fit - -/f-? * <e

NBSIR 79-1934

Proof Testing of Ceramics:

I. Experiment

J. E. Ritter, Jr. and P. B. Oates

Mechanical Engineering Department

University of Massachusetts

Amherst, MA 01003

E. R. Fuller, Jr. and S. M. Wiederhorn

National Bureau of Standards

Fracture and Deformation Division

National Measurement Laboratory

Center for Materials Science

National Bureau of Standards

December 1979

Prepared for Department of Energy

Fossil Fuel Utilization Division

Washington, D.C.

NBSIR 79-1934

PROOF TESTING OF CERAMICS:

I. EXPERIMENT

J. E. Ritter, Jr. and P. B. Oates

Mechanical Engineering Department

University of Massachusetts

Amherst, MA 01003

E. R. Fuller, Jr. and S. M. Wiederhorn

National Bureau of Standards

Fracture and Deformation Division

National Measurement Laboratory

Center for Materials Science

National Bureau of Standards

December 1979

Prepared for Department of Energy

Fossil Fuel Utilization Division

Washington, D.C.

U S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

o

o*
.
PROOF TESTING OF CERAMICS: I. EXPERIMENT

J.E. Ritter, Jr. and P.B. Oates

Mechanical Engineering Department

University of Massachusetts

Amherst, MA. 01003

E.R. Fuller, Jr. and S.M. Wiederhorn

National Bureau of Standards

Washington, D.C. 20234

ABSTRACT

The effectiveness of proof testing as a method of improving component

reliability was studied by comparing the inert strength distributions of

soda-lime-silicate glass before and after proof testing. The effects of

unloading rate from the proof stress, hold time at the proof stress, and

proof- test environment were examined. The results indicate that the proof

test must be conducted with rapid unloading rates and good environmental

control to be effective. The theoretical implications of these results

are discussed.
I. INTRODUCTION

Proof testing is one means used to assure the mechanical reliability

of structural ceramics. In proof testing, ceramic components are subjected

to stresses that are greater than those expected in service in order to

break the weak components and thus truncate the low end of the strength

distribution. In this manner, weak components are eliminated before they

can be placed in service. Proof testing has been applied to spacecraft

12 3

windows, * electrical porcelain insulators, and vitrified grinding

4

wheels.

5-7

Wiederhorn, Evans, and Fuller have provided a mathematical foundation for the selection of the proof-test stress and the establishment of

proof-test conditions. Their analysis is based on the assumption that

failure of ceramics occurs from the growth of preexisting flaws. By

characterizing this crack growth and coupling crack growth parameters

with proof testing, they derived the strength after proof testing assuming

flaw growth during the proof-stress, load-unload cycle. The resulting

theory indicates that crack growth must be minimized to have effective

proof testing. This can be achieved by having rapid unloading from the

proof stress and good environmental control during the proof test.

o In support of the proof-test theory, Ritter has shown recently for

soda-lime silicate glass after proof testing that the inert strength distribution

and failure time under static stress agree with that predicted from theory.

Aside from this study, there has been no extensive experimental confirmation

of proof-test theory. The purpose of the present study, therefore, was

to conduct a detailed study of the proof- test technique and to assess the

2
validity of the theory in predicting the strength after proof testing.

In particular, the effectiveness of proof testing and the applicability

of proof-test theory was determined by comparing the inert strength

distributions of soda-lime silicate glass before and after proof testing

over a range of proof-test conditions. The major proof test variables

were unloading rate from the proof stress and the proof-test environment.

Soda-lime-silicate glass was chosen as the model material for this study

because it is readily available and because its subcritical crack behavior

is well characterized.

II. EXPERIMENTAL PROCEDURE

All specimens used in this study were soda-lime-silicate glass,

microscope slides* (7.62 x 2.54 x 0.10 cm). The slides were annealed at

500°C for 1 h» furnaced cooled, and then abraded in the center with a

standard blast of No. 240 Si C grit. After abrasion, the samples were

aged for 24 h in distilled water to normalize their strength and then

stored in a desiccator prior to testing. Over 2000 samples were prepared

in this manner and they were randomly selected for testing.

The inert strength measurements before and after proof testing were

made in liquid nitrogen using four point bending. The bending apparatus

had inner and outer supports of 2.54 and 5.08 cm., respectively. All

strength testing was done on a universal testing machine+ using a constant

crosshead speed of 0.2 cm/min, corresponding to a stressing rate of 5. 23 MPa/s.

