POOLS, J. P.
BEOCKWAY GLASS (X~ANY, INC. BEOCKWAY, I ~ Y L V A N I A U.S.A.
INTRODUCTION This paper will deal with the properties of glass which control its forming characteristics and behavior, and the mechanical and equi~nental aspects of glass forming processes.
While the emphasis
is on the production of glass containers, it is probably applicable to most glass products. A thorough understanding of these properties is essential to the optimum utilization of existing forming equipment for the efficient production of quality containers as well as for the modification of existing equipment or the deslg~ of the new forming equipment which will be required in the future to meet the lighter weight, higher strength container needs of the industry. Glass fonmlng processes perform best when they do not force the glass to flow or cool more quickly than its intrinsic nature will permit it.
This puts limits on the forming process.
operating limits are exceeded, troubles result.
The goal is then a
more con~olete understanding of these limiting properties of glass so that the process can be more exactly, [email protected]
About ten years ago, the author presented a paper entitled Glass Workability I in which a ntm~oer of observations that had been related to undesirable disturbances to the forming behavior of glass containers were catalogued.
The intent of this earlier paper was to demon-
strate that in spite of even exquisite process control, abnormal variations of the efficiency and quality of glass container production could still occur.
Such upsets were believed to be due primar-
ily to some change to a property of the glass itself. Workability was defined as the Droperty or properties which can be related to the ease with which glass can be formed.
workability manifests itself as an increase in checks, splits, poor distribution, or inadequate strength. it as brittle glass. -309-
Operators frequently describe
At that time, it was indicated that workability problems often resulted frcm: l)
Small changes in alumina
An increase in calcia content beyond some critical value
A decrease in content or number of minor ingredients such as
Variations in retained sulfate
baria and potassia
Variations in visible or Infrax~d transmission
Excessive use of cullet
At the same time, it was stated that large variations in silica content and glass hcmogeneity did not seem to have an adverse effect on workability.
No analytical or volume property measurement could
be found which could distinguish between glasses having 5ood or bad workability. The purpose of this present paper is to review the major changes which have occurred to the above listing, discuss new knowledge that has been developed during the intervening years, and to once 8 ~ n , point out the direction that future studies should take as well as to indicate the practical needs and requirements for a mere precise control of glass forming processes. RECENT PRACTICAL OBSERVATIONS RELA~ED TO WORKABII/IX Since the earlier paper on workability, ninny changes have occurred in the glass container industry.
Many of the earlier
observations which seemed to be valid are no longer so.
following are the more important examples: A.
Cullet During the recent soda ash shortage, as well as because of the
increased cullet recycling efforts, it is not uncommon to use 20 to 25% cullet or more for extended periods of time.
production problems no longer occur. B.
Alunlna Level Increasing difficulty in obtaining reliable sand supplies has
resulted in variations in altmdma content of the glasses well beyond the +0.1% formerly believed to adversely affect shearing, marking, -310-
and reheat characteristics but no such troubles are now observed. C.
Minor Ingredient Levels Since 1967, because of its extreme cost, barla has been
removed, partlally or completelyp frcm many glasses without ill effect. D.
Sulfate Variations Because of saltcake and soda ash shortages, variations in
sulfate level, both above and below the desired amount, have frequently been necessary. increases to a 35% removal.
These varlaticns have ranged from 300% While melting varlaticn certainly did
occur, no problems of a workability nature were encotmtered. E.
Transmission Variation The sand supply problem mentloaed above also resulted in much
larger variations in Iron than desirable, resulting in large variations in arher color and infrared transmission without causing forming problems. These more recent observations cam be interpreted in two ways: l)
The original observations were in error.
The current forming process is less sensitive to such comp~siticnal variations.
As the ori~ual observations were based on over 25 years of experience, It would seem desirable to examine the process changes which could have reduced the sensitivity of the forming process to such variations. Tnls examination produced three factors that have been developing over the last flve to ten years that are believed to have made significant contributions to the reduction in workability problems. qhese factors are: I)
A change in minor ingredient practice in flint glasses f~sm the tradltlcrmA arsenlc/nltre oxidation to a partial reduction by carbon.
