Non-proportionality analysis of multi-axial fatigue stress histories in trailing edge adhesive joints of wind turbine rotor blades

Balzani, Claudio; Noever Castelos, Pablo

doi:https://doi.org/10.5194/wes-10-1249-2025

Articles | Volume 10, issue 7

https://doi.org/10.5194/wes-10-1249-2025

© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/wes-10-1249-2025

© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 10, issue 7

Research article

|

07 Jul 2025

Research article |

| 07 Jul 2025

Non-proportionality analysis of multi-axial fatigue stress histories in trailing edge adhesive joints of wind turbine rotor blades

Claudio Balzani and Pablo Noever Castelos

Download

Final revised paper (published on 07 Jul 2025)
Preprint (discussion started on 15 Jan 2024)

Interactive discussion

Status: closed

RC1:
'Comment on wes-2023-167', Alexander Krimmer, 31 Jan 2024

The manuscript presents a combined approach to determine the non-proportionality factor for fatigue loads in bond lines of wind turbine rotor blades. It thereby enables to account for both, deviatoric and hydro-static stress contributions. The method is compared to available approaches that are the basis for this combined method and shows very good results. Afterwards the method is applied to three different rotor blade structures available in the literature and the non-proportionality factors are compared and assessed.
To my understanding, there are two fundamental outcomes, that can be highlighted more prominently.
1.) Ignoring non-proportionality seems to be making errors on the conservative side.
2.) Accounting for the S/N curve exponents of the applied adhesives, the relation between the dominant (z-axis) stresses and the other stresses makes the z-axis stresses by far the dominant design relevant contributions. Therefore it is expected that accounting for the non-proportionality within these three designs may have little to no influence on the final fatigue damage.
Anyhow, this is a significant learning for future rotor blade designs!
Detailed comments can be found in the attached *.pdf document.

Citation: https://doi.org/10.5194/wes-2023-167-RC1
- AC2: 'Reply on RC1', Claudio Balzani, 07 May 2024
  
  Dear Alexander Krimmer,
  Thank you very much for taking the time for reviewing our manuscript and submitting your comments. We have tried to address all your comments thoroughly and have uploaded the review documents in the meanwhile. Please find our response, that you will also receive via the publisher, in the enclosed PDF file.
  Best regards,
  Claudio Balzani
  
  Citation: https://doi.org/10.5194/wes-2023-167-AC2
RC2:
'Comment on wes-2023-167', Anonymous Referee #2, 18 Feb 2024
The analysis presented in this paper is well worth investigation and adds new knowledge for wind turbine blade designers. However, a major revision to the paper is required, due to the structure of the paper and some investigations that are missing. The specific changes requested are:
The results in this paper are based on a finite element analysis of a wind turbine blade. However, there are very little details of this model and no validation. Both of these should be added to demonstrate that the authors are starting with an accurate model.

From the outset of the paper, the authors acknowledge that “The results do not reveal any correlation between the degree of non-proportionality and the blade size. General conclusions are hard to draw, as the blade response does not only depend on the turbine size, but also on the blade design philosophy.” However, a very limited selection of blade (3) are used, two of which are of similar length. Therefore, I would suggest adding more blades to the analysis in order to draw better conclusions for the trailing edge design consideration that is presented in the paper.

The conclusion largely summarises the work carried out in the paper. A paragraph on the impact of the study should be added to Section 4.

Although much of these details are included throughout the paper, please add a methodology section that clearly outlines the study aim, objectives, materials, methods and overall methodology.

Section 3 is 8 pages long – please divide it into subsections to make it easier for the reader.
Citation: https://doi.org/10.5194/wes-2023-167-RC2
- AC3: 'Reply on RC2', Claudio Balzani, 07 May 2024
  
  Dear referee,
  Thank you very much for taking the time to review our manuscript and submitting your comments. We have tried to address all your comments thoroughly and have uploaded the review documents in the meanwhile. Please find our response, that you will also receive via the publisher, in the enclosed PDF file.
  Best regards,
  Claudio Balzani
  
  Citation: https://doi.org/10.5194/wes-2023-167-AC3
AC1: 'Comment on wes-2023-167', Claudio Balzani, 15 Apr 2024

Dear Madam or Sir,
Thank you very much to all reviewers and editors for the professional, detailed and yet fast review of our manuscript. We are very grateful for your work and the consideration of our manuscript for the Wind Energy Science journal. Your valuable contributions helped to improve the manuscript and to better present its content.
We prepared responses to each of your concerns in the supplementary file and look forward to the upcoming steps.
The Authors:

