving Gaussian heat source for a TEE joint and evaluating the resulting temperature field, heat-affected zone, cooling behavior, and thermal history.
1. TEE Joint Geometry for Laser Welding Simulation
A representative TEE joint consists of a base plate and a vertical plate joined along their intersection. For the laser welding simulation in Abaqus, the geometry should provide sufficient space around the weld to capture the thermal gradients and heat-affected region.
The following parameters define a practical example for the Gaussian Heat Source Model:
Important: These values are example parameters, not universal welding conditions. Actual laser power, absorption efficiency, Gaussian radius, and travel speed should be obtained from the experimental process or welding procedure being simulated.

The vertical plate should intersect the base plate without creating unintended gaps or overlaps. The geometry at the intersection directly affects the local heat-flow path and therefore the predicted temperature distribution.
For a thermal-only model, the two plates can be represented as a single connected thermal domain when the primary objective is temperature prediction. However, separate parts with appropriate interaction definitions may be preferable when the model will later be extended to thermo-mechanical analysis, residual stress, or welding distortion.
Geometry Considerations for the TEE Joint
The TEE intersection deserves particular attention because the local heat-flow direction changes rapidly around the weld. Before generating the Abaqus mesh, verify the following:
- The base and vertical plates intersect correctly.
- The weld path is geometrically continuous.
- No unintended gaps or overlaps exist at the joint.
- The laser travel direction is clearly defined.
- The heat-source location can be mapped to the weld centerline.
- The element size near the weld is sufficiently small to resolve the Gaussian heat distribution.
Modeling note: A geometrically incorrect TEE intersection can produce smooth and visually convincing temperature contours while still giving physically incorrect thermal results. Always verify the weld path and heat-source position before performing a detailed mesh or parameter study.
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2. Transient Heat Transfer Step in Abaqus
For a laser welding thermal model, a transient heat transfer analysis is normally appropriate. The transient formulation allows the model to capture the moving laser, rapid temperature changes, and subsequent cooling of the TEE joint.
In Abaqus/Standard, create a transient heat transfer step and define the total welding time from the weld length and laser travel speed:
where:
- Lweld is the welding length.
- v is the laser travel speed.
Example: If the laser travels 80 mm at a speed of 5 mm/s, the welding time is:
The analysis should normally continue beyond the end of laser travel when the cooling stage is important. This allows the model to capture the thermal cycle after the heat source leaves the joint and provides more useful information about the cooling rate and residual thermal field.
Recommended Abaqus Welding Simulation Sequence
A practical simulation sequence for the TEE joint can be organized into the following stages:
- 1 Initial temperature definition: Assign the initial temperature of the TEE joint before laser heating begins.
- 2 Transient laser heating: Activate the moving Gaussian heat source through the DFLUX subroutine.
- 3 Laser movement along the TEE joint: Move the heat source continuously along the predefined weld centerline.
- 4 Post-welding cooling: Continue the analysis after laser shutdown to capture the cooling thermal field.
- 5 Thermal-history extraction: Extract temperature versus time at selected locations around the weld.
- 6 Experimental comparison: Compare the predicted thermal cycles and weld dimensions with experimental measurements.
3. Moving Gaussian Heat Source for Laser Welding
The Gaussian heat source should move continuously along the weld path during the laser welding simulation. For a surface-based Gaussian distribution, the applied heat flux can be expressed as:
where:
- P = laser power.
- η = absorption efficiency.
- r₀ = Gaussian beam radius.
- r = distance from the instantaneous laser center.
Absorbed Laser Power
The heat source should account for the fraction of laser power absorbed by the material. The absorbed laser power is:
For a laser power of 1000 W and an absorption efficiency of 0.8:
Moving Laser Source Position
The position of the Gaussian heat source changes with time as the laser travels along the weld. If the laser moves in the global X direction, its instantaneous center can be defined as:
where x₀ is the initial laser position and v is the laser travel speed.