A change in the ~ c e
temperature - tcrm~ge operating
schedule at low pulls. -311-
A modification of all
furnaces in the direction
d e p t h and i n s u l a t i o n . While a d e c r e a s e d s e n s i t i v i t y
t o some c c ~ p o s i t l o n a l v a r i a t i o n
has occurred during this period, workability variations means d i s a p p e a r e d . areas ~Ich
have a c o n s i d e r a b l e i n f l u e n c e on t h e f o ~
p r o c e s s w i l l be d i s c u s s e d i n some d e t a i l . heterogeneities,
have by no
Durir~ the remainder of t h i s paper, t h r e e major These t h r e e a r e a s a r e
t h e o l o g y , and s u r f a c e and m i n o r i n g r e d i e n t e f f e c t s .
CONSIDEHATIONS CRITICAL TO THE FOHMING PROCESS
Heterogeneities In most of the fundamental research studies carried out on glass,
a great effort is made to prepare completely homogeneous samples or melts.
This has been necessary in order to achieve universal
reproducibility of measurement and interpretation.
such ideal glasses do not exist in the real world of glass forming processes. The very fact that producing a truly homogeneous glass, even for optical use, is such a difficult task, if indeed it is possible at all, should in itself teach a lesson to those concerned with solving the normal problems encountered in glass production. While Tamman2 and his school investigated the conditions necessary to inhibit crystallization in glass, and a whole host of workers after Goldschmidt 3, Zachariasen 4, and Warren5 developed theories to explain properties of glasses based on their structures, Hartlei~ and Dietzel 7 were the first to discuss network modifiers as being distributed in clusters rather than statistically throughout the bulk glass. S. P. Jones 8 was one of the first to point out that most cc~mercial glasses, if con~oared thermodynamically to liquids, were not ideal liquids.
A deviation from ideality is n o b l y
tion of phase separation, c c ~ u n d
formation or association.
considered the freezing point depression typical of ideal liquids with the addition of a non-volatile solute.
In glasses, the
freezing point and liquldus t e ~ r a t u r e are synonymous. -312-
2, and 3 show that for soda/lime/silica glasses, whose primary phase is wollastonlte or devitrlte, the addition of A1203, CaO, SrO, MgO, and ZnO increases the liquldus temperature.
These same additions to
a glass whose prima~ phase is tridymite lower the liquidus temperature, consistent with Raoult's Law applicable to ideal solutions.
', f o
SlO 2 - 6 6 7 0 WT
CoO NO O -
I 6 O0
zoo PRIMARY ,8 1060
~,o~o~ ,,, ~ - ~ i
~ P- IO00+o
, ' /7o •
sroF FIG 2
S,02 - 7 1 O0 WT %
CoO - I I
~o~,~-"" I °
No20-- 18 O0 WT %
5 Mol %
u % IO30 '~' "-.
S,O 2 -
7 5 O O WT %
9 50 WT°/o
15 5 0 W T %
; ,o,oi ~
~ Q MgO Ba 0
MOI % ADDITION
As glasses in the tridymite field have a high SiO 2 content, they at~ also quite difficult to melt so the advantage, if any, to forming consistency can nor~ally not be realized.
On the other hand,
glass~kei~s invariably add soda ash or increase furnace ten~peratures when in trouble.
This has the same effect.
5he first realization of the role that micro-heterogeneities nff~ght play in coraTercial glasses was from Botwinkin9.
It was not
until the development of electron microscopy that the structural arguments between the network and crystallite theories were resolved. A complete review of the development of theories of glass structure is presented by Vogel I0 who also demonstrated that phase separation is not confined to special glasses of unique composition but is probably a common phenomenon i n all glasses.
