Prediction of Weld Geometry in Laser Overlap Welding of Low-Carbon Galvanized Steel

Abstract

Accurate prediction of weld bead geometry is critical for optimizing laser overlap welding of low-carbon galvanized steel, as it directly affects joint quality and mechanical performance. Traditional finite element method (FEM)-based models provide reliable predictions but are computationally expensive and impractical for real-time applications. This study presents an artificial neural network (ANN)-based predictive model trained on a combination of experimental data and validated FEM simulations to estimate key weld characteristics, including depth of penetration (DOP), weld bead width at the surface (WS), and weld bead width at the interface (WI). The ANN model was evaluated using various improved statistical metrics. Results demonstrated a strong correlation between ANN predictions and experimental measurements, with R² values exceeding 95% for WS and DOP and 92% for WI, and mean errors below 7%. A comparative analysis between ANN, FEM, and experimental data confirmed the model’s reliability across different welding conditions. Additionally, ANN significantly reduced computational time compared to FEM while maintaining high accuracy, making it a practical tool for real-time process optimization. These findings highlight the potential of ANN models as efficient alternatives to conventional simulation techniques in laser overlap welding applications. Future improvements may involve integrating real-time sensor data and deep learning techniques to further enhance predictive performance.

1. Introduction

Laser overlap welding is a cutting-edge technique that uses laser technology to create strong, precise welds on thin sheets of metal, like low-carbon galvanized steel. This method offers several advantages over traditional welding, including minimal heat distortion, preservation of the material’s protective coating, and superior joint quality [1]. Low-carbon galvanized steel, renowned for its combination of high strength, ductility, and corrosion resistance, finds extensive application in industries such as automotive, construction, and electronics [2]. Laser overlap welding offers the potential to preserve the zinc coating and achieve high-quality joints.

However, the laser welding of zinc-coated steel faces some challenges primarily due to the behavior of the zinc coating under high temperatures. Zinc, with a boiling point of approximately 907 °C, vaporizes much earlier than steel melts at 1500 °C. This disparity leads to the rapid generation of high-pressure zinc vapors during the welding process. In zero-gap configurations, where the steel sheets are in direct contact, these vapors become trapped, destabilizing the molten pool and keyhole. This results in defects such as spattering, porosity, and irregularities like blowholes and undercuts, which compromise the weld quality [3,4]. Additionally, zinc penetrates steel grain boundaries, forming brittle Fe-Zn intermetallic phases, such as Γ-Fe3Zn10 and δ-FeZn10, during cooling. These phases weaken the grain boundaries and promote intergranular cracks, a phenomenon known as liquid metal embrittlement (LME). LME is particularly severe in deep, partial penetration welds where zinc vapor cannot escape effectively [5]. To address these challenges, the findings of Zhang et al. [6] suggest that weld bead geometry plays a critical role in achieving optimized overlap laser welding of galvanized steel. Their study demonstrates that parameters such as laser power, welding speed, and the introduction of a slot influence the weld bead’s width, depth, and overall quality. Proper weld bead geometry not only enhances tensile resistance, achieving a maximum of 6.54 kN [6], but also reduces defects like porosity and spatter by allowing effective zinc vapor escape. These results imply that weld bead geometry is an essential criterion for evaluating and improving welding conditions in galvanized steel applications.

A limited number of experimental and numerical studies have been conducted to address the challenges associated with overlap laser welding of low-carbon galvanized steel. One effective solution involves introducing a small gap between the steel sheets, as demonstrated by Hao et al. [4], where a gap of 100 µm reduced zinc vapor velocity from 81 m/s to 33 m/s, stabilizing the keyhole and eliminating spatter formation. Similarly, Zhang et al. [6] showed that using an oscillating laser beam technique with optimized parameters (oscillation frequency of 300 Hz and amplitude of 0.5 mm) promoted uniform energy distribution, allowing zinc vapors to escape effectively, and reduced defects like porosity and blowholes. Advanced numerical and experimental models by Karganroudi et al. [7] optimized parameters, such as laser power (2.2 kW) and scanning frequency (500 Hz), to minimize void formation, achieving an average void area reduction of 35%. Spatter quantification methods, proposed by Hao et al. [8], introduced metrics such as Zout (zinc vapor load) and Zp (keyhole vulnerability), with measured spatter frequency dropping from 300 Hz in zero-gap conditions to negligible levels in gapped setups. Tailored laser beam shaping techniques, with elliptical profiles, further mitigated the disruptive effects of zinc vapor by controlling heat input distribution. These quantitative strategies have significantly enhanced weld quality, reduced defects, and improved mechanical performance in zinc-coated steel laser welding.