Claudio Balzani

Pablo Noever Castelos

Citation: https://doi.org/10.5194/wes-2023-167-AC1

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Claudio Balzani on behalf of the Authors (07 May 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (13 May 2024) by Julie Teuwen

RR by Anonymous Referee #3 (17 Jun 2024)

RR by Anonymous Referee #4 (23 Jun 2024)

Suggestions for revision or reasons for rejection

The submitted work has some minor and major deficiencies which must be clarified before considering it for publication:

1. The document does not adhere to a standard paper format, mixing different parts. Thus, segments of Chapter 3 should be included in the introduction, while the mathematical analysis should be placed under the Methodology section.
Moreover, the introductory paragraph seems misleading, as it does not accurately convey the paper's focus. The paper's essence is not about the importance of non-proportionality on the material level, which is majorly discussed in the intro; instead, it focuses on the non-proportionality of wind turbine blades and derives an equivalent value for their life span. Thus, the intro must focus on state-of-the-art research on the latest topic.
Additionally, it is used to add the motivation at the end of the introductory paragraph so the reader can follow what the research is about.
Thus, a major restructuring is recommended for chapters 1, 2, and 3.

2. Estimating the manufacturing-induced residual stresses is essential for the bond line stress analysis. Neglecting them will result in erroneous assumptions and conclusions, diverging from the material performance in the real structure and adding complexity which can be misleading.

3. Figure 7. The results of the finite element (FE) analysis should be interpreted with caution. Using the boundary elements of the bond line for stress analysis might affect the conclusions, as the stresses in these regions do not converge with a finer mesh. To implement the results accurately, a few rows of elements should be discarded. Similar cases can be found in the literature.

4. To the reviewer's knowledge, there is no literature evidence that the trailing edge adhesive cracks develop in an inclined plane other than the one transverse to the blade length. It is recommended to include photographic evidence or references that demonstrate a maximum stress plane different from the transverse plane.

Referee Report: PDF

Hide

ED: Reconsider after major revisions (08 Jul 2024) by Julie Teuwen

AR by Claudio Balzani on behalf of the Authors (26 Aug 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (02 Sep 2024) by Julie Teuwen

RR by Anonymous Referee #3 (16 Sep 2024)

RR by Anonymous Referee #5 (07 Jan 2025)

Suggestions for revision or reasons for rejection

SUMMARY

Reliable fatigue design tools are essential for blade design engineers. Generally, physically-based and validated analytical models are preferred over computationally inefficient models.
In this manuscript, the authors present the derivation of a non-proportionality (NP) factor that indicates the degree of NP in stress histories, meaning the extent to which stress components are out of phase. They claim that global criteria, such as Beltrami, do not conservatively capture stress exposure when the NP is high, i.e., highly out of phase. To this end, they analyzed the NP along the trailing-edge adhesive joint of two theoretical blade models and one actual built model. They conclude that, under certain wind speeds, the NP can be significant at specific span-wise positions along the blade. The designer should decide based on the NP whether to use a global criterion or a critical plane approach to evaluate fatigue stress exposure.
In the present state the manuscript highlights that there may be an issue when global criteria are used but unfortunately does not prove it, i.e., by demonstrating the impact of NP on damage.
According to the comments listed below, I need to suggest a major revision of the manuscript.

MAJOR COMMENTS

MAC.01 In order to significantly strengthen the manuscript, I strongly recommend proving the impact of the NP on the damage criterion. This could be achieved by conducting a relative comparison of NP hot spots in the blade models using a global criterion, such as Beltrami, alongside a critical plane criterion that accounts for NP. This would address the most important aspect of your study: whether it has been demonstrated that there is an issue when global criteria are employed without considering NPs in blades. Otherwise, your study appears incomplete, like a cliffhanger, and the reader cannot resolve this independently.
Please add the missing calculations to substantially increase the relevance of your study.

MAC.02 (Results) You present the NP factor results for the range of r/R = 0.45 to 0.9. However, some interesting areas of the blades were not analyzed, specifically those where high crack densities have been observed in the adhesive in commercial blades in the field (r/R = 0.2 to 0.65) [1] and during full-scale type certification testing (r/R = 0.25 to 0.5) [2]. These areas also include the positions of the largest fatigue stress exposure calculated for a commercial blade design at r/R = 0.35 [3].
Please extend the analysis to include these areas to enhance the representativity of your study.