Another classic work that showed the effect of micro-heterogeneities of strength was reported by Watanabe and Moriya ll. They considered the time dependence of viscosity, visco-elastlcity and strength and related these to the internal structure, conslderlng it to be non-homogeneous, theory and experiment.
and found good agreement between
Considering this was done in 1960, this was
a remarkable achievement, and does relate 'brittle' glass to interpretation. Bobkova and Rudakov 12 clearly showed that the micro-structure of a glass was also dependent upon its melting history. micro-heterogeneities
were not relics of the melting process,
derived from coarse or refractory materials, but were in addition to these.
They related it to a definite stage in glass formation.
When they exiit, one must conclude the process has not been completed.
only by very high melting temperatllres.
can be completely eliminated They conclude that micro-
inhomogeneities should be considered as defects in the structure inherent in r~my actual glasses but they do not characterize the structure of glass whose structural transformations have been completed. It should also be mentioned that relics of the actual melting process do exist and can have a very important role to play in the forming bel]avlor of a glass.
When an undissolved sand or nephelite
grain or a refractory stone remains in the glass, the effect can range from a visible defect whlch is easily discarded to a small volume element, not visible even microscopically, whose co~position and therefore rheological and crystallization properties will differ vastly from the matrix glass. To have structural as well as melting remnants, serves only to cc~npllcate the problem further.
However, for either condition to
be eliminated, an adequate melting time and temperature is required. Most of the recent major workability problems that have occurred in the author's production facilities have all had their origin in micro-het erogeneit ies. -316-
These fonming problems manifested themselves by poor distribution (thick and thin sidewalls), excessive checks and splits in the finish, thermal shock failures on most shops of a thirteen shop, three tank operation, and pressure breakage on all such shops.
of these is from a different plant and includes both flint and amber glass.
In some cases, it was noted that fibers for routine
viscosity measurement were difficult to draw and were also fragile. Simi1<~rly, bottles taken at the forming machine often disintegrated spontaneously during cooling. Figures 4-7 are electron mlcrographs of glasses taken during the periods of poor workability while Figure 8 is typical of the glass affter the problem had been solved.
c6~ 1 , , s o o x
Fig. 6 Poor Workability
8) 66,62S X
In most cases, sc~e portion of the meltlng/forehearth system had become too cold although a coarse feldspar was a factor in one of them.
The low te~eratures were due to the use of ten~porary or
standby, oil-flrlng systems during gas curtailments or to excessive pulls.
In no case were visible devltriflcation or batch stones
found, although daily stone checks are made routinely. The relationship between splits, checks, thermal shock and pressure failures and mlcro-heterogeneities
is fairly apparent as
the latter must act as a stress concentrator.
In the case of wall
thickness variations, however, the micro-inhomogeneities must have caused a difference in the flow characteristics of various portions of the glass being formed.
This will be dealt with in the next
Rheology A knowledge of the flow characteristics of glass as a function
of temperature and composition would seem to be essential to understanding its forming properties or workability. The author has shown in a previous paper that no correlation could be found between incidents of difficult forcing and viscosities in the annealing range although correlation was found between periods of excessive wall thickness variation and the viscosity changes observed while it was being measured continuously in the forehearth. As normal laboratory measurements of viscosity are carried out at or near equilibrium conditions at very low shear rates where the flow is Newtonian, no correlation with forming can be expected if the viscosity is non-Newtohian at high shear rates. The concept that liquids may fracture in shear derives from a paper by Reiner and Weissenberg 13 who found that failure should occur at a certain limiting value of the shear stress.
later used the same concept to explain the effect now known as melt fracture in the extrusion of molten polymeric materials at high velocities. -320-
J. F. Hutton 15 showed experimentally that ~ as a polydimethylsiloxane
elastic liquid such
when sheared in the gap of a cone plate
viscometer will f~cture in shea~- at a certain critical stress.
theoIif was extended to the flow of an elastic liquid through a capillary and could predict fracture when a certain flow rate was exceeded.
