Bak, C., Zahle, F., Bitsche, R., Kim, T., Yde, A., Henriksen, L. C., Natarajan, A., and Hansen, M. H.: Description of the DTU 10 MW Reference Wind Turbine, Tech. rep., DTU Wind Energy, Report-I-0092, 2013.
a,
b,
c,
d
Balzani, C., Noever-Castelos, P., and Wentingmann, M.: Finite element analysis and failure prediction of adhesive joints in wind turbine rotor blades, in: Proceedings of the 6th European Conference on Computational Mechanics and the 7th European Conference on Computational Fluid Dynamics, edited by: Owen, R., de Borst, R., Reese, J., and Pearce, C., CIMNE, 3779–3790, ISBN 9788494731167, 2018. a
Bangaru, A. K., Miao, X.-Y., Sørensen, B. F., and Chen, X.: Prediction of crack growth at trailing edge bondlines of a wind turbine rotor blade for the assessment of remaining service life, IOP Conf. Ser.-Mat. Sci., 1293, 012037,
https://doi.org/10.1088/1757-899X/1293/1/012037, 2023.
a
Beber, V. C., Fernandes, P., Schneider, B., Brede, M., and Mayer, B.: Fatigue lifetime prediction of adhesively bonded joints: An investigation of the influence of material model and multiaxiality, Int. J. Adhes. Adhes., 78, 240–247, 2017.
a,
b
Beltrami, E.: Sulle condizioni di resistenza dei corpi elastici, Il Nuovo Cimento, 18, 145–155, 1885. a
Bishop, J. E.: Characterizing the non-proportional and out-of-phase extent of tensor paths, Fatigue Fract. Eng. M., 23, 1019–1103, 2000.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k
Boopathi, K., Mishnaevsky Jr., L., Sumantraa, B., Premkumar, S. A., Thamodharan, K., and Balaraman, K.: Failure mechanisms of wind turbine blades in India: Climatic, regional, and seasonal variability, Wind Energy, 25, 968–979,
https://doi.org/10.1002/we.2706, 2022.
a
Chen, X., Berring, P., Madsen, S. H., Branner, K., and Semenov, S.: Understanding progressive failure mechanisms of a wind turbine blade trailing edge section through subcomponent tests and nonlinear FE analysis, Compos. Struct., 214, 422–438,
https://doi.org/10.1016/j.compstruct.2019.02.024, 2019a.
a,
b
Chen, X., Haselbach, P. U., Branner, K., and Madsen, S. H.: Effects of different material failures and surface contact on structural response of trailing edge sections in composite wind turbine blades, Compos. Struct., 226, 111306,
https://doi.org/10.1016/j.compstruct.2019.111306, 2019b.
a,
b
Christensen, R. M.: A two-property yield, failure (fracture) criterion for homogeneous, isotropic materials, J. Eng. Mater.-T. ASME, 126, 45–52, 2004. a
de Castro, J. T. P. and Meggiolaro, M. A.: Fatigue Design Techniques Under Real Service Loads, Volume II – Low-Cycle and Multiaxial Fatigue, CreateSpace Independent Publishing Platform, 1st edn., ISBN 9781530797042, 2016. a
Deng, Q.-Y., Zhu, S.-P., He, J.-C., Li, X.-K., and Carpinteri, A.: Multiaxial fatigue under variable amplitude loadings: review and solutions, International Journal of Structural Integrity, 13, 349–393, 2022. a
Deng, Q.-Y., Zhu, S.-P., Niu, X., Lesiuk, G., Macek, W., and Wang, Q.: Load path sensitivity and multiaxial fatigue life prediction of metals under non-proportional loadings, Int. J. Fatigue, 166, 107281,
https://doi.org/10.1016/j.ijfatigue.2022.107281, 2023.
a
DNV GL: DNVGL-ST-0376 – Rotor blades for wind turbines,
https://www.dnv.com/energy/standards-guidelines/dnv-st-0376-rotor-blades-for-wind-turbines/ (last access: 1 July 2025), 2015.
a,
b,
c
Eder, M., Bitsche, R., Nielsen, M., and Branner, K.: A practical approach to fracture analysis at the trailing edge of wind turbine rotor blades, Wind Energy, 17, 483–497,
https://doi.org/10.1002/we.1591, 2014.
