⚡ electrical engineering

Prediction of plastic deformation zone width in SAW-welded structural steel butt joints using numerical simulations and analytical models

This paper presents a methodology combining numerical simulations based on a Gaussian disc heat source model and analytical approximations to accurately predict the width of the plastic deformation zone in SAW-welded structural steel butt joints across varying plate thicknesses.

Original authors: Tomasz Urbański, Maciej Taczała

Published 2026-10-16

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CC BY 4.0

Original authors: Tomasz Urbański, Maciej Taczała

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

When massive steel structures like ship hulls or offshore oil platforms are built, they are assembled by fusing metal plates together with intense heat. This process, known as welding, creates a complex cycle of rapid heating and cooling. As the metal melts and then solidifies, it expands and contracts, generating invisible internal forces that can warp the entire structure. If these distortions are not predicted and managed, the final vessel might not fit together correctly, requiring expensive corrections or even compromising its safety. Engineers have long relied on powerful computer simulations to map out these thermal cycles, but running these detailed models for every single weld in a large ship is often too slow and computationally expensive. To solve this, researchers look for simpler ways to estimate the most critical part of the process: the width of the area where the metal has been permanently stretched or squashed by the heat. This zone, where the metal yields and changes shape irreversibly, dictates how much the rest of the structure will bend.

In a recent study, researchers from the West Pomeranian University of Technology in Szczecin, Poland, set out to create a faster, more reliable method for predicting the size of this deformed area in steel joints welded using a technique called submerged arc welding. Instead of running thousands of slow, detailed computer simulations for every possible scenario, the team used a statistical strategy called the design of experiments. They treated their computer model as a "black box," feeding it specific combinations of real-world variables—such as the amount of heat applied, the thickness of the steel plates, and the strength of the metal—to see how the output changed. They focused on two distinct categories of steel plates: thinner ones typical of ship hulls, ranging from 6 to 26 millimeters thick, and much thicker plates used in offshore structures, ranging from 30 to 50 millimeters. For each category, they ran a carefully planned series of simulations to gather data on how the plastic deformation zone responded to different conditions.

The researchers discovered that the size of this deformed zone is not random; it follows a predictable pattern driven primarily by two factors: the total heat energy fed into the weld and the thickness of the plate. By analyzing the results of their simulations, they developed two separate mathematical formulas, or regression models, that can estimate the width of the deformed zone with high accuracy. For the thinner shipbuilding plates, the model showed that the width of the affected area grows significantly as the heat input increases, but it is also heavily influenced by the thickness of the plate and the strength of the steel itself. For the thicker offshore plates, the relationship was slightly different; while heat input and thickness remained the dominant drivers, the initial temperature of the metal before welding—often called preheating—did not play a statistically significant role in determining the final width of the deformed zone within the range they tested. This finding suggests that while preheating is crucial for preventing cracks, it does not drastically change the overall size of the area that gets permanently distorted.

To ensure their new formulas were trustworthy, the team compared their predictions against both their own detailed computer simulations and older, established analytical methods found in engineering textbooks. The results were clear: the new models derived from their simulations were far more accurate than the traditional formulas. When tested against the complex computer data, the new equations predicted the width of the deformed zone with very small errors, often within a few millimeters. In contrast, the older methods sometimes missed the mark by a wide margin, particularly for the thinner plates where the conditions are most complex. The researchers noted that while their models are highly accurate within the specific ranges of heat and thickness they tested, they are not a universal fix for every possible welding scenario. They are best used as a rapid engineering tool to estimate the deformed zone for standard ship and offshore construction, allowing designers to anticipate distortions without waiting for days of computer processing time.

The study concludes that by separating the analysis into thin and thick plate categories and focusing on the most influential variables, engineers can now use these streamlined equations to make better, faster decisions during the design phase. This approach bridges the gap between slow, high-fidelity simulations and the need for quick, practical estimates in the real world. It confirms that while the physics of welding are complex, the resulting distortion can be tamed with the right predictive tools, ensuring that the massive steel structures of the maritime world remain straight, true, and safe.

Technical Summary: Prediction of Plastic Deformation Zone Width in SAW-Welded Structural Steel Butt Joints

Problem Statement
Accurate prediction of welding-induced distortions is critical for the design and fabrication of large-scale steel structures, particularly in marine and offshore applications. A fundamental prerequisite for simplified distortion prediction methods—specifically those based on inherent strain theory and equivalent loads—is the accurate determination of the width of the plastic deformation zone ( $b_{pl}$ ), also known as the inherent strain zone. While traditional thermo-elasto-plastic finite element analyses (TEP-FEM) offer high accuracy, their computational cost is often prohibitive for complex structures. Conversely, existing analytical models often rely on simplified assumptions that may not fully capture the complex thermomechanical interactions in Submerged Arc Welding (SAW) of structural steels. There is a need for robust, computationally efficient predictive relationships that account for specific technological and design parameters to estimate $b_{pl}$ accurately across different plate thickness ranges.