The initial inert strength distribution was determined from 79 samples while

the after-proof, strength distributions were determined from about 30 samples.

+Corning No. 2947

f

Instron Corp., Canton, MA.

3
The bend apparatus was also used for proof testing. The samples were

loaded up to the proof stress at a stressing rate of 5.29 MPa/s and then

unloaded at various rates (132.33, 5.29, and 1.32 MPa/s). The time at the

proof stress varied from momentary (less than 0.5 s) to 60 s. The proof

test environments were liquid nitrogen, dry nitrogen gas (about 5% Relative

Humidity), ambient air (55-65% Relative Humidity) and water. The last three

test environments were at room temperature, about 23°C. Groups of 50 samples

were proof tested for each proof-test condition and proof- test stresses were

chosen to break approximately 40% of a set of test specimens, leaving about

30 samples for the determination of the inert strength distribution after

proof testing.

III. RESULTS AND DISCUSSION

5-7

The strength after proof testing has been derived for 3 conditions:

no flaw growth during proof testing, flaw growth up to unloading, and

flaw growth during the entire proof-stress cycle. If no flaw growth occurs

during the proof test, then the inert strength for a given specimen before

and after proof testing are equal; however because the weak samples have

been eliminated from the initial distribution, the cumulative failure probability after proof testing (F,) will have changed

a

F - F

F = Er a 1 - F. ( 1 )

where F is the cumulative failure probability before proof testing and Fp *

is the cumulative failure probability of the proof test.

Assuming that a single power law relationship exists between subcritical

crack velocity and the stress intensity factor.

F is obtained by ordering a set of strength data. F is given by r/(N+l) where

N is the total number of datum points and r is the position of each point in

the ordered set. r = 1 for the lowest strength, r = 2 for the second lowest and

so forth.

4
V ( 2 ) = A Kj

11

where A and n are constants for a given material and test environment, the

inert strength after proof testing (S^) can be derived accounting for crack

growth during the proof-stress cycle. Considering crack growth up to

5 6

unloading but not during unloading, the distribution is given by: *

where n is the crack propagation parameter appropriate for the proof- test

environment, a is the proof stress, and m and S are the Wei bull shape and

scale parameters, respectively, of the initial inert strength distribution.

If flaw growth occurs during the entire proof stress cycle, the distribution

6

is now:

For purposes of identification in the following discussion, the various

predicted distributions will be labelled:

Type I, based on Eq. (1) for no flaw growth.

Type II, based on Eq. (3) for no flaw growth on unloading.

Type III, based on Eq. (4) for flaw growth during entire proof

stress cycle.

For all three types of distributions it can be shown that is greater than

the initial strength at all levels of failure probability, provided m < n - 2.

For Type I and II distributions, the distribution is truncated at a ;

hence, represents the minimum inert strength after proof testing. When

flaw growth occurs on unloading (Type III distribution), the strength distribution is not truncated and no assurances of a minimum strength can be given.

5
The experimental inert strength distributions after-proof testing could

be divided generally into one of four distributions depending on the proof

test conditions. First, under inert proof-test conditions (liquid nitrogen)

the strength distributions after proof testing agreed with that predicted

from either a Type I, II, or III distribution (Fig. 1). In this case the

C

Type II and III distributions were determined by assuming an n = 120.

As can be seen in Fig. 1 there was no significant difference between the three

predicted distributions within the range of the after-proof data. This

observation just reflects the fact that for an inert environment such as

liquid nitrogen little or no crack growth can occur because of the high n

value appropriate for this environment.

Second, with rapid unloading rates in the dry nitogen and air environments,

the strength distributions after proof testing agreed with that predicted

8 9

from either a Type II or III distribution where n = 18.4 * (Fig. 2). Since

the strength distributions after proof testing are shifted significantly to the

left of the Type I distribution, it is evident that crack growth occurs during

proof testing in these "moist" environments; however, it could not be

determined if the after-proof strength distributions were truncated at a .

To conclusively show truncation, much larger sample size after proof testing

would have to be used (about 10000 samples).

Finally, when good proof-test controls were not used, i.e. relatively

slow unloading rates and/or moist proof-test environments, the strength

distributions after proof testing either were not different significantly

from the initial distribution (Fig. 3) or were weaker than the initial

distribution (Fig. 4). In these cases none of the theoretical distributions

could explain the observed distributions after proof testing since the strengths

were much weaker than predicted from theory.

