high-strength, high-modulus glass fibers

.IOCIHNAL O F POLYMER SCIENCE: PART C NO. 19, PI'. 117-150 (1967)

Hig h-S trengt h, High-Modulus Glass Fibers

ALBERT LEWIS and DAVID L. ROBBINS,* Glass Technology Department, Chemical and Structural Products Division,

Aerojet-General Corporation, Azusa, California 91 703

Synopsis This paper describes work that was conducted to develop high-strength, high-modillits

glass fibers. Statistical experimental design and data analysis were used t,o determine some of the sampling, testing, and fiberizing variables that affect. the dispersion of mechanical property data of glass fiber specimens. The simplex lattice experimental design was iised in glass compounding studies. The experimental method is described. Three glass c:ompositions with high mechanical properties are described. One of these glasses is romposed of R.IgO-A1203-Si02. The other two are 4-component glasses and c*oiitain hlg0-Al2O3-SiOr and BeO, or LazOa.

I. INTRODUCTION

High-strength, high-modulus glass fibers are important t,o the Air Force efiort to make strong, lightweight structures. The glass fibers are used as structural members to reinforce plastic parts. The glass fiber-plastic com- posites are used for many applications in rocket, missile, and aircraft structures.

This paper describes current work to develop superior glass reinforcing materials. The work is primarily involved in glass composition studies. Processing parameters have considerable influence on glass fiber properties, however, and different evaluation techniques can result in apparently different property values; therefore, these aspects of the problem were also studied.

11. EXPERIMENTAL EQUIPMENT AND PROCEDURES

Normal procedures were used to prepare the glass specimens during thew studies. The raw materials used were technical or reagent grade chemicals. The batch materials were weighed to an accuracy of 0.1 g. and dry-mixed in a twin-shell blender for l/Z hr. A standard batch size of ,500 g. was used. Sufficient water was added to the mix to form a crumbly mass in order to prevent excessive dusting when the batch was charged into a preheated crucible in a pot furnace.

* Present address: Aerospace Corporation, San Bernardino, California. 117

118 A. LEWIS A N D D. L. IIOBBINS

The glasses were melted in platinum crucibles or in zirconia-alumina melting containers if the glass attack on this material was not excessive.

Melting was accomplished in temperature-controlled, compressed air- natural gas furnaces. After the melt was free of unmelted particles and excessive gas bubbles, the glass was fritted in water.

I’iberization of the frit was conducted in a single-orifice platinum alloy furnace. Each fiber furnace consists of a platinum-rhodium bushing coated with a high-alumina ceramic and mounted in a high-temperature insulating refractory. The furnace is self-heated by resistance with a high-amperage, low-voltage, 20-kva power supply. The furnace temperature is controlled by a platinum-rhodium thermocouple connected through a pyrometer to a magnetic amplifier and saturable core reactor. The bushing is designed to accommodate a glass level of more than 2 in. and utilizes a capillary diameter of 0.078 in. in the orifice.

The take-up equipment used to draw the glass filaments operates at speeds ranging between 2000 to more than 10,OOO ft./min.

During fiberization, the glass temperature, hydrostatic head, and drawing speed were varied as required for each glass composition. The glass temperature was determined optically from glass a t the top of the bushing because grain growth in thermocouple wires results in inaccurate thermocouple readings.

Specimens were taken from a fiber captured between the bushing orifice and the take-up drum. Two specimens were taken from each capture. A minimum of six captures were made for each glass composition. The fiber specimens were cemented on cardboard tabs using Duco cement. The cardboard acted aa specimen holders and gripping cushions during testing. A typical specimen mounted on a cardboard tab is shown in Figure 1.

Tensile testing was accomplished using an Instron tensile testing instrument with rubber-coated jaws. This instrument utilizes a strain-gage type loading-measuring system in combination with a constant speed crosshead drive. The crosshead travel is synchronized with the movement of the recording chart. The strain rate used was 0.2 in./min. The test specimens are 1 in. long.

The diameter of one specimen obtained from each capture was opticitlly determined at a magnification of approximately 300X. An image-shearing eye-piece, which will be described later, was used for this determination.

The tensile strength was determined from the load-diameter relationship. Young’s modulus was calculated from the stress-strain curve, and/or by sonic methods. When the stress-strain curve was used, deviations from linearity were corrected by extending the initial portion of the curve. No corrections were made for deflections in the test machine or for grip end effects.

Density determinations were made using the Archimedes method on un- annealcd bulk glass. Picrcs of frit,, or “onions,” obtained from the bushing were used for this purpose. It may be assumed that the densities of the glass fibers are somewhat lower than the densities of the bulk glass.

1f 1GII-STRENGTH, HIGH-MODULUS GLASS FIBERS 119

Fig. 1. Mounted monofilament.

111. MANUFACTURING AND TESTING PARAMETERS

A. Sampling and Testing Procedures and Variables

1 . Fiber Diameter Measurements a. Precision. A critical measurement required for determination of

the mechanical properties of a fiber is the cross-sectional area of the fiber. I>or brittle materials like glass, it is assumed that no plastic flow takes place and that the cross-section of the fiber is the same at failure as in the unstressed state. The cross-section is most easily calculated from a direct measurement of the fiber diameter.

The critical nature of the diameter measurement can best be illustrated by an example. The average diameter of glass fibers subjected to testing is approximately 0.00035 in. Assuming a tensile strength of 700 ksi and n tensile modulus of 14 X lo6 psi, an error of 10% (35 X in.) in the diameter measurement will result in an error of more than 100 ksi in tensile strength and more than 2 X lofi psi in tensile modulus. Accurate deter-

120 A. LEWIS AND D. L. ROBBINS

mination of fiber diameter assumes extreme importance in a research area where the last 100 ksi of tensile strength and 1 X lo6 psi of tensile modulus are most difficult to achieve.

Most research facilities measure fiber diameter by using a graticulated or traveling fiduciary line (filar micrometer) imposed optically from above. This technique is subject to inaccuracies resulting from parallax, differences in contrast between the scale and the fiber, lack of in&umental or fiber stability vitiating the scale-fiber relation, placement of the fiduciary line, etc.

In a successful attempt to reduce these inaccuracies, an image-shearing eyepiece (Vickers-AEI image-splitting measuring eyepiece, manufactured by Cooke, Troughton, and Simms, Inc., Malden, Massachusetts) was substituted for the filar micrometer. I n this device, a prism system is interposed between the microscope objective and the eyepiece to produce a double image of the microscope field of view. The prism system is precisely

TABLE I Data Comparing Two Instruments, Diameter Measurements

Meaaured diameter,. pin.

1 2 3 4 5 6 7 8 9

Filar Eyepiece

Operator A 262 262 262 312 713 779 755 755 484 Operator B 279 279 270 262 771 771 771 755 476

Split-Image Eyepiece

Operator A 330 345 322 353 805 836 805 813 537 Operator B 330 353 322 353 805 836 805 813 537

* Column headings represent specimen numbers.

rotatable by a micrometer screw. Upon rotation of the prisms, double images of objects in the field of view traverse one another. Measurement is accomplished by a micrometer reading of the amount of prism rotation necessary to traverse the double images exactly from one edge to the opposite edge. Measurement is accomplished in the plane of the object and is therefore free from the inaccuracies inherent in the filar eyepiece. The accuracy of measurement obtainable with the image-shearing eyepiece arid a 40X objective lens is 0.0000128 in., or for a fiber with a nominal diameter of 0.00035 in., the error is *3.66%. Using a fiber with the properties as previously given in the example, this would represent an error of less than 50 ksi in tensile strength and less than lo6 psi in tensile modulus.

The precision of fiber diameter measurements was determined in an experiment in which the diameters of nine fibers were measured by two operat,ors. F;ach operat,or used a filar eyepiece and the image-shearing eyepiece to measure the diamct,er of each fiber. The data are shown i n Table I.

z U e k2

TA

BL

E I

1 A

naly

sis

of V

aria

nce

Dia

met

er a

s M

easu

red by

Tw

o D

iffe

rent

Ins

trum

ents

5

Sum

of

Deg

rees

of

3

Sour

ce

squa

res

free

dom

M

ean

squa

re

F ra

tio

Ope

rato

rs

138.

