NBSIR 80-2047

Application of Fracture

Mechanics in Assuring Against

Fatigue Failure of Ceramic

Components

J. E. Ritter, Jr.

Mechanical Engineering Department

University of Massachusetts

Amherst, MA 01003

S. M. Wiederhorn, N. J. Tighe and E. R. Fuller, Jr.

National Bureau of Standards

Fracture and Deformation Division

National Measurement Laboratory

Center for Materials Science

U.S. Department of Commerce

Washington, DC 20234

I June 1980

Prepared for

- P^^^^^partment of Energy

pugj Utilization Division

100 ashington, DC

.056

80-2047

1980

c. 2

HATIOMAL XmSAtJ

or 89ANIXAKDS

UBKART

JUL 2 ] 1980

NBSIR 80-2047 flat dCC -Cj'C

APPLICATION OF FRACTURE

MECHANICS IN ASSURING AGAINST

FATIGUE FAILURE OF CERAMIC

COMPONENTS

6 - 3- '

J. E. Ritter, Jr.

Mechanical Engineering Department

University of Massachusetts

Amherst, MA 01003

S. M. Wiederhorn, N. J. Tighe and E. R. Fuller, Jr.

National Bureau of Standards

Fracture and Deformation Division

National Measurement Laboratory

Center for Materials Science

U.S. Department of Commerce

Washington, DC 20234

June 1980

Prepared for

Department of Energy

Fossil Fuel Utilization Division

Washington, DC

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
.- ..iA*'!'-:*, .V T- ' ‘ ijJ V.1L ' i^OtrA:Vj 4 r'Ar-J:.

’/ 'J ,, I -
APPLICATION OF FRACTURE MECHANICS IN ASSURING AGAINST FATIGUE

FAILURE OF CERAMIC COMPONENTS

J. E. Ritter, Jr.

University of Massachusetts

Amherst, MA. 01003

S. M. Wiederhom, N. J. Tighe and E. R. Fuller, Jr.

Fracture and Deformation Division

National Bureau of Standards

Washington, D. C. 20234

INTRODUCTION

The use of ceramics in high performance applications offers

a challenge to scientists and engineers: the challenge of

designing structural components with brittle materials. Design

problems arise for two reasons when brittle materials are used

as structural components: 1. The strength of brittle materials

is not a well defined quantity, but can vary widely depending on

the material; 2. The strength of brittle materials is time

dependent so that these materials often exhibit a time delay to

failure. This time dependence and scatter of strength so typical

of most ceramic materials occurs because of the presence of defects

such as cracks or crack-like flaws in these materials. When

subjected to an applied tensile stress, these defects act as stress concentrators and fracture occurs when the applied stress

intensity factor reaches a critical value. Scatter in the

strength of ceramic materials is a consequence of the scatter in

the size of the most critical defect in the ceramic. The time

dependence of strength results from subcritical crack growth

which gradually lengthens the crack until it reaches critical

dimensions, at which time failure occurs. The time delay to

failure is the time required for the crack to go from a subcritical

to a critical size.
Methods of dealing with design problems involving fatigue

of ceramic materials have been developed over the past 10 years

through the application of the techniques and concepts of, fracture

mechanics (1-3) . Since fracture mechanics techniques can be

used to characterize both the conditions for subcritical crack

growth and the conditions for crack instability, they can be

used for purposes of design to estimate the allowable applied

stress and the expected lifetime for a given component. This is

accomplished by estimating the initial crack size in a ceramic

component and the time required for the crack to grow from its

initial size to a final critical size. Several mutually independent techniques have been developed recently to provide these

types of estimates. Since these techniques promise to revolutionize the way in which structural components made of ceramic

materials are designed, a complete understanding of these techniques, their application, and their limitations will be necessary

to use them correctly.

This paper will review the application of fracture mechanics

theory to the prevention of delayed failure of ceramics. Three

successful applications of this theory of assuring the mechanical

reliability of ceramics are discussed in order to demonstrate

the viability of the theory for purposes of engineering design.

Finally, a description is presented of practical limitations of

the theory with regard to heat engine application. Methods of

overcoming these limitations through modification of test procedures, and application of statistical theory are then presented.

THEORY

Since fracture mechanics concepts can be used to characterize

both the conditions for subcritical crack growth and the conditions

for crack instability, they can be used to predict the failure

of ceramic materials under given service conditions. This is

accomplished by estimating the initial crack size in a ceramic

component and the time for the crack to grow from its initial

size to a final critical size. As the crack grows to its

critical size, the crack velocity (V) is assumed to be dependent

on the applied stress intensity factor (K^) by (1)

V = A (1)

where A and N are crack growth constants that depend on the

environment and material composition. From Equation (1) and

relation a=K /Y/a, it can be shown that the time to failure

under constant applied tensile stress (a ) is (3)

3

t

f B S

N-2

the

(Cj)

( 2 )
2 N—

2

where B = 2/ (AY (n-2)K^^ ), K = critical stress intensity

factor, and S = fracture strength in an inert environment where

no subcritical crack growth occurs prior to fracture. From its

definition, B is a crack propagation constant that depends on the

environment and material composition.

In Equation (2) , t^ represents the time required for a flaw

to grow from an initial, subcritical size, to dimensions critical

for catastrophic propagation; B and N are the constants that

characterize this subcritical crack growth. The initial flaw

size is characterized in Equation (2) by the fracture strength

in an inert environment*. From Equation (2) it is seen that the

time to failure decreases with increasing stress, i.e. fatigue

under a static stress.

Also from Eq. (1) , a relationship can be derived between

the fracture strength cr^ and stressing rate d. In this case

flaws grow from subcritical to critical size under constantly

increasing stress. The results of this analysis is (1-3):

N+1 cN-2 . = B (N+1) S a (3)

where B and N are the same fatigue constants as in Eq. (2)

.

From Equation (3)- it is seen that fracture strength decreases

with decreasing stressing rate since the flaws have more time to

grow. This behavior is known as dynamic fatigue , i.e. fatigue

under constant stressing rate conditions.

The probability of failure (F) for a given lifetime and

applied stress can be obtained from Equation (2) by expressing

the inert strength in terms of its failure probability distribution. Generally, the inert strength distribution of ceramics

can be approximated by the Weibull relationship (3)

In In = m In -| (4) o where m and S are empirical constants evaluated by a fit of the

strength data. Likewise, the strength distribution at a fixed

stressing rate can be obtained by substituting Equation (4)

into Equation (3).

