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^^REFERENCE

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PUBLICATIONS

NBSIR 87-3584

Effect of Slag Penetration on the Mechanical

Properties of Refractories:

Final Report

Report Prepared by

S.M. Wiederhorn and R.F. Krause, Jr. U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Institute for Materials Science and Engineering

Ceramics Division

Gaithersburg, MD 20899

under

Contract Number DE-AI05-83OR21349

for

OAK RIDGE NATIONAL LABORATORY

Oak Ridge, Tennessee 37831

operated by

MARTIN MARIETTA ENERGY SYSTEMS, INC.

for the

U.S. DEPARTMENT OF ENERGY ^

under Contract No. DE-AI05-83OR21349

100

»[)%
DISCLAIMER

This report was prepared as an account of work sponsored by an

agency of the United States Government. Neither the United

States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product,

or process disclosed, or represents that its use would not infringe

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manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the

United States Government or any agency thereof. The views and

opinions of authors expressed herein do not necessarily state or

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thereof.

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Printed copy: A07

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EFFECT OF SLAG PENETRATION ON THE MECHANICAL

PROPERTIES OF REFRACTORIES:

FINAL REPORT

NBSIR 87-3584

Research sponsored by the U.S. Department of Energy

Advanced Research and Technology Development

Fossil Energy Materials Program

Report Prepared by

S. M. Wiederhorn and R. F. Krause, Jr. U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Institute for Materials Science and Engineering

Ceramics Division

Gaithersburg, MD 20899

under

Contract Number DE-AI05-83OR21349

for OAK RIDGE NATIONAL LABORATORY

Oak Ridge, Tennessee 37831

operated by

MARTIN MARIETTA ENERGY SYSTEMS, INC.

for the

U.S. DEPARTMENT OF ENERGY

under Contract No. DE-AI05-83OR21 3490

September 30, 1986

Issued June 1987

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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EFFECT OF SLAG PENETRATION ON THE MECHANICAL

PROPERTIES OF REFRACTORIES

Page No.

INTRODUCTION 1

APPENDED PUBLICATIONS

1. Compressive Strength and Creep Behavior of a Magnesium Chromite Refractory 5

2. Creep and Fracture of a Vitreous -Bonded Aluminum

Oxide 14

3. Nucleation and Growth of Cracks in Vitreous Bonded

Aluminum Oxide at Elevated Temperatures 29

4. Rising Fracture Toughness of an Alumina Ceramic

Using the Bending Strength of Indented Specimens 64

5. Coal Slag Penetration in a Magnesium Chromite

Refractory 88

i
V

.J;

.*r;
1 . INTRODUCTION

Recently, in a review of materials for coal gasification applications,

Bakker and Stringer noted that the most critical material problem for slagging

coal gasifiers is the selection of refractory insulation for the gasifiers.

This problem of selecting refractory insulation is the result of refractory

lining exposure to the gasifier environment and to slag present in that

environment. The lifetime of the refractory depends on the temperature of

operation and the composition of slag at the hot face of the refractory.

Higher temperatures (1500°C to lyOO^C) and more corrosive slags (high alkali;

high Fe) reduce the lifetime of refractories. Since slag is a universal

solvent for refractories, all refractories eventually dissolve in coal slag.

However, by appropriate materials design, the resistance of the refractory to

dissolution (and hence lifetime) can be increased.

This project involved basic research to provide fundamental data and

models necessary to improve the mechanical behavior of refractories in

gasifiers, particularly those of the wet bottom type. The project consisted

of two tasks: ( 1 ) to characterize the fracture and deformation behavior of

high chromia refractories penetrated by slag, and ( 2 ) to evaluate the creep

and creep rupture behavior of model refractories in terms of mechanisms that

explain cavity formation, cavity coalescence, and crack growth in ceramic

materials

.

2. TECHNICAL PROBLEM AND APPROACH

This project dealt primarily with the structural integrity of

refractories that have been penetrated by coal slag. In part 1 of this study,

the fracture and deformation behavior of high-chromia refractories, penetrated

by slag were characterized. The creep behavior of high-chromia refractories, were determined as a function of applied load and temperature. Changes in

density and microstructure were studied for high-chromia refractories

subjected to creep deformation. Data were evaluated in terms of mechanisms

that have been developed to explain cavity formation, cavity coalescence and

crack growth in ceramic materials.

In part 2 of this study, experimental data were collected on model

ceramic refractories to identify and quantify high temperature mechanisms that

lead to a loss in the mechanical integrity of refractory materials. Studies were conducted on vitreous bonded aluminiim oxide to duplicate the type of

structure expected at the hot face of refractories in slagging gasifiers.

Microstructural variables were the grain size of the AI2 O3 , and the quanti ty

and viscosity of glass at the grain boundaries. Experiments were of two

types: ( 1 ) application of mechanical loads to the model refractories to

determine the creep and fracture behavior as a function of temperature; and

( 2 ) analyses of the microstructure of the deformed ceramics to determine the

mechanisms that control their mechanical behavior at elevated temperature.

1
3. PRINCIPAL FINDINGS

The output on this project included five technical papers in various

stages of the publication process. Subjects studied include; an analysis of

creep and creep rupture behavior of glass impregnated ceramics ; crack

nucleation and growth processes in glass impregnated ceramics, creep behavior

of magnesium chromite refractories and finally, slag penetration of magnesium

chromite refractories; and the effect of slag penetration on strength of

magnesium chromite refractories. Complete copies of these publications are included as part of this report.

Principal findings of the project are summarized below:

Magnesium Chromite Refractories :

o Compressive strength of magnesium chromite refractory was measured to ISOO’C; strength decreased with increasing

temperature above 1200“C.

o Creep of magnesium chromite refractory was characterized

as a function of compressive stress and temperature in the

range 1300“C to 1600“C.

o The stress exponent and activation energy for creep were

evaluated from strain rate data.

o Magnesium chromite spinel dissolution by slag resulted

from the diffusion of Fe0/Fe203 and AI2 O3 from slag into

the refractory to form a low melting solid solution.

o Viscosity of the slag that penetrated the refractory

controlled both dissolution rate of the magnesium chromite

spinel and the rate of diffusion of the ions from the

brick to the slag. Dissolution rate of the brick is

exacerbated by the presence of Ca and Mg which lowers the

viscosity of the slag in the brick.

o Improvement of brick performance might be achieved by the

addition of network formers such as AI 2 O 3 to the

refractory.

Creep and Creep Rupture of Vitreous Bonded Alumina Ceramics :

o Creep rupture data for vitreous bonded alumina ceramics can be represented by a modified Monkman-Grant equation,

which relates the rupture time to the creep rate of the

material

.

2
o Creep rates depend on the viscosity of the glass bonding

the aluminum oxide grain: increasing the viscosity of the

glass bonding phase reduces the creep rate of the

composite material. Devitrification of the bonding phase

appears to be a useful way of increasing the viscosity.

o Crack nucleation occurs in the amorphous intergranular

phase in vitreous bonded ceramics . Crack growth occurs primarily through the glass phase, failure occurring at a rupture strain of 0.1% for a ceramic containing 8%

vitreous phase and at 1% for a ceramic containing 30%

vitreous phase.

o A new, inexpensive method was developed for determining

R-curve behavior of ceramic materials at elevated

temperatures. Data collected at room temperature are consistent with data obtained with other techniques of

measurement.

Detailed discussion of each of the above accomplishment are given in the

papers included in this report. During the course of this project, a total of

8 lectures were presented at scientific meetings and seminars. In addition,

five technical papers have been or are in the process of being published. A

list of these are given below:

Publications

:

1. R.F. Krause, Jr. "Compressive Strength and Creep Behavior

of a Magnesium Chromite Refractory," Ceram. Eng., and

Sci. Proc. of Amer. Ceram. Soc. , 220-228, Jan/Feb (1986).

2. S.M. Wiederhorn, B.J. Hockey, R.F. Krause, Jr. and K.

Jakus, "Creep and Fracture of a Vitreous -Bonded Aluminium

Oxide," J. Mater. Sci. 21, 810-824 (1986).

3. K. Jakus, S.M. Wiederhorn and B.J. Hockey, "Nucleation and

Growth of Cracks in Vitreous Bonded Aluminum Oxide at

Elevated Temperature," J. Amer. Ceram. Soc. 69, 725-31

(1986)

.

4. R.F. Krause, Jr., "Rising Fracture Toughness from the

Bending Strength of Indented Alumina Beams," J. Amer.

Ceram. Soc., submitted.

5. S.M. Wiederhorn, R.F. Krause, Jr. and J. Sun, "Slag

Penetration in a Magnesium Chromite Refractory," Bull.

Amer. Ceram. Soc., in preparation.

3
Technical Talks:

1. R.F. Krause, Jr., "High Temperature Creep Measurements of

Refractory Materials," The American Ceramic Society, 86th

Annual Meeting, Pittsburgh, PA, May 1, 1984.

2. R.F. Krause, Jr., "Compressive Strength and Compressive

Creep of a Magnesium Chromite Refractory in Nitrogen," The

Norton Company, Worcester, MA, September 28, 1984.

3. R.F. Krause, Jr. and S.M. Wiederhom, "Creep Behavior of a Magnesium Chromite Refractory," The American Ceramic

Society, 87th Annual Meeting, Cincinnati, OH, May 7, 1985.

4. R.F. Krause, Jr. and S.M. Wiederhom, "Creep Behavior of a Vitreous -Bonded 85 Percent Alumina Refractory, The American

Ceramic Society, 87th Annual Meeting, Cincinnati, OH, May 7,

1985.

5. R.F. Krause, Jr., Jing Sun and S.M. Wiederhom, "Effect of

Coal Slag on the Composition and Creep Behavior of

Magnesium Chromite Refractory," The American Ceramic

Society, 88th Annual Meeting, Chicago, IL, April 29, 1986.

6. S.M. Wiederhom, R.F. Krause, T.-J. Chuang and K. Jakus,

"Creep and Fracture of Vitreous Bonded Ceramics," 86th

Annual Meeting of the American Ceramic Society,

Pittsburgh, PA, April 29-May 3, 1984.

7. S.M. Wiederhom, "Strength versus Crack Size in Vitreous

Bonded Aluminum Oxide at Elevated Temperatures," 4th

International Symposium on the Fracture Mechanics of

Ceramics, Blacksburg, VA, June 19-21, 1985.

8. S.M. Wiederhom, "Creep Rupture of Ceramic Materials",

University of California- Santa Barbara Winter Study Group,

4-16 January 1986.

4
Reprinted from the Ceramic Engineering and Science Pr(Kccdme>. Voi 7. No, 1-2. January-Fehruary

Copyright 1986 hy The American Ceramic Society Compressive Strength and Creep Behavior of a

Magnesium Chromite Refractory

Ralph F. Krause, Jr.

National Bureau of Standards

Gaithersburg, MD 20899

The compreaaive strength of a magnesium chromite refractory in nitrogen was measured

by rapidly loading specimens to fcdlure at several temperatures up to ISOO^’C. Strength

retrogression was observed at temperatures above 1200°C. The creep behavior of the

refractory in nitrogen was measured as a function of compressive stress in the range from 1.4 to 5. 6 MPa and as afunction of temperature in the rangefrom 1300 to 1600^C. A nitrogen atmosphere was used to suppress distillation of CrOj. Generally, the

experiments were terminated when the specimens sustained from 0.01 to 0.02 creep

strain. The creep strain (t) at a given stress (a) and a given absolute temperature (T) was represented by the following function of time (t), e = C t", where (C) depends on

stress and temperature. The time exponent (m) was evaluated as less than unity, indicating a strain-hardening model, and was independent of stress and temperature

within the precision of measurements. The creep strain rate was represented by the

relationship, (de/dt) sA a" exp ( - Q/RT), in which (R) is the molar gas con- stant The material constant (A), the stress exponent (n), and the activation energy

(Q) were evaluated from a least squares fit of this relationship to the creep data at constant strain.

Introduction

Magnesium chromite refraaory brick is a candidate for use as hot face linings in slagging coal gasifiers. Laboratory studies’ in which cylindrical

specimens are rotated in high temperature coal slags indicate that refractories with high chromia content are very resistant to wear by coal slags. However,

refractories obtained from a pilot plant after several hundred h service were

deeply penetrated by slag and contained intergranular cracks parallel to the hot face, suggesting that creep cracking can be a major cause of failure.' In the present study the compressive strength and creep behavior of a commercial magnesium chromite refractory are characterized at high temperatures.

This will provide a basis to compare the creep behavior of the refractory when

it is impregnated with slag in future studies.

Test Material

Based on a manufacturer’s report,^ the magnesium chromite refractory

material which was used in the present work consisted of 20 wt% MgO and

80 wt*7o CrjOj. The CrjO, was slightly in excess over the compound

MgCr204. The refractory was single phase, having the cubic structure of the

spinel group. Fused-grain aggregates of magnesium chromite, some of which

were as large as 3 mm across, had been sintered in a porous bonding matrix

of much smaller grains of the same material. Bulk density measurements

indicated a porosity of 14 to 16% based upon the theoretical crystal density

of 4.414 g/cm^ at 25°C.

220

5
The sample of refractory supplied^ was a cross-sectional slice (9 mm x 62

mm X 102 mm) of a manufactured brick from current production. Test specimens were diamond-sawed from the sample and diamond-ground with

a 50 fim finish to make bearing faces flat, parallel, and perpendicular to adjacent sides. These specimens (nominally 8 mm x 9 mm x 18 mm high) were

used in compressive strength tests and in a series of creep tests described below.

Test Environment

During the high temperature tests, the refractory specimens were kept in a nitrogen atmosphere to suppress oxidation and subsequent distillation of

chromia,

CrA (s) -H (g) = 2CA (g) 0)

At 1600“C the minimum vapor pressure of MgCr204 (s) occurs with an

oxygen partial pressure of about 10-“* atm.^ At higher oxygen pressures, the

partial pressure of C1O3 (g) becomes predominant and increases with increas- ing oxygen pressure. When the partial pressure of oxygen is less than 10““

atm, the partial pressure of Cr (g) becomes predominant and increases with

decreasing oxygen pressure. A flow at 500 mL/min of 99.99 vol*7o nitrogen was maintained through a gas-tight furnace to keep decomposition of the MgCr204 specimen at a minimum. An alumina tube (100 mm x 28 mm inside diam) surrounded the specimen in the center of the hot-zone of the furnace

and was supported on legs to clear both the furnace floor and ceiling by 25

mm. In this way the furnace interior was protected from exposure to any

chromium vapor species. The furnace interior remained uncontaminated while gas circulated freely around the specimen, leaving a slight film of chromia

condensed inside the protection tube near its openings.

The gas-tight box furnace had a hot-zone cavity (150 mm cube) that was

radiantly heated by molybdenum disilicide resistive elements and could be

controlled to operate at a temperature as high as 1600°C. Figure 1 shows a

test specimen as mounted between 99.8 wt<^o recrystallized AI2O3 discs

(5 mmx 19 mm diam) to prevent contact between the specimen and silicon carbide loading rods (19 mm diam). New discs were ground flat and parallel for each test and were easily separated from the specimen and the loading rods

following a high temperature run. The loading rods protruded into the center of the furnace cavity through upper and lower ports which were made in the

stainless steel shell and alumina fiber insulation of the furnace. The loading

rods were supported and aligned by set screws in socket fixtures that had gastight seals with the furnace. The upper fixture was attached to the underside

of a moveable crosshead in a frame and was surrounded by a bellows assembly

between the crosshead and the furnace top. The lower fixture was attached

to a load cell on the frame and was surrounded with a bellows assembly between

the load cell and the furnace bottom. Water from a controlled 24°C constant temperature bath circulated through these fixtures to avoid uncertain thermal

deformations, which would be especially troublesome in the creep measurements discussed below. This circulating water also cooled the rubber

seals of the front door of the furnace and the radiation shields which were

placed above and below the furnace shell. The furnace was heated from

ambient to 1200°C in about 20 min and thereafter about 20 K/min to attain the test temperature. After reaching temperature, approximately another hour

221

6
was required for steady-state temperature equilibration. The temperature of

the furnace cavity was controlled within ±0.5 K and was determined by a

calibrated Pt and 6% Rh vs Pt and 30'^'o Rh thermocouple.

Compressive Strength Measurements

The furnace was established in the frame of a universal test loading

machine. The gear-driven crosshead of the machine was used at a constant speed of 0.5 mm/min to apply uniaxial, compressive loading on a specimen

through a hemispherical block of silicon carbide. Loading was indicated by

a linear strain gauge type of load cell and was recorded on a constant-speed

chart. The load cell was calibrated at the full scale of the chart with a known

10 kg mass acting at the local 9.801 m s”^ acceleration of gravity. Calibration was performed with the furnace at the elevated temperature of a given

test to avoid any systematic error due to thermal changes in the spring action

of the bellows attached to the load cell. Alternative proportional chart scale factors besides unity (2, 5, 10, 20, 50, and 100) allowed larger loads to be read

within ±0.2% full scale. Figure 2 shows two examples of typical loading versus displacement curves

for specimens of the magnesium chromite refractory. The dashed curve, which

represents a test at 1200°C, is similar to that obtained in a room temperature

test. In these tests, failure of the specimen occurred suddenly. The solid curve, which represents a test at 1500°C, is similar to ail tests conducted at temperatures at 1300°C and higher; broadening of the peak load is due to specimen creep. Figure 2 indicates that the displacement, which was deduced

from the chart and crosshead speeds, corresponds to about 2% rupture strain

at the peak loads. Figure 3 shows the results of duplicate tests on separate specimens at room

temperature in air and at 1200, 1300, 1400, 1500, and 1600®C in nitrogen.

The compressive strength for a given specimen was calculated from the observed peak load divided by its initial cross-sectional area. The compressive

strength of the magnesium chromite refractory appears to decrease at temperatures above 1200°C and at 1600°C is about one-third of the room

temperature value.

Compressive Creep Measurements

Creep specimens of the refractory were mounted in the same apparatus

as that used for the compressive strength measurements. A preload of 50 N

was applied to a specimen prior to heating in order to maintain alignment.

Crosshead movement was controlled automatically by the test machine to accommodate thermal expansion during heat up and to maintain the preload

within 10% variation. Temperature equilibration of the loading train at the

test temperature was indicated by a steady crosshead position. A linear voltage

displacement transducer, calibrated with gauge blocks, was used to monitor

the crosshead displacement resulting from the specimen deformation. The

transducer was sensitive to ± 1 >im displacement which corresponds to about

± (5) 10*’ creep strain. A creep test was initiated by application of a test load in the range from 100 to 400 N. The load was held constant within ± 0.5%

full scale chart throughout the test by automatic adjustment of the crosshead

position, using intermittently a crosshead speed of 0.8 mm/h. Variation in stress due to specimen deformation during the test was assumed negligible.

Creep strain was measured as a function of time following the initial elastic

222

7
and plastic strain. Generally, the experiments were terminated when the specimens sustained from 0.01 to 0.02 creep strain. Creep measurements were conducted on 9 specimens. The stress and

temperature applied to a given specimen were kept constant during a test. In the collection of tests the stress ranged from 1.4 to 5.6 MPa and the temperature

ranged from 1300 to 1600°C. The duration of the creep tests varied from about

3 to 170 h. Figure 4 shows a typical experiment of creep strain vs time. Absolute

Absolute values of strain were used to facilitate an analysis. Note that no

steady-state creep rate was attained.

Analysis of Creep Data

The compressive creep strain (c) of a given specimen under a constant

stress and at a constant temperature was found to be represented within 1 *7o by the following primary creep function'* of time (t)

c = Cr (2)

in which (C) and (m) are coefficients that were evaluated by a least squares

fit of Eq. 2 for each experiment. An example of such a fit is the line in Fig. 4. No systematic trend of the time exponent (m) was apparent either as a

function of the applied stress or as a function of temperature. Figures S and

6 show (m) as the slope of log, (c) versus log^ (/) for various stresses applied

to specimens kept at constant temperature, and for various temperatures

applied to specimens held at constant stress, respectively. In these figures the

slopes are roughly parallel. The mean value of (m) for 9 experiments was 0.74

with ±0.16 standard deviation of an individual measurement. If any creep

strain that might have occurred during the period of temperature equilibration of a specimen under the preload were included, a lower value of (m) and

perhaps a better precision would have resulted. Differentiation of Eq. 2 and substitution of the strain equivalent of time

gives

d£/dt = mC""e<‘-'^'"> (3) which shows a strain-hardening effect for (m) < 1. Thus, the creep rate (ck/dt)

decreases continually as the strain (c) increases, exemplifying primary creep. The parameter (C) is a function of the applied stress (a) and the absolute

temperature (T). Using customary stress and temperature functions,’ the creep strain rate can be represented as follows: (k/dt = A o" exp (-Q//?7) (4) where {A) is a material constant, (n) is the stress exponent, (Q) is the activa- tion energy, and (R) is the molar gas constant. Strain rates were calculated from Eq. 3, using values of strain generated in increments between 0.002 and

0.02. At constant strain k) and the mean value of the time exponent (m), the

coefficients A, n, and Q were evaluated by a least squares fit of the log* of

Eq. 4 to the strain rates at their respective stresses and temperatures. Although

the resulting values of the coefficients of Eq. 4 had a slight systematic trend over the generated range of strain, they could be considered constant within

the precision of measurements. Table I shows the values of these coefficients. Figures 7 and 8 show the stress exponent (n) and the activation energy (0

as slopes of log, (df/dt) vs log, (a) and vs l/T, respectively.

223

8
Summary

The compressive strength of a magnesium chromite refractory was measured at temperatures up to 1600°C. The strength decreased with increas- ing temperature above 1200°C.

The creep behavior of the magnesium chromite refractory was measured

as a function of compressive stress in the range from 1.4 to 5.6 MPa and as a function of temperature in the range from 1300 to 1600°C. The strain rate of this refractory was represented by a strain -hardening model.

The stress exponent and the activation energy for the creep of the magnesium chromite refractory were evaluated from the strain rate data at constant strain. Acknowledgment

Funding was provided by the U.S. Department of Energy, Fossil Materials

Program, Oak Ridge National Laboratory, Oak Ridge, TN. Helpful discus- sions with Sheldon Wiederhom, who suggested the work be undenaken, and

with Robert Polvani are gratefully acknowledged.

References

'W. T. Bakker, S. Greenberg, M. Trondt, and U. Gerhardus, Am. Ceram. Soc. Bull., 63

870-6 (1984). ^M. E. Washburn, private communications. The Norton Company, Worcester,

Massachusetts, March 9, 1984.

’T. Sata, T. Sasamoto, H. L. Lee, and E. Maeda, Rev. Int. Hautes Temp. Refract., 15 237-48 (1978).

*J. D. Lubahn and R. P. Felgar, p. 157 in Plasticity and Creep of Metals, John Wiley and

Sons, Inc., New York, 1961.

’J. T. Boyle and J. Spence, pp. 12-13 in Stress Analysis for Creep, Butterworths, London,

1983.

Table I. Values of the coefficients of Eq. 4 for the creep of magnesium

chromite refractory at l*f^o strain m 0.74 ±0.16

n 2.26 ±0.23

Q, kJ/mol 364 ±29

log. A* 12.95 ±1.97

Number runs 9

Residual standard

deviation of

log* (ck/dt) ±0.28

Corresponds to stress in MPa and time in h. The uncertainties are the standard deviations of the respettive coefficients.

224

9
SiC rod attached

with bellows to crosshead

SiC rod attached

with bellows to load cell

Fig. 1. Schematic of compressive loading of specimen.

Fig. 2. Typical compressive loading tests conducted at constant 0.5 mm/min displacement rate for magnesium chromite refrac- tory specimens (8 mm x 9 mm x 18 mm high) in nitrogen at 1200°C (dash) and 1500°C (solid).

225

10
Fig. 3. Compressive strength of magnesium chromite refrac- tory specimens in nitrogen as a function of temperature.

Fig. 4. Typical experiment for compressive creep of a magnesium chromite refractory specimen in nitrogen, in this case

at 1400°C under an applied stress of 2.25 MPa. The circles denote

observed values, and the line represents Eq. 2 fitted by a least squares method.

226

11
Fig. 5. Time exp>onent (m) as the sbpe of log, of aeep

strain vs log, of time at various applied stresses on a magnesium chromite refractory in nitrogen at 1500 °C.

