⚡ electrical engineering

LEFM-Based Evaluation of Structural Stress Approaches for Fatigue Assessment of Welded CHS with Large Geometric Scale Differences

This study evaluates five structural stress approaches for assessing fatigue in welded circular hollow section joints with large geometric scale differences, finding that the Xiao–Yamada method aligns best with linear-elastic fracture mechanics references while revealing limitations in applying conventional extrapolation procedures to such geometries.

Original authors: Stefan Vogts, Jörg Baumgartner, Julian Unglaub, Klaus Thiele

Published 2026-11-06

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CC BY 4.0

Original authors: Stefan Vogts, Jörg Baumgartner, Julian Unglaub, Klaus Thiele

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

Offshore wind turbines stand as giants in the sea, their massive steel towers anchored to the ocean floor to capture the wind's energy. These structures are constantly battered by the rhythmic, relentless push and pull of waves and wind, a cycle of stress that can eventually cause metal to crack and fail. To keep these towers standing, engineers attach secondary structures, like small platforms for workers to board boats, directly onto the main tower. These attachments are welded on, creating a junction where two pieces of steel meet. The danger lies in the fact that the main tower is enormous, while the attached platform is relatively small. This stark difference in size creates a complex stress pattern at the weld, a hidden hotspot where fatigue cracks are most likely to begin. For decades, engineers have relied on standard rules to predict how long these joints will last, but those rules were written for joints where the connected parts are more similar in size. When the parts are vastly different, as they are in modern offshore wind farms, those old rules may no longer be accurate, potentially leaving structures vulnerable or forcing them to be built heavier than necessary.

A team of researchers set out to test whether the standard methods for checking these welded joints still work when the size difference is extreme. They focused on a specific type of connection where a smaller tube is welded to the side of a much larger tube, a configuration common in the secondary structures of wind turbines. To understand the true behavior of these joints, the team did not just rely on existing formulas. Instead, they built a vast library of digital models, simulating thousands of different joint shapes and sizes. They subjected these virtual joints to various forces, mimicking the real-world loads of wind and waves, and then calculated the stress at the weld using five different established methods. To see which method was truly telling the truth, they compared all five against a highly detailed computer model based on the physics of how cracks actually grow through metal. This physics-based model served as an independent referee, providing a baseline of what the fatigue life should be regardless of the calculation method used.

The researchers found that the choice of calculation method makes a significant difference, and that difference depends heavily on the shape of the joint and how it is being loaded. When they applied the standard rules used for plate structures or typical tubular joints, the results varied widely from the physics-based truth. These conventional methods, which estimate stress by looking at the surface of the metal a short distance away from the weld, struggled to capture the true stress state in these large-scale, mismatched connections. The location where the measurement is taken relative to the weld became a critical factor; because the geometry is so unusual, the standard measurement points sometimes landed in areas that did not reflect the actual danger zone. In contrast, two alternative methods performed much better. One of these methods, which looks at the stress just one millimeter below the surface of the metal along the path a crack would take, matched the physics-based reference almost perfectly. Another method, which calculates stress by balancing the forces and moments through the thickness of the metal, also showed strong agreement. The standard surface-extrapolation methods, however, showed much more scatter, meaning their predictions were less consistent and less reliable for these specific, large-scale joints.

The study also revealed that the factors controlling the stress are not the same for every situation. When the main tower itself is being bent or pulled, the stress at the weld is driven primarily by the ratio of the wall thicknesses and the slenderness of the attached arm. However, when the attached arm itself is being loaded, the story changes. In those cases, the stress depends on a complex mix of the thickness ratio, the relative diameters of the two tubes, and the slenderness of the main tower. The researchers discovered that these factors do not simply add up; they interact in non-linear ways, meaning that changing one dimension can have a surprising effect on the stress depending on the other dimensions. This complexity suggests that simply applying old formulas to these new, larger structures is risky. The standard rules, developed for joints where the parts are more comparable in size, do not automatically translate to the massive monopiles used in offshore wind.

Ultimately, the work highlights a gap in current engineering practice. The standard procedures for assessing fatigue in welded tubular joints are not directly transferable to the large-scale attachments found on modern offshore wind foundations. The researchers demonstrated that using the wrong method can lead to inconsistent safety assessments. The method that looks at the stress just below the surface provided the most consistent and reliable picture of the joint's fatigue life across all the different shapes and loads they tested. This finding suggests that for these specific, large-scale connections, engineers may need to move away from the traditional surface measurements and adopt approaches that better capture the subsurface stress gradients that drive crack growth. While the study was conducted using computer simulations and idealized weld shapes, the results provide a clear warning: the geometry of these massive offshore structures is unique, and the tools used to ensure their safety must be equally precise. Before these new insights can be written into design codes, they will need to be confirmed with physical tests on real welded joints, but the path forward is now much clearer.