Because ceramics exhibit a wide spread in strength values

(ra is typically 4-8) , the allowable stress in service is quite

*The initial crack size, a, can be calculated, if desire?^, ^r^m

the well known fracture mechanics relationship: a = K^^“/Y S , where Y is a constant that is determined by the geometry of the

specimen and the crack. In subsequent discussion, a is assumed

to be small relative to component dimensions so that Y is a singl

valued constant.
low if low failure probabilities are required. Proof testing

offers one means of increasing the design stress for ceramics (1-3)

The value of proof testing is that it characterizes the largest

effective flaw possible in a tested component, since any larger

flaws would have caused failure during the proof test.

Assiaming that flaw growth during the proof test cycle is

given by Equation (1) (i.e. one region of crack growth) and

that the initial inert strength distribution can be characterized

by Equation (4), the inert strength after proof testing (S ) is

given by (4) : ^ N -2 (N -2)/m

(S /S ) P = (-ln(l-F )-ln(l-F )) ^ a o a p

(N -2)/m N -2

-(-ln(l-F ))

P + (S IS ) P

p min o

(5)

where' N is the crack propagation constant appropriate for the

proof tist environment, F is the failure probability after

proof testing, F is the failure probability of the proof test

and S . is the Minimum inert strength of a sample that just

passes ?he proof test cycle, i.e. the truncation strength. It

is significant to note that the inert strength after proof

testing is truncated at S . and will be greater than the initial

inert strength at all levels of failure probability if m < N -2 (4)

For a given material and proof test environment, S . is

determined only by the unloading rate (a ) from the proof^stress

(4) : u

S . min B (N -2)]^'^^

P P

1/(N -3)

[3/(Np+D] P

( 6 )

where B is the crack propagation constant appropriate for the

proof tlst environment. If d >0, Equation (6) shows that

proof testing always truncates the strength distribution. The

higher d , the greater is the strength level, S . , at which

truncation occurs. However, since S . cannot Se^greater than

the maximum stress, a , during the proof test, a is an upper

bound for S . . Substitution of a for S . in Equation (6)

gives the minimum unloading rate fBr whicK^o is approximately

equal to the truncation strength. Equation fb) also shows that

good proof test conditions (high N^) result in a high

The failure probability of the proof test (F ) can be

determined directly from the number of specimens Ehat break

during the proof test or can be predicted from (4)

-ln(l-F ) = (S (D /B

P o p p

( 7 )
where D = (t) dt represents the amount of strength

P

t /

N

For a typical proof

constant rate, held at

then unloaded

degradation during the proof stress cycle.

test, the component is loaded at a the maximum proof, stress , a , for a time t , and

at a constant rate, d . Integrating the equation for this

. u,. p typxcal proof stress cycle gives:

N N

+1^ ^ [a_ P D /(N_+l)] (1/d. + 1/d^) (8) =

P

t +

P u

By coupling Equation (5) with Equations (2) and (3) , the t^ and distribution after proof testing can be predicted for

any service environment (4) . Of particular interest is the

minimum lifetime (t . ) in service of a component after proof

testing. This is obtained by substituting for S in Equation

(2) so that:

min

t . = BS , '"-2 a min min a

(9)

where now B and N are the appropriate crack parameters for the

service environment.

Equations (5) - (9) summarize failure predictions for

ceramic materials after proof testing. These failure predictions

are dependent on the crack propagation parameters B and N. These

parameters must be determined in a test environment that simulates

the appropriate proof-test and service conditions and can be

obtained from one of three type of experiments: crack velocity

experiments, stress rupture experiments, and stressing rate

experiments (3). From crack velocity experiments. Equation (1) is

used to determine A and N; is determined in a separate

experiment. Stress rupture data (t^ vs. a ) and the inert

strength data are used to determine'^B and ^ from Equation (2) , whereas stressing rate data (S vs. d) and median inert strength

data are used to calculate B and N from Equation (3). The stress

rupture and stressing rate techniques are commonly referred to as static-fatigue and dynamic fatigue, respectively.

APPLICATION

The fracture mechanics principles described in the previous

section have been experimentally verified for soda-lime glass

(3) and alumina (5) in a moist environment. Specifically, these

studies showed that the three experimental techniques for

measuring the crack propagation parameters B and N give equivalent

results, that the time-to-failure and strength failure probability

distributions can be predicted from Equations (2) and (3) coupled

with Equation (4), and that strength distributions after proof
6

testing can be predicted on the basis of Equation (5) . The

purpose of this section is to describe three applications of

fracture mechanics principles in assuring against the fatigue

failure of ceramic components in service.

Failure Statistics

For alumina substrates fabricated by cofired metallurgy,

stress corrosion cracking can be a serious problem. The metals

most commonly co fired with alumina are either molybdenum or tungsten. Because these metals possess lower thermal expansion

coefficients than alumina, their cosintering can cause the

ceramic to retain residual tensile stresses of considerable

magnitude. Subsequent cleaning and plating baths, necessary to

render the metallurgy solderable, expose the substrate to

conditions that promote stress corrosion cracking in the alumina.

To statistically assess the susceptibility of polycrystalline

(MPa/SEC)

0 . 1 1 10 100

LOG STRESSING RATE IMPa/SEC)

Figure 1. Dynamic fatigue data of polycrystalline alumina in a KOH cleaning solution at 100°C, in a gold-plating bath

at 78°C, and in moist air at 30°C and 80% RH (from

Ref. 6).
Lit

L«i

(l/l-FI

aliomina to stress corrosion cracking under processing conditions,

the stressing rate technique was used to characterize the crack

propagation parameters for alumina in a KOH cleaning solution at

100°C and a gold plating solution at 78°C (6).

Figure 1 gives the experimental results of strength as a function of stressing rate of al\imina in the KOH and gold

solutions (6). For comparison, the fatigue strength results

determined for the same alumina in a moist air environment are included (5) . From this data and a knowledge of the inert

strength of the samples, the crack propagation parameters B and

N were determined from Equation (3) for the various environments.

To validate the applicability of fracture mechanics principles

in predicting failure probability in the processing solutions, the

actual fatigue strength distributions were compared to predictions

based on Equation (3) using the appropriate values for B and N and

the inert strength distribution of the samples. Figure 2 gives

these comparisons and it is evident that agreement between the

theoretical predictions and the actual fatigue strength distributions

S(MPa)

100 ISO 200 300

Lfi S (MPo)

S (MPo) 100 ISO 200 300

Ln S (MPa)

Figure 2. Comparison to theoretical predictions of the strength

distributions of polycrystalline alumina in a) KOH

cleaning solution at 100°C and b) gold plating bath at

78°C (from ref. 6).
is good. It should also be noted that these strength distributions

are bimodal since the low strength regime of the distribution

was caused by gross flaws induced in the samples during grinding.