9 Sp

ecim

ens

945,

856.

8 R

esid

ual (

read

ing-

3,

306.

1

Tot

al

949,

301.

8 er

ror v

aria

nce

Fila

r E

yepi

ece

1 8 8 17

-

Split

-Im

age

Eye

piec

e

138.

9 ?J

ot s

igni

fica

nt

413.

3a

118,

232.

1 28

6.1

Not

sig

nifi

cant

com

pare

d w

ith

inde

pend

ent.

esti

mat

e

Ope

rato

rs

3.5

1

3.5

N

ot s

igni

fica

nt

m %

17

?? z

Spec

imen

s 91

2,66

7.1

8 11

4,08

3.4

31 ,6

89.8

R

esid

ual

(rea

ding

- 2

8.5

8

3.6

Tot

al

912,

699.

1

413.

3 3.

6 ~

- - 1

14.8

sig

nifi

cant

ly

v,

smal

ler

-

erro

r va

rian

ce)

m

M

a In

depe

nden

t est

imat

e of

read

ing

erro

r, m

ean

squa

re =

330

(88

deg

rees

of

free

dom

).


An analysis of variaiice was conducted for each instrument t,o det,ermine Table I1 shows the reading error variance for the filar

in. This variance the reading error. eyepiece to be 413.3, or a standard deviation of 20 x

TABLE 111 Slurunary of Round-Robin Test Data

Variation,. %

Filar eyepiece Split-image eyepiece

Comparisoir Air Oil Air Oil

Firm 1 vs. Firm 2 -6.14 -7.eo + I .84 -1.47 Firm 1 VB. Firm 3 + 3 .95 +1.84 +14.60 +9.41 Firm 2 vs. Firm 3 -13.05

Filar eyepiece vs. split-image eyepiece, fibers in air: --9.650/; filar eyepiece VH.

split-image eyepiece, fibers i i i oil: -524475.

is not significantly different from a previous estimate of 330 obtnined for measurements with the filar instrument.

The reading error variance for the image-shearing eyepiece is shown to be only 3.6 (in Table II), or a standard deviation of 1.9 X in. (an order of magnitude smaller). This value is obviously (and statistically) significantly smaller than the reading error variation obtained with the filar eyepiece. The experiment showed that much more precise fiber diameter measurements can be obtained with the image-shearing instrument than with a filar eyepiece.

b. Accuracy. The data in Table I indicate that the image-shearing eyepiece provided fiber diameter measurements significantly larger than those obtained with the filar eyepiece. Both instruments were calibrated against the same stage micrometer and the techniques used to mount fibers for observation were the same for both.

To determine the accuracy of each instrument and to compare fiber diameter measurements with those of other investigators in the field, a round-robin test involving three firms was initiated.

The diameters of specimen fibers were measured in air with flar and split-image eyepieces. The other participants in the program then measured the fibers using their routine techniques: the fibers were immersed in an oil with a refractive index close to the index of the fiber, and measured using a filar eyepiece. The round-robin data are summarized in Table 111.

Table I11 shows that the measurements in air, using the filar eyepiece, were approximately 6% smaller than those obtained by Firm No. 2 and 4y0 larger than those obtained by Firm No. 3. With the split-image eyepiece the measurements were approximately 2% larger and 15% larger, respectively.

Because the measurements with the filar eyepiece in air were the median of the measurements, it was decided to use the filar air readings as ~t

temporary standard in our laboratory. Accordingly, the image-shearing

HIGH-STRENGTH, HIGH-MODULUS GLASS FIBERS 123

eyepiece calibration was corrected to correspond with the values obtained with the filar eyepiece.

Parenthetically it may be noted that dynamic modulus of elasticity determinations do not depend upon diameter determinations while static determinations of the same property require diameter measurements. Good correlation was obtained between the modulus determined by both methods using the corrected calibration. The good correlation increases the confidence in the accuracy of the diameter measurement.

To improve the accuracy of fiber diameter measurements and to provide a realistic standard, measuring the cross-section diameter of the fibers was attempted. This technique would eliminate the effects of light diffraction and penumbra which now make accurate diameter measurements difficult. In this technique fibers were mounted approximately vertically in an opaque mounting medium. The fiber ends were polished with the aim of providing a plane surface. Internal reflections cause the fiber to behave as a “light pipe,” and the fiber was observed as a circle of light in a dark field. Measurement errors resulting from improper mounting are a function of the cosine of the mounting angle but are minor in comparison with the error resulting from light diffraction. It was found, however, that the fiber ends could not be polished to a plane surface. A good method was not found to preserve the fiber edges; as a result, the fiber end acted as a lens and the method was abandoned.

2. MonoJilainent Sampling and Testing

The fiber was illuminated at one end.

,411 area most critical to this program was that of testing or evaluating glass monofilaments to determine their mechanical properties. The properties so obtained are the measures used to determine the merit of a glass composition as well as to show the effects of modifications in composition or treatment.

A study was performed to develop a procedure to reduce t,he data variation apparently caused by sampling and testing procedures.

a. Experimental Plan. The experiment was conducted by two experi- enced operators who used the same glass and obtained fibers from the same bushings. The fiber-bushing parameters (temperature, glass level , drawing speed) were maintained constant throughout the test.

The Aerojet procedure for testing a glass fiber requires that the operator captures a fiber, mounts the fiber on a cardboard tab, separates two specimens from each mounting, measures and records the fiber diameter of each specimen, inserts the specimen in the testing machine, cuts the holder, and records tensile measurements.

Figure 2 illustrates an experimental sequence that was used to separate and estimate the variation due to most of these operations. Each operator made four captures. Statistically it would have been better to completely randomize the order in which the operators made their captures; to facilitate the experiment, however, they alternated captures. Before starting, the operators and testing machines were numbered so that the

124 A. LEWIS AND D. 1,. ROBBINS

~ @ ~ m i i ’ Specimen 1 Specimen 2 Spclmen 1 _ _ -~

order of participation or use was randomized. Figure 2 shows the alloca- tion of the order of captures to operators and test machines. Operator 1 made the first capture and used Test Machine 2; Operator 2 made the second capture and used Test Machine 2, etc.

Figure 2 shows that six specimens (i,e., three mountings) were obtained from each capture. Two independent diameter measurements were made

Mounting 1 Mounting 2

CAPTURE 4

CAPTURE 5

-~ speclmen 2 Mounting 3 - Speclmen 1 Speclmen 2 Mountlng 1 Speclmen 1 I Mountlng 2 Specimen 2

~-

CAPTURE -

Spclmen 1 ,

MACHINE 1

Swimen 1 I

Specimen I Sp@=< Mountlng 3

Specimrn2 hunting 1 Speclnmn 1 Mountlnq 2 Speclmen 2 ~ CAPTURE 2 Specimen 1 Speclmen 2 Mountlng 3 Spclmen 1

_- ~

Specimen 1

~~

MACHINE 2 - ~-

TESTING

OPERATOR 2 -

-~ MACHINE 1

MACHINE 2

OPERATOR 1

MELT I

on each specimen in random order. The specimens from each capture were then tested in random order.

b. Analysis. (I) Diameter Measurements. The filar eyepiece was used for this study. Table IV summarizes the analysis of variance for diameter measurements.

