NBSIR 79-1960

Effect of Strain Rate on

Fracture Toughnessj^f*Silicon

Nitride at 1400°C

R. J. Fields, N. J. Tighe and E. R. Fuller, Jr

Fracture and Deformation Division

National Measurement Laboratory

Center for Materials Science

National Bureau of Standards

U.S. Department of Commerce

Washington, DC 20234

National Bureau of Standards

Library, E-01 Admin. Bldg.

MAR 1 1 1931

NBSIR 79-1 960 SIDoE)

t % f EFFECT OF STRAIN RATE ON THE

FRACTURE TOUGHNESS OF SILICON

NITRIDE AT 1400°C

i<iSo

rot

R. J. Fields, N. J. Tighe and E. R. Fuller, Jr.

Fracture and Deformation Division

National Measurement Laboratory

Center for Materials Science

National Bureau of Standards

U.S. Department of Commerce

Washington, DC 20234

October 1979

Issued October 1 980

Interim Report

Prepared for Department of Energy

Division of Fossil Fuels

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
1

1
ABSTRACT

The critical stress intensity factor for fracture, K » was measured

i> in Si-N, at lAQO^C as a function of strain rate. It was found that K__

3 4 IC

increased with decreasing rates of bending of notched bars. This effect

could be approximately predicted using a time dependent plastic zone

IC*

correction to K.
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1 . INTRODUCTION

At very high temperatures, ceramics can deform extensively by time dependent

deformation processes like creep. This permanent deformation is stress

and time dependent and is not predicted by elasticity theory. Whether

or not it is appropriate to apply linear elastic fracture mechanics to

creeping materials depends mainly on the extent of creep deformation

relative to certain specimen dimcx;sions . With this in mind, the strain

rate dependence of the fracture toughness of silicon nitride was investigated

at 1400°C. 12 3 Work on silicon nitride, aluminum oxide, and silicon carbide

have shown that at high temperatures and at moderate to slow strain

rates, the fracture toughness is above the room temperature value by a

factor of two or more. Under the same conditions, these materials are

3 4 observed to creep. ’ It is believed that it is this creep deformation

which is mainly responsible for the increased toughness. Since the

stress at which creep deformation is observed is highly rate sensitive,

there should be a correspondingly strong dependence of the high temperature

on strain rate or loading rate. Figure 1 shows the toughness of

silicon nitride measured by various researchers as a function of temperature.

Two groups find a strong increase in K with temperature, and two

groups find no increase or even a slight decrease. The fracture was in

all cases a fast fracture; that is, the specimen broke in two under its

own elastic strain energy and the load dropped immediately to zero,

faster than the loading or straining system could follow. The main

difference in these results is the rate at which the tests were carried

out. In impact loading studies with displacement rates greater than 100

mm/sec , no enhanced toughness was observed; whereas, increased toughness

-1
TEMPERATURE (*C)

Effect of Temperature ancT Strain Kate oh tne tracrure

Toughness of Silicon Nitride as Measured by Various

Researchers

.

fTgT r.
was observed for slow bend tests or double torsion tests carried out at

a displacement rate of 1 mm/sec or less. Such a rate effect is observed

g in metals at much lower temperatures and is generally ascribed to the

rate dependence of the yield stress. In such cases, a plasticity

correction can be made to to predict with some success the effect of

9

rate on toughness. In the present paper, the effect of strain rate on

both the fracture toughness and the stress for the onset of creep is

measured for silicon nitride at 1400°C. The creep stress data is used

to predict the influence of strain rate on toughness.

2. EXPERIMENTAL PROCEDURE

Bars having a rectangular cross-section were cut from a billet of

NCX3A, yttria doped silicon nitride. A narrow notch was introduced using a 1/2 mm

thick diamond slitting wheel. Two sizes of bars were tested having the

approximate dimensions listed in Table (1) . The tests were performed in

% four point bending (See Figure 2) using a rig made of silicon carbide.