The severity of the processing conditions on the alumina

substrates can be most easily assessed by means of a lifetime

prediction diagram (Figure 3) based on Equation (2) and the inert

strength distribution of the substrates. Although the strengths

of the substrates could not be measured directly, they were

estimated from the strength distribution of the samples and the

Weibull size relationr

Si = (10)

where and are the strengths of the substrates and samples,

respectxvely , and A^ and A^ are the surface area of the substrates

and samples, respectively. Figure 4 shows the estimated inert

strength distribution of the substrates. It should be noted that

it was assumed that the inert strength distribution of the

Figure 3. Lifetime prediction diagram for polycrystalline alumina

in wet processing environments and moist air (from ref.

6 ).
9

I

S. (MPa)

£

CQO

Q£

Q.

Figure 4. Estimated Weibull inert strength distribution for

alumina substrates (from ref. 6)

.

substrates was not altered through any interaction between the

metal and alumina during sintering.

The residual tensile stress in a substrate having cofired

metallurgy is dependent on the thermal expansion mismatch

between the metallurgy and the ceramic, the temperature difference

between the set point of the system and room temperature, and the

geometry of the metallurgy in the system. In molybdenum-alumina

substrates residual stresses of 200 MPa can be generated. If

substrates having such stresses are subjected to the KOH cleaning

solution or the gold-plating solution for 30 minutes, respective

S /a ratios of 1.75 and 2.27 are predicted (Figure 3). Since a

is known, S can be calculated and a failure probability determined

from Figure 4. With a 200 MPa residual stress, an 8% failure rate

would be expected for the substrates in the 10% KOH solution, and

40% of the substrates in the gold-plating bath would crack after

30 minutes. Also, substrates having a residual stress of this

magnitude would have a failure rate of 8% in hot, humid air.

Clearly, failure rates of this magnitude are unacceptable.
The failure probability of the substrates can be lowered by:

(1) using a stronger alumina to make the substrates, (2) reducing

the processing times, or (3) reducing the residual stress in the

substrates. The obvious choice is to reduce the residual stress

in the ceramic. This can be accomplished by reducing the thermal

expansion mismatch between the metal and the ceramic, by altering

the geometry of the system, or by a combination of both. Since

the thermal expansion differential can be reduced only by altering

the metal configuration and/or the ceramic, this choice alone is

not particularly attractive. Similarly, if the stress is lowered

only through geometric redesign, the potential geometric density

of the metallurgy in the system becomes limited. Thus, a combination of both approaches is generally considered most effective in

reducing stress.

Obviously, the ideal solution would be to completely eliminate

any residual tensile stress in the substrates; this, however, is

not always possible without drastically altering the material

system. The problem then is to reduce the failure probability of

the substrates to a magnitude compatible with good product reliability.

Regardless of the technique used, if the stress in the ceramic

is lowered, for instance, to 50 MPa, the lifetime prediction diagram and the inert strength distribution can again be used to

assess the probability of stress corrosion cracking of the substrates. If substrates having a residual stress of 50 MPa are placed in the KOH cleaning solution or in the gold plating bath

for 30 minutes, it can be determined from Figure 3 and 4 that the

failure probabilities are 0.2 and 0.34% respectively. While the

possibility of stress corrosion cracking of substrates during

processing is not completely eliminated by reducing the residual

stress to 50 MPa, the resultant failure rates are now low enough

so as to offer a minimal impact on product reliability.

The above examples of lifetime predictions serve to illustrate the importance of fracture mechanics theory in designing

electronic substrates fabricated by cofired metallurgy, namely,

that substrates of various designs can be compared for the probability of stress corrosion cracking due to the residual tensile

stress in the substrates. In this way, fracture mechanics theory

is useful in making more rational design decisions. These predictions can also be checked by fabricating substrates of several

designs with different residual stresses, and then subjecting the

substrates, for instance, to the gold-plating bath for a given

period of time. By comparing the incidence of stress corrosion

cracking with that predicted by fracture mechanics theory, the

theory can be experimentally validated. This was done in the present research program, and the experimental results generally

agreed with those theoretically predicted (6)

.
13

S (p$i)

3000 4000 5000

Figure 6. Comparison of wheel bursting strengths before and after

proof testing for wheel specification VGW2 (from ref. 7)

.

characterize the strength and fatigue behavior of ceramics at

elevated temperatures to establish allowable stress levels for

component design. To study the high temperature strength and

fatigue behavior of high purity alumina (Wesgo AL 995) the

stressing rate test technique was used because of its simplicity (8)

.

The effect of temperature on the strength and fatigue behavior

of high purity alumina is given in Figure 7 (8) . The temperature

dependence of both strength and fatigue behavior is small up to

500®C. From 800 to 1100‘’C both the strength and fatigue resistance

decreases markedly. A convenient way to show the effects of

fatigue is to compare minimum lifetime predictions, based on Equation (9) taking S . to be equal to a , as a function of temperature. Figure 8 gxves these predictioRs and clearly illustrates

that there is little difference in the fatigue behavior of high

purity alumina from 23 to 500°C; however at higher temperatures

fatigue effects become very important. For example, to assure a minimum lifetime of one year under a service stress of 100 MPa the

required proof stress ratio is 2.27 for a temperature of 23°C but

for 1000°C it is 6.90 and for 1100“C it is 14.91. These elevated

temperature proof stress ratios would result in such large proof

stresses that no sample would be able to pass the proof test. To

get more reasonable proof stresses, the expected minimum life or allowable stress in service must be decreased for these elevated

temperatures. For example, if the allowable stress is reduced Co

30 MPa, then the proof stress to insure a minimum lifetime of 1 year at 1000°C is 179 MPa and 361 MPa at 1100°C.

i
14

TEMPeRATURC (*F)

300 1000 1300 2000

? N-36 0 i

O 9 * ^97 MPo/i

A 9--0 397 MPo/l

300 730 TEMPCRATURE (*0)

Figure 7. Median fracture strength of alumina as a function of

temperature and stressing rate (from ref. 8).