The circles, triangles, and squares denote observed values

for separate specimens under applied stresses of 1.4, 2.2,

and 3.5 MPa, respectively. The lines represent the log, of Eq. 2 fitted by a lectst squares method.

Fig. 6. Time exponent (m) as the slope of log, of creep

strain vs log, of time at various temperatures of a magnesium chromite refractory under applied stress of 3.5

MPa in nitrogen. The circles, triangles, and squares denote

observed values for separate specimens at temperatures of 1400, 1500, and 1600®C, respectively. The lines represent

the log, of Eq. 2 fitted by a least squares method.

227

12
Fig. 7. Stress exponent (n) as the slope of log* of stress for a magnesium chromite refractory in nitrogen. The circles are observed strain rates that were temperature corrected

to 1500®C, using the fitted value (Q) in Eq. 4, and the line represents the log* of Eq. 4 fitted by a least squares method.

1000/T

Fig. 8. Activation energy (Q) as the slope ( - Q/R) of

log, of strain rate at 0.01 creep strain vs absolute reciprocal

temperature for a magnesium chromite refractory in nitrogen. The circles are observed strain rates that were stress corrected to 3.5 MPa, using the fitted value (n) in Eq. 4, and

the line represents the log, of Eq. 4 fitted by a least squares method.

228

13
JOURNAL OF MATERIALS SCIENCE 21 ( 1986) 810-824

Creep and fracture of a vitreous-bonded

aluminium oxide

S. M. WIEDERHORN, B. J. HOCKEY, R. F. KRAUSE, Jr

National Bureau of Standards, Gaithersburg, Maryland 20899,. USA

K. JAKUS

University of Massachusetts, Amherst Massachusetts 01003, USA

Creep and creep-rupture behaviour of a commercial grade of glass-bonded, 96% aluminum

oxide was characterized as a function of temperature and applied stress. The creep data were

fitted to the classical empirical relation usually used to describe this phenomenon. The

apparent activation enthalpy, A/f = 926 kJ mol"’, and the stress exponent, n = 4.8, lie at the

high end of the range reported for two-phase materials, primarily as a result of structural

modifications that occur during creep. A stress-modified Monkman-Grant relationship was

fitted to the creep-rupture data to give a stress exponent of -4.2. None of the available

theories of creep rupture provided a satisfactory description of the present set of data. Analytical electron microscopy was used to characterize the composition and structure of this

material. In the as-received material the intergranular phase was a glass of nearly uniform

composition. During high-temperature exposure, devitrification of the glass resulted in the

formation of various crystalline phases within the intergranular region of the material. Devitrification depended on both the proximity to the surface, where it was most pronounced, and on the state of stress. In this regard, flexural creep samples exhibited extensive crystallization

within the tensile region of the flexural specimens, but little crystallization within the compressive cross-section. From the composition of the retained glass, estimates of the viscosity

of the glass at the grain boundaries were made and used, in combination with microstructural

information, to compare the creep behaviour with available theories of creep. The results of

this paper are consistent with percolation and solution precipitation mechanisms of creep

deformation. By contrast cavitation did not seem to play a major role in the creep deformation

process.

1. Introduction

Current interest in the mechanical behaviour of multiphase ceramics has its origin in the potential use of

these materials in high-temperattire structural applications. In the automotive industry, for example, two- phase ceramics such as sintered silicon nitride and

glass-bonded cordierite are being used as structural materials for combustors, turbines, turbochargers and

heat regenerators [1]. In the power industry, two- phase materials are being considered for heat

recouperators and for linings in slagging gasifiers [2]. In these applications, the mechanical response of the ceramic to external forces depends on the microstructure, in particular on the refractoriness and chemical

activity of the phases that make up the ceramic. Most

high-temperature structural ceramics consist of highly

refractory grains bonded by a less refractory vitreous

intergranular phase. Therefore, creep and creep rupture of these materials depend primarily on the

physical and chemical properties of the vitreous phase

and on the amount and distribution of the vitreous

phase within the ceramic structure. Because of the importance of the intergranular

vitreous phase for the structural integrity of hightemperattire ceramics, most recent studies on these materials have concentrated on characterizing the behaviour of the vitreous phase as a means of understanding the behaviour of the ceramic composite.

Thus, Lange et al. [3] have shown how the compressive

creep behaviour of silicon nitride can be modified by

changing the composition and volume fraction of the

glassy phase vdthin hot-pressed silicon nitride. These

authors also demonstrated that high-temperature

exposure, which removes glass modifiers from the vitreous matrix, also greatly reduces the susceptibility

of the hot-pressed silicon nitride to creep [4]. These

findings reinforced earlier findings of Kossowsky,

Miller and Diaz [5], who showed that glass modifiers,

such as calcium, reduce the viscosity of glass and

therefore increase the susceptibility of hot-pressed sili- con nitride to creep. Similar findings were made by

others on porcelains [6], fire bricks [7] and glass

ceramics [8]. Despite our general understanding of the import- ance of glass composition and structure in creep and

fracture, it is only now with the development of high

resolution analytical microscopy that the chemical

composition of the glass bonding phase can be deter810 14 0022-2461/86 S03.00 + .12 © 1986 Chapman and Hall Ltd.
mined. Evaluation of the glass composition opens the

possibility of estimating physical properties of the

glass matrix, such as diffusivity or viscosity, which are required for the critical evaluation of most theories of

creep and creep rupture. By analysing the composition

of the vitreous matrix, these physical properties can

either be determined experimentally on a similar composition of glass, or estimated theoretically, and a

direct comparison between these theories of creep and

creep rupture, and experimental creep and creep- rupture data, can then be made.

In this paper analytical electron microscopy is used

to elucidate the creep and creep-rupture behaviour of

a commercial grade of vitreous bonded aluminum

oxide. The chemical composition of the glass bonding

phase is determined before and after static annealing

and creep deformation. From the chemical compositions, theoretical estimates of the viscosity of the

glasses are made in order to compare creep and creep- rupture theory with experimental data. The electron microscope is also used in a more classical way: as a method of identifying changes in the microstructure

that occur during creep. Using these methods, the creep rate is shown to be determined by the viscosity

of the glass, suggesting that viscous flow and/or solu- tion precipitation contribute to the creep process. Although cavitation is not observed to occur homogeneously in our specimens, cavitation at select boundaries foUowed by crack growth is believed to be

important in later stages of the creep process.

2. Experimental procedure

Creep and creep-rupture experiments were conducted on a commercial grade of vitreous bonded aluminum

oxide, COORS AD-96,* reported to contain 96% alu- minum oxide. Experiments were conducted using

four-point bending as a test technique. This technique was selected for ease of testing and for the fact that specimens for the electron microscope could be

obtained from the tensile and compressive portions of

the same specimen, thus excluding thermal history

and extent of strain in comparative analysis. Creeptest specimens, 3 mm high and Smm wide, were

loaded on a bending flxture of silicon carbide with

outer and inner loading points of 40 and 10 mm,

respectively. Approximately half the specimens were

polished on the tensile surface to permit identiflcation of incipient failure sites and crack nuclei as they

formed during creep. Dead-weight loads from 40 to 100 N were applied via a lubricated rubber diaphragm

air cylinder, which, in combination with a two-step,

continuous leak pressure regulator, was capable of

maintaining the applied load to within + 1 .5 N. Stress and strain were calculated by the procedure given by

Hollenberg et al. [9], assuming a stress exponent of

unity. No further corrections to the estimated stresses and strains were made in the present paper. The loading point displacement during creep was

monitored by a linear voltage displacement transducer

(LVDT) that was attached to the upper ram of the test equipment. The loading point displacement of speci- mens was measured to within ± 2/im. To enhance the long-term accuracy of the displacement readings, a block of sintered silicon carbide, of the same grade as that used for the rams, was used in one of the three test stations in each furnace. Since the block did not undergo creep at the loads and temperatures used in the present study, any displacement measured by the LDVT on the block reflected changes in the test facility due to electronic drift or to fluctuations in the ambient temperature. These displacement fluctuations were subtracted from the displacements measured on

the specimens in the other two stations of the same

furnace, so as to minimize errors due to electronic drift or to differential thermal expansion of the test flxture. Even though two specimens were tested in the same

furnace for each nm, the failure of one specimen was

never observed to affect the other in the course of our

investigation, primarily because pneumatic pistons

and rubber shock absorbers were used to restrain the propagation of stress waves.^ Recognizing that phase changes often occur in ceramics during extended high-temperature exposure

[6, 7], most specimens were annealed at 1050° C for a

period of 96 h before testing to stabilize the ceramic

against composition or structural changes that might

influence the creep behaviour. Since most of the creep

studies in this programme were typically less than

100 h duration, it was hoped that this annealing period

would be sufficient to ensure a constant structure for the present investigation. Despite this precaution, some phase changes were observed during creep. The

affect of annealing on both creep and microstructure

represents an important aspect of our results, and

accordingly will be discussed extensively below.

To establish the temperature range to be investi- gated, a stepped-temperature creep test [10] was con- ducted using an initial applied stress of 60 MPa, which was approximately one-third of the reported breaking

stress at 1000° C. In this test a constant load was

applied to the specimen, and the temperature was

increased at various time intervals either until failure occurred, or deformation was so severe that further creep was pointless. Significant creep activity for this material starts at approximately 950° C; at 1050° C the creep of the ceramic is relatively rapid, failure occurring in approximatey 24 h at approximately 0.14%

strain. Based on these results, experiments were con- ducted at temperatures ranging from 980 to 1 100° C,

and at applied stresses ranging from 40 to 100 MPa.

Specimens for examination by transmission elec- tron microscopy (TEM) were obtained from the deformed bend bars using standard sectioning, polishing and ion-milling techniques. Two types of sections were used in these studies (Fig. I). Specimens with the major plane of the foil parallel to the plane of maximum tensile or compressive stress were used to analvse the near-surface regions of the specimen, i.e.

•Coors Porcelain Co., 600 Ninth Street. Golden. Colorado. Identification of this material is not to be construed as endorsement by the National Bureau of Standards.

* Bellows are a non-inertial method of loading the specimens, and the air gaps in the bellows do not permit the passage of a stress wave. Hence, when a specimen breaks, the stress waves resulting from the fracture are largely dissipated before reaching the second specimen.

15

811
Ftpire I Schematic diagram of bend bar showing regions from

which thin sections were prepared for examination by transmission

electron microscopy.

from 0 to 50 /xm from the external surface. Specimens

with the plane of the foil perpendicular to the bending

axes were used to examine changes in composition and

structure at greater distances (0.2 to 1 mm) from the

tensile or compressive surfaces of the creep specimens.

This orientation was selected to examine the ceramic

structure as a function of distance from the tensile and

compressive surfaces of the bend bars.

3. Experimental results

3.1. Microstructure

A representative view of the material used in this study

is shown in Fig. 2. The material consists principally of

aluminum oxide grains (A) bonded by an inter- granular glassy phase (M). Interspersed throughout

the material there are also abnormally large grains of

spinel (MgAljO*), S, ranging in size from 20 to 40 /xm,

and irregularly shaped tjores of microscopic (5 to 10;xm) dimensions. Us? :'-^? the line-intercept method,

the mean grain size of jO} was determined to be

3 jxm, but ranged from 3 ,o 20 /xm. The volume frac- tion of intergranular glassy phase, which was located

primarily at multi-grain junctions, was roughly 8%.

The porosity of the material was also roughly 8% by

volume.

In applying TEM, major emphasis was placed on

determining the structure and chemical composition

of the intergranular phase. Chemical compositions were determined by energy dispersive X-ray analysis

(EDX) using the ratio method in the thin-foil approximation [11] after background subtraction by linear extrapolation. The required K values for the various

oxides* were determined from spectra obtained from

two glass standards (Table I), which were also prepared by ion milling. In all cases, spectra from

either the standards or the unknowns were taken

under similar conditions (beam current, beam size, angle of tilt, etc.), a precaution necessitated by the presence of sodium in both the glass bonding phase

and in one of the crystalline products of devitrification. The highly volatile nature of sodium during

electron irradiation, moreover, placed severe restric- tions on the imposed electron beam flux and duration

of exposure. Most generally, this precluded the use of

a focused probe regardless of other operating conditions and required the use of defocused beams of

(typically) 400 /xm or greater in diameter. While many

grain-boundary widths were considerably smaller than this limiting probe size, most joined continuously

with triple junctions of larger dimensions. As a check on spacial resolution, “hole count” spectra obtained

from etched-out grain boundaries and triple junctions

showed only an insignificant aluminum intensity

enhancement, while differences in the elemental composition of the various intergranular phases allowed

for a ready check on possible “overlap”. In all cases, chemical compositions are given in terms of average

values obtained from at least ten determinations.

Transmission electron microscopy provided not only a more detailed view of the microstructure, but

also revealed that pronounced changes occur within

the intergranular bonding phase due to prolonged

static annealing and creep. In the as-received material, the intergranular bonding phase was found to consist

entirely of a glass (Fig. 3). EDX analyses of the glass

found at triple junctions (Fig. 3a), two-grain boundaries (Fig. 3b), and larger multi-grain junctions or “pockets” gave a fairly uniform composition listed in Table II. Though not particularly evident in Fig. 3. most AI2O3 grains were separated by a glass film

Figure 2 Light micrograph of longitudinal cross- section from creep sample. Relief polishing distin- guishes intergranular phase (M) from aluminium

oxide grains (A) and abnormally large spinel grains

(S). Also evident are large pores, inherent in the material. Arrow indicates tensile creep crack that extends part way through the sample. Note that crack path is entirely intergranular.

t It was assumed that all constituents were present as stoichiometric oxides. 16 812
TABLE I Glasses used for calibration purposes in the present study

Glass Component (wt fraction)

SiOj A1,0, B,0, FeO Na,0 K.,0 MgO CaO

Soda- lime silica 0.72 0.02 — - 0.14 0.01 0.04 0.07 K-412* 0.45 0.09 - 0.10 - - 0.19 0.L5 CI720^ 0.62 0.17 0.05 — 0.01 - 0.07 0.08 coosot 0.73 0.01 - - 0.17 - 0.04 0.05 *NBS Standard Reference Material, SRM 470. Compositions in the standard are reported to better than two significant figures. ^Coming Glass Co. See Hutchins and Harrington [21] for compositions. The use of this glass does not imply endorsement by the National Bureau of Standards.

which, due to the irregtilar morphology of the AI2O3

grains, ranged in thickness from roughly lOnm

upwards of several tenths of a micrometre. In this regard, the relatively wide, glassy grain-boundary

region — as well as the apparent AljO} surface facet- ing — seen in Fig. 3b was not uncommon. The results thus indicate that, in the as-received condition, the bonding phase can be regarded as a continuously

linked, glassy structure. Upon prolonged annealing (1050°C, 96 h), pro- nounced changes were found within the bonding phase

due to partial devitrification of the glass. Specifically, devitrification results in the formation of various

crystalline phases and, as a consequence, changes the volume fraction and composition of the retained

glassy phase. Although devitrification occurs throughout the samples, it is most pronounced within the

surface regions. Accordingly, results obtained from

the interior and from the surface regions of bulk,

annealed samples are described separately. Within the

interior of annealed samples, analytical electron microscopy revealed only the presence of two different magnesia aluminosilicate phases within the bonding

phase: one having an average composition of 4MgO * AI2O3 • 4Si02 and being isomorphic with orthorhombic

enstatite (MgSi03), the other having an average composition of 2MgO * 2AI2O3 * Si02 and being isomorphic

with monoclinic sapphirine (4MgO * 5AI2O3 * 2Si02).

Moreover, small crystallites of one or both of these phases were found within many, but not all, of the

larger triple junctions or multi-grain “pockets” (Fig.

4a), and never within two-grain boundaries. Because

of this, devitrification results in only a minor decrease

in the volume fraction of the glassy phase, (estimated

at less than 10%). This, however, is sufficient to produce a significant change in glass composition

which from Table II is seen to be nearly depleted in MgO. Here it is important to note that the observed

change in glass composition was uniform throughout

the interior of annealed samples, regardless of whether

localized crystallization had occtirred. As indicated earlier, devitrification was especially

pronounced within the surface regions, where it is estimated that from SO to 7S% of the intergranular

glassy phase devitrified during annealing. Although

enhanced formation of both magnesio-aluminosilicate

crystalline phases at the surface played a role in reducing the volume fraction of glass, the reduction of the

glass fraction was primarily related to the formation

of a triclinic, sodium-calcium aluminosilicate phase

identified by electron diffraction and chemical analyses (Table II) as intermedite plagioclase.* Unlike the magnesio-aluminosilicate phases, the intermedite

plagioclase formed more uniformly throughout the intergranular regions and often resulted in the (apparently) complete crystallization of two-grain

TABLE II Chemical analysis of residual glass at grain boundaries of AO-% aluminum oxide

Treatment Composition (mol %)

NajO MgO CaO AljO, SiO,

As-received 5.03 (1.25)* 11.21 (1.63) 2.77 (0.37) 16.11 (0.91) 64.88 (2.33) Annealed^ 5.05 (0.86) 3.37 (0.35) 3.72 (0.44) 16.09 (0.76) 71.78 (1.80) (unstressed

material) Annealed 4.41 (1.85) 2.50 (0.76) 0.66 (0.16) 14.60 (0.96) 77.78 (3.13) (lOO/im thin section) Tensile surface 3.52(1.44) 2.74 (0.39 0.65 (0.12) 13.42 (0.45) 79.67 (1,49) Tensile surface 3.66(1.09) 2.62 (0.04) 0.92 (0.17) 14.13 (0.63) 78.52 (1.65) Compressive 3.61 (0.67) 3.02 (0.65) 0.92 (0.13) 14.70 (0.47) 77.75 (1.42) surface Tensile section 2.83 (1.73) 3.03 (0.82 1.97 (0.55) 15.26 (0.90) 76.% (2.36) Compressive 3.24 (1.78) 3.31 (0.72) 3.44 (0.40) 16.48 (1.17) 73.59 (2.46) section *The standard deviation of each measurement is given in piarentheses. ^Annealed for %h at 1044'' C, then subjected to creep for — SO h at an initial applied stress of 60 MPa. The unstressed material was taken from the end of the specimen.

^e chemical composition of members of the plagioclase series is generally given in terms of its pure end-members anorthite (An), CaAIjSijO, and albite (Ab), NaAISi,0,. On this basis, the average composition listed in Table II corresponds to 50% Ab 50% An.

although considerable variations in compositions and a systematic calcium deficiency were observed. 17 813
Figurt 3 TEM illustratiiig microstnjctuie of vitreous bonded alumina in as-received condition, (a) Representative view showing non-uniform morphology of aluminium oxide grains and glassy binder phase at triple junctions, (b) Enlarged view of structureless glassy phase at triple junctions and between widely separated grains. Surface faceting of aluminium oxide grains evident in (b) was characteristic feature of

vitreous-bonded material.

boundaries and multi-grain junctions (Fig. 4b). Moreover, the additional crystallization of plagioclase

within the siuface regions results in a retained glass

phase composition (Table II) which is more silica-like, and hence is different from the glass phase found

within the interior. To a large extent, analytical electron microscopy

results for annealed samples provide a basis for summarizing the differences in microstructures found

within samples that were preannealed at 1050° C and

then deformed in creep to —0.1 % strain at an applied

stress of 60 MPa. Particular emphasis is again placed on the intergranular regions, since this is where

deformation occurs. With reference to Fig. 1, samples

taken from within 100 jon of the tensile and compressive surfaces of deformed samples were virtually

indistinguishable from each other and from those

from the surfaces of statically annealed samples. In

each, the intergranular binder phase was largely

crystalline (again estimated as up to 75% of binder

phase volume), due to the formation magnesioaluminosilicates and intermediate plagioclase. From

Table II, the compositions of retained glass in the surface intergranular regions were also quite similar. Tensile surface sections were, however, marked by the occasional presence of stoichiometric, orthorhombic

cordierite and, in samples where the original surface was retained, by the presence of discrete magnesioaluminosilicate crystallites along the periphery of twograin boundaries and multi-grain junctions. By scan- ning electron microscopy (SEM) these crystallites were determined to lie on the surface, thus indicating a transfer of material from the interior to the tensile surface. Further examination of deformed samples, using

longitudinal cross-sections (Fig. 1), provided clear evidence that the stresses developed during testing

have a significant effect on the devitrification process, and hence on the structure and composition of the intergranular bonding phase. Within the tensile regions, extensive devitrification of the glass binder

phase resulting in 50 to 70% crystallization, extending

to distances of approximately one-fourth the sample

thickness, the limit of observations (Fig. 5). In con-

;

I

Figure 4 TEM results, (a) Discrete crystallites of magnesio-aluminosilicate phases (see text for description) produced within multi-grain junction after prolonged heat treatment at 1050° C. Nature and extent of crystallization typifies partial devitrification of glassy binder phase

that occurs within interior of bulk samples, (b) Fully crystallized integranular structure typically produced within near-surface regions after similar heat treatment. More complete devitrification is related to additional formation of intermediate plagioclase. As described in text, (a)

is also typical of compressive subsurface regions and (b) typical of tensile subsurface regions after flexural creep. 814 18
trast, the degree of devitrification diminished rapidly

below the compressive surface, and at a depth corre- sponding to one-tenth the sample thickness the bonding

phase was essentially glassy. Within the compressive

regions, the structiuv and composition of the bonding

phase was, in fact, nearly identical to that found

within the interior of bulk annealed samples, whereas

within the subsurface tensile region it closely

resembled that found at the surface. These results suggest a net increase in specific volume of the bonding phase (i.e. the combined volume change of the

glass and crystalline phases at the grain boundaries) as a result of the devitrification process. Thus, devitrifi- cation would be enhanced in the tensile cross-section

of the specimen, and retarded in the compressive

cross-section of the specimen.^

Creep samples were also examined for evidence of

void or cavity formation within the intergranular

phase. In contrast to earlier results for hot-pressed

Figure 5 TEM results. Examples of crystallized grain boundary

structures, invariably intermediate plagioclase, produced within

tensile regions of flexural creep samples.

silicon nitride (tested in both tension and compression) [3, S, 13-15] and for a glass-bonded alumina

(tested in compression) [16], definitive evidence for widespread cavitation was not found.^ Nevertheless,

observations on tensile surface regions by SEM (Fig.

6a) clearly showed intergranular cavitation, though it was generally restricted to the neighborhood of well- developed creep cracks. In addition, TEM studies on

similar tensile surface sections revealed occasional evi- dence of grain-boundary delamination in the form of narrow plate-like cavities (Fig. 6b). While it appears

clear that grain-boundary delamination eventually

leads to the formation of fully developed cracks that are responsible for creep rupture, the necessary conditions and processes involved in crack formation

remain the object of continuing study.

3.2. Creep data

Examples of creep data obtained in the present exper- iments are illustrated in Figs. 7 and 8. There was little indication of Stage 3 creep prior to failure in any of the creep tests. Failure often occurred without any change

in the creep rate, suggesting that a second process, such as rapid crack growth, abruptly cuts off the normal creep process in these specimens. Sometimes a

slight increase in the creep rate is observed just before

Figure 6 (a) SEM illustrating cavitation at grain boundaries and triple junctions in vicinity of developing creep crack on tensile surface, (b) TEM showing plate-like cavities at inclined grain boundary after creep deformation. Formation and growth of such cavities is considered

responsible for intergranular creep crack extension.

^The thermodynamics of devitrification of grain boundaries has been discussed recently in some detail by Raj and Lange (12).

^ While cavity-like holes were often found within multi-grain junctions even in thick regions of TEM samples, they were similarly present

in tested and untested samples and are, therefore, attributed to preferential ion-thinning. 19 815
Time (min) Time (h)

Figun 7 Creep of AD-96 alumina under an applied stress of 60 MPa at 1044° C. (a) No prior annealing. Note that failure occurred within 30min of initial load application for both specimens, (b) Specimen annealed for 96h at 1044° C prior to testing. Annealing results in an

approximate two hundred-fold increase in specimen lifetime, primarily as a consequence of grain-boundary devitrification.

failure, but the sort of creep-rate enhancement often reported for structural metals does not occur for this ceramic. This slight increase in creep rate is probably

due to an increase in specimen compliance resulting

from rapid crack growth.