The extrapolation ¢f this concept to glasses as a mecha-
nism for the formation of checks and splits during forming would appear, to be reasonable, particularly as it is k~own that gob shearing occur~ as a result of fractu~e. Li and Uh!mann 16 studie~i a binary RbyO-SiO 2 glass ~lown to be homogeneous within the limits of electron microscopic observations to dete~nJ~le whether inorganic., oxide liquids deviate from Newtoniar~ behavio~ ~ and if so, the kind of stress dependence upon flow that can be expected. As Newtonian behavior is Followed at stress levels up to 107 d ~ e s / c m 2, the study extended the stress levels even to the rankle where fracture occurred. I~] the range of ten~perature of the experiments, low stress viscosities were between ]013.5 and 1017"1 poises. were extended beyond 109 .5 dynes/cm 2"
~ney found that beyond some
critical stress of about 109.1 dynes/cm 2, the viscosity decreased with increasing stress. dent of temperature.
This critical stress appeared to be indepen-
The viscosity decrease that occurred above the
critical stress was i to 2 orders of m~gnitude from the values measured at low stress where flow was still Newtoniar~. Figure 9 shows the variation of normalized fluidity with stress using data from the indicated temperatures.
Normalized fluidities are ~/~o
where ~o is the low stress fluidity at this same temperature, fluidity ~ being the reciprocal of the viscosity.
~ 480°C O .J
9 LOG ~ ~)YNES/CM2] 8
VARIATION OF NORMALIZED
WITH STRESS USING DATA FROM
In a subsequent work, Li and Uhlmannl7 studied the effects of phase separation on the viscosities of a soda-slllca and boroslllcate glass up to tensile stresses of 2.3 x lO lO dynes/cm 2.
case of the soda-sllica glass, non-Newtonlan behavior was observed after short times but wlth extended times up to 30 days, the viscosity was more dependent upon the morphology of the phase separation, increasing slg~ificantly with time.
was not observed in either glass after phase separation had been 1~Llly developed. From these studies, It has been shown that glasses can exhibit non-Newtonian flow above same critical shear stress or shear rate, phase separation can cause a significant increase in viscosity with
time at a constant temperature, and melt fracture, or in glasses, checks and splits can be anticipated when shear stresses exceed the critical shear stress. It remains now to detenm[ne the shear rates typical of various parts of the forming process to see if any of the effects described above can be operational in the f o n T ~
In a research program sponsored by the GCIRC over a number of years, detailed studies were conducted for this purpose. of the work was reported by J. Mills 18.
details of all the research are available only to those GCIRC members who supported it. Mills stresses the role of viscoelasticity in the forming process for glass containers.
He points out that the strain time
conditions of a typical forming operation are such that only transient stresses are created.
The viscosity on the other hand,
which is normally considered to be the characterizing parameter, requires steady state conditions. As it is necessary because of the transient conditions to determine the instantaneous stresses created during forming, Mills uses a theological equation of state developed for linear viscoelastic materialsl9.
(t)---/ G(t--s) 7(s) ds 0
Stress at time t
Stress relaxation n~odulus
Instantaneous strain rate
Using the stress relaxation data of Kur~ian 20 and Eisenberg and Takahashi 21, Mills develops the relationship between the stress relaxation modulus and time at different viscosities. This permits ~dm to calculate the stresses as a function of time and viscosity for both the gob shearing and finish pressing operations, using times determined frcm the observed operations. These relationships are shown in Tables I and II: Table I.
Stresses (lb in-2) predicted in gob cutting operation as a
function of time and viscosity, assuming a shear rate of 2 x l06 s-1 Viscosity (P)
From Table I, it can be seen that the gob shearing operation works by fracture with a shear rate of 106 S-I and a localized viscosity of 106 poises. Table If.
Stress (lb in-2) predicted for neck press operation as a
function of time and viscosity Time (s) Viscosity 10-5
Shear rate (s-l)*
* Upper and lower shear rate limits by calculation from machine parameters ** S t e a d y s t a t e
Table II continued: Viscosity
400 ].5 12.5 145
i0 58 580
5800 57500** 570000
*Upper and lower shear rate limits by calculation from machine parameters **Steady state flow established By the same token, Table [I shows that in the viscosity range of 104 - 105 poise where finish pressing normally occurs, steady state flow is readily achieved and no large stresses develop.
would confirm normal experience as finish pressing is obviously successfully carried out, most of the time.