MAC.03 (Methods) Assuming that you extract the stresses at or close to a corner of the inner adhesive edge, the concave shape of the inner adhesive contour (Fig. 7) seems unrealistic compared to what we observe in the field. As the trailing-edge bond-line is glued blindly, for example, for r/R > 0.37, the adhesive either gets squeezed inside the blade, forming a convex shape [5], or takes on an elliptical "clip" shape for the inner contour. The shape, particularly the fillet angle, can significantly impact the corner stress exposure and the signs of different stress components, as noted in [5]. From Fig. 7, it appears that the fillet angle varies from blade to blade and may also differ from radius to radius.
Please use a representative shape along the span and ensure that the fillet angle is consistent across the blades, so that the results are not biased by this variable.

MAC.04 (F6) Why do you show the stress histories for all blades at r/R = 0.77 and not for a location with high NP or expected high stress exposure? Wouldn't this be more useful as you focus on NPs as a tool for conservative blade design?

MAC.05 The structure of the manuscript seems poorly organized. Please: a) Combine C2, C3, and C4 into one Methods chapter. b) Split C5 into one Results chapter (only for results and observations) and one Discussion chapter (for interpretation of results). c) Move interpretations from the Conclusions into the Discussion chapter. d) Shorten the Conclusions to summarize only the most important points and what has already been addressed in previous chapters, and add future work. e) Shorten the Introduction, as it seems overly lengthy like a review article; I suggest removing sub-chaptering and lengthy explanations, while referring to relevant aspects for this manuscript. f) Remove repetitions and redundancies throughout the manuscript.

MAC.06 (Intro) Revise lead-lag, as it is not equal to edge-wise, see [4].

MINOR COMMENTS

MIC.01 Check the overall English quality, preferably by a lecturer.
MIC.02 Check the language for consistency, for example, ensure 'velocity' and 'speed' are used appropriately and consistently throughout the manuscript.

REFERENCES

[1] Rosemeier, M., Gebauer, T., and Antoniou, A., “Sub-component versus full wind turbine blade structure: Influence of manufacture-induced thermal residual stresses on tunneling crack initiation in adhesive joints”, in 20th European Conference on Composite Materials (ECCM20)–Composites Meet Sustainability, (Jun. 26, 2022–Jun. 30, 2022), assilopoulos, A. and Michaud, V., Eds., vol. 5, Lausanne, Switzerland, 2022. doi: 10.5075/epfl-298799_978-2-9701614-0-0.

[2] Rosemeier, M., Melcher, D., Krimmer, A., Wroblewski, W., and Antoniou, A., “Validation of crack initiation model by means of cyclic full-scale blade test”, in Journal of Physics: Conference Series–The Science of Making Torque from Wind (TORQUE 2022), IOP Publishing, vol. 2265, 2022, p. 032 045. doi: 10.1088/1742-6596/2265/3/032045.

[3] Rosemeier, M. and Saathoff, M., “Assessment of a rotor blade extension retrofit as a supplement to the lifetime extension of wind turbines”, Wind Energy Science, vol. 5, no. 3, pp. 897–909, 2020. doi: 10.5194/wes-5-897-2020.

[4] IEC, IEC 61400-23 - Wind Turbines Part 23: Full-scale Structural Testing of Rotor Blades, 1st ed. Geneva, Switzerland: International Electrotechnical Commission, 2014.

[5] Rosemeier, M., 2024. Engineering approach for predicting tunneling crack initiation in trailing-edge adhesive joints of wind turbine blades under mechanical fatigue and thermal residual stresses. doi: 10.14279/depositonce-19144

Hide

ED: Reconsider after major revisions (09 Jan 2025) by Julie Teuwen

AR by Claudio Balzani on behalf of the Authors (01 Mar 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (04 Mar 2025) by Julie Teuwen

ED: Publish as is (18 Mar 2025) by Athanasios Kolios (Chief editor)

AR by Claudio Balzani on behalf of the Authors (28 Mar 2025) Author's response Manuscript

Short summary

Wind turbine rotor blades consist of subcomponents that are glued together. Such connections are subject to fatigue loads. This paper analyzes the fatigue load characteristics of three different wind turbine rotor blades in trailing edge adhesive joints. It is shown that the fatigue loads have measurable degrees of non-proportionality and that the choice of the procedure to calculate the fatigue damage is crucial for designing reliable blades.