Skip to main content
SpringerLink
Log in

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

  • Research Paper
  • Published:
Glass Structures & Engineering Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

(Reproduced with permission from Bernard and Daudeville 2009)

Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

References

  • 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 

  • ANSYS, Inc.: Ansys, 18.1 (2017)

  • Aronen, A.: Modelling of Deformations and Stresses in Glass Tempering. Ph.D. Thesis, Julkaisu-Tampere University of Technology. Publication, 1036 (2012)

  • Beason, W.L., Morgan, J.R.: Glass failure prediction model. J. Struct. Eng. 110(2), 197–212 (1984)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Carre, H., Daudeville, L.: Numerical simulation of soda-lime silicate glass tempering. J. Phys. IV 6, 175–85 (1996)

    Google Scholar 

  • Carre, H., Daudeville, L.: Load-bearing capacity of tempered structural glass. J. Eng. Mech. 125(8), 914–21 (1999)

    Article  Google Scholar 

  • Daudeville, L., Bernard, F., Gy, R.: Residual stresses near holes in tempered glass plates. Mater. Sci. Forum 404–407, 43–48 (2002)

    Article  Google Scholar 

  • EN 12150-1: Glass in building—thermally toughened soda lime silicate safety glass—part 1: definition and description (2015)

  • Gardon, R.: The tempering of flat glass by forced convection. In: VIIth International Congress on Glass, Brussels, Belgium, Paper No. 79, pp. 14 (1965)

  • Gardon, R., Narayanaswamy, O.S.: Stress and volume relaxation in annealing flat glass. J. Am. Ceram. Soc. 53(7), 380–85 (1970)

    Article  Google Scholar 

  • Kurkjian, C.: Relaxation of torsional stress in transformation range of soda–lime–silica glass. Phys. Chem. Glasses 4(4), 128–36 (1963)

    Google Scholar 

  • Laufs, W.: Ein Bemessungskonzept zur Festigkeit thermisch vorgespannter Gläser. Ph.D. Thesis, RWTH Aachen (2000)

  • 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)

  • Narayanaswamy, O.S.: A model of structural relaxation in glass. J. Am. Ceram. Soc. 54(10), 491–98 (1971). https://doi.org/10.1111/j.1151-2916.1971.tb12186.x

    Article  Google Scholar 

  • Narayanaswamy, O.S.: Stress and structural relaxation in tempering glass. J. Am. Ceram. Soc. 61(3), 146–52 (1978)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Nielsen, J. H.: Tempered glass: bolted connections and related problems. Ph.D. Thesis, Technical University of Denmark, Dept. of Civil Eng (2009)

  • 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)

  • Schneider, J.: Festigkeit und Bemessung punktgelagerter Gläser und stoßbeanspruchter Gläser. Ph.D. Thesis, Technische Universität Darmstadt (2001)

  • 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)

    Article  Google Scholar 

  • Schneider, J., Kuntsche, J., Schula, S., Schneider, F., Wörner, J.D.: Glasbau Grundlagen, Berechnung, Konstruktion, 2nd edn. Springer, Berlin (2016b)

    Google Scholar 

  • Schwarzl, F., Staverman, A.J.: Time-temperature dependence of linear viscoelastic behavior. J. Appl. Phys. 23(8), 838–43 (1952)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University of Darmstadt, Franziska-Braun-Str. 3, 64287, Darmstadt, Germany

    N. Pourmoghaddam & J. Schneider

Authors
  1. N. Pourmoghaddam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Schneider
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Pourmoghaddam.

Appendix

Appendix

See Tables 8 and 9

Table 8 Material properties (Carre and Daudeville 1999)
Full size table
Table 9 Weighting factors w and relaxation times \(\tau \) for the viscous relaxation (shear and bulk); Weighting factors C and relaxation times \({\uplambda }\) for the structural relaxation (\(T_{ref}~=~864\) K) (Carre and Daudeville 1999)
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pourmoghaddam, N., Schneider, J. Finite-element analysis of the residual stresses in tempered glass plates with holes or cut-outs. Glass Struct Eng 3, 17–37 (2018). https://doi.org/10.1007/s40940-018-0055-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40940-018-0055-z

Keywords

Search

Navigation