Considerable run-to-nm scatter was observed in the

failure times for a given test condition, even when

specimens were tested simultaneously in the same

furnace. Scatter in the failure times by as much as a

factor of three was not uncommon. By contrast, the minimum creep rate for a given test condition was

relatively constant from run to run. Finally, annealing

has an enormous effect on the creep behaviour of this material. The annealing treatment of 96 h at ^ 1050° C decreased the creep rate and increased the

lifetime by a factor of almost 100 (Fig. 7). As will be

disctissed below, this decrease in the creep rate can be

directly attributed to devitrification and to the changes in the volume fraction and the viscosity of the

glass at grain boundaries.

The creep data illustrated in Figs. 7 and 8 may be

summarized by expressing the minimum strain rate, s, as a fimction of applied stress, a, and temperature, T:

c » Aialat^y ^HIRT) (1)

where is the gas constant and A, n and are

empirically determined constants. The constant A has

units of h~' and the normalization constant, for the stress has units of MPa. In the present experiment

the constants A, n and A/f were determined by a

least-squares fit of Equation 1 to 28 sets of the exper- imental data. The values of these constants and their standard deviations are In = 53.6 ± 5.0; n =

4.85 ± 0.45; A/f = 926 ± 58kJmol~‘. The stan- dard deviation of the fit was approximately ± 0.45.

3.3. Creep-rupture behaviour

The creep-rupture data obtained in the present exper- iments are summarized in Fig. 9, where the logarithm

of the minimum creep rate is plotted as a function of

the logarithm of the rupture time. As can be seen from

this figtire, there is a negative correlation between the minimum strain rate and the time to failure. If the

failiue time is expressed as a power function of the minimum strain rate, then the data shown in Fig. 9 can be expressed by the following equation:

ti“ = b (2) where the constants and their standard deviations.

Time (h)

Figure 8 Comparison of short- and long-term creep of AD-96 alumina at 1044° C; initial applied load (a) 80 MPa, (b) 40 MPa. In neither creep measurement could a distinct steady-state region be identified. This is particularly true for the long term runs (b), which suggest continual work-hardening. The upper curve in (b) was in an advanced state of fracture and yet gave no indication of Stage 3 behaviour. In the other creep curves of Figs. 7 and 8, the initial and final stages of creep tend to overlap. 20 816
Rupturt tiiM, t (h)

Figure 9 Creq>-rupture data fitted to a Monkman-Grant type of

plot for AD-96 aluminium oxide.

a = 1.10 ± 0.11 and In b = —8.97 ± 0.13, were

obtained by a linear regression analysis of In t upon

In e for 21 sets of data. The standard deviation of the

fit was approximately 0.72. Equation 2 is the Monkman-Grant [17] equation, first used to describe

the creep of metals. The exponent, a, in this equation

is not significantly different from 1, the value usually

used to describe creep. The variance of the data about the regression line in Fig. 9 can be reduced significantly if temperature

and/or applied stress are introduced as variables. This

is illustrated in Fig. 10 where the data from Fig. 9 have

been replotted and identified as either constant temperature (Fig. 10a) or constant stress (Fig. 10b) data. In both representations, the data are observed to be

layered: the points lie on straight lines of either constant temperature or constant stress. Furthermore, it can be seen that the scatter of the data about the lines, in either representation, appears to be less than that given by the Monkman-Grant relation, indicating the importance of temperature and stress as experimental

variables. The introduction of temperature and applied stress into the analysis can be quantified by assuming that

the creep rupture data fit an empirical equation of the following type:

By taking the natural logarithm of both sides of the above equation, the equation can be linearized and the constants a, B, m and A//' can be determined by a

linear regression analysis of the data. The results of

this analysis are given in Table III. A large and signifi- cant dependence of ti on applied stress and temperature indicates that some of the variance in Fig. 9 can be attributed to a variation in these two par- ameters. In fact, the standard deviation of the fit, ± 0.34, is reduced by a factor of approximately onehalf by taking temperature and stress into account.

3.4. Strain at failure

Another relationship that can be obtained from the creep-rupture data is that of the maximum strain to

failure. In the metals literature, the assumption of a constant maximum strain to failure is often used as a

criterion for failure [18]. The unmodified MonkmanGrant relation of Equation 2, for example, is essentially a constant strain to failtire criterion. By plotting the strain to failure as a fimction of other test vari- ables, it should be possible to provide additional data

for comparing creep and creep-rupture data with

theory. In Fig. 11, the total strain to failure is plotted as a function of the applied stress.* Although the scatter of

the data is considerable, the figure suggests a negative

correlation between these two variables, so that as the

stress applied to the specimen is decreased the failure strain is observed to increase. This correlation is sup- ported by data collected on two other specimens

loaded at 40 MPa and 1044° C for a period of 350 h. Although they did not fail, the strains on the speci- mens at the time the tests were discontinued were 0. 17 and 0.21%, which were greater than any of the failure strains indicated in Fig. 1 1 . Similar observations were made by Clarke [16], who also noted that failure shown in compressive creep correlated inversely with

applied stress.

4. Discussion

4.1. Grain-boundary viscosity

In the temperature range used in the present investi- gation, all but a few high-silica glasses behave as viscous liquids. Therefore, the glasses at grain boundaries in the present study are also most likely to be

liquid, and liquid-enhanced creep undoubtedly dominates the creep results presented in this paper. In all of

ti‘ = B<r exp I RT) (3) the theories developed to describe the effect of inter- TABLE III Summary ofcreep-rupture data*

In B a m

(kJ mol”‘)

Standard

deviation of fit

Degrees of freedom

-7.95 (0.1 6)t 1 (assumed) 0 (assumed) 0 (assumed) 0.71 20 -8.97 (0.13) l.l (0.1) 0 (assumed) 0 (assumed) 0.72 19 -7.6 (3.6) 1 (assumed) -4.2 (0.56) 195 (54.0) 0.334 18 -8.0 (7.9) 1.0 (0.1) -4.2 (0.94) 200(141.3) 0.344 17 *Oata fitted to the logarithmic form of Equation 3: In t In B - a In 2 + /n In <r — \H!RT.

^Standard deviation given in parentheses.

*The total strain at failure includes that determined from the minimum creep rate (ti) and that determined from the transient portion of

the creep curve. The total strain ranged from ~ I.S to — 2.S ti. 21

ft17
Figure 10 Creep-rupture dau for AD-96 plotted as in Fig. 9, but identifying points of either (a) constant temperature, or (b) constant applied

stress; (v) 980“ C, (O) 1000“ C. (O) 1030“ C. (Q) 1050“ C. (a) 1100“C.

granular liquids on creep deformation, the viscosity of

the liquid is an important variable which should be

evaluated to fully understand the creep process. Therefore, in this section the viscosity of the inter- granular glass is calculated from its composition. In

the next section, these calculated viscosities are used to evaluate mechanisms of creep. The viscosities of the vitreous grain-boundary

phases were estimated from the compositions given in Table III, by using empirical equations developed by

Urbain et al. [19] for this purpose. These equations were developed from experimental data on a series of

calcia-alumina-silica glass melts, and were tested on a number of slags and glasses for which the equations gave values of viscosity that agreed with exper- imental measurements to within a factor of 5 [20]. The

equations were, however, developed for the low vis- cosity range < 10^ Pa sec, so that agreement between

these equations and experimental data is not expected over the entire range of viscosities.

Figure II Strain to failure as a function of initial applied stress. 818 22

Before using the equations of Urbain et al. [19] on

the present set of data, the equations were applied to commercial glasses with known compositions and vis- cosities. The glasses selected for comparison were made by the Coming Glass Works (Houghton Park. Coming, New York) and have the composition indi- cated in Table I [21]. The calculated and experimental

values of the viscosity for C0080 glass, (Fig. 12) agree

to within an order of magnitude for the viscosity range

10“ Pa sec (530° C) to 10^ Pa sec (1000° C), which was

almost the entire practical range of viscosities for annealing and forming this glass. For Cl 720 (Fig. 12) an order-of-magnitude agreement between calculated and measured viscosity is obtained for viscosities lying

between 10^ Pa sec (900° C) and 1 Pa sec (1200°C).

Figure 12 Viscosiiy of two commercial glasses compared with vis- cosities calculated from the equations of Urbain et al. [I9|.
Figure 13 Calculated viscosities of gia«« composition given in Table III. The insert shows how the glass viscosity changes from the tensile to the compressive cross-section of the bend bars at a temperature of 1044° C.

This agreement between calculated and measured vis- cosides is considered reasonable for the present study.

The viscosides of the glass composidons given in Table III arc shown in Fig. 13. The figure demonstrates the rather sizeable effect of annealing and

deformadon on the viscosides of these glasses. At any

given temperature, changes by a factor of ten in vis- cosity are observed as a consequence of annealing and

creep deformadon. This increase in glass viscosity

should reduce the creep rate of the annealed specimens

by a commensurate amount, because the creep rate is inversely propordonal to the viscosity in most theories of creep. Similarly, the addidonal factor of ~ 10

increase in the glass viscosity in both the tensile and

compressive surfaces of the annealed specimens suggests that the surface of the specimens are more resist- ant to creep than the body of the specimens. This

finding raises the possibility of surface embrittlement

as a consequence of devitrificadon during annealing.

The difference in composidon of the glass in the

tensile and compressive cross-sections suggests a dif- ference in viscosity of the glasses in these cross- secdons. Using the formuladon of Urbain et al. [19], the viscosity of the glass in the tensile cross-section is calculated to be approximatly a factor of three greater

than that in the compressive cross-secdon. The

presence of crystalline material at the grain boundaries of the tensile cross-section magnifies the viscosity difference even further, so that the effective viscosity

of grain boundaries that have been devitrified will be

greater than that indicated by the viscosity of the glass alone. Thus, the effective viscosity of the material at the grain boundaries in the tensile cross-section should be more than a factor of three greater than the

effective viscosity of the material at the grain boundaries of the compressive cross-section.

These effects of composidon on viscosity have

interesdng implicadons with regard to the effects of

the state of stress on the creep rate. If the effective grain-boundary viscosity were the sole determinant of

creep rate, then one would expect tensile specimens to be more creep-resistant than compressive test speci- mens, for an equivalent temperature and applied

stress. In fact, experimental studies on this subject

reach the opposite conclusion; creep occurs more

easily in tension than in compression [22]. Therefore,

while grain-boundary viscosity is important, it is not

the only physical or structural parameter determining

the creep rate. The overall rheology of the test speci- men vis-a-vis the state of stress must also be considered. Creep no doubt depends on details of the microstructure such as level of agglomeradon, level of

homogeneity and amount of direct contact between

grains of the microstructiire. These effects of microstructure have not yet been considered for ceramic

materials. In fact, most theories of creep assume a homogeneous microstructure, an assumpdon that is clearly not consistent with the structure of most

materials investigated. Thus, while intergranular vis- cosity is probably of paramount importance in deter- mining the creep rate of a component subjected to a

particular state of stress, other factors must be considered when the state of stress is a variable. The effect of devitrification on the creep rate can be

quantified by comparing the creep rate of the annealed

specimens with that of the as-received specimens. At

1044°C and an inidal applied load of 60 MPa. a hundred-fold decrease in the creep rate is observed

upon annealing the specimens. Based on most theories of creep, this result suggests a factor of 100 decrease in the effective grain-boundary viscosity. Since the vis- cosity of the glass at the grain boundaries decreases by

23 819
only a factor of ten due to annealing, a change in glass

composition alone cannot explain the decrease in creep rate. Crystallization of the grain boundaries

effectively increases the average viscosity of the grainboundary phase by another factor of ten, and in this way decreases the creep rate of the specimens.

4.2. Models of creep

The simplest model of liquid-enhanced creep is that of

lubricated flow wherein the grain-boundary glass

behaves as a lubricant, reducing the friction between

grains. For an applied deviatoric stress a, the creep

rate i is given as a function of grain size d, grain

boundary thickness w and viscosity rj [23]:

where a is a constant having a value of approximately

Substituting 5 = 40 MPa, d = 8/mi, = 10* Pa

sec (the value for the annealed specimen at 1040° C)

into Eqtiation 1, we obtain a calculated value of the grain boundary thickness, w, of 1.8 x 10~'^m for a

creep rate of 3 x 10"’ sec" ‘ (60 MPa applied stress, 1040° C). This estimated value of w is of course subatomic, indicating that frictional forces at grain

boundaries provide almost no impediment to the

creep process. Therefore, lubricated flow cannot

possibly be an acceptable mechanism for the creep

results in the present study. As noted by others [23,

24], lubricated flow is probably never an explanation

for liquid-enhanced creep because the mechanism

does not take into account the complexity of the microstructure for most materials. Grains that form

the microstructure do not lie in ordered planes, as assiuned in the model of lubricated flow. When subjected to stress, grains tend to lock up as the solid is deformed, greatly increasing the forces required to maintain a given rate of creep. In this way, the material work-hardens. For flow to continue, i.e. for the grains to slide over one another, an increase in the volvune (a dilatation) must occur [2S, 26]. Therefore, if liquid lubrication were the only possible process, creep would become more and more difficult as the strain increased and the creep would eventually stop. In fact, creep continues because there are mechanisms of

accommodation that relieve the stresses caused by the volume expansion. In the order to be discussed below

these mechanisms include (a) fluid flow or percolation,

(b) pressure solution or sqlution precipitation, and (c) grain-boundary cavitation. Percolation, or fluid flow, was first mentioned as a mechanism of accommodation by Reynolds [25], and

later by Frank [26]. The effect of fluid flow on creep was quantified by Drucker [27] and by Lange [24], who calculated the rate of creep resulting from the

localized flow of liquid from the compressive to the

tensile surfaces of individual grains. The equation

developed by Drucker for the strain rate is

where <r is the applied tensile or compressive stress. 820

The model assumes that the grains lie in a two- dimensional hexagonal array and that flow is homogeneous throughout the material. Substituting exper- imental values of (10* Pa sec), <r(60MPa) and

d (8/im) into this equation yields the following rela- tion between e and w: e/w^ = 6.7 x 10‘*sec"'m"\

from which a grain-boundary thickness of 3.5 nm is calculated for a creep rate of 3 x 10"’ sec"' at 1044° C. This value of the grain-boundary thickness

lies at the lower end of the range normally observed

for glass-bonded aluminum oxide, which suggests that a significant resistance to fluid flow only occurs along

the narrowest boundaries of the composite. During

deformation, glass flows easily from pores or external

siufaces along triple junctions and therefore wide

grain boundaries offer little resistance to fluid flow. By

contrast fluid Sow along narrow grain boundaries is difficult, so that the local stresses will be greatest along

these boundaries. Because of these preferred paths for Suid Sow, deformation of polyphase materials is most

likely non-homogeneous. DevitriScation increases the

difficulty of Suid Sow by increasing the effective grainboundary viscosity by a factor of approximately ten over that calculated for the glass in the annealed

specimens. This increase in viscosity should increase the estimate of the grain-boundary thickness by a

factor of approximately two. Turning now to solution precipitation as a means of

liquid-enhanced creep, two types of mechanism have

been suggested. In one, the grains of the solid are in Srm contact and the driving forces for solution and

precipitation result from the high stress that occurs at contact points [23, 28, 29]. The creep rate can then be

limited either by the kinetics of solution and precipitation. or by the rate of transport from regions of high

to regions of low stress, the transport processes being

driven by the gradient of the chemical potential and its dependence on pressure. These mechanisms were dis- counted in the present experiments because no evi- dence of intergranular contact was found in microstructural analyses of deformed specimens. If contact

sites were present they would appear as well-defined

regions of strain contrast, as has been reported by

Lange et al. [30] in TEM studies of hot-pressed silicon

nitride. Similar patterns of strain contrast due to inter- granular contact have been observed in hot-pressed

silicon nitride in our own laboratory [31]. In the glassbonded aluminum oxide, however, no such strain contrast was observed at grain boundaries in the present

study. Therefore, either the contact sites were not

there, or they were so widely spaced that their obser- vation would have been rare. In this section we assume

that the grains were not in contact, and that each grain

of solid was completely surrounded by glass.

When glass forms a continuous phase around the

grains, then stress gradients within the glass result from the high viscosity of the glass, which resists the imposed forces and prevents the grains from touching.

Solution reprecipitation for this situation has been

analysed by a number of investigators [32-35], and

creep equations similar to the following one by Rutter

[34] have been reported for transport limited processes:

24
naVCoDw

NokTQd^ ( 6)

where V is the molar volume of the solid (AKO,), Q

is the concentration (massvol"') of the diffusing

species in the solution, D is the diffusivity, A^o is Avogadro’s constant, k is Boltzmann’s constant and q

is the density of the solid. In our treatment of creep by solution precipitation, the diffusivity must be estimated in order to evaluate

the creep rate. Usually, the Stokes- Einstein relation

(Z) = kT!6t\nr) is used in solution precipitation

theories to estimate the diffusivity in terms of the

liquid viscosity, t\, and the radius, r, of the diffusing

species. Whereas the Stokes- Einstein relation works

well for liquid metals and molten salts, problems are encountered in its application to liquids, such as

glasses and polymeric melts, that have a network

structure [36]. In these structures, most atoms diffuse through the network. By contrast, viscous flow is determined primarily by the structure of the network,

i.e. by the breaking of network bonds, so that the two

processes may not be closely related, and consequently the errors in estimating the diffusivity can be

large [36, 37]. Thus, before using the Stokes- Einstein

relation, its potential for error should be recognized

and if possible the equation should be assessed on known sets of data. In the present investigation the transport of alumi- num ion, Al^***, probably controls aluminum oxide

diffusion, because its rate of diffusion is much less than that of oxygen, 0^~, in silicate melts [ 38, 39]. To

test the applicability of the Stokes- Einstein relation

to Al^'*', experimental parameters for viscosity and

diffusivity assembled by Cooper and Kingery [39] were used. At 1400° C the diffusivity of AJ^"^ is — 2.6 X 10~’cm^sec"', while the viscosity is 23.3 poise (2.33 Pa sec), from which an ionic radius of — 0.02 nm is calculated. This value is about a factor of

2.5 smaller than that (0.05 nm) estimated by Pauling

[40] from wave-mechanical considerations. The dif- fusivity and the viscosity also appear to have similar temperature dependencies (A/f = — 272 kJ mol” ' for

diffusion and — 229 kJ mol” ' for viscous flow). Based on this comparison, the Stokes- Einstein relation is expected to give an order-of-magnitude estimate for the diffusivity of Al^*^ in the temperature range used

for the present study.

Substituting the Stokes- Einstein equation into Equation 6, the following relation is obtained for the creep rate; ZlaVC^w

SNgtjrQd^

(7)

Using appropriate experimental values (

V

= 25.5 cm^

mol”', Co = 0.625gcm”\ r = 0.02nm, e = 4g

cm”’) in Equation 7, the relation between z and w is given by e/w = 8.7 x 10”^ sec”', from which a grainboundary thickness of 34 nm is calculated for an initial applied stress of 60 MPa at a temperature of 1044° C. This grain-boundary thickness lies within the range of

values observed in the present experiment. In view of

the assumptions made in obtaining this number, the

fact that this estimate of grain-boundary thickness is an order of magnitude greater than that for percolation with the same experimental parameters cannot

be considered significant. Within the accuracy of the models and the material property estimates, therefore, the solution precipitation and the percolation models

of creep must be considered competitive.

Nucleation and growth of cavities within grain

boundaries provides a third mechanism by which

work-hardening resulting from the dilatant behaviour

of the polycrystalline solid can be relieved. Cavitation

is commonly observed as a means of accommodation

in metals, and has been reported in a number of

studies for ceramics tested in tension, bending and

compression [3, 5, 13-16, 20]. Since homogeneous

cavitation was not observed in the present study it must be concluded that cavity formation and growth

did not play a major role during creep deformation.

This conclusion is very different from that reached by

Clarke [16], who found that high-temperature defor- mation of glass-bonded alumina was dominated by

cavitation within the glass phase. The reasons for the

difference between our results and Clarke’s are not

ftiUy understood at the present time, but may reside in differences in the composition and viscosity of the

glasses used in the two studies. Although the two

studies were conducted over roughly the same temperature range, the viscosity of the glass bonding

phase in Clarke’s study was approximately two orders

of magnitude less than in our own study. In fact, the

viscosity of the glass used by Qarke [16] was similar to that of the glass in the unannealed specimens in our smdy. Further studies are indicated to clarify the role of cavitation in the creep process, and the conditions

under which cavitation occurs in two-phase ceramics.

Although extensive cavity nucleation, of the type

reported in the creep-rupture literature, was not observed in the present study, isolated and fairly

widely spaced grain-boundary delaminations were

observed. The delaminations occurred at the tensile surface where the stresses were highest, and where the surfaces were embrittled by extensive devitrification of

glass at the grain boundaries. These delaminations

form preferentially at two grain boundaries where,

according to percolation theories of creep, the stresses are highest. These delaminations may be precursors of

cracks that nucleate in the tensile surface of the speci- men and grow to a critical size during the course of the creep experiment.

4.3. Creep and creep-rupture

phenomenology

Although the initial purpose of this study was to estimate the creep behaviour of a two-phase ceramic

from an analysis of the microstructure of the ceramic,

the extensive collection of creep and creep-rupture

data presented in this paper warrants some brief comment on the data and its comparison with other data

of the same type. In this section, discussion is limited

to vitreous-bonded oxides including refractories, porcelains and glass -ceramics, which are closest in struc- ture to the material used in the present study.

25 001
4.3. 1. Stress exponent

In the present paper the classical power-law creep expression given by Equation 1 was fitted to the creep

data. Both the power-law exponent, n = 4.85, and the apparent activation enthalpy, AH = 926 kJ mol" lie at the high end of values reported for creep processes. Literature values of n range from ~ 1 to 6 depending on the material tested and the level of stress [6, 7, 22,

41, 42]. The value of n tends to increase as the stress

is increased, but does not appear to depend on the sign

of the applied stress, i.e. whether the applied stress is tensile or compressive [20]. In view of these comments,

the value of n obtained in the present experiments is not unusual, even though it lies at the high end of the range of values. Since most theories of creep are linear in applied

stress (n a 1) they cannot be used in unaltered form

to explain non-linear aspects ofcreep or creep rupture.

Most often, investigators have suggested cavitation or microcrack formation as the primary explanation for a high creep exponent [3, 22]. As cavities are formed

the applied stress is transferred from the cavitated to the uncavitated portion of the specimen, and the creep

rate increases as a result of both cavity nucleation and

cavity growth. Since the rate of nucleation and growth

of cavities is basically a non-linear function of applied

stress [14], the creep process is also a non-linear function of stress. Thus, Moreel and Ashbee [22], Lange et

al. [3], Qarke [16] and others have used cavitation as a means of explaining the non-linear dependence of

creep on stress. In the present experiments, no evidence of cavitation at grain boundaries was obtained, and therefore

it is difficult to explain the non-linear creep behaviour

by cavitation. Instead other time-dependent processes such as devitrification and premature termination of

the creep process by fracture are probably responsible

for the observations. The importance of crystallization or devitrification was first noted by Norton [6] in a study of the tensile creep of porcelain. Devitrifica- tion increases the effective viscosity of the grainboundary phase and hence increases the resistance of

a two-phase material to creep deformation. Norton [6] noted that when crystallization has sufficient time to occur, as when the applied loads are low, then the changes in the microstructure increase the amount of

work-hardening and reduce the apparent steady state creep rate. The converse is true at high loads, when

creep is rapid and devitrification does not have sufficient time to occtir. In this case, the apparent steady

state creep rate is higher than would be determined

from a linear dependence of creep rate on applied

load. In addition to the structural effects discussed above,

premature termination of the creep process by speci- men fracture can also play a role in establishing a high

value of the creep exponent n. When crack nucleation

and crack growth are strongly dependent on the applied stress, then the time to failure may depend on

the applied stress in a way that is independent of the creep process. At high levels of applied load, failure is likely to occur in an early stage (i.e. Stage 1) of the creep process, so that the creep rate will be greater

than that obtained if creep were not interrupted by

fracture. By contrast, failure at low levels of applied

stress is likely to occur much later in the creep process

(i.e. Stage 2) so that the two measured creep rates will not correspond to the same portion of the creep curve. The net effect of representing such a set of data by

Equation 1 is to obtain a non-linear dependence of

creep rate on applied stress. In the present experiments both devitrification and

premature specimen failure played a role in establish- ing the high value of n. Creep occurs initially in a

“crack-free” condition; the specimen deforms, workhardens, and then at some point in time grainboundary delamination results in crack formation

and eventtially in specimen failure. The minimum

creep rate achieved during each run depends both on

the devitrification process, and on the crack nucleation and growth process, both of which lead to a non-linear dependence of the creep rate on applied

stress.