I 2 3 4 3 6 7 lO

Figure 8. Minimum lifetime prediction diagram for alumina as a function of temperature (from ref. 8).
1

'I

i!

i Scanning electron micrographs showed that the fracture in

I this high purity alumina changed from transgranular at 23°C to

i; intergranular at temperatures above 800°C (8) . In addition, a

I glassy phase was found at the fracture origins of the samples

' tested at above 800°C, giving evidence that the glassy phase is

I playing a major role in determining the strength and fatigue

j behavior of high purity alumina at elevated temperatures. However,

j: proof test results (8) showed that the preexisting flaw population

jj is not altered at elevated temperatures. Figure 9 compares the

j strength distribution of alumina at 23 and 1100°C before and after

proof testing at room temperature. It is evident that this proof

I test eliminated the weak samples so that the after proof strength

1 distribution at low failure probabilities are stronger than the

i initial distributions and that agreement between theory and experii ment is good. On the other hand, Figure 10 shows that proof

testing alumina at 1000°C is not effective in improving the

I strength distribution at 1000°C; however, the good agreement

; between experiment and theory gives evidence that fracture mechanics

' theory applies. In this case weak samples are eliminated by proof

I testing at 1000®C, but flaw growth during the proof test weakens

ii the survivors to such a degree that proof testing is not effective

in improving the strength distribution.

STRESS (MPo) ITS 225 250

; Ln STRESS (MPa)

i

I

I Figure 9. Effect of room temperature proof testing on the

strength distribution of alumina at 23°C and 1000°C

(from ref. 8)

.
SlHhSS (MPo)

ISO I7S 200 22S

>

03<S

o

o:

0.

UJX

3

i

Figure 10. Effect of proof testing at 1000°C on the strength

distribution of aliimina at 1000°C (from ref. 8).

In summary, it is believed that at moderate temperatures

the fatigue failure of alumina is caused by moisture assisted

subcritical crack growth; whereas, at elevated temperatures it

is caused by subcritical crack growth enhanced by the presence

of a glassy phase. It is also thought that the same pre-existing

flaws control the strength both at room temperature and at

elevated temperatures.

LIMITATIONS OF THE LIFETIME PREDICTION METHOD

The lifetime prediction theory presented in this paper is

based on the assumption that subcritical crack growth from preexisting flaws is the only mechanism of strength degradation.

Using this assumption, component lifetime can be predicted once

the initial flaw population, the crack growth rate and the

critical crack size have been determined. The theory is deterministic because the element of chance is eliminated from the

lifetime prediction once these parameters have been evaluated.

The accuracy of the lifetime prediction will depend on both the

accuracy with which the pertinent parameters can be evaluated

(9-11), and the adequacy of the crack growth equation (12).

This requirement does not detract from the basic deterministic

nature of the method. The prediction scheme can, however, be
invalidated when the basic assumptions of the theory are not

satisfied. Thus, fracture processes, other than subcritical

crack growth, can invalidate failure predictions based on this

theory. Unfortunately, other fracture processes do occur for

materials currently under consideration for use in heat engines,

so that alternate mechanisms of failure must be considered for

any scheme of predictive failure for heat engine components. As

will be shown, proper modeling of these factors permits extension

of the theory to handle fracture situations that are not currently

included in the method of lifetime prediction.

As with most other ceramic materials, silicon nitride and

silicon carbide fail at low temperatures from preexisting flaws.

As discussed by Rice et al. (13,14) and by Richerson and Yonushonis

(15) , these flaws are usually surface cracks introduced into

silicon nitride and silicon carbide components by machining when

the components are manufactured. For hot-pressed silicon nitride

at temperatures less than '^>1000°C, fracture originates from

surface flaws in a completely brittle manner (13,14). At higher

temperatures, however, plasticity of components and effects

resulting from the reactive nature of the test environment

intervene to alter the mode of fracture (13) . The same types of

effects occur for hot-pressed silicon carbide at higher temperatures

('V^1400®C) . In oxidizing environments, the effects of temperature

on mechanical behavior can be attributed to: (1) enhanced

plasticity at the crack tip which results in subcritical crack

growth by creep fracture (16,17), and (2) surface oxidation which

results in the healing of surface machining cracks, and for some

materials, the generation of new flaws that act as new origins

for fracture (13-15, 18-20). Both processes have to be considered

to accurately predict the lifetime of high temperature structural

components. A variety of other processes (thermal shock, particle

impact, chemical corrosion, component contacts, etc.) can also

intervene to effect the fracture behavior of heat engine ceramics.

Although a complete theory of failure would require all of these

processes to be considered, such extensive considerations are

clearly beyond the scope of this paper. The discussion in the

remainder of this paper will be more limited in scope, dealing

with pit formation, crack healing and crack growth. Materials

to be considered are magnesia-doped, hot-pressed, silicon nitride

and reaction bonded silicon nitride for which the processes that

occur at elevated temperatures are best understood.

High temperature oxidation has been shown to be particularly

effective in altering the initial flaw population in hot-pressed,

silicon nitride (NC132) . Investigations of the strength and

oxidation behavior of this material have shown that surface

induced machining flaws are reduced in severity by high temperature oxidation of the ceramic surface (13-15, 18-20). The
oxidation process is complex involving mass transport of impurities

from the matrix, and transport of oxygen and nitrogen through

the glass oxide layer that forms on the surface of the ceramic

(17,21). As the oxide scale grows, the initial silicon nitride

surface recedes, reducing the size of the surface cracks and

thus their severity (Figure 11) . If oxidation continues long

enough, the surface cracks can be completely removed from the

ceramic surface. In addition to crack removal by dissolution,

plastic deformation at elevated temperatures also permits blunting

of machining flaws and relief of surface stresses, thus enhancing

the strength of the component (22,23). The effectiveness of

oxidation in reducing flaw severity can be illustrated by the

introduction of fresh cracks into the surface of silicon nitride

by indentation (20,24). As illustrated in Table 2 on hotpressed silicon nitride (billet B), exposure at 1200°C in air

increased the strength from 408 MPa at room temperature to 488

MPa after 100 hours exposure, largely as a result of decreasing

the severity of the flaw associated with the indentation.

Because of the beneficial effect of oxidation, high temperature

exposure in air is being used as a means of improving the finish

of hot-pressed silicon nitride ceramic blades (15,23). Similar

strengthening results are observed for reaction bonded silicon

nitride (NC350) ~ (23, 24)

.

EFFECT OF OXIDATION ON

FLAWS IN Si3N4

) • —J—59

OXIDE-

-Si3N4-

(a) (b) (c)

Figure 11. Effect of exposure at 1200°C on flaws in silicon nitride

(a) surface crack and subsurface inclusion before ex- posure; (b) after exposure crack size is reduced by

surface dissolution and subsurface flaw reacts with

environment. At the same time, crack blunting or crack

healing occurs; (c) oxide growth has removed the subsurface crack and enlarged the subsurface flaw to produce a pit in the silicon nitride (from ref. 34).
Table 2.

Strength of Indented Specimens: 2kg Load (34)

Material

Test-Temp.