Methodology
The study employed a hybrid approach combining numerical simulations, statistical design of experiments (DOE), and regression analysis to develop predictive models for $b_{pl}$ .

Numerical Modeling: Transient thermal analyses were conducted using ANSYS with a surface Gaussian heat source model. The simulations covered two distinct plate thickness categories based on thermal behavior:
- Thin plates ( $b_{pl-tp}$ ): 6–26 mm, representative of marine ship hulls.
- Thick plates ( $b_{pl-hp}$ ): 30–50 mm, representative of offshore structures.
  The model utilized a non-uniform mesh with local refinement near the weld to capture temperature gradients accurately. The boundary of the plastic zone was defined by the "first yield temperature" ( $T_{Y1}$ ), a threshold where irreversible deformation begins, calculated based on material yield strength and thermal expansion properties.
Design of Experiments (DOE): A three-level Box–Behnken design (BBD) was implemented with 15 experimental runs for each plate group.
- Independent Variables for Thin Plates: Welding heat input ( $q_l$ ), base metal yield strength ( $\sigma_{YB}$ ), and plate thickness ( $h$ ).
- Independent Variables for Thick Plates: Welding heat input ( $q_l$ ), initial/preheating temperature ( $T_0$ ), and plate thickness ( $h$ ).
- Dependent Variable: The width of the plastic deformation zone ( $b_{pl}$ ).
Model Verification: The numerical model was verified against benchmark results from Grams [17] for ASTM A36 and AISI 316L materials, showing agreement within 8–10%.
Regression Analysis: Statistical analysis using STATISTICA software generated polynomial predictive equations. The significance of variables and interaction terms was evaluated at a 95% confidence level.
Comparative Analysis: The developed regression models were compared against existing analytical formulations by Ueda et al. [4, 5] and the numerical simulation results to assess predictive accuracy.

Key Contributions and Results

Development of Predictive Equations: The study derived two distinct regression models with high statistical validity ( $R^2_{adj} \approx 0.97$ for thin plates and $\approx 0.98$ for thick plates).
- Thin Plate Model ( $b_{pl-tp}$ ): Identified welding heat input ( $q_l$ ), plate thickness ( $h$ ), and yield strength ( $\sigma_{YB}$ ) as significant factors, including interaction terms ( $q_l \cdot \sigma_{YB}$ , $q_l \cdot h$ , $\sigma_{YB} \cdot h$ ) and a quadratic term for thickness ( $h^2$ ).
- Thick Plate Model ( $b_{pl-hp}$ ): Identified welding heat input ( $q_l$ ) and plate thickness ( $h$ ) as the dominant factors, with a significant interaction term ( $q_l \cdot h$ ) and a quadratic term for heat input ( $q_l^2$ ). Notably, preheating temperature ( $T_0$ ) was found to be statistically insignificant within the tested range (100–200°C) and was excluded from the final equation.
Dominant Factors: The analysis confirmed that welding heat input is the most influential parameter governing the plastic zone width in both groups, followed by plate thickness. The interaction between heat input and thickness was critical in both models.
Accuracy and Validation:
- The regression models demonstrated excellent agreement with the numerical simulation data. For thin plates, 12 out of 15 cases had prediction errors within 0–5 mm; for thick plates, all 15 cases were within this range.
- When compared to the analytical formulas of Ueda et al., the developed regression models showed substantially lower average prediction errors. The Ueda models exhibited larger discrepancies, particularly for thin plates under high heat input conditions (errors up to 32 mm in some cases), whereas the proposed models maintained errors generally below 10 mm.
Thermal Regime Transition: The study physically justified the classification of plates into thin (6–26 mm) and thick (30–50 mm) categories by observing a distinct transition in temperature distribution and heat flow mechanisms between 26 mm and 30 mm thicknesses.

Significance and Claims
The paper claims that the proposed methodology provides a reliable, computationally efficient alternative to full TEP-FEM simulations for estimating the width of the plastic deformation zone in SAW-welded structural steel butt joints. By integrating DOE with numerical simulations, the authors established that separate predictive models are necessary for thin and thick plates due to differing thermal behaviors.

The authors emphasize that these predictive relationships are particularly valuable for:

Simplified Distortion Prediction: Providing accurate input parameters (specifically the width of the inherent strain zone) for equivalent load and inherent strain-based distortion prediction methods, which are widely used in the preliminary design of marine and offshore structures.
Engineering Application: Offering a tool that balances accuracy and efficiency, suitable for the design and fabrication stages where rapid assessment is required.
Process Optimization: Enabling engineers to understand the sensitivity of the plastic zone width to key parameters like heat input and plate thickness without resorting to expensive simulations.

The study concludes that while the models are robust within the investigated experimental domain, extrapolation beyond the defined ranges of heat input and plate thickness should be avoided to maintain prediction accuracy. The work does not claim to replace detailed FEM for final design but rather to serve as a validated, physics-based approximation for the critical intermediate parameter of plastic zone width.

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