TA

BL

E I

V

Ana

lysi

s of

Var

ianc

e D

iam

eter

(Sa

mpl

ing

and

Tes

ting

Esp

erim

entl

Sour

ce o

f va

riat

ion

Sum

of

Deg

rees

of

squa

res

free

dom

M

ean

squa

re

F ra

tio

Exp

ecta

tion

of

mea

n sq

uare

Ope

rato

rs

Cap

ture

s (w

ithi

n op

erat

ow)

Mou

ntin

gs

(wit

hin

capt

ures

)

Spec

imen

s (w

ithi

n m

ount

ings

)

Ilea

ding

s (m

rithi

ri

Tot

al

spec

imen

s)

0.084

10.8

53

0.6

24

0.4

53

1 .X

37

1 6 16

24

44: -

13.8

51

95

0.084

1.8

09

S8

~~

Not

sig

nifi

cant

5

4.8

2 (s

igni

fi-

cant

at

0.1%

le

vel)

N

ot s

igni

fica

nt

48u.

’ +

12u?

+ 40

2 +

2@2 +

n2

12r,

2 +

4u,2

+ 2u

.2 + U

P2

4u

2 +

2u2

+ Or2

Not

. eig

nifir

ant

2u,2

+

u,2

* (0

2)

\‘ari

alic

e.

Sktb

rrri

pts:

(0

) op

erat

ors:

(c

) ca

ptur

e; (

m) m

ount

ings

; (

8)

spec

imen

s; (

T)

read

ings

.


The mean-square values arc estimates of a linear combination of variances as shown in the “expectation of mean square” column. The variance due to variation between specimens is denoted by us2. If this variance exists, the ratio (2uS2 + ur2)/ur2 will be significantly greater than unity, as can be checked statistically by an F-ratio test. The same line of reasoning can be used to test the variances of mountings, captures, and operators, each mean square being tested against the one just below it in the table. In practice, however, nonsignificant mean squares are combined or pooled when they are estimates of the same quantity in order to increase the sensitivity of the F-ratio tests.

In Table IV the mean square for specimens was pooled with that for readings because the F value was small. Pooling is accomplished by dividing the total sum of squares by the total degrees of freedom for the two classes. The mean square for mountings was then tested against the pooled value. Because the F ratio was not significantly large, this mean square was also pooled.

The pooled value from all three sources is 0.033 and is shown beside the brace in Table IV. When the mean square for captures is tested against this pooled value, the F ratio is very large. The probability that this will happen by chance is small, and it can be assumed that uc2 really exists. Because am2 and us2 have been taken to be zero as a result of the previous test, the expectation of the significant mean square, 1.809, is 12uc2 + u , ~ .

Because an estimate of 0.033 exists for ur2, an equality can be set up to solve for uc2 as follows:

12u: + urz = 1.809

12uC2 + 0.033 = 1.809

u: = 0.148

This value was used to determine the number of captures rrquired to obtJairi a desired precision for a diameter measurement.

The mean square for captures could not be pooled because it was significantly large and it was used to test the mean square for operators. Because it waa small relative to the mean square for captures, the operator mean square was not statistically significant indicating no operator differ- ence.

Table V summarizes the analysis of variance for modulus of elasticity measurements. The mean squares for mountings and specimens were pooled to give an estimate of 1.157 for us2. The mean square for captures was significantly large and could not be pooled so that it was necessary to test operators and machines and their interaction against the mean square for captures. The choice of the captures mean square for these tests is indicated by the expectation of mean square column in Table V. Although the mean square for operators appeared large, it was not significant at the 5% level. This level was taken as an arbitrary dividing line between chance and nonchance events.

(2) Modulus Measurements.

TA

BL

E V

A

naly

sis

of V

aria

nce

hlod

ulus

of

Ela

stic

ity (

Sam

plin

g an

d T

estin

g E

xper

imen

t)

Sour

ce o

f Su

m o

f D

egre

es o

f va

riat

,ion

squa

res

free

dom

M

ean

squa

re

F r

atio

E

xpec

tatio

n of

mea

n sq

uare

"

Ope

rato

rs

24.1

69

Mac

hine

s 0.

573

Ope

rat,o

r-m

achi

ne

4.21

2

Cap

ture

s (w

ithin

15

.708

in

tera

ct,io

n

oper

ator

s an

d m

achi

nes)

capt

ures

) M

ount

ings

(with

in

15.5

93

Spec

imen

s (w

ithin

29

.545

m

ount

ings

) T

otal

89

.800

Not

sig

nifi

cant

N

ot s

igni

fica

nt

24

~~

2

+ 6u

c2 +

2um

2 + us

z

24

~~

2

+ 6rc2 + 2

am2 +

usz

1

24.1

69

1 0.

573

1 4.

212

Not

sig

nifi

cant

12

r,,,*

+

6uC

2 + 2u

mZ

+ u

aZ

4 3.

927

3.39

(si

gnif

ican

t 6r

,P +

2um

2 + us

z

5y0

leve

l)

Not

sig

nifi

cant

2

02

+ u.

2

t 1.157

0.97

5

23

1.28

5 U

S2

46 -

-

* Sub

scri

pt (o

zm) o

pera

tor-

mac

hine

int

erac

tion

Oth

er s

ymbo

ls d

efin

ed in

Tab

le IV

.

I28 A. LEWIS AND D. L. ROBBINS

h estimate of the variance for captures was obtained in the manner described above. Because

6uC2 + us2 = 3.927

the substitution of us2 = 1.157 yields

uc2 = 0.462

Table VI summarizes the analysis of vari- The results follow the same pattern as those

The mean square for mounting was pooled wit,h The

The estimated value

(3) Strength Measurements. ance for tensile strength. obtained for modulus. the mean square for specimens to yield an estimate of 5294 for us2. mean square for captures was significantly large. for the capture variance, u,2, is given by

6uC2 + 5294 = 20,842

which yields

uC2 = 2591

The remaining sources of variation were not statistically significant. c. Comments. As an example of the use of these estimated quantities,

consider the variance of the average of the tensile strength of several specimens taken from the same melt under identical variance between specimens and between captures is lows :

u.2 = 5294

uC2 = 2591

conditions. The estimated as fol-

If oiie specimen is taken from one capture, the variance of the deterniinatioii is estimated by

U 8 2 + uc2 = 7885

If n specimens are mounted from each of k captures, the variance of the average of the nk determinations is given by

If the number of specimens to be tested is limited, for exanqdc, to 12, tlic equation can be solved for the combination of n and li giving minimum variance. Assuming that it was possible to obtain 12 specimens from onc capture, the variance would be

US2 5294 12 12 no2 + - = 2591 + ___

= 3032

TA

BL

E \'

I A

naly

sis

of 17

aria

nce

Ten

sile

Str

engt

,h (S

ampl

ing

and

Tes

ting

Exp

erim

ent)

Sow

re o

f Su

m o

f D

egre

es o

f va

riat

ion

squa

res

free

dom

M

ean

squa

re

F r

atio

E

xpec

tatio

n of

mea

n sq

riar@

Ope

rato

rs

Mac

hine

s O

pera

tor-

mac

hine

in

tera

ct,io

n C

aptu

res

(with

in

oper

ator

s an

d m

achi

nes)

A

Ioun

tings

(w

ithin

ca

ptur

es

Spec

imen

s (w

ithin

Tot

al

mou

ntin

gs

37,0

19

27,1

23

151

83 , 3

68

77,0

55

129,

430

354,

146

--

1 37

,019

N

ot s

igni

fica

nt

24uO

2 + 6u

c2 +

2um

2 + ud

2 N

ot s

igni

fica

nt

24um

2 + 6.

~~

2

+ 2u

m2 +

ua2

1

27,1

23

1 15

1 N

ot s

igni

fica

nt

12uO

zm +

6u,2

+ 2u

m2 +

us2

4 20

,842

3.

94 (S

igni

fican

t 6u

c2 +

2um

2 + u.*

at 1

% le

vel)

4,81

6 N

ot s

igni

fica

nt

2u,2

+

u2

23

5,62

6 u

*2

46 -

8 S

ymbo

ls d

efin

ed in

Tab

les

IT.' a

nd V

130 A. LEW18 AND D. L. HOBBlNS

TABLE VII Variance of Average of Strength Determination9

(Sampling and Testing Experiment)

Estimated variance k n of average

1 2 3 4 6

12

12 6 4 3 2 1

3032 1737 1305 1089 873 657

* Variance of average of nk = 12 strength determinations where n is the number of specimens per capture and k is the number of captures.