However, other studies in laser welding of different materials have demonstrated that artificial neural network (ANN)-based methods provide a highly accurate and precise approach for predicting weld bead geometry. These methods excel at modeling the complex and nonlinear relationships between welding parameters, such as laser power, speed, and focal position, and the resulting bead geometry characteristics, including width, depth, and penetration. Kalpana et al. [9] used a multi-scale convolutional neural network (CNN) to predict bead geometry parameters, such as depth of penetration and top surface width, during laser overlap welding of low-carbon galvanized steel, achieving a high prediction accuracy of 98.61%. Similarly, Dey et al. [10] combined numerical simulations and multilayered feed-forward ANN to model weld width and throat length in lap joint welding of aluminum alloy 2024, highlighting ANN’s superior precision compared to traditional methods. In butt-joint welding of SS316L stainless steel, Chuang et al. [11] developed a framework combining finite element simulations and ANN, achieving improved angular distortion control (<564 µm) and tensile strength optimization (662 MPa). For gas metal arc welding (GMAW), Li et al. [12] employed an ANN with a three-layer backpropagation structure to predict bead width and reinforcement in Q235 steel, achieving up to 99% prediction accuracy. Nikolić et al. [13] explored multiple AI approaches, including ANN, Extreme Learning Machine (ELM), and Genetic Programming (GP), to forecast weld geometry in low-carbon and stainless steel, with ELM showing the best performance (highest R² and lowest RMSE). In laser oscillation welding of aluminum alloy 6061, Ai et al. [14] employed backpropagation neural networks (BPNNs) to predict weld area with an R² > 0.85 and relative error <8.8%, demonstrating robustness in nonlinear modeling. Tran et al. [15] applied deep learning neural networks (DLNNs) to predict geometric weld characteristics in SMAW (shielded metal arc welding), MIG (metal inert gas welding), and TIG (tungsten inert gas welding) processes, achieving high accuracy with mean squared error (MSE) optimization. For laser beam welding (LBW) of maraging steel, Katz et al. [16] compared multiple regression analysis (MRA) and AI models, finding R² values exceeding 0.91 for penetration depth and weld width using AI. Ahmed et al. [17] developed radial basis function neural networks (RBF-NNs) to predict penetration depth and reinforcement in SMAW of mild steel, achieving a correlation coefficient of R ≈ 0.97. Kshirsagar et al. [18] combined support vector machines (SVMs) with ANN to classify welding parameters and predict bead geometry in TIG welding of stainless steel, achieving an error rate below 0.005. In the context of wire and arc additive manufacturing (WAAM), Karmuhilan et al. [19] utilized a forward ANN to model bead dimensions in GMAW, attaining R² values exceeding 99% for width and height predictions. Lastly, Yadav and Paswan [20] reviewed various ANN and mathematical approaches for predicting bead geometry in arc welding, concluding that ANN methods significantly reduce experimental requirements while maintaining high accuracy. Rodríguez-Gonzálvez and Rodríguez-Martín [21] implemented a decision tree-based machine learning approach for weld bead classification in low-carbon steel, achieving classification accuracies of 85–95% and ROC (receiver operating characteristic) curve values up to 99%.

Despite extensive research on using artificial neural networks (ANNs) to predict weld bead geometry, their application to laser overlap welding of zinc-coated low-carbon steel remains unexplored. This welding configuration presents challenges like zinc vaporization-induced defects, requiring precise control of process parameters. Given ANNs’ proven ability to model complex, nonlinear relationships with high accuracy, this study develops an ANN-based model tailored for this specific welding process. The aim is to accurately predict weld bead geometry, optimize parameters, and address existing challenges, advancing both weld quality and ANN applications in this field.

2. 3D Numerical Modelling

A comprehensive three-dimensional numerical model was developed to simulate the weld bead geometry characteristics in laser overlap welding of low-carbon galvanized steel. This model utilized the finite element method (FEM), implemented in COMSOL Multiphysics (Version 4.4), to predict thermal fields, weld pool dynamics, and bead geometry. The simulation focused on a Gaussian volumetric heat source to replicate the dual characteristics of conduction and keyhole welding modes. The heat source parameters were calibrated to experimental conditions corresponding to a 3 kW Nd:YAG laser system operating at a wavelength of 1.06 µm, with a focal spot diameter of 0.3 mm, laser power ranging from 2000 W to 3000 W, and welding speeds between 1.5 m/min and 3 m/min. This modeling approach builds upon the authors’ previous work, as detailed in [22]. Various models such as surface Gaussian, Goldak’s double ellipsoidal, and conical volumetric heat sources exist; however, Gaussian volumetric models remain widely used for conduction-dominated cases due to their balance of accuracy and simplicity. Based on weld cross-sections, the majority of experimental conditions in this study exhibited conduction or partial penetration characteristics, justifying the model selection [23].