°C

Exposure

Conditions

Strength

MPa

Fracture

at indentation

NC132 25 as indented 397 + 12 Yes

Billet A 25 16 hr 1200°C 432 + 27 Yes

25 100 hr 1200®C 461 + 42 No

1200 1/2 hr 1200°C 438 + 15 Yes

1200 16 hr 1200°C 396 + 42 Yes

1200 100 hr 1200°C 402 + 12 No

NC132 25 as indented 408 + 17 Yes

Billet B 25 100 hr 1200®C 524 + 47 Yes

1200 1/2 hr 1200“C 441 + 10 Yes

1200 100 hr 1200°C 488 + 11 Yes

NC350 25 as indented 115 + 24 Yes

25 33 hr 1200°C 181 + 22 Yes

25 100 hr 1200®C 225 + 38 Yes

1200 100 hr 1200°C 188 + 64 Yes

NCX-34 25 as indented 491 + 16 Yes

Y-0- 25 100 hr 1200®C 616 51 No

2 3 1200 100 hr 1200®C 744 + 25 Yes

If flaw removal were the only process occurring during

oxidation then the lifetime prediction methods presented earlier

in this paper could be used as a conservative basis for component

design. In this case, the starting flaws would decrease in size

as oxidation occurred, and the component would become stronger,

not weaker. Research on hot-pressed silicon nitride (NC132) has

shown that flaw generation during long term (>100 hr.) exposure

results in a decrease in the strength of this material (15, 20,

22). The strength decrease results from pit formation at the

ceramic surface due to rapid localized oxidation. Although the

exact cause of localized oxidation is not fully understood, it

probably results from the presence of impurities in the ceramic

which increase the oxidation rate as the oxide interface approaches

the location of the impurity (Figure 11; 20,26). The formation

of glass-like oxide mounds over the pits with holes in the

center of the mounds suggests that rapid gas generation is

associated with the nucleation and growth of these pits (20)

.
20

Figure 12. Effect of oxidation at 1371°C (2500 ®F) on the strength

of silicon nitride (NC132) . Note that at time zero

the scatter in strength is considerably greater than

that occurring after substantial periods of exposure

(from ref. 25).

The effect of pit formation on the long term strength is

illustrated in Figure 12 which shows that after 1000 hours

exposure magnesia-doped, hot-pressed silicon nitride has lost

approximately 50 percent of its strength (25) . This strength

decrease seems to occur most rapidly during the initial stages

of exposure, suggesting rapid formation of pits initially, and

then stabilization of the pit structure after periods of about

1000 hours. Whether or not the pit structure has reached a state of static equilibrium, or is in a state of dynamic equilibrium has not yet been determined.

In freshly machined specimens the combined effect of crack

healing, and flaw generation should result in a strength enhancement followed by a strength degradation as pits form in the

material (20,24). This type of behavior has been confirmed by a mmiber of investigators. Richerson and Yonushonis (15) have

shown, for example, that the strength of transverse ground

silicon nitride is increased by exposure to temperatures of

982°C or 1066‘^C for 50 hours (Table 3) . At higher temperatures

or for longer periods of time, a strength decrease is observed

as pits are formed in the surface. Wiederhorn and Tighe (20,24)

showed that this type of behavior depended on the particular

billet used for study, since some billets increased in strength
Table 3.

Room Temperature Strength of Hot-Pressed, Silicon Nitride (NC132)

Transverse Ground Specimens Tested in 4-Point Bending (15)

Exposure Strength and

®C (“F) Standard Deviation

time MPa (KSl)

Control 450 + 36

(63.0 + 5.0)

982 (1800)

50 hours

657 + 61

(92.0 + 8.6)

1066,(1950)

50 hours

636 + 41

(89 + 5.7)

1129 (2065)

140 hours

593 + 36

(83 + 5.0)

1129 (2065)

240 hours

' 443 + 58

(62.0 _± 8.1)

1204 (2200)

24 hours

529 + 19

(74.0 _+ 2.6)

1371 (2500)

24 hours

457 + 29

(64 +4.1)

Samples

Tested

Predominant Fracture

Region

12 Grinding Groves

50 Surface (Flaws not

obvious)

11 Surface (Flaws not

obvious)

6 Surface Pits

6 Surface Pits

12 Surface Pits

12 Surface Pits

with exposure at 1200°C (for times of 100 hr.) while others

decreased for the same exposure conditions. Richerson and

Yonushonis (15) have made similar observations on hot-pressed,

silicon nitride. More recently, the combined effect of flaw

healing and pit formation was demonstrated by Jones and Rowcliff

(22) , for silicon nitride exposed at temperatures of 1370°C for

periods up to 64 hours. For both indented (knoop; 1 Kg) and

transverse ground specimens, the strength first increased then

decreased as the exposure time increased (Figure 13)

.

Reaction bonded silicon nitride behaves in a manner quite

different from that of the hot-pressed material. Flaw healing

results in a significant strength increase in this material at

elevated temperatures. \Tnen the material is cooled to room

temperature, however, much of this increase is lost as a result

of surface cracking caused by a phase transformation of cristobalite in the oxide coat that forms on the surface at high temperatures (27). The absence of strength degradation (at 1200^0
123456789

(TIME AT TEMPERATURE)’'^ -hours’'^

Figure 13. Effect of high temperature exposure on the strength

of silicon nitride (NC132) measured at room temperature (from ref. 22).

after sustained (1000 hr.) exposures (28), suggests that pit

formation and subcritical crack growth are not significant

factors limiting the lifetime of this material.*

LIFETIME ESTIMATE: EFFECT OF FLAW HEALING AND PIT FORMATION

From the above discussion, we conclude that flaw healing,

pit formation and subcritical crack growth must be considered

simultaneously in order to establish an accurate method of

lifetime prediction. The development of a failure prediction

method requires each of these processes to be evaluated independently. Once they have been characterized, mathematical techniques

can be used to determine the relative contribution of each of

these processes to the total failure time.

Subcritical crack growth can be characterized either by

strength or fracture mechanics techniques. However, when flaw

healing or pit formation is occurring, the use of strength

techniques for evaluating crack growth parameters may not be a good procedure, since both of these processes have an independent

effect on the material's strength. The feasibility of quantifying

the crack growth rate by fracture mechanics techniques has been

demonstrated by Evans and Wiederhorn (30)

,

who have shown that

*Recently, Richerson et al. (29) have observed pit formation in

heavily oxidized reaction bonded silicon nitride.
the crack velocity can be represented as a power function of the

applied stress intensity factor (Equation 1) . Details on the

application of fracture mechanics techniques to crack growth

data can be found in ref. 31.