4.3.2. Apparent activation enthalpy

Based on the discussions in Sections 4.1 and 4.2, the temperature dependence of the creep rate might be

expected to be determined primarily by the glass vis- cosity, and the dependence of the glass viscosity on

composition. For the glass compositions given in Table II, the apparent activation enthalpy for viscous

flow is estimated to be ^ 330 kJ mol"'. This estimate can be increased somewhat by taking into account changes in glass composition that result from changes

in temperature. The magnitude of this effect is inferred from the net change in composition due to annealing.

From Fig. 13, annealing results in approximately

two orders of magnitude increase in viscosity,

which should increase the estimated value of the apparent activation enthalpy for viscous flow from

'*'330 to '*'550kJmol“', a value that is clearly not enough to explain the high apparent activation enthalpy, 926 kJ mol" ', for creep in the present experi- ment.

This lack of agreement between the estimated and

measured activation enthalpies clearly indicates that

factors other than glass viscosity play a role in establishing the temperature dependence of the creep

process. Grain-boundary devitrification may be one

such factor, since it is known to occur during creep and should have a dramatic influence on the effective viscosity of the grain boundaries. If grain-boundary

devitrification is important, then the enthalpy of solu- tion of grain-boundary phases will contribute to the apparent activation ehthalpy of the creep process. The

importance of the heat of solution in the creep process has been suggested by Raj and Morgan [43] for a number of high-temperature processes in hot-pressed

silicon nitride, and has been applied by Wang and Raj

[44] to explain the high activation energies

( ~ 700 kJ mol" ‘ ) for the creep of glass -ceramics. The

heat of solution is also important when solution precipitation occurs during creep. Further studies will be

required to fully elucidate the importance of grainboundary devitrification in the creep of multiphase

ceramics.

822

26
4.3.3. Creep rupture

The creep-rupture data shown in Figs. 10 and 1 1 were found to fit the modified Monkman-Grant relation given by Equation 3. This equation was selected to represent the creep-rupture data because theoretical work by Evans and Blumenthai [45, 46] have been

represented in this format. Furthermore, the creep- rupture experiments presented by Johnson et al. [47] on direct-bonded aluminum oxide have been shown to

fit this type of equation. In this regard, it may be

significant that the stress exponent of ti obtained by

Johnson et al [47], — 6 ± 2, is close to the value

obtained in our own experiments, —4.2 ± 0.9, despite the great difference in the microstructtires of

the two materials. Most theories that have been developed to; describe

the creep rupture of polycrystalline systems assume a

rather simple microstructure. For two-phase ceramics,

the microstructure is usually viewed as a collection of

equiaxed grains separated by a viscous fluid [14, 45,

48]. For this type of material, models of crack nucleation, crack coalescence and crack growth have been

developed. Generally, these predict a small dependence of ti on applied stress. To be more specific, ti for nucleation-controlled creep rupture is predicted to be

stress-independent. In view of this prediction, crack

nucleation cannot be considered rate-limiting in the present study. For crack-growth controlled fracture,

ti is proportional to where n is the stress exponent for creep and p is the stress exponent for

.crack growth.* From theoretical considerations, Tsai

and Raj [48] suggest p ^ 4 for crack propagation in two-phase materials. Combining p = 4 with the value n = 4.85 measured in the present paper yields a value

for the stress exponent of re, 0.85, which is not consistent with the experimental results of the present paper. Thus, crack growth alone cannot be used to rationalize the present set of creep-rupture data. The remaining theory of creep rupttire, the coalescence theory, is not sufliciently developed to be compared with the present set of data [51]. From the above discussion we must conclude that the theories of two-phase creep fracture that have

been developed to date are not able to explain the

stress dependence of ti for the current set of data. In view of the complexity of the material used in the present investigation, this finding is not. perhaps, surprising. Alteration of the material by stress-dependent

devitrification undoubtedly plays a role in both the nucleation and crack-growth processes. Additional

theoretical work is clearly needed to model the effect of devitrification on crack growth and crack nucleation. In addition, microscopic studies will be needed

to elucidate the importance of nucleation and of subcritical crack growth to the failure process.

5. Summary

This paper presents the results of an investigation of

the creep and creep rupture of a commercial grade of

glass-bonded aluminum oxide. Analytical electron

microscopy was used to evaluate the chemical composition of glass at the grain boundaries, and the

variation of the composition of the glass with exposure

to elevated temperature and creep deformation. The

type and degree of devitrification that occurred during

creep clearly appeared to be stress-dependent. The

glass at grain boundaries in the tensile cross-section of

the test specimens was approximately three times as viscous as the glass in the compressive section of the

test specimen. This finding is consistent with the pattern of devitrification observed in these specimens.

Devitrification was greatest at the tensile surface, which

suggests an embrittlement of the surface compared

with the rest of the specimen cross-section. The viscosity of the glass at the grain boundaries was estimated from its chemical composition and was

used to compare the measured creep rates in the present study with models that have been developed to describe creep in two-phase ceramics. The creep mechanisms that most closely represent our results are

the viscous flow (percolation) mechanism and the solute precipitation mechanism, both of which were

suggested by a number of authors. Cavitation was

discounted because of the lack of evidence for homogeneous cavitation in the tensile portions of the bend

specimens. During later stages of creep, however,

grain-boundary delaminations were observed at the

tensile surfaces and are probably the origins of cracks

that are eventually responsible for the failure of these specimens. Additional studies were recommended to

clarify the relative importance of crack nucleation and

crack growth to the creep-rupture process. Acknowledgements

This work was jointly supported by the Department of

Energy (Fossil Energy Program) and by the Department of Defense (Air Force Office of Scientific Research).

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31. N. J. TIGHE. unpublished data.

32. D. W. DURNEY. Va/we 235 (1972) 315.

33. Idem, PhU. Trans. R. Soc. A283 (1976) 229.

34. E. H. RUTTER. /6id. A283 ( 1976) 203.

35. R. L. STOCKER and M. F ASHBY. Rev. Geophvs.

Space P/i.vi. II (1973) 391.

36. E. T. TURKDOGaN. "Physicochemical Properties of Molten Slags and Glasses” (The Metals Soaety. London.

1983).

37. R. H. DOREMUS. in "Modem Aspects of the Vitreous

State". Vol. 2, edited by J. D. Mackenzie. (Butterworths. London, l%2) p. I. 38. R. TERAl and R. HAYANIC. J. Non-Crvst. Solids 18 (1975) 217.

39. A. R. COOPER. Jr. and W D. KINGERY. J. .Amer Ceram. Sac. 47(1) (1964) 37. 40. L. PAULING, “Nature of the Chemical Bond". 3rd edn.

(Cornell University Press. Ithaca. I960) p. 514.

41. F. H. CLEWS. H. M. RICHARDSON and A. T GREEN. Trans. Br. Ceram. Soc. 15(1945) 161. 42. S. E. BOLD and G. W GROVES, J. Mater. Sci. 13 (1978) 611.

43. R. RAJ and P. E. D. MORGAN. J. Amer. Ceram. Soc. 64(1981) C-I43.

44. J.-G. WANG and R. RAJ. ibid. 67(1984) 399.

45. A. G. EVANS and W BLUMENTHAL. in “Fracture Mechanics of Ceramics”. Vol. 6. edited by R. C. Bradt. A. G. Evans, D. P. H. Hasselman and F. F. Lange (Plenum

Press, New York, 1983) p. 423.

46. Idem, in “Deformation of Ceramic Materials IP. Matenals

Science Research. Vol. 18. edited by R. E. Tressler and

R. C. Bradt (Plenum Press. New York. 1984) p. 487.

47. S. M. JOHNSON. B. J. DALGLEISH and A G

EVANS, J. Amer. Ceram. Soc. 67 (1984) 759.

48. R. L. TSAI and R. RAJ, Acta Metail. 30 (1982) 1043.

49. J. E. RITTER. Jr., in “Fracture Mechanics of Ceramics".

Vol. 4, edited by R. C. BradL D. P. H. Hasselman and

F. F. Lange (Plenum Press, New York, 1978) p. 667.

50. F. F. LANGE. Int. J. Fract. 12 (1976) 739.

51. A. G. EVANS and A. RANA, Acta Metail. 28(1980) 129

Received 25 March

and accepted 22 April 1985
J. Am. Ceram. Soc. 725-31 (1986).

NUCLEATION AND GROWTH OF CRACKS IN VITREOUS BONDED ALUMINUM OXIDE

AT ELEVATED TEMPERATURES

K . Jakus

University of Massachusetts

Amherst, MA

S.M. Wiederhorn

B . J . Hockey

National Bureau of Standards

Gaithersburg, MD 20899

Abstract

The nucleation and growth of cracks was studied at elevated

temperatures on a grade of vitreous -bonded aluminum oxide that

contained approximately 8 volume percent glass at the grain

boundaries. Cracks were observed to nucleate within the vitreous

phase, close to the tensile surface of the flexural test

specimens used in these experiments. Crack nucleation occurred

at a strain of »0.08 to 0.12 percent, which corresponded to a

crack nucleation time of »35 percent of the time to failure by

creep rupture. Once nucleated, cracks propagated along grain

boundaries, as long as the stress for crack propagation was

maintained. The crack velocity for cracks that were nucleated by

the creep process was found to be linearly proportional to the

apparent stress intensity factor, whereas for cracks that were

nucleated by indentation, the crack velocity was proportional to

the fourth power of the apparent stress intensity factor.

29
1. Introduction

At the thermal limit of application of most high-temperature

structural ceramics, creep deformation often precedes fracture.

Because ceramics are not fully ductile even at the highest

temperatures, cavities and micro-cracks are generated by the

creep process, so that once a material starts to creep, the

defects that eventually lead to failure arise as a natural

consequence of creep [1]. Crack size and crack growth rate,

which are the most important factors controlling lifetime at room

temperature, are replaced in importance at elevated temperatures

by nucleation, growth, and coalescence of micro-cracks and voids

[ 1 ] . To develop high temperature techniques of assuring

reliability, these events must be incorporated into the method of

lifetime prediction.

In this paper, the results of a study to elucidate mechanisms of

crack nucleation and crack growth in a commercial grade of

vitreous -bonded aluminum oxide are presented. This material was

chosen for study to simulate the microstructure of structural

ceramics that contain glass at their grain boundaries. The

importance of crack nucleation and crack growth to component

lifetime is emphasized for this material. Data from this study

are compared with data obtained on a commercial grade of

hot-pressed aluminum oxide.

30
2. Experimental Procedure

Experiments were conducted on a grade of vitreous -bonded aluminum

oxide (COORS AD-96 that had been used earlier to characterize

the creep and fracture behavior of vitreous-bonded materials [2].

The material has a nominal silica content of 4 percent by weight.

Glass and porosity are each *8 percent by volume, and both are

located primarily at three grain intersections. The mean grain

size was approximately 8 um, with a range of from approximately 3

to 20 urn.

Test specimens, 3x5x50 mm, were machined from plates that were

cut by the manufacturer from a rectangular billet. Following

machining, specimens were heat-treated in air at 1050°C for 96

hours to stabilize the microstructure. They were subsequently

polished with 3 vim diamond paste on three adjacent sides to

permit microscopic detection of cracks that formed during the

creep tests. The choice of temperature and duration for the

initial heat-treatment was dictated by the results of an earlier

study [2] on the microstructure and creep characteristics of this

material. In that study, it was found that prolonged high

temperature exposure strongly affected the creep behavior of the

material. Specifically, heat-treatment caused the creep rate to

31
decrease and the creep life to increase by two orders of

magnitude. The cause of the change in creep behavior was related

to the partial crystallization of the glassy intergranular phase.

In the "as-received" material, the grains were separated by a

layer of glass that ranged in thickness from approximately 10 nm

to approximately 500 nm. This represented only a fraction of the

total glass content in the material; the bulk of the

intergranular glass was located at three grain intersections,

figure la. Heat-treatment caused considerable devitrification of

the intergranular glass, figure lb, particularly within the

surface region. Based on the results of the earlier study, it

was felt that the test duration in the present study was short

enough compared to the heat-treatment time that further

microstructural changes during the tests were minimal and

therefore did not influence crack initiation and growth.

In the creep cracking experiments the test bars were subjected to

"dead-weight" loads in four-point bending (40 mm outer, 10 mm

inner spans) at nominal temperatures of 1000°C and 1050°C. All

studies were conducted in air. At temperature, the material

exhibited considerable creep deformation, and eventually failure

occurred due to the nucleation and growth of cracks. In order to

correlate the extent of creep with the process of crack growth,

additional creep tests were made in which the tests were

periodically interrupted by cooling the specimens to room

temperature under load. Upon each interruption, the permanent

deformation of the specimen was measured from the radius of

32
curvature of the deformed specimens. The accumulated creep strain

was calculated from these measurements 2 . in addition, all of the

polished surfaces were searched for cracks, to establish the time

for crack nucleation, and after nucleation, to measure the crack

velocity as a function of crack size. If any cracks were found,

their location and size were recorded and the average crack

velocity was calculated from the amount of growth between

observation periods.

Following the crack size measurements, the specimen was reheated

under load to the operating temperature and the creep test was

continued for another period of time. This interruption sequence

was repeated until either the specimen broke, or the largest

crack became comparable to the specimen size. It should be noted

that during the creep tests, the loading point deflection was

also monitored continuously giving an additional measure of the

extent of creep deformation. Creep data (strain rate versus time

and time-to-failure) obtained in this way did not differ

significantly from those obtained earlier using uninterrupted

creep tests [2]. For cracks that were nucleated by creep, the

velocities of at least 10 cracks of equal size were used to

obtain an average value of the crack velocity. Nucleation was

considered to be complete when the cracks reached a size of

approximately 3 grain diameters (30 ym) at which point cracks

were generally stable and continued to grow, provided a sustained

creep load was maintained on the specimen. Occasionally, cracks

smaller than *100 yjn were observed to heal, probably as a

consequence of a localized reduction of the stresses during

33
creep. Some of the test bars were indented with a diamond

pyramidal indenter prior to the start of the test so that the

growth rates of indentation cracks could also be studied using

the same interruption technique that was used to study the growth

of creep nucleated cracks.

3 . RESULTS

3.1 Crack Nucleation

Creep deformation of vitreous bonded aluminum oxide eventually

results in the nucleation of intergranular cracks at the tensile

surface of the specimen, [2]. These cracks gradually grow into

the body of the test specimens causing failure. The details of

the nucleation and growth process can best be studied by the use

of a combination of optical and electron microscopy (TEM and

SEM) . Based on TEM examination of thin sections taken from

various regions of the creep samples, cracks appear to nucleate

at grain boundaries near the tensile surface. This is evidenced

by the observation of grain boundary delaminations or clusters of

voids within two grain junctions near the tensile surface, figure

2. Delaminations such as those shown in figure 2a are not

observed at the compressive surface of the specimens, or at large

distances from the tensile surface. At later stages of growth,

figure 2b, these delaminations enlarge and clearly exhibit a

crack-like character. They gradually spread along the tensile

surface of the flexural test bars to form the cracks that

34
eventually lead to failure of the specimen. After failure,

examination of the gauge-section of the flexural specimen by

optical microscopy reveals many such cracks in various stages of

development, figure 3. Some of these cracks had grown almost all

the way across the tensile surface and had penetrated deeply into

the body of the specimen, figure 3, before fracture occurred

elsewhere

.

As indicated above, creep nucleated cracks propagate only through

the vitreous intergranular phase of the ceramic. The widths of

these cracks were less than approximately 1 um, even after

considerable growth, figure 4. Of particular interest to the

present study is the observation that as creep cracks grew, grain

boundary segments of unbroken material remain behind the crack

front, figure 5-6, partially binding the surfaces together. For

relatively short cracks, less than =100 ym, the crack surfaces

are attached by these unbroken segments, or ligaments, at many

points along their entire length. Since these connecting

segments must be separated by sliding and opening modes of

displacement during crack growth, they are believed to retard

crack advance by applying a closing force to the crack surfaces.

3.2 Creep Crack Growth

The manner in which cracks nucleated and grew in vitreous bonded

aluminum oxide is illustrated in figure 7 for a specimen tested

at 1000°C and an applied stress of 80 MPa. After creep for a

35
period of less than approximately 70 hours, no cracks were

observed in the surface of the specimen, suggesting a minimum

time for crack nucleation. Somewhere between 70 and 78 hours,

cracks nucleated in the specimen and at 78 hours (corresponding

to an estimated strain of 0.076 percent) 9 cracks with lengths of

300 um or less were observed scattered at random within the gauge

section of the specimen, figure 7a. With time these cracks grew,

and additional cracks were generated, as can be seen by comparing

figures 7b and 7c for exposure times of 82.5 and 87.5 hours,

respectively. The crack size distributions at these times,

figure 8, show that cracks as large as 600 or 700 um were found

in the specimen surface. However, most of the cracks were

freshly nucleated and consequently had dimensions of the order of

100 urn or less.

Although the cracks shown in figure 7 are distributed throughout

the gauge section, there are regions on the tensile surface that

contain no cracks at all. Although this distribution of cracks

may be entirely random, it is tempting to suggest that the crack

distribution is, in fact, a consequence of heterogeneous

deformation within the material. If deformation is much more

severe along the boundaries that separate the crack free regions,

then it is along these boundaries that stresses are high. As a

consequence, nucleation and growth of cracks is expected to

occur preferentially along these boundaries. Preferred

deformation is also expected to result in microstructural damage,

which decreases the resistance of the boundaries to crack growth,

making them the preferred paths for fracture in later stages of

36
the deformation process. Linkage of the small cracks shown in

figure 1 , may also play a role in the final failure process.

The growth of both creep and indentation nucleated cracks was

monitored at a temperature of 1050®C and an applied stress of 60

MPa. Ranging in size from *70 to *180 urn, the indentation cracks

were formed by the loads given in table 1. As indicated in this

table, 70 urn cracks do not seem to propagate when subjected to

an applied stress of 60 MPa at 1050°C. By contrast, cracks

larger than *100 vut do propagate under the same conditions. This

behavior suggests the existence of a threshold stress for the

growth of indentation cracks in this material. By contrast,

cracks of an equivalent size, but nucleated by the creep process

at the same temperature and stress, exhibited no threshold stress

for crack growth. As long as the stress is maintained on the

specimen, these cracks continue to grow, with few exceptions,

until failure occurs. In figure 9, the crack velocity for both

types of cracks is plotted as a function of applied stress

intensity factor^. The v-Kj plot determined from the indentation

cracks has a slope of approximately 4, whereas the v-Kj plot for

the creep nucleated cracks has a slope of only 1. A comparison of

the observed crack velocities in figure 9 shows creep cracks

growing at a faster rate than indentation cracks for most of the

range of applied stress intensity factors. Thus, the two types of

cracks exhibit a substantial difference in their response to

applied stress.

37
3.3 Creep Strain for Crack Nucleation

Because the time required for crack nucleation can account for a

considerable fraction of the failure time, [3], the strain at

which crack nucleation first occurs is a relevant experimental

variable for high temperature structural reliability. Creep

strain results of this study are summarized in figure 10, which

presents creep strain as a function of creep time. For all four

sets of data, crack nucleation occurred somewhere between 0.075

and 0.115 percent strain. For the data taken at 60 MPa and

1050°C this strain corresponded to a range of between 15 and 35

hours of creep as indicated on figure 10. These values are

approximately one-third of the time required for failure at this

applied stress and temperature, i.e. 50 to 90 hours. For the

specimen tested at 1000°C and 80 MPa, the points labelled A, B,

and C represent the strain of the crack nucleation data given in

figure 7. Prior to crack nucleation, the creep curves the creep

curves in figure 10 exhibit the characteristic shape of primary

creep. In this regime, the creep rate continues to diminish as

the material "work hardens." Crack nucleation occurs during the

later stages of primary creep, after the apparent creep

resistance of the material has increased substantially.

38
4. DISCUSSION OF RESULTS

4.1 Creep and Nucleation

The results presented above can be best understood in terms of

the microstructure of the aluminum oxide selected for study. In

principle, creep can occur in this two phase material by

deformation of both the aluminum oxide grains, and the

intergranular phase. Because of the low temperatures of the

experiments relative to those required to deform the aluminum

oxide, creep is expected to occur mainly in the intergranular

phase of the material, so that the aluminum oxide grains behave

as elastic particles in a viscous matrix. This expectation was

supported by microstructural analyses of the test specimens. An

examination of the aluminum oxide grains by transmission electron

microscopy after deformation gave little evidence of dislocation

activity within the grains (by comparison with the as received

material ) , suggesting that the aluminum oxide grains did not

deform plastically at the temperatures and stresses of

investigation. Diffusional processes also do not appear to

contribute to the creep process, since the measured creep rate

[2] is approximately two orders of magnitude greater than that

obtained from a deformation mechanism map on 10 um aluminum oxide

[8] for the same test conditions. By contrast, estimates of the

glass viscosity of the intergranular vitreous phase in this

material [2], showed the viscosity to be less than approximately

1 q 7 Pa*s over the entire range of study. Since this viscosity

lies close to the softening point (io^*65 pa*s) of the glass, the

39
glass is expected to deform readily when subjected to applied

stresses and to play the dominant role in determining the

deformation and fracture behavior of this material. At

temperatures >1000°C the crystalline silicate intergranular

phases are also expected to be highly ductile relative to the

a-Al203 granular phase. Thus, at 1000°C and 1050°C, creep in

this material is almost exclusively controlled by deformation of

the intergranular phase whether vitreous or crystalline.

Crack nucleation and growth in vitreous -bonded materials can be

understood in terms of the deformation that occurs in these

materials when they undergo creep. As discussed above, creep

occurs primarily by deformation of the vitreous intergranular

phase of the material, and is relatively easy as long as the

grains of the solid do not interlock. However, as the grains

begin to interlock, work hardening occurs and the ease of creep

decreases as the amount of strain increases. For creep to

continue, the grains must slide over one another, causing a

localized volume expansion of the material, i.e. a dilation in

the vicinity of the deformation [4,5]. This dilation results in

large localized stresses between the grains as deformation

continues. Dilation is accommodated by the flow of the viscous

intergranular phase from grain boundaries and triple junctions

where the local pressure is high to boundaries where the pressure

is low. Known as percolation, this process of creep is highly

non-linear, so that specimens that are subjected to this type of

creep also exhibit nonlinear creep behavior [6,7].

40
other processes are also activated to assist the deformation.

Solution precipitation is one such process, which relieves local

stress concentrations by the dissolution and diffusive transport

of material from portions of the grain boundaries where the

pressure is high to portions on the grain boundary where the

pressure is low [ 9 - 14 ] 4 . in the present study, the material

dissolved in this process can be the aluminum oxide grains

themselves, or the devitrified precipitates in the intergranular

phase. Stresses can also be redistributed by microcracking and

cavitation in both the compressive and tensile regions of the

bend specimens [15-20]. In an earlier study, it was concluded

that both solution precipitation and percolation were important

processes in the creep of the AD-96. It was also concluded that

cavitation and void formation throughout the body of the solid

played little role in the deformation process. However, at the

tensile surface where localized stresses and dilational strains

are probably greatest, grain boundary delamination or

void formation probably accounts for the microscopic observations

of crack nucleation described in the present paper^.

Based on the observations presented here and in reference 2, we

conclude that crack nucleation in vitreous -bonded ceramics is a

process of cavity formation and growth within the vitreous phase

of the material [21,22]. Crack nucleation is driven by the

average stress distribution that develops within the bend

41
specimen as a consequence of creep. When "work hardening" occurs

and grains interlock, this average creep stress is magnified, so

that the local, internal stresses that cause crack nucleation in

the grain boundary phase are larger than the average creep

stress

.

Once conditions for cavitation have been achieved, voids that

nucleate within the vitreous phase are forced to grow between the

aluminum oxide grains into crack- like cavities [1, 21, 22],

These cavities eventually extend into the cracks that are the

major cause of failure in this material. The results of this

paper suggest that cracks do not grow from internally nucleated

cavities, or from the 10 um pores that are present within the

material. Instead they nucleate from grain boundaries that are

close to or at the specimen surface, which suggests that

conditions for crack nucleation are most favorable at the tensile

surface. The grain boundaries that cavitate always lie

perpendicular to the applied stress, figure 5, and nucleation

appears to occur by the recession of the glass into the

intergranular space. The fact that devitrification is greater at

the tensile surface than in the bulk of the material also assists

the process of microcrack initiation by embrittlement of the

surface [2].