Technical Summary: LEFM-Based Evaluation of Structural Stress Approaches for Fatigue Assessment of Welded CHS with Large Geometric Scale Differences

Problem Statement
Fatigue assessment of welded offshore structures, particularly monopile foundations with secondary attachments like boat landings, traditionally relies on hot-spot stress (HSS) approaches derived for standard tubular joints. However, these joints often exhibit pronounced geometric scale differences between the massive monopile shell and the relatively small attached braces. Such configurations frequently fall outside the applicability ranges of established recommendations (e.g., IIW, CIDECT, DNV), which are based on conventional tubular joint geometries. The direct transfer of these surface-extrapolation procedures to monopile attachments is uncertain, as the specific geometric parameters (small diameter ratios $\beta$ , large chord slenderness $\gamma_0$ ) may invalidate the underlying assumptions of current design codes. Consequently, there is a need to evaluate whether existing structural stress definitions can consistently account for the geometry-dependent fatigue response in these large-scale, single-sided welded circular hollow section (CHS) joints.

Methodology
The study employs a combined numerical and analytical framework to compare five structural stress approaches:

IIW Plate Extrapolation: Standard surface extrapolation for plate structures.
IIW/CIDECT and DNV-RP-C203 Tubular Extrapolation: Surface extrapolation methods specific to CHS joints, utilizing geometry-dependent reference points.
Xiao–Yamada (XY) 1 mm Stress Approach: Evaluation of normal stress 1 mm below the weld toe along the expected crack path.
Dong Structural Stress Method: Calculation of structural stress based on membrane and bending components derived from the through-thickness stress distribution.

The investigation utilizes a Design of Experiments (DoE) and Response Surface Modeling (RSM) framework. Linear-elastic finite element analyses (FEA) were conducted on a wide range of geometric parameters ( $\beta, \gamma_0, \gamma_1, \tau, \theta$ ) covering dimensions relevant to monopile attachments, including those extending beyond typical laboratory specimen scales. A screening DoE identified significant parameters, followed by a main DoE using a Central Composite Inscribed (CCI) design to derive RSMs for various loading conditions (axial, in-plane bending, out-of-plane bending) and evaluation paths (crown, saddle heel, saddle toe).

To provide an independent benchmark, an analytical Linear Elastic Fracture Mechanics (LEFM) model was developed. This model calculated fatigue life based on crack propagation (Paris law) using weight functions. The resulting fatigue lives were transformed into an equivalent nominal FAT class ( $\Delta\sigma_{C,nom,LEFM}$ ) at $2 \times 10^6$ cycles. This LEFM-derived value serves as a stress-definition-independent reference to assess how well each structural stress approach normalizes the geometry-dependent fatigue resistance.

Key Contributions and Results
The study quantifies the differences between the five stress approaches and their ability to correlate with the LEFM-based fatigue reference.

Method-Dependent Differences: Significant variations in Stress Concentration Factors (SCFs) were observed between approaches. These differences are not constant but depend heavily on the loading condition, evaluation position, and joint geometry. The largest deviations occurred for brace in-plane bending (IPB) at the crown position. Surface-extrapolation methods (IIW, CIDECT, DNV) generally yielded lower SCFs compared to the XY and Dong methods, with the XY approach showing the most pronounced increase for brace loading cases.
Correlation with LEFM Reference: The Xiao–Yamada (XY) method demonstrated the strongest agreement with the LEFM-based reference, achieving a coefficient of determination $R^2 = 0.999$ . The Dong method also showed high consistency ( $R^2 = 0.980$ ). In contrast, conventional surface-extrapolation approaches exhibited lower correlation coefficients (ranging from 0.946 to 0.955).
Residual Scatter: When LEFM-derived fatigue strengths were transformed to the structural stress level of each method, the XY approach resulted in the lowest residual scatter ( $T_\sigma = 1.07$ ), indicating the most consistent normalization of geometry-dependent effects. The Dong method followed ( $T_\sigma = 1.33$ ), while surface-extrapolation methods showed higher scatter ( $T_\sigma$ between 1.51 and 1.66).
Geometric Parameter Sensitivities: The governing geometric parameters vary significantly by loading mode:
- Chord Loading: Primarily influenced by the thickness ratio ( $\tau$ ) and brace slenderness ( $\gamma_1$ ).
- Brace Loading: Influenced by $\tau$ , chord slenderness ( $\gamma_0$ ), and diameter ratio ( $\beta$ ). Brace inclination ( $\theta$ ) was also significant for specific paths.
- The analysis revealed that these influences involve significant interaction and quadratic terms, suggesting that SCF responses cannot be adequately represented by independent linear parameter effects, especially for geometries outside conventional ranges.

Significance and Claims
The paper claims that the direct transfer of established CHS-based extrapolation procedures to monopile attachments with pronounced geometric scale differences is uncertain and may lead to inconsistent fatigue assessments. The study highlights that the Xiao–Yamada 1 mm stress approach and Dong's structural stress method offer superior consistency in capturing the geometry-dependent fatigue response compared to traditional surface-extrapolation methods for these specific large-scale joints.

The authors emphasize that their findings are conditional on the modeling assumptions, including the idealized AWS-oriented weld geometry, the fixed normalized chord length, and the specific assumptions of the analytical LEFM reference. They explicitly state that the reduced scatter observed for the XY and Dong methods indicates improved consistency with the adopted LEFM reference rather than definitive proof of superior fatigue-life prediction. Consequently, the authors assert that experimental validation on representative welded joints, ideally incorporating measured as-built weld geometries, remains necessary before these trends can be transferred to design practice. The study serves as a computational investigation to identify governing parameters and evaluate the suitability of different stress definitions, rather than proposing immediate code changes without further experimental verification.

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