21

NBS MONOGRAPH 6

Properties of High-Temperature

Ceramics and Cermets

Elasticity and Density at Room Temperature

U.S. DEPARTMENT OF COMIMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMJMERCE • Frederick H. Mueller, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Dinctor

Properties of High-Temperature Ceramics and Cermets

Elasticity and Density at Room Temperature

S. M. Lang

National Bureau of Standards Monograph 6

Issued March 1, 1960

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 20 cents
Contents

Page

1. Introduction 1 2. Materials and procedure 2

2.1. Materials 2

2.2. Preparation of specimens i 2

2.3. Elastic moduli 2

2.4. Density 4

2.5. Precision 5

2.6. Statistical treatment 5

3. Results and discussion ^ 5

3.1. Presentation of data 5

3.2. Restdts for different materials 6

a. Aluminum oxide—AI2O3 6

b. Ruby alumina—AlaOa+CraOg 7

c. Magnesium oxide—MgO 8

d. MuUite—3Al203-2Si02 8

e. Mullite +ZrO, 8

f. Spinel—MgO-Al^Os 9

g. Thorium dioxide—Th02 9

b. Uranium dioxide—UO2 9

i. Stabilized zirconia—Zr02+CaO 9

j. Alumina +cliromium—Al203+Cr 10

k. Ni-bonded titanium carbide—-TiC +Ni 10

1. Boron carbide—B4C 11 m. Boron carbide +titanium diboride—B4C +TiB2 11

n. SUicon carbide—SiC 11

0. Silicon carbide +boron carbide—SiC+B4C 12

p. Zii'conium carbide—ZrC 12

q. Zil'conium diboride—ZrB2 12

r. Molybdenum disUicide^—-MoSi^ 12

s. Nickel aluminide—NiAl 12

3.3. Discussion 12

AppendLx I. Statistical treatment of data 15

Appendix II. Tabular information 16

4. References 45

n
Properties of High-Temperature Ceramics and Cermets

Elasticity and Density at Room Temperature ^

S. M. Lang2

In order to provide some of the basic data necessary for the efiFective utilization of ceramics and cermets in various high-temperature applications, a specimen "bank" of such

materials, mainly commercially fabricated, was established for the measurement of physical

properties and constants. This Monograph describes: (1) The materials and some of their fabrication data; (2) bulk densities; (3) theoretical densities; and (4) the dynamic roomtemperature elastic constants. Data are given for 46 sets of specimens, representing 20

dififerent materials; these include oxides, carbides, borides, cermets, and an intermetallic compound. A statistical evaluation was used for analyzing the data. Results of the room-temperature measurements show that: (1) Significant variations are common both in the specimens of one group and from group to group of specimens pre- pared of the same material; (2) the largest variations occur for specimens formed by hotpressing, although average values are higher for hot-pressed specimens ; and (3) measurements

of the dynamic elastic constants by the sonic method are more sensitive as indicators of homogeneity and group uniformity than bulk-density measurements,

1. Introduction

Recent outstanding advances in the field of jet,

rocket, and atomic-powered heat engines have

strongly stimulated an accompanying development

in high-temperature ceramic and cermet materials

' to withstand the high temperatures and corrosive

atmospheres involved. The new ceramics have

been well described by E. J. Rimck [1] ^ who

states that they are commercially produced by

"radical departure from orthodox processes and

I materials", bemg "ceramic bodies . . . that possess no silica or clay in their structure. The

coarse nonplastic portions of these new refrac-

' tories have high purity and are processed at high

temperatures, even up to fusion .... The mixtures are compacted and fired . . . usually above

[ 1,600° C. In firing, these materials do not form

, glassy bonds, but sinter or recrystallize by solid

reactions."

Designers have been severely handicapped by a

lack of sufficient data for the high-temperature

ceramics and, in addition, the available data have

not always been consistent [2]. This lack of consistency could result from differences in experimental conditions, or could be a real variation of

properties of nominally the same material caused

I by uncontrolled differences in fabrication or batch

composition. To fill the critical need for more

I complete and reliable engineering data for these

ceramic materials, a "bank" of these products

• Financial support for this investigation was supplied by the Division of Besearch of the U.S. Atomic Energy Commisslcn.

» Present address, Owens-Illinois Technical Center. Toledo, Ohio. Since Mr. Lang's departure from NB3, this paper has been revised by M. D,

Burdiclj and S. Spinner.

' Figures in brackets Indicate the literature references at the end of this

I Monograph.

has been established. This bank contains samples

from the leading manufacturers as well as some

fabricated at the National Bureau of Standards.

Also included are a number of cermets. These

are metal-ceramic combinations designed for use

at elevated temperatures.

The long-range goal of the investigation is to supply reliable engineering data for these new

classes of materials. The properties to be investigated include mechanical strength, elastic and

anelastic characteristics, the temperature dependence of these properties, and thermal properties

generally. Since all these properties will be determined on the same set of specimens by the same

test procedure, valid comparisons will then be

possible.

The particular pm'poses of the present investigation were: (1) To determine the room-temperattire elastic properties by a dynamic (sonic)

method; (2) to determine both the bulk and

theoretical densities; (3) to evaluate from a

statistical treatment of the data the variability of fabrication of the different types of materials,

using the above-determined elastic and bulkdensity data; and (4) to compare measurements

of the elastic properties and densities for their

usefulness as indicators of significant variations

in fabrication.

Density and elastic properties were determined

first because, in addition to being important

properties in themselves, the experimental method

for their determination is nondestructive. It thus

becomes possible to perform further measurements

of other properties without diminishing the number of available specimens.

1
The present paper contains detailed descriptions

of the methods used in calculating both the elastic constants and the statistical parameters. These

detailed descriptions have been included for two

2. Materials

2.1. Materials

A complete list of the materials along with

pertinent fabrication data is given in table 1 (appendix II). Most of these materials are commercially available; some are experimental (at the

time of this investigation) including all those from

source G. Some additional information concerning these materials that could not be listed in table 1 conveniently is included under results.

2.2. Preparation of Specimens

A convenient size and shape of specimen for the

elastic modulus measurements, and one that was

used whenever possible, was a rectangular prism

6 in. by in. by % in. However, all of the speci- mens that were fabricated by the hot-pressing

technique were supplied as approximately 3-in. long by }{-in. wide by }^-in. thick bars, rather than

6-in. long bars, because the shorter specimens

could be made denser and with greater uniformity.

In order to achieve this with available equipment,

the blanks were hot-pressed perpendicular rather

than parallel to the length. Pressing parallel to the length would have produced a low-density zone near the center of the specimens.

AU specimens were finish ground to the final dimensions. For the harder specimens, such as B4C, B4C+TiB2, and SiC+B4C, the machining

operation was slow and tedious, even with diamond

tools. 2.3. Elastic Moduli

a. Method

The equipment and technique for determining

the elastic moduli by the sonic method were the same as those reported by Spinner [3], and pre- viously described by Hornibrook [4]. The method

consists of inducing the mechanical resonant fre- quency of the specimen, usually by means of a

tweeter-type speaker, driven by an audio oscUlator.

The resultant oscillations are detected by means

of a crystal pickup which, together with the signal

from the audio oscOlator, produces a Lissajou

pattern on a cathode ray oscilloscope.

One of the basic characteristics of the dynamic

method is that the elastic moduli are determined

at very low-stress levels. Thus, the possibility

of the occurrence of creep, elastic hysteresis,

plastic flow, or similar effects is reduced to a minimum [5]. Whenever possible, the fundamental resonant

frequency of four types of vibration was determined for each specimen. These were the longitudinal, Fi; flexural vibrating flatwise, Ffv,;

reasons: (1) To leave no doubt as to the exact

procedure, and (2) to act as a guide to other

workers who might wish to make similar determinations.

and Procedure

| flexural vibrating edgewise, Ffe] and torsional Ft. ; The first three types of vibration were used to detei'mine Young's modulus, whereas the torsional

mode yielded the shear modulus. The reason for

determining two elastic moduli is that aU the

elastic constants for isotropic materials are inter-!

related by well-known equations in such a way

that, if any two are known, the others may be

calculated. In this investigation, Poisson's ratio,

fi, and the bulk modulus, K, were calculated after : Young's and the shear moduli had been obtained.

For some specimens, usually the shorter ones, the longitudinal resonant frequency was too high

to be detected with the equipment used. In these

cases, only the flexural and torsional resonance : frequencies were determined.

In three instances, Code 44 (B4C), Code 43

(BiC+TiBs), and Code 37 (SiC+B4C) the combination of size and density were such that the

resonant frequency of the test specimens could

not be detected either in the longitudinal or in the

torsional modes. One specimen of each of these

materials was reshaped so that the resonant tor- sional frequency could be obtained. The re- mainder of the specimens in the group were not

reshaped because (1) the grinding and polishing

operations were difficult and time consuming due

to the extreme hardness of the B4C constituent,!:

and (2) the reshaping operation made the speci-i' mens unsuitable for other testing. j The shear moduli and values of Poisson's ratio' were calculated for each of these reshaped speci- mens. These values of Poisson's ratio were then

assumed to be representative of the entire group j of specimens of that mixture and were used to calculate the shear and bulk moduli for the re- mainder of the specimens. Because only one? specimen was measured in shear, the data fori these groups were not treated statistically. It may be noted that it is usually possible to obtain adequate responses even when frequencies

are considerably higher than what is usually

regarded as the upper limit of the audiofrequency

range (20 kc). 'This is because the frequency

response of a driver or pickup is usuaUy higher

than its rated value. The upper frequency limit

for a good crystal pickup is ordinarily given as around 10 to 11 kc. Although this is the fre-' quency above which the response faUs off from^

being flat, it does not drop immediately to zero.; There continues to be a reduced response at much^

higher frequencies. With the apparatus used,

frequencies weU above 20 kc could usually be

detected. The actual upper limit of frequency)

response was between 25 to 30 kc. ^
b. Calculations

All of the follo'tt'ing equations for calculating

the elastic constants from the various resonant

frequencies are based on the assumption that the

specimens are isotropic and homogeneous. Although the individual crystals comprising the

specimens are elastically anisotropic, their dis- tribution and orientation within the specimen are random so that the assumption of isotropy would

appear to be valid. However, as will be seen

i later, certain differences in Young's modulus,

when calculated from flexural and longitudinal

: frequencies, indicate that either or both of these

• conditions (isotropy and homogeneity) were not

I'i completely satisfied in all cases.

If! The following well-kno\\-n equations were used

to calculate the speed of sound, Vc, and Young's

1 modulus, El, from the longitudinal resonant freI quency, Fi

V,=2lFi, (1)

' where ^=length in cm, Fi is in cps, and Vc is in

cm/sec, and

Ei=V,'p, (2)

where p=densit3^ in g/cm^ If Vc is in cm/sec,

then El will be in d3Ties/cm2. All elastic moduli

* are given in kUobars where

10^ d}Ties/cm^=l kUobar.*

j Correction for cross-sectional effect was neg-

,1 lected as too small to be significant. The foUowing equation from Giebe and Scheibe [6] gives the

amount by which the fundamental longitudinal

' frequency, Fi, of a prism of given rectangular

cross section is less than that of an infinitely thin

rod of the same length

i^y^iw'-e') ' (3) 24/^

1

' where i^m= longitudinal resonant frequency of an

1 infinitely thin rod,

( M=Poisson's ratio,

w=width,

1 g =edge or thickness,

I Z=length of the specimen.

1 * The cgs system is used throughout as being a more desirable form in which

^ to develop the equations and present the final data. However, for the con- venience of those who are more familiar with the English system of units, the

final data, in appendix II, are presented in the English as well as the metric system.

Kilobars may be converted to psi by means of the following equation,

KilobarsX14,503.8=psi.

(This conversion factor assumes a value for the acceleration of gravity, g,=

980.1 cm/sec2.)

Substituting the dimensions for the long (6 in.)

specimen and, assuming a ii value of 1/4

Fr„=im02Fi (4)

or, the resonant longitudinal frequencies of bars of the dimensions used here are 2 parts in 10,000 less than for an infinitely thin rod of the same length.

This is a higher order of precision than the reso- nant frequency determination itself (1 part in

3,000), and therefore may be neglected. Since the

entu-e lateral correction is neglible and, since

Poisson's ratio is only one of the factors entering

into the correction, the value of Ei is, within the

precision used here, independent of Poisson's

ratio. To calculate Young's modidus from the flexural frequencies and the shear modulus from the

torsional frequency, the relations developed by

Pickett [7] were used. These equations have been

modified to conform to the cgs system.

The following pair of equations relate Young's

modulus to the flatwise and edgewise flexural frequencies,

£',„=9.464XlO-i«0J ^ mF,J (5)

£',,=9.464X10-i°(^y ^ mF,/ (6)

Young's modulus as determined from flat- wise flexural vibration, £';-e= Young's modulus

as determined from edgewise flexural vibration,

Ffe; and m=mass of specimen in grams. The

numerical constant in eqs (5) and (6) is chosen so that Young's modulus will be in kilobars. The

factor, Ti, depends upon r/l, the ratio of the radius

of gyration of the cross-sectional area in the

du-ection of vibration (=0.288675Xe_ or 0.288-

675 Xw, depending on whether the vibration is flatwise or edgewise) to the length of the specimen.

Pickett gives algebraic relations, graphs based on

these relations, and also a table of selected numerical values from which Ti can be determined as a function of Poisson's ratio for values of 0, }i, and

ji. Subsequently, the following equation has been

offered [8] from which Ti can be evaluated for Poisson's ratio values other than those given by

Pickett, ri + (0.26M+3.22M^)r/n

' L l+0.1328X?'/^ J

where n is the particular value of Poisson's

ratio and T is Pickett's value of Ti for n = % for the corresponding value of r/l. The nature of the function relating Ti to r/l is such that not only does Ti increase as r/l increases,

but also the values of Ti diverge from each other more rapidly for different values of Poisson's

ratio. Therefore, the accuracy of /x becomes more

critical in the accurate determination of Ef^, and

Efc, as r/l increases.

3
The shear modulus, G, was calculated, from the

torsional resonant frequency Ft, by means of the

following equation,

0=BmF\ (8) where B is defined by the following relation

B-- (9)

where a is the cross-sectional area and R is the

ratio of the polar moment of inertia of this cross- sectional area to the "shape factor" [9] for the same cross section. The following approximation

for rectangular cross section is given by Pickett

[7] and based on Roark's Monograph [9],

R-- e/w-\-w/e

'4(e/w)-2.52(e/w)2+0.21(e/w)«

(10)

A reexamination of the accm-acy of the equation for R for the dynamic shear modulus calculations has been presented [10]. The revised re- lation for the specimen sizes used in this study,

all with width-to-thickness ratios of about 2, is not significantly different from those calculated

from the relation given.

Once Young's modulus and the shear modtdus

were determined, Poisson's ratio was calculated

from the following equation.

(11)

For the 3-in. specimens, where Ej could not be

determined, Ef^, or Efe (eq (5) or (6)) was used

in eq (11). However, the importance of an ac- curate value of n for the determination of Ef^, or

Efe has already been mentioned. The procedure

that was followed, then, was to assume a reasonable value of M in calculating Ef^^ or E^^ from eq

(5) or (6); then by successive approximation in- creasingly accurate values of E^^ or E^^ and /x were

obtained. The process ceased when two successive calculations of Ef^^ or Efe did not vary by

more than about 2 in the fourth significant figure.

Usually, no more than two recalculations were

necessary. The subscript in the symbol for Poisson's ratio

(mz, M/w, or life) indicates whether the longitudinally

or flexurally determined values of Young's modulus

were used in eq (11).

For those specimens where Fi could not be determined, the speed of sound was calculated from

the equation

lEf^^

(12) P The bulk modidus, K, is obtained from the

following equation

As with Poisson's ratio, the symbols Ki or Kfjj, indicated whether Ei and or and ^i/i^ were

used in the equation for the btilk modulus.

2.4. Density

a. Bulk Density

The bulk density was determined from the mass and volume which was calculated from the

dimensions.

In order to determine the mass accurately, the

specimens were cleaned with soap and water, then

with trichloroethylene, and dried to constant

weight either by heating at 800° C in an electri- cally heated muffle furnace or, if there was any

doubt about the oxidation resistance of the materials at 800° C, they were vacuum-dried at an

absolute pressure of about 1 X 10~^ mm of Hg. A

few of the specimens were vacuum-dried in a

desiccator at about 30 microns pressure. After cleaning and drying, all of the specimens were stored in desiccators until they could be

weighed on an analytical balance. The mass was

corrected for the air buoyancy referred to a barometric pressure of 760 mm of Hg and 20° C

by the equation

I

so 1ft

(14)

Corr. mass=[mass in air X 0.99986]

+[volume X0.001 2].

b. Theoretical Density

The theoretical density, P, was determined from

X-ray diffraction examination, using the following

relation

^-VA ^^^^

where is the number of molecules per unit cell, M is the molecular weight, V is the volume of the unit cell in angstrom units, and A is Avogadro's number (6.024X10^^) used in conjunction

^vith the newly adopted angstrom length unit.

The molecular weights of solid solutions were

calculated assuming that electrostatically neutral

structures exist. No theoretical density computations were made in those instances where the

type of solid solution was not known, where a number of solid solutions and compounds could

exist, and where the reactions between these

phases were not known, and when the structures

of the material were of various low orders of

symmetry and the angular values of the intersecting axes were not readily available. When it could reasonably be assumed that no reactions

occurred between the two or more phases present

in some of the test specimens, the theoretical

densities were calculated as though the specimen were composed of a "mechanical" mixture of

the component phases and that the densities of

each were additive according to the amounts

present.

4
2.5. Precision

The precision of the resonant frequency

1 measurements has been given as about 1 part in

I 3,000 (2.3b). The speed of sound, when calcuj lated from the longitudinal frequency, is the most

' precise of all the constants given since it depends

only on the length, known to about 1 part in

: 6,000, and the longitudinal frequency. The

I error in this determmation is less than 0.1 percent.

; When combined with the other factors involved

j in its determination the precision of Ei is estimated

I to be better than 0.4 percent. The precision of

I G, Efu,, Efe, and Vc from eq (12) are estimated

I to be about 0.4 percent. The precision of the

Poisson's ratio and bulk modulus values are, from

I the nature of then* determination, reduced by

a factor of 10, from 0.4 percent to 4 percent.

The precision of the bulk density measurements

I is estimated to be about 0.2 percent.

2.6. Statistical Treatment

A detailed description of the statistical techniques employed and their application to the

particular problems of this investigation is pre- sented in appendix I. The basic features of this

statistical approach were as follows:

In most cases two or more groups, usually consisting of 10 specimens each, of a single type of

material, were supplied by the manufacturer.

The different groups were either fabricated at

different times, using the same batch, or fabricated using batches prepared at different times.

The first condition was designed to test the uniformity of fabrication, whereas the latter condition tested the uniformity of batch preparation.

As mentioned in the introduction, the elastic constants and densities were used independently

as indicators of the uniformity of production.

The specimens of a single group were designated "acceptable" if the coefficient of variation was 1 percent or less. This rather arbitrary cri- terion of acceptability seemed reasonable on the

basis of earlier testing [11, 12] and the data re- ported here. This standard of acceptability could

favor some materials at the expense of others,

and it should not be interpreted as a rigid criterion of the quality of an}^ material or manufacturer's

product.

The i^-test was used to determine whether or not two or more groups of specimens were significantly different in the degree of scatter. The t- test was used to determine whether or not the

averages of two groups of data were alike. For

both these tests, the 95 percent confidence level was used. The ^-test was applied only if the

i^-test showed the two groups to have the same

degree of scatter within the specified 95 percent

confidence level. The following table illustrates how these two tests were employed to evaluate

the parameters of fabrication and batch preparation for the two or more groups of specimens of each material.

Statistical test

Entire batch mixed

at one time; speci- mens fabricated at

different times. No significant differ- ence means that

the separate fabri- cation procedures

result in products

of comparable variability. No significant dif- ference means that not only were the

fabrication proce- dures of comparable variability

but they were sufficiently uniform

to permit production of products

with the same

properties.