For a source moving over a planar surface, the radial distance from the instantaneous laser center can then be calculated as:
Important for TEE Joint Modeling
The planar formulation above is not sufficient for a typical TEE joint. The weld region is not necessarily located on a single global plane, and the local surface orientation changes around the intersection of the two plates. Therefore, the heat-source coordinates should be defined relative to the actual weld path or a suitable local coordinate system.
For the TEE-joint model, the next step is to replace the simple global-coordinate distance calculation with a local weld-coordinate formulation. This allows the Gaussian heat source to remain correctly positioned along the weld centerline throughout the Abaqus simulation.
4. Local Weld Coordinate System for the Gaussian Heat Source in TEE Joint
The most important improvement over a simple plate model is to define the heat source using a local weld coordinate system. This allows the Gaussian distribution to follow the actual weld trajectory instead of relying only on global X-Y coordinates.
Define three local unit vectors:
- et = tangent vector along the welding direction.
- en = local surface normal.
- ew = transverse direction across the weld.
Moving Laser Center
The laser center can then be described using the initial weld position, welding speed, and local tangent vector:
At every time increment, the instantaneous laser center is updated along the welding direction. This makes the heat source move continuously along the weld path.
Local Coordinates at Each Integration Point
For each integration point, calculate its position relative to the moving laser center. The resulting vector can then be projected onto the local weld coordinate directions.
The local coordinates perpendicular to the welding direction define the distance from the laser center.
Here, ξ and ζ are the local coordinates perpendicular to the laser travel direction. They determine how far each integration point is from the instantaneous center of the Gaussian heat source.
Why Use Local Coordinates?
This approach is considerably more robust than defining the Gaussian distribution directly in global X-Y coordinates. The heat source can follow the weld trajectory even when the weld orientation changes relative to the global coordinate system.
Why This Matters for a TEE Joint
A TEE joint introduces a geometric complication because the base plate and vertical plate have different surface orientations. The weld region therefore cannot always be represented accurately using a single global plane.
Follow the Actual Weld Trajectory
If the laser interacts primarily with the fillet region, the heat source should follow the actual weld trajectory, not simply a line defined in the global coordinate system. Otherwise, the heat flux may move too far from the physical weld region as the laser travels.
Practical Abaqus Implementation
- Define the weld centerline and its travel direction.
- Calculate the local tangent vector et.
- Define the local transverse and normal directions.
- Update the laser center according to the welding speed and simulation time.
- Project each integration-point position into the local coordinate system.
- Use the local transverse coordinates to evaluate the Gaussian heat flux.
In Abaqus, this local-coordinate formulation provides the foundation for a more reliable DFLUX implementation, especially when modeling laser heating around complex weld geometries such as TEE joints.
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5. Implementing the Heat Source with DFLUX
A practical laser welding simulation in Abaqus can implement the moving Gaussian heat source using the DFLUX user subroutine. DFLUX allows the applied heat flux to change with the laser position and welding conditions throughout the transient analysis.
Parameters Available to DFLUX
Current analysis time
Current integration-point coordinates
Analysis step number
Current increment number
Nominal or absorbed power
Heat-source travel speed
Spatial heat distribution
Laser movement vector
Weld-based heat-source system
DFLUX Heat-Source Logic

Important for TEE-Joint Welding
The code above is only a simplified representation of a moving Gaussian heat source. It assumes a fixed global plane and a laser moving along the X direction. A realistic TEE-joint Abaqus model should instead use the actual weld trajectory and a local weld coordinate system. This is particularly important because the base plate and vertical plate have different surface orientations.
Practical Implementation Strategy
For a TEE joint, define the weld centerline first. Then calculate the laser center from the welding speed and analysis time. Project the current integration-point position into the local weld coordinate system and evaluate the Gaussian distribution using the local transverse distances. This approach provides a more robust DFLUX implementation and can later be extended to curved welds and complex laser trajectories.

6. Defining the Parameters for Laser Welding in a TEE Joint
For a TEE joint laser welding simulation in Abaqus, a useful approach is to define the laser centerline along the intersection between the two plates. This allows the moving heat source to follow the actual weld path instead of relying only on fixed global coordinates.
