Advertisement

Optimal Design of Thickness and Young’s Modulus of Multi-Layered Foldable Structure Considering Bending Stress, Neutral Plane and Delamination under 2.5 mm Radius of Curvature

  • Yunsik Chae
  • Gee Sung Chae
  • Yeo O Youn
  • Sangwook Woo
  • Sang Hak Shin
  • Jongsoo Lee
Regular Paper
  • 7 Downloads

Abstract

The present study included the finite element analysis and optimal design of a multi-layered foldable structure (foldable display) to satisfy stress, neutral plane, and delamination requirements under a 2.5 mm radius of curvature (i.e., 2.5R) due to static bending load. Two bending types (inner folding and outer folding) were considered to accommodate the repeated bending, and their maximum stress values were evaluated. In the approximate optimization for the thickness and Young’s modulus of multiple film layers, the objective was to minimize the folding stress subjected to constraints on the positioning of the largest stress value to a neutral plane and prevention of delamination. Through the simultaneous change in thickness and Young’s modulus, the study identified the new position of a neutral axis so that a 16% improvement in the stress magnitude was obtained. A simulation-based T-peel test was also performed to analyze the fracture behavior of the adhesive, and the relation between the fracture toughness GC and separation load LP could be expressed as Lp = 12.687Gc. The optimized objective function value of von Mises stress was improved by 18% compared to an initial design, and constraints of the delamination indicator and positioning of the neutral plane were satisfied.

Keywords

Multi-layered foldable display 2.5R bending Neutral plane Delamination Simulation based t-peel test Thickness and young’s modulus optimization 

