J . Am. Cerum. SOC., 71 [lo] 876-78 (1988)

Tempering Glass with Modulated Cooling Schedules ROBERT GARDON*’*

Research Staff. Ford Motor Company, Dearborn, Michigan 48 121

Modulated quenching is a variant of the tempering process that gives one independent control over the strength and frac- ture characteristics of glass. Thus the strength of nondicing “heat-strengthened” glass can be raised to that of “fully tem- pered” glass. Conversely, the break pattern of glass having the strength of fully tempered glass can be made to range from nondicing to fine dicing.

I. Introduction

HERMALLY tempered glass has two special attributes: one is T an enhancement of its strength; the other a propensity, when broken, to disintegrate into a large number of small fragments. Different applications value these attributes differently. In tem- pered automotive glass one usually seeks both high strength and, upon fracture, a high particle count, i.e., small fragments. In this situation, the higher the temper, the better. The situation is some- what different for tempered products for which both upper and lower limits are set to the allowed particle count. Yet different re- quirements apply for heat-strengthened glass for some architec- tural applications and for tempered ovenware, in which one seeks increased strength without risk of fragmentation into many small pieces. One may, indeed, wish for the glass to break into no

Manuscript No. 199598. Received September 8, lYX7; approved April 26. 1988. Presented at the Glass Division Meeting of the American Ceramic Society. Bed-

for!, PA, September 30, 1987 (Glass Division, Paper No. 7-G-87F)

*Now retired and a consultant, restding a[ 28405 Eastbrook Court, Farmington Hi!ls. MI 48018.

‘The balance of forces and moments in the glass is maintained. in the face o f these large changes in SC/CT, by relatively small changes in the shape of stress dis- tributions across the thickness of the glass.

Member. the American Ceramic Society

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I I I I I I I I

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Fig. 1. Temper stresses produced by conventional tempering

more than two or three large pieces, though preferably without the sharp edges associated with shards of annealed glass.

While the enhancement of the strength of tempered glass is de- termined by the compressive stress in its surfaces, its propensity to “dice,” i.e., to break into many small fragments, is believed to be governed by the interior tension. In conventional tempering these two stresses bear a more or less constant relation to one an- other, so that a given strength is always associated with a corre- sponding particle count. To increase the versatility of tempered glass products, it would be useful to be able to vary the surface compression and center tension independently of one another. This paper explores ( 1 ) whether this can be done by modulating the intensity of quenching and (2) the different fracture character- istics that can be achieved in this manner.

11. Background

The ratio of surface compression (SC) and central tension (CT) in glass is often regarded as more or less fixed: it is taken to be 2 for annealed glass and about 2.2 for tempered glass. In fact, val- ues of 2.6 have been obtained in experiments on quenching with air,’ and values in excess of 4 in some liquid-quenched, su- pertcmpered Russian glass. ’,’ The point to be made here is that the SC/CT ratio can vary widely. However, the mere attainment of high SC/CT ratios in very highly tempered glass is of no inter- est, as such, for it does not reflect separate control over surface compression and center tension. What will be of interest in what follows are changes in the SC/CT ratio that are obtained by more or less independent control over SC and CT, individually.

To illustrate conventional tempering practice and to define some terms associated with dicing, Fig. 1 is a plot of the surface compression and center tension produced in 6-mm-thick glass quenched from various initial temperatures (To) and at various rates, the latter being characterized by the (constant) heat-transfer coefficients (h) employed to cool the glass. Figure 1 shows that the surface compression is a stronger function of both To and h than is the center tension. To impart a center tension of 47 MPa to 6-mm glass (with quenching air at 37°C) requires quenching with a heat-transfer coefficient of 155 to 170 W/(m‘. “C), depend- ing on To. Also, depending on To, the surface compression in the glass will then be from 109 to 115 MPa.

Dicing is brought about by the propensity of fractures in tem- pered glass - once initiated - to propagate and to bifurcate spontaneously, i.e., without any additional energy being supplied to the glass from outside. The energy for such spontaneous propagation and bifurcation comes from the tensile strain energy locked in the tempered glass.3 There is no clear-cut threshold separating dicing from nondicing glass, and, unlike temper stresses, the strength and fracture characteristics of glass are only statistically determined. It seems, however, that spontaneous propagation of fractures does not occur in 6-mm glass with a cen- tral tension less than about 34 MPa.4 As the interior tension is increased above this threshold, there is an increasing tendency for fractures to propagate and bifurcate spontaneously. The surface cornpression also increases, and with that the effective strength of the heat-treated glass. At a level of interior tension of about 47 MPa, dicing is fine enough-and the corresponding enhance- ment of strength high enough-for such glass to meet the ANSl standard’ for tempered automotive safety glass. This glass has therefore been known as “fully tempered,” even though it corre- sponds to no limiting state. Both higher strengths and finer dicing (smaller fragments) can be produced.