6
Table I summarizes all the proof- test results. It is evident that

for effective proof testing crack growth must be minimized through use

of good proof test conditions, namely, rapid unloading rates and good

environmental control. In addition, under experimental conditions where

proof testing was not effective,

+ none of the theoretical, after-proof

distributions agreed with the data. There was only one exception to

these trends and that was for the proof test conducted in water at an

unloading rate of 5.29 MPa/s. It is not known why this one set of

results did not fit into the general pattern.

To provide additional support to the general conclusions made above

regarding the effectiveness of proof testing, a large group of asreceived microscope slides were proof tested in very dry nitrogen (less

than 0.1% R.H.) and in moist nitrogen (50% R.H.) using an unloading rate

of about 13.2 MPa/s. Because the dry nitrogen gas was a relatively

inert environment, it was used as the test environment for the strength

measurements before and after proof testing. Figure 5 and 6 shows that

these results are in agreement with the trends shown in Table I. When

good proof-test controls are used, proof testing is effective and the

strength distribution after proof testing can be characterized theoretically (Fig. 5). On the other hand, when a relative slow unloading

rate is used in a moist environment, proof testing is not effective in

truncating the distribution and the after-proof strength distribution

does not agree well with the theoretical distributions (Fig. 6).

+The reader is cautioned not to jump to the conclusion that when good proof

test controls are not used, proof testing will not be beneficial. It must be

remembered that our conclusion is based on a group of uniformly abraded

samples that could statistically be characterized by a single strength, i.e.

flaw, distribution. If in a set of samples to be proof tested, some samples

contain gross flaws, perhaps due to incorrect manufacturing, then proof

testing even without ideal conditions, would undoubtedly eliminate these weak

samples from the population, thereby, improving the reliability of the

remaining samples.

7
Based on the above proof test results, the question of why strengths

after-proof testing under non-ideal conditions are significantly weaker

than that predicted must be addressed. The use of Eq. (2) is a

key assumption in deriving the strength after-proof testing. Experiments

have characterized the dependence of crack velocity on stress intensity

factor by three principal regions of behavior (Fig. 7).^

Regions I and II result from a stress corrosion reaction between the

glass and water in the environment. The rate of the reaction between

water and the glass controls crack motion in Region I, whereas diffusion

of water to the crack tip controls crack motion in Region II, where the

crack velocity is essentially constant. In Region III the stress intensity

factor is close to and crack velocity does not depend on water in the

environment. Since Eq. (2) represents Region I crack growth, the equations

derived for the strength after-proof testing are based on the assumption

that the strength is controlled exclusively by subcritical crack growth in

Region I. If the behavior shown in figure 7 is important, then Eq. (2) would

overestimate crack velocity when the stress intensity factor of the crack

was in the range that characterizes region II, and the theory would predict

failure when in fact, the samples may just pass the proof test. The samples

that just survive the proof test would then be weak, and the distribution

after the proof test would not be predicted from equation 3 or 4. Therefore,

an analysis that takes into account Region II crack growth is necessary to

account for the observed strength distributions after proof testing under

non-ideal conditions. An analysis of this sort is presented in Part II

of this paper.

8
ACKNOWLEDGEMENTS

Two of the authors (JER and PBO) are grateful for the support of

the National Science Foundation Grant No. DMR 77-05647 for this research;

the other (E..R. Fuller, Jr. and S. M. Wiederhorn) are greatful for the

support of the Department of Energy, Fossil Fuel Utilization Division.

9
REFERENCES

1 .

2 .

3.

4.

5.

S.M. Wiederhorn, A.G. Evans and D.E. Roberts, "A Fracture Mechanics

Study of the Skylab Windows," pp. 829-41 in Fracture Mechanics

of Ceramics , Vol . 2 , Edited by R.C. Bradt, D.P.H. Hasselman and

F. F. Lange, Plenum Press, New York (1974).

S.M. Wiederhorn, A.G. Evans, E.R. Fuller and H. Johnson, "Application

of Fracture Mechanics to Space-Shuttle Windows", J. Am. Ceram. Soc.,

57, 319-23 (1974).