Batches mixed at dif- ferent times; speci- mens fabricated all at one time. No significant differ- ence means that both groups of batch

materials were of comparable variability as were the mixing procedures.

No significant dif- ference means that not only were the batches of comparable variability but

that they were sufficiently uniform to permit fabrication

of products with the same properties.

3. Results and Discussion

3.1. Presentation of Data

All tabular data are presented in appendix II. For illustration only, complete data and calcu-

' lations are given for one material. Code 4, .A.I2O3,

i in tables 2, 3, and 4.

I Table 5 gives results of the X-ray diffraction

I examinations. This table includes descriptions

of the phases present, the unit cell parameters,

and the theoretical densities calculated from the

diffraction data.

Table 6 presents a summary of the elastic properties and densities for all the materials

studied.

Tables 7 to 25 inclusive give the following data

for each type of material separately: (a) the

average value for each physical property; (b) the

95 percent confidence limits are given by the numbers following the average values; (c) the coefE.- ... / standard deviation. A

cient of variation { = XI00 I; V average /

(d) the calculated and critical ^^-test number;

and, (e) the calculated and critical f-test number

when applicable.

The discussions of the 20 materials, generally, are given in the following order: (1) Description

of each type of material, fabrication, heat treat- ment, and general comments on their appearance;

5
(2) acceptability with respect to the coefficients of variation of the bulk densities and elastic constants; (3) comments on the significance of the

statistical comparison calculations; and, (4) other

discussion of data, when appropriate.

3.2. Results for Different Materials

a. Aluminum Oxide—AI2O3 (Tables 7 and 7a)

Code 1: The six groups of hot-pressed fused

AI2O3 were made from the same batch and heattreated under the same conditions but at different

times. These specimens were gray in color suggesting that tliey contained some carbon or graphite. However, one specimen of group I was heated

for 30 minutes at 1,200° C in an oxidizing atmosphere with no appreciable loss in weight (0.01%)

and no color change.

Based upon their measm-ed bulk densities, all of the groups would be considered "acceptable."

With the exceptions of the specimens of groups IV

and V, the specimens would be "acceptable" ac- cording to the variations of the elastic constants. As a single group, however, these specimens would

not be "acceptable" when based upon the coeffi- cients of variation of either their bulk densities or the values of the elastic constants. Code 27: This group of seven specimens is one

of a series fabricated to produce a high density,

polycrystalline material, by cold-pressing and sin- tering. Although a relatively high density was

achieved with very small variability in the bulk

density measurements, the specimens would not

be "acceptable", on the basis of their elastic constants variations.

Code 26: Two additional groups of specimens were fabricated using the best method developed

for the Code 27 specimens. Both of these groups

would be "acceptable" according to their variations in bulk densities and group II would be

"acceptable" with respect to the elastic constants

variations. Comparisons of the properties of

both groups show that the batches and the fabrication procedures that were established were

satisfactory to provide specimens having reproducible physical properties.

Code Jf.: Two groups of 10 specimens each were

prepared from a very high-piu^ity AI2O3. The

specimens were semitranslucent and appeared to be impervious. Each group was cold-pressed and

sintered at the same temperature but at different

times. Both groups would be "acceptable" on

the basis of the coefficients of variation of the

determined properties. Statistical comparisons of the properties of both groups indicate that this material and the particular fabrication process can be used to produce uniformly reproducible

specimens.

Code 3: This group of five specimens had a composition and fabi-ication similar to those of

Code 4.

The group would be "acceptable" on the basis ii| of the variation of any physical property. No • i statistical comparison calculations were made for'

this and either of the groups of the Code 4 mate- 1 rial because examination of the values of the it, physical properties shows that there is little, if;, any, difference.

Code 2: Two groups of 10 specimens per group j were fabricated from the same material, but group

I was heat-treated in a production kiln and group

II was heat-treated in a laboratory kiln. Those

heated in the production kiln attained a slightly

higher temperature. Both groups would be

"acceptable" on the basis of then bulk density

variations; only the group I specimens could be

considered almost "acceptable" with regard to

their elastic constants variation. More impor-:

tant, when the various property values of both

groups, with the exception of the values for

Poisson's ratio, are compared statistically, the

two groups are significantly different. In this

instance, then, one could not predict the characteristics of a production product if that prediction is based upon the characteristics of a laboratory product.

Code 14- Twelve specimens of a high-purity'

AI2O3 were cold-pressed and sintered to produce

a product that was said to be impervious to gases i at elevated temperatures, however, the densities

,

and elastic moduli given m table 7 were relatively i low. These specimens would be "acceptable" on

the basis of the coefficients of variation of any

of the physical properties.

Code 15: These eight specimens were fabricated

in the same manner as that used for the Code 26

and 27 specimens, but using a different supplier's

materials. Neither high density nor high values

for the elastic constants were obtained, and the

specimens would be "acceptable" only on the

basis of the bulk density variations.

Code 6: Eleven specimens of a very highpurity AI2O3 were cold-pressed and sintered in a "high-temperature" production kiln. A lowdensity product resulted that would be "acceptable" only on the basis of the small variation of

the bulk density values

General Comments: Figure 1, based on the

data in table 7, shows the relationship between

the average bulk density, the average values of

speed of sound. Young's modulus, and the shear j modulus for the AI2O3 specimens. These residts i \ are in general agreement with those of Coble and jj !pj Kingery [13] who found the elastic moduli of ; ^ AI2O3 specimens to increase with decreasing [ jj porosity. Wlien one considers that the data n j, represent the products of tliree different fabricators j and some five different batches, the regularity of t ^ the results is quite surprising. When the curves ^ ,5 are extrapolated to the value of the theoretical ] ^ X-ray density, the values of the elastic constants ^ compare very favorably with those determined ^ for the hot-pressed specimens that attained jj ^ almost theoretical density. ( ^

6
b. Ruby Alumina—AlaOs+CriOj (Table 8) Two groups of five specimens each were obtained on loan. One gi"oup contained weight

percent CraOa (Code 6) and the other (Code 7)

contained l]^ weight percent Cr203 simulating one

of the compositions of natural ruby. The alumina

used in compounding these specimens is the same

i as that used for the Code 5 specimens (sec. a). As received, the specimens were extremely porous

as the result of the very low-temperature treat- ment that they had received. Because of small

size and density, none of the resonant longitudinal

vibration frequencies could be obtained. After

the data given in table 8 were obtained, the speci- mens were heat-treated at 1,800° C, reshaped and

again tested.

The results, which are given in table 8 as codes

6B and 7B showed that, when these specimens were heated at a sufficiently high temperature,

they would be considered "acceptable" only on the

basis of the variation of the bulk density values.

Although a considerable decrease was noted in the

coefficients of variation of the elastic constants for the group containing the ^ weight percent Cr203

"impurity" when they were reheated, no appreciable changes occurred in the coefficients of variation for the group containing weight percent

Cr203. It was more interesting, however, that

additional heat treatment caused only small

changes in the calculated values of Poisson's ratio. The change in value for the Code 6 specimens is the reverse of the bulk density-Poisson's ratio

524074—60 2 7
trend shown for practically all of the other data

available for other materials.

c. Magnesium Oxide—MgO (Tables 9 and 9a)

Code 2Ij.: Two groups of specimens were fabricated from the same batch but heat-treated at

different times to produce high-purity, highdensity test specimens by cold-pressing and

sintering. Both groups would be "acceptable"

because of the small variation of the bulk densit}^

values, but only group II would be "acceptable" on the basis of variations in the elastic constants.

Statistical comparison of the property values

(i-test) of the two groups indicates that this material and fabrication procedure may be considered satisfactory for producing, from time to time, specimens of about the same characteristics.

Code 25: These two groups of specimens were

fabricated sunilarly to the Code 24 specimens.

Some slight differences occurred during the preparation.

Either group would be "acceptable" on the basis

of the variation of their bulk densities. Statistical

analyses of both groups showed that, although no

really significant difference in the variability of the material was introduced because of the slight

procedural change, as indicated by the /^-test results, the change did affect the average values

significantly, as indicated by the ^-test residts. Code 23: These two groups were the first trials at producing a high-purity, high-density product.

Each was made from a dift'erent source of magnesium carbonate. Each would be considered

"acceptable" only on the basis of their bulk

density variations.

Code 9: Two groups of 10 specimens each were

fabricated from a fused MgO material by coldpressing and sintering. This material has a purity

of +95 percent. The test specimens were ex- tremely porous, somewhat friable, and tan in color,

speckled with light-brown areas. Both groups were prepared from the same material and both

were heat-treated simultaneously, but in different

parts of the same kUn.

The only basis for "acceptability" of both

groups would be the low coefficients of variation of the bulk density values. Comparison of data

obtained for each of the physical properties of

both groups shows that this material, treatment,

and location in the particidar kiln were such that

with two exceptions {nfy, and Ki), there was no

really significant difi^erence according to the F- and

^-tests.

d. Mullite—3Al203-2Si02 (Tables 10 and 10a)

Code 16: Five groups of hot-pressed mullite,

totaling 20 specimens, were made from the same

material but heat-treated at different times, pre- sumably under the same pressure-temperature

conditions. Although the purities of the starting

materials were about the same in Codes 16, 17,

and 18, those of Code 16 were contaminated with

graphite from the arc-fusion process and the

graphite mold of the hot-pressing apparatus. In

addition, X-ray diffraction examination of one

specimen showed that it contained mullite and at

least 10 percent of free AI2O3.

With the exception of group IV, all would be

"acceptable" on the basis of their bulk density

variations; however, the entire lot as a group

would be "unacceptable" on the same basis. Only

group II, containing but 2 specimens, would be

"acceptable", according to the coefficients of variation of the elastic properties. There appears

to be some difference among most of the groups

listed. Because all specimens were made from the same material, it would seem that variations in the

control and operation of the hot-pressing facility were sufficient to cause sig-nificant changes in the

product in three of the five groups processed.

Codes 17. and 18: Two groups of ten cold-pressed

and sintered specimens each were obtained separately. The Code 17 specimens were subjected to a "short burn", while the Code 18 specimens

sustained a "long burn", both at the same temperature. X-ray diffraction examination of one specimen of each group indicated that both were

single-phase materials.

Both groups would be considered "acceptable" on the basis of their bulk density variations and

the Code 18 specimens would be "acceptable"

with respect to the elastic constants variation.

Comparison of the physical properties of both

groups by the <-test shows that the heat treat- ment significantly affected the characteristics of

the test specimens. It is evident that the longer

heating period, although it did not materially

affect the bulk density, or elastic modulus values,

did result in a more uniform product.

e. Mullite+ZrOz (Table 11) Code 22: One group of 10 cold-pressed and

sintered specimens were obtained that were com- pounded from a mixture of mullite (the same as that used for the Code 17 and 18 mullite specimens) and zircon. These were fabricated and 1 heat-treated m a manner similar to that used for

the Code 17 and 18 mullite specimens. X-ray

diffraction examination of one of the test speci- mens showed no zircon present and also that the

specimen contained mullite and about 20 percent

of monoclinic Zr02. No hjrpothesis is advanced

for the loss of silica from the zircon, but the SiOa

formed from the decomposition is assumed to have

entered the mullite phase [14]. This gToup could be considered "acceptable"

both on the basis of the coefficients of variation for bulk density and elastic constants. If it can be

assumed that these specimens and those of Code

17 received the same fabrication and heat treat- ments, then it appears that the addition of zircon

is almost as beneficial as a "long burn" in producing more uniform property characteristics, but

that the densities and elastic moduli are reduced.

8
f. Spinel—MgO Al.Os (Tables 12 and 12a)

j| Code 20: Five groups of hot-pressed spinel,

totaling 20 specimens, were fabricated from

the same batch composition but heat-treated at

different times. The specimens appeared to be

\ coarsely cr\-stallme, grains of ]i in. diam being

visible. The specimens were freely speckled with

j black areas. These areas are believed to be con- taminations from both the arc-fusion process and

the hot-pressing operation. X-ray diffraction ex-

' amination of one specimen showed that it contained magnesia spinel and less than 5 percent of

free MgO.

j AH of the groups, individually or as a lot, Avere

!j "acceptable" according to their bulk density varia-

:j tions, but "unacceptable" from the standpoint of

variation of the elastic constants. When the

properties of each of the groups are compared

with those of all of the specimens, a surprisingconsistency is noted. In fact, this spinel is one

of the few hot-pressed materials that gave a fairly

consistent product.

Code 21 : Two gTOups of 8 and 1 0 specimens each were made from the same material as was used for the Code 20 specimens, except that they were

fabricated by cold-pressing and sintering. Each

group was heat-treated at different times. The

test specimens were snow-white in color, very

porous, somewhat friable, and rather weak. Two

of group I were broken in handhug. Unlike those

of Code 20, the specimens were fine-gi"ained.

The group II specimens could be considered

"acceptable" on the basis of the bulk densities but

not on the basis of the elastic properties. The

group I specimens were not "acceptable" on any

basis. When the two groups were compared with

each other by the F- and f-test, it can be seen that the differences that occiurred from processing

at different times caused a significant difference in

all properties, except in.

g. Thorium Dioxide—ThOo (Tables 13 and 13a)

Both types of thoria described in this report.

Codes 10 and 51, contain ]{ weight percent of CaO

(usually added as CaCOs) for densification.

The thoria used in the preparation of Code 10

specimens was electricaUy-fused, while that used

for the Code 51 specimens was a very pure

(99.9 -f%), low-temperature calcined material.

Code 10: Two groups of 10 specimens each were

cold-pressed from the same mixture and simidtaneously sintered at the same furnace temperature,

but in different parts of the furnace. The speci- mens were a light-brown with a pink cast. Statistically, both groups would be considered

"acceptable", although some of the calculated

elastic constants had variations that exceeded the

acceptability limits. The F-te&i showed significant differences for bulk density and bulk modulus;

the only property that showed a significant differ- ence by the i-test was the shear modulus. This

uniformity indicates that the position in the

fm-nace did not seriously affect the characteristics

of the products.

Code 61: This group of 10 specimens were

fabricated from a mixture of very pure, low-temperature calcined Th02 and CaCOa by cold-pressing and sintering. The specimens were off-white

in color. The statistical treatment showed that

the group would be "acceptable" on the basis of

both the bulk densities and the elastic constants.

h. Uranium Dioxide—UOo (Table 14) Code 19: The five specimens of this group,

which were prepared by cold-pressing followed by

sintering in a hydrogen atmosphere, had a bulk

density about 95 percent of theoretical. The

m'anium oxide used in fabricating the specimens

had 2.05 moles rather than 2.00 moles of oxygen.

This ratio changed during fabrication to 2.02. The group would be "acceptable" on the basis

of both the bulk density and on all elastic constants, except Ki and K;^.

Code 19a: One test specimen was fabricated by

cold-pressing and sintering an "ammonia-pi'ecipitated" UO2 material. The measured values are included in table 14.

i. Stabilized Zirconia—ZrOz+CaO (Tables 15 and 15a)

All of the materials described in this section

contain about 5 weight percent of CaO. Wlien

such mixtures are heated they form cubic solid

solutions which are free from the discontinuous

volume changes associated with the monoclinictetragonal inversions that occur between 800° C

and 1,200° C in pure ZrOs [15, 16]. Code 11: Four groups of hot-pressed stabilized

zirconia, total'uig 18 specimens, were made from

the same mixture but heat-treated at dift'erent times.

All groups would be "acceptable" on the basis

of their coefficients of variation for the bulk

density, but none would be "acceptable" according

to the variations of the elastic constants. A comparison between groups seems unjustified because

of the extremely large variations (about 30%)

of all of the specimens, considered as a group.

Anticipating data to be presented later in this section, inspection of the data in table 15 shows

that, although these hot-pressed specimens at- tained a very high bulk density, the values of the

elastic constants were as low as (and in some

instances lower than) the values determined for the cold-pressed and sintered specimens. It is believed that this anomaly is due to internal

laminations and cracks in the specimens. Such

faults in these test specimens could sometimes

be shown to exist, although thek full extent could not be readily evaluated, by judicious

"probing" during the resonant frequency determinations. At times, the duection and magnitude of the flaw can be approximated, but it does not appear feasible to attempt a quantitative evaluation of the effects. Therefore, all of

these, and the later, data given for stabilized
zirconia are suspect. Although there was a small

spread in the bulk density measurements, apparently indicating production uniformity, the

very large spread of the elastic constants indicated

that actually this was not the case. This is an

excellent example of the value of the dynamic

measurements in determining the variability of

specimens.

Code 13: Two groups of 10 specimens, which

were fabricated by cold-pressing and sintering, were made from the same material and heattreated simultaneously at the same furnace temperatm-e, but the groups were located in different

parts of the furnace.

Either group would be "acceptable" only with

respect to the low coefficients of variation for the bulk densities; they would not be "acceptable"

with respect to the elastic constants. With the

exception of the bulk density values, statistical comparison of the elastic constants of both groups

showed that the location in the furnace (assuming

all else equivalent) significantly affected the characteristics of the products.

Code 12: These two groups of 10 specimens each were submitted by the fabricator with the com- ment that "considerable fabrication difficulty was

experienced with longitudinal seams and trans- verse cracks." Both groups were made by coldpressing and sintering. They were prepared from

the same mixture and heat-treated at the same

temperature, but at different times, in a laboratory

fiirnace. These two groups showed the lowest bulk densities of any of the stabilized zirconias. On the

other hand, the elastic constants are not only the

highest but also the most uniform. For example,

the group II specimens would be considered "ac- ceptable" on the basis of most of the physical

properties. Statistical comparison of the elastic properties of the two groups indicates that the

fabricator supplied this material with uniform

characteristics in spite of his fabrication difficulties.

j. Alumina+ Chromium—Al203+Cr (Tables 16 and 16a)

Code 29: The group numbers of the 19 speci- mens of this cermet were considered as one group.

Another two groups of the same material are described in the next section. With the exception

of the low variation of the bulk density values, the

Code 29 specimens as a single group would not be

considered "acceptable".

Code 30: These two groups of 10 specimens each were cold-pressed and sintered. They have the same composition as the Code 29 specimens. The

two groups were made from the same mixture but

heat-treated at different times.

Both groups could be considered "acceptable" on the basis of bulk density or the elastic constants,

with the possible classification of group I as a

borderline case when considering the elastic properties. Again, because of the borderline nature of one of the groups, it is difficult to say, statistically,

10

that the mixture can or cannot be fabricated with

uniform characteristics from time to time.

Code 28: Two groups of cold-pressed and sintered Al203+Cr cermet, 10 specimens per group^ were prepared from the same mixture but heat- i treated at different times. The composition is similar to, but not identical with, the Code 30

specimens. As was the case for all of the AI2O3-I- Cr mixtures, the X-ray diffraction examinations

showed only a single chromium-metal phase. A

possible explanation for the absence of AI2O3 reflec- tionsis that the chromium-metal became "smeared" f over the surface during polishing, thus masking », the alumina phase. , Only the group I specimens could be considered , "acceptable" on the basis of their low coefficients

of variation for the bulk densities and elastic constants. When the physical properties of each

group are compared statistically, it is apparent

that variations in heat-treatment caused a significant change in all of the properties with the

possible exception of the values for Poisson's

ratio.

k. Ni-bonded Titanium Carbide—TiC+Ni (Tables 17 and 17a)

Four TiC+Ni mixtures containing 10 to 30

weight percent of Ni were fabricated by coldpressing and sintering. The TiC had about 6

weight percent of tantalum and niobium carbides

in solid solution. Each of the four codes was

prepared and heat-treated separately under identical conditions. The nickel content of these

mixtures are: Code 31—about 10 wt % Ni

Code 32—about 20 wt % Ni

Code 33—about 30 wt % Ni

Code 34—about 30 wt % Ni (a modified Code

33 composition)

Code 31: Both groups of specimens would be

considered "acceptable" on the basis of the coeffi- cients of variation for both the bulk densities and

elastic constants, although group I might be

borderline. Comparison of the physical properties by the i5-test of the two groups shows that

the mixing and general fabrication controls are such that materials having about the same variability can be produced at different times; also,

the f-test shows that this cermet can be reproduced with substantially the same physical

properties.