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October 1988 Tempering Glass with Modulated Cooling Schedules 877

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Fig. 2. produced by modulated quenching.

Ratio of surface compression to center tension

The term “heat-strengthened glass” is not as well-defined. It may refer to glass that is stronger than annealed glass but breaks into only two or three pieces, or to glass strengthened to the point of dicing, though less finely than tempered glass. In this paper, the term will be used to denote the strongest glass that will just not dice, i.e., glass with a central tensile stress of about 34 MPa.

Taking 47 and 34 MPa as the central tensile stresses corre- sponding to “fine dicing” and “no dicing,” respectively, Fig. 1 shows the surface compression in “fully tempered” glass to be about 115 MPa, while heat-strengthened glass that will break without dicing can have a maximum surface compression of only about 80 MPa. Surface compression raises the strength of heat- treated glass above that of annealed glass, which, for design pur- poses, might be taken as 35 MPa. Full tempering thus raises the usable strength of glass by a factor of about 4, and conventional heat-strengthening- to the point of just not dicing-by a factor of about 3.

Even though the surface compression is a stronger function of both h and To than is the center tension, the ratio of SC/CT - for conditions of conventional tempering - varies but little, from about 2.2 to 2.4. Only by going well beyond the range of Fig. 1 , i.e., by using very high initial temperatures and quenching rates, does one obtain the high values of SC/CT that accompany “supertempering .”* In conventional tempering practice, by con- trast, one usually stays with the lowest T,’s that will avoid in- process breakage of the glass. Higher initial glass temperatures are viewed as risking the loss of form without any offsetting benefit.

111. Modulated Quenching

Modulated quenching (Mod-Q for short) was conceived to in- crease the range of usefulness of both heat-strengthened and tem- pered glass.

In heat-strengthening one seeks to increase strength (surface compression) without unduly raising the propensity of the glass to dice upon fracture. As has been noted, the enhancement in the strength of a nondicing glass, attainable by conventional means, cannot exceed 80 MPa. One aim of Mod-Q is to allow one to make a nondicing glass stronger than that.

$The models underlying these programs are discussed in Refs. 6. They are vali- dated exoerimentallv in Refs. 6b. 6c. and 7. References 8 illustrate some other applications.

‘Cooling by radiation, which plays a significant role at low rates of convective cooling, is taken into account in all these simulations, along with radiative transfer in theglass. (cf Ref. 6a).

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Fig. 3. Temper stresses produced by modulated quenching

In tempering, on the other hand, where dicing is desired in ad- dition to high strength. excessive dicing sometimes is a problem. Here, Mod-Q should allow one to reduce the propensity of tem- pered glass to dice, while maintaining its strength, or, conversely, to raise its strength without increasing its propensity to dice.

Modulated quenching seeks to achieve these objectives by al- tering the ratio of surface compression to center tension, without significantly altering both. The central idea is to start cooling the glass at a relatively high rate in order to “freeze in” high stress gradients near the surfaces, and then to reduce the cooling rate so as to minimize stress gradients in the interior.

The following results were obtained in an exploration of the potential of this process by computer simulation. The programs required for this existed from prior work on heat transfer and stress generation in glass.‘

( I ) Results of Computer Simulations Figures 2 and 3 illustrate the results of one particular set of

simulations. Like Fig. 1, Figs. 2 and 3 pertain to 6-mm-thick glass. This is now quenched at a variable rate, always starting from an initial temperature of 650°C and with an initial heat- transfer coefficient (h,) of 350 W/(m’. “C). After a time f I , the heat-transfer coefficient is reduced to hz . For different cal- culations in this set, h2 ranges from 350 (no change) down to 12.5 W/(m*.”C) (which is about the lowest possible, corre- sponding to cooling by natural convection).‘ Times for the change in heat-transfer coefficient vary from 0 s (cooling with h2 throughout) to 8 s . Quenching with h , is substantially complete in about 20 s . While step changes in heat-transfer coefficient are indicated here, similar results are obtained with changes in h fol- lowing a (relatively steep) ramp function.