a
Eder, M. A. and Bitsche, R. D.: Fracture analysis of adhesive joints in wind turbine blades, Wind Energy, 18, 1007–1022,
https://doi.org/10.1002/we.1744, 2015.
a
Eder, M. A., Semenov, S., and Sala, M.: Multiaxial Stress Based High Cycle Fatigue Model for Adhesive Joint Interfaces, in: Computational and Experimental Simulations in Engineering – Proceedings of ICCES2019, Mechanisms and Machine Science, vol. 75, edited by: Okada, H. and Atluri, S., Springer, Cham, 621–632,
https://doi.org/10.1007/978-3-030-27053-7_53, 2020.
a
Endo, T., Mitsunaga, K., Takahashi, K., Kobayashi, K., and Matsuishi, M.: Damage evaluation of metals for random or varying loading – three aspects of rain flow method, Mech. Beh. M., 1, 371–380, 1974. a
Fan, J., Vassilopoulos, A. P., and Michaud, V.: Mode I fracture of thick adhesively bonded GFRP composite joints for wind turbine rotor blades, Compos. Struct., 327, 117705,
https://doi.org/10.1016/j.compstruct.2023.117705, 2024.
a
Fatemi, A. and Shamsaei, N.: Multiaxial fatigue: An overview and some approximation models for life estimation, Int. J. Fatigue, 33, 948–958, 2011. a
Gilat, A., Goldberg, R. K., and Roberts, G. D.: Strain Rate Sensitivity of Epoxy Resin in Tensile and Shear Loading, NASA, Springfield, NASA/TM—2005-213595,
https://ntrs.nasa.gov/api/citations/20050179433/downloads/20050179433.pdf (last access: 1 July 2025), 2005.
a,
b
Haselbach, P. U. and Branner, K.: Effect of Trailing Edge Damage on Full-Scale Wind Turbine Blade Failure, in: Proceedings of the 20th International Conference on Composite Materials (ICCM20), Copenhagen, Denmark, 19–24 July 2025,
http://www.iccm20.org/proceedings/ (last access: 20 June 2025), 2015. a
Haselbach, P. U., Eder, M. A., and Belloni, F.: A comprehensive investigation of trailing edge damage in a wind turbine rotor blade, Wind Energy, 19, 1871–1888,
https://doi.org/10.1002/we.1956, 2016.
a
Hu, W., Choi, K. K., Zhupanska, O., and Buchholz, J. H. J.: Integrating variable wind load, aerodynamic, and structural analyses towards accurate fatigue life prediction in composite wind turbine blades, Struct. Multidiscip. O., 53, 375–394,
https://doi.org/10.1007/s00158-015-1338-5, 2016.
a
Hu, W., Zhao, W., Wang, Y., Liu, Z., Cheng, J., and Tan, J.: Design optimization of composite wind turbine blades considering tortuous lightning strike and non-proportional multi-axial fatigue damage, Eng. Optimiz., 52, 1868–1886,
https://doi.org/10.1080/0305215X.2019.1690649, 2020.
a
Hu, Y., Xia, Z., and Ellyin, F.: Deformation behavior of an epoxy resin subject to multiaxial loadings. Part I: Experimental investigations, Polym. Eng. Sci., 43, 721–733, 2003.
a,
b
International Electrotechnical Commission: Wind energy generation system – Part 1: Design requirements, International Standard No. 61400-1:2019,
https://webstore.iec.ch/en/publication/26423 (last access: 20 June 2025), 2019. a
Itoh, T., Sakane, M., Ohnami, M., and Socie, D. F.: Nonproportional Low Cycle Fatigue Criterion for Type 304 Stainless Steel, J. Eng. Mater.-T. ASME, 117, 285–292, 1995.
a,
b,
c,
d,
e
Jager, D. and Andreas, A.: NREL National Wind Technology Center (NWTC): M2 Tower, Boulder, Colorado, Measurement and Instrumentation Data Center (MIDC) of NREL (National Renewable Energy Laboratory) [data set],
https://doi.org/10.7799/1052222, 1996.
a
Jørgensen, J. B., Sørensen, B. F., and Kildegaard, C.: The effect of residual stresses on the formation of transverse cracks in adhesive joints for wind turbine blades, Int. J. Solid. Struct., 163, 139–156,
https://doi.org/10.1016/j.ijsolstr.2018.12.020, 2019.