Code 32: Both groups of specimens would be

"acceptable" except for Poisson's ratio and bulk

modulus. Comparison of the physical properties

of the two groups shows that, although the mixing

and general fabrication controls were such that a

material with the same scatter in values can be

reproduced from time to time, the materials were

not consistent in their physical properties.

Codes 33 and 34: The same statistical comments

that were given for the Code 32 material are applicable to these materials.
General Comments: Figure 2 shows the extent

of the variation of the values of the elastic constants and the bulk density with the nominal nickel content. The average values of the two groups of

each mixture for codes 31, 32, and 33 were av^er- aged to provide the data for these ciirves.

1. Boron Carbide—B4G (Table 18) Two groups of 10 hot-pressed specimens (Code

44) were made from the same batch but each was

prepared and heat-treated at a different time.

For the reasons stated in section 2.3(a), torsional

frequencies were determined for only one specimen of a group; and consequently, no statistical comparisons were made.

m. Boron Carbide+ Titanium Diboride—B4C+TiB2

(Table 19) Code 43: These four groups of five specimens were hot-pressed from the same mixture of 82

parts (volimae) of B4C and 18 parts of TiB2, but

each group was heat-treated at a different time.

The same comments that were given for specimen

size, reshaping, and calculation method for boron

carbide (sec. 2.3(a)) are apphcable to these speci- mens. The addition of titanium diboride in- creased the bulk density but did not significantly

affect the values of the elastic constants.

n. Silicon Carbide—SiC (Tables 20 and 20a)

Code 45: "High-purity" materials, probably

less than 3 percent of uncombined silicon or carbon

excess, were used for both Codes 45 and 35. Two

groups of cold-pressed and sintered specimens,

9 and 8 specimens, respectively, were prepared

from the same material but heat-treated at dif- ferent times. The resonant longitudinal vibration frequencies could not be determined with the

available equipment on the 15-cm long specimens

because of the high values of the speed of sound.

Therefore, the elastic moduli were calculated only

from the flexural mode of vibration.

Both groups would be "acceptable" on the basis

of their variation in bulk density values, and group

a. o

o

COo

0.

0.210

0.200

0.190

_io ^n Oq: 5 <

CC CD

<. O

UJ -J

1650

1600

1550

1500

5O UJ

4000

3900

3800

3700

—

UJ . UJ Q

<f> O

10

8600

8500

8400

8300

8200

8100

8000

7900

E

10 20 30 NOMINAL Ni- METAL CONTENT. %

Figure 2. Compositional dependence of the elastic constants and bulk density for TiC + Ni (codes SI through 34).

11
II would be "acceptable" with respect to the

variability in elastic constants. When the physical properties of the two groups are considered, it

is apparent that the two groups, except for Efe, are significantly different.

Code 35: Two cold-pressed and sintered groups, were prepared from the same material but heattreated at different times. X-ray diffraction ex- amination on one specimen revealed that it was

composed of a mixture of cubic crystals with

several hexagonal SiC phases. It has been shown

[17] that there are some 15 or more hexagonal

polytypes of SiC, all or any of which may coexist

with or without the cubic form.

On the basis of the coefficients of variation for their bulk densities only, both groups could be

considered "acceptable". When the other property values of the two groups are compared by

by the F- and i-test, it appears that the materials and fabrication methods can, in general,

provide reproducible products, but with rather

poor uniformity of physical property characteristics; the imiformity of bulk density appears to be the exception.

o, Silicon Carbide+ Boron Carbide—SiC+ B4C

(Table 21)

Code 37: Each of the 4 groups of 5 specimens of

this material (designated as "boron carbide

bonded sUicon carbide") were made from the same

mixture but hot-pressed at different times. The

SiC was the same as that used for the Code 35

specimens; the B4C was of "commercial" grade.

The same comments given for specimen size,

reshaping, and method of calculation for boron

carbide (sec. 2..3(a)) apply here. However, it will be noted that the addition of the 10 parts of B4C

very substantiaUy increased the bulk density and

elastic moduli values.

p. Zirconium Carbide—ZrC (Tables 22 and 22a)

Code 38: Six groups of hot-pressed zirconium

carbide, totaling 20 specimens, were made from

the same material but pressed and heat-treated

at different times. The material was of commercial grade. X-ray diffraction examination of one

specimen showed it to be essentially a single phase

material (ZrC) but that it contained a very small

amount of free graphite.

Groups III, IV, V, and VI would be "acceptable" on the basis of the low variation for the

bulk density values ; however, the entire lot would

not be "acceptable" according to the coefficients of variation of the elastic constants. Assuming

all else equal, the results in table 22 show that

considerable variations in heat-treatment must

have occurred during the fabrication of these test specimens. As was the case with many other

materials, there was very little change in Poisson's

ratio with heat-treatment.

q. Zirconium Diboride—ZrB2 (Tables 23 and 23a)

Code 41 ' Four groups of five hot-pressed speci- mens were made from the same material but heattreated at different times.

With the exception of the specimens of group

III, all other groups would be considered "acceptable" because of their low coefficients of variation

for both the bulk density and elastic constants

values. When the values of each of the groups

are compared with the values for the entire code,

it is apparent that the values for the physical

properties were not reproduced from time to time.

Code Jf.2: Two groups of 10 hot-pressed specimens, whose composition is a modification of Code 41, were fabricated at different times.

Comparison of the values of both gi^oups shows

that nonuniform specimens can be fabricated with

reproducible properties, although neither of the

groups would be "acceptable" under the criteria established.

r. Molybdenum Disilicide—MoSi2 (Tables 24 and 24a)

Code 39: Six groups of hot-pressed specimens,

19 in all, were prepared from the same material

designated as of "high purity" but heat-treated

at different times.

All of the groups, with the exceptions of II and

III, would be "acceptable" on the basis of the

low variation of their bulk densities, although the

entire code would not be "acceptable"; groups IV

and VI would be "acceptable" according to the

coefficients of variation for the elastic constants.

s. Nickel Aluminide—NiAl (Tables 25 and 25a)

Code 4.0 : Two groups of cold-pressed specimens were fabricated from the same mixture but heattreated at different times. The mixtiu-e was a

proprietary modification of the basic composition.

Only the specimens of group I would be "acceptable" and then only on the basis of the bulk

densities. When all of the physical properties of

the two groups are compared, it should be noted

that the indicated similarity has little meaning

because of the large variability of the physical

properties.

3.3. Discussion

One of the interesting observations was that

Young's moduli obtained from the longitudinal

mode of vibration were 1 to 2 percent less in most

cases than those obtained from the flexural modes.

Similar measurements made with glasses [3] and

other homogeneous isotropic materials [18] have

shown good agreement for Young's moduli calculated from the flexural frequencies with Young's

moduli calculated from the longitudinal frequencies using the same equations for both calculations

as in this investigation. The observed lack of

agreement for many of the materials studied here

may be attributed to one or more of the following

causes aiising from some part of the fabrication

process: (1) Variations in density in the specimen;

(2) The presence of cracks within the specimen.

If these cracks are not randomly distributed, their

if

1

1

E lull

,[ri

) op W

dyi

12
gross effect ^vill be that of a structural inlioinogeneity; (3) The segi'egation of grain sizes durmg

fabrication [19]; and, (4) The lack of complete

randomness in the orientation of tlie crystalline

particles composing the specimen.

If the particles forming the structiire assume some preferred orientation, then macroscopically

the specimen viiB. not be completely isotropic.

Roth [20] has definite^ found evidence of such

cr^'stallhie orientation in small pressed pellets of

ceramic materials from X-ray diffraction examination. The presence of some orientation is sho^vn

by a different intensit}" of certain lines than Avould

be the case for a completeh' random orientation.

Although no such clear-cut evidence was found for the specimens studied here, the possibihty is not

ruled out that such small preferred orientations were present.

From the few isolated mstances where information was available for laboratorj" and production

specimens, less variation occurred when the same

material was fabricated as a production item than

when it was fabricated as a laboratorj" item. A

possible explanation is that, in each of these

instances, a higher heat-treatment temperature was used for the production product. There were

also some data available for materials heattreated in the same furnace at the same temperature but for different time intervals. In

these, appreciably smaller variations in density

and elastic constants occurred for those specimens

heat-treated for a longer period of time. It would

seem, therefore, that, although production econ- omies would dictate a minimum time at minimum

heat-treating temperatures, a more uniform and

reproducible product would result from increasing

both firing time and temperature. This improvement in the product appears to be readU}' achievable at a slightly increased production cost. The

value of a statistical analysis for selecting the

optimum temperature and time should be apparent.

It is anticipated that significant advances wiU

be achieved in the uniformity of conamercialh^

available materials only recently developed, such

as hot-pressed stabilized zirconia. As more general

experience in the hot-pressing techniques is accu- mulated, one can reasonably expect to realize the

advantages of both higher density and of optimum

uniformity of the products.

The d}Tiamic elastic constants, as measured

here, appear to be more sensitive indicators of

product uniformity in quality control than are bulk density measurements. However, in the

case of cold-pressed and sintered specimens in which the bulk densities are ^vithin a few percent

i of the theoretical value, for example, thorium and

uraniima dioxide. Codes 10 and 19, bulk density

appears to be as sensitive a criterion as the

dynamic elastic constants. The reported information for the various types

of "stabilized" zirconia (sec. 3.2.9) gives one of the

very few examples available of the relative values

of bulk density and dynamic elastic constants as production-control measurements for materials

that are difficult to fabricate. The bulk density

values of each of the four groups of hot-pressed

specimens (Code 11) show little variation. The coefficient of variation of the bulk density of the entire code of 18 specimens is only percent, yet the

Young's modulus values for the same specimens

var}^ from 1,100 to 2,050 Idlobars, and the coeffi- cient of variation is on the order of 30 percent. Although the calculations are not shown in table 15,

the two groups of Code 13, when considered as a whole, show a coefficient of variation of less than

K percent in bulk densities. On the other hand,

the average value for the 20 specimens as a whole was 1,380 Idlobars with a coefficient of variation of only 8.3 percent. In the set of specimens in

which difficulties were encountered from laminations and fissures (Code 12), the coefficients of

variation of both the bulk density and elastic modulus values are low, although the average value

of Young's modulus was 1,483 kilobars compared

to 1,380 for the average of Code 13. Although it might appear facetious, it seems possible that the

Code 12 specimens were fabricated with uniform

imperfections.

Inasmuch as the precision of the elastic modulus

measurements was estimated to be about 0.4 per- cent whereas that of the density measurements was estimated as about 0.2 percent, it is pertinent

to inquire to what extent the coefficients of variation of these two properties were affected by the

precision of the measurements themselves. Or,

stating the problem in another way, it is necessary

to ascertain whether the greater variability found

for the elastic modulus measurements represents a

real variation from specimen to specimen, thus

supporting the claim of greater sensitivity for this method as an indicator of specimen uniformity, or whether this increased variability was not merely

a reflection of the lower precision of the dynamic

measurements.

The equation relating the contribution to the

total variability, expressed here as o-^, in a property

measm"ement, from that due to the variability in

the measurement itself, a-j„ and that due to the

variation from specimen to specimen, as, is as

follows,

or, in terms of the coefficient of variation, V,

Vr^^'YTW/- (17)

In this investigation, V^=zl percent was chosen

as the criterion of acceptability, 1^^=0.2 percent

for density measurements, and Fm=0.4 pei'cent

for elastic modulus measurements.^

' Actually, r„ for elastic and density measurements was better than the

values given. In a normal distribution, the coefiicient of variation includes about 34 percent of the cases, whereas the estimated measures of precision would probably include more than 80 percent of the cases. The results, then, make the contribution of the precision of the measurements to 1 V even smaller than shown in the text. 13
Therefore, for the elastic determinations

l=V(0.4)2+Ff

and Vs=0.92 percent

for density measurements,

1=V(0.2)2+F|

and

Vs=0.98 percent.

Thus, it is seen that for a coefficient of variation of

1 percent, the difference in precision of the elastic modulus and density measurements is a negligible

factor since in both instances, by far the greater

contribution to the coefficient of variation, Vt,

stems from a real difference from specimen to specimen. Furthermore, as the coefficient of variation increases, the contribution from the precision

of the measurement grows increasingly smaller.

Conversely, the contribution from the precision

of the measurements grows larger for coefficients of

variation less than 1 percent. However, this is of no practical importance since all coefficients of

variation of 1 percent or less were considered

"acceptable" without regard to degree. However,

for those elastic constants which were more in- directly computed, such as m and K, and hence

of decreased precision, the 1 percent coefficient of

variation as a criterion becomes much less significant as, in these cases, the contribution of the precision of the measurement becomes more important

and may overshadow any real specimen variability.

The problem may also be approached in another way, as follows: If a 1 percent coefficient

of variation is set as a criterion of acceptability

for density measurements and the precision of this measurement is 0.2 percent and the contribution

of Vs is found to be 0.98 percent then what would

be an equivalent coefficient of variation to set for

elastic modulus measurements? These have a

precision of 0.4 percent and Vs is also 0.98 percent.

The coefficient of variation under these conditions

is obtained from

Fj,=V(0.4)=*+ (0.98)2=1.05%.

This value is seen not to be significantly difi^erent from the coefficient of variation actually set and

groups of specimens having such a coefficient of

variation would indeed be classed as borderline

cases of acceptabihty.

In addition to its use as an indicator for determining the uniformity of production for particular groups of specimens, it is interesting to estimate the variability of the elastic moduli of

all the materials of this investigation, taken as a whole ; and to compare this variabihty with that

of a different material, steel, which is generally

considered to be much more uniform with respect

to this same property.

Taking Ei whenever available, and Ef^, otherwise, the following summary was prepared for

all the materials studied

:

Range in coefficient

of variation 0 to 1%

0 to 2%

0 to 2.5%

0 to 3.0%

Percentage of specimens

44

62

72

81

Analagous data for steel is not readily found.

However, one study [21] gives the following results

for specimens of "black sheet steel": V, for speci- mens cut in direction of rolling =2.4 percent.

Average of E = 1 ,962 kilobars ; V, for specimens cut

transverse to direction of rolling=2.6 percent,

average of E=2,053 kilobars; V, for specimens

taken as a single group, 3.3 percent, average value

of E =2,006 kilobars. Thus, it is seen that, if either value of V for steel is taken for comparison,

about 70 percent of all the specimens of this in- vestigation would be included, and, if the coefficient of variation of all the steel specimens without regard to direction of rolling had been taken

for comparison (which seems more reasonable),

then more than 80 percent of all the materials of

this investigation would be included. These data

[21] were for only one type of steel and may not be

representative. But, if they are at all indicative,

then the materials of this investigation, as a whole,

compare favorably with a material which has

traditionally been regarded as quite uniform.

It is believed that the present study shows that a relatively simple statistical approach can be

valuable not only to the designers and engineers,

but also to the fabricators and suppliers. One

of the main deterrents to the use of ceramic and

cermet materials in many applications where they seem to be potentially useful is the lack of knowledge of the physical properties and constants of

these materials, and, when such information is available, the lack of confidence in the uniformity

or reliability of the reported values. A great deal

of information on product uniformity could be

provided by the fabricators and suppliers, usually

without additional expense, by statistically ana- lyzmg the data that are already available to the

manufacturer.

The author thanks Jack Shartsis for performing

most of the computations, Nancy Tighe for per- forming some of the later experiments and calculations, and Robert S. Eoth for performing the Xray analysis.

14
Appendix I. Statistical Treatment of Data

The following description is not intended as a

basic exposition of the statistical concepts in- volved but rather as an aid to those who might

desire to perform the same (or similar) calculations and wish to have some understanding of the

significance of the results. All of the computations used in this report are discussed and described in detail by Youden [22] and Dixon and

Massey [23]. Let "x" lepresent a value of any property in one group of specimens, "y" represent a value for the same property of another group, "x" represent the average value of any property of the first group, "y" represent the average value of the same property of the second group, "n" represent

the niunber of values determined for any property

LQ the first group, and "w" represent the number

of values determined for the same property of the

second group; then statistical calculations (based

upon the assumption that the sets of data of all of

the determined properties cf the materials follow

follow the normal distribution law) are performed

according to formulas (A), (B), (C), and (D)

which apply to the fu'st group. SimUar formulas

with X replaced hy y apply to the second group.

Parts (E) and (F) apply to both groups.

(A) Standard deviation of an individual determination= 5'=

a' variance

or .(&)n

71-1

+a:i+ . . . +xl) — {xi+X2+ . . +XnYln

n-1

(B) Standard deviation of the average of "n"

S

individual values =*S"=^

fC) Coefficient of variation^, in %=£(100)

(D) Ninety-five percent confidence limits

(C. L.) for the average are given by

I±S'tm %

~

Where t is the upper 2.5 percent point of the i dis- tribution for n—1 degrees of freedom. If such

limits are calcidated for many sets of data, there

will be approximately 95 percent of the sets for which the limits enclose the true average.

(E) The F-test, essentially, is a method for comparing the "precision" of two sets of data for the same property. It provides one with a cri- terion for determining at a selected confidence level whether a significant difference exists between the

.524074—60 3

scatter of two (or more) sets of data; that is, whether the groups (or materials, etc.) used to obtain that data are of a different degree of variability. In this study, the 95 percent confidence

level was used. The i^-number that is calculated from the expression,

F=Sa

where S/ is always the larger number of the two

being examined, is compared to tabulated critical i^-values. The tabulated critical i^-value selected,

is in this situation that for the upper 2.5 percent

point of F. If the calculated value is higher

than the critical value, a significant difference

does exist. (F) The ^-test, essentially, is a method for comparing the "accuracy" of two sets of data for the same property. The t-test should be applied

to the data of two groups only when the F-test has shown that these data sets are of comparable

variability. The t-test provides one with a cri- terion for determining whether a significant dif- ference exists at a selected confidence level between

two averages, x and y, on the basis of the spread of the individual values, Sx and Sy, used to compute

those averages. This test, however, does not

allow one to determine the accuracy of either x or y unless, of course, the true value is known.

As is the case with the F-test, the ^-value that

is calculated is compared to tabulated critical ^-values and, if the calculated value is higher

than the critical value, a significant difference does

exist (see the similar discussion of significance

under subsection (E), preceding). The calculated

value is obtained from the expression

_ x—y nXm

with 71+m— 2 degrees of freedom, where Sp is the pooled standard deviation of the individual

values of both groups, and Sy, and is obtained

from

S

[Zi^i- (&,) vn]+[z:j/f- (j:yir/m] (n-l) + (m-l)

During the early part of this study, it was a part

of the computation procedure to perform the F

and i-tests to compare the values of Ei, Efy,, and

Efe, in pairs, and those of /x, and /x/w Very rarely were significant differences found to exist and,

therefore, the time-consuming calculations were

neglected for at least the latter half of the data

obtained. However, occasional check calculations were made, but the results of such comparisons

within a group are not included in this compilation

of data.

45
The preceding relations could be applied to the

data obtained in this investigation in several ways.

The approach selected is given as follows. Each

of the suppliers of materials for the "bank" was

asked to prepare his specimens in either of two

ways: (1) Compound the same starting composition at two different times but fabricate each

group identically; or, (2) compound one large

quantity of the starting composition and fabricate

each group separately. All fabrications were to achieve the maximum practical bulk density and

it was to be uniform throughout the specimens.

The calculations of the standard deviation of an

individual measurement of each group and the

coefficient of variation for all of the properties

permits one to use the reliability of the measure- ments of any property as a criterion for determining the product uniformity or acceptability.

That acceptability may be based upon an arbitrary

or specified standard variation. If average values were determined repeatedly and if in each instance

95 percent confidence limits were calculated for the

average value, then in the long run we would

expect that 95 percent of the confidence limits

would include the true average value.

Application of the F- and i-tests to the data

obtained from specimens prepared under the

first condition allows one to state that there was or was not a significant difference in the

compounding procedures of the same nominal

composition at different times. In a similar way

the F- and f-tests can show whether or not

the fabrication differences (such as heating at

different times, or in different types of furnaces,

or at different temperatures in the same furnace)

had a significant effect on either the scatter of

the values obtained or the average of the property

values determined.

