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Cited by 14Solar Thermal and Photovoltaic SystemsStructural Analysis of Composite MaterialsMechanical and Thermal Properties Analysis

On Residual Stresses and Reference Temperatures in Thermomechanical Simulations of Photovoltaic Modules Using the Finite Element Method

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Springer, Martin, Bosco, Nick·2022·IEEE Journal of Photovoltaics
DOI 10.1109/jphotov.2022.3143458
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Abstract

Thermomechanical simulation of photovoltaic (PV) modules using the finite element method (FEM) is a useful tool to evaluate module design features in terms of structural integrity, reliability, and durability. One of the main challenges in the numerical modeling of a PV module is the incorporation of residual stresses induced by the manufacturing process. Modeling assumptions and abstractions are necessary to limit the model complexity and reduce the computational time. However, oversimplifications and incorrect assumptions can lead to erroneous numerical results. Unfortunately, much simulation work still neglects process-induced stresses. This can lead to incorrect predictions of the stress–strain history and erroneous conclusions during the design process. Here, we review current modeling practices for incorporating process-induced stresses, and contrast numerical models that consider residual stresses with those that neglect them. We find that the simulation objective and available material properties dictate which process steps need to be modeled, and explore in depth the modeling of residual stresses induced by the lamination process. We demonstrate that a simplified cooldown procedure at the beginning of the simulation can increase the model accuracy and discuss appropriate choices for starting and reference temperatures in the finite element model.

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  • The experimental stress-strain data for copper agree well with the Ramberg-Osgood model.

    “As shown in Fig.4, the experimental data agree well with the Ramberg-Osgood model, with fit parameters reported in the literature to characterize copper[14][15].”

    From Stress evolution and degradation in zero-busbar silicon photovoltaic modules under thermal cycling: A finite element study (2026) · cites this paper as [15]

    The Geometry and Material Models section describes material models for glass, silicon, encapsulant, and backsheet, but does not report experimental copper stress–strain data or a Ramberg–Osgood fit. Searches for those terms found no passage in our copy that addresses the claimed agreement. (LLM, conf=0.75)

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Research works printed but not linked: 37