Regardless of the number of specimens, the variance would always be estimated as 2591 or more.

Table VII shows the variance for other combinations of n and k for nlc = 12. In this case, the procedure giving the best precision (smallest variance) would call for 12 captures and the mounting of one specimen from each.

d. Conclusions. Only two important sources of variation were found for diameter, modulus, and tensile strength measurements.

For diameter, there is a variation within each specimen (as measured by repeated readings) that is probably a measure of the precision of the measurement. There is also a definite variation in diameter between captures under identical experimental conditions.

For modulus and strength measurements, there is the basic variation between specimens and again a significant additional variation between captures.

There were no apparent differences between operators or tensile test machines and no observable differences between mountings made from the same capture.

It can be concluded that improved precision of observation would require several captures. The optimum number of captures and specimens per capture can be determined by specifying the total number of specimens to be tested. In the present work it was decided to test 12 fibers from each glass composition. These fibers were obtained by making six captures from which two tensile determinations were made. In this case, the estimated variance of average is 873.

B. Fiberization Variables

Conditioning Temperature

An experiment was conducted to determine the effect of the following variables on the tensile strength, modulus, and diameter of glass fibers : (a ) the effect of feeding glass to the bushing with normal delay before fibers are drawn; ( b ) the effect of conditioning time in the bushing before

1. h’flects of Adding Glass to Bushing, Conditioning Time, and

lllGl I-S‘rI1ENGTII. IIIGII-MODULUS GLASS FIBERS 131

fibers are drawn; and ( c ) the interactions of conditioning temperature with conditioning time and glass feeding.

In order to combine conditioning time and conditioning temperature, it was necessary to clean the bushing and start with fresh glass after half of the experiment was completed. This complication required a “split-plot” type of experiment in which the blocks were confounded with the main effect (conditioning temperature in this case). The experiment provided a good estimate of all of the temperature interactions, but not a good estimate of the simple effect of conditioning temperature.

TABLE VIII Experimental Trials for Evaluation of Five Fiberiaing Variablese

A Con- B C D E

Trial ditionhig Condit.ioning Glass Glass Drawing no. t,emp., O F . time, hr. feed level, in. temp., OF.

2840 2840 2840 2840 2840 2840 2840 2840

2 2 2 2

16 16 16 16

Block I None None Added Added None None Added Added

2940 2800 2800 2940 2800 2940 2940 2800

Block I1 !) 2460 4 None 2 2800

10 2460 2 None 1 /2 2940 11 2460 2 Added 2 2940 12 2460 2 Added 1 /2 2800 13 2460 16 None 2 2940 14 2460 16 None 1 /2 2800 15 2460 16 Added 2 2800 16 2460 16 Added 1 /2 2940

a Half replicate of 2& factorial, defining contrast I = ABCDE, Factor A confounded with blocks.

The problem of the glass level in the bushing had to be considered berause the addition of glass would affect this parameter. Drawing temperature was also included as a controlled variable because the experimental plan allowed the evaluation of an additional variable with very little additional experimental time.

These additions resulted in an experiment with five independent variables.

a. Experimental Plan. Table VIII shows a half replicate of a 26 factorial design consisting of 16 trials in two blocks of 8 trials. Each of the independent variables is at two levels. The levels of the variables were

132 A. LEWIS AND D. L. HOBBINS

TABLE IX Analysis of Variance, Tensile Strength

(Evaluation of Five Variables)

Source of variation

Sym- Sum bol Variable of squares

Degrees of hlean freedom square F ratio“

A Conditioning temp. (blocks)

B Conditioning time

AB Cond. temp. X cond. time

C Glassfeed AC Cond. time X

BC Cond. time X

1) Glass level AD Cond. temp. X

glass level BD Cond. time X

glass level CD Glaasfeed X

glass level E Drawing temp. AE Cond. temp. X

BE Cond. time X

CE Glass feed X

1)E Glass level X

Error bet,ween captures

Error between specimens

glass feed

glass feed

drawing temp.

drawing temp.

drawing temp.

drawing temp.

Total error

1,141.03

117,120.01

15,711.44 923 , 658.28

48,675.00

8,625.44 594,928.27

345.03

103,286.17

459,740.62 61,116.07

84,942.16

3,632.16

25.78

59,410.30

1,569,408.06

Il222,Z26.0

1

1

1 I

1

1 1

I

1

1 1

1

1

I

1

95

103

2,791,634.06 198

1,141.03 <1 (ns)

117,120.01 7.09 (sl)

15,711.44 < I (ns) 923,658.28 55.91 (s0.1)

48,675.00 2.95 (ns)

8,625.44 <1 (ns) 594,928.27 36.01 (s0.1

345.03 <1 (nu)

103,286.17 6.25 (s5)

459,740.62 27.83 (sO.1 61,116.07 3.70 (ns)

84,942.16 5.14 (85)

3,632.16 <1 (us)

“.7X < I (11s)

59,410.30 3.60 (11s)

16,520.08 1.39 (s5)

11,866.27 -

14 , 099.16

* F ratios obtained from ratio of each mean square to the “between capt>ures” mean square. Symbols have the following meanings: (ns) not significant at 5y0 level; (95) significant a t 5% level; (sl) significant a t 1% level; (sO.1) significant a t 0.1% level.

fixed after a preliminary study to determine the fiberization limits imposed by the glass level, drawing temperature interaction. The levels on these two variables were set as wide as practicable. The bushing was cleaned out and reloaded once during the experiment-between Trials 8 and 9.

The plan was designed to cause the high glass level in the bushing to coincide with the additioii of feed. Trials 5 and 13, however, required a high glass level aiicl no feed. This was accomplished by feeding the twsh- ing immediately after Trials 4 and 12 before the long conditioning time.

IIIGII-STRENGTII, IIIGI-I-MODULUS GLASS FIBERS 133

Each trial at a high glass level was followed by one at a low glass level. The low level was achieved by removing glass from the top of the bushing with a Pyrex rod. Glass was added to the bufihing in the form of frit crushed to pass a 1/4-in. screen. The frit was crushed and blended before the experiment was started to assure a uniform glass supply. Whenever glass was added to the bushing, the next specimens were normally obtained only after a delay of l /2 hr. Whenever the glass temperature was changed, the next specimens were obtained only after a normal delay of ‘/4 hr. The drawing speed was maintained constrant at 86.50 ft~./min. through the experiment.

Except for a few instances of fiber breakage, 14 values were obtained from each trial consisting of two specimens from each of seven captures. Table IX shows the analysis of variance for tensile strength. The total error mean square was divided into the two components associated with variation between captures and variation between specimens within captures. The variation between captures was significantly larger than that between specimens. The tests of significance for the processing variables in the analysis of variance were thus made using the “between- captures” mean square. Table X provides two-way tables of mean values that illustrate all the significant effects for tensile strength. The significance level for each effect is indicated for convenience.

Table X reveals that glass addition resulted in a much lower average strength even if the glass level (and the associated tensile strength) was originally high. It shows that glass level has a large effect only when no glass is added. Because the low glass level (accompanied by reduced strength) was obtained by removing glass, a possible inference from the data is that strength is reduced by glass addition, glass removal, or both. The upper right cell of the interaction table represents the case of no disturbance and averages about 200 units higher than the other three cases.

There is some indica- tion that conditioning time is more important at the low glass level. The interaction between conditioning temperature and drawing temperature shows that a high drawing temperature may compensate for a low conditioning temperature.

Table XI summarizes the analysis of variance for modulus of elasticity. For this variable, the variation between captures was not significantly larger than that between specimens within captures so that these two mean squares could have been pooled if desired. The tests of significance for the controlled variables were made as they were for tensile strength, however, by using the between-captures mean square.