Suppose the weld path is represented by:
where s is the distance measured along the weld path. The laser center can then be defined as:
This formulation is especially useful when the weld path is curved or when the joint geometry becomes more complicated. The heat source can follow the weld geometry directly, making the model easier to extend and maintain.
Straight TEE Joint
For a straight weld path, the laser center can be described using the initial position and the welding direction:
Curved Weld Path
For a curved weld, the laser center should be evaluated directly from the mathematical or geometric representation of the weld path.
A Scalable Laser-Welding Framework
Defining the laser position from the weld trajectory provides a scalable framework for extending an Abaqus welding model to more complex geometries and manufacturing paths.
6.1. Choosing the Gaussian Radius
The Gaussian radius strongly affects the predicted weld pool, temperature distribution, and thermal gradient. It should therefore be treated as an important calibration parameter rather than an arbitrary input.
Smaller r₀
- Higher peak heat flux.
- Higher local temperature.
- Narrower heated region.
- Steeper thermal gradients.
Larger r₀
- Lower peak heat flux.
- Wider temperature distribution.
- Lower local temperature.
- Broader thermally affected region.
The peak heat flux varies with 1/r₀². Therefore, changing the Gaussian radius from 2 mm to 1 mm does not simply double the peak heat flux. It increases the peak value by a factor of four.
6.2. Laser Power and Absorption Efficiency
The thermal model should use the absorbed laser power, not automatically the nominal laser power.
| Parameter | Value |
|---|---|
| Laser power | 1000 W |
| Absorption efficiency | 0.80 |
| Absorbed power | 800 W |
| Welding speed | 5 mm/s |
| Nominal line energy | 200 J/mm |
| Absorbed line energy | 160 J/mm |
Laser Line Energy
The nominal linear energy is:
The absorbed linear energy is:
For the example:
El,abs = 800 / 5 = 160 J/mm
These values provide a useful first-order check of whether the simulated thermal response is physically reasonable.
7. Temperature-Dependent Material Properties for Laser Welding
Using constant material properties can produce significant errors in a laser welding simulation.
At minimum, define temperature-dependent:
- Thermal conductivity.
- Specific heat.
- Density.
For a more realistic model, account for the melting range and latent heat.
A typical material definition should therefore follow the form:
| Property | Temperature dependence |
|---|---|
| Density | Required |
| Conductivity | Required |
| Specific heat | Required |
| Latent heat | Recommended |
| Solidus temperature | Required for melting treatment |
| Liquidus temperature | Required for melting treatment |
Thermal conductivity can change substantially with temperature. Specific heat may also increase around phase transformation regions.
If these effects are ignored, the predicted peak temperature and cooling rate may be misleading.
8. Initial and Boundary Conditions of TEE Joint
Set the initial temperature according to the physical welding condition.
For room-temperature welding:
A typical value may be:
Apply heat losses from exposed surfaces using convection and radiation.
The convective heat loss can be represented by:
Radiation can be represented by:
Both mechanisms can become important during the cooling stage.
For a laser welding simulation, radiation becomes increasingly important at high temperature, so using only a constant convection coefficient may not provide sufficient accuracy.
9. Mesh Strategy for Laser welding of the TEE Joint
Mesh density has a direct effect on the predicted temperature gradients.
The highest mesh density should be concentrated around:
- The laser path.
- The weld region.
- The TEE intersection.
- Expected fusion-zone boundaries.
- The heat-affected zone.
A practical strategy is:
Fine mesh
Near the weld and laser path.
Intermediate mesh
Around the heat-affected zone.
Coarse mesh
Far from the weld where temperature gradients become small.
The mesh should not be uniformly fine throughout the entire model unless the geometry is small enough to justify the additional computational cost.

Recommended element type
For a three-dimensional transient thermal analysis, an 8-node brick heat-transfer element such as DC3D8 is often a practical choice. Check it out here to see how to select right element type for welding models.
Where geometry requires greater flexibility, tetrahedral thermal elements can be used, but the resulting mesh should be checked carefully around the weld.
Mesh Independence Study
A single mesh should not be trusted simply because the temperature contour looks smooth.