The major span was 40 mm and the minor span was 10 mm. All tests were

performed in air in furnaces which were brought to temperature (1400°C)

in about 3 hours. The furnaces had feed-throughs in the top and bottom

for silicon carbide push rods. One push rod was attached to a load cell

and the other to the cross-head of a displacement-rate controlled testing

machine. The cross-head was driven at rates from 1.25 to 0.005 mm/minute.

In general, a subcritical crack initiated stably from the slit and

grew a few millimeters before fast fracture occurred. This avoided

ambiguities associated with the sharpness of the slit and eliminated the need

to precrack or fatigue crack the specimen. For fracture tests at rapid

displacement rates or at room temperature, where little or no subcritical

crack growth occurs, relatively long pre-cracks were sometimes grown in by

bending at 1400°C with a displacement rate of 0.0125 mm/min. After producing

these cracks, the specimens were kept at temperature unloaded for at least one hour

before cooling or testing.
Table 1

Nominal Specimen Dimensions (mm)

Large Specimen Small Specimen

Length, 5, 52 52

Width, W 10 5

Thickness, t 5 A.

5

Slit depth, c 3 and 5 1.5
p

Fig. 2. Schematic of Four-Point Notched Bend Test.
After fracture, the crack length(a) was determined as the sum of slit

depth plus the extension resulting from the subcritical crack growth.

This, together with the load at the onset of fast fracture (P^) was used

to calculate according to the formula^^

K

IC

3Pf(ii-il2)

2 B

/tT F(a/W) ( 1 )

where TTa^ F(a/W) =

i^2W tan IT a

TTa 2W

0.923 -r 0.199 (1-sin-^)

Zw cos (iTa/2W)

and where 2,^ and bhe major and minor spans of the four point

bending rig, B is the specimen thickness, and W is the specimen width.

This formula was used rather than the more common polynomial^ ^ because

it is purported to be accurate for any crack length/specimen width (a/W)

ratio. The pol^momial expression is only good for (a/W) less than or

equal to 0.6.

Additionally, two other types of fracture tests were performed.

One test consisted of slowly growing a crack at a displacement rate of

0.0125 ram/min., waiting a time (At), and then fracturing at a faster

* displacement rate of 1.25 mm/min. This test was performed for various

At's. The other type of test consisted of growing in a crack at 0.0125

mm/min and then cooling under load to room temperature and fracturing at

0.05 mm/min.

To describe the influence of displacement rate on the fracture

behavior, the creep behavior of this particular material was needed.

We made the assumption here that the creep behavior would correlate well with

the stresses at which the load-deflection curves became non-linear.

These proportional limit stresses were obtained for displacement rates

from 0.125 to 0.0125 mm/min. Small cubes (5 mm on a side) were cut

- 6 -
from some of the fracture bars. These were compressed between the silicon

carbide push rods. Cross-head displacements agreed with dimensional changes

measured on the specimens after the test. No attempt was made to reach

steady-state creep. It is known that creep behavior of ceramics is very

4 different in tension and compression. However, the primary stage of

creep is probably dominated by some viscous component like grain boundary sliding

rather than a cavitational component (which dominates tertiary creep) in the

12 material's mechanical behavior. This viscous deformation should not

depend strongly on the sign of the loading.

To investigate the extent of creep deformation in the fracture

process, a fine array of Vicker's indentations was made on the side of a

flexural specimen (Fig. 3) which was then loaded at a displacement rate

of 0.0125 mm/min. The positions of the indentations were measured

before and after with a precision of 0.0075 mm.