Table XI1 presents the average values that illustrate each significant effect. The apparent effect of conditioning temperature shown in Table XI1 should he disregarded berause it is indistinguishable from the cff ects of blocking. The high glass level gave better results as it did for tensile strength. The simple effect of glass feed did not show up for modulus. The reason for this can be seen in the interaction table for glass feed and

b. Analysis.

Long conditioning time also degraded strength.

TA

BL

E X

A

vera

ge V

alue

s Il

lust

ratin

g Sig

nific

ant E

ffec

ts fo

r T

ensi

le S

tren

gth.

(E

valu

atio

n of

Fiv

e V

aria

bles

)

Gls

ss fe

ed (s

O.1

)

Non

e: 5

09.6

A

dded

: 38

1.2

Gk

le

vel (

sO.1

) G

lass

fe

ed

LOW

Hig

h

Non

e 41

2.8

606.

4 A

dded

37

5.0

387.

4

Dra

win

g te

mp.

~~

Gla

ss le

vel (

SO. 1

) C

ondi

tioni

ng ti

me

(sl)

Low

: 39

3.9

Hig

h: 4

96.9

Sh

ort:

468

.3

Lon

g: 4

22.5

Con

ditio

ning

G

lass

leve

l (s5)

Shor

t 43

8.2

498.

3

time

LOW

Hig

h

Lon

g 34

9.5

495.

5

Con

ditio

ning

LO

W

Hig

h

tem

p. (6)

LO

W

407.

1 45

0.6

Hig

h 47

9.1

444.7

a S

ymbo

ls u

sed

have

the

follo

win

g mea

ning

s: (

sl) s

igni

fican

t at 1

% le

vel;

(sO

.1) s

igni

fican

t at 0

.1%

leve

l; (s5) s

igni

fican

t at 5%

leve

l.

?

c:

U. e r

I IIGII-STRENGTH, HIGH-MODULUS GLASS FIBERS 135

glass level. Glass addition gave better results at, the low glass level a d poorer results at the high glass level. Therc was some iiidicat,iori that lengthy conditioning degraded the modulus. The interaction between conditioning time and glass feed indicated that glass addition after long conditioning may have a reviving effect on the modulus of elasticity. The interaction between drawing temperature and glass feed indicated that a low teniperature compensates for the effect of glass addition. The Mter

TABLE XI Analysis of Variance, Modulus of Elas1ic.i tg

(Evaluation of Five Variahles)

Source of varitlt,ion

Yym- Sum of 1)egrees of bol Variable squares freedom Mean square F ration

A

B

A 13

C AC

BC

D AD

BD

C I1

E AE

BE

CE

DE

Conditioning temp. (blocks)

Conditioning time

Cond. time x cond. time

Glass feed Cond. temp. x

glass feed Cond. time X

glaas feed G l w level Cond. temp. X

glass level Cond. time X

glass level Glass feed x

glass level Drawing temp. Cond. temp. X

Cond. time X

Glass feed X

(>laus level X

drawing temp.

drawing temp.

drawing temp.

drawing temp. Error between

captures Error between

specimens

Total error

21.8749

5.2216

0.0002 0.0002

0.3302

6.1779 14.8114

3.0179

4.8616

10.0302 0.1607

0.2314

0.7545

5.3445

1.4464

120.8699

1

1

1 1

1

1 1

1

1

1 1

1

1

1

1

95

98.7800 103

21.8740

5.2216

0.0002 0,000!2

0,3302

6.1779 14.81 14

3.0179

4.8616

10,0;30‘J 0 . 1607

0 .23 14

0.7545

5.3445

1 .4464

1 ,2723

0.9590

219.6498 198 1.1093

17.19 (s0.1)

4.10 (s5)

<1 (ns) <1 (ns)

< I (11s)

4.86 (95) 11.64(SO.l)

2.37 (ns)

3.82 (ns)

7.XH(H1) <1 (11s)

<I (ns)

<1 (11s)

4.20 ( s 5 )

1.14 (11s)

1.33 (11s)

-

a F ratios obtained from ratio of each mean square to the “between captures” mean square. Symbols have the following meanings: (ns) = not. significant at 5% level, (s5) = significant a t 570 level, (sl) = significant a t 1% level, and (~0 .1 ) = significant a t 0.1 % level.

Con

ditio

ning

tem

p.

(blo

cks)

(S

O.1

)

Low: 1

4.91

H

igh:

14

.28

Gla

ss

feed

L

OW

H

igh

Gla

ss le

vel (

sl )

Glass

leve

l (sO

.1)

Low

: 14

.34

Hig

h: 1

4.85

Con

ditio

ning

tim

e (6)

Shor

t: 14

.75

Lon

g: 1

4.44

Con

ditio

ning

tim

e (s

5)

Gla

ss

feed

Sh

ort

Lon

g

TABLE

XI1

A

vera

ge V

alue

s Il

lust

ratin

g Si

gnif

ican

t Eff

ect8

for

Mod

ulus

of

Ela

stic

itya

(Eva

luat

ion

of Fi

ve V

aria

bles

)

Non

e 14

.13

15.0

6 A

dded

14

.55

14.0

6

Gla

ss

Feed

Non

e A

dded

__

Non

e 14

.91

14.2

8 A

dded

1

4.5

8

14.6

1

Dra

win

g te

mp.

(s5

)

Low

H

igh

14.4

1 14

.72

14.7

8 14

.47

a Sy

mbo

ls us

ed h

ave

t.he f

ollo

win

g rne

anin

m: (s

5) si

gnif

ican

t at 5

% le

vel;

(sl)

sign

ific

ant a

t 1%

leve

l; (s

O.1

) sig

nifi

cant

at 0

.1%

leve

l.

1 IIGH-STRENGTH, HIGH-MODULUS GLASS FIBEHS 137

intrractioii may be a real effect, hut, seems vontr:try to expectations; thc significance level was not very high and this could well be a chance effect.

2. Influence of Amount of Glass Added to Bushing, Delay Time Before Drawing, and Glass Level

It was found that glass addition and/or the maintenance of a low glass level in the bushing had a detrimental effect on the mechanical properties of a glass. Because it is necessary to add glass to the bushing to maintain a high level in any moderately long operation, an experiment was performed to determine (a) the effect of adding different quantities of glass, ( b ) the optimum delay time after glass addition and before fiberization, and ( c ) the optimum glass level in the bushing.

a. Experimental Plan. The drawing speed, conditioning time and temperature, and drawing temperature were maintained constant throughout the experiment at 8650 ft./min., 2 hr., 2800"F., respectively. Three levels of feed, four of delay time, and three of glass level were examined. The experimental plan required that the bushing be cleaned and refilled nine times, once for each combination of glass level and amount of feed. An initial 2-hr. conditioning period was allowed after the bushing was initially charged. Fibers were obtained immediately after the bushing recovered to the drawing temperature following glass addition.

TABLE XI11 Experimental Trials for Evaluation of Three

Drawing Variables ( 3 x 3 Split-Plot Factorial)

Trial numberss Glass Delay

level, in. time, min. 5 g. 10 g. 15 g.

1 0 30 60 90

1 . 5 0 30 60 90

3 . 0 0 30 80 90

3A 3B 3 c 31) 4A 4B 4 c 4D 8A 8B 8C 8D

* Column headings show weight, of feed in grams.

2A 1A 2R 1B 2C 1c 2D 1 I ) 5A !)A 5B 9B 5 c OC 51) 91) 6A 7A 6R 7B 6C 7c 6D 7D

Table XI11 illustrates the design which is in t,he form of a 3 X 3 X 4 factorial. The delay time, however, was evaluated within each combination of the other two variables and the result was a split-plot type of experiment. The design thus consists of 36 trials in nine blocks of 4 trials. The order of the trials is shown in each block and was obtained from a table of random numbers.