The temperature-dependent thermal and physical properties of galvanized steel were incorporated into the model to enhance accuracy. Thermal conductivity was defined to range from 20 W/(m·K) at room temperature to 50 W/(m·K) near the melting point. Specific heat capacity increased from 450 J/(kg·K) at 25 °C to 650 J/(kg·K) near the melting point. The density was maintained constant at 7850 kg/m³, and the latent heat of fusion was set to 272 kJ/kg. The melting point of the steel base material was taken as 1536 °C, while the zinc coating, with a boiling point of 907 °C, was assumed to vaporize upon heating, affecting the boundary conditions. Solid-state phase transformations, such as the α–γ transition in steel, were not explicitly modeled. However, temperature-dependent thermal properties were applied, which partially reflect the influence of such transformations on heat absorption behavior.

Heat losses were modeled using convective and radiative boundary conditions. The emissivity was set to 0.85, and the heat transfer coefficient was fixed at 30 W/(m²·K) to simulate ambient cooling. The initial ambient temperature was assumed to be 25 °C, and simulations were performed for temperatures exceeding 1700 °C to account for vaporization of zinc and melting of steel. The modeled geometry consisted of a lap joint configuration with sheet thicknesses of 1 mm and 2 mm, including a zinc coating thickness of 15 µm. Symmetry boundary conditions were applied along the longitudinal axis to reduce computational requirements while maintaining the integrity of the results. The finite element mesh was refined near the weld pool region, with element sizes ranging from 50 µm in the weld pool to 200 µm in the surrounding material, ensuring numerical stability and accurate heat flow representation. The finite element mesh consisted of three-dimensional tetrahedral elements with linear shape functions, implemented using COMSOL Multiphysics. This configuration ensures both numerical accuracy and computational efficiency. Further meshing and modeling details are available in our previous work [22].

The 3D numerical model operates under several assumptions and limitations. The Gaussian heat source assumes a uniform energy distribution within the laser focus area, which may deviate in practice due to variations in laser beam quality. Zinc vaporization was incorporated as a boundary condition but does not account for the detailed dynamics of zinc vapor or its interaction with the molten pool. Additionally, the model neglects fluid flow within the weld pool, which limits its representation of convection and Marangoni effects.

The model calculates weld bead geometry by analyzing the temperature distribution across the welded material. This distribution is determined through 3D finite element analysis (FEA), which solves the heat conduction equations to predict the thermal field in the workpiece during welding. The governing equation for heat conduction is given in Equation (1). Where ρ is material density (7850 kg/m³ for low-carbon steel), C_p is specific heat capacity (450 J/(kg·K) at room temperature, increasing to 650 J/(kg·K) near the melting point), T °C is temperature, k is thermal conductivity (20 W/(m·K) at room temperature, increasing to 50 W/(m·K) near the melting point), and Q(x,y,z,t) is heat input from the laser.

$$\rho C_p{\displaystyle \frac{\partial T}{\partial t}}=k{\nabla }^{2}T+Q(x,y,z,t)$$

(1)

To account for phase change, the effective heat capacity method was used, where the latent heat of fusion is included by enhancing the specific heat over a narrow temperature range near the melting point. This approach enables smooth thermal transitions without requiring explicit tracking of phase boundaries.

Points where the temperature reaches the liquidus (the melting temperature of the material, 1536 °C for the base steel) are used to define the molten pool dimensions. These dimensions directly influence the weld geometry. The key weld characteristics were the depth of penetration (DOP), measured from the top surface to the deepest point of the molten pool, ranging up to a maximum of 1.5 mm depending on laser power and welding speed; the surface bead width (WS), representing the width of the molten pool at the top surface, varying between 0.3 mm and 1.2 mm, influenced by welding parameters; and the interface bead width (WI), the width at the interface between the sheets, typically up to 2 mm, depending on the welding conditions. The values are shown schematically in Figure 1.

3. Experimentation and 3D Model Validation

The experimental phase was conducted to investigate the weld bead geometry and validate the developed three-dimensional numerical model.