I

A.G. Evans, S.M. Wiederhorn, Melvin Linzer and E.R. Fuller, Jr.,

"Proof Testing of Procelain Insulators and Application of Acoustic

Emission", Am. Ceram. Soc. Bull., 54, 576-81 (1975).

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

ASsure Against Delayed Failure", to be published Am. Ceram. Soc. Bull.

(1978).

A.G. Evans and S.M. Wiederhorn, "Proof Testing of Ceramic Materials - An Analytical Basis for Failure Predictions", Int. J. Frac. Mech., ljl, 379-92

(1974).

6. A.G. Evans and E.R. Fuller, "Proof Testing - The Effects of Slow

Crack Growth", Mat. Sci . and Engr., T_9 , 69-77 (1975).

7. S.M. Wiederhorn, "Reliability, Life Prediction, and Proof Testing of

Ceramics", pp 635-65 in Ceramics for High Performance Applications , Ed. by J. J. Burke, A.E. Gorum and R.N. Katz, Brook Hill Publishing Co.,

Chestnut Hill, MA. (1974).

8. J.E. Ritter, Jr., "Engineering Design and Fatigue Failure of Brittle

Materials", pp 667-686 in Fracture Mechanics of Ceramics, Vol. 4 , Edited by R.C. Bradt, D.P.H. Hasselman, and F.F. Lange, Plenum

Publishing Co., New York (1978).

9. P.B. Oates, "A Detailed Study of the Proof-Test Technique for Assuring

the Mechanical Reliability of Glass", M.S. Thesis in Mechanical

Engineering, University of Massachusetts (1976).

10. S.M. Wiederhorn, "Influence of Water Vapor on Crack Propagation in

Soda-Lime Glass", J. Am. Cera. Soc., 50_, 407-14 (1967).

10

-
Table I. Summary of the Proof-Test Data for Soda-Lime Silica Glass.

Proof-Test Proof-Stress Hold Time at After-Proof Inert

Environment Unload Rate (MPa/s) Proof Stress (s) Strength Distribution

Liquid Nitrogen 132.22 < 0.5 I, II, III +

Liquid Nitrogen 5.29 < 0.5 I, II, III

Dry Nitrogen Gas 132.33 < 0.5 II, III

Dry Nitrogen Gas 5.29 < 0.5 Same as Initial

Dry Nitrogen Gas 1.32 < 0.5 Same as Initial

Dry Nitrogen Gas 5.29 60 Same as Initial

Air 132.33 < 0.5 II, III

Air 5.29 < 0.5 Weaker than Initial

Air 1.32 < 0.5 Weaker than Initial

Air 5.29 5 Same as Initial

Water 132.33 < 0.5 Same as Initial

Water 5.29 < 0.5 II, III

Water 5.29 5 Same as Initial

+

Type theoretical distributions that agreed with after-proof data.

11
FIGURES

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Inert strength distributions of soda-lime-silicate glass before

and after proof testing compared to the theoretical, after-proof

distributions. Proof testing was in liquid nitrogen at unload

rate of 5.29 MPa/s and a

p = 127.5 MPa, F

p = 0.36, n = 120,

m = 8.19, = 137.4 MPa.

o

Inert strength distributions of soda-lime-silicate glass before

and after proof testing compared to the theoretical, after-proof

distributions. Proof testing was in air at unload rate of 132.3

MPa/s and a = 79.3 MPa, F = 0.33, n = 18.4, m = 8.19,

r r = 137.4 MPa.

o

Inert strength distributions of soda-lime silicate glass before

and after proof testing compared to the theoretical, after-proof

distributions. Proof testing was in water at unload rate of 132.3

MPa/s and a = 68.6 MPa, F = 0.37, n = 18.4, m = 8.19, S = 137.4 MPa.

r r ^

Inert strength distributions of soda-lime silicate glass before

and after proof testing compared to the theoretical, after-proof

distributions. Proof testing was in air at unload rate of 5.29 MPa/s

and a = 79.3 MPa, F o = 0.47, n = 18.4, m = 8.19, S = 137.4 MPa.

p p o

Strength distributions for soda-lime-silicate glass in very dry

nitrogen gas before and after proof testing compared to the

theoretical, after-proof distributions. Proof testing was in very

dry nitrogen gas at unload rate of 13.2 MPa/s and a

p = 103.9 MPa,

F

p = 0.30, and n = 120.