TABLE XIV Analysis of Variance, Tensile Streiigt.h

(Evaluation of Three Drawing Variables)

Source of variation8

Linear feed and

Nonlinear feed and

Linear delay Nonlinear delay Total, regression

level

level

Lack of fit (setup

Capture error Specimen error Total, deviation

Total

error)

Degrees of Sum of squares freedom

Regression

1,137,362.6 2

403.788.6 3

208,462.9 1 213,812.4 3

1,963,426.5 9

Deviation About Regression

908,905.8 26

2,197,085.0 216 1,664,474.0 242

483 4,770,464.8

6,733,891.3 492 -

Mean sqiiare

568,681.3 ( s l )

134,596.2 (s5)

208,462.9 ( s l ) 71,270.X ( s l )

34,957.0 (sl)

10,219.0 ( s l ) 6,878 . 0 -

* Feed and level t e r n tested against setup error. Delay terms tested against rapture error. Symbols used in last column have the following meanings: ( s5 ) significant at 5%, level; ( s l ) significant at 1% level.

b. Analysis. Except for a few instances of fiber breakage, 14 values were obtained from each trial consisting of two specimens from each of seven captures.

Table XIV summarizes the analysis of variance for tensile strength. Two levels of experimental error were considered in this experiment. One error is associated with the feed and level; it can be considered a “setup” error because the bushing had to be cleaned and refilled for each combination of these variables. The second level of error is localized within a setup and consists mainly of testing error. A direct estimate of the testing error was available. The setup error was arbitrarily estimated by the lack of fit to a quadratic regression equation. All the terms in Table XIV associated with delay were tested against the capture error. The remaining terms were tested for significance against the lack of fit (setup error). It was found that both linear and nonlinear terms of a quadratic regression ex- plain a significant amount of the total observed variation. The equation can thus be used for predictions of strength at given levels of three independent variables. The equation is

Y . = 526.121 - 56024x1 + 195.092Xn + 0.104X3 + 6.745XlXz - 0.14Xix3 - 0.486X2X8 + 2.140xi2 - 52.869X2’ + 0.013X32

where Y , = tensile strength, ksi; XI = amount of feed, g.; Xz = glass level, in.; X, = delay time, min.

LIIGH-STRENGTH, HIGH-MODULUS GLASS FIBERS 139

TABLE XV Andyxis of Variance, Modulus of Elasticity (Evaluation of Three Drawing Variables)

Degrees Source of variationw Sum of squares of freedom Mean square

Linear feed and

Nonlinear feed and

Linear delay Nonlinear delay Total, regression

level

level

Lack of fit (mtup

Testing error Total, deviation

Total

error)

Regression 16.4360 2

4.3405 3

8.6451 1 2.4113 3

31.8330 9

Deviation About Regression

28.8505 26

287.4164 456 482 316.2669

348.0999 49 1 d

8.2180 (s l )

1.4468 (ns)

8.6451 ( s l ) 0,8038 ( a s )

1.1096 (s5)

0.6303 -

a Feed and level terms tested against setup error. Delay t e r n tested against testing Symbols used in last column have the following meanings: (ns) not significant error.

:It 5% level; (s5) significant a t 5% level; ( s l ) significant at 1% level.

Table XV summarizes the analysis of variance for modulus of elasticity. As a rough test of significance, the total variation explained by regression could be tested against the total deviation about regression. This gives a significantly high F ratio which indicates that the total equation can be used for prediction. The breakdown to linear and nonlinear terms shown in Table XV reveals, however, that the relationship of the modulus to the three independent variables is essentially linear in the observed range of experimental data. This means that a simpler equation can be used but a recalculation of the regression would be required. The complete quadratic equation is

Y , = 13.33911 + 0.17738Xi + 0.26786X2 - 0.01512X3 - 0.04714XiX2 + 0.00027XiX3 f O.OO36lXzX3 - 0.00413X12

- 0.07024Xz2 + 0.0003X3'

where I'M is the modulus of elasticity (lo6 psi), and XI, X2, and X3 are as defined above.

IV. GLASS COMPOSITION STUDIES

A. Statistical Technique

Glass composition research has traditionally been conducted on a highly empirical basis. This has been necessary because the inherent (theoreti- cal) mechanical properties of the glasses are rarely achieved in practice

140 A. LEWIS A N D D. L. HOBBINS

owing to the extreme sensitivity of tensile strength to the surface coriditioil of the fiber. Under these conditions, theory was used only as a guide and experiniental economy was developed by the use of statistical planning.

The statistical approach is usually more econoniical than the classical method because the experimental data can be manipulated to yield more in- formation for the same experimental cost. Furthermore, the data evaluation is more objective. Personal judgement is partially replaced by a numerical test of significance, and a statement can be made regarding the uncertainty of the conclusions. In addition, random or uncontrolled variation in the experiments can be accurately measured.

On the other hand, statistical planning usually requires a more extensive experimental program and complete commitment to the approach can ser- iously inhibit the investigation of creative or intuitive “hunches” that often result in major advances. Both experimental methods were conse- quently used in this program: the statistical method to assure efficient investigation of areas of known interest and the classical method for ex- ploration of the development of new glasses.

Statistical planning was used for efficient investigation of glass composition areas of known interest. Blocked central composite second-order designs used early in the program were discarded because they were cumber- some, they required comparatively large data inputs before analyses could be made, and extensive statistical training was necessary before analyses could be conducted. These designs were replaced with simplex lattice designs which proved very satisfactory.

Statistical analysis of the data was generally less satisfactory, because wide variability made the data nonsignificant; this work, however, indicated a need for more stringent controls over the process and teRting methods in order to reduce the data variation.

1 . Blocked Central Composite Secmd-Oder Design The statistical plan used during the initial phase of this program was the

blocked central composite second-order design. In this design the func- tional relationship between the response and the controlled variable is assumed to be continuous and to have a unique maximum. The optimum region of the response is determined, using as few experimental observations as possible, by sequential examination of blocks of experimental points that represent small subregions of the range of limits imposed by the independent, variables. A linear model is assumed as a first approximation of the response surface. If it is found that the linear model is acceptable (i.e., that second-order interaction effects are small), the experiment proceeds toward the optimal region using the method of steepest ascent by selecting a new subregion of variables. If a first-order model does not adequately describe the data, additional experimental points are added to allow the development of a second-order equation.

Blocking the experiment provides an opportunity to eliminate nonrandom disturbances from data analysis thereby reducing the estimate of ex-

HIGII-STRENGTH, HIGH-MODULUS GLASS FIBERS 141

perimental error. It also permits a sequential approach: The data already generated are cornposited and evaluated at the end of each block and the investigative program can be reoriented toward the region of experimentation that appears most promising.

The major difficulties encountered in the use of this plan were: (I) many experiments were required before even tentative conclusions could be drawn; (2) one of the composition ingredients (usually silica) had to be treated as a “filler” that was varied to make the composition add up to 100%; (3) analysis required extensive statistical training and a digital vomputer breakdown of the data ww usually necessary.

2. Simplex Lattice Design

The experimental plan used for most of the program was based on a simplex lattice design. The simplex lattice was developed by Scheffe’ for designing experiments with mixtures of materials that total loo%, and it is therefore directly applicable to glass composition studies. It provides an important new tool for investigating the properties of mixtures over a wide range of compositions. It is especially advantageous for systems of four or more components but is successfully used with three-component systems. Accurate mapping of responses over wide ranges of composition, in some cases outside of areas of immediate interest, should result in in- creasingly effective experimentation. The method is particularly useful when several properties are of interest. When applied to tensile strength studies, for example, the method can at the same time be used to define boundaries of interest resulting from other limitations such as Young’s modulus and density.

The method has several features of interest to glass research chemists: (a) Experiments are laid out according to simple lattice designs that

are similar to phase diagrams, i.e., a three-component system uses a tri- angular lattice, a four-component system uses a tetrahedral lattice, and systems with more than four components use mathematical representations of simple lattices.

(b) Very few experimental points are required to characterize a system, e.g., a four-component system can be characterized by ten experiments.

(c ) I’olynominal equations having a special correspondence to the experimental points are used to predict the properties over the entire com- positional range. Coefficients in the polynomials are simple functions of the measured properties at the experimental points. The predicting equation can therefore be developed rapidly without resorting to computer runs or employing the services of expert statisticians.