3.1. Experimentation

ASTM A635CS steel with an A40 zinc coating was welded using a 3 kW IPG YLS-3000-ST2 fiber laser system, a HIGHYAG BIMO laser head (Coherent, Ditzingen, Germany), and a FANUC M-710iC robot (FANUC, Yamanashi, Japan) (Figure 2).

Table 1. Chemical composition (wt.%) of the upper (1 mm) and lower (2 mm) galvanized steel sheets.

Sheet Position	C	Mn	P	S	Si	Cu	Ni	Cr	Al	N
Upper Sheet	0.05	0.24	0.009	0.013	0.007	0.029	0.012	0.037	0.04	0.0024
Lower Sheet	0.09	0.35	0.005	0.01	0.02	0.05	0.04	0.06	0.03	0.0029

details the chemical composition. Key parameters include power (2000–3000 W), welding speeds (40–70 mm/s), and focal spot diameters (300–490 µm), and gap of 0.05–0.15 mm. Welding was carried out under 24 conditions. DOP, WS, and WI were measured using optical microscopy with an optical microscope, with values averaged over three repetitions.

3.2. 3D Model Validation

The developed 3D numerical model was validated by comparing its predictions with experimental measurements obtained under identical welding conditions. The comparison of numerical predictions with experimental data showed excellent agreement. This is aligned with the previous research of the authors where statistical analysis showed that for DOP, the model achieved a Coefficient of Determination (R²) value of 90.94%, with a Mean Absolute Percentage Error (MAPE) of 6.94% and a Root Mean Squared Error (RMSE) of 3.04%. WS predictions exhibited the highest accuracy, with an R² value of 96.09%, an MAPE of 2.44%, and an RMSE of 1.09%. WI predictions showed slightly higher variability, with an R² value of 94.12%, an MAPE of 7.28%, and an RMSE of 3.32%. The maximum prediction error for WI was less than 7.5%, attributed to small variations in experimental gap control.

4. Artificial Neural Network-Based Predictive Modelling

To optimize the prediction of weld bead geometry in laser overlap welding of low-carbon galvanized steel, a data-driven approach based on artificial neural networks (ANNs) was developed. While the finite element method (FEM)-based numerical model provided accurate predictions, its computational cost and long processing time made it unsuitable for real-time applications. To address this limitation, an ANN-based predictive model was implemented, leveraging data obtained from both validated FEM simulations and experimental measurements. The primary objective of this model is to enable rapid and reliable predictions of weld characteristics under varying welding conditions while maintaining high accuracy.

This approach allows for a computationally efficient surrogate model that can replace time-intensive numerical simulations while retaining predictive precision. The ANN model was trained on an extensive dataset encompassing both experimental and simulated results, ensuring its ability to generalize across a broad range of welding parameters. By establishing a robust relationship between input welding conditions and output weld characteristics, the ANN model serves as a practical tool for optimizing welding processes in industrial applications.

4.1. Modelling Conditions

The ANN model was designed to predict three key weld bead geometry characteristics:

• Depth of penetration (DOP);
• Weld bead width at the surface (WS);
• Weld bead width at the interface (WI).

The selected input process parameters included:

• Laser power (P): 2000–3000 W;
• Welding speed (S): 40–70 mm/s;
• Laser beam diameter (D): 300–490 μm;
• Gap between sheets (G): 0.05–0.15 mm.

These parameters were chosen based on their dominant influence on weld geometry, as identified through experimental studies and numerical simulations.

The dataset used to train the ANN model was generated from experimental data collected from laser welding trials and validated FEM simulations, which provided additional data points across a broader range of welding conditions. Since experimental investigations are often constrained by cost and time, the validated FEM model was used to generate additional synthetic data, extending the dataset and enhancing the ANN’s learning capability. This approach ensured that the model was trained on a diverse set of welding conditions, leading to more robust and reliable predictions.

To enhance the model’s accuracy and generalization, the following preprocessing steps were applied:

• Data normalization was performed to standardize input variables, ensuring uniform weighting of parameters;
• The dataset was split into 80% training and 20% validation to assess model performance;
• A six-fold cross-validation strategy was employed to minimize overfitting and improve robustness.

A multi-layer perceptron (MLP) architecture was selected for the ANN model due to its capability in capturing complex, nonlinear relationships between input parameters and weld geometry. The network configuration consisted of:

• Input layer: four neurons (one for each input parameter: P, S, D, G);
• Hidden layer: A single layer containing 2 × p + 1 neurons (p being the number of input variables), optimized to balance complexity and computational efficiency;
• Output layer: three neurons (one for each predicted weld characteristic: DOP, WS, WI).