42
4 . 2 Crack Growth

Once cracks have been nucleated, the lifetime of structural

components is determined by the time it takes for one of the

cracks to reach a critical size. In the present study, two types

of cracks were studied, one was introduced by indentation at room

temperature, the other was introduced by the creep process. The

v-Kj plots for these two types of cracks indicate that the curve

for the creep nucleated cracks had a slope of approximately onequarter that of the curve for the indentation nucleated cracks.

Furthermore, at any given value of Kj, the velocity of the creep

cracks was greater than that of the indentation cracks. Although

the explanation for this difference in behavior is not

immediately obvious, it is possible that the damage resulting

from the creep process plays an important role in determining the

response of crack motion to the applied load. The fact that

creep cracks are nucleated by the flow field resulting from the

creep, suggests that the microstructural damage and stresses that

are generated by this field are responsible for the difference in

the crack growth behavior. In effect, after extensive creep, the

structure of the ceramic has been modified by the structural

damage and, as a consequence, the fracture behavior of the

ceramic is also modified by the damage.

The microstructural observations of the crack tip structure and

the crack growth data obtained on indentation cracks are

consistent with the model of creep crack growth suggested by Tsai

and Raj [21], who assumed that the crack opens by a combination

43
of shear and opening mode failure. Shear ligaments are formed

behind the crack tip offering resistance to the crack motion, and

these ligaments must be overcome for the crack to continue its

motion. The model predicts a v-Kj curve with a slope of 4 in the

high velocity range of crack growth data, a value that is close

to that obtained in the present study for the growth of

indentation cracks. The microstructure of the crack tip is also

similar to that assumed by Tsai and Raj and it may well be that

this model can be used to explain crack growth data for

indentation cracks. The model, however, sheds little light on the

crack-growth behavior of creep nucleated cracks.

The threshold for sub-critical crack growth can be calculated

from the data in table 1 by assuming that the crack advances by

the flow of viscous glass between the grains of aluminum oxide.

This threshold is estimated from the condition G = 2r, where G

is the strain energy release rate and r is the surface tension of

the molten glass. Since the indentation cracks were

semi-circular, G»4a2a/ (uE) , where a is the crack radius and E is

Young's modulus. For aluminum oxide, Ea380 GPa, for silica

glass, FaO.3 J/m^ [23], yielding a threshold stress of 71 MPa for

a 70 urn (a=35 urn) crack. This stress is slightly greater than

the 60 MPa stress applied to the specimen in the present

experiment. Hence, crack propagation is not expected for this

crack. Using the same approximation, the 100 uni crack is

at the fatigue threshold. These findings are consistent with the

data discussed in the present paper.

44
4.3 Comparison with Other Creep-Rupture Studies

Closely related to the data presented in the present paper are

the data published by Dalgleish et al. [24], Blumenthal and Evans

[25] and Johnson et al. [26] on fine grained (2 and 4 um)

,

hot-pressed aluminum oxide. The material studied by these

authors contained no glass at the grain boundaries and thus

differed considerably from the vitreous -bonded material studied

in the present paper. Studies were conducted by these

investigators at temperatures ranging from 1300°C to 1400®C, and

failure was characterized by the nucleation of cracks from

chemical or microstructural heterogeneities. Crack nucleation

was followed by a short period of crack growth that was

terminated by crack arrest and crack tip blunting, in which shear

bands generated and propagated as side lobes from the tip of the

crack [25]. Failure finally occurred by the nucleation and

coalescence of cracks along the shear bands of several of the

initial blunted cracks resulting in a serrated fracture surface

that followed the initial cracks and the shear bands.

Their study also showed that when specimens containing

indentation cracks were stressed below the threshold for crack

growth, the same kind of shear bands formed around crack tips as

were observed for the creep nucleated cracks. Above the

threshold, crack propagation occurred along grain boundaries. In

contrast to the arrested cracks, cracks remained relatively sharp

as they propagated. The tips of these cracks were, in fact,

similar in appearance to those reported in the present paper for

45
vitreous -bonded aluminum oxide. Although the cracks were more

open than those of the present study, the same kind of ligament

formation was observed behind the crack tip. Finally, they also

found that crack growth from creep nucleated cracks occurred at

values of Kj that were less than that required for the growth of

indentation cracks.

A comparison of the creep behavior of hot-pressed and

vitreous-bonded aluminum oxide reveals a number of differences

between the two materials. As discussed in an earlier section of

the paper, creep deformation in the vitreous -bonded material is

not homogeneous. Therefore, crack nucleation depends more on the

details of the creep process than on the presence of

microstructural or chemical heterogeneities in the material. Once

nucleated, cracks in the vitreous material tend to propagate

until failure occurs, indicating that nucleation and growth are

related processes in the sense that both are driven by the

localized stresses arising from the creep. Crack blunting and

shear band formation of the type discussed by Blumenthal and

Evans [25] are not observed in the vitreous-bonded material.

Cracks are narrow, < 1 um, figure 4, and neither blunting, nor

shear band formation was observed even when indentation cracks

are loaded below the crack growth threshold.

These differences in behavior between the vitreous bonded and

hot-pressed material probably result from the fact that higher

temperatures were used in the study of the hot-pressed aluminum

oxide. At these higher temperatures deformation of aluminum

A6
oxide occurs by a number of mechanisms including: grain boundary

sliding, bulk and grain boundary diffusion, and activated slip

and climb [8]. Thus, the stresses in the vicinity of crack tips

can be relieved by a number of mechanisms, and as a consequence,

crack tip blunting can occur. At lower temperatures aluminum

oxide grains are expected to remain rigid, so that the blunting

of cracks would have to be accommodated only within the

intergranular phase by cavitation, viscous flow or by solution

reprecipitation. The fact that blunting and shear band formation

did not occur indicates that the kinetics of these processes were

too slow at the temperature selected for study to accommodate the

crack tip stresses. The study by Clarke [20] suggests that

microstructural features similar to those observed in hot-pressed

aluminum oxide are probable in the vitreous-bonded materials at

higher temperatures. Additional studies will be needed to test

this point.

Acknowledgement: Support of the Department of Energy, Fossil

Energy Program is gratefully acknowledged by S.M.W. and

K.J. is pleased to acknowledge the support of the National

Science Foundation.

A7
Footnotes

:

1.

The use of this material does not constitute endorsement by

the National Bureau of Standards.

2. This procedure was different from that used in reference 1,

wherein the creep strain was calculated from the load point

displacement. Significant differences were obtained between these

two measurement procedures.

3. The stress intensity factors used in figure 9 were calculated

from the formula for a circular crack of radius a in a uniform

stress field of magnitude a: Kj=( 2/VTi)aVa. For various reasons

[1], these values of the stress intensity factor can only be

considered approximate measures of the driving force for

fracture.

4. This assumes a positive pressure and a net decrease in volume

when solution occurs within the intergranular phase.

5. It is worth emphasizing that the cavitation discussed in this

paper does not occur throughout the volume of the material, but

only at 2 grain boundaries close to the tensile surface. The

discussion of crack nucleation refers only to these near surface

cavities or voids.

48
Figure Captions

1. Intergranular phase in vitreous bonded aluminum oxide

(AD-96); (a) In the as-received material, the bonding phase is

amorphous consisting of an aluminosilicate glass which also

contains calcium, magnesium and potassium as network modifiers;

(b) After heating at 1050°C for 96 hours, the bonding phase

crystallizes into a number of silicate minerals (see reference 2

for details of the composition and crystal structure of this

material)

.

2. Delamination occurring at grain boundaries as a consequence

of stresses resulting from creep at lOSOOC; (a) Initiation of

cavities in the intergranular phase. The cavities are located

between grain boundary facets, and the geometry of the cavities

appears to be dictated by the size of the facets and the

thickness of the grain boundary; (b) Cavities after propagation.

The boundary of the cavity looks much like the cavity boundary in

2(a); the center has opened sufficiently to observe the spacing

between the two surfaces.

3. Tensile surface of a flexural test specimen just prior to

failure. Cracks have grown almost completely across the tensile

surface (middle micrograph) and half-way through the thickness

(top and bottom micrographs) of the specimen. The total specimen

width (s5 mm), and the total specimen thickness (=3 mm) are shown

in this figure.

4. Optical micrograph from cross-section through flexural creep

sample (top edge of micrograph corresponds to intersection with

tensile surface). Relief polishing reveals distribution of

binder phase, M, and Porosity, P, between aluminum oxide grains,

A. View also shows portions of creep crack, C, that developed at

the tensile surface. Note, crack growth occurs only within the

intergranular binder phase; relatively narrow crack opening

displacements are maintained.

5. Scanning electron micrograph of surface crack at an early

stage of propagation. Note that the crack is not completely

open, but is joined across its faces by unbroken ligaments, L,

that must also break for crack propagation to proceed.

6. Unbroken ligament joining the surfaces of a creep crack. The

dislocations in the aluminum oxide grains are a consequence of

surface polishing and do not result from the process of creep.

Specimens taken from locations that lie further from the surface

show no evidence of dislocations within the alumina grains, see

figure 2 for example. This transmission electron micrograph

shows the ligament separation occurring by shear deformation.

49
7.

Sequence of fracture and the distribution of cracks formed in

the vitreous bonded aluminum oxide as a consequence of creep at

lOOQOc and 80 MPa applied stress: (a) 78 hours and 0.076 percent

strain; (b) 82.5 hours and 0.077 percent strain; (c) 87.5 hours

and 0.078 percent strain. Note that some areas within the gauge

section are completely free of microcracks, suggesting the

absence of plastic deformation in these regions during creep.

Also, once cavitation starts, very little extra strain is needed

to open a much larger set of cracks: =0.076 percent strain for

crack pattern shown in (a); =0.078 percent strain for the crack

pattern shown in ( c )

.

8. Histogram of crack size distribution established in vitreous

bonded aluminum oxide by creep. Note that most of the cracks lay

at the small end of the crack size distribution, indicating more

recent nucleation and less crack growth.

9. Crack propagation curves for both creep nucleacad and

indentation nucleated cracks in vitreous bonded aluminum oxide.

The slope of the curve for the indentation nucleated cracks is

about four times that of the curve for creep nucleated cracks.

The standard deviation of the slope was approximately 0.3 for

both curves.

10. Creep curves for vitreous bonded aluminum oxide demonstrating

the time required for crack nucleation. Note that all curves are

still in the primary stage of creep, and that crack nucleation

for all runs occurred at between 0.075 and 0.115 percent strain.

50
Table 1: Crack size (um) as a function of exposure time at

1050°C and an initial applied stress of 60 MPa.

Indentation

Load (N) 0

Exposure

6.2

Time (hrs.

)

12.2 17.6

10 70±11* 74 + 10 81118 78117

20 101+17 112114 130118 3651200

40 184132 227123 3301123 8021200

Strain (%) 0 0.049 0.062 0.082

* The crack size presented here is the full length of the

indentation crack intersecting the tensile surface of the flexure

specimen.

51
REFERENCES

1. A.G. Evans and W. Blumenthal, "High Temperature Failure in

Ceramics," pp. 423-448 in Fracture Mechanics of Ceramics, Vol. 6,

Measurements, Transformations and High-Temperature Fracture, R.C.

Bradt, A.G. Evans, D.P.H. Hasselman and F.F. Lange, eds. Plenum

Press, New York (1985).

2. S.M. Wiederhorn, B.J. Hockey, R.F. Krause, Jr. and K. Jakus,

"Creep and Fracture of Vitreous Bonded Aluminum Oxide, J. Mater.

Sci., 21, 810-824 (1986).

3. A.G. Evans, "Structural Reliability of Ceramics: A

Processing Dependent Phenomenon," J. Am. Ceram. Soc. 127-37

(1982)

.

4. O. Reynolds, "On the Dilatancy of Media Composed of Rigi.

Particles in Contact. With Experimental Illustrations," Phil,

Mag. 469-489 (1885).

5. F.C. Frank, "On Dilatancy in Relation to Seismic Sources,"

Rev. Geophysics, 2/485-503 (1965).

6. D.C. Drucker, "Engineering and Continuum Aspects of

High-Strength Materials," pp. 795-833 in High Strength Materials,

V.F. Zackay, ed. , John Wiley and Sons, Inc., New York (1965).

7. F.F Lange, "Non-Elastic Deformation of Polycrystals with a

Liquid Boundary Phase," pp. 361-381 in Deformation of Ceramic

Materials, R.C. Bradt and R.E. Tressler, eds. Plenum Press, New

York (1972).

8. H. J. Frost and M. F. Ashby, Deformation-Mechanism Maps: The

Plasticity and Creep of Metals and Ceramics, Pergamon Press, New

York (1982).

9. D.W. Durney, "Solution-transfer, and Important Geological

Deformation Mechanism," Nature, 235 , 315-16 (1972).

10. D.W. Durney, "Pressure Solution and Crystallization

Deformation," Phil. Trans. R. Soc. A283, 229-40 (1976).

11. E.H. Rutter, "The Kinetics of Rock Deformation by Pressure

Solution," Phil. Trans. R. Soc. Lond. A283 , 203-219 (1976).

12. R.L. Stocker and M.F. Ashby, "on the Rheology of the Upper

Mantle," Rev. Geophys. and Space Phys. 11, 391-421 (1973)

13. R. Raj, "Creep in Polycrystalline Aggregates by Matter

Transpr^-t Through a Liquid Phase," J. Geophys. Res. 87 [B6],

4731-3 (1982).

14. R. Raj and C.K. Chyuang, "Solution-Precipitation Creep in

Glass Ceramics," Acta Met. 29./159-66 (1981).

52
15. R. Kossowsky, D. G. Miller and E.S. Diaz, "Tensile and Creep

Strengths of Hot-Pressed Si 3 N4 ," J. Mater. Sci. 983-97

(1975).

16. F.F. Lange, B.I. Davis and D.R. Clarke, "Compressive Creep of

Si 3 N4MgO Alloys: Pt. 1 Effect of Composition," J. Mater. Sci. 15,

601-10 (1980).

17. M.H. Lewis, B.S.B. Karunaratne, J. Meridith and C. Pickering,

pp. 365 in Creep and Fracture of Engineering Materials and

Structures, B. Whilshire and D.R.J. Owens, eds. Pineridge Press,

Swansea (1981).

18. J.E. Marion, A.G. Evans, M.D. Drory and D.R. Clarke, "High

Temperature Failure Initiation in Liquid Phase Sintered

Materials," Acta Met. 3^, 1445-57 (1983).

19. N.J. Tighe. S.M. Wiederhorn T.-J. Chuang and C.L. McDaniel,

"Creep Cavitation and Crack Growth in Silicon

Nitride," pp. 587-604 in Deformation of Ceramic Materials II,

Materials Science Research, Vol. 18, R.E Tressler and R.C. Bradt,

eds. Plenum Press, New York (1984).

20. D.R. Clarke, "High Temperature Deformation of a

Polycrystalline Alumina Containing an Intergranular Glass

Phase," J. Mater. Sci. 20, 1321-32 (1985).

21. R.L. Tsai and R. Raj., "Creep Fracture in Ceramics

containing Small Amounts of a Liquid Phase," Acta Met. 30 , 1043-58 (1982).

22. M.D. Drory and A.G. Evans, "Effects of Voids at Three-Grain

Junctions on Sintering and Creep Damage," J. Am. Ceram. Soc. 67 , 721-7 (1984).

23. W.D. Kingery, H.K. Bowen and D.R. Uhlmann, Introduction to

Cermics, 2nd Edition, John Wiley and Sons, New York (1976)

24. B.J. Dalgleish, S.M. Johnson and A.G. Evans,

"High-Temperature Failure of Polycrystalline Alumina: I, Crack

Nucleation," J. Am. Ceram. Soc. §1_, 741-50 (1984).

25. W. Blumenthal and A.G. Evans, "High-Temperature Failure of

Polycrystalline Alumina: II, Creep Crack Growth and Blunting," J.

Am. Ceram. Soc. §1^, 751-59 (1984).

26. S.M. Johnson, B.J. Dalgleish and A.G. Evans,

"High-Temperature Failure of Polycrystalline Alumina: III,

Failure Times" J. Am. Ceram. Soc. §1_, 759-63 (1984).

53
1. Intergranular phase in vitreous bonded aluminum oxide

(AD-96): (a) In the as-received material, the bonding phase is

amorphous consisting of an aluminosilicate glass which also

contains calcium, magnesium and potassium as network modifiers;

(b) After heating at 1050°C for 96 hours, the bonding phase

crystallizes into a number of silicate minerals (see reference 2

for details of the composition and crystal structure of this

material)

.

54
2. Delamination occurring at grain boundaries as a consequence

of stresses resulting from creep at 1050°C: (a) Initiation of

cavities in the intergranular phase. The cavities are located

between grain boundary facets, and the geometry of the cavities

appears to be dictated by the size of the facets and the

thickness of the grain boundary; (b) Cavities after propagation.

The boundary of the cavity looks much like the cavity boundary in

2(a); the center has opened sufficiently to observe the spacing

between the two surfaces.

55
3. Tensile surface of a flexural test specimen just prior to

failure. Cracks have grown almost completely across the tensile

surface (middle micrograph) and half-way through the thickness

(top and bottom micrographs) of the specimen. The total specimen

width (~5 mm), and the total specimen thickness (=3 mm) are shown

in this figure.

56
4. Optical micrograph from cross-section through flexural creep

sample (top edge of micrng-raph corresponds to intersection with

tensile surface) . Relief polishing reveals distribution of

binder phase, M, and Porosity, P, between aluminum oxide grains,

A. View also shows portions of creep crack, C, that developed at

the tensile surface. Note, crack growth occurs only within the

intergranular binder phase; relatively narrow crack opening

displacements are maintained.

57
i

i

5. Scanning electron micrograph of surface crack at an early

stage of propagation. Note that the crack is not completely

open, but is joined across its faces by unbroken ligaments, L,

that must also break for crack propagation to proceed.

58
6. Unbroken ligament joining the surfaces of a creep crack. The

dislocations in the aluminum oxide grains are a consequence of

surface polishing and do not result from the process of creep.

Specimens taken from locations that lie further from the surface

show no evidence of dislocations within the alumina grains, see

figure 2 for example. This transmission electron micrograph

shows the ligament separation occurring by shear deformation.

59
TIME 78 hrs daTENSILE SURFACE OF INNER SPAN da

(a) CRACK

I 500/j.m

LOADING PIN * 1 I—[—I LOADING PIN *2

(b)

(c)

7. Sequence of fracture and the distribution of cracks formed in

the vitreous bonded aluminum oxide as a consequence of creep at

lOOO^C and 80 MPa applied stress: (a) 78 hours and 0.076 percent

strain; (b) 82.5 hours and 0.077 percent strain; (c) 87.5 hours

and 0.078 percent strain. Note that some areas within the gauge

section are completely free of microcracks, suggesting the

absence of plastic deformation in these regions during creep.

Also, once cavitation starts, very little extra strain is needed

to open a much larger set of cracks: =0.076 percent strain for

crack pattern shown in (a); =0.078 percent strain for the crack

pattern shown' in (c).

60
EVOLUTION OF CREEP CRACK DISTRIBUTION IN 96% ALUMINA

(80 MPa/ 1000°C)

O

10

0

CREEP TIME 78 hrs

MAX. CREEP STRAIN

ZZZZzzzzSZZZ! ^

0 100 200 300 400 500

CRACK LENGTH (/^m)

0.076%

__i I 600 700

8. Histogram of crack size distribution established in vitreous

bonded aluminum oxide by creep. Note that most of the cracks lay

at the small end of the crack size distribution, indicating more

recent nucleation and less crack growth.

61
LOG (K) - (MPa

9. Crack propagation curves for both creep nucleated and

indentation nucleated cracks in vitreous bonded aluminum oxide.

The slope of the curve for the indentation nucleated cracks is

about four times that of the curve for creep nucleated cracks.

The standard deviation of the slope was approximately 0.3 for

both curves

.

62
CREEP STRAIN OF 96% ALUMINA IN 4-PT. BENDING

10. Creep curves for vitreous bonded aluminum oxide demonstrating

the time required for crack nucleation. Note that all curves are

still in the primary stage of creep, and that crack nucleation

for all runs occurred at between 0.075 and 0.115 percent strain.

63
Rising Fracture To . gnness o^' an Alumina Ceramic

Using the Bending Strength of Indented Specimens

Ralph F. Krause, Jr.

National Bureau of Standards

Gaithersburg, MD 20899

The fracture toughness of a vitreous-bonded 96 percent alumina ceramic was

determined to increase as a power function of crack extension. Controlled

flaw sizes were produced by Vickers indentation loading between 3 and 300 N

and were placed in the center of polished, prospective tensile surfaces of

respective foui—point bend specimens, previously annealed. The corresponding

surface cracks were measured by a shadow technique of optical microscopy.

The log of the bending strength was observed to be a linear function of the

log of indentation load in two series of experiments: (I) including the

residual stress due to indentation and (II) having the residual stress

annealed at an elevated temperature. The plots of these functions ior botn

series of experiments yielded within the precision of measurement the same

slope, being about 32 percent less than the -1/3 slope which a fracture

toughness independent of crack extension would indicate. Considering the

criterion for crack extension and the criterion for specimen failure,

solutions were derived to accord with the respective conditions of the two

series of experiments, and both of these methods gave the same value within

the precision of measurements for the rising fracture tougnness of tlie

alumina ceramic.

K 'words: Alumina ceramic, bending stress, crack ectension, indentation

*-v:.aQ, fracture toughness, residual scress, stress intensity factor.
Nomenclature

a Crack depth (Fig. 1).

3q Initial notch depth.

a-| Crack depth produced by an indentation load.

Crack depth when crack growth becomes unstable.

A Coefficient evaluated by a least squares fit of eq 18.

b Half-width of specimen (Fig. 1).

B,C Coefficients evaluated by a least squares fit of eq 15.

c Half-length of surface crack (Fig 1).

c-| Half-length of surface crack produced by an indentation load.

E Modulus of elasticity for a given material.

F Load required to rupture a specimen.

k Coefficient of fracture toughness

(Subscript 0 denotes a^ = o, and subscript 1 aenotes a^ = a-] in

eq 2)

.

K Applied stress-intensity factor (plane strain).

Kjj Stress-intensity factor due to a bending stress.

K^, Critical stress-intensity factor (fracture toughness) for a given

material.

Residual stress-intensity factor due to an indentation load cycle on

a specimen.

1-

| Mc]or span for loading a bend speclmei:.

2-

2 Minor span for loading a bend specimen.

m Crack-depth exponent of fracture toughness.

M Bending moment on a specimen.

P Indentation load.

R Crack-growth resistance i. ''nc^gy ner unit of cracked surface) of a given material.

S Bending strength, stress on the outer fiber required to rupture a specimen.

65
t Thickness of specimen in direction of crack depth (Fig. 1).

X Coefficient of residual stress-intensity factor.

Y Configuration coefficient for bending stress-intensity factor.

V Poisson's ratio.

a Bending stress on the outer fiber of a specimen.

4) The angle which defines a point on the crack front of a serai-elliptical surface crack (Fig. 1).

I. Introduction

Recently, Cook, Lawn and Fairbanks [1] used controlled indentation

flaws to study the strength characteristics of ceramics as a function of

crack size relative to grain size. They observed that the strengths of

several ceramics first showed a steady Increase on diminishing the

indentation load, but subsequently tended to a plateau as the contact size

began to approach the characteristic grain size. They postulated the

existence of a mlcrostructural driving force, analogous to the residual

indentation driving force, to describe a tendency for the strength to become

somewhat smaller than one would expect from a macroscopic toughness value as

the flaw size gets smaller. This Interpretation is the converse of the

concept of fracture tcughneso of a material increasing as a funci^lor. ei crack

extension except that the authors advocated that their calculated values of

rising fracture toughness be specified by two limiting parameters. The

indentation-controlled region of large-scale crack behavior would define the

first limit as the conventional macroscopic fracture toughness response,

where [d log (S)/d log (P) = -1/3] corresponds to a maximum valu-^ ^f fracture

toughness independent of crack extension. The microstructure-controlled

region of small cracks would define the second limit where the strength is no

66
longer dependent on Indentation load, but the authors acknowledged a

suggestion by others that the observed toughness would not drop below the

value appropriate to either single-crystal or grain-boundary fracture.