A second method of collecting crack velocity data was

illustrated recently by Rowcliff (22) , who used 3 point bend

specimens to study the static fatigue of silicon nitride and

silicon carbide. The specimens were all indented to form wellcharacterized cracks in the tensile surface of the specimens.

The technique is based on the assumption that equation 1 is the

correct form of the crack velocity equation. By rearranging

Equation 2, the following equation is obtained for the failure

time, t, of a component that is subjected to a constant applied

load

2a.

X

(n-2)v^

( 11 )

Thus, by measuring the initial crack size, a., and the time to

failure, t, the initial crack velocity, v., can be deteirmined.

The stress intensity factor th^t corresponds to v, is obtained

directly from a, (K_ . = aY/a7) . 1 Ix X

Data on flaw healing or on pit formation can be obtained

from strength measurements. Data on magnesia-doped, hot-pressed

silicon nitride and reaction bonded silicon nitride suggest that

crack healing occurs relatively quickly and is completed before

pits begin to form in the component surface. Therefore, strength

changes during the early stages of component exposure can be

used to characterize the crack healing process; strength changes

occurring after extended exposure can be used to characterize

the pit formation process. For normally machined surfaces,

quantification of both of these processes requires the collection

of extensive strength data so that the strength distribution can

be determined accurately as a function of exposure time.

Data on hot-pressed silicon nitride suggests that both the

mean strength and its standard deviation change with exposure

time when flaw healing occurs (20,24,25). In terms of a Weibull

distribution. Equation 4, both the Weibull strength, S , and the

shape parameter, m, are a function of time. Data on reaction

bonded silicon nitride suggests that only is a function of

*The validity of the data obtained by this technique is limited by

the assumption that the crack size at failure is small relative to

the specimen dimensions. As has already been noted, this same

limitation applies to earlier parts of this paper.
time (28). The effect of flaw healing on specimens that contain

large initial cracks can be determined from studies on specimens

that have been indented so that relatively large cracks are introduced into the specimen surface. Studies of this type have

been conducted recently by Tighe and Wiederhorn (20,24) and by

Cubicciotti et al. (22). The investigation by Singhal et al. (25) of

strength degradation after long term exposure suggests that for

both crack healing and pit formation S and m seem to approach

fixed values after a certain amount of time, so that both distributions eventually become stable with regard to further exposure.

Once crack growth, flaw healing, and pit formation have been

quantified, the combined failure probability, and the total time

to failure can be estimated. To obtain these estimates it is

necessary to develop a procedure to determine which mechanism

controls failure at a given probability level. Flaw healing and

pit formation as a combined failure mechanism will be discussed

first. For simplicity it is assumed that the Weibull slope, m^,

for crack healing is less than the Weibull slope, m^, for pit

formation, and that m^ and m^ do not depend on time. The

Weibull strength for crack healing, S^, and that for pit formation,

S^, are assumed to follow exponential decay curves that can be

fxt to the following formulae:

(flaw healing) Si=S + AS (1-exp (-at))

oi oi

(12)

(pit formation) S 2=S - AS (1-exp (-3t))

02 02

(13)

where S , S , AS , AS ,. a and 3 are determined from experimental

strengtH^data? The^initx^l Weibull strengths for flaw healing and

pit growth are S and S respectively, while AS and AS are the

changes in strength for ?ftese two processes after°txtended°^exposure

times, a and 3 determine the rate at which these changes in

strength occur. If Equations 12 and 13 are substituted into

Equation 4, time dependent strength distributions are obtained

that describe the effect of exposure time on strength.

The type of behavior expected from Equations 12 and 13 is

shown schematically in Figure 14. We see that during the initial

stages of exposure, failure is determined entirely by the initial

flaw population, while in the later stages of exposure, pit

formation dominates the strength distribution. At any point in

time, the combined failure probability, F, is given by the

following relation (32):

(1-F) = (1-F^) (l-F^) (14)

where F^ and F^ are the time dependent failure probabilities

flaw healing and pit formation respectively. Thus, a unique

for
25

log (STRENGTH)

Figure 14. Schematic representation of the effect of high temperature exposure on the strength distribution: (a) initial

strength distribution. Curves are assiimed to move in

the direction of the arrows as the exposure time is

increased; (b) distribution after the flaw structure

has reached a state of "equilibrium”. Proof testing

or nondestructive evaluation can be used to improve,

reliability at stresses lower than the point of intersection of the two lines, statistics can be used to

the right of the point of intersection.

equation is obtained that relates the failure strength, S, to

the failure probability, F.

With regard to lifetime prediction, the above discussion is

sufficient to draw several important conclusions with regard to

proof testing and nondestructive testing. At any time during

exposure, the strength of components to the left of the point of

intersection of the two curves shown in Figure 14 will be controlled by the initial flaw population. Those specimens that lie to

the left of the intersection will contain the largest flaws and

consequently will be the ones to be eliminated by proof testing

or nondestructive inspection. Since the initial flaw population

controls the strength in this regime, proof testing and nondestructive evaluation techniques can be used to truncate the population,

and the theory presented earlier in this paper can be used to

provide a conservative estimate of the component lifetime. The

intersection of the two curves shown in Figure 14 provides an upper limit to the proof test load that can be usefully employed

to truncate the initial flaw population. Above this load,

component strength depends not on the flaws initially present in
the component, but on those that are generated by exposure to

elevated temperatures (20,24),

After long periods of exposure, proof testing or nondestructive evaluation can be applied again over the entire range of

strengths provided the flaw distribution (pits and cracks) has

reached a static state. If, however, the distribution to the

right of the intersection in Figure 14 represents a dynamic

state of equilibrium, then new pits will be continuously generated

as the old ones are removed. As a consequence, nondestructive

evaluation and proof testing will not be a viable lifetime

prediction technique. For the dynamic equilibrium situation,

statistical techniques such as those described earlier in this

paper would have to be used fo^ purposes of lifetime prediction.

Pits generated by the oxidation process would serve as the

initial flaw distribution for the lifetime prediction.

The combined effects of subcritical crack growth and pit

formation on strength can be determined by considering the rate

-at which each of these processes degrade the strength. As long

as strength degradation due to pit formation exceeds that

resulting from crack growth, subcritical crack growth will not

play a major role in the strength degradation process; when the

converse is true, crack growth will dominate the strength degradation process. The switch from one controlling mechanism to the

other will occur when the two strength degradation rates _are

equal

,

The rate of strength degradation due to pit formation can

be determined by substituting S 2 of equation 13 for S of

Equation 4, and differentiating with respect to time:

dS/dt = -B AS [exp(-Bt)] [In(l-F)”^]^^TM (15)

°2

The rate of strength degradation due to crack growth has

been derived by Fuller et al. (4) and is given by the following

expression:

dS/dt = - (AY^K^^^“^/2) (a/S)'^S^ (16)

where A and n are defined by equation 1; Y is a geometric constant

a is the applied stress and S is the instantaneous strength.

