Glass Structures & Engineering

, Volume 3, Issue 1, pp 17–37 | Cite as

Finite-element analysis of the residual stresses in tempered glass plates with holes or cut-outs

  • N. PourmoghaddamEmail author
  • J. Schneider
Research Paper


Due to the increased mechanical strength and with respect to safety, tempered and strengthened glass plates are increasingly employed in modern buildings as architectural and structural components. However, regarding the complete fragmentation by disturbing the equilibrated residual stress state in thermally toughened glass, drillings or cut-outs must be done before quenching the glass. The present paper demonstrates 3D results of the thermal tempering simulation by the Finite Element Method in order to calculate the residual stresses in the area of the holes or cut-outs of a tempered glass plate. A viscoelastic material behavior of the glass is considered for the simulation of the tempering process. The structural relaxation is taken into account using Narayanaswamy’s model. Due to different cooling rates of the convection areas such as edge, chamfer, hole’s inner surface and far-field area, heat transfer coefficients are estimated using experimental data from the literature. It is the objective of the paper to demonstrate the simulation of the residual stresses in tempered glasses with holes or cut-outs and to quantify the amount of temper stresses based on a variation of different geometrical parameters and the local heat transfer coefficient. The residual stresses are thus calculated varying the following parameters: the hole diameter, the plate thickness, different geometries of the cut-outs and heat transfer coefficient.


Residual stresses Tempered glass Holes and cut-outs Heat transfer coefficient Finite element simulation 


  1. Aben, A., Anton, J., Errapart, A.: Modern photoelasticity for residual stress measurement in glass. Strain Int. J. Exp. Mech. 44, 40–48 (2008)Google Scholar
  2. ANSYS, Inc.: Ansys, 18.1 (2017)Google Scholar
  3. Aronen, A.: Modelling of Deformations and Stresses in Glass Tempering. Ph.D. Thesis, Julkaisu-Tampere University of Technology. Publication, 1036 (2012)Google Scholar
  4. Beason, W.L., Morgan, J.R.: Glass failure prediction model. J. Struct. Eng. 110(2), 197–212 (1984)CrossRefGoogle Scholar
  5. Bernard, F., Daudeville, L.: Point fixings in annealed and tempered glass structures: modeling and optimization of bolted connections. Eng. Struct. 31(4), 946–55 (2009)CrossRefGoogle Scholar
  6. Carre, H., Daudeville, L.: Numerical simulation of soda-lime silicate glass tempering. J. Phys. IV 6, 175–85 (1996)Google Scholar
  7. Carre, H., Daudeville, L.: Load-bearing capacity of tempered structural glass. J. Eng. Mech. 125(8), 914–21 (1999)CrossRefGoogle Scholar
  8. Daudeville, L., Bernard, F., Gy, R.: Residual stresses near holes in tempered glass plates. Mater. Sci. Forum 404–407, 43–48 (2002)CrossRefGoogle Scholar
  9. EN 12150-1: Glass in building—thermally toughened soda lime silicate safety glass—part 1: definition and description (2015)Google Scholar
  10. Gardon, R.: The tempering of flat glass by forced convection. In: VIIth International Congress on Glass, Brussels, Belgium, Paper No. 79, pp. 14 (1965)Google Scholar
  11. Gardon, R., Narayanaswamy, O.S.: Stress and volume relaxation in annealing flat glass. J. Am. Ceram. Soc. 53(7), 380–85 (1970)CrossRefGoogle Scholar
  12. Kurkjian, C.: Relaxation of torsional stress in transformation range of soda–lime–silica glass. Phys. Chem. Glasses 4(4), 128–36 (1963)Google Scholar
  13. Laufs, W.: Ein Bemessungskonzept zur Festigkeit thermisch vorgespannter Gläser. Ph.D. Thesis, RWTH Aachen (2000)Google Scholar
  14. Lee, E.H., Rogers, T.G., Woo, T.C.: Residual stresses in a glass plate cooled symmetrically from both surfaces. J. Am. Ceram. Soc. 48(9), 480–87 (1965)Google Scholar
  15. Narayanaswamy, O.S.: A model of structural relaxation in glass. J. Am. Ceram. Soc. 54(10), 491–98 (1971). CrossRefGoogle Scholar
  16. Narayanaswamy, O.S.: Stress and structural relaxation in tempering glass. J. Am. Ceram. Soc. 61(3), 146–52 (1978)CrossRefGoogle Scholar
  17. Nielsen, J.H., Olesen, J.F., Poulsen, P.N., Stang, H.: Finite element implementation of a glass tempering model in three dimensions. Comput. Struct. 88(17–18), 963–72 (2010a)CrossRefGoogle Scholar
  18. Nielsen, J.H., Olesen, J.F., Poulsen, P.N., Stang, H.: Simulation of residual stresses at holes in tempered glass: a parametric study. Mater. Struct. 43(7), 947–61 (2010b)CrossRefGoogle Scholar
  19. Nielsen, J. H.: Tempered glass: bolted connections and related problems. Ph.D. Thesis, Technical University of Denmark, Dept. of Civil Eng (2009)Google Scholar
  20. Pourmoghaddam, N., Nielsen, L. H. and Schneider, J.: Numerical simulation of residual stresses at holes near edges and corners in tempered glass?: A parametric study. In: Engineered Transparency International Conference at Glasstec. pp. 513–525 (2016)Google Scholar
  21. Schneider, J.: Festigkeit und Bemessung punktgelagerter Gläser und stoßbeanspruchter Gläser. Ph.D. Thesis, Technische Universität Darmstadt (2001)Google Scholar
  22. Schneider, J., Hilcken, J., Aronen, A., Karvinen, R., Olesen, J.F., Nielsen, J.H.: Stress relaxation in tempered glass caused by heat-soak-testing. Eng. Struct. 122, 42–49 (2016a)CrossRefGoogle Scholar
  23. Schneider, J., Kuntsche, J., Schula, S., Schneider, F., Wörner, J.D.: Glasbau Grundlagen, Berechnung, Konstruktion, 2nd edn. Springer, Berlin (2016b)Google Scholar
  24. Schwarzl, F., Staverman, A.J.: Time-temperature dependence of linear viscoelastic behavior. J. Appl. Phys. 23(8), 838–43 (1952)CrossRefzbMATHGoogle Scholar
  25. Tool, A.Q.: Relation between inelastic deformability and thermal expansion of glass in its annealing range. J. Am. Ceram. Soc. 29(9), 240–53 (1946)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Technical University of DarmstadtDarmstadtGermany

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