The property of fracture toughness increasing as a function of crack

extension has been shown to exist for some materials which consist of

irregular-shaped aggregates that are joined together in a matrix of another

phase. Krause and Fuller [2] determined the fracture toughness of a polymer

concrete material to increase with crack extension which was controlled by

various chevron-notched configurations. Using a compliance method,

Stelnbrech, Knehans, and Schaarwachter [3] performed fracture experiments

under conditions of slow crack growth with prenotched, three point bend

specimens of polycrystalline alumina. They examined the Influence of grain

size on crack-grcwth resistance; coarser grained material showed less

resistance initially for small cracks, but the increase of resistance in the

coarse-grained material was greater with crack propagation than a

fine-grained material.

The concept of crack growth resistance rising with crack extension

represents the situation that as a crack propagates, more energy per unit of

cracked surface is required, perhaps due to the tractions of aggregate

interlock and puilouu or cue increase of multiple fine cracks at the main

crack tip. \Vhile the calculated crack area is generally assumed planar, the

fact that the actual crack path is tortuous, possibly along grain boundaries,

would merely constitute a roughly constant factor systematic error. As a

matter of convenience the present work will address this phenomenon in terms

of plane-straii-' fracture toughness 'K^), which is proportional to the

square-root of crack-growth resistance (R)

67
= [E R/(1-v2)]1/2 ( 1 )

A derivation of a function for rising (R) has been presented [4] and is

adapted here in terms of (K^). a rising (R or is assumed to be a

function of crack extension (a-a^) only and to be invariant with the Initial

notch depth (a^). The simple condition for the derivation is that the

critical crack depth is approximately proportional to the initial notch

depth. The general solution follows

= k (a - Sq)"' (2)

where (k) and (m) are constants. The basis for the derivation of eq 2

follows from the criterion for slow, stable crack extension

K = (3)

and from the criterion for rupture which is the point of tangency

dl^/da - dK^/da

where (K) is the applied stress-intensity factor.

In the following presentation expressions will be derived based on

eqs 2, 3, and 4 to relate observed bending strength data as a function of

indentation load in 'wo series of experiments: (I) including the residual

stress due to indentation and (II) having the residual stress annealed at an

elevated temperature. Through a least-squares method these expressions will

be fitted to evaliiate the coefficients (k) and (m) for an alumina ceramic.

68
II. Experimental

The indentation-strength measurements were carried out on a vitreousbonded ceramic of 96 weight percent Al 20 ^. The microstructure and chemical

composition of this commercially manufactured ceramic was characterized

extensively in an earlier Investigation of its creep and creep rupture

properties [5]. Originally, the irregular-shaped grains of AI

2 O

3

, having

dimensions from 3 to 20 pm in any direction, were bonded by a vitreous phase

consisting of S 102 , AI 2O

3

, and MgO. Flexure specimens were cut to a nominal

size of 3 mm X 5 mm X 50 mm with a metal-bonded 60 pm diamond blade. The

prospective tensile and compressive surfaces were ground flat and parallel

and the edges slightly chamfered by a reslncid-bonded 30 pm diamond wheel.

The prospective tensile surface was in addition polished with 9 pm diamond

paste to produce a finish for subsequent optical microscopic examination.

The finished specimens were annealed ^ da at 1050°C to make them less

susceptible to creep rupture. Following this annealing process some

devitrification occurred in the bonding phase [5].

A series of three uniform flaw sizes were produced 2 mm apart in the

center of the pr '.rpective tensile surface of ;acl' flexure specimen by a

Vickers diamond pyramid. Care was taken to orient one sec of radial cracks

of an Indentation flaw to be parallel to the cross-section of the specimen

where the prospective rupture would occur. Flaw sizes were controlled with

Indentation loads ranging from 3 to 300 N. All indentations were made at

room temperature in air with a displacement rate of appi'o>;).macely 0.4 mm/sec.

The pyramid was allowed to contact the specimen surface for about 30 sec;

then the loaded pyramid was withdrawn to complete the load cycle.

69
Surface cracks in the direction of prospective rupture were measured

immediately after the indentations by a shadow technique of optical

microscopy. Illumination of a small area alongside the surface crack cast a

shadow over the slightly raised edges of the crack. The photographed Image

was compared to that of a calibrated scale of the same magnification, ranging

from 1 MO to 310 times for large to small cracks, respectively.

Strength tests were conducted at room temperature In two series of

experiments: (I) Including the residual stress due to indentation and (II)

having the residual stress annealed at an elevated temperature. While Series

I experiments were performed Immediately following Indentation, the specimens

used in the Series II experiments were annealed approximately 1 h at 1050°C

following Indentation. Heating and cooling rates were approximately 20

deg/min. All specimens ruptured at an Indentation. A universal testing

machine was used to produce the load (F) required to rupture a specimen under

4 point bending. The gear-driven crosshead of the machine was operated at a

constant speed of 0.5 mm/mln, and the load was transmitted through a

seml-spherlcal block with fixed loading rods of 3 mm diameter. Loading was

indicated by a linear strain gauge and was recorded on a constant speed

chart. The gauge was calibrated at the full scale of the chart with a known

10 kg mass and the local 9 801 m/s^ acceleration of gravity. Tl'? bending

moment (M) and bending strength (S) were calculated respectively from

M = {F/2)U^-%^)/2 (5)

and

S = 6M/2 b t^ (6)

70
In which 2,^ = Lio mm, 2-2 = ''0 b = 2.5 mm, and t = 3 mm were the nominal

dimensions as shown in Figure 1 .

III. Analysis

When a significant load (P) is applied to a sharp Indenter in contact

with a test material and the indenter is then unloaded, semi-circular radial

cracks will develop to their final lengths in the test material [7]. The

driving force of the crack system may be characterized by a residual

stress-intensity factor

Kp = X P/a3/2 (7)

where (X) is a constant characteristic of the material. The crack will grow

as long as (K^ > K^), and an equilibrium position will be attained when

(K^ = Kq), which is the criterion of eq 3. This phenomenon is described by

the (K^) curve and point I in Figure 2. When eq 2 with (a^^ = 0), is equated

to eq 7, the crack depth at Indentation equilibrium becomes

( 8 )

Where A = k^/X is a constant.

Consider that in the Series I experiments a freshly indented tesc

specimen which has a controlled flaw of size (a-j) is subjected to a small

bending stress (a). A stress-lnr,ensity factor due to tliis luina stress

71
wll] be superposed upon (Kj.), the crack system will grow as long as (K > K^,),

and an equilibrium position will again be attained when (K = K^). The

bending stress-intensity factor may be expressed as

where (Y)is a configuration coefficient that is dependent on relative crack

parameters. Catastrophic failure ensues when the criterion of eq 4 is

satisfied. Figure 2 shows (K) corresponding to (o = S), the bending strength

of a specimen with an original flaw size (a^). The point of tangency, point

T of Figure 2, defines the crack depth (a^) at rupture.

The crack depth at rupture can be determined by substituting the

appropriate forms of eqs 2, 7, and 9 in eqs 3 and 4 to give

( 9 )

( 10 )

and

mko 1/2 YSa^“''/2 - 3/2 XPa^"5/2 ( 11 )

respectively.

Solution of eqs 10 and 11 yields

= [4P/A( 1 -2m) 3+2m) ( 12 )

Dividing eq 12 by eq 3 gives the rupture to indent crack depth ratio

a^/ai = [4/(1-2m)]2/(3+2m) ( 13 )

72
The coefficient of fracture toughness 0<q) has the subscript zero to denote

that (K^) is defined by assuming ( a^ = 0). This means that extending the

crack from (a-|) to (at) includes the history of any tractions which might

exist up to (a^). An alternative definition of (Kq) corresponds to (sq = a^

)

where the prior history of any tractions is neglected. In this second

definition the coefficient of fracture toughness has the subscript one and is

simply related to the former by

= ko/(1-ai/at)"’ (1^)

Experimentally, the bending strength (S) is measured as a function of

indentation load (P). When eq 12 is substituted for (a^) in eq 10, the result

may be rearranged to the general form of

log (S) = B log (P) + log (C) (15)

Accordingly, the crack-depth exponent of fracture toughness is given by

m - ( i^-3B)/1^-2B) (1C)

and the coefficient of fracture toughness is given by

!<q = YC(-AB)^ (1-B)^^"^^ (

1

7 )

73
The coefficients (B) and (C) can be evaluated by a least-squares-f it of eq 15

for the observed (P) and (S) data of the series I experiments. Rearrangement

of eq. 8 in which eq 16 is substituted for (m) gives the coefficient

A = P/a^2/(1-B) (^ 3 )

Using the observed (P) and (a^) data in eq 18, a mean value of (A) can be

calculated.

Now consider that in the Series II experiments a test specimen is

annealed at an elevated temperature to relieve the residual stress resulting

from an indentation load. If fracture toughness is defined by (a^ = o) in

eq 2, application of a small bending stress (o) to the specimen would produce

no further crack extension until (a) is increased to (S) to satisfy the

criterion of eq. 3. But since the criterion of eq M is already satisfied at

this point, catastrophic failure occurs (a^. = a^ )

.

Combining the appropriate

forms of eqs 2 and 9 to solve for ^a^ and equating it to eq 8 give

(YS/kQ)“2/(1“2m) ^ (p/^)2/( 3+2m) (^g)

When eq i9 is rearranged to the general form of eq 15, the exponent of crack

extension (m) is again given by eq 16; out the coefficient of fracture

toughness is determined as

k^ - YCA® (20)

The coefficients (B) and (C) can be evaluated by a least-squares-f it of eq 15

for the observed (P) and (S) data of the Series II experiments.

74
If the alternative definition of fracture toughness (a^ = ai ) is assumed

for the Series II experiments, the crack would extend somewhat beyond (a^")

before rupturing. Substituting the appropriate forms of eqs 2 and 9 into

eqs 3 and M gives

K, (at-a,)” - JSat'''2 (21 )

and

mk^ = 1/2 (22)

respectively. Solution of eqs 21 and 22 gives

(23)

IVhen eqs 21 and 23 are combined to eliminate (YS/k-|), the rupture to indent

crack depth ratio is given by

a^/ai = 1/(1-2m) (24)

Substituting eq 23 for (a^) in eq 21 results in the general form

The exponent of crack extension (m) is again given oy eq 16, but

coefficient of fractu'^e toughness for the alternative definition

of eq 15.

the

is given by

k^/r f 2m) 2 '^-( 1 -2m) (

1

^ 3

- 2 m ) /8 o

-

( 25 )

where (k^) is given by eq 20.

75
IV. Results

Figure 3 shows plots of the observed bending strength versus indentation

load in the two series of experiments on the vitreous-bonded 96 percent

alumina ceramic. The indentation load covered the range between 3 and 300 N

in the Series I experiments, but only between 25 and 300 N in the Series II

experiments. The coefficients (B) and (C) were evaluated by a least-squares

method to fit the general form of eq 15 to the respective sets of data.

A' These values and their respective standard deviation are given in Table 1

.

While the imprecision of the Series II experiments is approximately twice as

large as that for the Series 1 experiments, both series of experiments yield

the same slope [B = d log (S)/d log (P)] within the precision of

measurements. The exponent of crack extension (m) was calculated from (B) by

eq 16. The parameter log (C) is the log (S, Pa) intercept at log (P, N) = 0.

The standard error of (S) was approximately the same in both series of

experiments

.

The coefficient (A) was determined from eq 18 in which (a^) was assumed

the same as (c^). The half-length surface cracks were measured with ±5 ym in

tile directlui'i of prospective rupture ^.1 nominal indentatlou loads of 30, ICO,

170, and 300 N, respectively. No systematic trend of (A) was evident over

this range of loads. The mean value and standard error of log (A) is 7.991 ±

0.036 for these 4 measurements in SI units.

The configuration coefficient (Y) was calculated from published [9]

scr’<' 3s-intensity factor equations for the surface crack on a specimen subject

to a bending stress. The stress-intensity factor at any point along the

76
crack front depends on the parameters (a/t, a/c, c/b, and }>) which are

defined In Fig 1 . The calculations are valid for 0 _< a/t < 1 , 0 < a/c _< 1 ,

c/b < 0.5, and 0 _< (p _< tt radians. Figure M shows that the calculated value

of (Y) is from 10 to 20 percent greater at the surface than at = it/2

radians for the range of semi-circular cracks (a-j = ) generated by

indentation loading. Consequently, if a bending stress were applied, the

crack front would tend to develop initially more at the surface than

depth-wise to make the crack front become semi-elliptical. The special case

where the stress-intensity factor is approximately uniform along the crack

front as it grows was found to exist at

the (Y) for this special case can be expressed simply as a function of (a/t)

as shown by curve 1 in Fig 4. Individual values of (Y) were calculated at

(a^) and (a^) for all the values of (P) in the Series I experiments, except

(P = 300 N) which gave (c^-Zb > 0.5). As the crack-depth varies over the

range from (a-j) to (a^), the calculated (Y) decreases approximately 0.6

percent at the lowest (P) and decreases approximately 5 per-cent at the

highest (P). The mean and standard deviation of the calculated (Y) at the

midpoint of the respective 8 ranges is 1.17^ ± t'.Oii. Cui'vo ^ in Fig 4 gives

(Y) calculated for a straight-through crack [10] for comparison.

(a/c) = -1 .5 (a/t) 0.95 ( 26 )

Considering that

(c/b) = (a/t)(a/c)“^ tb“^ (27)

77
Table 1 gives the values of the coefficient of fracture toughness (k^)

that were determined from eqs 17 and 20 for the Series I and II experiments,

respectively. The values are surprisingly close despite the imprecision of

the two sets of measurements. When the (k^ ) and (ko) values from the Series

I experiments are compared, the difference can not be distinguished within

the precision of measurements. Thus, any tractions that might exist on the

cracked surface up to (a^) are negligible compared to those existing between

(a-|) and (a^-). Just the Inverse appears, however, in the Series II

experiments. If the tractions which exist on the indentation cracks were

ignored in the Series II experiments, the coefficient of fracture toughness

would be over-estimated by 28 percent.

Figure 5 shows fracture toughness Increasing as the power function of

crack extension expressed by eq 2. The Series I experiments correspond to

(K^) increasing from 3*36 to ^.83 MPa*m^^^ while covering the observed range

of rupture cracks from 67 to 1140 pm, respectively. The Series II

experiments correspond to (K^) Increasing from 3-48 to 4.23 MPa*m^^^ while

covering the observed range of rupture cracks from 88 to 405 pm,

respectively.

V. Discussion

The present work provides an alternative method for determining rising

fracture toughness, but it differs in several respects wish that of Coolc,

Lawn, and Fairbanks [1]. Essentially the formulation in the present work is

based on the assumption that the rup ture-crack depth (a^) is proportional to

the indent-crack depth (ai). Alternatively, the formulation in the earlier

78
work is based on the assertion that a microstructural driving force may be

regarded to account for the apparent decline in the fracture toughness on

entering the domain of low contact loads.

The experimental results of the two methods differ remarkably. Neither

of the two limiting parameters which were advocated by Cook et al. were

observed in the present work. Instead, the log of bending strength was

interpreted in the present work to be a linear function of the log of

indentation load. The slope of this function was found approximately

32 percent smaller than the -1/3 slope which corresponds to a fracture

toughness independent of crack extension (m = 0). Cook et al. contended that

a slope of - 1/3 was characteristic of the large crack domain, which was the

same in both investigations; and they advocated that the corresponding

macroscopic fracture toughness was one of the limiting parameters.

Incidentally, the belief that the macroscopic fracture toughness was

independent of crack extension no doubt encouraged Cook et al. to adopt the

condition that (dK/da) be zero for the criterion of crack-growth instability;

but the formulation in the present work was based on the more general

condition of eq

The other limiting parameter, which Cook et al. advocated would account

for the apparent decline in fracture toughness, is based on the appearance

that strength is invariant in the small-crack domain. The lower limit of

indentation load used in the present work was slightly above a published [6]

threshold load of 2 N for an alumina material. The spatial scale of the

contact for a smaller load was beJ ieved insufficient to extend crack nuclei

[6]. If smaller indentation loads were to induce cracks, the/ would he

roughly the size of the grains of the alumina material used in the present

work. It is conceivable that some grains would not be vitreous-bonded and

79
that these breaches would constitute Inher'ent flaws In the microstructure.

Consequently, the "plateau" of maximum strength would reflect the Inherent

flaw-size which should dominate over a smaller crack due to Indentation. In

fact, the success of contact-source failures in the earlier work [1]

diminished markedly at the lower loads. Any apparent success could easily be

attributed to chance. The correlation of an Invariant strength and

indentation loading In the small-crack domain to give a decline in fracture

toughness Is regarded with suspicion.

References

1 .

2 .

4 .

R.F. Cook, B.R. Lawn, and C.J. Fairbanks, "Microstructure-Strength

Properties in Ceramics: I, Effect of Crack Size on Toughness,"

J. Amer . Ceramic Soc . , 6^ [11] 604-615 (1985]

.

R.F. Krause, Jr. and E.R. Fuller, Jr., "Fracture Toughness of Polymer

Concrete Materials Using Various Chevron-Notched Configurations,"

Chevron-Notched Specimens: Testing and Stress Analysis , ASTM STP 855,

J.H. Underwood, S.W. Freiman, and F.I. Baratta, Editors, American

Society for Testing and Materials, Philadelphia, 1984, pp. 309-323.

R. Stelnbreoh, R. IQiehans, and J. Sciiaarwaci'itei' , "Inorsase of Crack

Resistance During Slow Crack Growth In A120:; Bend Specimens,"

J. Materials Science . 1

8

, 265-270 (1983).

D. Broek, Elementary Engineering Fracture Mechanics , Noordhoff

International Publishing, Leyden, The Netherlands, 1974, pp. 122-126,

185-191

.

80
5. S.M. Wiederhorn, B.J. Hockey, R.F. Krause, Jr., and K. Jakus, "Creep and

Fracture of Vitreous-Bonded Aluminum Oxide," J. Materials Science , 21,

( 1986 ).

6. B.R. Lawn and D.B. Marshall, "Hardness, Toughness, and Brittleness: An

Indentation Analysis," J. Amer . Ceramic Soc . , 62 [7] 397-350 (1979).

7. G.R. Anstis, P. Chantikul, B.R. Lawn, and D.B. Marshall, "A Critical

Evaluation of Indentation Techniques for Measuring Fracture Toughness:

I, Direct Crack Measurements," J. Amer . Ceramic Soc., ^ [9] 533"538

( 1981 )

.

8. P. Chantikul, G.R. Anstis, B.R. Lawn, and D.B. Marshall, "A Critical

Evaluation of Indentation Techniques for Measuring Fracture Toughness:

II, Strength Method," J. Amer . Ceramic Soc . , 69 [9] 539-593 (1981).

9. J.C. Newman, Jr. and I.S. Raju, "An Empirical Stress-Intensity Factor

Equation for the Surface Crack," Engineering Fracture Mechanics , 15 ,

185-192 (1981).

10.

J.E. Srawley and B. Gross, Cracks and Fracture , ASTM STP 601, American

Society for Testing Materials, Philadelphia, 1976, pp. 559-579.

81
Table 1 . Experimental values of parameters that define fracture toughness of

a vitreous-bonded 96 percent alumina ceramic. The uncertainty for

each value is its standard deviation.

Parameter Series I Kc = Kp > KbSeries II

Kc = Kb

log (C) 8.5601 ± 0.0101 8.7340 ± 0.0248

B -0.2284 ± 0.0063 -0.2177 ± 0.0124

m 0.1281 ± 0.0083 0.1424 ± 0.0167

11.50 ± 0.76 11.59 ± 1 .62

1 .058 1 .278

Standard Error of S

(percent)

±0.94 ±1 .09

Number of experiments 27 10

^Based on values of^ (A) and (Y) given in the text.

82

md
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87

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COAL SLAG PENETRATION IN A MAGNESIUM CHROMITE REFRACTORY

S.M. Wiederhorn and R.F. Krause, Jr.

Institute for Materials Research and Engineering

National Bureau of Standards

Gaithersburg, MD 20899

Jing Sun

Shanghai Institute of Ceramics

Shanghai, Peoples Republic of China

ABSTRACT

The effect of coal slag on the microstructure and creep behavior of a MgCr20^ refractory was evaluated. As the slag penetrated the refractory,

ion exchange between the refractory and the slag changed the composition of

the slag from anorthite-like to diopside-like. This modification of the

slag composition is believed to have reduced its viscosity and enhanced its

reactivity. The creep rate of the refractory brick increased by a factor of

s: 3 when slag penetrated into the brick. Creep behavior was rationalized in

terms of the spacing and size of the aggregate particles within the

refractory, and the structure and composition of the material bonding the

aggregate particles together. It is suggested that refractory

disintegration involves creep deformation at the hot face of the brick

caused by mechanical loading and stresses due to ion exchange within the

brick. The results of this paper suggest that refractory performance can be

improved by chemical modification of the brick so as to prevent a reduction

of slag viscosity during penetration. This improvement of performance might

be achieved by the replacement of MgO in the brick by a network former such

as AI2O3

.

88
1. INTRODUCTION

Magnesium chromite refractories are prime candidates for use as linings

at the hot face of slagging coal gasifiers. Indeed, this type of refractory

is currently being used in pilot plants and in full size coal gasification

plants in the United States and Europe [1]. Experience in the field

indicates that these refractories are resistant to high temperature

dissolution by the types of slags that are present in slagging gasifiers.

This field experience is consistent with earlier laboratory studies that

suggested high chromia refractories as likely candidates for slagging

gasifiers [2-4]. Despite their promise, however, these refractories do

exhibit cracking and spalling near the hot face under some conditions [5].

The cracking seems to result from the penetration of the slag into the hot

surface of the refractory with subsequent reaction to destroy the

structural integrity of the refractory.

To improve the performance of refractories in slagging gasifiers, a

deeper xinderstanding of the penetration process and its role in controlling

creep and rupture of these refractories is needed. In this paper, the

results of an investigation of the role of coal slag composition on

penetration and creep behavior of a MgCr204 refractory is presented. The

data suggest a strong correlation between structural stability of the

refractory and the viscosity of the intergranular vitreous phase that forms

in the refractory as a consequence of slag penetration. The lower the

viscosity of the vitreous phase, the more readily the surface of the

refractory disintegrates. The chemical processes that control the viscosity

of the vitreous phase and the effect that this vitreous phase has on creep

and creep rupture are discussed.

89
2. EXPERIMENTAL PROCEDURE

The material selected for study was a MgCr204 refractory composed of

approximately 20 weight percent MgO and 80 weight percent Cr203 . The

refractory consisted almost entirely of the spinel crystal structure, but

since the material was chromia rich, corxindum grains of Cr203 were found

scattered as precipitates in the spinel. Samples of the material were from

two sources: a new brick obtained directly from the manufacturer; and a

section of a brick obtained from a gasifier plant. The latter had been

cycled from ambient to approximately 1200°C-1600°C at least 11 times and

had been in service for at least 475 hours under a variety of coal residues

before being removed for testing.

In order to simulate the creep behavior of the material in service and

to investigate the cause of the spalling observed in the hot face of the

refractory, it was important to duplicate the structure of the refractory

taken from the slagging gasifier plant. Hence, specimens from the newly

manufactured refractory brick were impregnated with several synthetic

slags, the compositions of which are given in Table 1. The synthetic coal

slag, which was similar to that from a Western coal, has been used

extensively at Argonne National Laboratories in studies of the corrosion of

ceramic refractories exposed to coal slag [6]. The anorthite slag, which

has only three major components of the synthetic coal slag, was selected as

a simplified version of this slag. The diopside slag was included because

its composition resembles that found by a microchemical analysis of the

vitreous phase inside the MgCr204 refractory from the coal gasifier. The

slags in Table 1 were synthesized from weighed portions of reagent grade

90
CaC03 » AI2O3 , Si02 » Fe203 , MgO, K2 CO3 and Na2 C03 powders. After each

mixture of powders was blended, a small amount was melted in the

temperature range 1500°C to 1600°C in a platinum vessel. The remainder was

then added slowly until the total batch of 200 to 600 g formed a melt. The

melt was stirred with a platinum propeller for about 2 hours.