If, however, circumstances
permit the viscosity to be raised to 107 or 108 poise by some delay in loading or a localized compositional or structural inhomogeneity in the glass, then very large stresses are encountered and fracture levels can be exceeded. While the stresses that have been calculated are only order of magnitude estimates because of the assumptions necessary, they are likely to be on the conservative side as linear behavior was assumed while non-linear effects are known to occur at large strain values. In non-linear viscoelasticity, an effect exists which could substantially increase the accumulation of stresses during short forming times.
This effect is called stress overshoot which occurs
at the sudden onset of steady shear, and was later confirmed by Mills 22 . Figure i0 is a stress-time response to onset of steady shear curve which shows stress overshoot. plate rheomet er. -325-
This data was obtained by a cone
/ 500 P-4O0--~
t:4o - - - - - -
TIME (SEC.) FIG. IO
Quantitative measurements of glass at high strain rates and high temperatures is an extremely difficult experin~ntal task. Figure ll shows a straln-tlme plane with areas delineated where measurements have been made as well as material behavior under such conditions.
. . . .
CONE AND PLATE
R H E O M E T E~R
...'" " ,.. : ::'.:'.'. :':;
CTO.E/ ~x';-'.'. \
/~:! :; vtSCostty,
q, m,\ ULTRASONIC~x(
-5 L \ \ ~ - ~ ~ \ \ \ %
NON-LINE~R~" ~ - /
LOG TIME (SEC) FIG I I
REGIONS OF MATERIAL
Of particular interest are the transition zones between linear, non-linear, and fracture if one is seeking a mechanism for checks and splits during forming. Fracture experiments in liquids have been carried out by Mackenzle23 using a high speed projectile fired into a molten glass at various temperatures.
While qualitative, fracture occurs at -327-
viscosity levels from 104 to 105 poise and at stress levels estimated to be about 25,000 psi. Additional studies utilizing a cone plate rheometer ~nd projectile penetration would seem to be very worthwhile and should produce si~9~ificant new information cfoout this little known area. It is obvious tlmt after proper exper~nental tehcniques have been developed, the scope of the research is enormous for to be practically useful, it must include such variables as composition, heat treatment, and melting history. As an indication of the complexity of the problem, the work of Hart and Kim 24, who studies the dispersed two-phase flow of viscoelastic polymeric melts, should be repeated for glasses.
study showed that the viscosity of the bl~nd went throuy~h a minimum and then a maximum at certain blending ratios, and that the elasticity of the blend goes through a ~ _ x i n ~ and a minimum at certain blending ratios.
The maximum in viscosity occurred with the minimum in
elasticity and vice versa. W. Wey125 st~m~rizes the co~nents on poor working or brittle glass as follows: "It is actually unimportant for a skater whether his lake is covered with ice that is cracked or whether the smooth ice cracks when he steps on it.
For the same ~ a s o n a
glass might become brittle or unworkable when it is molded.
No mechanical property can be measured without a
disturbance to the system.
Tn the most general way, we
describe a surface of a brittle solid as a potential crack system whether it has actual flaws or not.
In the same way
we describe a brittle glass as a system which differs from a workable glass in its energy and entropy inasmuch as it becomes brittle when mechanically deformed." C.
Effect of S~irface and Minor Ingredients The im~oortance of the viscosity of the surface layer of glass
during forming to the forming operation is common knowledge.
and ~brboe 26 discuss at length the differences in glass structure
between the surface and the b u l k
~nls composition difference, as
well as the tendency for impurities to concentrate in the surface, greatly complicates any study of the forming processes. Sul~ir as a mold lubricant has a dramatic effect on the forming process.
Part of this effect may be due to the tendency for a
sulfured glass surface to greatly increase
its water content, as
reported by Mochel, Nordberg, and Elmer27.