The model was trained using the Levenberg–Marquardt backpropagation algorithm, which is well-suited for fast and precise learning in nonlinear regression problems. Training was performed iteratively, with the network weights adjusted to minimize prediction errors.

Following training, the ANN model was tested on an independent dataset to verify its predictive accuracy. The results were compared against experimental measurements to assess the ANN’s capability in replacing FEM simulations while maintaining predictive reliability. Detailed information of the ANN modeling is presented in [24].

4.2. Modeling Evaluation

The performance of the developed ANN-based predictive model was evaluated by comparing its predictions with both experimental measurements and FEM-generated data. The accuracy of the model was assessed using statistical metrics, including the MAPE, the RMSE, and the R². These measures provided insight into the reliability and predictive capability of the ANN model across varying welding conditions. The dataset was divided into training and validation subsets, with 80% of the data used for training and 20% reserved for validation. Additionally, a six-fold cross-validation technique was employed to prevent overfitting and enhance model generalization.

The ANN model demonstrated a high correlation with actual weld bead geometry, effectively capturing the nonlinear relationships between welding parameters and weld characteristics. The coefficient of determination (R²) exceeded 95% for depth of penetration (DOP) and weld bead width at the surface (WS), while the weld bead width at the interface (WI) showed a slightly lower R² value of 92%. The MAPE values remained below 7% for all weld characteristics, confirming the model’s ability to produce precise predictions across various welding conditions. The RMSE values indicated minimal deviation between predicted and actual values, further validating the ANN model’s reliability. A summary of the ANN model’s performance is provided in

Table 2. Validation metrics for numerical model predictions.

Parameter	R2 (%)	MAPE (%)	RMSE (%)
DOP	95.3	6.2	2.9
WS	97.1	2.8	1.5
WI	92.0	6.9	3.3

, presenting the error metrics for each weld characteristic.

A sensitivity analysis was also conducted to assess the influence of individual welding parameters on the ANN predictions. The results indicated that welding speed had the most significant effect on DOP, contributing to over 56% of its variation. Laser power was identified as the dominant factor influencing WS, accounting for 47% of its variation. The WI predictions exhibited a combined dependence on welding speed (45%) and laser power (28%), while beam diameter and gap size played minor roles. These findings align with both experimental observations and numerical simulations, reinforcing the robustness of the ANN-based predictive model.

Overall, the ANN model demonstrated its capability to accurately and efficiently predict weld bead geometry in laser overlap welding of low-carbon galvanized steel. Its ability to generalize across different welding conditions, while significantly reducing computational time compared to FEM simulations, makes it a valuable tool for process optimization in industrial applications. By replacing time-intensive FEM simulations with a data-driven approach, the ANN model provides a rapid and reliable method for estimating weld characteristics, enabling real-time process control and parameter optimization.

5. Conclusions

This study developed an ANN-based predictive model for estimating weld bead geometry in laser overlap welding of low-carbon galvanized steel. The ANN model was trained using a combination of experimental data and validated FEM simulations, allowing it to accurately predict DOP, WS, and WI under varying welding conditions. The results demonstrated a high correlation between ANN predictions and experimental measurements, with R² values exceeding 95% for WS and DOP, and 92% for WI. The ANN model consistently maintained a mean error below 7%, confirming its reliability and precision.

Compared to FEM, ANN provided real-time predictions while maintaining similar accuracy, making it a more practical tool for industrial applications. The comparison between ANN, FEM, and experimental data confirmed the model’s capability to generalize across different welding conditions with minimal deviations. These findings highlight the potential of ANN models as efficient, data-driven alternatives to computationally expensive FEM simulations for weld geometry prediction.

It is important to note the application limits of the developed ANN model. The model is valid within the range of process parameters used during training, including laser power, welding speed, beam diameter, and gap size. It is specifically tailored for laser overlap welding of galvanized low-carbon steel in a lap joint configuration using 1 mm and 2 mm thick sheets. The model assumes homogeneous and isotropic material properties and does not explicitly account for microstructural changes or defect mechanisms such as porosity or cracking. As such, predictions made outside the trained parameter space or for different material systems should be interpreted with caution.

Future work could focus on enhancing the ANN model by incorporating additional welding process parameters, exploring deep learning approaches for improved prediction accuracy, and integrating real-time monitoring data for adaptive control in industrial applications.