This series of statistical computations has

another important value. Some of the suppliers

of the specimens for this "bank" took the opportunity to fabricate specimens, from the same batch

composition, both in the laboratory and on the

production line. Here, then, was an excellent

opportunity to evaluate the results of a laboratory

or pilot-plant experiment and a production run.

It seemed, therefore, that the statistical methods j described should be of considerable interest for many types of laboratory and production-control

evaluations.

When it was shown that a significant difference ' existed for the i^-test, it was concluded that the

.

materials were not of comparable variability due to a variation either during the compounding or the

fabrication stages depending upon the production

conditions. Under these conditions, one must

'

logically conclude that the i-test is not appli- ' cable because the materials of each group were

not of comparable scatter (i^-test results). j| Briefly then, under the conditions imposed, the

results of the i^-test show whether material of

comparable variability is produced, and the t- test shows whether it can be supplied with re- producible properties from time to time. It must be re-emphasized that one must not blindly

apply such conclusions to groups of data for which other conditions may have been varied.

| The F- and i-tests are not as restrictive as may

be implied from this discussion.

Appendix II. Tabular Information

The locations of the tabular data for each material discussed in the previous sections of this

report are presented below.

Page Table 7—Data for AI2O3 22 Table 8—Data for Ruby Al.Os 24

Table 9—Data for MgO 24 Table 10—Data for Mullite—3Al203-2Si02 26 Table 11—Data for Mullite + Zr02 26

Table 12—Data for Spinel—MgO - AI2O3 28

Table 13—Data for ThOj 30

Table 14—Data for UO2 30

Table 15—Data for "Stabilized" Zr02 32 Table 16—Data for Al203-|-Cr 34 Table 17—Data for TiC+Ni 36

Table 18—Data for B4C 36

Table 19—Data for B4C + TiB2 38

Table 20—Data for SiC 38 Table 21—Data for SiC + B^C 40

Table 22—Data for ZrC 40

Table 23—Data for ZrBj 42 Table 24—Data for MoSi2 42

Table 25—Data for NiAl 44 16

The symbols in the tables have the following

significance

:

£( = Young's modulus from the longitudinal resonant

frequency.

i?/„ = Young's modulus from the flexural resonant! frequency in flatwise vibration.

i?/(,= Young's modulus from the flexural resonant frequency in edgewise vibration. (?= Shear Modulus.

/ii=Poisson's ratio using Ei and G.

/i/-^=Poisson's ratio using E;^ and G,

/ii/(,= Poisson's ratio using Ef^ and G. K;=Bulk modulus, using Ei and

K/u^= Bulk modulus, using Ef^ and nfu,.

Underlined F and t values indicate that a significant difference exists between the compared groups. The F and t ratios marked with an asterisk indicate that the comparison has been made with the critical value similarly marked. Two critical values derive from

the fact that in choosing this tabulated (critical) value

different numbers of specimens are involved.
Table 1. Materials, source, and general fabrication data

Material Nominal composition Code Source No. of No. of Reported

Manufacturer's Fabrica

tion 0 Temperature No. specimens groups purity Designation Control No. method of heating b

Alumina AI2O3 1 H 20 6 %99+

98+ 99+

99+

C-5633 HP

° C.

(2, 000+)

1, 725

1, 750

2 H 20 2 LA7365 CP

3 H 5 1 LA 603 CP

4 H 20 2 LA 603 CP 1, 750

5 F 11 1 Pure 562V CP 1, 650

14 F 12 1 Vitreous 655Q CP 1, 680

1,800

1,800 1,800

1,800

1,800

1, 780 1,800

1,800

1,800

(1, 750+)

1,650

1, 650

15 G 8 1 99.9 CP

26 G 14 2 99.9 CP

27 G 7 1 99.9 CP

Ruby alumina 99.5% AI2O3+O.5 Cr203

98.5 AI2O3+I.5 Cr203

6 F 5 1 A33A CP

7 F 5 1 A34A CP

9 H 20 2 Fused M-202 CP

Magnesia MgO 23 G 10 2 99.9 CP

24 G 11 2 99.9 CP

25 G 14 2 99.9 CP

Mullite 3Al203-2Si03 16 H 20

8

5 Fused C-5657 HP

17 F 1 CP

18 F 10 1 CP

MulUte+zirconla 3.Vl203-2Si02+ZrOj MgO.Al203

22 F 10 1 397Z CP 1, 650

(1,850+)

1,785

1,785

1, 800

Spinel 20 H 20 5 Fused C-5633 HP

21 H 18 2 431927 CP

Thoria ThO2+0.5% CaO 10 H 17 2 431924 CP

51 G 10 1 CP

TTrania -— UO2 19 C 5 1 99.9 MCW CP 1,750

1, 750

(2, 000+)

1, 720

(1, 700+)

19a G 1 1 99. 9 NHs-ppt

C-5633

CP

Zr02+5% CaO 11 H 18 4 HP

12 H 20 2 LZ7590 CP

13 H 20 2 LZ604

MT895/823

Mi.xed

CP

Chromium bonded alumina Chromium bonded alumina LT-1 LT-IB

Al203+Cr Al203+Cr+Mo+Ti02

28

29 DD

20

19 21 Cast Cast

(1,600)

(1,600)

(1, 600)

1, 300 to 1, 500

1, 300 to 1, 500

1, 300 to 1, 500

(modified)

Nickel bonded titanium

30 D 20 2 LT-IB 4168/169

3010/3011 2459/SC297

2697/2739

2752/2889 X431925 B5592

Cast TiC+Ni 31 E 20 2 K150B CP

carbide. 32 E 20 2 K151B CP

33 E 20 2 K152B CP

34 E 2 K162B CP

Boron carbide BiC+TiBj (82/18 vol)

44 H 20

20

2 HP

Boron carbide — titanium 43 H 4 HP

boride.

Silicon carbide SiC 35 H 19 2 5347/5343 CP

45 B 17 2 ZT CP (1, 800+)

SiUcon carbide—boron car- SiC+BjC (90/10 wt) 37 H 20 4 C-5572 HP

bide. Zirconium carbide ZrC 38 H 20 6 C-5633 HP

Zirconium di-boride ZrB2 41 H 20 4 5572/5592

178-10/20 HP

42 A 20 2 101 CP (2, 000+) Molybdenum dlsilicide MoSi2 NiAl

39 H 19 6 2372/5592

927 A/B

HP

Nickel aluminlde 40 A 14 2 1505 CP (1. 500+)

» HP represents hot-pressed in graphite mold, CP represents cold-pressed and sintered, and Cast represents slipoast and sintered,

b The heating temperatures given in parenthesis are approximate.

17
Table 2. Room temperature dynamic elastic constants for AI2O3

Code 4

Specimen

4.1 4.2

4.3 4.4

4.5 -. 4.6.

4.7

4.8 - 4.9 4.10 Average 95% C.L

Std. dev

Coef. var

4.11- - 4.12 4.13-.- --.

4.14 -

4.15

4.16

4.17

4.18- 4.19

4.20 Average 95% C.L

Std. dev

Coef. var

F-test: Critical

Calculated

t-test:Critical. . - Calculated

p iLi

mlsec. i\.\LOu(lTS j\llOO(lTS JxilOOClTS

.—

KilobaTs Kilobars

3. 829 9699 ''ODUi. 0 oOot 3593 1447 0. 244 0. 238 2348 2280

3. 813 9649 3550. 2 3523 3537 1425 . 246 . 236 2330 2226

3. 831 9696 oDUi. * ^C.7(i OO/O 0000 1445 . 246 . 238 2363 2273

3. 810 9635 3537. 3 3509 3546 1421 . 245 . 235 2311 2206

3. 819 9679 3577.

3

3555 3563 1437 .245 .237 2334 2251 3.828 9682 3588. 3 3566 3571 1439 .247 .239 2361 2276

3. 825 9673 oo/y, 0 3550 3562 1437 . 245 . 235 2340 2233

3. 824 9684 OOoD. 0 3566 3573 1441 . 244 . 237 2338 2263

3. 831 9714 3615. 2 3599 3608 1449 . 248 . 242 2386 2324

3. 829 9691 3596. 5 3574 3584 1441 .248 .240 2378 2292

3. 824 9680 oOoo. 00 3561 3572 1438 0. 246 0. 238 2349 2263

0. 005 17 18. 3 20 15 7 0. 001 0. 002 17 25

0. 008 23 25. 54 0(1 01 9 0. 001 0. 002 23 35

0. 27o 0. 2% 0. 71% U. 5% 0. 6% 0. 6% 0. 5% 0. 9% 1. 0% 1.5%

3. 832 9694 0000 ooy.6 1445 0. 245 0. 239 2356 2291

3. 816 9653 3555. 7 3546 1428 . 245 . 237 2323 2235

3. 815 9683 3577. 3 0O0.2 3564 1436 . 241 . 233 2307 2215

3. 830 9688 oov't. t 000£i 1444 . 245 . 237 2346 2263

3. 819 9673 3572. 7 3542 3556 1433 .247 .236 2351 2236

3. 821 9677 3577. 8 3549 3566 1436 .246 .236 2347 2239

3. 817 9667 3567. 7 OOoD 3550 1433 . 245 . 234 2329 2214

3. 819 9668 oooy. 0 3546 3551 1432 . 246 . 238 2342 2255

3. 834 9691 3600. 5 3580 3588 1446 . 245 . 238 2352 2275

3. 820 9677 3577.

1

3550 3555 1437 .245 .236 2338 2239

3. 822 9677 3579. 32 3554 3565 1437 0. 245 0. 236 2339 2246

0. 005 9 lU. 0

1 Qio 1

9

4 0. 001 0. 001 11 18 0.007 12 14.84 18 17 6 0. 001 0.002 15 25 •

0. 2% 0. 1% 0. 41% 0. a"/o 0. 5% 0. 4% 0. 6% 0. 8% 0. 7% 1- 1%

4.03 4. 03 4.03 4. 03 4.03 4. 03 4, 03 4. 03 4. 03 4.03

1. 16 3. 59 2.96 2. 37 1.62 2. 20 1. 13 1. 30 2. 26 2. 01

2. 10 2. 10 2.10 2. 10 2. 10 2. 10 2. 10 2. 10 2. 10 2. 10

0. 79 0. 39 0. 43 0. 60 0.84 0. 35 1. 30 1.64 1. 13 0. 42

oThese data are reported to give figures only for the purpose of illustrating the statistical computations shown in table 3.

Table 3. Statistical calculations for AI2O3

Young's modulus Code 4^

Computation

Average=3;=total/no. values

2i =x ... J (2Xiyln = (.X1+X2 . . x„)yn

Deg. of freedom=No. determinations—!

Standard deviation=S= VS2^

CoefBcient of variation ^SXIOO

X

95%c.l. = S4

Group I (Specimens 1 to 10)

35833.5/10 = 3683.35

128,409,842.1 128,403,972.2 5869.9

10-1 = 9

5869.9/9 = 652.2

25.54

25-54X100

3583.35

"-^^Z"

25.54X0.7153=18.3

Group II (Specimens 11 to 20)

35793.2/10=3579.32

128,117,298.2

128,115,316.6

1981.6

10-1 = 9

1981.6/9 = 220.2

14.84

14.84X100 ^

3579.32 14.84X0.7153=10.6

jF-test F=S IS^, where S is larger of the two. F= 652.2/220.2= 2.96 1 There is no significant difference between

Critical value of F=4.03/ the scatter of group I and group II.

<-test _x-y

with n+m—2 deg. freedom

^436 = 20.89

^ 3583.35- 3579.32 / 10X10 _„

) There is no significant difference

20 89 V 10+10~ i between the average values of

I group I and group II. Critical value of <=2.10 1

« The actual data records each value to the least one significant figure more

than those given in table 2.

\t8
Table 4. Bulk density and dynamic elastic constants calculations for specimen 4.I —see table 2

Length=2=15.253 cm; width = = 1 .270 cm; edge = e=0.6359 cm. Weight =47. 1555 grams. Resonant frequencies: longitudinal, i^i=31,792 cps.

flexural flatwise, F/„=2,700 cps.

flexural edgewise, F/, = 5,302 cps.

torsional, Fi=14,948 cps.

Volume= (15.253) (1.270) (0.6359) = 12.318 om3. Corrected mass=(massX0.99986)+(volumeX0.0012) = (47.1555X0.99986)+(12.318X0.0012) =47.1633 grams.

Bulk density, p=M/y=^^=3.829 gm/cms.

Voting's modulus, Ei=v\ where l^,=2ii?i=2(15.253)(31,792)(10-2)°=9,699 m/sec.

£1= (9,699)2(3.829) (10-5)£n''=3,601 kilobars

or £i=4/2f,2p=4(15.253)2(31,792)2(3.829)(10-«)°=3,601 kilobars

Shear modulus, G=MFr-B where B= V4(./u,) +2.52(./«;)2+0.21(e/^)e J

^^^^^^^

ew G= (47.1633) (14,948)2(137 .307) (10-9)° = 1,447 kilobars

Poisson's ratio, '"=^-l=^§^f^-l=0-244

(Average value of in for this group is 0.246)

Bulk modulus, K,^^^^^^-^^^=2,3i,^im.rs

Young's moduZas, £'/„=9.464X10-!« Mr2fw — ( —V Ti w \ e J r i +(0.26M+3.22M2)'-/n , n,iR L 1+0.1328V? J

where Ti = T = l-°136

where T=1.01182

r/,= «:HM635?-^ = 0.012035

15.200

;i=0.246

£/. = (9,464X10-i«)(47.1633)(2,700)2 {jWo) (sUl)' d -0136) =3,584 kilobars

YouTui's modulus.Ei, =9.464X10-i»MF2re (^)'

V. rv , „,,o„ ri+''0-26)(0.246)+(3.22)(0.246)2(0.024036)T , where r, = 1.0ll82 [ 1+ (0.1328) (0.024036) J^^-O^^^

£/,= (9.464X10-'») (47.1633) (5,302)2 (^~^^ (t^^)' CI -"511) =3,593 kilobars

Poisson's ratio, ''/»-=f^-l=^^^)-l=0.238

B,ak modulus, g/^=3(iS;,j °

3[i_yo.mr ^''^''' "^""^^^^

cin rnGtsrs dyGGS The factors 10-2, 10-5, and 10-' are necessary for the conversion of the units given, such as — to for "Kc and „ to kilobars for elastic moduli.

sec sec om2

19
Table 5. Summary of X'-ray diffraction and hulk density data

Material

AI2O3

Ruby AI2O3

MgO

MuUite:

3Al203-2Si02

Mumte+Zr02

Spinel: MgO-AkOs

Th02'>

UO2

Stab. Zr02

AbOs+Cr

TiC+Ni

B4C

B4C+TiB2

SiC

SiC+BjC

ZrC

ZrB2

MoSi2

NiAl

Code

X-ray examiaation

Phases present

1 Single phase_

2 Single phase_

22

Single phase solid solution,.

Single phase solid solution.

MgO

MuUite plus at least 10% AI2O3-,

Single phase_

Single phase. MuUite plus about 20% monocllnic

Zr02, no zircon.

Spinel plus small excess MgO.

Spinel plus smaU excess MgO.

Single phase solid solution.

Single phase solid solution,. UO2 --

Single phase solid solution Solid solution plus small amount

monocllnic Zr02. Cr+faint peak; poor pattern because Cr smear. Cr+AbOs (see Code 28)..., TiC+(Ni).

TiC+Ni,,.

TiC+Ni,..

TiC+Ni...

B4C+Cg._,

BiC+TiB2,

Mixture of cubic and several hexag

onal poly types.

Same as Code 35 plus BiC

ZrC plus faint Cg peak.,, ZrBz and few unknown peaks. ZrB2 and few unknown peaks,

MoSi2

NiAl and few unknown peaks..

Lattice constants Structure

A

a = 4.7589 0 = 12.993 a = 4.7596 c= 12,993

a=4.760i

C = 12.993 a = 4.7588 C = 13.003

a=4.2125

a=8.085o

a=5.5968

a=5.597

a=5.471

a =5. 1195 a=5.n73

Cr, a=2.88+

Cr, a=2.936 TiC, a =4.3254 TIC, a=4.330i TiC, a=4.3328 TiC, a=4.331,

B4C

TiB2

fa=5.61

\c = 12.07 |a=3.028

lc=3.228

a=4.6865

a=3.166(i c=3.5365

a=3.20

c = 7.85

a=4.0824

Hex.

Hex.

Hex.

Hex.

Cubic

Ortho.+

Hex.

Ortho. Ortho. Ortho.+ Mon.

Cubic

Cubic

Cubic Cubic

Cubic Cubic

Cubic

Cubic

Cubic Cubic

Cubic

Hex.

Hex.

Cubic

Hex.

Tetragonal

Cubic

Theoretical density

3. 986

3. 985

3. 991

4. 004

3. 580

3. 576

9. 821

10. 949

5. 754

5. 762

Bulk density

Group No. spec. Av,

All

AU

b 5,430

b 5. 800

b 6, 174

b 6. 367

6, 661

6, 102

6,29

8. 382

AU

III

III

AU

III

III

III

IIIAU

AU

AU

III

3.942

3. 714 3.684

3. 728

3, 661

3. 502

2, 963

2. 771

2, 779

3, 510

2, 451

2, 522

9, 722

9, 664

9, 702

10. 37

5, 634

4, 966

4, 971

5. 958

5, 944

6. 053

5,341

5, 343

5, 654

5, 541

5, 862

5, 821

5. 723 5,882

2.506

2. 815

2. 576 2,596

3, 103

3, 128

3,082

6.118

5. 585

4. 657

4. 524

5,987

5, 763

5. 656

1 Values based upon the calculated bulk density and the theoretical density calculated from the NBS lattice constant determination,

b Values based upon the assumption that no reaction occurs between the two phases present and, therefore, that they are "mechanical" mixtures.

« These high density materials contain wt % CaO.

20
Table 6. Summary of the dynamic elastic constants and other -physical constants'^

Material Code Fabrication t Bulk density Speed of sound Young's modulus Shear modulus Poisson's

ratio Bulk modulus

HP

g/cm^ lo/ffi m/sec ft/sec Kilobars ' psi Kilobars psi Kilobars psi AI2O3 1 3.942 246.

(••lO, 020) (32, 870) (3, 958) (57.41X10') 1, 565 22. 70X10* (0. 254) (2, 645) (38 36X10')

27 CP 3. 904 243.7 (9, 540) (31,300) (3, 555) (51 56) 1,453 21. 07 (. 221) (2,' 129) (30.88) 26 CP 3. 902 243. 6

/A nriA\ (9, 900) (32, 480) (3, 824) (55. 46) 1, 548 22. 45 (. 236) (2, 415) (35. 03) 4 CP 3. 824 238.7 9. 680 31, 760 3,583 51.97 1,438 20 86 .246 2 349 34 07

3 CP 3. 825 238.8 9, 675 31, 740 3, 580 51. 92 1,445 20.96 . ZOif 2,289 33. 20 2 CP 3. 714 231. 9 9, 361 30, 710 3, 255 47. 21 1, 321 19. 16 .232 2,018 29. 27

14 CP 3. 470 216. 6 8, 676 28, 460 2, 612 37! 88 1, 067 15. 48 .224 1, 579 22. 90

15 CP 3. 335 208. 2 8, 340 27, 360 2, 317 33! 61 977 14. 17 187 1, 235 17. 91

5 CP 2. 850 177.9 6,236 20, 460 1,109 16. 08 479 6. 95 !l70 533 7. 73 Ruby AI2O3 6 CP 3. 728 232. 7 (9, 570) (31, 400) (3, 412) (49. 49) 1, 368 19. 84 (0. 247) (2, 251) (32. 65) 7 CP 3. 661 228. 6 (9, 470) (31, 070) (S! 284) (47.' 63) 1,285 18. 64 (. 258) (2, 234) (32. 40) MgO 24 CP 3. 506 218.9 (9, 170) (30, 090) (2, 947) (42. 74) 1,243 18.03 (0. 186) (1, 564) (22. 68) 25 CP 3.483 217.4 (9, 080) (29, 790) (2, 873) (41. 67) 1, 242 18 01 {. 157) (1, 401) (20 32) 23 CP 3. 479 217.2 (9, 090) (29, 820) (2, 872) (41 65) 1,207 17.51 (. 191) (1, 564) (22. 68) 9 CP 2. 648 165.