Creep measurements on the newly manufactured brick were conducted on

specimens nominally 12 by 12 by 35 mm. Specimens were diamond-sawed to the

nominal size and their surfaces diamond-ground flat and parallel to a 30 pm

finish. Specimens were either tested without further preparation, or were

preheated to 1500°C and soaked for a period of 24 hours in a volume of slag

(Table 1) that was *30 times the volume of the specimen. After withdrawal

from the slag, specimens were annealed at 600°C for several hours before

cooling to room temperature. They were then reground to final dimensions

for high temperature creep studies. Because the thickness of the section of

brick from the gasifier was only * 10 mm, it was sawed into smaller

specimens, 8 by 8 by 16 mm, than those from the new brick.

Creep studies were conducted in a gas tight furnace where a 500 ml/min

flow of 99.99% pure nitrogen gas maintained a low partial pressure of

oxygen in the environment; this environment limited decomposition of the

MgCr204 during each creep test. To protect the furnace interior from

contamination, a muffle tube of AI2O3 surrounded each specimen. Specimens

were separated from the silicon carbide push rods by 99.9 percent AI2O3

loading platens, 6 mm thick, and alignment was maintained during testing by

a hemispherical silicon carbide cap located between the upper push rod and

the alumina platen. New platens used for each creep test were easily

separated from the push rods afterwards.

91
Slag-free specimens were tested in compressive creep without further

preparation. Slag penetrated specimens, however, had to be protected and

sealed in order to prevent reaction of the slag within the specimens with

the AI2O3 platens and the silicon carbide push rods^. To retain the slag

within the refractory during the test, specimens were wrapped around their

sides with platinum foil, 0.09 mm thick. Both loading ends were covered

with platinum foil 0.03 mm thick. The side seam of the foil was welded

closed at room temperature, whereas the bottom and top seams self -welded at

the test temperature. Experiments using the same techniques on a

vitreous -bonded AI2O3 indicated little difference in creep behavior between

wrapped and unwrapped specimens, suggesting that the platinum foil has a

negligible effect on the creep rate of these specimens at the test

temperature.

Creep studies were conducted in the temperature range 1350°C to 1550°C.

Specimens were soaked at temperature for at least one hour before testing;

then a constant load was applied to the specimen by setting the load cycle

control of a universal testing machine to narrow limits [7]. Displacements

were measured using a linear variable differential transformer to determine

the position of the cross-head of the test machine. Experiments were

terminated generally at 0.02 to 0.04 percent maximum strain. The true value

of the strain was used to calculate the creep rate of this material at a

given stress and temperature.

92
The microstructure of the refractory was evaluated by both optical and

scanning electron microscopy. Specimens taken from various positions in

the brick were vacuum impregnated with epoxy resin to avoid microstructural

damage and pull-out during polishing. Standard diamond polishing

techniques were used to prepare specimens for microscopic examination.

Chemical compositions of both the slag within the refractory, and the

grains of the refractory were determined using x-ray energy dispersive

spectroscopy. To attain a high degree of accuracy in the analysis,

specimens of known composition were used to calibrate the principal

elements (Ca, Mg, Al, Cr, Fe) found in the refractory. Finally, the

crystalline structure of all phases present were confirmed by x-ray

diffraction analysis.

3. RESULTS

3.1 Microstructural Analysis

3.1.1 Brick from the Gasifier

A section of the brick from the coal gasifier is shown in figure 1. As

can be seen, the slag from the gasifier penetrated to a depth of * 55 mm

from the hot face, and cracks developed at depths of up to * 15 mm from the

hot face of the brick. The section of the brick shown in figure 1 was

sectioned to obtain specimens for microstructural analysis. Specimens were

taken from the hot face, from the boundary determined by the limits of slag

penetration and from the unpenetrated portion of the brick.

93
The microstructure of the impenetrated portion of the brick, figure 2,

is similar to that of the freshly manufactured brick. The brick contained

MgCr204 aggregate particles 1 to 3 mm in dimensions, bonded in a matrix of

much finer grains of MgCr204 . The black area in figure 2 represents the

finer grains of the brick, which were not easily penetrated by the epoxy

resin used to mount the specimens. The scanning electron micrograph of

figure 3 shows the dark region to consist of submicron size particles of

Mgf'.r 204 . As only slight traces of Si02 were detected in the impenetrated

portion of the brick, the MgCr204 grains may have been directly bonded, or,

as is more likely considering recent studies of the structure of grain

boundaries in oxide and nitride ceramics [8-9], were bonded by a thin layer

(~ 1-2 nm) of an amorphous phase. The fact that many of the MgCr204

(spinel) grains contain plate-like Cr203 (corundum structure) precipitate

particles, figure 4, indicates a chromium rich composition in the newly

manufactured brick. The measured bulk density of the newly manufactured

brick suggested a porosity of * 19 volume percent. Since the brick appears

to be readily penetrated by slag, this porosity is largely interconnected,

and permits easy access of the slag to the interior of the brick during

high temperature exposure.

The appearance of the penetrated portion of the brick, figure 5, is in

sharp contrast to that of the impenetrated portion of the brick. The

region between the large aggregate particles now contains grains that are

much larger (~ 10 to 100 pm) than the original submicron size grains,

suggesting considerable growth of these grains as a consequence of the slag

penetration. Slag shows up between the spinel particles as the dark grey

areas in figure 5, and forms about 6 volume percent of the inter-aggregate

region in the penetrated portion of the brick. The black areas in figure 5

94
are voids, v/hich form = 20 volume percent of the inter-aggregate region.

These voids appear to be unconnected and, therefore, do not form a

continuous path through the penetrated portion of the brick. The connected

porosity of the original brick is apparently filled by the slag, leaving

behind remnant, isolated voids in the brick after penetration.

Micrographs of the cracks that appear near the hot face of the brick

show that these are not cracks at all, but blunted, elongated cavities,

figure 6. The roots of these crack-like cavities were slag filled with

siT.ill * 50 pm grains of magnesium chromite floating in the slag. The

rounded shape of the cavities suggests a flow process as an important

factor in their formation. These crack- like cavities undoubtedly were

formed at elevated temperatures as a result of creep deformation at the hot

face of the refractory.

The principal elements in the spinel grains near the hot face of the

brick were chromixam, magnesium and iron^, figure 7. The concentration of

iron at the hot face was approximately 18 weight percent. The iron

concentration diminished rapidly with distance from the hot face so that at

2.5 mm from the hot face, the concentration of iron was nearly zero.

Apparently iron does not travel with the slag into the brick, but is

absorbed by the MgCr204 spinel grains at the hot face. The spinel

effectively getters the iron from the slag that penetrates the brick. At

depths greater than « 3 mm from the hot face, the composition of the grains

of the brick approach that of the unreacted brick, which is slightly rich

in chromivim sesquioxide (0.515 moles of Cr203 to 0.485 moles of MgO).

Thus, only the spinel grains in the immediate vicinity of the coal-slag,

refractory interface are altered by reaction with the slag. The iron that

95
is normally present in the slag is apparently leached from the slag at the

hot face and does not penetrate beneath the surface of the brick.

The chemical composition of the vitreous phase within the refractory

brick was also determined as a function of distance from the hot face,

Table 2. Beyond the 25 mm limit of this table, the vitreous phase was

present in quantities that were too low for accurate chemical analysis by

the techniques used^. Despite the presence of iron within the spinel grains

at distances less than 2.5 mm from the hot face, figure 7, iron was not

detected in the vitreous phase within this distance. As no iron was found

in the vitreous phase, iron probably penetrated into the brick by solid

state diffusion. Because Cr203 is slightly soluble in the slag, it remained

at the * 3 percent level in all measurements^. The AI2O3 penetrated a

distance of * 15 mm from the hot face of the brick, but was not present in

measurable quantity beyond this distance. Finally, as the distance from

the hot face increased, the MgO concentration in the slag increased. Since

the only source of MgO was the MgCr204 of the brick, these results suggest

that during high temperature exposure, MgO was leached from the brick by

the slag. The MgO then migrated through the vitreous phase to the hot face

of the brick where it was removed by the slag running down the wall of the

gasifier. These observations are consistent with phase diagrams [10-11]

which indicate a limited solubility of Cr203 in a Mg0 -Ca0 *Si02 melt at

1500°. Tliey are also consistent with earlier data by Kennedy et al. [2-A]

on the same subject. Apparently, when MgCr204 is placed in contact with

slag, the MgO can readily leave the spinel phase, whereas the Cr203 cannot.

96
3.1.2 Bricks Impregnated by Slag in the Laboratory

The composition of the intergranular vitreous phase in the refractory

specimens that were slag penetrated in the laboratory is given in Table 3.

Analyses were conducted on material located both at the surface and at the

center of each test specimen. The intergranular vitreous phase was formed

by penetration of the slag through the porous bonding matrix of the

refractory. In the present study, approximately the same composition of

MgO, CaO, Si02 and Cr203 was found in the intergranular vitreous phase for

all slags and exposures. Significantly, these compositions were essentially

identical to that found in the brick from the slagging gasifier.

Although the synthetic coal slag contained both iron oxide and aluminum

oxide in substantial concentrations, table 1, neither of these are found in

the vitreous phase at the center of test specimens, indicating that these

oxides are leached from the slag at the surface of the refractory during

impregnation. These findings confirm those reached after examination of

the brick from the coal gasifier: neither iron oxide, nor aluminum oxide

penetrated much beyond the slag-refractory interface. Finally, the leaching

of MgO from the MgCr204 grains of the refractory is also confirmed by the

fact that MgO is found in the intergranular vitreous phase formed by

penetration of anorthite slag into the MgCr204 specimens. Since the

anorthite slag originally contained no MgO, the MgO had to come from the

refractory brick.

Chemical analyses of the MgCr204 grains in test specimens exposed to

the laboratory slags are summarized in Table 4. These results complement

those obtained on the vitreous phase. Table 3. Iron and aluminum oxide that

97
leave the slag are found only in the surface grains of the refractory which

are now depleted of magnesium oxide. By contrast, the grains at the

interior of the specimens contain only Cr203 and MgO, a finding that is

consistent with the iron and aluminum oxide being leached from the slag

primarily at the external surface of the specimen. The general reduction of

MgO concentration in the specimen interior also suggests a general

migration of the MgO from the interior of the refractory to the

slag-refractory interface.

Microstructural modification of the refractory depends on the slag to

which the refractory is exposed. Exposure to the synthetic coal slag

resulted in a dense spinel coat at the external surface of the specimen,

figure 8a. Contained within this coat were fine precipitate particles of

Cr203 . Although penetrated by the slag, the microstructure of the interior

of the specimen, figure 8b appeared to be much denser and better integrated

than that of specimens taken from the hot face of the slagging gasifier,

figure 2. The much higher concentration of Cr203 (bright phase in figure

8b) in the interior is consistent with a general loss of MgO from the

specimens. An extreme example of this behavior is illustrated by the

specimen exposed to the anorthite slag, figure 9, which showed a ring of

corundiam grains around the entire surface of the specimen. Apparently,

leaching of the MgO was sufficiently complete as to convert all of the

spinel phase to coriindum. The interior of these specimens were similar in

appearance to that of the specimen exposed to the synthetic coal slag.

Of the three synthetic slags tested, the most aggressive one was the

diopside slag. When exposed to this slag for 24 hours at 1500°C, the

MgCr204 refractory completely disintegrated. Similar exposure to the other

98
slags left the specimens in tact with relatively good microstructural

integrity. To obtain some idea of the mechanism of attack, an exposure of

only 4 hours at 1500°C was used with the diopside slag. At this exposure,

the initiation of disintegration is apparent from the microstructure in

figure 10. Although some areas of the microstructure were similar in

appearance to that obtained from the synthetic coal slag exposed

refractory, figure 10a, other areas figure 10b, suggest that penetration of

the diopside slag through the fine aggregate particles forced the grains

apart leaving large pools of slag between the grains. Deep crack- like

cavities were observed along the route of slag penetration. This

microstructure resembled that of specimens taken from the hot face of the

slagging gasifier, suggesting an important role for diopside in the process

of refractory degeneration.

3 . 2 Creep Measurements

Typical creep tests conducted on specimens taken from the slagging

gasifier and from specimens prepared in the laboratory are illustrated in

figures 11 and 12, respectively. The creep strain, e, at a given applied

stress, a, and temperature, T, was represented by the following function of

time, t:

e = A‘t® (1)

where the coefficient. A, is a function of o and T. The coefficient A and

the time exponent, m, were evaluated by a least squares fit of equation 1

to the observed creep data. Since tertiary creep behavior occurs prior to

failure, the equation was fitted only to the point of inflection of the

99
data. The mean value and standard deviation of the time exponent, m, are

summarized in Table 5 for all test conditions. The value of this parameter,

~0.6 to =0.7, indicates a work hardening behavior for most of the specimen

lifetime. The deviation of the observed creep behavior (circles) from

equation 1 (solid line) indicates incipient failure in compressive creep^;

hence, the point of inflection of these curves was taken as the

strain- to- failure.

The creep data for the slag -impregnated MgCr204 refractory taken from

the coal gasifier (solid curves) are compared in figure 11 with creep data

from newly produced refractory [7] (dashed curves). At each temperature and

stress, the creep strain of the slag impregnated refractory exceeds that of

the newly produced refractory. This increase in the strain at a given time

was also typical of the refractory that was penetrated in the laboratory.

The strain rates of the impregnated refractories can also be compared

with that of the newly manufactured refractory by differentiating equation

1 to obtain the strain rate as a function of creep strain:

de/dt = (2)

Table 6 gives the strain rates calculated from equation 2 at 1 percent

strain for selected temperatures and applied stresses. The table presents

data for: (A) newly produced refractory; (B) slag impregnated refractory

made in the laboratory; and (C) slag impregnated refractory from the coal

gasification plant. These data are compared in Table 6 with creep data

published earlier on another sample of newly produced refractory. The

results from Table 6 indicate little difference between the creep rate

100
measurements in the two lots of freshly manufactured refractory. By

contrast, slag appears to enhance the creep rate by a factor of ~3.

4. DISCUSSION

4.1 Slag Penetration

In this paper the effect of coal slag on the structural integrity of a

MgCr204 refractory was investigated. By exposing specimens of this

refractory to different compositions of synthetic slag, it was possible to

elucidate the microstructural changes that resulted from slag exposure at

elevated temperatures. These changes were related to physical and chemical

processes that occurred at the hot face of the refractory brick. On initial

contact with the hot surface, molten slag penetrates the brick by

capillarity and travels to a depth that is determined by the temperature of

the brick [12]. As the temperature decreases from the hot face, the slag

viscosity increases and eventually the slag becomes too viscous to flow

perceptibly further into the brick. Viscosity is also important as a

measure of the rate of diffusive transport within the refractory after

penetration by the slag. In keeping with the Stokes-Einstein equation

[13-14], ionic diffusion within the slag is inversely proportional to

viscosity, so that changes in composition that reduce viscosity also

enhance transport within the slag, and hence accelerate degradation

processes that depend on diffusive transport.

In the present experiment, acceleration of transport processes occurs

as a consequence of chemical modifications of the slag during penetration.

At the hot face of the refractory brick, Al'*’^ and Fe'^^/Fe'*'^ leave the slag

101
and enter into the spinel structure of the MgCr204 refractory grains^,

while Mg'*'^ leaves the grains and enters the slag, figure 13. The net

effect of this exchange process is to change the composition of the coal

slag from one that lies in the anorthite phase field of the Ca0 -Al203 -Si02

phase diagram, to one that lies in the diopside phase field of the

Ca0-Mg0-Si02 phase diagram. Since Al"^^ and Fe'*’^ are both network formers,

their elimination from the slag reduces its viscosity. Such a reduction in

viscosity as a function of composition is observed in mixtures of anorthite

and diopside glasses [15], for which the viscosity decreases as the

composition is changed from anorthite to diopside. Based on this result,

the vitreous phase that forms in the intergranular space of the refractory

as a consequence of slag penetration is expected to have a lower viscosity

than the slag in the gasifier, and therefore should provide a more active

medium for chemical reaction and degradation of the refractory brick.

The loss of integrity of refractory bricks in slagging gasifiers

probably involves both enhanced dissolution, and swelling and disruption of

the bricks at the hot face [1-6]. The increase in dissolution rate is a

consequence of lowering the melting point of the spinel phase due to the

p'.resence of iron and aluminum oxides in the coal slag [10, 11]. As the

melting point is lowered, grains are dissolved at their boiindaries and

eventually detach from the walls of the refractory to be carried away with

the flowing slag [1, 6]. This mechanism of dissolution is consistent with

the appearance of the hot face of the refractory at the slag refractory

interface, figure 5. Although it is an important mechanism for loss of

refractory, dissolution by itself cannot be used in a simple way to explain

the appearance of cracks within the hot face of the brick. Furthermore, the

fact that refractories often wear out more rapidly in the field than is

102
predicted by laboratory measurements of dissolution rate, suggests that

other processes contribute to refractory failure [1, 5]. Swelling of the

hot face and subsequent spalling is one such cause of accelerated failure

of refractories in slagging gasifiers. [1, 5].

A number of physical and chemical processes may be envisioned to

explain the swelling that eventually results in cavitation and spalling of

the hot face of the gasifier walls. As noted earlier by Bakker [1],

failure probably occurs as a consequence of creep during which cavities and

voids are generated at high temperature^. Stresses driving the creep arise

either from chemical instabilities and reactions at the hot face of the

refractory, or from mechanical forces that develop as a consequence of the

wall construction. Mechanical forces are mainly due to the weight of the

wall and to thermal expansion within the wall when the gasifier is cycled

between room temperature and the operating temperature. Because the

temperature of the refractory wall is greatest at the hot face, creep

strains from these stresses are also greatest at the hot face. The

importance of thermal expansion and structural loading to wall design has

been discussed in some detail by Chen and Buyukozturk [16-17], who note

that with proper design these mechanical causes of structural failure can

be minimized.

Stresses at the hot face of the gasifier walls are also caused by

processes that are more chemical in nature. As a consequence, differences

in solubility or in rates of diffusion within the various phases of the

refractory brick can lead to osmotic type of pressures that also cause the

refractory to creep. The absorption of FeO/Fe203 and AI2O3 into the

spinel phase of the brick, for example, is equivalent to a net transport of

103
matter from the slag to the hot face of the brick, resulting in an increase

in the volume of this phase. Under the physical constraints existing at

the hot face, this increase in volume results in creep of the brick towards

the center of the gasifier [1, 5] thereby providing a mechanism for

cavitation at the hot face^. In this regard, it may be significant that

cavitation at the hot face occurs over the same 15 mm depth that is

observed for the absorption of the AI2O3. Creep at the hot face of the

brick can also result from differential dissolution of the MgO from the

MgCr204 . Because crystals usually expand their volume upon dissolving or

melting, the dissolution of the MgO from the MgCr204 results in a volume

expansion of the vitreous phase within the refractory brick. If the

microstructure of the brick is sufficiently restrictive and the viscosity

of the vitreous phase is sufficiently high to prevent the free flow of the

vitreous phase between the interior and exterior of the brick, a build-up

of pressure due to dissolution will also lead to creep at the hot face of

the refractory.

4.2 Creep and Creep Rupture

Whatever the driving force for creep, refractory failure occurs only

when a critical creep strain is exceeded, so that the development of a

useful theory for creep induced spalling of refractories requires an

understanding of microstructural and environmental factors that determine

the critical strain for creep rupture. In particular, an understanding of

void generation and cavity growth within refractories is needed. Despite

recent experimental and theoretical advances on creep rupture of ceramics

[18-19], the level of understanding needed for the development of a useful

theory of creep rupture of refractory materials has not yet been achieved.

104
However, in the absence of a detailed understanding of failure mechanisms,

empirical relations, such as the Monkman-Grant relation [ 20 ], may be useful

for the development of failure models. The Monkman-Grant relation suggests

an inverse linear relation between the failure time and the minimum creep

rate; ceramics such as hot-pressed silicon nitride [21], dense fine-grain

AI2O3 [ 22 ] and vitreous bonded AI2O3 [ 23 ] all obey this type of equation.

Furthermore, unpublished data by the present authors indicate that a

zirconia-alumina-silica refractory also obeys this relation. If a

Monkman-Grant relation is also applicable to the failure of MgCr204

refractory, then an increase in creep rate of * 3 as a consequence of slag

penetration, would lead to a factor of 3 decrease in lifetime of the slag

penetrated refractory.

Results from the present study on the creep of slag impregnated MgCr204

indicate a low sensitivity of the creep rate to slag penetration. Although

the inter-aggregate space in the refractory was completely filled with

slag, creep rates increased by only a factor of =3 over that for the

as -manufactured brick [ 7 ]. This modest increase in creep rate can be traced

to changes in microstructure when slag penetrates the brick. Because of

their large size, 1 to 5 mm, the aggregate particles of the MgCr204

refractory may be considered rigid with regard to the binder or

inter-aggregate microstructure that holds the aggregate particles together,

so that resistance to deformation is solely determined by this fine grained

microstructure. Vfhen slag enters into the fine grained inter-aggregate

microstructure, it effectively lubricates the grain boundaries of this

structure by providing an easy path for mass transport and dissolution,

both of which enhance creep in two phase ceramics. This enhancement of

creep rate is opposed by the grain growth that occurs within the

105
inter-aggregate microstructure when penetrated by slag. Thus, two opposing

factors influence the creep behavior of this structure and the effect of

slag penetration on creep will depend on the balance of these two factors.

Using current theories of two phase creep, these ideas can be expressed

in more quantitative terms. The creep of rigid particles in creeping matrix

can be expressed in terms of the size, D, of the aggregate particles, the

spacing, W, between the aggregate particles, and the effective viscosity,

u’ , of the bonding phase, figure 14. For most theories, the creep rate is

inversely proportional to the viscosity and is related to W and D through a

simple power function of these two variables. Creep equations for

percolation [24] (eq. 4), and transport controlled solution-precipitation

[25, 26] (eq. 5) are presented here as examples of the role of

microstructure on creep:

The creep rate depends on the structure of the material primarily

through the parameters W and D, and, since the inter-aggregate bonding

phase also has structure, through the effective viscosity, m*» of the

inter-aggregate phase. Because the aggregate particle size and spacing are

vinaffected by slag penetration, the influence of slag on the creep behavior

of these materials will occur almost entirely through the role that slag

plays in determining the effective viscosity of the inter-aggregate phase.

de/dt a (o/m' )

• (W/D)^ (4)

de/dt a (o/m ' )

* (W/D)D“^ (5)

106
If one defines the viscosity of the inter~aggregate phase as the ratio

of local stress driving the creep of this phase, to the creep rate of the

inter-aggregate phase, then the viscosity, m'. depends on microstructure as

is illustrated by the following three equations: eq. 6 for transport

controlled solution-precipitation creep [25-27]; eq.7 for interface

controlled solution-precipitation creep [25-27]; and eq.8 for percolation

[24]:

1/m' a (l/M)*(w/d) d~2 (6)

1/m' a (l/M)*(w/d) (7)

1/m' a (l/M)*(w/d)3 (8)

w and d are the intergranular spacing, and grain size of the

inter-aggregate phase, and p is the viscosity of the glass in the

inter-aggregate phase, figure 14.

As the ratio w/d increases, each of these equations predicts an

increase in the creep rate at a given temperature and applied stress. For

dilute slag concentrations, w/d is proportional to the voltune fraction of

slag, so that when creep is determined by interface controlled solution

precipitation or percolation, the creep rate depends only on the volume

fraction of slag. When creep is determined by transport controlled

solution precipitation, the creep rate also depends independently on the

grain size of the inter-aggregate particles. Regardless of the particular

107
theory considered, the ratio w/d in the slag penetrated brick will have to

be greater than that in the newly manufactured brick in order to explain

the enhancement of the creep rate as a consequence of slag penetration.

From the micrographs of the present study, semi -quantitative estimates

of w/d can be obtained. For the impregnated brick w/d » 0.1 (from figure

5); for the as -manufactured brick w/d ranges between 0.1 and 0.001. The

upper value for the as -manufactured brick was determined from scanning

electron micrographs which suggest a grain boundary width, w, of less than

* 100 nm. The lower value is based on observations (using transmission

electron microscopy) that most polycrystalline ceramic materials have

amorphous grain boundaries with thicknesses greater that = 1 nm [8-9].

Using the above estimates of the grain boundary thickness of the

inter-aggregate phase, the following estimates of creep acceleration due to

slag penetration are obtained: solution-precipitation (transport

controlled), 0.01 to 1; solution-precipitation (interface controlled), 1 to

100; percolation, 1 to 10^. From these estimates, it is concluded that

transport controlled solution precipitation is probably not a controlling

nechanism for creep. By contrast, interface controlled

solution-precipitation and percolation are both consistent with the creep

data provided the grain boundary thickness, w, of the inter-aggregate phase

is * 100 nm. Further investigations of the microstructure of these

refractory materials will be necessary to distinguish between these two

mechanisms.

