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Effect of glass temperature before cooling and cooling rate on residual stresses in tempering

Authors:
Antti Aronen at Glaston Finland Oy
Antti Aronen
  • Glaston Finland Oy
Reijo Karvinen at Tampere University
Reijo Karvinen
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Abstract and Figures

Understanding of heat transfer and development of the temperature field in a glass during tempering is very important because it affects the quality. By numerical modeling, it is possible to study the effect of glass temperature before cooling and the values of heat transfer coefficients which determine the cooling rate and material properties on transient and residual stresses during cooling. Also, the effect of thermal and mechanical properties of glass, which are obtained experimentally, can be easily observed. In the present study, the tempering process of glass sheets with different glass thicknesses has been simulated. The paper presents modeling results, which explain the effect of the initial temperature before cooling and cooling rate on the residual and transient stresses of glass sheets of different thicknesses. The paper also shows that results can be presented independent of glass thickness by using two variables: the maximum temperature difference between surface and mid-plane during the cooling and the difference between glass transition and glass initial temperature. Because the mechanical properties of glass are experimental and are not very accurately known, the effect of their variation on residual stresses is also shown.
Sketch of a tempering process. On the left is a heating part and on the right is a cooling part. Trad\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{rad}$$\end{document} is the heating radiator temperature, b is the thickness of glass, h is the heat transfer coefficient in cooling, and T∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\infty }$$\end{document} is the ambient temperature. x and z are distances in horizontal and vertical directions, respectively
Sketch of a tempering process. On the left is a heating part and on the right is a cooling part. Trad\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{rad}$$\end{document} is the heating radiator temperature, b is the thickness of glass, h is the heat transfer coefficient in cooling, and T∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\infty }$$\end{document} is the ambient temperature. x and z are distances in horizontal and vertical directions, respectively
… 
Effect of heat transfer coefficient h and glass temperature before cooling T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}$$\end{document} on glass transition temperature Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{g}$$\end{document} at mid-plane for different glass thicknesses
Effect of heat transfer coefficient h and glass temperature before cooling T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}$$\end{document} on glass transition temperature Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{g}$$\end{document} at mid-plane for different glass thicknesses
… 
Surface compressive residual stress presented using maximum temperature difference ΔTmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta T}_\mathrm{max}$$\end{document} and glass temperature before cooling T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}$$\end{document} for different thicknesses
Surface compressive residual stress presented using maximum temperature difference ΔTmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta T}_\mathrm{max}$$\end{document} and glass temperature before cooling T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}$$\end{document} for different thicknesses
… 
Surface compressive residual stress for different glass thicknesses as a function of the difference between the glass temperature before cooling and the glass transition temperature at mid-plane T0-Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}-T_\mathrm{g}$$\end{document}, and the maximum temperature difference between the mid-plane and surface during cooling ΔTmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta T}_\mathrm{max}$$\end{document}.
Surface compressive residual stress for different glass thicknesses as a function of the difference between the glass temperature before cooling and the glass transition temperature at mid-plane T0-Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}-T_\mathrm{g}$$\end{document}, and the maximum temperature difference between the mid-plane and surface during cooling ΔTmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta T}_\mathrm{max}$$\end{document}.
… 
Surface maximum tensile stress during cooling as a function of the difference between the glass temperature before cooling and the glass transition temperature at mid-plane T0-Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}-T_\mathrm{g}$$\end{document}, and the maximum temperature difference between the mid-plane and surface during cooling ΔTmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta T}_\mathrm{max}$$\end{document}, for glass with different thicknesses b
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Surface maximum tensile stress during cooling as a function of the difference between the glass temperature before cooling and the glass transition temperature at mid-plane T0-Tg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{0}-T_\mathrm{g}$$\end{document}, and the maximum temperature difference between the mid-plane and surface during cooling ΔTmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta T}_\mathrm{max}$$\end{document}, for glass with different thicknesses b
… 
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Glass Struct. Eng. (2018) 3:3–15
https://doi.org/10.1007/s40940-017-0053-6
RESEARCH PAPER
Effect of glass temperature before cooling and cooling rate
on residual stresses in tempering
Antti Aronen ·Reijo Karvinen
Received: 12 February 2017 / Accepted: 14 November 2017 / Published online: 5 December 2017
© Springer International Publishing AG, part of Springer Nature 2017
Abstract Understanding of heat transfer and devel-
opment of the temperature field in a glass during tem-
pering is very important because it affects the quality.
By numerical modeling, it is possible to study the effect
of glass temperature before cooling and the values of
heat transfer coefficients which determine the cool-
ing rate and material properties on transient and resid-
ual stresses during cooling. Also, the effect of thermal
and mechanical properties of glass, which are obtained
experimentally, can be easily observed. In the present
study, the tempering process of glass sheets with dif-
ferent glass thicknesses has been simulated. The paper
presents modeling results, which explain the effect of
the initial temperature before cooling and cooling rate
on the residual and transient stresses of glass sheets of
different thicknesses. The paper also shows that results
can be presented independent of glass thickness by
using two variables: the maximum temperature differ-
ence between surface and mid-plane during the cooling
and the difference between glass transition and glass
initial temperature. Because the mechanical properties
of glass are experimental and are not very accurately
A. Aronen (B)
School of Physics, University of Sydney, Sydney,
NSW 2006, Australia
e-mail: antti.aronen@sydney.edu.au
R. Karvinen
Tampere University of Technology, 33101 Tampere,
Finland
e-mail: reijo.karvinen@tut.fi
known, the effect of their variation on residual stresses
is also shown.
Keywords Glass tempering ·Numerical modeling ·
Residual stresses
1 Introduction
Windows are commonly made of annealed soda-lime
glass. This type of glass is strong under compres-
sion, but relatively weak under tension. The low tensile
strength is due to small surface flaws that tend to grow
under tension. However, the strength of glass can be
increased by tempering, which results in compressive
stress in the surface region. In a tempering process,
these compressive stresses are produced by a process
involving heating of the glass to above 600 ◦C, followed
by rapid cooling. Good-quality tempered glass requires
precise control of heat transfer during the tempering
process. In a thermal tempering process, the heating
occurs due to simultaneous radiation and forced con-
vection (Karvinen 1998). In the traditional tempering
process, in order to temper the glass uniformly and to
reduce visual faults like roller waves, the glass is moved
while quenching (Rantala 2015).
Cooling is also important part of the tempering pro-
cess for achieving well-defined residual stresses in the
glass. To form the residual stress distribution through
the glass thickness, the glass is rapidly cooled to below
the glass transition temperature. During the cooling, the
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... Likewise, Pourmoghaddam et al. performed a paramet-ric study to analyse the behaviour of residual stresses near holes in glass components (Pourmoghaddam and Schneider 2018). Aronen et al. developed an efficient one-dimensional methodology to analyse the influence of several parameters on the temperature and residual stresses of glass (Aronen and Karvinen 2018). ...
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