5, 732 18, 810 870 12! 62 374 5. 42 430 6. 24 MuUite: 16 HP 2.963 185.0 (7, 840) (25, 720) (1, 819) (26. 38) 704 10.21 (0 293 (1, 501) (21. 77) SAhOs-aSiOj 18 CP 2. 779 173. 5 7, 176 23, 540 l!431 20. 75 578 8. 38 .238 910 13. 20

17 CP 2. 771 173.0 7, 144 23,440 1, 415 20.52 573 8. 31 .233 883 12. 81 Mullite + Zr02 22 CP 2. 768 172. 8 6, 767 22, 200 1,268 18. 39 524 7. 60 0. 211 732 10. 62

Spinel- 20 HP 3. 510 219.1 (8, 670) (28. 440) (2, 636) (38. 23) 1,019 14. 78 (2, 173) (31. 52) Mgb-AIaOa 21 CP 2. 451 153.

5, 219 17, 120 ' 665 9. 64 271 3. 93 .228 408 5. 92

TI1O2

10 CP 9. 722 606.9 4, 972 16. 310 2,404 34. 87 942 13 66 0 275 1, 785 25 89

51 CP 9.702 605.7 4, 957 16, 260 2 384 34. 58 930 13. 49 ^282 1,819 26. 38 TTOi 19 CP 10. 37 647.

4, 314 14, 150 1, 929 27. 98 741 10. 75 0. 302 1,620 23. 50 19a CP 10.19 636.1 4, 230 13, 880 1, 823 26. 44 706 10. 25 291 1,457 21. 13

Stabilized 11 HP 5. 634 351. 7 (4, 940) (16, 210) (1, 376) (19. 96) 510 7. 40 (0. 337) ' (810) (11.75) ZtOi 13 CP 5. 149 321.

5, 216 17, 110 1,' 401 20. 32 585 8. 48 .255 955 13. 85

12 CP 4. 971 310. 3 5, 481 17, 980 l!493 21! 65 584 8. 47 279 1, 125 16. 32 Al203+Cr 29 Cast 6. 053 377.9 6, 667 21, 870 2,690 39. 02 1,074 15.58 0. 253 1, 813 26.30

30 Cast 5. 958 371.9 6,787 22, 270 2, 585 37. 49 1, 032 14. 97 . 252 1,732 25. 12

28 Cast 5.691 355.3 6, 870 22, 540 2,686 38. 96 1,114 16. 16 . 205 1, 512 21.93 TiC+NI 31 CP 5.343 333.6 8, 549 28, 050 3, 905 56. 64 1,631 23. 66 0. 197 2,150 31. 18 32 CP 5. 654 353.

8, 467 27, 780 4, 053 58. 78 1, 681 24. 38 . 206 2, 295 33. 29 33 CP 5.862 366.0 8, 023 26, 320 3. 773 54. 72 1, 560 22. 63 !210 2, 168 31. 44 34 CP 5. 882 367.2 8, 056 26, 430 3, 817 55.36 1,586 23.00 . 204 2, 147 31. 14

44 HP 2. 058 128.5 (14, 700) (48, 230) (4,467) (64. 79) ' (1, 850) 26.83 ' (0. 207) ' (2, 542) (36. 87) B4C+TiB2 43 HP 2. 816 175.8 (12, 600) (41, 340) (4, 485) (65. 05) ' (1, 860) 26.98 ' (0. 206) ' (2, 539) (36. 82) SiC 45 CP 3. 128 195.3 (11, 300) (37, 070) (4, 013) (58. 20) 1, 683 24. 41 (0. 192) (966) (14.01) 35 CP 2.596 162.1 8, 744 28, 690 1,985 28. 79 836 12. 12 . 187 1,057 15. 33 SlC+BiC 37 HP 3. 082 192.4 (11,600) (38, 060) (4, 151) (60. 21^ f (1, 699) 24.64 f (0. 221) f (2,478) (35. 94) ZrC 38 HP 6 118 381 9 {7 MiX) \^Of 'iOKJJ (3, 117) (45. 21) 1 240 17 98 (0. 257) (2 142) 31. 07 ZrB2 41 HP 5.585 348.7 (8, 880) (29, 130) (4, 399) (63. 80) 1. 922 27. 88 (0. 144) (2, 077) (30. 12) 42 CP 4. 557 284.5 (7, 340) (24, 080) (2, 455) (35. 61) 1,085 15.74 (. 131) (1, 110) (16. 10) MoSi2 39 HP 5. 966 372.4 (7, 980) (26, 180) (3, 795) (55.04) 1, 629 23.63 (0. 165) (1,887) (27. 37) XiAl 40

1 CP 5.763 359.8 (5, 620) (18, 440) (1, 817)1 (26. 35) 723 10. 49 (0. 261) (1,320) (19. 14)

« When two groups of specimens were available, the average values of the more dense group are given. When three or more groups were available, as with

the hot-pressed specimens, the average values of all of the specimens are given.

*> The fabrication code used is: HP=hot-pressed, CP = cold-pressed and sintered, and Cast =slip-cast and sintered.

' 1 kilobar = 10» d>Tics/cmz=14,503.8 lb./in.2 The accuracy of values in parenthesis is less than that of the other values.

' Contains \i percent CaO.

' These values are not considered reliable because of an assumption that was made during the calculation.

21
Table 7. Data

Source Statistical parameters

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average

No. of speci- mens

20

Bulk density

3.974±0.005 g/cm'

(248.1±0.3 Ib/fts) 0.1%

3.983±0.005 g/cm3

(248.7±0.3 lb/ft3) 0.1%

3.980±0.004 g/cm3

(248.5±0.2 lb/ft3) 0.0%

3.907±0.063 g/em3

(243.9±3.9 Ib/fts) 1.0%

3.876±0.044 g/cms

(241.6±2.71b/tt3) 0.7%

3.962d=0.104 g/cm3

(247.3±6.5 lb/ft3) 0.3%

3.942±0.021 g/cm3

(246.1±1.3 lb/ft3) 1.2%

3.904±0.003 g/cm3

(243.7±0.2 lb/ft3) 0.1%

3.902±0.016 g/cm3

(243.6±1.0 lb/ft3) 0.5%

3.902±0.017 g/cm3

(243.6±1.1 lb/ft3) 0.3%

3.824±0.005 g/om3

(238.7±0.3 lb/tt3) 0.2%

3.822±0.005 g/cm3

(238.6±0.3 lb/ft3) 0.2%

3.825±0.006 g/cm3

(238.8±0.4 lb/ft3) 0.1%

3.714±0.005 g/cm3

(231.9±0.3 lb/ft3) 0.2%

3.584±0.014 g/cm3

(223.7±0.9 lb/ft3) 0.6%

3.470±0.002 g/cm3

(216.6±0.1 lb/ft3) 0.1%

3.332±0.017 g/cm3

(208.0±1.1 lb/ft3) 0.5%

2.850±0.005 g/cm3

(177.9±0.3 lb/ft3) 0.3%

Speed of sound

9680±17.0 m/seo

{31.76±0.06X103 ft/sec) 0.2%

9677±9.0 m/sec

(31.7fi±0.03X103 ft/sec) 0.1%

9675±26.0 m/sec

(31.74±0.09X103 ft/sec) 0.2%

9361±18.0 m/sec

(30.71±0.06X103 ft/sec) 0.3%

8995±38.0 m/sec

(29.51±0.12X103 ft/sec) 0.6%

8676±8 m/sec

(28.46±0.03X103 ft/sec) 0.1%

8349±93 m/sec

(27.39±0.31X103 ft/sec) 1.2%

6236 ±69 m/sec

(20.46 ±0.23X103 ft/sec) 1.7%

Young's modulus

El

3583±18.0 liilobars (51.97±0.26X106 psi) 0.7%

3579±11.0 kilobars (51.91±0.16X10» psi) 0.4%

3580±25.0 kilobars (51.92±0.36X10« psi) 0.6%

3255±16.0 kilobars (47.21±0.23X106 psi) 0.7%

2899±34.0 kilobars (42.05±0.49X10» psi) 1.7% 2612±6 kilobars (37.88±0.09X108 psi) 0.4%

2316±63 kilobars (33.59±0.91X10« psi) 2.9%

1109±25 kilobars (16.08±0.36X10« psi) 3.3%

3997±42 kilobars (57.97±0.61X106 psi) 0.7%

4047±72 kilobars (58.70±1.04X106 psi) 1.1% 4020±24 kilobars (58.31±0.35X10» psi) 0.1%

3916±104 kilobars (56.80±1.51X10« psi) 1.7%

3803±132 kilobars (55.16±1.91X10« psi) 2.2%

4034±75 kilobars (58.51±1.09X10» psi) 0.2%

3958±48 kilobars 57.41±0.70X106 psi) 2.6%

3555±151 kilobars (51.56±2.19X106 psi) 4.6%

3824±44 kilobars (55.46±0.64X109 psi) 1.4%

3784±42 kilobars (54.88±0.61X10« psi) 0.7%

3561±20 kilobars (51.65±0.29X10« psi) 0.8%

3554±13 kilobars (51.55±0.19X106 psi) 0.5%

3576±24 kilobars (51.87±0.35X106 psi) 0.5%

3260±22 kilobars (47.28±0.32X10« psi) 1.0%

2926±29 kilobars (42.44±0.42X10« psi) 1.4% 2613±9 kilobars (37.90±0.13X10» psi) 0.6%

2326±67 kilobars

(33.74 ±0.97X109 psi) 3.1%

1119 ±20 kilobars

(16.23 ±0.29X109 psi) 2.7% The torsional frequency of only one or two specimens could be measured. Based on less than 20 specimens. Table 7a. Statistical data for the F and t values for

Critical Code Compared groups value Bulk Speed of Young's modulus

density sound

El E,„

26 f'-test: I and II 14.6 2. 98 3. 94

(-test:I and II 2.23 0.03 1.29

4 F-test:

I and II 4. 03 1.16 3. 59 2. 96 2. 37

i-test:I and II 2. 10 0. 70 0. 39 0. 43 0. 60 2 F-test:

I and II 4. 03 = 8^07 4 50 5. 81 1.73

(-test:I and II 2. 10 20.5

" Underlined figures indicate compared groups. that a significant difference does exist between the

22
/or AI2O3

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

Ef. 0 Ml K, if/. 400±41 kilobars 1,585 kilobars = 0.258 " 2755 kilobars" (58.03±0.59X106 psi) 0.7%

(22.99X105 psi) a (3996 X10« psi)«

4,012±16 kilobars 1,591 kilobars » 0.264 » 2841 » kilobars (58.19±0.23X10» psi)

0.2<7c. (23.08X10* psi)

(41.21 aXlO' psi)

4,01 6±0 kilobars 1,595 kilobars " 0.261 » 2797 " kilobars (58.25±OX108 psi) 0.0%

(23.13X10' psi)«

--- - - (40.57 "XIO* psi)

3,918±113 kilobars 1,563±51 kilobars 0.253±0.011 2645±82 kilobars (56.83±1.64X106 psi) 1.0/0 (22.67±0.74X106 psi) ^1 /o 2.7%

(38. 36±1. 19X10' psi) 1.9%

3,846±90 kilobars 1,518±54 kUobars 0.253±0.003 2560±100 kilobars

(55.78±1.31X106 psi) 1.5%

(22.02±0.78X10« psi) 2 2% 0.7%

(37. 13zbl. 45X10' psi) 2.5%

4,038±34 kilobars 1,616±78 kilobars 0.248±0.037 2671±407 kilobars (58.57±0.49X109 psi) 0.1%

(23.44±1.13X108 psi) 0.5% 1.7%

(38. 74zb5.90X10' psi) 1.7%

3,961±37 kilobars 1,565±24 kUobarsi' 0.254 biO.OOS 2655 ±59 kilobarsb (57.45±0.54X10« psi) 2.0%

(22.70±0.35X106 psi)b 2.7% 2.3%

(38. 65±0. 86X10' psi) 3.8%

3,520±125 kilobars 1,453±69 kilobars 0.221±0.018 2129±226 kilobars (51.05±1.81X106psi) 3.8%

(21.07±1.00X10« psi)

41.U /o 7.9%

(30, 88±3. 28X10' psi) 10.1%

3,806±53 kilobars 1,548±11 kilobars 0.236±0.009 2415±108 kilobars

(5.5.20dz0.77X109 psi)

1 7^^ (22.45zb0.16X10e psi) 4.6%

(35.03±1.57X10« psi) 5.3%

3,772±39 kilobars 1,533±14 kilobars 0.234±0.003 2372±48 kilobars (54.71±0.57X10« psi) (22.23±0.20X109 psi) 0.6% 0.7%

(34.40±0.70X10« psi) 1.3%

3,572±15 kilobars (51.81±0.22X10« psi) 1,438±7 kilobars (20.86±0.10X109 psi) 0.246±0.001 0.5%

0.238±0.002 0.9%2349±17 kilobars (34.07±0.25X109 psi) 1.0%

2263±25 kilobars (32.82±0.36X10« psi) 1.5%

3,565±1 2 kilobars (51.71±0.17X10« psi) 0 5%

1,437±4 kilobars (20.84±0.06X10« psi) 0.245-±0.001 0.6%0.236±0.001

0.8%

2339±11 kilobars (33.92±0.16X109 psi) 0.7%

2246±18 kilobars (32.58±0.26X10» psi) 1.1%

3,554±23 kilobars (51.55±0.33X10« psi) 0

1,445±7 kilobars , (20.9e±0.10X109 psi)

u.t /o

0.239±0.002 0.7%

0.237±0.001 0.4%2287±30 kilobars (33.17±0.44X10« psi) 1.1%

2270±22 kilobars (32.92±0.32X10» psi) 0.8%

3,245±18 kilobars (47.06±0.26X10» psi) 0.8%

1,321±11 kilobars (19.16±0.16X10« psi)

1-^/0

0.232±0.005

2.9%

0.234±0.001 0.9%2018±31 kilobars (29.27±0.45X109 psi) 2.1%

2044±33 kilobars (29.65±0.48X10« psi) 2.2%

2,897±37 kilobars (42.02±0.54X109 psi) 1.8%

1,180±13 kilobars (17.11±0.19X10» psi) 1.5%

0.228±0.003 1.8%0.240±0.005

2.9%

1787±27 kilobars (25.92±0.39X109 psi) 2.1%

1881±32 kilobars (27.28±0.46X10« psi) 2.4%

2,601±5 kUobars

(37.72±0.07X108 psi) 1,067±3 kilobars (15.48±0.04X10» psi) 0.224±0.001 1.0%

0.225±0.002

1.4%

1579±7 kilobars (22.90±0.10X109 psi) 0.7%

1583±16 kilobars (22.96±0.23X10' psi) 1.6%

2,331 ±33 kUobars

(33.81±0.48X10« psi) 1-5%

975±21 kilobars (14.14±0.30X109 psi) 2.3%0.188±0.014 7.8%0.192±0.014 8.1%1217±84 kilobars (17.65±1.22X10« psi) 7.5%

1264±85 kilobars (18.33±1.23X10' psi) 7.3%

1,141±16 kilobars (I6.55±0.23X109 psi) 2.1%,479±7 kilobars (6.95±0.10X10« psi) 2.1%,

0.170±0.013

8.3%,

0.172±0.005 3.2%

533±45 kilobars (7.73±0.65X109 psi) 9.2%

574±19 kilobars (8.33±0.28X10« psi) 3,5%

analysis of values given in table 7 F and t values for—Continued

Young's modulus

Continued

E,.

0.89

1.62

0.84

4. 12

Shear modulus

2. 17

0. 87

2.20

0. 35

1.35

18.7

Poisson's ratio

1. 13

1.30

2.80

1.63

41.8

1.30

1.64

1. 15

1.73

Bulk modulus

Ki

2.26

1.13

1.37

12.8

Kiu,

18.2

2. 01

0.42

1.05

8. IC

23
Table 8. Data

Code

and

group

No. oi

speci- mens

Source Statistical parameters

6-A F Average 5 V

6-B Average 5 V

7-A F Average 5 V

7-B Average 5 V

Bulli density

2. 780±0. 083 g/cm3

(173. e±5. 21b/ft3) 2.4%

3. 728±0. 024 g/cms

(232. 7±1. 6 lb/ft3)

0. 5%

2. 682± 0. 013 g/cm3

(167. 4±0. 8 lb/ft3)

0. 4%

3. 661±0. 035 g/cm3

(228. 6±2. 2 lb/ft')

0. 8%

Speed of sound

Yoimg's modulus

El

1217±127 kilobars

(17. 65±1. 84X10« psi) 8.4%

3412±112 kilobars

(49. 49±1. 62X10' psi) 2.6%

1031±50 kilobars

(14. 95±0. 73X10» psi) 3.9%

3234±126 kilobars

(46. 91±1. 83X108 psi)

3. 2%

Table 9. Data

Code

and

group

24-1

24-n

25-1

25-n

23-A"

23-Bi>

9-1

9-II

Source Statistical parameters

Average V

Average V

Average V

Average

Average V

Average V

Average V

Average V

No. of

speci- mens

Bulk density

3.502=t0.012g/cm3

(218. 6±0. 7 lb/ft3) 0.3%

3. 506d=0. 006 g/cm3

(218. 9±0.41b/ft3) 0.1%

3. 120±0. 021 g/cm3

(194. 8±1.31b/ft3)

0. 7%

3. 483±0. 015 g/cm3

(217. 4±0.91b/ft3)

0. 6%

3. 463±0. 034 g/cm3

(216. 2±2. 1 lb/ft3)

0. 8%

3. 479±0. 010 g/cm3

(217. 2±0. 6 lb/ft3)

0. 2%

2. 644±0. 017 g/cm3

(165. 1±1. 1 lb/ft3)

0. 9%

2. 648±0. 012g/cm3

(165. 3dz0. 7 lb/ft3)

0. 7%

Speed of sound

5710±77 m/sec

(18. 73±0. 25X103 ft/sec) 1.9%

5732±40 m/sec

(18. 81d=0. 13X103 ft/sec) 1.0%

Young's modulus

El

8G2±28 kilobars

(12. 50±0. 41X10" psi)

4. 6%

870±15 kilobars

(12. 62i0. 22X106)

2. 5%

E,y,

2900±71 kilobars

(42. 06ztl. 03X10" psi) 2.3%

2947±22 kilobars

(42. 74±0. 32X106 psi) 0.6% 2U5±36 kilobars

(30. 68±0. 52X106 psi) 1.8%

2873±51 kilobars

(41. 67±0. 74X106 psi) 2.3%

2832±115 kilobars

(41. 07±1. 67X106 psi)

3. 3%

2872±20 kilobars

(41. 65±0. 29X106 psi)

0. 6%

847±26 kilobars

(12. 3±0. 4X106 psi) 4.3%

851±15 kilobars

(12. 3±0. 2X106 psi)

2. 5%

o Theseltwo groups were made using difierent starting'materials. Table 9a. Statistical data for the

Code

24

25

Compared groups

F-Ust:

I and II

i-test:I and II.

F-test:

I and li- nest:I and II.

J'-test: I and II.

<-test:I and II..