  1. J. N. Reddy, Introduction to the Finite Element Method, Fourth Edition. McGraw-Hill Education, 2019. [Online]. Available: https: //www.accessengineeringlibrary.com/content/book/9781259861901
  2. M. Springer and N. Bosco, "Environmental influence on cracking and debonding of electrically conductive adhesives," Engineering Fracture Mechanics, vol. 241, p. 107398, Jan. 2021. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0013794420309760
  3. P. Nivelle, J. A. Tsanakas, J. Poortmans, and M. Daenen, "Stress and strain within photovoltaic modules using the finite element method: A critical review," Renewable and Sustainable Energy Reviews, vol. 145, p. 111022, Jul. 2021. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1364032121003129
  4. D. C. Jordan, T. J. Silverman, J. H. Wohlgemuth, S. R. Kurtz, and K. T. VanSant, "Photovoltaic failure and degradation modes," Progress in Photovoltaics: Research and Applications, vol. 25, no. 4, pp. 318-326, 2017, eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/pip.2866. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/pip. 2866 · DOI · Paper page
  5. N. Bosco, M. Springer, J. Liu, S. Nalin Venkat, and R. H. French, "Employing Weibull Analysis and Weakest Link Theory to Resolve Crystalline Silicon PV Cell Strength Between Bare Cells and Reduced- and Full-Sized Modules," IEEE Journal of Photovoltaics, vol. 11, no. 3, pp. 731-741, May 2021, conference Name: IEEE Journal of Photovoltaics.
  6. M. Sander, S. Dietrich, M. Pander, M. Ebert, and J. Bagdahn, "Systematic investigation of cracks in encapsulated solar cells after mechanical loading," Solar Energy Materials and Solar Cells, vol. 111, pp. 82-89, Apr. 2013. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/S0927024812005612
  7. W. Weibull, "A statistical theory of strength of materials," Ingenioersvetenskapsakad.-Handl., vol. 151, p. 45 pp., 1939.
  8. F. W. Zok, "On weakest link theory and Weibull statistics," Journal of the American Ceramic Society, vol. 100, no. 4, pp. 1265-1268, Apr. 2017. [Online]. Available: https://onlinelibrary.wiley.com/doi/10.1111/ jace.14665 · DOI
  9. O. Borrero-L´ T. Vodenitcharova, M. Hoffman, and A. J. opez, Leo, "Fracture Strength of Polycrystalline Silicon Wafers for the Photovoltaic Industry," Journal of the American Ceramic Society, vol. 92, no. 11, pp. 2713-2717, 2009, eprint: https://ceramics.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1551- 2916.2009.03287.x. [Online]. Available: https://ceramics.onlinelibrary. wiley.com/doi/abs/10.1111/j.1551-2916.2009.03287.x · DOI
  10. L. Zhao, D. Nelias, D. Bardel, A. Maynadier, P. Chaudet, and B. Marie, "On the fracture of multi-crystalline silicon wafer," Journal of Physics D: Applied Physics, vol. 49, no. 47, p. 475601, Nov. 2016, publisher: IOP Publishing. [Online]. Available: https://doi.org/10.1088/0022-3727/49/47/475601 · DOI
  11. F. Kaule, M. Pander, M. Turek, M. Grimm, E. Hofmueller, and S. Schoenfelder, "Mechanical damage of half-cell cutting technologies in solar cells and module laminates," AIP Conference Proceedings, vol. 1999, no. 1, p. 020013, Aug. 2018, publisher: American Institute of Physics. [Online]. Available: https://aip.scitation.org/doi/10.1063/1.5049252 · DOI
  12. S. Schoenfelder, S. Meyer, and F. Kaule, "Benchmarking Mechanical Strength Data for New Solar Cell Concepts," 33rd European Photovoltaic Solar Energy Conference and Exhibition, pp. 276-279, Nov. 2017, iSBN: 9783936338478 Publisher: WIP. [Online]. Available: http://www.eupvsec-proceedings.com/proceedings?paper=42108
  13. M. W. Rowell, S. G. Daroczi, D. W. J. Harwood, and A. M. Gabor, "The Effect of Laminate Construction and Temperature Cycling on the Fracture Strength and Performance of Encapsulated Solar Cells," in 2018 IEEE 7th World Conference on Photovoltaic Energy Conversion (WCPEC) (A Joint Conference of 45th IEEE PVSC, 28th PVSEC 34th EU PVSEC), Jun. 2018, pp. 3927-3931, iSSN: 0160-8371.
  14. R. Samuel, S. Chandrasekar, T. N. Farris, and R. H. Licht, "Effect of Residual Stresses on the Fracture of Ground Ceramics," Journal of the American Ceramic Society, vol. 72, no. 10, pp. 1960-1966, 1989, eprint: https://ceramics.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1151- 2916.1989.tb06007.x. [Online]. Available: https://ceramics.onlinelibrary. wiley.com/doi/abs/10.1111/j.1151-2916.1989.tb06007.x · DOI
  15. C. Funke, E. Kullig, M. Kuna, and H. J. M¨ "Biaxial oller, Fracture Test of Silicon Wafers," Advanced Engineering Materials, vol. 6, no. 7, pp. 594-598, 2004, eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/adem.200400406. [On- line]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/adem. 200400406 · DOI
  16. C. Yang, F. Mess, K. Skenes, S. Melkote, and S. Danyluk, "On the residual stress and fracture strength of crystalline silicon wafers," Applied Physics Letters, vol. 102, no. 2, p. 021909, Jan. 2013, publisher: American Institute of Physics. [Online]. Available: https://aip.scitation.org/doi/10.1063/1.4776706 · DOI
  17. A. J. Beinert, P. Romer, A. Büchler, V. Haueisen, J. Aktaa, and U. Eitner, "Thermomechanical stress analysis of PV module production processes by Raman spectroscopy and FEM simulation," Energy Procedia, vol. 124, pp. 464-469, Sep. 2017. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1876610217342261
  18. S.-H. Schulze, M. Pander, S. Müller, C. Ehrich, and M. Ebert, "Influence of Vacuum Lamination Process on Laminate Properties -Simulation and Test Results," in 24th European Photovoltaic Solar Energy Conference, Hamburg, Germany, Sep. 2009, pp. 3367 -3372.