The simplex lattice designs used during this program are modifications of Gorman and Hinman.*

The lattice design has two key features: properties or responses are measured at lattice composition points, and polynomial equations having a


special correspondence to the lattice points arc used to represent the responses.

a. Lattice Points. The number of equidistant points k required for any lattice may be computed from

(1) (m + q - I)! m! (q - l)!

k =

where q is the number of components under consideration and m is an integer related to the spacing of points on the lattice (m = number of points on a binary joint minus one). The total number of experimental points is therefore determined by the spacing. Table XVI gives the number of

TABLE XVI Number of Blends in Various Lattices

No. of blends No. of

components, Quadratic Special cubic Cubic Quartic Q m = P m = 2 m = 3 m = 4

3 6 7 10 15 4 10 14 20 35 5 15 25 35 70 6 21 41 56 126 8 36 92 120 330

10 55 175 220 715

* (m) spacing integer.

lattice blends for various values of rn and q. The “special cubic” lattice in Table XVI refers to the condition in which m = 2, but all possible mixtures consisting of ‘/a combinations of each component are added.

b. Polynomial Representation of Response. In theory, a polynomial expression can be developed to represent any continuous distribution of responses. In practice, polynomial models are limited to low order because of the large number of coefficients in higher-order models.

With three-component systems the most general models of the 2nd, 3rd, and 4th order that express a response (7) as a function of composition are :

Quadratic 7 = plxl + p2XZ + p3x3 + fllZxlxZ + 813Xlx3 + 823XZx3 (2)

Cubic rl = plxl + 82x2 + + 812xlx2 + 8laXlX3 + 823XZx3 + y,2X1Xz(X1 - XZ) + y13X1X9(X1 - X3) + y23xzx3(x~ - X3) + P123XlX2X3 (3)

Quartic 7 = 83x1 + pZxZ + p3x3 + 8lZxlxZ + 813XlXa + p23xZx’I + ylZxlx2(x1 - XZ) + yl3XlXa(X1 - x3) + y23(x2 - x3) + 812xlX2(x) - x2)’ + 81&1X3(X1 - x3)’ + 823(XZ - 1 3 ) ’ + 81123xl2X2x3 f 81223x1x22xS + p1233x1x2x32 (4)

I IIGH-STRENGTH, HIGH-MODULUS GLASS FIBERS 143

where 0, y, and 6 are coefficients, and X is the fraction of component in the composition varying from 0 to 1.

The subscripts on a response designate three things: (a) the number of subscripts equals the denominator in the fractions used in the mixture; ( b ) the number of distinct numbers or letters indicates how many components are in the mixtures; (c) the number of times a number or letter appears shows the relative proportion present. As an example, 71123 has four subscripts; therefore, combinations of compositions with fractions 1/4

are used, the three distinct numbers indicate a three-component system, arid the properties are '/z for Component 1 and '/4 each for Components 2 and 3.

c. Transformation of the X Variables. The quantities X1, X2, XI, etc. represent the composition variables in the lattice. Equations (3)-(6) were developed under the assumption that each quantity is allowed to vary between zero and 100% (0-1) in the region of investigation. For glass composition experiments, the variation of the components is limited to a narrow range. The transformation to the X variables is

(6) z - Z m i n

z m * x - Zni in X =

where Z represeiits the actual fraction of the coniporieiit under consideration. Thus,

Z m a x - Z m i n

z m a x - Z m i n Xmax = = I

and

Z m i n - Z m i n

z m a x - Z m i n X m i n = = o

d. Calculation of Polynomial Coemcients. Polynomial coefficients are readily expressed as functions of the response measured at the lattice points. The number of coefficients in the models exactly corresponds to the number of points in associated lattices. As an example, the quadratic model for a three-component system requires six coefficients and the quadratic lattice contains six composition points. This leads to six independent equations relating response to composition from which the coefficients are evaluated. For example, for the composition XI = 1, Xz = 0, XI = 0, eq. (3) reduces to

Pi = rlr

I44

Similarly,

A. I X W I S AND 1). I,. HOBBINS

8 2 = '12

Pa = qa

For the composition X1 = X2 = 1/2, X , = 0,

112 = l / 2 8 1 + l / 2 8 2 + ' / e a l Z

Or

8 1 2 = 4112 - 211 - 2.12 Similarly,

= 4r/13 - 211 - 2vy

8 2 3 = 4 1 2 3 - 212 - 273

All coefficients in eqs. (3)-(6) may be similarly evaluated by simple al- gebra from data for the appropriate lattice related to each model. All coefficients are simple fuiic tioris of responses. Coefficients for q-component systems for all models through the quadratic are shown in Table XVII.

TABLE XVII Soliition for Polynomial Coefficients for q Components

HIGIT-STRENGTII, HIGH-MODULUS GLASS FIBERS 145

Coefficients for the low-order terms Bi and flu are identical for quadratic, special cubic, and quartic models.

e. Interpretation of Terms. The first q terms in each of the q-component equations represent linear blending. If a linear blending model holds, coefficients for all other terms are zero. The net values of all terms other than the linear ones thus expresses synergism or antagonism effects. For the quadratic model applied to a binary mixture of Components 1 and 2, synergism is represented in the term j312XlX2, and 812 is the coefficient of binary synergism. For the special cubic models, 8123 is the cubic coefficient of ternary synergism of Components 1, 2, and 3.

References 1 and 2 provide a more complete discussion of the simplex lattice design (variance of predicted values, suitability of the model, plot- ting of contour surfaces, derivation of equations, etc.).

B. Properties of Glass Compositions

The three-component system Mg0-A1203-Si02, and the four-coniponent systems Mg0-A1203-Si02 and -Laz03-Be0-Ce02, and -CuO have been in- vestigated using simplex lattice designs. In every case, only quadratic models were used since the dispersion of the data did not appear to war- rant higher-order equations.

The data was reduced to empirical equations with the aid of a desk calcu- lator. Typical equations for tensile strength and density are shown for the AMg0-A1208-Laz03-Si02 system :

146 A. LEWIS AND I). L. 11OBL)lNS

ul- (ksi) - 575x1 + 393x2 + 628Xs + 473X4 + 316Xlx2 + 338X1Xa - 272XlX4 - 38XPXa + 612XZ4 + 246XaXa

p(g./cm.3) = 2.61X1 + 2.70X2 + 2.63X3 + 2.GGX4 + 0.32X1Xa

The equations were solved to determine compositions that displayed equal values of a given property. For example, in the 1/I&-A1203-L&03- Si02 system, plots of the tensile strength of compositions containing 18.5y0 MgO are shown in Figure 3. Similarly, the densities of compositions containing 50.5% silica are shown in Figure 4. Similar plots were obtained for modulus of elasticity.

These data were used to develop compositions that appeared to display an optimum combination of properties.

Three glass compositions were developed from this work that displayed unusually high mechanical properties. These glasses were in the MgO- A1203-Si02, R I g0-Al2Oa-L&O3-SiO2, and BeO-Mg0-Al~03-SiOz systems.

Fig. 4. Densities of glasses in MgO-AlzOrL&Oa-SiOz system.

1 . Glass Composition M-19

Glass coniposition M19 is composed of 65 wt.-yo SiOz, 20% and 15y0 MgO. The glass displays good fiberizing characteristics and can be melted and fiberized using state4f-the-art materials and techniques. The glass composition was studied using fourteen different 500-g. batches. Half of the batches were melted in platinum crucibles and half in zirconia- alumina crucibles. The highest temperature required during melting and refining was 2845OP. The glass The average melting time was 48 hr.

111GI I-STRENGTH, IIIGH-MODULUS GLASS FIBERS 147

showed very little or no attack on the platinum but moderate attack on the ceramic crucible.