Critical value

9. 36

2. 23

2. 18

4.03

2. 10

F and t values for

Bulk

density

5. 35

0. 88

1. 19

'32.8

1.92

1. 29

Speed of sound

3.69

1.70

Young's modulus

El

3. 36

0. 98

"14. 24

1. 79

3. 04

23.2

2. 87

0.83

» Underlined figures indicate that a significant difference does exist between the compared groups. 24
for ruby AI2O3

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

G Ml M/u. Ki

12tl±150 kilobars

(18. 00±2. 17X106 psi) 9.8%

3339±106 kilobars

(48. 43±1. 54X106 psi) 2.6%

1060±82 kilobars

(15. 37±1. 19X10» psi)

0. 0 , 0 3111±126 kilobars

(45. 12dzl. 83X108 psi) 3.3%

480±55 kilobars

(6. 96±0. 80X106 psi) 9.3%

1368±44 kUobars

(19. 84±0. 64X106 psi)

2. 6%

411±19 kUobars

(5. 96±0. 28X105 psi)

0. 0/0 1285±50 kilobars

(18. 64=b0. 73X108 psi) 3.2%

0. 269±0. 041 12.4%

0. 247±0. 009

3. 0%

0.254±0. 012

3. 9%

0. 258±0. 015

4. 8%

865±74 kilobars

(12. 65±1. 07X108 psi) 6.9%

2251±120 kilobars

(32. 65±1. 74X10« psi) 4.3%

700±54 kilobars

(10. 15±0. 78X106 psi) 6.2%

2234±167 kilobars

(32. 40±2. 42X108 psi)

6. 0%

for MgO

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

E„ K,

2888zt48 kUobars

(41.89±0.70X10»psi) 1.6%

2937±31 kUobars

(42.60±0. 45X106 psi)

0. 9%

2137±30 kUobars

(30. 99±0. 44X108 psi) 1.5%

2935±40 kUobars

(42. 57±0. 58X106 psi) 1.8%

2870=fc53 kilobars (41.63±0. 77X108 psi) 1.5%

2904±31 kUobars

(42.12±0. 45X108 psi) 0.9%

845dh28 kUobars

(12. 3±0. 4X106 psi) 4.6%

854±15 kUobars

(12. 4±0. 2X106 psi) 2.4%

1227zt34 kUobars

(17. 80±0. 49X106 psi) 2.6%

1243±14 kUobars

(18. 03±0. 20X108 psi) 0.9%

893±14 kUobars

(13. 0±0. 2X10 8psi) 1.7%

1242±22 kUobars

(18. 01±0. 32X106 psi) 2.3%

]204±30 kUobars

(17. 40±0. 44X106 psi)

2. 0%

1207±48 kUobars

(17. 51±0. 70X106 psi)

3. 2%

371±12 kUobars

(5.38±0. 17X106 psi)

4. 4%

374±7 kUobars

(5. 42±0. 10X108 psi)

2. 6%

0. 161±0. 004 3.5%

0. 163±0. 002

2. 0%

0. 182±0. 012 6.4%

0. 186±0. 007 3.1%

0. 184±0. 016 9.1%

0.157±0. 017

14. 1%

0. 177±0. 078 35+%

0. 191±0.043 18+%

0. 140±0. 006

5. 7%

0. 137±0. 004

3. 6%

424±16 kUobars

(6. 15±0. 23X106;psi) 5.4%

430±7 kilobars

(6. 24±0. 10X106 psi) 2.1%

1522±64 kilobars

(22. 07±0. 93X106 psi)

4. 0%

1664it34 kilobars

(22. 68±0. 49X108 psi)

I. 8%

1117±67 kUobars

(16. 20±0. 97X106 psi) 6.3%

1401 ±82 kUobars

(20. 32±1. 19X108 psi) 7.6%

1537±683 kilobars

(22. 29±8. 46X106 psi) 30+%

1564±218 kUobars

(22. 68±3. 16X106 psi)

II. 2%

393±14 kUobars

(5. 70±0. 20X108 psi)

4. 8%

390±8 kUobars

(5. 66±0. 12X106 psi) 3.0%

analysis of valves given in table 9

F and t values for—Continued

Young's modulusContinued

Shear modulus Poisson's ratio Bulk modulus

Et. G MI Ki

Z. 36

2. 51

2.83

31.1

3. 48

2.00

8.63

1.25

3. 56

25.6

2. 88

1.40

4. 16

3. 48

1.74

2. 34

2. 56

3.76

4. 96

1.66

2. 27

5.31

3. 17

1.13

2.96

2. 04

6.29

25
Table 10. Data for

Code

and Source Statistical No. of speci- Bulk density Speed of sound Young's modulus

group parameters mens

E,

16-1 H Average 4 2.737±0.032 g/cmS

(170.9±2.0 lb/ft3) 0.7%

(21.90±0.75X10« psi) V 2.2%

16-11 Average 2 2.966±0.040 g/cm3

(185.2±2.5 lb/ft3) 0.2%

1,942±115 kilobars (28.17±1.67X10« psi) V 0.7%

16-III Average V4 3.039±0.033 g/cm3

(189.7±2.1 lb/tt3) 0.7%

l,908d=78 kilobars (27.67±1.13X10« psi) 2.6% 16-IV Average 5 3.041±0.063 g/cm3

(189.8±3.9 lb/ft3) 1.7%

1,911±97 kilobars (27.72±1.41X108 psi) V 4.1% 16-V Average 5 3.003±0.026 g/cm3

(187.5±1.6 lb/ft3) 0.7%

1,856±35 kilobars (26.92±0.51X10« psi) V 1.5%

16-All Average V

20 2.963±0.057 g/cm3

(185.0±3.6 lb/tt3) 4.1%

1,819±79 kilobars (26.38±1.15X10« psi) 9.2%

18 F Average V

10 2.779±0.006 g/cm3

(173.5±0.4 lb/tt3) 0.3%

7,176±11 m/sec

(23.54±0.04X 103 ft/sec) 0.2%

l,431zt7 kilobars (20.75±0.10X10« psi) 0,6%1,428±9 kilobars (20.71±0.13X10« psi) 0.9%

17 = F Average V

8 2.771±0.008 g/om3

(173.0±0.5 lb/ft3) 0.4%

7,144±39 m/seo

(23.44d=0.13X103 ft/sec) 0.5%

1,415±21 kilobars (20.52±0.30X109 psi) 1.4%1,420±21 kilobars (20.60±0.30X106 psi) 1.8%

> These two materials, after having been coded and examined, were found to be the same except that Code 18 was heat-treated for a longer time.

Table 10a. Statistical data for

F and t values for

Code Compared groups

Critical value Bulk

density Speed of sound

Young's modulus

El E,„

" 17-18 J'-test: 17 and 18 "4.20-4.48* 1.43 a b 5. 59* 5. 00* 3.66

Mest:

17 and 18 2. 12 2. 01 0.09

» F and ( values marked with an asterisk indicate comparison with the critical value

similarly marked.

>> Underlined figures indicate that a significant difference does exist between the compared groups.

Table 11. Data

Code

and

group

Source Statistical parameters

No. of speci- mens

Bulk density Speed of sound Young's modulus

El

22 F Average V

10 2.768zt0.010 g/cms

(172.8±0.6 lb/ft3) 0.5%

6,767±11 m/sec

(22.20±0.04X103 ft/sec) 0.2%

1,268±9 kilobars (18.39±0.13X10« psi) 0.9%

1 ,265±9 kilobars

(I8.35±0.13X10i! psi) 1.0%

26
MuUite: 3 A1203-2 SiO.

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

Q ft Ki

l,5o3dz68 kilobars 2.8%

580±39 kilobars 0.301±0.049 1,244±258 kilobars (18.04±3.74X108 psi) 4.2% 10% 13.%

1,992±50 kilobars ^^.oy±u. ^op\iu" poly 0.3%731d=33 kilobars 0.327±0.018 1,920±76 kilobars

(27.85±1. 10X10* psi) 0.5% 0.6% 0.4%

1,896±66 kilobars

2.2%

739±32 kUobars 0.291±0.004 1,551 ±68 kilobars (22.50±0.99X10« psi) 2.7% 0.8% 2.7%

1.923±103 kilobars 740=b41 kilobars 0.291±0.009 1,525±86 kilobars (22.12±1.25X10« psi) 4.3% 4.5%

^^lU. /OitU.Oy ^xU" pal/ 4.4% 2.3%

1,869±20 kilobars (27.11±0.29X10« psi) 0.9%

730±71 kilobars 0.277±0.092 1,474±424 kilobars

(21.38±6.15X10'' psi) 23.%(10.59±1.03X10« psi) 7.8% 27.%

1,837±73 kilobars

(26.&4d=1.06X108 psi) 8.5%

704±34 kilobars 0.293±0.018 1,501±37 kilobars (21.77±0.54X106 psi) 5.2%

(10.21=h0.49X109 psi) 13.%

1.425±7 kilobars (20.67±0.10X10« psi) 0.6%

578±3 kilobars (8.38±0.04X10« psi) 0.7%0.238±0.002 1.3%0.235±0.003 1.6%

910±5 kilobars (13.2±0.1X10« psi) 0.7%

899±5 kilobars (13.0±0.1X10« psi) 0.7%

1,409±14 kilobars (20.44±0.20X10« psi) 1.2%

573±7 kilobars (8.31±0.10X10» psi) 1.5%

0.233±0.005 2.2%0.240±0.009 4.5%883±15 kilobars (12.8±0.2X108 psi) 2.0%

911±39 kilobars (13.2±0.6X106 psi) 5.2%

the analysis of values given in table 10

F and ( values for—Continued

Young's modulus

Continued

Shear modulus Poisson's ratio Bulk modulus

Ef. G A"! Ki

3.38

2.53

3.80

1. 87

2. 81'

22.9

8. 29* 6.86* 51.2

jor mullUe plus Zr02

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

Ef. a fit Ki

1,273±9 kUobars

(18.46±0.13X10« psi) 1.0%

524±4 kilobars (7.60±0.06X10« psi) 0.9%

0.211±0.003 1.9%

0.208±0.001 0.8%

732±8 kilobars (10.62±0.12X10« pFi) 1.5%

724=tll kilobars (10.50±0.16X106 psi) 2.1%

27
Table 12. Data for

Source Statistical parameters

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

No. of speci- mens

Bulk density

3.487±0.084 g/cms

(217.7±5.2 Ib/ft3) 0.3%

3.502±0.043 g/cm3

(218.6±2.3 lb/ft3) 1.0%

3.539±0.019 g/em3

(220.9±1.2 lb/ft3) 0.3%

3.533±0.022 g/cm3

(220.6±1.4 lb/ft3) 0.5%

3.473±0.044 g/cm3

(216.8±2.7 lb/ft3) 0.8%

3.510±0.016 g/cm3

(219.1±1.0 lb/ft3) 1.0%

2.451±0.025 g/cm3

(163.0±1.6Ib/ft3) 1.2%

2.522±0.010 g/cm3

(157.4±0.6 lb/ft3) 0.6%

Speed of sound

5,219±155 m/sec a7.12±0.51X103 ft/sec) 3.6%

5,647±66 m/sec

(18.53±0.22X103 ft/sec) 1.6%

Young's modulus

665±39 kilobars (9.65±0.57X106 psi) 7.1% 805±22 kilobars

(11.68=t0.32X10« psi) 3.7%

2,573±821 kilobars (37.32±11.91 X10« psi) 3.6%

2,625±62 kilobars (38.07±0.90X10» psi) 1.9%

2,685±116 kilobars (38.94±1.68X106 psi) 2.7%

2,674±45 kilobars (38.78±0.65X106 psi) 1.4%

2,584±65 kilobars (37.48±0.94X106 psi) 1.6%

2,636±31 kilobars (38.23±0.45X10« psi) 2.6%

652±47 kilobars (9.46±0.68X10« psi) 8.6% 785±27 kilobars (11.39±0.39X106 psi) 4.8%

Table 12a. Statistical data for the

F and t values for—

Code Compared groups

Critical value Bulk

density Speed of SOUBd

Young's modulus

El

21 F-test:

I and II 4.20 4. 13 4. 10 2. 46 2. 22

t-test:I and II 2. 12 » 2. 85 6. 42 7.64 6. 06

• Underlined figures Indicate that a significant difference does exist betvifeen the compared groups.

28
Spinel: MgO-AlaOs

Young's modulus—Con- Shear modulus Poisson's ratio Bulk modulus

2, 547^=713 kllobars (36.94±10.34X106 psi) 3.1%

2,611±59 kilobars (37.87±0.86X10« psi) 1.8%

2,659±131 kilobars

(.S8.o7±1.90X106 psi) 3.1%

2,6o7±43 kilobars (38.54±0.62X10« psi) 1.3%

2.619±54 kilobars (37.99±0.78X105 psi) 1.3%

2,628±28 kUobars

(38.12±0.41X109 psi) 2.3%

655±48 kilobars 9.50±0.70X10» psi) 8.8%

79l±20 kUobars

(11.47±0.29X10« psi) 3.6%

1,017±71 kilobars (14.75±1.03X106 psi) 0.8%

1,017±76 kilobars

(14.75d=1.10X10« psi) 6.0%

1.041±12 kOobars

(15.10±0.17X106 psi) 0.7%

l,028±lo kilobars (14.91±0.22X108 psi) 1.2%

990=t26 kilobars (14.36±0.38X109 psi) 1.6%

1,019±16 kilobars (14.78±0.23X10« psi) 3.4%

271±20 kilobars (3.93±0.29X108 psi)

329±8 kilobars (4.77±0.12X109 psi) 3.4%

0.228±0.017 9.0%

0.221±0.008 4.8%

0.265

21. %

0.293±0.066 18.%

0.290±0.054 12.%

0.300±0.008 2.1%

0.305±0.008

I.6%

0.294±0.015

II. %

0.202±0.007 4.2%

0.191±0.030

22. %

408±13 kilobars (5.92±0.19X10« psi) 3.7%

482±23 kilobars (6.99±0.33X108 psi) 6.5%

1,916±600 kilobars (27.79±8.70X10» psi) 35.%

2,191±427 kilobars (31.78±6.19X109 psi) 16.%

2,158±568 kilobars (31.30±8.24X10» psi) 16.%

2,249±113 kilobars (32.62±1.64X10« psi) 4.0%

2,198±56 kilobars (31.88±0.81X10« psi) 1.6%

2,173±132 kilobars (3!.52±1.91X106 psi) 13.%

365±33 kilobars

(5.29±0.48X10ii psi) 11.% 428±42 kilobars (6.21±0.61X108 psi) 14.%

analysis of values given in table 12

F and i values for—Continued

Young's modulus

Continued

Shear modulus Poisson's ratio Bulk modulus

E,. G Ml Ki Kf„

4.23 4. 59 3. 72 24.7 4. 45 3. 94

6. 59 0. 93 2.77

29
Table 13.

»

Code

and Source Statistical No. of speci- Bulli density Speed of sound

Young's modulus

group parameters mens

El

lO-I TT Average V

9 9.722±0.034 gm/cm3

(606.9±2.1 gm/cm3) 0.5%

4,972±9 m/sec

(16.31±0.03X103 ft/sec) 0.2%

2,404±13 kilobars (34.87±0.19X10» psi) 0.7%

2,434±23 kilobars (35.30±0.33%108 psi) 1.2%

10-11 Average V

8 9.664±0.012 gm/cm3

(603.3±0.7 gm/cm3) 0.2%

4,960±12 m/sec

(16.27±0.04X103 ft/sec) 0.3%

2,378±8 kilobars 2,406±18 kilobars

/OA fin 1 f\ ocv.'irtfi w^n:\ (o4.yo±o.2oxio° psi) 0.4% 0.9%

51 G Average V10 9.702±0.008 gm/cm3

(605.7db0.5 gm/em3)

0.1%

4,957±3 m/sec

(lfi.26±0.01X103 ft/sec) 0.1%

2,384±5 kilobars (34.68±0.07X109 psl) 0.3%

2,395±6 kilobars (34.74±0.09X108 psi) 0.3%

a These compositions contain H weight percent CaO as a densifying agent.

Table 13-a. Statistical data for the

if and t values for

Code Compared groups Critical value Bulk

density Speed of sound

Young's modulus

Bt Er^

10 i-'-test: I and II

<-test:I and II

a 4. 90-

4. 53*

2. 13

bp. 01 1.38*

0. 32

3. 14

0. 62

1.90

0. 37

" F and t values marked with an asterisk indicate comparison with the critical value similarly marked.

^ Underlined figures indicate that a significant difference does exist between the compared groups.

Table 14

Code No. of Young's modulus

and Source Statistical speci- Bulk density Speed of sound

group parameters mens

El

19 C Average 5 10.368±0.021 g/cm3 4,314±9 m/sec 1,929±10 kilobars 1,936±11 kilobars (647.3±1.3 lb/ft3) (14. 15±0.03X 103 ft/sec) (27.98±0.15X106 psi) (28.08±0.16X10» psi) V 0.2% 0.2% 0.4% 0.5%

19a G Average 1 10.188 g/cm3 4.230 m/sec 1,823 kilobars 1,737 kilobars

(636.0 lb/tt3) (13.88X103 ft/sec) (26.44X106 psi) (25.19X10S psi)

30
Data for ThOz

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

Ef. G lit

2,424±12 kOobars

(35.16zt0.17X109 psi) U.O/0

943±9 kilobars (13.68±0.13X109 psi) 1.2%

0.275±0.006 3.0%

0.291±0.003 1.4%

1,785±46 kilobars (25.89±0.67X108 psi) 3.4%

1,945±37 kilobars (2,821±0.54X106 psi) 2.5%

2,399±11 kilobars (34.79±0.16X10» psi) 0.5%

930±7 kilobars (13.49±0.10X109 psi) 0.9% 2.7% 3.6%

i,'yo±4o KUODars

(26.01±0.70X106 psi) 3.2%

1,948±94 kilobars (28.25±1.36X10» psi) 5.8%

2,384±3 kilobars (34.58±0.04X10« psi) 0.2%

930±3 kilobars (13.49±0.04X106 psi) 0.5%0.282±0.004 1.3%

0.288±0.004 2.0%

1,819±7 kilobars (26.38±0.10X106 psi) 0.5%

1,881 ±35 kilobars (27.28±0.51X109 psi) 2.6%

analysis of values given in table 13

F and t values for—Continued

Young's modulus

Continued

Shear modulus Poisson's ratio Bulk modulus

Ef. G Ki

1.47 1.95 1.23 5.43* 1.10 5.43*

0. 59 2.72 0.90 0.73 0. 27

Dala for UO2

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

E,. G Ml K,

1,930±15 kilobars (27.99±0.22X10« psi) 0.6%

1,842 kilobars

741± 4 kilobars (10.75±0.06X10« psi) 0.4%

706 kilobars

0.302±0.003 0.8%

0.291

0.306±0.003 0.7%

1.620±26 kilobars (23.50±0.38X108 psi) 1.3%

1,457 kilobars (21.13X109 psi)

1,662±30 kilobars (24.11±0.44X108 psi) 1.4%

(26.72X10« psi) (10.24X109 psi)

31
Table 15. Data

Source Statistical parameters

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

Average V

No. of speci- mens

Bulk density

5.634±0.026 g/cm3

(351.7±1.6 lb/ft') 0.4%

5.639±0.027 g/cms

(352.0±1.7 lb/ft3) 0.3%

5.654±0.045 g/cm^

(353.0±2.8 lb/ft3) 0.6%

S.603±0.024 g/cms

(349.8±1.5 lb/ft3) 0.3%

5.634±0.015 g/cm3

(351.7±0.9 lb/ft3) 0.5%

5.149±0.016 g/cm3

(321.4±1.0 Ib/ftS) 0.4%

5.1i52±0.013 g/cms

(322.3±0.8 lb/ft3) 0.4%

4.967±0.017 g/cra3 (SlO.lil.l lb/ft3) 0.5%

4.971±0.011 g/cm3

(310.3±0.7 lb/ft3) 0.3%

Speed of sound

6216±51 m/sec

(17.11±0.17X103 ft/sec) 1.4%

4950±184 m/sec

(16.24±0.60X103 ft/sec) 5.1% 6456±20 m/sec

(17.90±0.07X103 ft/sec) 0.5%

5481±10 m/sec

(17.98±0.03X103 ft/sec) 0.3%

Young's modulus

El

1401±23 kilobars (20.32±0.33X10e psi) 2.3%

1268d=93 kilobars (18.39±1.35X10« psi) 10.3% 1478±15 kilobars (21.44±0.22X10« psi) 1.4% 1493±8 kilobars (21.66±0.12X106 psi) 0.8%

1157±83 kilobars (16.78±2.65X10° psi) 5.8% 1072±44 kUobars

(16.55±0.64X108 psi) 2.6%

2051±81 kilobars (29.75±1.17X10« psi) 3.2%

1111±385 kUobars

(16.11±5.68X108 psi) 22%

1376±222 kilobars (19.96±3.22X10« psi) 32%

1391±26 kilobars (20.17±0.38X10« psi) 2.6%

1269±92 kilobars (18.41±1.33X106 psi) 10.1% 1483±15 kilobars (21.61±0.22X10» psi) 1.4%

1499±10 kilobars (21.74±0.15X10« psi) 1.0%

0 This composition contains about 6 wt % of CaO as the stabilizing agent.

' Because of the very high and diverse values calculated for Poisson's ratio, the calculated bulk modulus values have little significance.