  19. W. J. R. Song, S. K. Tippabhotla, A. A. O. Tay, and A. S. Budiman, "Numerical Simulation of the Evolution of Stress in Solar Cells During the Entire Manufacturing Cycle of a Conventional Silicon Wafer Based Photovoltaic Laminate," IEEE Journal of Photovoltaics, vol. 8, no. 1, pp. 210-217, Jan. 2018, conference Name: IEEE Journal of Photovoltaics.
  20. S. K. Tippabhotla, W. J. R. Song, A. A. O. Tay, and A. S. Budiman, "Effect of encapsulants on the thermomechanical residual stress in the back-contact silicon solar cells of photovoltaic modules -A constrained local curvature model," Solar Energy, vol. 182, pp. 134-147, Apr. 2019. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/S0038092X19301549
  21. S. Dietrich, M. Pander, M. Sander, S. H. Schulze, and M. Ebert, "Mechanical and thermomechanical assessment of encapsulated solar cells by finite-element-simulation," in Reliability of Photovoltaic Cells, Modules, Components, and Systems III, vol. 7773. International Society for Optics and Photonics, Aug. 2010, p. 77730F. [Online]. Available: https://www.spiedigitallibrary.org/conference-proceedings-of- spie/7773/77730F/Mechanical-and-thermomechanical-assessment-of- encapsulated-solar-cells-by-finite/10.1117/12.860661.short · DOI
  22. M. Gonzalez, J. Govaerts, R. Labie, I. De Wolf, and K. Baert, "Thermo- mechanical challenges of advanced solar cell modules," in 2011 12th Intl. Conf. on Thermal, Mechanical Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, Apr. 2011, pp. 1/7-7/7.
  23. U. Eitner, M. Pander, S. Kajari-Schr¨ ontges, and H. Altenbach, oder, M. K¨ "Thermomechanics of PV Modules Including the Viscoelasticity of EVA," in 26th European Photovoltaic Solar Energy Conference and Exhibition, 2011, pp. 3267 -3269.
  24. S. Dietrich, M. Pander, M. Sander, and M. Ebert, "Mechanical Investigations on Metallization Layouts of Solar Cells with Respect to Module Reliability," Energy Procedia, vol. 38, pp. 488-497, Jan.
  25. Q. Z. Zhang, B. F. Shu, M. B. Chen, Q. B. Liang, C. Fan, Z. Q. Feng, and P. J. Verlinden, "Numerical investigation on residual stress in photovoltaic laminates after lamination," Journal of Mechanical Science and Technology, vol. 29, no. 2, pp. 655-662, Feb. 2015. [Online]. Available: https://doi.org/10.1007/s12206-015-0125-y · DOI
  26. P.-C. Hsiao, C. Chen, G. Chen, X. Zhang, A. Lennon, Z. Wang, N. Song, Y. Li, Z. Ouyang, C. Hall, C. Zhu, J. Lv, and C. Shen, "Comparative Models of Induced Thermomechanical Stress in Silicon Solar Cells Interconnected with Conventional Tabbing and Wire-Based Interconnection Methods," 2019 IEEE 46th Photovoltaic Specialists Conference (PVSC), 2019.
  27. G. Li, M. W. Akram, Y. Jin, X. Chen, C. Zhu, A. Ahmad, R. H. Arshad, and X. Zhao, "Thermo-mechanical behavior assessment of smart wire connected and busbarPV modules during production, transportation, and subsequent field loading stages," Energy, vol. 168, pp. 931-945, Feb. 2019. [Online]. Available: https://www.sciencedirect.com/science/article/ pii/S0360544218323685
  28. J. Y. Hartley, A. Maes, M. Owen-Bellini, T. Truman, E. Elce, A. Ward, T. Khraishi, and S. Roberts, "Effects of Photovoltaic Module Materials and Design on Module Deformation Under Load," in 2019 IEEE 46th Photovoltaic Specialists Conference (PVSC), Jun. 2019, pp. 0511-0516, iSSN: 0160-8371.
  29. J. Y. Hartley, "Effects of Frame Constraints on Internal Module Damage During Mechanical Load Testing," in 2021 IEEE 48th Photovoltaic Specialists Conference (PVSC), 2021.
  30. H. Li, D. Zhang, Z. Qin, L. Li, and E. Zhang, "Analysis of Deformation and Strength of Solar Module Support under Wind-Wave Load." Atlantis Press, Dec. 2015, pp. 1626-1629, iSSN: 2352-5401. [Online]. Available: https://www.atlantis-press.com/proceedings/icmse-15/25845821
  31. N. Bosco, T. J. Silverman, and S. Kurtz, "Climate specific thermomechanical fatigue of flat plate photovoltaic module solder joints," Microelectronics Reliability, vol. 62, pp. 124-129, Jul. 2016. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0026271416300609
  32. N. Bosco, M. Springer, and X. He, "Viscoelastic Material Characterization and Modeling of Photovoltaic Module Packaging Materials for Direct Finite-Element Method Input," IEEE Journal of Photovoltaics, vol. 10, no. 5, pp. 1424-1440, Sep. 2020, conference Name: IEEE Journal of Photovoltaics.
  33. H. F. Brinson and L. C. Brinson, Polymer Engineering Science and Viscoelasticity: An Introduction, 2nd ed. Springer US, 2015. [Online]. Available: https://www.springer.com/gp/book/9781489974846
  34. M. L. Williams, R. F. Landel, and J. D. Ferry, "The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids," Journal of the American Chemical Society, vol. 77, no. 14, pp. 3701-3707, Jul. 1955, publisher: American Chemical Society. [Online]. Available: https://doi.org/10.1021/ja01619a008 · DOI · Paper page
  35. M. Springer, J. Hartley, and N. Bosco, "Multiscale Modeling of Shingled Cell Photovoltaic Modules for Reliability Assessment of Electrically Conductive Adhesive Cell Interconnects," IEEE Journal of Photovoltaics, vol. 11, no. 4, pp. 1040-1047, Jul. 2021, conference Name: IEEE Journal of Photovoltaics.
  36. M. Fischer, M. Woodhouse, S. Herritsch, and J. Trube, "International Technology Roadmap for Photovoltaic (ITRPV)," VDMA, Tech. Rep. 13. Edition, 2021.
  37. M. Springer and N. Bosco, "Linear viscoelastic characterization of electrically conductive adhesives used as interconnect in photovoltaic modules," Progress in Photovoltaics: Research and Applications, vol. 28, no. 7, pp. 659-681, 2020. [Online]. Available: https: //onlinelibrary.wiley.com/doi/abs/10.1002/pip.3257 · DOI