12
Fig. 6

Fig. 7

Strength distributions for soda-lime-silicate glass in very dry

nitrogen gas before and after proof testing compared to the

theoretical, after-proof distributions. Proof testing was in

50% R.H. nitrogen gas at unload rate of 13.2 MPa/s and a = 103.9 MPa,

r Fp = 0.58, and n = 18.4.

Crack propagation behavior of soda-lime-silicate glass in moist

nitrogen gas environments. Percent relative humidity is given

on the right hand side of diagram (after Wiederhorn, reference 10).

13
Strength (MPa)

100.0 115.0 130.0 150.0 175.0

Fig. 1. Inert strength distributions of soda-lime-silicate glass before

and after proof testing compared to the theoretical, after-proof

distributions. Proof testing was in liquid nitrogen at unload

rate of 5.29 MPa/s and a

p = 127.5 MPa, F

p = 0.36, n =120,

m = 8.19, S

Q = 137.4 MPa.
100.0 175.0

I

Strength (MPa)

115.0 130.0 150.0

ig. 2. Inert strength distributions of soda-lime-silicate glass before

and after proof testing compared to the theoretical, after-proof

distributions. Proof testing was in air at unload rate of 132.3

MPa/s and a

p = 79.3 MPa, F

p = 0.33, n = 18.4, m = 8.19,

So =137.4 MPa.

o
Strength (MPa)

100.0 115.0 130.0 150.0 175.0

Fig. 3. Inert strength distributions of soda-lime silicate glass before

and after proof testing compared to the theoretical, after-proof

distributions. Proof testing was in water at unload rate of 132.3

MPa/s and a = 68.6 MPa, F = 0.37, n = 18.4, m = 8.19, S = 137.4 MPa.

r r

v"/
150.0 175.0

Strength (MPa)

100.0 115.0 130.0

90.0

70.0

50.0

30.0

10.0

5.0

1.0

F (%)

Fig. 4. Inert strength distributions of soda-lime silicate glass before

ana after proof testing compared to the theoretical,, after-proof

distributions^ Proof testing was in air at unload rate of 5.29 MPa/s

and Cp = 79.3 MPa, F

p = 0.47, n = 18.4, m = 8.19, S

Q ^ 137.4 MPa.
Strength (MPa)

70 85 100 115 130

Fig. 5. Strength distributions for soda-1 ime-siTicate glass in very dry

nitrogen gas before and after proof testing compared to the

theoretical, after-proof distributions. Proof testing was in very

dry nitrogen gas at unload rate of 13.2 MPa/s and a

p = 103.9 MPa,

F = 0.30, and n =120.
Strength (MPa)

70 85 100 115 130

F(%)

g. 6. Strength distributions for soda-lime-silicate glass in very dry

nitrogen gas before and after proof testing compared to the

theoretical, after-proof distributions. Proof testing was in

50% R.H. nitrogen gas at unload rate of 13.2 MPa/s and cjp = 103.9 MPa,

Fp = 0.58, and n = 18.4.
Fig. 7. Crack propagation behavior of soda-lime-silicate glass in moist

nitrogen gas environments. Percent relative humidity is given

on the right hand side of diagram (after Wiederhorn, reference 10).
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. 79-1934

’Tgo*!’ Accession NoJ 3. ffedment's

' ••*•••••• • • Accession‘ No-

. 7 —;

4. TITLE AND SUBTITLE

Proof Testing of Ceramics: I. Experiment

5. Publication Date

8. Perform! ng Organization Code

v . ^-vv ' %*.• v ' v

‘

7 . author(S) ^ E> Ritters Jr<j P> B< Oates, E. R. Fuller, Jr.

md S. M. Wiederhorn

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

18. Project/Task/Work Unit No.

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11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, ZIP)

Department of Energy

Fossil Fuel Utilization Division

Washington, D. C.

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

16. ABSTRACT (A 200-word or leaa factual summary of moat significant information. If document includes a significant bibliography or

literature survey, mention it here.) The effectiveness of proof testing as a method of improving component reliability

was studied by comparing the inert strength distributions of soda-lime-silicate glass before and after proof testing. The effects of unloading rate from the proof stress,

hold time at the proof stress, and proof- test environment were examined. The results indicate that the proof test must be conducted with rapid unloading rates and good environmental control to be effective. The theoretical implications of these results

are discussed.

17. KEY WORDS (a ix to twelve entries; alohabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Ceramics; crack growth; fracture; glass; proof testing; strength

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