Table 15a. Statistical data for the

F and t values for

Code Compared groups Critical Young's modulus

value Bulk Speed of density sound

El Ef^

13 F-test:

I and II 4.03 1.51 a 13.2 15.9 12.4

<-test:

I and II 2. 10 1.48

12 i?-test: I and II 4. 03 2. 58 3. 95 3. 15 2.04

<-test:I and II 2. 10 1. 56 2. 46 1.98 2. 02

» Underlined figures indicate that a significant difference does exist between the compared groups.

i

32.
jor "stabilized" Zr02''

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

Ef, G K,

1202±80 kilobars 455±39 kilobars 0.274±0.022 857±43 kUobars

(17.43±1.16X10» psi) 5.4%

(6.60±0.57X109 psi) 6.9% 6.4%

(12.43±0.62X108 psi) 4.0%

1122±58 kilobars 423±13 kilobars 0.268±0.02 772±93 kUobars

(16.27±0.84X109 psi) 3.2%

(6.14±0.19X10« psi) 2.0% 4.6%

(11.20±1.33Xpsi) 7.5% 2031±68 kilobars 725±48 kilobars 0.416±0.052 W

(29.46±0.99X10» psi) 2.7%

(10.52±0.70X10» psi) 5.3% 10.1% 1132±372 kilobars 398±70 kilobars 0.386±0.218 W

a6.42±5.40X10« psi) 21%

(5.77±1.02X109 psi) 11.0% 36%

1399±208 kilobars 510±71 kilobars 0.337±0.046» w (20.29±3.02X10« psi) 30%

(7.40±1.03X10« psi) 28% 27%

1394±22 kilobars (20.22±0.32X10« psi) 2.2%558±7 kUobars

(8.09±0.10X108 psi) 1.9%

0.255±0.006 3.3%0.246±0.008 4.6%

955±37 kilobars (13.85±0.54X10» psi) 5.3%906±59 kUobars

(13.14±0.86X106 psi) 9.1%

1259±94 kUobars

(18.26±1.36X10« psi) 10.5%

514±33 kUobars

(7.45±0.48X10« psi) 9.1%

0.232±0.012 7.0%

0.234±0.010 6.2%796±92 kilobars (11.54±1.33X106 psi) 16%802±87 kUobars

(11.63±1.26X10«psi) 15%

1479±12 kilobars (21.45±0.17X10» psi) 1.2%

575±6 kilobars (8.34±0.09X108 psi) 1.4%0.285±0.005 2.6%0.289±0.0a5 2.4%1144±26 kilobars (16.59±0.38X10«psi) 3.2%1168±12 kilobars (16.94±0.17X10» psi) 1.4% 1492±10 kilobars (21.64±0.15X10« psi) 0.9%

584±4 kilobars (8.47±0.06X109 psi) 1.0%

0.279±0.002 1.1%0.284±0.002 0.8%1125±11 kUobars

(16.32dz0.16X10» psi) 1.4%

1157±30 kUobars

(16.78±0.44X10« psi) 3.6%

analysis of values given in table 15

F and t values for—Continued

Young's modulus

Continued

Shear modulus Poisson's ratio Bulk modulus

Ef. G Ki

19.1 20.2 3. 83

3.90

5.31

1.64

2. 07

1.08

1.53

6. 41 2.19

2.24

1. 57 6. 67

1.88

2. 08

2.65

5.94

35
Table 16. Data

Code

and Source Statistical No. of speci- Bulli density Speed of sound

Young's modulus

group parameters mens

29 D Average 19 6.053±0.021 g/cm3

(377.9±1.3 lb/£t3) U./ /o

6667±22 m/sec

(21.87±0.07X103 ft/sec)

u.; /o

2690±25 kilobars {39.01±0.36X108 psi) i.yyo

2711±19 kilobars (39.32±0.28X10« psi) i-oyo

30-1 D Average 10 5.958±0.017 g/cm3

(371.9±1.1 Ib/£t3) 6587±18 m/see

(21.61±0.06X10' ft/sec) 2585±21 kilobars (37.49±0.30X108 psi)

1 1 or

2611±25 kilobars (37.87±0.36X109 psi) i.47o 30-11 Average

Y"

10 6.944±0.016 g/cm3

{371.1±0.9 lb/ft3) 0 dC7 U.1/0

6563±11 m/sec

(2l.53zb0.04X103 ft/sec) n 907

2560±15 kilobars (37.13±0.22X108 psi) n fi07 U.S70

2589±17 kilobars (37.55±0.25X10«psi)

n Q07

28-1 D Average V

10 5.691±0.006 g/cm'

(355.3±0.4 Ib/fts) 0.2%

6870±12 m/sec

(22.54±0.04X103 ft/sec) 0.2%

2686±12 kilobars (38.96±0.17X109psi) 0.6%

2713=t20 kilobars (39.35±0.29X108 psi) 1.0%

28-11 Average 10 6.564±0.041 g/cm3

(347.4±2.6 Ib/fts) 1.0%

6712±47 m/sec

{22.02±0.15X103 ft/sec) 1.0%

2507±53 kilobars 2543±56 kilobars V

(36.36±0.77X10« psi) 2.9%(36.88±0.81X106 psi) 3.1%

« Code 28 composition is slightly different than compositions of codes 29 and 30 specimens.

Table 16a. Statistical data for the

F and t values for

Code Compared groups

Critical value Bulk

density Speed of sound

Young's modulus

El Ely,

30 J'-test: I and II

^-test:I and II

4.03

2. 10

1.23

1.43

2. 56

2.59

1. 95

2. 25

1.70

1.80

28 i!'-test: I and II

<-test:land II

4. 03

2. 10

a 40. 8 14.9 18.3 7.67

"Underlined figures indicate that a significant difference does exist between the compared groups.

34
Jot AliOs-l-Cr^

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

Er.

- G III

2694±23 kilobars

(39 07-H) 33X10* psi) 1.8%

1071±S kilobars

(15 58±0 12X10* psi) 1.5%

0.253±0 2.3%003 0.262±0.001 0.9%1813±35 kilobars

(26.30 ±0.51X106 psi) 4.0%

1900±14 kilobars (27.o6±0.20X106 psi) 1.5%

2602±28 kilobars

(37 74±0 41X10* psi) 1.5%

1032±8 kilobars

(14 97±0 12X10* psi) 1.0%

0.252±0 1.5%

003 0.264±0.003 1.5%1732±22 kilobars (25.12±0.32X106 psi) 1.8%1845±29 kilobars (26.76±0.42X10« psi) 2.2%

2578±17 kilobars

(37 39-H) 25X10* psi) 0.9%

1023zfc6 kilobars

(14 84±0 09X10* psi) 0.8%

0.2o2±0 0.6%001 0.266±0.002 1.2%1724±9 kilobars (2o.00±0.13X106 psi) 0.8%1848±22 kilobars (26.80±0.32X109 psi) 1.7%

2682db20 kilobare

(38.90=t0.29X10« psi) 1.0%

1114d=6 kilobars (16.16±0.09X10* psi) u.oyo

0.205±0 1.0%001 0.217±0.004 2.2%lol2±8 kilobars (21.93±0.12X10« psi) 0.8%1601±30 kUobars

(23.22±0.44X10ii psi) 2.7% 2514±56 kilobars (36.46±0.81X108 psi) 3.2%

1042zfc27 Mlobars

(15.11±0.39X10* psi) 3.0%

0.203±0 0.8%001 0.221 ±0.004 2.6%

1434dz29 kilobars

(20.80=t0.42X106 psi) 2.8%

1517zt39 kilobars (22.00±0.o7X109 psi) 3.6%

analysis of values given in table 16

F and t values for—Continued

Young's modulus

Continued

Shear modulus Poisson's ratio Bulk modulus

Er. G PI Ki

1.75 1.90 5.74 1.62 5.48 1.77

1.94 2.27 0. 15 0.20

8.45 13.8 1.34 1.39 12.3 1.65

2. 16 1.33 3.83

35
Table 17. Data for TiC

Code

and

group

Source Statistical No. ofspeci- Bulk density Speed of sound

Young's modulus

parameters mens

El

Average V

10 5.341±0.012 g/cm3 0.3%8576±23 m/see 0.4%

3928±29 kilobars (56.97±0.42X106 psi) 1.0%

4035±30 kilobars (58.62±0.44X1C8 psi) 1.0% Average V

10 6.343±0.008 g/cm3

t.OOo. DztU.O lU/ll'^j 0.2%

8549±15 m/sec 0.3%3905±19 kilobars (66.64±0.28X106 psi) 0.7%

3996±16 kUobars

(57.96±0.23X10» psi) 0.6% Average V

10 5.654±0.003 g/cm3

^'2K'i n_i_n o iK/f+i\ 0.1%

8467±8 m/sec

i.iii./ozhu.uoXi'j'' It/sec^ 0.1%

4053±8 kilobars (58.78±0.12X108 psi) 0.3%

4086±9 kilobars

(59.26d=0.13X105 psi) 0.3% Average V

10 5.541±0.004 g/cm3

1,010. yztu.^ iuiii^) 0.1%

8249±9 m/sec 0.2%

3770±9 kilobars (64.68±0.13X10« psi) 0.3%

3866±15 kilobars (56.07±0.22X108 psi) 0.5% Average V

10 5.862±0.002 g/cm3 0.0%8023±6 m/sec

(.ii0.o/±U.U/XlU'* II/S6CJ 0.1%

3773±5 kilobars (64.72±0.07X106 psi) 0.2%

3808±7 kUobars

(56.23±0. 10X106 psi) 0.3% Average V

10 5.821±0.005 g/cm3

l,OOo.1itU.O iUIll") 0.1%

7998±9 m/sec 0.2%3749±9 kUobars

, (54.37±0.13X106 psi) 0.3%

3757±12 kilobars (54.49±0.17X106 psi) 0.6% Average V

10 5.723±0.003 g/cm3

(357.3±0.2 Ib/fts) 0.1%

8267±7 m/sec

(27.12±0.02X103 ft/sec) 0.1%

3911±7 kilobars (56.72±0.10X106 psi) 0.3%

3917±11 kilobars

(56.81db0.16X106 psi) 0.4% Average V

10 5.882±0.006 g/cm3

(367.2±0.4 lb/ft3) 0.1%

8056±5 m/sec

(26.43±0.02X 103 ft/sec) 0.1%

3817±6 kilobars (56.36±0.09X106 psi) 0.2%

3904±9 kilobars (56.62±0.13X10« psi) 0.3%

31-1

31-11

32-1

32-11

33-1

33-11

34-1

34-11

» Code 31 contains about 10 wt % Ni. Code 32 contains about 20 wt % Ni. Code 33 contains about 30 wt % Ni. Code 34 contains about 30 wt % Ni

(Modified). Table 17a. Statistical data for the

F and i values for

Code Compared groups Critical Young's modulus

value Bulk Speed of density sound

El

31 F-test: land II 4. 03 1.94 2.25 2. 35 3.48

<-test:I and II 2. 10 0.30 2. 22 1.53 2.60

32 J'-test: I and II 4. 03 1.71 1.15 1. 22 2. 53

<-test:I and II 2. 10 »47. 2 41.2 52. 4 28.

1

33 i;'-test: I and II 4. 03 6.11 3. 72 2.78 3. 29

i-test:I and II 2. 10 49.7 5. 47 8.31

34 J'-test: I and II 4. 03 5. 14 2.20 1.50 1.58

(-test:I and II 2. 10 56.5 24.0 2.20

Code

and

group

Source Statistical parameters

No. of

speci- mens

Bulk density Speed of soimd

Young's modulus

El Ef„

44-1

44-11

H Average V

Average V

10

10

2.506±0.002 g/cms

(156.4±0.1 lb/ft3) 0.1%

2.505±0.002g/cm3

(156.4±0.1 lb/ft3) 0.1%

4467±24 kilobars (64.79±0.35X10» psi) 0.7%

4481±19 kilobars (64.99±0.28X109 psi) 0.6%

a Underlined figures Indicate that a significant difference does exist between the compared groups. Table 18. Data

» These values are not considered reliable because of an assumption that was made during the calculation. ''M=0.2O74 assumed value for one specimen see sec. 2.3(a). 36
- 10 to SO wt % Xi»

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

Ef, Q Ml K,

4027dz29 kilobars 1.0%

1654±U kilobars 0.9%

0.188±0.003 2.1%

0.220±0.003 2.1%2099±25 kilobars (30.44±0.36X108 psi) 1.7%2403±29 kilobars (34.85±0.42X108 psi) 1.7% 4031±15 kilobars 0.5%

1631zb8 kilobars 0.6%

0.197±0.003 1.9%

0.225±0.002 1.5%2149±18 kUobars

(31.17±0.26X108 psi) 1.2%

2427±11 kilobai-s (35.20±0.16X108 psi) 0.7%

4081±8 kilobars

/^Q 1Q_[_n 19VinS nQil 0.3%

1681rb3 kilobars 0.2%

0.206±0.003 2.0%

0.216±0.003 2.0%2295±23 kilobars (33.29±0.33X106 psi) 1.4%2394±4 kilobars (34.72±0.06X10S psi) 0.2%

3851±10 kilobars 0.4%1M8±6 kilobars 0.5%0.197±0.004 3.0%

0.228±0.005 3.4%2078±30 kilobars (30.14±0.44X106 psi) 2.0%

2368±42 kilobars (34.34±0.61X106 psi) 2.5% 38(M±8 kilobars 0.3%

1560±6 kilobars 0.5%

0.2I0zt0.001 0.9%0.221±0.002 1.1%2168±5 kilobars (31.44±0.07X106 psi) 0.3%

2275±5 kilobars (33.00±0.07X108 psi) 0.3%, 3741±13 kilobars 1538±6 kilobars 0.5%

0.219±0.003

1.8%

0.222±0.002 1.4%2226±13 kilobars (32.29±0.19X10« psi) 0.8%

2249±1 5 kilobars

(32.62±0.22X10i! psi) 0.9%

1699±3 kilobars (24.64±0.04X10' psi) 0.3%0.151±0.003 0.153±0.0(M 1871±10 kilobars (27.14±0.23X106 psi) 1.2%1882±24 kOobars

(27.30±0.35X108 psi) 2.7% 3.5% 1.8% 3886±9 kilobars

(56.36=i=0.13X10« psi) 0.3%

1586±2 kilobars

(23.CI0±0.03X10» psi) 0.2%

0.204±0.002 3.2%

0.231±0.003 1.7%

2147±3 kilobars (31.14±0.04X105 psi) 0.2%

2417±28 kilobars (35.06±0.41X106 psi) 1.6%

analysis of values given in table 17

F and t values for—Continued '

Young's modulusContinued

Shear modulus Poisson's ratio Bulk modulus

Ef. G K,

3.62 2.00 1. 18 1. 69 2. 06 6.73

0.24 3.98 5. 55 2. 89 3.75

1.46 5.60 1. 98 3 08 1. 62 1.98

40.8 3. 64 4 31 13.1 1. 41

2.65 1.07 4 22 1 76 7.79 9. 57

9.75 5.84 0 68

-

1.78

64.8

2.85

35.3

1.81

36.8

3. 06

38.3

1. 38

32.7

for BiC

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

E,. G Mi Ki Kfu,

4450±23 kilobars (64.54±0.33X10« psi) 0.7%

4457±15 kilobars

r54.(>4±0.22X105 psi) 0.5%

1

1850±10 kUobars ^ (26.83±0.15X109 psi) 0.7%

1856±8 kilobars <^ (26.92±0.12X10» psi) 0.6%

W

(»)

2544±13 kUobars » (36.90±0.19X10« psi) 0.7% 2552±5 kilobars f (37.01±0.07X106 psi) 0.6%
Table 19. Data

Code

and

group

Source Statistical parameters

No. of

speci- ' mens

Bulls density O^tJcU, ijl oULLilU. Young's modulus

El

43-1

43-11

43-III

43-IV

43-All

H Average V

Average V

Average V

Average V

Average V

5

5

6

5

20

2.814=b0.006 g/cm3

(175.7±0.4 Ib/fts) 0.2%

2.815±0.006 g/cm3

(175.7±0.4 lb/ft3) 0.2%

2.815±0.006 g/cm'

(175.7±0.4 lb/ft3) 0.2%

2.818±0.004 g/cm3

(175.9±0.21b/ft3) 0.1%

2.816±0.002 g/cm3

(176.8±0.1 lb/ft3) 0.2%

4454±58 kilobars (64.60±0.84X108 psi) 1.1%

4513±101 kUobars

(65.46±1.46X10» psi) 1.9%

4474±43 kilobars

(64.89dz0.62X108 psi) 0.8%

4500±31 kilobars (65.27±0.45X108 psi) 0.6%

4485±25 kilobars (65.05±0.36X108 psi) 1.2%

"This mixture contains 82 parts (volume) of BjC and 18 parts TiBj.

b These values are not considered reliable because of an assumption that was made during the calculation.

''/j=0.2056 assumed value for one specimen, see sec. 2.3(a).

Table 20.

Code

and

group

Source Statistical parameters

No. of speci- mens

Bulk density Speed of sound

Young's modulus

El Ef^

45-1

45-11

35-1

35-11

B Average V

Average V

Average V

Average V

9

8

10

9

3.103±0.012 gm/cmS

(193.7±0.7 Ib/fts) 0.5%

3.128±0.002 gm/cm'

(195.3±0.1 lb/ft3) 0.1%

2.576±0.004 gm/cm'

(160.8±0.2 Ib/fts) 0.2%

2.596±0.005 gm/cm3

(162.1±0.3 Ib/fts) 0.2%

3,948±64 kilobars (57.26±0.93X108 psi) 2.1%

4,013±15 kilobars (58.20±0.22X109 psi) 0.4%

2,021±43 kilobars (29.31±0.62X10« psi) 3.0%

1,963±50 kilobars (28.47±0.73X106 psi) 3.3%

H 8,818 ±87 m/sec

(28.93±0.29X 103 ft/sec) 1.4%

8,744±81 m/sec

(28.69±0.27X103 ft/sec) 1.2%

2,003±41 kilobars (29.05±0.69X10« psi) 2.9%

l!985±39 kilobars (28.79±0.67X109 psi) 2.5%

Table 20a. Statistical data for the

Code Compared groups Critical value

F and t values for

Bulk

density Speed of sound

Young's modulus

El Ef„

45

35

F-test:

I and II

<-test:I and II

if-test: I and II

i-test:I and II

4. 90-

" 4. 53*

2. 13

4. 36-

4. 10*

2.11

b 12.2 22. 4*

1.71*

7.85

1.34

1.92

1.33

0. 71

1.15*

2.03

» F and t values marked with an asterisk indicate comparison with the critical value

similarly marked.

b Underlined figures indicate that a significant difference does exist between the compared groups.

