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Simulation of residual stresses at holes in tempered glass: a parametric study

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Abstract

This work presents a full 3D numerical study of the residual stresses in tempered (toughened) glass near holes using Narayanaswamy’s model for the tempering process. It is the objective of the paper to elucidate the influence on the minimal residual compressive stresses at holes from variations in: the far-field stress, plate thickness, hole diameter and the interaction between holes and edges and corners. The work presents novel results for the sensitivity of the residual stresses to geometric features and provides a design tool for estimating residual stresses at holes for different geometries. An example of how to extrapolate the results in terms of far-field stresses is given.

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Notes

  1. Experimental observations indicate crack healing during the tempering process which increases the strength further, see e.g. [11].

  2. ly, e = 53 mm is the minimum distance to an edge according to [9]

  3. The term −T · 1.8e −7 J T2/kg K found in [7] for (12) is omitted here due to insignificance for the considered temperatures.

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Authors and Affiliations

  1. Department of Structural Engineering, Technical University of Denmark, Kongens Lyngby, Denmark

    J. H. Nielsen, J. F. Olesen, P. N. Poulsen & H. Stang

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  1. J. H. Nielsen
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  2. J. F. Olesen
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  3. P. N. Poulsen
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  4. H. Stang
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Correspondence to J. H. Nielsen.

Appendix: parameters for the model

Appendix: parameters for the model

The material parameters for the exponential series used for viscoelasticity and for the structural response function are found in Tables 3 and 4, respectively. Here (g n , λ g n ) is a set of constants used for the deviatoric part of the relaxation function and (k n , λ k n ) is used for the hydrostatic part of the relaxation function and (m n , λ m n ) defines the response function for the structural volume relaxation. A more in-depth explanation is given in [20].

Table 3 Material data for the generalized Maxwell material
Full size table
Table 4 Material data for the response function for the structural volume relaxation
Full size table

The initial temperature used was 923.15 K and the ambient temperature was 293.15 K. The thermal conductivity, λth, and the specific heat, C, for soda-lime-silica glass are modeled as temperature dependent and may be found in [7]Footnote 3:

$$ \lambda_{\rm th}=0.741\,\hbox{W}/\hbox{m\,K}+T\cdot 8.58\hbox{e} -4\,\hbox{W}/\hbox{m\,K}^2 $$
(11)
$$ C= \left\{\begin{array}{ll} 1433\,\hbox{J}/\hbox{kg\,K} + T\cdot 6.5\hbox{e} -3\,\hbox{J}/\hbox{kg\,K}^2 & \hbox{for}\; T \geq 850\,\hbox{K} \\ 893\, \hbox{J}/\hbox{kg\,K} + T \cdot 0.4\, \hbox{J}/\hbox{kg\,K}^2 & \hbox{for}\; T < 850\,\hbox{K} \\ \end{array}\right. $$
(12)

The forced convection coefficients from Table 5 may be found in [6].

Table 5 Forced convection constants used for the model [7]
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Nielsen, J.H., Olesen, J.F., Poulsen, P.N. et al. Simulation of residual stresses at holes in tempered glass: a parametric study. Mater Struct 43, 947–961 (2010). https://doi.org/10.1617/s11527-009-9558-z

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