108
4.3 Refractory Lifetime

Penetration of slag into the refractory not only provides a mechanism

for spalling of the hot face of the refractory, but also reduces the

resistance of the refractory to creep, thereby decreasing its lifetime,

.'^.ince increasing slag viscosity decreases both slag reactivity and creep

rate, the present study suggests that refractory lifetime can be improved

by increasing the viscosity of the vitreous phase formed by the penetration

of slag into the hot face of the refractory. In the MgCr204 refractories,

viscosity is reduced by ion transfer of magnesium from the spinel structure

to the slag. Elimination of the MgO from the refractory or reducing its

concentration should help to reverse this process. The addition of a

network former, such as AI2O3 , to the brick should also help to increase

slag viscosity by reducing the driving force for AI2O3 absorption from the

slag. Methods such as these are currently being explored to increase the

durability of chromite refractories in slagging gasifiers [28].

5. CONCLUSIONS

In this paper, the effect of slag penetration on the microstructure and

creep behavior of a MgCr204 refractory was evaluated. The most interesting

and significant finding relates to changes observed in chemical composition

of the slag as it penetrated the refractory. Ionic reactions at the

surface of the brick produced an intergranular vitreous phase with a

diopside like (Ca0 *Mg0 * 2Si02 ) composition in contrast to the usual

anorthite like (Ca0 *Al203 * 2Si02 ) compositions foxond in western coal slags.

Because of this change in composition, the viscosity of the intergranular

vitreous phase formed in the refractory is probably lower and hence more

109
reactive than that of the original coal slag. These results suggest that

refractory performance can be improved by chemical modification of the

brick to prevent the reduction of slag viscosity during penetration, as by

the addition of a network former such as AI2O3 to the refractory

The process of refractory disintegration is believed to involve creep

deformation of the hot face of the brick, caused either by mechanically

induced stresses, or by stresses that arise as a consequence of ion

exchange reactions between the slag and the refractory brick. Mechanical

stresses arise from the weight of the refractory wall, or from differential

thermal expansion of the refractory. Stresses due to ion exchange reactions

arise as a consequence of transport of AI2O3 and Fe0/Fe203 from the slag

to the spinel phase of the refractory brick, which results in a volume

expansion of the hot face of refractory. Because of mechanical constraints

at the hot face, this volume expansion also causes creep of the refractory

brick.

As an increase in the creep rate of a factor of * 3 occurred when slag

was present in the refractory brick, creep of the refractory brick was

found to be sensitive to penetration by slag. Creep of this refractory

depends on the microstructure of the inter-aggregate bonding phase, in

particular on the ratio, w/d, of the grain boundary width to the grain size

of this phase. For the creep rate to increase as the refractory is

impregnated with slag, w/d has to increase. More detailed experimental

data on the microstructure will be needed for a quantitative comparison of

these creep data with theory.

110
Footnotes

:

1. In earlier experiments no protection was provided, and the slag reacted

with the pure alumina loading platens and the ends of the silicon carbide

push rods, whose deterioration indicated an erroneously high creep rate for

the refractory specimen.

2. Although aluminum oxide is also present in the surface grains of the

spinel phase, its concentration is less than ~ 2 Z and therefore is not

shown in figure 7. As with ironoxide, the aluminum oxide is restricted to

the surface of the refractory brick.

3. The precision of the analysis is determined by electron-beam spreading

and interference of signals from the picrochromite grains with those from

the glassy phase.

4. This slight solubility of the Cr203 in the slag at the temperature of

operation of the gasifier is the primary reason that picrochromite

refractories are resistant to coal slags.

5. Several specimens tested in the course of this study failed shortly

after the strain exceeded the point of inflection on the stress-strain

curve

.

6. At the low oxygen pressures typical of gasifiers [2], iron will be

present mainly in the +2 state.

7. Crack evolution by gas generation (e.g. iron bursting) is not believed

to be a factor in the present study because of the absence of iron in the

brick and because of the lack of evidence of other chemical reactions that

might lead to gas evolution.

8. The simultaneous loss of MgO from the hot face provides a mechanism for

a volume decrease, however, since the spinel phase is largely maintained at

the hot face, the loss of MgO is accommodated by defects in the spinel

structure. Therefore, the total volume loss should be minimal.

Ill
Table 1. Chemical composition (weight %) of selected slags used in

laboratory studies.

Slag CaO AI2O3 Si02 FeO MgO Na20

synthetic

coal slag

16 17 53 6 4 3

anorthite 22 22 56

diopside 26 55 19

112
Table 2. Composition of the intergranular vitreous phase in a Mg204

refractory from a coal gasifier plant. weight %.

Distance from

hot face.

(mm) MgO AI2O3 Si02 K2

O CaO Cr203

5 3.9 7.6 59.6 1.6 23.2 3.1

10 5.6 6.5 63.5 2.1 19.0 2.5

15 8.5 1.8 62.9 2.2 18.7 4.3

20 9.4 — 66.8 1.9 15.8 5.5

25 11.9 — 66.2 2.1 15.5 2.9

113
Table 3. Weight percent composition of the intergranular vitreous phase at

the interior of MgCr204 refractory specimens after exposure to slag at

1500°C.

Vitreous

phase MgO Cr203 CaO

Synthetic

coal slag 84 20

Anorthite

slag 9 2 24

Diopside

slag 9 3 23

Si02

68

65

65

114
Table 4. Weight percent composition of MgCr204 grains in refractory

impregnated with slag at 1500°C.

Location of Grains MgO Cr203 AI2O3 FeO

Original grains 20 80

Coal gasifier slag

Hot face 10 70 1 18

Specimen interior

(>2 cm)

18 82

Synthetic coal slag

Specimen edge 11 69 5 15

Specimen interior 14 86

Anorthite slag

Specimen edge 94 6

Specimen interior 15 85

Diopside slag^

Specimen edge 15 85

Specimen interior 15 85

^ Specimen exposed only 4 hours instead of the 24 hour period used for the

synthetic coal slag and anorthite slag exposures.

115
Table 5. Time exponent for the creep of a MgCr204 refractory before and

after impregnation by slag. The creep strain, c, is characterized by a power fxinction in time, t: e = A't*’*', where A and m are empirical constants

for the fit [ 7 ]

.

Test specimen number of tests m (s.d.)

Before Impregnation:

Series I ^ 9

Series II 6

After Impregnation:

Slag impregnated

in gasifier 4

Series II

synthetic slag 5

^ Reference 7.

0.74 (0.16)

0.64 (0.09)

0.65 (0.06)

0.60 (0.09)

116
Table 6. Compressive creep strain rates calculated at 1 percent strain for

Relative

Creep Rate^

1.1

0.6

0.5

1.7

1.0

0.8

Mean 0.95 ±0.43

2.9

2.0

1.1

MgCr204 refractory.

T/(°C) o/(MPa) 105 (de/dt)/h

(A) Series II, Newly Produced

1350 5.06 16.0

1400 2.25 5.73

5.08 36.1

1450 1.52 5.04

2.27 12.5

5.09 77.4

(B) Impregnated by synthetic coal slag.

1450 0.75 2.9

1.5 10.0

3.02 26.2

1550 0.75 13.3

1.50 90.3

(C) Impregnated by coal gasifier slag.

1400 3.01 19.9

4.25 40.6

1500 0.65 6.3

1.5 50.2

^ Relative to Series I fit in reference 7.

3.2

4.6

Mean 2.76 ±1.32

1.8

1.7

4.2

5.0

Mean 3.18 ±1.68

117
Figure Captions:

1 . View of the sample of MgCr204 refractory brick from the coal gasifier

plant. Crack like cavities are clearly visible near the exposed surface

(right hand portion) of the brick. Slag penetration is indicated by the

lighter shade of the brick towards the exposed surface. The major

divisions of the graph in the backgroxind are in 1 cm units.

2 . Microscopic view of an unpenetrated portion of the MgCr204 refractory

brick that had been exposed in the gasifier plant. This portion of the

brick was furthest from the hot face, and therefore was not penetrated by

the slag. The dark areas in these micrographs are not void space, but

regions of the microstructure that were not penetrated by the epoxy resin

used to prepare polished section.

3 . Scanning electron micrograph of one of the dark regions shown in figure

2 . X-ray energy dispersive spectroscopy indicates these submicron grains

to consist largely of MgCr204. Traces of calcium, aluminum and silicon are also observed in these areas.

4 . Plate-like Cr203 (corundiom structure) particles in the MgCr204

aggregate indicates a chromixim rich structure. The observation of this

precipitate is consistent with reported and measured average compositions

of the refractory brick.

5 . Microscopic view of a slag penetrated portion of the refractory brick

that had been exposed in the gasifier plant, (a) Regions between the large

fused aggregate particles that were formerly the dark areas of figure 2 now consist of MgCr204 grains ~ 10 pm in size, indicating considerable grain

growth during exposure, (b) Grains near the hot face of the brick show an increase in the amount of intergranular vitreous phase.

6 . Slag-filled, crack-like cavities in the slag impregnated hot face of

the refractory from the gasifier. These are the same features that look

like cracks in figure 1 . The rounded shape of these cavities indicate a slow deformation process in their formation, probably caused by internal

stresses in the hot face of the refractory.

7 . Chemical analysis of the spinel grains in the penetrated portion of the

brick obtained by using a scanning electron microscope with an x-ray energy

dispersive spectroscopy attachment. Although aluminum was also detected

close to the hot face, its concentration was less that 2 % and hence was not included on the figure.

8 . Effect of a synthetic coal slag on the microstructure of an MgCr204

refractory brick specimen: (a) dense spinel coat on the external specimen

surface indicates the transfer of aluminum and iron oxide from the slag to

the surface of the specimen; (b) interior of the specimen indicates full

penetration by slag. The specimen appears to be denser than a similar slag

penetrated section from the coal gasifier.

118
9. Effect of anorthite slag on the microstructure of MgCr 204 refractory

brick: Coating of Cr203 (corundum) grains is found around the exterior

surface of the specimen. Leaching of the MgO was sufficiently complete as to convert the spinel phase to corundum. The interior of the specimen was similar to figure 8b.

10. Effect of diopside slag on the microstructure of MgCr204 refractory

brick. (a) Portion of slag-penetrated specimen wherein structural

integrity has been maintained. Considerable grain growth has occurred

within the inter-aggregate region; (b) Slag penetrated area of the specimen

wherein the structure has been disrupted by the slag. Note the long

crack- like cavities near the specimen surface.

11. Compressive creep strain of a MgCr204 refractory impregnated with slag

from a coal gasifier. Observed strain (circles) was determined for

specimens subjected to applied stresses of (a) 3.01 MPa and (b) 4.25 MPa in

nitrogen gas at 1400°C. A solid curve is a least squares fit of equation 1 while a dashed curve predicts [7] the strain of the newly produced

refractory under the same stress and temperature.

12. Compressive creep strain of a MgCr204 refractory impregnated with

synthetic coal slag. Observed strain (circles) and least squares fits of

equation 1 for work-hardened creep (solid line) are plotted for tests

conducted in nitrogen gas at 1450°C under applied stress of 1.5 and 3.0 MPa

respectively.

13. Schematic diagram of mechanisms of slag attack on MgCr204 refractories.

Al"*"^ and Fe'*'^/Fe'*‘^ enter into the spinel structure at the hot face, while

Mg'*’^ and Cr"*"^ leave the surface grains of the refractory. The iron and the

aluminum reduce the melting point of the spinel grains, a consequence of

which is enhanced solution of the refractory in the slag. Within the

refractory, the aluminum and iron leave the slag to be replaced by chromium

and magnesium, which changes the composition from one similar to an anorthite melt to one similar to a diopside melt. At the same time, the

submicron grains that lie between the larger aggregate particles grow in

size. This grain growth coupled with transport of matter from the melt to

the spinel grains of the brick cause the hot face to bloat, crack and

eventually spall from the main body of the refractory brick.

14. Schematic diagram of the microstructure of a refractory brick. The

spacing and size of the large aggregate grains is given by W and D

respectively. The aggregate particles are bonded together by a much finer

grain microstructure, in which small grains of refractory of size d are bonded by a vitreous matrix. The spacing between the finer grain particles

is w. Because deformation occurs more easily within the finer grain bonding

microstructure, the creep rate of the refractory is largely determined by

this inter-aggregate microstructure.

119
References

:

1.

W.T. Bakker, S. Greenberg, M. Trondt and U. Gerhardus, "Refractory

Practice in Slagging Gasifiers," Am. Ceram. Soc. Bull., 63^ [7], 870-76

(1984).

2. C.R. Kennedy, "Coal Slag - Refractory Compatibility Studies Progress to

Date," Am. Ceram. Soc. Proc., 2^[11-12], 1156-70 (1981).

3. C.R. Kennedy, "Refractories for Application in Slagging Gasifiers,"

Proc. Fourth An. Conf. on Mat. for Coal Conv. and Util., Gaithersburg, MD,

Oct. (1979), DOE Rep. CONF 791014, 1979.

4. C.R. Kennedy, "Compatibility of Water-Cooled Chromia-Containing

Refractories with a High Iron Oxide Acidic Coal-Ash Slag at 1575°C," Mat.

for Energy Systems, 3[3], 39-47 (1981).

5. W.T. Bakker, "Design Aspects of Refractory Wear by Slag

Erosion/Corrosion," Am. Ceram. Soc. Proc., 2[11-12], 1202-8 (1981).

6. S. Greenberg and R.B. Poeppel, "The Corrosion of Ceramic Refractories

Exposed to Synthetic Coal Slags by Means of the Rotating-Cylinder

Technique: Final Report," Tech. Report No. ANL/FE-85-15, Argonne National

Lab., Argonne, IL, April, 1986.

7. R.F. Krause, Jr., "Compressive Strength and Creep Behavior of a Magnesium Chromite Refractory," Ceramic Eng. and Science Proc. 7_, [1-2],

220-228 (1986).

8. D.R. Clarke, "On the Detection of Thin Intergranular Films by Electron

Microscopy," Ultramicroscopy, 4[1], 33-44 (1979)

9. D.R. Clarke, "On the Equilibrium Thickness of Intergranular Glass

Phases in Ceramic Materials," J. Am. Ceram. Soc., in press.

10. R.M. El-Shahat and J. White, "Phase Equilibrium relationships in

Spinel-Silicate Systems," Trans. Brit. Ceramic Soc. 309-36, (1966).

11. R.M. El-Shahat and J. White, "The systems MgAl204*MgCr204*Ca2Si04 and

MgFe204‘MgCr204*Ca2Si04," Trans. Brit. Ceramic Soc. 313-30 (1964).

12. E-S Chen and 0. Buyukozturk, "Modeling of Long Term Corrosion Behavior

of Refractory Linings in Slagging Gasifiers," Am. Ceram. Soc. Bull. 54[7]

,

995-1000 (1985).

13. W.J. Moore, Physical Chemistry, Prentice-Hall In,. Englewood Cliffs,

NJ (1972).

14. R. Terai and R. Hayanic, "Ionic Diffusion in Glasses," J. Non-Cryst.

Solids, 18, 217-64 (1975).

120
15. C.M. Scarfe, D.J. Cronin, J.T. Wenzel and D.A. Kauffman,

Viscosity-Temperature Relationships at 1 atm in the System

Diopside-Anorthite, " Am. Mineralogist, 1083-88 (1983).

16. E.-S. Chen and 0. Buyukozturk, "Methodology for Thermomechanical

Analysis of Brittle Systems," Am. Ceram. Soc. Bull. ^[7], 982-988 (1985).

17. E.-S. Chen and 0. Buyukozturk, "Thermomechanical Behavior and Design of

Refractory Linings for Slagging Gasifiers," Am. Ceram. Soc. Bull. 54[ 7 ]

,

988-94 (1985).

18. A.G. Evans and W. Blumenthal, "High Temperature Failure in Ceramics,"

pp. 423-448 in Fracture Mechanics of Ceramics, Vol. 6, Measurements,

Transformations and High-Temperature Fracture, R.C. Bradt, A.G. Evans,

D.P.H. Hasselman and F.F. Lange, eds. Plenum Press, New York (1983).

19. A.G. Evans and W. Blxomenthal, "High Temperature Failure Mechanisms in

Ceramic Polycrystals," pp. 487-505 in Deformation of Ceramic Materials II:

Materials Science Research, Vol. 18, R.E. Tressler and R.C. Bradt, eds..

Plenum Press, New York (1984).

20. F.C. Monkman and N.J. Grant, "An Empirical Relationship between Rupture

Life and Minimum Creep Rate in Creep-Rupture Tests," Proc. ASTM 56, 593-620

(1956).

21. R. Kossowsky, D. G. Miller and E.S. Diaz, "Tensile and Creep Strengths

of Hot-Pressed Si 3N4

," J. Mater. Sci. 1^, 983-97 (1975).

22. S.M. Johnson, B.J. Dalgleish and A.G. Evans, "High-Temperature Failure

of Polycrystalline Alumina: III, Failure Times" J. Am. Ceram. Soc. 67 , 759-63 (1984).

23. S.M. Wiederhom, B.J. Hockey, R.F. Krause, Jr. and K. Jakus, "Creep

and Fracture of a Vitreous-Bonded Aluminum Oxide," J. Mater. Sci. 21 , 810-824 (1986).

24. D.C. Drucker, "Engineering and Continuvim Aspects of High-Strength

Materials," pp. 795-833 in High Strength Materials, V.F. Zackay, ed. , John

Wiley and Sons, Inc., New York (1965).

25. R. Raj, "Creep in Polycrystalline Aggregates by Matter Transport

Through a Liquid Phase," J. Geophys. Res. 87 [B6], 4731-39 (1982).

26. R. Raj and C.K. Chyxing, "Solution-Precipitation Creep in Glass

Ceramics," Acta Met. 29, 159-66 (1981).

27. J.-G. Wang and R. Raj, "Mechanisms of Superplastic Flow in a Fine-Grained Ceramic Containing some Liquid Phase," J. Am. Ceram. Soc. 67,

399-409 (1984).

28. L.J. Trostel, Jr., private communication. The Norton Company,

Worcester, MA.

121
1. View of the sample of MgCr204 refractory brick from the coal

gasifier plant. Crack like cavities are clearly visible near the

exposed surface (right hand portion) of the brick. Slag

penetration is indicated by the lighter shade of the brick

towards the exposed surface. The major divisions of the graph in

the background are in 1 cm units.

122
2. Microscopic view of an unpenetrated portion of the MgCr 204

refractory brick that had been exposed in the gasifier plant.

This portion of the brick was furthest from the hot face, and

therefore was not penetrated by the slag. The dark areas in

these micrographs are not void space, but regions of the

microstructure that were not penetrated by the epoxy resin used

to prepare polished section.

123
I

3. Scanning electron micrograph of one of the dark regions shown

in figure 2. X-ray energy dispersive spectroscopy indicates I these submicron grains to consist largely of MgCr204. Traces of [ calcium, aluminum and silicon are also observed in these areas.

j

I;

124
4. Plate-like Cr 203 (corundum structure) particles in the

MgCr 204 aggregate indicates a chromium rich structure. The

observation of this precipitate is consistent with reported and

measured average compositions of the refractory brick.

125
5. Microscopic view of a slag penetrated portion of the

refractory brick that had been exposed in the gasifier plant.

(a) Regions between the large fused aggregate particles that were formerly the dark areas of figure 2 now consist of MgCr 204 grains

~ 1.0 pm in size, indicating considerable grain growth during

exposure, (b) Grains near the hot face of the brick show an increase in the amount of intergranular vitreous phase.

126
6. Slag-filled, crack-like cavities in the slag impregnated hot

face of the refractory from the gasifier. These are the same features that look like cracks in figure 1. The rounded shape of

these cavities indicate a slow deformation process in their

formation, probably caused by internal stresses in the hot face

of the refractory.

127
WEIGHT

PERCENT

90

80

70 I( #

60 —

50

30 —

20 _

m

L

• •

• • • Cr2 O3

MgO

, 0 ?- FeO

t

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

DISTANCE FROM HOT FACE, mm

4.0

7. Chemical analysis of the spinel grains in the penetrated

portion of the brick obtained by using a scanning electron

microscope with an x-ray energy dispersive spectroscopy

attachment. Although aluminum was also detected close to the hot

face, its concentration was less that 2 % and hence was not

included on the figure.

128
8 . Effect of a synthetic coal slag on the microstructure of an MgCr20^ refractory brick specimen: (a) dense spinel coat on the

external specimen surface indicates the transfer of aluminum and

iron oxide from the slag to the surface of the specimen; (b)

interior of the specimen indicates full penetration by slag. The

specimen appears to be denser than a similar slag penetrated

section from the coal gasifier.

129
9. Effect of anorthite slag on the microstructure of MgCr 204

refractory brick: Coating of Cr 203 (corundum) grains is found

around the exterior surface of the specimen. Leaching of the MgO

was sufficiently complete as to convert the spinel phase to

corundum. The interior of the specimen was similar to figure 8b.

130
10. Effect of diopside slag on the microstructure of MgCr 204

refractory brick. (a) Portion of slag-penetrated specimen

wherein structural integrity has been maintained. Considerable

grain growth has occurred within the inter-aggregate region; (b)

Slag penetrated area of the specimen wherein the structure has

been disrupted by the slag. Note the long crack-like cavities

near the specimen surface.

\i

131
STRAIN

11. Compressive creep strain of a MgCr204 refractory impregnated

with slag from a coal gasifier. Observed strain (circles) was determined for specimens subjected to applied stresses of (a)

3.01 MPa and (b) 4.25 MPa in nitrogen gas at 1400°C. A solid

curve is a least squares fit of equation 1 while a dashed curve predicts [7] the strain of the newly produced refractory under

the same stress and temperature.

132
STRAIN

12. Compressive creep strain of a MgCr 204 refractory impregnated

with synthetic coal slag. Observed strain (circles) and least

squares fits of equation 1 for work-hardened creep (solid line) are plotted for tests conducted in nitrogen gas 1450°C under

applied stress of 1.5 and 3.0 MPa respectively.

133
Al 3

Sla

Mg + 2

13. Schematic diagram of mechanisms of slag attack on MgCr 204

refractories. Al^^ and Fe'*’2/Fe‘*’^ enter into the spinel structure

at the hot face, while Mg'*’^ and Cr'*'^ leave the surface grains of

the refractory. The iron and the aluminum reduce the melting

point of the spinel grains, a consequence of which is enhanced

solution of the refractory in the slag. Within the refractory,

the aluminum and iron leave the slag to be replaced by chromium

and magnesium, which changes the composition from one similar to an anorthite melt to one similar to a diopside melt. At the same

time, the submicron grains that lie between the larger aggregate

particles grow in size. This grain growth coupled with transport

of matter from the melt to the spinel grains of the brick cause

the hot face to bloat, crack and eventually spall from the main

body of the refractory brick.

134
lA. Schematic diagram of the mi

brick. The spacing and size of

given by W and D respectively,

bonded together by a much finer

small grains of refractory of si

matrix. The spacing between the

Because deformation occurs more bonding microstructure, the cree largely determined by this inter

crostructure of a refractory

the large aggregate grains is

The aggregate particles are grain microstructure, in which

ze d are bonded by a vitreous

finer grain particles is w. easily within the finer grain

p rate of the refractory is

-aggregate microstructure.

135
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139
NBS-lUA (REV. 2-80

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See instructions) NBSIR 87-3584 JUNE 1987

4. TITLE AND SUBTITLE

EFFECT OF SLAG PENETRATION ON THE MECHANICAL PROPERTIES OF REFRACTORIES

REPORT

: FINAL

5. AUTHOR(S)

S.M. Wiederhorn and R.F. Krause, Jr.

6. PERFORMING ORGANIZATION (If joint or other than N BS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No. DE-AI05-830R21349

S. Type ^ Period Covered

9. SP^

E

pN50fUNG ORGANIZATIOI^ NAME AND COMPLETE ADDRESS (Street. City. State. ZIP) r.r. Department oflnergy. Advanced Research and Technology Development, Fossil

nergy Materials Program, Oak Ridge National Laboratory, Oak Ridge, TN 37831

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) ceramics; corrosion; creep; gasification; refractories

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