a
Katsaprakakis, D. A., Papadakis, N., and Ntintakis, I.: A Comprehensive Analysis of Wind Turbine Blade Damage, Energies, 14, 5974,
https://doi.org/10.3390/en14185974, 2021.
a
Kuhn, M.: Non-proportional fatigue by example of fiber-reinforced rotor blade adhesive, PhD thesis, Leibniz University Hannover, Institute for Wind Energy Systems,
https://doi.org/10.15488/15770, 2023.
a
Kuhn, M., Manousides, N., Antoniou, A., and Balzani, C.: Effects of non-proportionality and tension–compression asymmetry on the fatigue life prediction of equivalent stress criteria, Fatigue Fract. Eng. M., 46, 3161–3178, 2023.
a,
b,
c,
d
Lahuerta, F., Koorn, N., and Smissaert, D.: Wind turbine blade trailing edge failure assessment with sub-component test on static and fatigue load conditions, Compos. Struct., 204, 755–766,
https://doi.org/10.1016/j.compstruct.2018.07.112, 2018.
a,
b
Lee, Y.-L. and Tjhung, T.: Chapter 3 – Rainflow Counti
ng Techniques, in: Metal Fatigue Analysis Handbook – Practical problem-solving techniques for computer-aided engineering, edited by: Lee, Y.-L., Barkey, M. E., and Kang, H.-T., Elsevier Inc., 89–112,
https://doi.org/10.1016/B978-0-12-385204-5.00003-3, 2012.
a
Liu, X., Lu, C., Liang, S., Godbole, A., and Chen, Y.: Vibration-induced aerodynamic loads on large horizontal axis wind turbine blades, Appl. Energ., 185, 1109–1119, 2017. a
Manolas, D. I., Riziotis, V. A., and Voutsinas, S. G.: Assessing the Importance of Geometric Nonlinear Effects in the Prediction of Wind Turbine Blade Loads, J. Comput. Nonlin. Dyn., 10, 041008,
https://doi.org/10.1115/1.4027684, 2015.
a
Meggiolaro, M. A. and de Castro, J. T. P.: An improved multiaxial rainflow algorithm for non-proportional stress or strain histories – Part I: Enclosing surface methods, Int. J. Fatigue, 42, 217–226, 2012. a
Meggiolaro, M. A. and de Castro, J. T. P.: Prediction of non-proportionality factors of multiaxial histories using the Moment Of Inertia method, Int. J. Fatigue, 61, 151–159, 2014.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k,
l,
m,
n,
o,
p
Meggiolaro, M. A., de Castro, J. T. P., and Wu, H.: On the use of tensor paths to estimate the nonproportionality factor of multiaxial stress or strain histories under free-surface conditions, Acta Mech., 227, 3087–3100, 2016.
a,
b
Noever Castelos, P. and Balzani, C.: The impact of geometric non-linearities on the fatigue analysis of trailing edge bond lines in wind turbine rotor blades, J. Phys. Conf. Ser., 749, 012009,
https://doi.org/10.1088/1742-6596/749/1/012009, 2016b.
a,
b,
c
Noever-Castelos, P., Haller, B., and Balzani, C.: Validation of a modeling methodology for wind turbine rotor blades based on a full-scale blade test, Wind Energ. Sci., 7, 105–127,
https://doi.org/10.5194/wes-7-105-2022, 2022.
a
Popko, W., Thomas, P., Sevinc, A., Rosemeier, M., Bätge, M., Braun, R., Meng, F., Horte, D., Balzani, C., Bleich, O., Daniele, E., Stoevesandt, B., Wentingmann, M., Polman, J. D., Leimeister, M., Schürmann, B., and Reuter, A.: Reference Wind Turbine IWT-7.5-164 Rev 4, Tech. rep., Fraunhofer Institute for Wind Energy Systems IWES, Bremerhaven, Germany,
https://doi.org/10.24406/IWES-N-518562, 2018.