38
for BiC + TiB,*

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

E,. G

4442±47 kilobars (64.43±0.68X10« psi) 0.9%

4455db46 kilobars

(64.81=fcO.67X109 psi) 0.8%

4466±37 kilobars (64.77±0.54X10» psi) 0.7%

4478±32 kilobars

(64.95d=0.46X109 psl) 0.6%

4460±16 kilobars

(64.69=t0.23X109 psi) 0.7%

1817±24 kilobars b (26.79±0.35X106 psi) 1.1% 1872±42kUobarsb

(27.15±0.61X108 psi) 1.8%

1856±18 kilobarsb

(26.92d=0.26X10« psi) 0.8%

1866±13 kilobars b (27.06±0.19X108 psi) 0.6%

1860±10 kilobars •> (26.98±0.15X10« psi) 1.2%

C)

(")

C)

C)

(°)

2521±33 kilobars b (36.56db0.48X109 psi) 1.1% 2545±57 kilobars b (36.91zt0.83X10« psi) 1.8%

2533d=25 kilobars b (36.74±0.30X10« psi) 0.8%

2547±18 kilobars b (36.94±0.26X10S psi) 0.6%

2539±14 kilobars b (36.83±0.20X103 psi) 1.2%

Data for SiC

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

G MI

3,997±11 kilobars (57.97±0.16X108 psi) 0.3%

3,931±21 kilobars (57.01±0.30X10« psi) 0.6%

2,035±30 kilobars (29.52±0.44X10* psi) 2.1%

1,993±42 kilobars

(28.91=fc0.01X10« psi) 2.8%

1,665±24 kilobars

(24.15dz0.36X10« psi) 1.9%

1,683±5 kilobars (24.41±0.07X10« psi) 0.4% , 851±19 kilobars (12.34±0.28X10» psi) 3.1%

836d=57 kilobars (12.13±0.83X10» psi) 8.9%

0.182±0.003 2.0%

0.192±0.005 3.3%

0.187±0.002 1.8%

0.173±0.005 3.7%

965±14 kilobars (14.00±0.20X108 psi) 1.8%

966d=5 kilobars (14.01±0.07X10' psi) 0.7%

1,078±24 kilobars (15.64±0.35X10« psi) 3.1%

1,002±38 kilobars (14.53±0.55X10» psi) 5.0%

0.117±0.003 2.1%

0.187±0.003 1.7%

1,034±18 kilobars (15.00±0.26X109 psi) 2.6%

1,057±15 kilobars (15.33±0.22X10« psi) 1.8%

analysis of values given in table 20

F and t values for—Continued

Young's modulus

Continued

Shear modulus Poisson's ratio Bulk modulus

Ef. G Ml K,

3. 01*

1.27

1.10»

1.70

28.9 2. 67*

4.63

3.78*

6. 08

7.82

7.95* 1.26*

5.58

1.93

2. 61

2. 23*

3. 97

39
Table 21. Data for

Code

and

group

Source Statistical parameters

No. of speci- mens

Bulk density Speed of sound

Young's modulus

El

37-1

37-11

37-III

37-IV

37-AU

H Average V

Average V

Average V

Average V

Average V

5

5

5

6

20

3.074±0.007 g/cm3

(191.9±0.4 lb/tt3) 0.2%

3.086±0.014 g/om3

(192.7±0.9 lb/ft3) 0.4%

3.083±0.003 g/cm3

(192.5±0.2 lb/ft') 0.1%

3.084±0.006 g/cm3

(192.5±0.4 lb/ft3) 0.2%

3.082±0.004 g/cm3

(192.4±0.2 lb/ft3) 0.3%

4120±45 kilobars (59.76±0.65X109 psi) 0.9%

4114±37 kUobars

(59.67±0.64X109 psi) 0.7%

4121±72 kUobars

(59.77±1.04X109 psi) 1.4% 4246±66 kilobars {61.58±0.96X10» psi) 1.3%

4151±31 kilobars (60.21±0.45X10« psi) 1.6% .

a This mixtui'e contains 90 parts of SiC and 10 parts of B4C (by weight).

t> These values are not considered reliable because of an assumption that was made during the calculation.

" M=0.2208 assumed value for one specimen, see sec. 2.3(a).

Table 22. Data

Code

and

group

Source Statistical parameters

No. of speci- mens

Bulk density Speed of sound

Young's modulus

El Ef^

38-1

38-11

38-III

38-IV

38-V

38-VI

38-All

H Average V

Average V

Average V

Average V

Average V

Average V

Average V

1

2

4

4

5

4

20

6.465 g/cm3

(403.6 lb/ft3)

6.177±0.602 g/cm3

(385.6±37.6 lb/ft3) 1.1%

6.148±0.028 g/cm3

(383.8±1.7 lb/ft3) 0.3%

6.202±0.009 g/cm3

(387.2±0.6 lb/ft3) 0.1%

6.016±0.031 g/om3

(375.6±1.9 lb/ft3) 0.4%

6.017±0.025 g/cm3

(375.6±1.6 lb/ft3) 0.3%

6.118±0.055 g/cms

(381.9±3.4 lb/ft3) 1.9%

3881 kilobars (56.29X109 psi) 3045±516 kOobars

(44.16=h7.47X10» psi) 1.9% 3220±72 kilobars (46.70±1.04X109 psi) 1.4% 3279±24 kilobars (47.56±0.35X109 psi) 0.6%

2961±65 kilobars (42.95±0.94X10« psi) 1.8% 2890±89 kilobars (41.92±1.29X10« psi) 1.9%

3117±113 kilobars

(45.21±1. 64X109 psi) 7.7%

l_

ii

40
SiC + BiCYoung's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

G Ki

4090±44 kilobars (59.32±0.64X109 psi) 0.9%

4100±67 kilobars (59.47±0.97X10« psi) 1.3% 4084±79 kilobars (59.23±1.15X10» psi) 1.6%

4321 ±29 kilobars (62.67±0.42X108 psi) 0.6%

4149±52 kaobars

(6O.18±0.75X10' psi) 2.7%

1688±18 kilobarsi" {24.48±0.26X10» psi) 0.9%

1685±15 kilobarsb (24.44±0.22X10« psi) 0.7%

1688±29 kilobarsb (24.48±0.42X109 psi) 1.4%

1739±27 kUobarst> (25.22±0.39X10« psi) 1.3%

1699±20 kilobars'' (24.64±0.29X109 psi) 1.6%

C)

(»)

(°)

(°)

C)

2460±27 kilobars >> (35.68±0.39X10« psi) 0.9%

2456±22 kilobars b (35.62±0.32X10« psi) 0.7%

2460±43 kilobars b (35.68±0.62X10« psi) 1.4% 2535±40 kilobars b (36.77±0.58X109 psi) 1.3% 2478±29 kilobars b (3S.94±0.42X10» psi) 1.6%

fcr ZrC

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

K,

3870 kilobars (56.13X106 psi) 3119±503 kilobars (45.24±7.30X10« psi) 1.8% 3249±51 kilobars (47.12±0.74X10« psi) 1.0%

3291±lo kilobars (47.73±0.22X109 psil 0.3%

3063±45 kilobars (44.43±0.65X10« psi) 1.2% 2995±59 kilobars (43.44±0.86X10« psi) 1.2% 3178±95 kilobars (46.09±1.38X106 psi) 6.4%

1540 kilobars (22.34X105 psi) 1223±40 kilobars (17.74±0.58X10« psi) 0.4%

1280±27 kilobars (18.56±0.39X106 psi) 1.3% 1317±7 kilobars (19.10±0.10X106 psi) 0.3%

1165±31 kilobars (16.90±0.45X10» psi) 2.2%

1149±35 kilobars (16.66±0.51X106 psi) 1.9% 1240±46 kUobars

(17.98±0.67X10» psi) 8.0%

0.260

0.245±0.170 7.7%

0.258±0.005 1.2%

0.245±0.010 2.5%

0.271±0.008 2.4%

0.258±0.003 0.7%

0.257±0.005 4.5%

2688 kilobars

(38.99X106 psi)

1999=t82 kilobars (31.27±1.19X10« psi) 9.8%

2206±115 kilobars (32.00±1.67X10« psi) 3.3%

2156±82 kilobars (31.27±1.19X10« psi) 2.4%

2136±68 kilobars

(30.98dz0.99X10» psi) 2.6%

2009±78 kilobars (29.14±1.13X10» psi) 2.5%

2142±76 kUobars

(31.07±1. 10X10' psi) 7.6%

41
Table 23.

Code

and

group

Source Statistical parameters

No. of

speci- mensBulk density Speed of sound

Young's modulus

El.

41-1

41-11

41-III

41-IV

41-All

42-1

42-11

Average V

Average V

Average V

Average V

Average V

Average V

20

5.968±0.015 g/cm3

(372.6±0.9 lb/ft3) 0.2%

5.308±0.013 g/cm3

(331.4±0.81b/ft3) 0.2%

5.271±0.i09 g/cm3

(329.1±13.01b/ft3) 3.2%

5.793±0.031 g/cm3

(361.6±1.91b/ft3) 0.4%

5.585±0.146g/cm3

(348.7±9.11b/ft3) 5.6%

4.557±0.034 g/om3

(284.5±2.1 Ib/ftS) 1.1%

4.524±0.056 g/cm3

(282.4±3.5 lb/ft3) 1.7%

5069±22kilobars

(73.52=t0.32X109 psi) 0.4%

3582±32kilobars

(51.95±0.46X10« psi) 0.7%

3405±148 kilobars (49.39±2.15X108 psi) 3.5%

4399±52 kilobars (63.80±0.75X108 psi) 1.0%

4114±321 kilobars (59.67±4.66X109 psi) 17%

2455±85 kOobars

(35.61±1.23X109 psi) 4.8%

2368±143 kilobars (34.34±2.07X109psi) 8.4%

Table 23a. Statistical data for the analysis

Code Compared groups Critical value

F and t values for

Bulk

density Speed of sound

Young's modulus

El Efy,

42 f-test

I and II

/-test

I and II

4. 03

2. 10

2. 68

0. 93

2. 82

0. 97

a Underlined figures indicate that a significant difference does exist between the compared groups.

Table 24. Data

Code

and Source Statistical No. of

speci- Bulk density Speed of sound Yoimg' s modulus

group parameters mens

Et

39-1 H Average V

4 5.987±0.072 g/cms

(373.8±4.5 lb/ft3) 0.8%

3815±106 kilobars {55.33±1.64X106 psi) 1.8%

39-11 Average V

5 5.874±0.300 g/em3

(366.7±18.7 lb/ft3) 4.1%

3664±125 kilobars (53.14±1.81X10» psi) 2.8%

39-III Average 1 5.974 g/cm3

(372.9 lb/ft3) 3839 kilobars (55.68X108 psi) 39-IV Average 4 6.041±0.022 g/cm3

(377.1±1.4 lb/ft3) 0.2%

3886±18 kilobars V

{56.36±0.26X109 psi) 0.3% 39-V Average V

2 5.966±0.485 g/cm3

{372.4±30.3 lb/ft3) 0.9%

3807±596 kilobars (65.22±8.64X10« psi) 1.7% 39-IV Average 3 5.991±0.008 g/om3

(374.0±0.5 lb/ft3) 0.1%

3839±19 kilobars V

(55.68±0.28X10« psi) 0.2%

39-All Average 19 5.966±0.038 g/cm3

(372.4±2.4 lb/ft3) 1.3%

3795±49 kilobars V

(55.04±0.71X109 psi) 2.7%

42
Data for ZrBj

Young's modulus—Con. Shear modulus Poisson's ratio Bulk modulus

G Ml

5090d=22 kOobars

(73.82±0.32X10« psi) 0.4%

3635±27 kUobars

(52.72±0.39X10« psi) 0.6%

3470±14o kilobars

(50.33=fc2.10X10» psi) 3.4%

4363±56 kilobars {63.28±0.81X10«psi) 1.0%

4139dz310 kilobars

(60.03=t4.50X10« psi) 16%

2458±95 kilobars (35.65±1.38X10« psi) 5.4%

2362±150 kilobars

(34.26zfc2.18X10« psi) 8.9%

2206d=14 kilobars (32.00±0.20X10« psi) 0.5%

1527±14 kilobars

(22.15d=0.20X10« psi) 0.7%

1482±62 kilobars (21.49±0.90X109 psi) 3.3%

1922±2o kilobars (27.88±0.36X10» psi) 1.0%

1784±143 kUobars

(25.87±2.07X10« psi) 17%

1085±35 kilobars (15.74±0.51X10« psi) 4.5%

1037±54 kilobars (15.04±0.78X10« psi) 7.3%

0.149±0.003 1.3%

0.173±0.002 0.8%

0.149±0.066

2205±15 kilobars (31.98±0.22X10» psi) 0.6%

1825dzl6 kilobars (26.47±0.23X108 psI)

0. 7%

1601±66 kilobars {32.22±0.96X10« psi) 3.3%

2077±27 kilobars (30.12±0.39X10' psi)

1. c%

1977±144 kilobars (28.67±2.09X109 psi) 16.0% 1110±48 kilobars (16.10±0.70X10» psi 6.1%

1104d=100 kilobars (16.01±1.45X10' psi) 13.0%

3.0%

0.144±0.003 1.5%

0.154±0.006 7.6%

0.131±0.005 5.0%

0.141±0.013 12%

of values given in table 23

F and t values for—Continued

Young's modulus

Continued

Shear modulusPoisson's ratio Bulk modulus

E,. G Ml M/i» Ki

2. 51

1.00

2. 36

1.37

» 7.04 4. 32

0. 13

for MoSi2

Young's modulus Shear modulus Poisson's ratio Bulk modulus

Ki

3805±67 kilobars (55.19±0.97X10« psi) 1.1%

3754 ±46 kilobars

(54.45=tO.67X109 psi) 1.0%

3807 kilobars (55.22X10' psi) 3866±13 kilobars (56.07±0,19X10» psi) 0.2%

3798±377 kilobars (55.09±5.47X10« psi) 1.1% 3804±5 kilobars

(55.17=fc0.07X109 psi) 0.1% 3804±23 kilobars (55.17±0.33X10» psi) 1.2%

1636±49 kilobars (23.73±0.71X108 psi) 1.9% 1582±44 kUobars

(22.95±0.64X108 psi) 2.2%

1638 kilobars (23.76X10«psi) 1665±10 kUobars

(24.15±0.15X108 psi) 0.4% 1628±272 kUobars

(23.61±3.95X10«psi) 1.9% 1648±6 kilobars

(23.90=t0.09X106 psi) 0.1%

1629±19 kUobars

(23.63±0.28X108 psi) 2.4%

0.166±0.005 1.7%

0.158±0.008

4.1%

0.172

0.167±0.005 2.0%

0.169±0.013 0.8%

0.165±0.006 1.5%

0.165±0.003 3.4%

1910±51 kilobars (27.70±0.74X108 psi) 1.7% 1790±102 kUobars

(25.96±1.48X10« psi) 4.6%

1931 kUobars

(28.01X106 psi) 1935±23 kilobars (28.06±0.33X106 psi) 0.8%

1920±324 kUobars

(27.85±0.46X108 psi) 3.9% 1918±48 kUobars

(27.82±0.70X108 psi) 1.0% 1887±36 kUobars

(27.37±0.52X106 psi) 3.9%

43
Table 25. Data

Code

and

group

Source Statistical parameters

No. of speci- mens

Bulk density Speed of sound Young's modulus

40-1

40-11

A Average V

Average V

10

4

5.763±0.024 g/cms

(359.8±1.5 lb/ft3) 0.6%

5.6S6±0.213 g/cms

(353.1±13.3 lb/ft') 2.4%

1817±48 kilobars (26.35±0.70X10» psi) 3.5%

1760±62 kilobars (26.53±0.90X109 psi) 2.2%

Table 25a. Statistical data for the

Code Compared groups

Critical value

F and t values for

Bulk

density Speed of sound

Young's modulus

Fi

40

I and II

J-tesf

I and II

5.08—

•14.5'

2. 18

b 15.3 •2. 92

1. 58

» F and? values marked with an asterisk indicate comparison witli the critical value similarly marked.

b Underlined figures Indicate that a significant difference does exist between the compared groups.

44
for NiAl

Young's modulus Shear modulus Poisson's ratio Bulk modulus

Ft. G Ml Ki

1786±43 kilobars (25.90±0.62X106 psi) 3.4%

1737±194 kilobars (25.19±2.81X10» psl) 7.0%

723±33 kilobars (10.49±0.48X10» psi) 6.4% 695±8 kilobars (10.08±0.12X103 psi) 0.7%

0.261±0.040 21%

0.265±0.039 9.2%

1320±177 kilobars (19.15±2.57X10« psi) 19%

1260±264 kilobars (18.27±3.68X10» psi) 13%

analysis of values given in table 25

F and t values for—

Young's modulus

Shear modulus Poisson's ratio Bulk modulus

Ft. G Ml M/i» A'i K,„

4.12 •82.2 •5.23 *2.40

1.03 0. 14 0. 45

4. References

[1] High temperature technology edited by I. E. Campbell, p. 29 (John Wiley & Sons, Inc., New York,

N.Y., 1956).

[2] W. E,. Sheridan, The use of refractory ceramics in rocket engines, Bull. Am. Ceram. Soc. 37 [2] 91

(1958).

[.3] S. Spinner, Elastic moduli of glasses by a dynamic

method, J. Am. Ceram. Soc. 37 [5] 229 (1954).

[4] F. B. Hornibrook, Application of sonic method to

freezing and thawing studies of concrete, ASTM

Bull. No. 101, p. 6 (Dec. 1939).

[5] J. M. Ide, Some dynamic methods of determination of Young's modulus, Rev. Sci. Instr. 6 [10] 296 (1935).

[6] W. G. Cadv, Piezoelectricity, p. 102, Isted. (McGrawHill Book Co., Inc., New York, N.Y., 1946).

[7] G. Pickett, Equations for computing elastic constants from flexural and torsional resonant frequencies of vibration of prisms and cylinders, ASTM Proc. 45,

846 (1945).

[8] ASTM book of standards, part 3, p. 1355 (C215-55T)

(1955).

[9] R. J. Roark, Formulas for stress and strain, 2d ed,

p. 154 (McGraw-Hill Book Co., Inc., New York,

N.Y., 1938).

[10] S. Spinner, and E. C. Valore, Jr., Comparison of theoretical and empirical relations between the shear modulus and torsional resonance frequencies

for bars of rectangular cross section, J. Research

NBS 60 [.5] 4.59 (19.58) RP2861.

[11] S. M. Lang, R. S. Roth, and C. L. Fillmore, Some

properties of beryllia and zirconia with titania, ceria and chromia, J. Research NBS 53 [4] 201

(1954) RP2534.

[12] S. M. Lang and F. P. Knudsen, Some physical properties of high-density thorium dioxide, J. Am.

Ceram. Soc. 39 [12] 415 (1956).

[13] R. L. Coble and W. D. Kingery, Effect of porosity on

physical properties of sintered alumina, J. Am.

Ceram. Soc. 39 [11] 377 (1956).

[14] K. Konopicky, Beitrag zur Untersuchung des Diagramms Al203-Si02, Berichte der Technischeu, Komission und des Forschungs—Institute der Feuerfest Industrie, Berichte 22 (1957).

[15] Otto Ruff and Fritz Ebert, Z. anorg. Chem. 180, 19

(1929). Also U.S. Patent 1,969,099.

[16] R. F. Geller and P. J. Yavorsky, Effects of some oxide

additions on the thermal length changes of zir- conia, J. Research NBS 35, 87 (1945) RP1662.

[17] L. S. Ramsdell and J. A. Kohn, Developments in sili- con carbide research, Acta Cryst. 5, part 2, p. 215

(March 1952).

[18] L. E. Mong and W. L. Pendergast, Dynamic and

static tests for mechanical properties of fired plastic refractories and other more resilient materials, J. Am. Ceram. Soc. 39 [9] 301 (1956).

[19] L. E. Mong and D. M. Adelman, Control of factors

affecting reproducibility of mechanical properties of refractory semidry press specimens, J. Am. Ceram.

Soc. 41 [7] 267 (1958).

[20] R. S. Roth (private communication).

[21] J. M. Frankland and H. L. Whittemore, Test of

cellular sheet-steel flooring, J. Research NBS 9, 131

(1932) RP463.

[22] W. J. Youden, Statistical methods for chemists, (John

Wiley & Sons, Inc., New York, N.Y., 1951).

[23] Wilfred J. Dixon and Frank J. Massey, Jr., Introduction to statistical analysis (McGraw-Hill Book Co.,

Inc., New York, N.Y. 1951).

WASHINGTON, D. C, July 28, 1958

45

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