Fibers were obtained from each of the glass batches under a wide variation in fiberization conditions. The average of 8-15 values for each fiberi- &ion test was found to vary between 469 and 811 ksi while the average Young’s modulus values varied between 13.0 X lo6 and 14.9 X lo6 psi. Figure 5 shows the distribution of the average tensile strengths (representing

im

90

80

m m

$ 6 0

8 % g a -

M

20

10

O 4.0 4.5 5.0 5.5 LO LS 7.0 7.5 ao a5 9.0 9.5 iao Average Tensile Strength. lo5 psi

Fig. 6. Average tensile strength vs. frequency: conditions.

M-19 glass, uncontrolled fiberizing

4.0 4.5 5.0 5.5 LO AS 7.0 7.5 ao as 9.0 9.5 iao Tensile Strength. lo5 psi

Fig. 6. Terisile strength vs. frequency: M-19 glass, controlled fiberizing conditions.

361 individual values). The average strength of the fibers was 637 ksi and the average modulus was 13.8 X lo6 psi. The wide distribution is probably caused by nonrandom variation in the experiments resulting from variation of the fiberizing conditions. Four fiberization trials conducted with the same batch of M-19 under the same fiberizing conditions produced the distribution shown in Figure 6. The skewness of the curve is fairly typical of strength distribution curves. The average strength of the glass is 700 ksi. During this experiment the glass was shown to have excellent

fiberizing characteristic and to consistently produce high-strength fibers. The standard deviation.of the tensile strength values is 64.7 ksi.

The large variation in the two sets of data obtained under uncontrolled and controlled fiberizing conditions appeared to be indicative of the great effect of fiberization variables on glasses having the same composition.

2. Glass Composition 967

Lanthana appeared to improve the strength and modulus properties of magnesia-alumina-silicate glasses. Composition 957 containing 5.0% lanthana and 50% %On, 32.5% A1203, and 12.5% MgO showed an average strength of 685 ksi when fiberized over a wide range of conditions. The frequency, tensile strength distribution of 97 fibers is shown in Figure 7. The average modulus of these fibers was 14.2 X loe psi.

18

16

14

12

10

8

6

4

2

0

Fig. 7. Tensile strength vs. frequeiicy : 957 glaw, uncontrolled fiberiaing conditions.

Lanthaiia was used as a glass constituent because of its ability to increase According to Griffith, the strength of a the surface tension of the melt.3

fiber, u, is determined by

u = j ( E y / c ) % (7)

where E is the modulus of elasticity of the material, y is the elastic surface energy, and c is the depth of the most severe crack. The surface tension of the glass, therefore, may have a pronounced influence on its strength. Glass 957 had good fiberization characteristics. The skewness of the curve in Figure 7 reflects the sensitivity of the glass to variation in the fiberizing vonditious. The standard devintioii of the tensile strength data is 142 ksi. Another problem encountered with the addition of lauthaiiu to a glass is rapid increase in glass density.' The specific gravity of glass 957 was 2.69.

IIIGI~-SI '~t iNGI'I f . HIGH-MODULUS GLASS PIBEHS 149

3. Gh88 Composition 967

Composition 967 had the most outstanding mechanical properties of the glasses developed during the program. Thirty fibers had an average tensile strength of 802 ksi. During one series of tests involving ten fibers, four had tensile strengths above lo6 psi. The average strength of 50 specimens fiberized over a wide range of conditions was 740 ksi; the average modulus was 16.1 X lo6 psi. The density of the glass is 2.M g . / ~ m . ~

10

9

a 7

- - " 6 P $ 5

$ 4

3

2

1

'3.5 40 4 5 5.0 5.5 60 a5 7.0 7.5 8.0 a5 9.0 9.5 iaoias Tensile Strength, 10 psi

Fig. 8. Tensile strength vs. frequency: 967 glass, uncontrolled fiberising conditions.

Glass composition 967 was composed of 7.5% BeO, 50% %On, 35% A1203

Beryllia has received extensive investigation as a constituent in glass and it is recognized as contributing high modulus properties to

the glass. Lowensteiq6 explains this behavior of beryllia as due to inter- stitial Be04 crosslinking, network-like groups.

The fiberization of glass 967 was generally difficult because of rapid de- vitrification at temperatures below the liquidus and because of high surface tension and low viscosity above the liquidus temperature.

Figure 8 presents a frequency vs. tensile strength histogram of glass 967; the wide dispersion reflects the variation in fiberizing conditions as well as tfhe short working range of the glass. The standard deviation of the strength data is 168 ksi.

:md 7.5% MgO.

This paper is based oil work performed for the U.S. Air Force under Contract AF 33- (615)-1371. Some of the work was conducted using Aerojet-General research funds. The authors appreciate t>he assistance given to them by L. R. Fbpp, Manager, Chemical and Structural Produks Division, Aerojet-General Corporation. Much of the data iiiducied i i i this pitper were obt.aiiied through t,he efforts of George Pltpai, George Bush, : i i d IA:twreiic*e Kclley of t,he C;lass Techiiology Deparhneiit, and H. 1). Farquhar,. Aclv:mred Biological Appliczri ioiis I)epart,inent, at, Aerojet-General Corporation, I7oii Kltrniaii Center.

150 A. LEWIS AND D. L. l{OUBlNS

References 1. H. Scheffe, J . Roy. Statis. SOC., B20, (1958). 2. J. W. Gorman and J. E. Hinman, Technometria, 4, (1962). 3. A. A. Apen and S. S. Kajalowa, “Experimental Basis for the Classification of Oxides

According to Their Influence on the Surface Tension of Silicate Melts,” in Advances i n Glass Technology, Part 2, Plenum Press, New York, 1963, p. 61.

4. G. W. Morey, The Properties of Glass, 2nd Ed., Reinhold, New York, 1954, Chap. 10.

5. K. L. Lowenstein, Phys. C b . Glasses, 2 (1961). 6. W. Capps and D. H. Blackburn, The Development of Glass Fibers Having High

Young’s Moduli of Elasticity, National Bureau of Standards Report No. 5188, April 1957.

7. J. A. Wough, V. E. Chiochetti, et. al., The Development of Fibrous Glasses Having High Elastic Moduli, WADC TR 55-290 Part 11, May 1958.

Rdsum6 Ce manuscrit decrit un travail qui a Bt6 effectue en vile de developper des fibres de

verre B haute force et module BlevB. Un projet de statistique experimental e t l’analyse des rksultats ont BM utilises pour determiner certaines variables de l’echantillonage d’essais et de formation de fibres qui affectent la dispersion des resultats de proprietks mbcaniques des Bchantillons de fibres il base de verre. Un dessin experimental du reseau a 6tB utilid pour les etudes de melanges Bvec le verre. La methode experimentale est dkcrite. Trois compositioris de verre B proprietes mbcaniques ont BtR dbcrites. Un de ces verres est composB de Mg0-AlZO8SiO2. Les deux autres sont des verres B quatre composanta et contiennent MgO-AIzOaSi02 et BeO, ou La208.

Zusammenfassung In dieser Mitteilung werden Arbeiten beschrieben, die eur Entwickluiig voii Glas-

fasern mit hoher Festigkeit und hohem Modul durchgefiihrt wurden. Stdstische Ver- suchsplanung imd Datenanalyse wurden aur Bestimmung einiger Variabler ffir Proben- nehmung, Testung und Faserbildung verwendet, welche die Datenstreuung bei den mechanischen Eigenschaften von Glasfaserproben beeinflussen. Bei der Untersuchung iiber die Glasfaserproben beeinflussen. Bei der Untersuchung iiber die Glasausammen- setaung wurde das Simplexgitter-Versuchsverfahren benutat. Die Venuchsmethode wird beschrieben. Drei Glaseusammenseteungen mit hochwertigen mechariischen Eigenschaften werden angegeben. Eines dieser Gliiser besteht ails Mg0-A1208Si02. Die anderen beideri sind 4-Komponentenglaser und enthalten Mg0-Al2Oa-Si0~ und Be0 oder LazOa.

high-strength, high-modulus glass fibers

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