a,
b,
c
Rosemeier, M.: Engineering approach for predicting tunneling crack initiation in trailing-edge adhesive joints of wind turbine blades under mechanical fatigue and thermal residual stresses, PhD thesis, TU Berlin, FG Luftfahrzeugbau und Leichtbau, Institute of Aeronautics and Astronautics,
https://doi.org/10.14279/depositonce-19144, 2024.
a
Rosemeier, M., Alexander, K., Bardenhagen, A., and Antoniou, A.: Tunneling crack initiation in trailing-edge bond lines of wind-turbine blades, AIAA J., 57, 5462–5474,
https://doi.org/10.2514/1.J058179, 2019a.
a,
b
Rosemeier, M., Krimmer, A., Bardenhagen, A., and Antoniou, A.: Fatigue impact of mechanical and thermal residual stresses on the trailing edge bond line of wind turbine blades, in: AIAA Scitech 2019 Forum, San Diego, California, USA, 7–11 January 2019, 1–13,
https://doi.org/10.2514/6.2019-0246, 2019b.
a,
b
Rosemeier, M., Gebauer, T., and Antoniou, A.: A practical approach for the peel stress prediction in the trailing-edge adhesive joint of wind turbine blades, IOP C. Ser.-Mat. Sci., 942, 012026,
https://doi.org/10.1088/1757-899X/942/1/012026, 2020.
a
Rosemeier, M., Gebauer, T., and Antoniou, A.: Sub-component versus full wind turbine blade structure: Influence of manufacture-induced thermal residual stresses on crack initiation in adhesive joints, in: 20th European Conference on Composite Materials (ECCM20), 26–30 June, Lausanne, Switzerland, Zenodo [data set],
https://doi.org/10.5281/zenodo.6786885, 2022a.
a,
b
Rosemeier, M., Melcher, D., Krimmer, A., Wroblewski, W., and Antoniou, A.: Validation of crack initiation model by means of cyclic full-scale blade test, J. Phys. Conf. Ser., 2265, 032045,
https://doi.org/10.1088/1742-6596/2265/3/032045, 2022b.
a,
b,
c,
d
Rubiella, C., Hessabi, C. A., and Fallah, A. S.: State of the art in fatigue modelling of composite wind turbine blades, Int. J. Fatigue, 117, 230–245,
https://doi.org/10.1016/j.ijfatigue.2018.07.031, 2018.
a
Rychlik, I.: A new definition of the rainflow cycle counting method, Int. J. Fatigue, 9, 119–121, 1987. a
Schleicher, F.: Der Spannungszustand an der Fließgrenze (Plastizitätsbedingung), J. Appl. Math. Mech., 6, 199–216, 1926. a
Socie, D. F. and Marquis, G. B.: Multiaxial fatigue, Society of Automotive Engineers, Warrendale, Pennsylvania, ISBN 9780768004533, 2000.
a,
b,
c,
d,
e
Stassi-D’Alia, F.: Flowand fracture of materials according to a new limiting conditionof yelding, Meccanica, 2, 178–195, 1967. a
Stephens, R. I., Fatemi, A., Stephens, R. R., and Fuchs, H. O.: Metal fatigue in engineering, John Wiley & Sons, New York, 2nd edn., ISBN 9780471510598, 2001. a
Söker, H.: 2 – Loads on wind turbine blades, in: Advances in Wind Turbine Blade Design and Materials, edited by: Brøndsted, P. and Nijssen, R. P. L., Woodhead Publishing, Philadelphia, 29–58,
https://doi.org/10.1533/9780857097286.1.29, 2013.
a
Tessmer, J., Montano Rejas, Z. M., Rose, M., Daniele, E., Stoevesandt, B., Riemenschneider, J., Hölling, M., and Balzani, C.: SmartBlades2 – Bau, Test und Weiterentwicklung intelligenter Rotorblätter, Final Report,
https://doi.org/10.2314/KXP:178353785X, 2021 (in German).
a
van Kuik, G. A. M., Peinke, J., Nijssen, R., Lekou, D., Mann, J., Sørensen, J. N., Ferreira, C., van Wingerden, J. W., Schlipf, D., Gebraad, P., Polinder, H., Abrahamsen, A., van Bussel, G. J. W., Sørensen, J. D., Tavner, P., Bottasso, C. L., Muskulus, M., Matha, D., Lindeboom, H. J., Degraer, S., Kramer, O., Lehnhoff, S., Sonnenschein, M., Sørensen, P. E., Künneke, R. W., Morthorst, P. E., and Skytte, K.: Long-term research challenges in wind energy – a research agenda by the European Academy of Wind Energy, Wind Energ. Sci., 1, 1–39,
https://doi.org/10.5194/wes-1-1-2016, 2016.