Tne enormous effect of
water content on viscosity has been discussed by Scholze 28 as well as by Fenstermacher 29 . It is also possible for excessive sulfur on the glass surface to form an extremely thin in~niscible sodi~n sulfate gall which d~astically alters its f o r ~
Elmer and Meissne~30haverecently found that carbon under proper conditions can be an excellent dehydroxylatLng agent, re~1oving s~lanol and boranol groups with a resultant increase in glass vlscosity. As both sulfur and carbon are cor~non components of mold lubricants, some further understanding of the mechanism y effectlve is now possible
which they are
As these effects are l~mited to a thin
surface film, until recently, i~ has been difficult to measure or even detect these changes with the instrumental techniques avallab]e Successful development of Auger technique for glass surfac ~ analys~s n~y provlde this analytlcal t~ol. The role of minor ingredients is not understood.
Interpret thelr effect as merely addlng complexity to the system whlch, as it would increase the entr ,py, would lower the system's free energy a~d thus minimize the need for the stability otherwise achieved by phase separation. The atmosphere over the melt as well as the redox of the melt, as reported by Hensler32, can have an effec~ on the viscosity, density, and strength of the flnal glass. Figure 12, after Sproul and Rindone33, shows a reversible change in l i ~ t
scattering and strength as a glass is exposed to vacuum or
This implies that 0 2 acts as a third co~onent in their
AMOUNT OF LIGHT
(PS.I. x I 0
c~ o o
Effect of Melting Time and Atomsphere on Strength
and the Degree of Light Scattering
The change in melting technique over the glass from oxidizing to partially reduced flint ccmpositions has coincided with a decrease in workability problems. Melt surfaces are now almost conlpletely covered with batch as co~pared to prior practices ~nich reduce
the volatiles lost from
the surface and thus the co~position difference between the surface and the bulk.
As the melting process has also been accelerated, it
should aid in the solution of the more refractory raw materials and lead to a reduction in mlcro-heterogeneities from this source. D.
Future Objectives Based on what has already been learned about various factors
that should or do have an effect on the forming characteristics of glass, it should be possible to determine the type of information that is still needed to accc~plish complete control and a detailed understanding of the mechanism of glass forming processes. As the two major factors affecting the forming process would appear to involve the rheology and micro-heterogeneitles of the system, the development of measurement techniques involving both are essential. Studies of stress relaxation rates should be D~ther refined and continued to permit a determination of the effect of composition, heat treatment, thermal history, and redox on this essential property Conditions should be sought which would result in the highest stress relaxation rates at all temperatures. To minimize the effect of micro-heterogeneities on the formlng process, as well as on the quality and performance of the resultant products, the preferred glass compositions would seem to require a low liquidus temperature, ideal thermodynamic behavlor to addition of i~purities or major ingredients, and a very low tendency toward phase separation of any type.
Absence of refractory or nucleating agents
in raw materials for preparing the glass would be desirable.
finished glass should be highly hc~ogeneous and free of seeds, blisters, or any inclusions. -331-
Conceivably, the melting process may have to incorporate some technique to expose all the glass produced somewhere in the process to extremely high ter~peratures for even a short time to destroy all structural ren~nants and achieve the necessary homogeneity. Routine control measurements are also essential if the ideality of the production glass is to be properly monitored. As a knowledge of homogeneity would seem most meaningful for this control function, the measurements should be capable of quantitatively detecting the degree of micro-heterogeneitles. Such techniques as light scattering by Shelyubski34 or Brillouin35 techniques, measurement of shape birefringence as described by Botvinkin and Ananich36, and even the determination of chemical durability should be useful. E.