Equating Equations 15 and 16, and substituting Equations 4 and 13

for S, an equation can be obtained which gives the time, t , at

which the mechanism of strength degradation changes from pi?

formation to crack growth. The total time to failure is then

equal to t , plus the time, t , for the crack to grow to a critical s?ze. t can be determined from Equation 2, (using

Equations 4 and l5 to evaluate the strength at which the degradation mechanism changes from pit formation to crack growth)

.
Although the mathematical scheme for obtaining the total time to

failure is straightforward, the equations are not included here

because of their complexity. Never- the-less , the procedure does

provide a rational method of obtaining the total time to failure

when pit formation plays a critical role in determining component

lifetime. It is worth noting that the final equation can be

expressed in terms of strength, probability and failure time.

This type of representation was first suggested by Davidge et

al. (33) as a method of design with ceramic materials.

SUMMARY

In this paper, a review is presented of current techniques

used to evaluate the lifetime capability of structural ceramics.

Three successful applications of these techniques are presented

and discussed in order to demonstrate the viability of the

techniques for purposes of engineering design. Finally, limitations of the techniques are discussed with regard to heat-engine

applications. An extension of theory is recommended to treat

crack healing and pit formation resulting from high temperature

exposure.

The theory presented in this paper is based on the theory

of linear-elastic, fracture mechanics. Failure of structural

ceramics is assumed to be the result of subcritical crack growth

from pre-existing flaws in the structural components. Lifetime

predications require evaluation of the initial flaw size and of

the rate at which cracks grow when subjected to applied loads.

The three techniques that can be used to evaluate the initial

flaw size are nondestructive evaluation, proof-testing and

statistics, while the three techniques that can be used to

evaluate the rate of crack growth are fracture mechanics techniques,

static fatigue techniques (stress rupture) and dynamic fatigue

techniques (constant loading rate to failure) . The critical

equations required for purposes of failure prediction are presented

in the paper. Successful applications of the lifetime prediction

method are illustrated for electronic-substrate ceramics, for

vitreous grinding wheels and for high-purity aluminxmi oxide at

elevated temperatures.

Potential limitations in applying the technique to heat

engine ceramics, such as silicon nitride and silicon carbide,

are discussed. These limitations arise because of flaw generation

and flaw healing that is observed to occur in these materials at

elevated temperatures. Flaw generation can be caused by a number of processes: oxidation or other environmental attack

which results in surface pit formation, particle impact or component contact which results in localized stresses that

nucleate cracks, and thermal shock which results in transient

stresses that can result in crack formation. Flaw healing can
28

1

i be attributed to surface dissolution caused by oxidation and j silicate glass formation. These processes change the initial

flaw population so that failure no longer occurs from machining ' flaws originally present in the ceramic. In this situation the

development of a model for failure prediction requires the

consideration of flaw generation processes.

Extension of the theory presented in earlier sections of

the paper is illustrated for the combined processes of flaw

healing, pit formation and subcritical crack growth. The method

independently evaluates these three processes and then determines

the relative contribution of each of these processes to the

total failure time. Conditions are established for proof testing

of as-received components. Because of the occurrence of pit

formation, a maximvim value for the proof test load is established,

above which proof testing does not contribute to component

reliability. After long term exposure, proof testing or nondestructive evaluation can be applied again provided the flaw (pit)

distribution has reached a state of static equilibrium. If,

however, the flaw distribution has reached a state of dynamic

equilibrium, then statistical techniques must be applied for

lifetime prediction. Assuming that the strength distribution of

pits can be represented by a two parameter Weibull distribution,

the application of statistics is discussed for the combined

failure modes of pit formation and crack growth. For these

conditions, equations are developed for determining the total

failure time.

ACKNOWLEDGEMENTS:

j One of the authors (JER) is pleased to acknowledge the

support of the Office of Naval Research, Metallurgy and Ceramics , Program, the other authors are pleased to acknowledge the j support of the Department of Energy, Division of Fossil Fuel

j Utilization. l

I REFERENCES :

1. A.G. Evans and S.M. Wiederhorn, ’’Proof Testing of Ceramic

| Materials-An Analytical Basis for Failure Prediction," Int. | J. Fract., jW, 379-92 (1974).

2. S.M. Wiederhorn, "Reliability, Life Prediction, and Proof

Testing of Ceramics," pp. 635-65 in Ceramics for High I Performance Applications , ed. by J. J. Burke, A.E. Gorum,

and R.N, Katz, Brook Hill Pub. Co., Chestnut Hill, MA.

(1974).

'
3 . J.E, Ritter, Jr., "Engineering Design and Fatigue Failure

of Brittle Materials," pp. 667-686 in Fracture Mechanics of

Ceramics

,

Vol. 4, ed. by R.C. Bradt, D.P.H. Hasselman, and

F. Lange, Plenum Press, NY (1978).

4. S.M. Wiederhorn, E.R. Fuller, Jr., J.E. Ritter, Jr., and

P.B. Oates, "Proof Testing of Ceramics: I. Experiment"

NBSIR 79-1934; "II Theory " NBSIR 79-1944, (December 1979).

5. J.E. Ritter, Jr. and J.N. Humenik, "Static and Dynamic

Fatigue of Polycrystalline Alumina," J. Mat. Sci., 626-

632 (1979).

6. J.N. Humenik and J. E. Ritter, Jr., "Susceptibility of

Alumina Substrates to stress Corrosion Cracking During Wet

Processing," to be published. Bull. Am. Ceram. Soc.

7. J.E. Ritter, Jr. and S.A. Wulf, "Evaluation of Proof Testing

to Assure Against Delayed Failure," Bull. Am. Ceram. Soc.

57, 186-190 (1978).

8. K. Jakus, T. Service, and J.E. Ritter, Jr., "High Temperature

Fatigue Behaviour of Polycrystalline Alumina," to be published,

J. Am. Ceram. Soc.

9. S.M. Wiederhorn, E.R. Fuller, Jr., J. Mandel, and A.G.

Evans, "An Error Analysis of Failure Prediction Techniques

Derived from Fracture Mechanics," J. Am. Ceram. Soc. 59 , 403-11 (1976).