NOMENCLATURE

A

Cross-sectional area

Keff

Effective stiffness

h

neutral axis position

y

centroid position of non-symmetric section

e

strain

d

displacement

s

stress

Subscript

e

Engineering

t

Tensile test

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen, Y., Au, J., Kazlas, P., Ritenour, A., Gates, H., and McCreary, M., “Electronic Paper: Flexible Active-Matrix Electronic Ink Display,” Nature, Vol. 423, No. 6936, Paper No. 136, 2003.Google Scholar
  2. 2.
    Kim, S., Kwon, H. J., Lee, S., Shim, H., Chun, Y., et al., “Low-Power Flexible Organic Light-Emitting Diode Display Device,” Advanced Materials, Vol. 23, No. 31, pp. 3511–3516, 2011.CrossRefGoogle Scholar
  3. 3.
    Petras, A., “Design of Sandwich Structures,” Ph.D. Thesis, University of Cambridge, 1999.Google Scholar
  4. 4.
    Grego, S., Lewis, J., Vick, E., and Temple, D., “Development and Evaluation of Bend-Testing Techniques for Flexible-Display Applications,” Journal of the Society for Information Display, Vol. 13, No. 7, pp. 575–581, 2005.CrossRefGoogle Scholar
  5. 5.
    da Silva, A. V., “Analytical Modeling of the Stress-Strain Distribution in a Multilayer Structure with Applied Bending,” M.Sc. Thesis, Universidade Técnica de Lisboa, 2010.Google Scholar
  6. 6.
    Harris, K., Elias, A., and Chung, H.-J., “Flexible Electronics Under Strain: A Review of Mechanical Characterization and Durability Enhancement Strategies,” Journal of Materials Science, Vol. 51, No. 6, pp. 2771–2805, 2016.CrossRefGoogle Scholar
  7. 7.
    Li, S., Liu, X., Li, R., and Su, Y., “Shear Deformation Dominates in the Soft Adhesive Layers of the Laminated Structure of Flexible Electronics,” International Journal of Solids and Structures, Vol. 110, pp. 305–314, 2017.CrossRefGoogle Scholar
  8. 8.
    Li, S., Su, Y., and Li, R., “Splitting of the Neutral Mechanical Plane Depends on the Length of the Multi-Layer Structure of Flexible Electronics,” Proceedings of the Royal Society A, Vol. 472, No. 2190, Paper No. 20160087, 2016.Google Scholar
  9. 9.
    Alzoubi, K., Lu, S., Sammakia, B., and Poliks, M., “Factor Effect Study for the High Cyclic Bending Fatigue of Thin Films on PET Substrate for Flexible Displays Applications,” Journal of Display Technology, Vol. 7, No. 6, pp. 348–355, 2011.CrossRefGoogle Scholar
  10. 10.
    Alzoubi, K., Hamasha, M. M., Lu, S., and Sammakia, B., “Bending Fatigue Study of Sputtered ITO on Flexible Substrate,” Journal of Display Technology, Vol. 7, No. 11, pp. 593–600, 2011.CrossRefGoogle Scholar
  11. 11.
    Li, T.-C., Han, C.-F., Chen, K.-T., and Lin, J.-F., “Fatigue Life Study of ITO/PET Specimens in Terms of Electrical Resistance and Stress/Strain via Cyclic Bending Tests,” Journal of Display Technology, Vol. 9, No. 7, pp. 577–585, 2013.CrossRefGoogle Scholar
  12. 12.
    Yeh, M.-K., Chang, L.-Y., Lu, M.-R., Cheng, H.-C., and Wang, P.-H., “Bending Stress Analysis of Flexible Touch Panel,” Microsystem Technologies, Vol. 20, Nos. 8–9, pp. 1641–1646, 2014.CrossRefGoogle Scholar
  13. 13.
    Lee, S., Kwon, J.-Y., Yoon, D., Cho, H., You, J., et al., “Bendability Optimization of Flexible Optical Nanoelectronics via Neutral Axis Engineering,” Nanoscale Research Letters, Vol. 7, No. 1, Paper No. 256, 2012.Google Scholar
  14. 14.
    Vella, D., Bico, J., Boudaoud, A., Roman, B., and Reis, P.M., “The Macroscopic Delamination of Thin Films from Elastic Substrates,” Proceedings of the National Academy of Sciences, Vol. 106, No. 27, pp. 10901–10906, 2009.CrossRefGoogle Scholar
  15. 15.
    Toth, F., Rammerstorfer, F., Cordill, M., and Fischer, F., “Detailed Modelling of Delamination Buckling of Thin Films under Global Tension,” Acta materialia, Vol. 61, No. 7, pp. 2425–2433, 2013.CrossRefGoogle Scholar
  16. 16.
    WIKIPEDIA, “Neutral Axis,” https://en.wikipedia.org/wiki/Neutral_axis (Accessed 7 JUN 2018)
  17. 17.
    Reddy, J. N., “Theory and Analysis of Elastic Plates and Shells,” CRC Press, 2006.Google Scholar
  18. 18.
    Lee, C.-J., Lee, S.-K., Ko, D.-C., and Kim, B.-M., “Evaluation of Adhesive Properties Using Cohesive Zone Model: Mode I,” Transactions of the Korean Society of Mechanical Engineers A, Vol. 33, No. 5, pp. 474–481, 2009.CrossRefGoogle Scholar
  19. 19.
    Song, K., Dávila, C. G., and Rose, C. A., “Guidelines and Parameter Selection for the Simulation of Progressive Delamination,” Proc. of ABAQUS User’s Conference, pp. 43–44, 2008.Google Scholar
  20. 20.
    Dassault Systems Simulia, Inc., “Abaqus/CAE User’s Guide,” http://dsk.ippt.pan.pl/docs/abaqus/v6.13/books/usi/default.htm (Accessed 7 JUN 2018)
  21. 21.
    Kim, M. G., Park, S. B., and Chae, S.-W., “A Study on the Design of Flexible Display Considering the Failure Characteristics of ITO Layer,” Journal of the Korean Society for Precision Engineering, Vol. 30, No. 5, pp. 552–558, 2013.CrossRefGoogle Scholar
  22. 22.
    Coelho, A. M. G., “Finite Element Guidelines for Simulation of Delamination Dominated Failures in Composite Materials Validated by Case Studies,” Archives of Computational Methods in Engineering, Vol. 23, No. 2, pp. 363–388, 2016.MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Meo, M. and Thieulot, E., “Delamination Modelling in a Double Cantilever Beam,” Composite Structures, Vol. 71, Nos. 3–4, pp. 429–434, 2005.CrossRefGoogle Scholar
  24. 24.
    Chae, Y., “Optimal Design of Multi-Layered Foldable Display Considering Bending Stress, Neutral Plane and Delamination,” M.Sc. Thesis, Yonsei University, 2016.Google Scholar
  25. 25.
    Sacks, J., Schiller, S. B., and Welch, W. J., “Designs for Computer Experiments,” Technometrics, Vol. 31, No. 1, pp. 41–47, 1989.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Fowlkes, W. Y., Creveling, C. M., and Derimiggio, J., “Engineering Methods for Robust Product Design: Using Taguchi Methods in Technology and Product Development,” Addison-Wesley Reading, 1995.Google Scholar
  27. 27.
    Sobieszczanski-Sobieski, J. and Haftka, R. T., “Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments,” Structural Optimization, Vol. 14, No. 1, pp. 1–23, 1997.CrossRefGoogle Scholar
  28. 28.
    Jansson, T., Nilsson, L., and Redhe, M., “Using Surrogate Models and Response Surfaces in Structural Optimization-with Application to Crashworthiness Design and Sheet Metal Forming,” Structural and Multidisciplinary Optimization, Vol. 25, No. 2, pp. 129–140, 2003.CrossRefGoogle Scholar
  29. 29.
    Kim, D. S. and Lee, J., “Structural Design of a Level-Luffing Crane through Trajectory Optimization and Strength-Based Size Optimization,” Structural and Multidisciplinary Optimization, Vol. 51, No. 2, pp. 515–531, 2015.CrossRefGoogle Scholar
  30. 30.
    Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, Vol. 6, No. 2, pp. 182–197, 2002.CrossRefGoogle Scholar

Copyright information

© Korean Society for Precision Engineering and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringYonsei UniversitySeoulRepublic of Korea
  2. 2.LG Display R&D CenterGyeonggi-doRepublic of Korea

Personalised recommendations