Conclusions It is obvious that a complete understanding of the n~chanlsms
involved in the formlng process is still far from being achieved. To accomplish this, much research fraught with experimental difficulties is yet to be done. At the same time, however, the shortage of energy, environmental problems, depletion of the most suitable raw materials, increase in foreign cullet, increased performance requirements of containers, and the threat to glass from competitive packaging materials all make it essential that at least portions of the overall problem be solved. The emphasis on increased tonnage with reduced fuel consumption and lower temperatures, while at the same time inferior raw materials and contaminated foreign cullet must be used as batch materials, will have a tendency to decrease glass product quality and performance as well as create the conditions which can adversely affect the consistency of the forming process itself. It is not an optimistic picture
Perhaps, however, simply
knowing what must be done is cause enough for optimism. a long time to develop the knowledge now available. essential steps can be taken. -332-
It has taken
Surely, the next
Poole J. P., Glass Ind. 48, 129-136 (1967)
Tanm~nn G., Krlstallisieren and Smelzen, BatCh, Leipzig (1903); Der Glaszustand, Voss, Leipzig (1933) Aggregatzustande, Voss, Leipzig (1923)
V. M., Skrifter norske Videnoskaps - Akad, Oslo,
Mathnaturvidensk~ K1. 1926, No. 8 p. 7.
W. J., J. Amer. Ceram. Soc. 54, 3841 (1932)
B. E., Z. Kristallogr., Mineralog. Petrogr. 86, 349
Hartleif G., Z. Anorg. Ailg. Chem. 238, 353 (1938)
Dietzel A., Z. Elektro. Chem. Angew. Physik. Chem. 48, 9 (1942); Glastechn. Ber. 22, 212 (1948/1949)
Jones S. P., Phys. and C]nem. of Glasses, 2, 55-67 (1961)
Botwlnkln O. K., Westnlk Akad, Nauk SSSR, Physik. Ser 4_, 600 (1940)
Vogel W., Angew Chem. Internat. Edit. 4_, 112-121 (1965)
Watanabe M. and Moriya T., Rev. Elect. Comm. Lab., Nippon Tel & Tel 9--50-71 (1961)
Bobkova N. M. and Rudakov V. V., Steklo i Keram]_ka 6, ll-16 (1967)
Reiner M. and Weissenberg K., Rheology Leaflet No. i0, 12 (1939)
Tordella J. P., J. Appl. Phys. 27, 454 (1956)
Hutton J. F., Proc. Roy~l Soc. 287, 222 (1965)
Li J. H. and Uhlmann D. R., J. Non.Cryst~ Sol. 3, 127-147 (1970)
~i J. H. and U h ~
D. R., J. Non.Cryst. Sol. 3, 205-224
Mills J. J., Glass Tech. 14, 101-105 (1973)
Ferr7 J. D., Viscoelastic Properties of Polymers, J. Wiley & -333-
REFERENCES (CONT'D) Sons (1970) 20.
KurkJian C. R., Phys. Chem. Glasses 4_, 128 (1963)
Eisenberg A. and Takahashi K., J. Nor~Cryst. Solids 9_, 279 (1970)
Mills J., Personal Communication
Mackenzie J. D., Personal C c ~ c a t i o n
Han C. D. and Kim Y. W., Trans. Soc. Rheo. 19:2, 245-269 (1975)
Weyl W., Personal Communication
Weyl W. and Marboe E., Constitution of Glasses, Intersclence Publishers N. Y., N. Y.
Mochel E. L., Nordberg M. E. and Elmer T. H., J. Amer. Ceram. SOc. 49, 585-589 (1966)
Scholze H. and Franz H., Glastech. Ber. 36, 347-355 (1963)
Fenstermacher J. E., Lesser R. C. and Ryder R. J., Glass Ind. 46, 518 (1965)
Elmer T. H. and Melssner H. E., J. Amer. Ceram. Soc. 59, 206-209 (1976)
Weyl W., J. Non.Cryst. SOl. 19, 1-25 (1975)
H e ~ l e r J. R., Advances in Glass Technology, Plenum Press, 25-27 (1963), New York
Sproull J. F. and Rindone G. E., J. Amer. Ceram. Soc. 5_7_7(4) 160-164, (1974), Columbus, Ohio
Shelyubskli V. I. and Gefen A. G., Steklo i Keramika, 19 (Ii) 13-15 (1962)
Huang Y. Y., Hunt J. L. and Stevens J. R., J. Appl. Phys. 447 (8) 3589-92 (1973), American Institute of Physics
Botvinkin O. K. and Ananich N. I., Advances in Glass Tech. 2 86 (1962) -334-