10. D. F. Jacobs and J.E. Ritter, Jr., "Uncertainty in Minimum

Lifetime Predictions," J. Am. Ceram. Soc. 5^, 481-486

(1976).

11. P.N. Thorby, "Experimental Errors in Estimating Times to

Failure," J. Am. Ceram. Soc. 514-16, (1976).

12. S.M. Wiederhorn, "Dependence of Lifetime Predictions on the

Form of the Crack Propagation Equation," pp, 893-901 in

Fracture 1977, Vol. 3, D.M.R. Taplin, Ed., University of

Waterloo Press, Waterloo, Ontario, Canada (1977).

13. R.W. Rice, S.W. Freiman, and J.J. Mecholsky, Jr., "Fracture

Sources in Si_N, and SiC," pp. 665 in Proceedings of the

1977 DARPA/NAVSM Ceramic Gas Turbine Demonstration Engine,

J.W. Fairbanks and R.W. Rice, Eds., Metal and Ceramics

Information Center Report MCIC-78-36, Battelle Columbus

Laboratories, Columbus, Ohio (1978).

14. S.W. Freiman, C. Cm. Wu, K.R. McKinney, and W.J. McDonough,

pp 655-663 in ref. 13.

15. D.W. Richerson and T.M. Yonushonis, "Environmental Effects

on the Strength of Silicon-Nitride Materials," pp. 247-71 in

ref. 13.

16. F.F. Lange, "Evidence for Cavitation in Crack Growth," J.

Am. Ceram. Soc. ^ 222-3 (1979).

17. N.J. Tighe, "Structure of Slow Crack Interfaces in Silicon

Nitride," J. Mater. Sci. IJ, 1455-63 (1978).
18. S.W. Freiman, A. Williams, J. J. Mecholsky and R.W. Rice,

"Fracture of Si_N, and SiC," pp. 824-34 in Ceramic Microstructures

’76, R.M. Fulrath and J.A. Pask, Eds., Westview Press,

Boulder, Colo. (1977).

19. S.W. Freiman, J.J. Mecholsky, W.J. McDonough, and R.W.

Rice, "Effects of Oxidation on the Room Temperature Strength

of Hot-Pressed Si^N^-MgO and Si^N.-ZrO^," pp. 1069-76 in

Ceramics for High Performance Applications," J.J. Burke,

E.M. Lenoe, and R.N. Katz, Brook Hill Publishing Co.,

Chestnut Hill, Mass. (1978).

20. S.M. Wiederhom and N.J. Tighe, "Proof-Testing of HotPressed Silicon Nitride," J. Mat. Sci. 13 , 1781-93 (1978).

21. D. Cubicciotti and K.H. Lau, "Kinetics of Oxidation of Hot

Pressed Silicon Nitride Containing Magnesia," J. Am. Ceram.

Soc. , ^ 512-7 (1978)

.

22. D.D. Cubicciotti, R.L. Jones, K.H. Lau, and D.J. Rowcliffe,

- "High Temperature Oxidation and Mechanical Properties of

Silicon Nitride," Interim Scientific Report 5522-2, Nov.

15, 1978, Prepared for Air Force Office of Scientific

Research/NE, SRI International.

23. T.M. Yonushonis and D.W. Richerson, "Strength of ReactionBonded Silicon Nitride," pp. 219-233 in ref. 13.

24. S.M. Wiederhom and N.J. Tighe, "Effect of Flaw Generation

on Proof-Testing," pp 689-700 in ref. 13.

25. A.F. McLean, E.A. Risher, R.J. Bratton and D.G. Miller, pp

133-134 in Brittle Materials Design, High Temperature Gas

Turbine, technical report AMMRC CTR 75-28 to the Army

Materials and Mechanics Research Center, Watertown, Mass.,

October 1975.

26. J.A. Rubin, "Probable Causes of Pitting in Hot-Pressed

Si-N, Ceramics," pp. 739-743 in ref. 13.

27. R.W. Davidge, A.G. Evans, A.G. Gilling and P.R. Wilgman,

"Oxidation of Reaction Sintered Silicon Nitride and Effects

on Strength," in Special Ceramics, _5, 329-44 (1972).

28. N.J. Tighe, to be published.

29. D.W. Richerson, private communication.

30. A.G. Evans and S.M. Wiederhom, "Crack Propagation and

Failure Prediction in Silicon Nitride at Elevated Temperatures,"

J. Mat. Sci., 9 , 270-278 (1974).

31. A.G. Evans, "Fracture Mechanics' Determinations , " pp. 17-48

in Fracture Mechanics of Ceramics, Vol. 1, R.C. Bradt,

D.P.H. Hasselman and F.F. Lange, eds.. Plenum Press, New

York (1974).

32. N.R. Mann, R.E. Shafer and N.D. Singpurwalla, Methods for

Statistical Analysis of Reliability Data, John Wiley and

Sons, New York (1974).
31

33. R.W. Davidge, J.R. McLaren and G. Tappin, "Strength-ProbabilityTime (SPT) Relationships in Ceramics," J. Mat. Sci.

1699-1705 (1973).

34. N.J. Tighe and S.M. Wiederhorn, "Fracture of Brittle Materials

at High Temperatures," Air Force Materials Laboratory

Technical Report: AFML-TR-78-83, July 1978.
1

\

)'

1

^

!'
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM.

EnBLIOG^APHIC DATA

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1. PUBLICATION OR REPORT NO. NBSIR 80-2047Acc®ssi{Hf No. Z* S AcC6$5.(0I1 Nq»

4. TITLE AND SUBTITLE

APPLICATION OF FPACTUEE MECHANICS IN ASSURING AGAINST

FATIGUE FAILURE OF CERAMIC COMPONENTS

5. Publication Date June 1980

7. AUTHOR(S) Fuller, Jr,

J. E. Ritter, Jr., S. M. Wiederhom, N. J. Tighe, and

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

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Department of Energy

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15. SUPPLEMENTARY NOTES

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I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200^word or leas factual summary of moat significant information. If document includes a signi ficant bibliography or

literature survey, mention it here.) This paper will review the application of fracture mechanics theory to the

prevention of delayed failure of ceramics. Three successful applications of this

theory of assuring the mechanical reliability of ceramics are discussed in order

to demonstrate the viability of the theory for purposes of engineering design.

Finally, a description is presented of practical limitations of the theory with

regard to heat engine application. Methods of overcoming these limitations through

modification of test procedures, and application of statistical theory are then

presented.

17, KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name

separated by semicolons)

Djmamic fatigue; fracture mechanics; lifetime prediction; proof testing;

stress corrosion; subcritical crack growth.

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