Cited by

Sorted by citations

Authors
Springer, M., & Bosco, N.
Affiliations
National Laboratory of the Rockies (US)
ORCID
Venue
IEEE Journal of Photovoltaics
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2022-05
Volume
12
Issue
3
Pages
853-859
ISSN
  • 2156-3381 (ISSN-L)
  • 2156-3403
DOI
10.1109/jphotov.2022.3143458
OpenAlex
W4220992273
Cited by
14
References
0
Citations by year
2026: 4 · 2025: 5 · 2024: 2 · 2023: 1 · 2022: 2
FWCI
0.45
Type
journal article
Language
en
Open access
Licence
Locations
  • IEEE Journal of Photovoltaics (publishedVersion)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
Funders
  • National Renewable Energy Laboratory
  • Alliance for Sustainable Energy, LLC
  • U.S. Department of Energy (DE-AC36-08GO28308)
  • Durable Modules Consortium
  • Office of Energy Efficiency and Renewable Energy
  • Solar Energy Technologies Office
Topics
  • Physical Sciences › Energy › Renewable Energy, Sustainability and the Environment › Solar Thermal and Photovoltaic Systems
  • Physical Sciences › Engineering › Mechanical Engineering › Structural Analysis of Composite Materials
  • Physical Sciences › Engineering › Mechanical Engineering › Mechanical and Thermal Properties Analysis
Keywords
photovoltaic modules, residual stress, reference temperature, thermomechanical modeling, process-induced stress, lamination, cooling process, module reliability, structural integrity, finite element analysis

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