Run at least three mesh levels around the weld. See this article to Learn How to mesh a 3D model in Abaqus
For example:
| Mesh | Weld-region element size |
|---|---|
| Coarse | 2.0 mm |
| Medium | 1.0 mm |
| Fine | 0.5 mm |
Compare:
- Maximum temperature.
- Peak temperature at selected points.
- Fusion-zone dimensions.
- HAZ width.
- Cooling rate.
- Thermal cycle.
If the difference between the medium and fine mesh is small, the medium mesh may provide a better balance between accuracy and computational cost.
This is particularly important for a Gaussian heat source because the heat flux changes rapidly over a small distance.
10. Time Increment Selection
The time increment must resolve the movement of the laser.
The approximate laser movement during one increment is:
A useful practical condition is to ensure that the laser does not move several element lengths during one increment.
For example, if:
and the weld-region element size is:
then an increment corresponding to approximately 0.1–0.25 mm of laser movement provides much better spatial resolution than allowing the laser to jump several millimeters between increments.
The exact increment should also be controlled by thermal convergence and the characteristic heating time.
11. Temperature Results to Extract
The temperature contour alone is not sufficient to validate the model.
Extract temperature histories at several locations around the TEE joint.
Recommended monitoring points include:
- Directly below the laser center.
- On the base plate beside the weld.
- On the vertical plate beside the weld.
- At the expected HAZ boundary.
- Several millimeters away from the weld.
- At different distances along the welding direction.
For each point, obtain:
The thermal cycle can then be evaluated in terms of:
- Peak temperature.
- Heating rate.
- Cooling rate.
- Time above critical temperatures.
- Thermal gradients.
12. Common Problems in Laser Welding Simulation in Abaqus
Several problems can occur when implementing a Gaussian heat source and DFLUX for laser welding in Abaqus. The following checks help identify whether the problem comes from the heat-source formulation, mesh, material properties, or model setup.
Recommended Troubleshooting Sequence
When a laser welding simulation produces unexpected temperatures or heat-flux results, troubleshoot the model in a controlled sequence rather than changing several parameters at once.
- Verify the laser trajectory and local coordinate system.
- Check the absorbed laser power.
- Verify the Gaussian radius and heat-source distribution.
- Check DFLUX coordinates, time, and travel speed.
- Verify the applied surface or active elements.
- Check mesh resolution near the weld.
- Verify temperature-dependent material properties.
- Compare fusion-zone and HAZ dimensions with experimental data.
14. Abaqus Workflow for TEE-Joint Laser Welding Simulation
A reliable TEE-joint laser welding simulation should follow a controlled sequence from geometry creation to experimental calibration. The workflow below covers the main steps required to build and verify the transient thermal model in Abaqus.
Geometry
Create the base and vertical plates. Verify the TEE-joint intersection and ensure that the weld region has the intended geometry.
Material
Define temperature-dependent thermal properties, including thermal conductivity and specific heat. Add additional high-temperature data when required.
Assembly
Position the base and vertical plates correctly and establish the welding region and weld trajectory.
Define Steps
Create the transient heat transfer step for laser heating and a separate cooling step when post-welding thermal evolution is important.
Initial Temperature
Apply the initial temperature to the model. Use the measured or experimentally specified initial thermal condition rather than assuming an arbitrary value.
Heat Losses
Define convection and radiation on exposed surfaces. Use appropriate ambient temperature, convection coefficient, and emissivity.
Mesh
Refine the mesh around the TEE intersection, weld region, and laser interaction zone. Use a coarser mesh away from regions with steep thermal gradients.
DFLUX
Implement the moving Gaussian heat source using the Abaqus DFLUX subroutine. Use the local weld coordinate system for complex TEE-joint geometry.
Verification
Before running the full analysis, verify the laser position, absorbed energy, heat-flux magnitude, and boundary conditions.
Run Analysis
Run the transient thermal analysis and monitor convergence, temperature evolution, and heat-source behavior during laser travel.
Post-Processing
Extract temperature contours, thermal histories, peak temperatures, and cooling rates. For thermo-mechanical models, evaluate residual stress and distortion after thermal loading.