Figure 2 shows the ratio SC/CT as a function of switching time ( t , ) for various values of the second heat-transfer coefficient (hJ . The roughly bell-shaped curves start and end with values of SC/CT representative of conventional (unmodulated) cooling. In between they pass through very pronounced maxima, which increase with decreasing hz, down to an h2 of 50 W/(m2. “C). A “switch” to this at I , = 4.6 s produces an SC/CT ratio of 3.56, the highest obtained for this glass thickness, To, and h i . Decreas- ing hz below 50 again produces lower maxima.

Practical implications of these results are brought out in Fig. 3. This shows center tension and surface compression as functions of the time t , at which the heat-transfer coefficient is “switched”

818 Journal of the American Ceramic Society-Gardon Vol. 71, No. 10

from h , = 350 W/(m2.”C) to hz , with h2 assuming the values indicated in the figure. The curves AA and BB are the loci of compressive stresses in the surface that correspond to the criteria of “no dicing” and “fine dicing” discussed in the context of Fig. 1. Not only do AA and BB extend over a range of stresses, but these stresses are also significantly higher than the corre- sponding single values of 80 and 115 MPa, respectively, that ap- ply for conventional (unmodulated) tempering.

(2) Discussion Two applications of these findings promptly suggest themselves: (1) We have noted that enhancement of the strength of a

nondicing heat-strengthened glass, produced conventionally, is limited to (a surface compression of) 80 MPa. In contrast, the maximum of the curve AA in Fig. 3 corresponds to a surface compression of 121 MPa. This means that with modulated quenching one should be able to produce a nondicing glass that is as strong as-or even stronger than-fully tempered glass. One way to achieve this within the framework of the present set of examples-i.e., with 6-mm glass, To = 650°C, and h , = 350 W/(m2-”C)-would be to “switch” to an h2 of 50 W/ (m’ . “C) at about 4.6 5. The glass thus made will have a surface compression of 121 MPa, 5% higher than conventional fully tempered glass. However, with an SC/CT ratio of 3.56, its center tension will by only 34 MPa, so that this glass will not dice.

(2) Figure 3 also suggests the possibility of producing glass with the strength of fully tempered glass but a reduced propensity to dice. This may be useful where, as in Europe, standards specify not only a minimum but also a maximum number of allowed fragments. To accomplish this, Fig. 3 suggests a variety of oper- ating conditions in the area between the line SC = 115 MPa, cor- responding to conventionally tempered glass, and the curve BB, which is the locus of surface compressions attainable with Mod- Q, all of which produce “fine” dicing. Thus, for example, a switchat3.5 s to75 W/(m*.”C)-or, a t5 .5sto25 W/(m2.’C)- is expected to produce a glass that has the “standard” surface com- pression of 115 MPa, but that will not dice. On the other hand, a switch at 5 s to 100 W/(m*.”C) should produce a glass that has the usual “fine” dicing pattern and an enhanced surface com- pression of 156 MPa, 36% higher than that of conventional fully tempered glass. Other combinations of strengths and dicing pat- terns are available between these limits.

The examples given employed relatively conservative operat- ing conditions. A willingness to employ higher initial tempera- tures and/or heat-transfer coefficients should further increase the range of properties obtainable by Mod-Q.

Incidentally, interrupting the quench is equivalent to switching to an h2 of about 12.5 W/(m2.”C), which corresponds to natu- ral convection. Doing so, from h , = 350 W/(m’. “C) at 6 s , will produce a nondicing glass with a surface compression of 108 MPa, practically equal to that of fully tempered glass. An interruption at 7.5 s will produce a finely dicing glass with a surface compression of 13.5 MPa. (Similar results could- more economically-also be obtained with h , lower than 350 W/ (m2 . “c) .

(3) A possible third application of Mod-Q, not dealt with in Fig. 3, would be to produce “friable glass,” i.e., a glass that will break into many small particles without being particularly strong. To produce this would entail a ‘‘reverse’’ Mod-Q, i.e., a switch from a lower to a higher cooling rate.

(3) Some Preliminary Experiments While computer simulation can reliably predict stresses pro-

duced by heat treatment, less is known about the fracture charac-

teristics of heat-treated glass, and the strength of glass is only statistically determined. Experiments were therefore needed to demonstrate the practical feasibility of the Mod-Q process and, especially, to test the products made by it.