a
van Kuik, G. A. M., Peinke, J., Nijssen, R., Lekou, D., Mann, J., Sørensen, J. N., Ferreira, C., van Wingerden, J. W., Schlipf, D., Gebraad, P., Polinder, H., Abrahamsen, A., van Bussel, G. J. W., Sørensen, J. D., Tavner, P., Bottasso, C. L., Muskulus, M., Matha, D., Lindeboom, H. J., Degraer, S., Kramer, O., Lehnhoff, S., Sonnenschein, M., Sørensen, P. E., Künneke, R. W., Morthorst, P. E., and Skytte, K.: Long-term research challenges in wind energy – a research agenda by the European Academy of Wind Energy, Wind Energ. Sci., 1, 1–39,
https://doi.org/10.5194/wes-1-1-2016, 2016.
a
Vassilopoulos, A. P.: Fatigue life prediction of wind turbine blade composite materials, in: Advances in Wind Turbine Blade Design and Materials, edited by: Brøndsted, P. and Nijssen, R. P., Woodhead Publishing Series in Energy, Chap. 8, Woodhead Publishing, 251–297, ISBN 978-0-85709-426-1,
https://doi.org/10.1533/9780857097286.2.251, 2013.
a
Veers, P., Dykes, K., Lantz, E., Barth, S., Bottasso, C. L., Carlson, O., Clifton, A., Green, J., Green, P., Holttinen, H., Laird, D., Lehtomäki, V., Lundquist, J. K., Manwell, J., Marquis, M., Meneveau, C., Moriarty, P., Munduate, X., Muskulus, M., Naughton, J., Pao, L., Paquette, J., Peinke, J., Robertson, A., Rodrigo, J. S., Sempreviva, A. M., Smith, J. C., Tuohy, A., and Wiser, R.: Grand challenges in the science of wind energy, Science, 366, eaau2027,
https://doi.org/10.1126/science.aau2027, 2019.
a
Veers, P., Bottasso, C. L., Manuel, L., Naughton, J., Pao, L., Paquette, J., Robertson, A., Robinson, M., Ananthan, S., Barlas, T., Bianchini, A., Bredmose, H., Horcas, S. G., Keller, J., Madsen, H. A., Manwell, J., Moriarty, P., Nolet, S., and Rinker, J.: Grand challenges in the design, manufacture, and operation of future wind turbine systems, Wind Energ. Sci., 8, 1071–1131,
https://doi.org/10.5194/wes-8-1071-2023, 2023.
a
von Mises, R.: Mechanik der festen Körper im plastisch-deformablen Zustand, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 4, 582–592, 1913. a
Wang, J., Huang, X., Wei, C., Zhang, L., Li, C., and Liu, W.: Failure analysis at trailing edge of a wind turbine blade through subcomponent test, Eng. Fail. Anal., 130, 105596,
https://doi.org/10.1016/j.engfailanal.2021.105596, 2021.
a
Wentingmann, M., Noever-Castelos, P., and Balzani, C.: An adaptive algorithm to accelerate thecritical plane identification for multiaxialfatigue criteria, in: Proceedings of the 6th European Conference on Computational Mechanics and the 7th European Conference on Computational Fluid Dynamics, edited by: Owen, R., de Borst, R., Reese, J., and Pearce, C., CIMNE, 3745–3754, ISBN 9788494731167, 2018.
a,
b
Wentingmann, M., Manousides, N., Antoniou, A., and Balzani, C.: Yield surface derivation for a structural adhesive based on multiaxial experiments, Polym. Test., 113, 107648,
https://doi.org/10.1016/j.polymertesting.2022.107648, 2022.
a
Wu, H., Qi, L., Qian, J., Cao, H., Shi, K., and Xu, J.: Experimental research on the compression failure of wind turbine blade trailing edge structure, J. Adhesion, 99, 1488–1507,
https://doi.org/10.1080/00218464.2022.2126313, 2023.
a