Calibration
Compare the predicted fusion-zone and HAZ dimensions with experimental data. Calibrate the heat-source parameters based on measured weld characteristics.
Recommended Modeling Logic
The most important point is to complete the verification stage before calibration. First confirm that the DFLUX implementation, laser trajectory, absorbed power, mesh, and thermal boundary conditions are correct. Then use experimental weld dimensions to calibrate the Gaussian heat-source parameters.
From Geometry to Experimental Validation
A robust TEE-joint laser welding model is not defined by the DFLUX subroutine alone. Reliable results require consistent geometry, temperature-dependent material data, appropriate mesh and time resolution, correct heat losses, a physically consistent Gaussian heat source, and experimental validation.
15. Improving the Gaussian Model for Deep-Penetration Laser Welding
A Gaussian heat source may not reproduce a deep-penetration laser weld accurately.
For example, the Laser Welding Simulation Using CIN Model applies heat throughout a three-dimensional volume. This makes it useful for representing narrow and deep penetration in beam welding.
Problems With a Purely Surface-Applied Source
If the real weld exhibits significant penetration, a purely surface-applied Gaussian distribution can produce:
- Incorrect penetration depth.
- Excessive surface temperature.
- Incorrect subsurface thermal gradients.
- Incorrect fusion-zone geometry.
Consider a Volumetric Heat Source
In such cases, consider a volumetric heat source or a combined surface-volumetric formulation. A volumetric source distributes heat through the material depth instead of applying all energy only at the surface.
General Volumetric Source
The volumetric heat input can be represented generally as:
Here, f controls the spatial distribution of heat through the weld depth and along the moving laser path.
Goldak-Type Alternative
A Goldak-type double-ellipsoidal heat source can also be considered when directional heat penetration needs to be represented. The two ellipsoidal regions can provide different heat distributions ahead of and behind the moving heat source.
Heat-Source Selection for a TEE Laser Weld
For a TEE laser weld, the appropriate heat-source model should be selected from the observed weld morphology. A surface Gaussian source is a practical starting point for shallow penetration, while a volumetric or combined source is more appropriate when the weld is narrow and deep. The source should also follow the actual three-dimensional weld trajectory rather than being defined only from global coordinates.
16. Final Technical Conclusion
A laser welding simulation in a TEE joint using a Gaussian heat source in Abaqus provides an effective approach for predicting temperature distribution, fusion-zone geometry, and HAZ behavior. For accurate results, define the heat source along the actual weld path and calibrate the model using experimental data. For deep-penetration welding, a volumetric or combined heat-source model may provide better accuracy.
17. Resources for Studying Laser Welding Simulation in Abaqus
If you want to develop reliable laser welding simulations in Abaqus, study the heat-source formulation, DFLUX implementation, thermal modeling, mesh and time-step selection, and experimental calibration together. The following resources provide a practical path from the Abaqus fundamentals to advanced laser-welding models.
DFLUX User Subroutine
Learn how Abaqus defines nonuniform surface and body heat fluxes using DFLUX. This is the foundation for implementing a moving Gaussian or volumetric laser heat source.
Laser Welding of T-Joints
Study the influence of laser heat-source inclination on melted-zone geometry, deformation, and stress. The paper is especially relevant to T-joint and TEE-joint welding simulations.
Hybrid Laser-Arc Heat Sources
A useful advanced example of combining laser and arc heat-source models in Abaqus through DFLUX. It also demonstrates experimental validation of temperature and deformation predictions.
CIN Volumetric Heat Source
A practical Abaqus example using DFLUX and a cylindrical involution normal (CIN) heat source for volumetric laser welding. Useful for studying deep-penetration thermal models.
Laser Welding & DFLUX Examples
Covers moving laser beams, Gaussian energy distributions, surface and volumetric heat fluxes, and different laser paths implemented with DFLUX.
Abaqus Welding Masterclass
Covers moving heat sources, DFLUX, Gaussian welding models, Goldak double-ellipsoid sources, and residual-stress workflows.