To date, two sets of experiments were performed: ( 1 ) On 1 by 4 in. specimens both surface compression and center tension could readily be measured, and these experiments substantially confirmed the stresses predicted by computer simulations. They also confirmed that Mod-Q’d glass with a surface compression of fully tempered glass broke without dicing. (2) For a better test of strength and fracture characteristics, 12-in. squares of both fi- and l/a-in.-thick glass were also Mod-Q’d and subjected to the ANSI ball drop test for tempered glass. The Y4-in. glass passed this strength test. The %-in. glass did not fully meet the re- quirements of no more than 2 failures out of 12 ball drops. Some further tuning of the Mod-Q process for processing larger pieces is still required. Clearly, however, both the %- and %-in. Mod-Q’d glasses showed enhanced impact strength in combina- tion with nondicing breaks.

IV. Conclusion

Modulated quenching is a variant of the tempering process that gives one independent control over the strength and fracture char- acteristics of glass. The feasibility of this process was explored by computer simulation and confirmed by experiments on both 1 by 4 in. and 12 in. square specimens.

Mod-Q allows one to make products that cannot be made by conventional tempering or heat-strengthening, with properties tailored to one’s need. Specifically, it allows one (1) to raise the enhancement of strength of nondicing 6-mm glass from 80 to 120 MPa, higher than that of convential fully tempered glass, ( 2 ) to tailor the break pattern of tempered glass with a “standard’ surface compression of 115 MPa to range from nondicing to the fine dicing required by the ANSI standard, and (3) (possibly) to make a friable glass, i.e., one that will break into many small particles without having the strength of tempered glass.

References ‘R. Gardon, ‘‘Thermal Tempering of Glass”; Ch. 5 (cf. Fig. 8) in Glass: Science

and Technology, Vol. 5. Edited by D. R. Uhlmann and N. J . Kreidl. Academic Prys, New York, 1980.

-1. A. Boguslavskii, F. F. Vitman, and 0. I . Pukhlik. “Further Hardening of Glass by Increased Quenching Stress,’’ Dokl. Akad. Nauk SSSR, 157, 87-90 (1964); Suv. Phys. -Dukl. (Engl. Transl.), 9, 587-89 (1965).

3P. Acloque and C. Guillemet, “The Course of Fracture Propagation under Vary- ing Strain”; pp. 95-106 in Advances in Glass Technology, Part 2. Edited by F. R. Matson and G. E. Rindone. Plenum Press, New York, 1962.

‘K. Akeyoshi and E. Kanai, “Mechanical Properties of Tempered Glass”; Paper No. 80 in Proceedings of 7th International Congress on Glass, Brussels, Belgium, 1965. Institut National du Verre, Charleroi, Belgium, 1965.

’American National Standards Institute, New York, Standard Z 26.1, 1973 (origi- nally promulgated in 1938).

‘(a) R. Gardon, ”Calculation of Temperature Distributions in Glass Plates Under- going Heat-Treatment,”J. Am. Ceram. Soc., 41 161 200-209 (1958). (b) R . Gardon and 0. S . Narayanaswamy, “Stress and Volume Relaxation in Annealing Flat Glass,” ibid., 53 [7] 380-85 (1970). (c) 0. S. Narayanaswamy, “A Model of Struc- tural Relaxation in Glass,” ibid., 54 [lo] 491-98 (1971).

’(a) 0. S. Narayanaswamy, “Stress and Structural Relaxation in Tempering Glass,” J . Am. Ceram. Soc., 61 [3-41 146-52 (1978). (b) R. Gardon, “Nonlinear Annealing of Glass,” ibid., 64 [Z] 114-19 (1981).

*(a) 0. S. Narayanaswamy, “Optimum Schedule for Annealing Flat Glass,” J . Am. Ceram. Soc.. 64 [2] 109-14 (1981). (b) R . Gardon, “Modelling Annealing Lehrs for Flat Glass,” ibid., 65 [8] 372-79 (1982). (c) F. Peltier, “Theoretical and Experimental Aspects of the ‘Temnization’ of Float Glass” (in Fr.); pp. 175-81 in Collected Papers, Vol. 3, XIV International Congress on Glass, New Delhi, India, 1986. Indian Ceramic Society, Calcuttta. India, 1986.