3 . RESULTS

The K measured at room temperature for a specimen which was precracked at 1400“C was 8.3 MPa v^. This high value is discussed in the next

section. The results of measuring at 1400°C as a function of displacement

rate are shown in Fig. 4. This shows an increase in toughness from

about the room temperature value to more than 18 MPa at the lowest

displacement rate of 0.0125 ram/rain. Evidence that this toughening is

due to a time dependent process, is shown in Fig. 5. A specimen was

loaded slowly until a crack started growing slowly. The specimen was

unloaded rapidly and then reloaded at 1.25 mm/min. If the reloading

took place immediately, the toughness value is close to that obtained

by breaking the specimen at the slow rate. If the specimen was allowed

to remain unloaded for several minutes before reloading, the toughness

fell. The maximum effect of delayed reloading was obtained in about 60

minutes after which time the toughness no longer decreased. This effect

- 7 -
Fig. 3. Array of Vicker's Indentations on Side of Flexural Specimen.

no-
T

1C X34 mi c \

\

il I _L

•Jfl l.tl 1.1 DISPUCEMEMT RATE (ea/nia)

Fracture Toughness of NCX34 as a Function of Cross-Head

Displacement Rate at 1400 C.
Hish^rr High “ ^^“Perature^To^rghness'with Time after Temperature Pre-Cracking.

Fig. 5,
was obtained in specimens which had been heated to 1400®C for several

hours as well as in the as-ground specimens.

In an attempt to "freeze-in” the cause of the toughening, a specimen

was loaded until a crack began to grow subcritically and then was cooled

under a slightly reduced load to room temperature. This resulted in a room

temperature K of 9.9 MPa /m which is a 20% increase in toughness. Tests

like this on alumina have obtained similar increments in room temperature

2

toughness.

The results of the creep tests are shown in Fig. 6.* From this

data, the relation between the strain rate and the stress at the onset

of creep may be represented by

A. 24

/(2.04 GPa sec)

where the pre-exponential term and the power were determined from a

least squares analysis of the data. The correlation coefficient was

0.96.

( 2 )

The extent of permanent creep deformation was determined approximately

from the flexural specimens on whose side faces an array of indentations

had been made. Within the resolution of the technique (0.075 mm in 10 ram),

the permanent deformation was confined to a 1 to 2 mm region around

the crack.

4. DISCUSSION

The room temperature value for 8.3 MPa is higher than that

13 usually reported for NCX34. This could be due to test technique,

since four point bending usually gives higher toughnesses than double

torsion tests, and slow creep cracks are probably blunter than indentation

cracks. Alternatively, this particular batch of NCX34 might be especially

*The least squares line has been drawn over the range of strain rates that

occur in the bending tests.
Proportional Limit Yield Stress as a Function of Strain Rate

in NCX3A at 1400°C.

- 12 -
strong as is suggested by other strength studies made on this billet.

In any case, regardless of the exact values reported here, the trends

with loading rate or delay time should represent general trends in hotpressed silicon nitrides.

Fig. 4 shows that there is a strong variation in toughness with

displacement rate. This raises a serious question as to the existence

of a unique fracture toughness which reflects a material’s microstructural

resistance to fracture. If there is no unique value, then K must be

measured for each strain rate in question. However, we feel that the

time dependent plastic response of this material at 1400°C is responsible for

lessening the intensification of the stress near the crack tip. Therefore,

the K measured at the highest rate will most nearly approach the purely

elastic case and ought to be the correct value for comparison of a material's

fracture properties. The average K_ for four specimens measured at

Xv,/ 1.25 mm/min (i.e. the fastest rate) and 1400°C is 7.9 + .6 MPa v^. This value is

slightly below the room temperature value in accord with the trend observed in

impact studies on NC132. While 1.25 mm/min is not an impact test, it is

very fast for a material with good creep resistance like NCX34. It is

interesting to note that there was no appreciable difference in toughness

between pre-cracked specimens and as-slit specimens.

The measured at lower rates represents some mixture of a material’s

fracture and deformation behavior. It is probably the more important

engineering quantity to specify since it is the effective toughness that

will be observed at a given, low strain rate.

Knowing both for the purely elastic case (rapid fracture with little

deformation) and the deformation behavior, allows one to predict the apparent

for the case of fracture preceded by deformation. One of the simplest

- 13-
adjustments is to recalculate assuming that the crack is longer than

the measured crack by an amount equal to the extent of the deformation

zone. Such an assumption works well for metals. It may be particularly

valid for silicon nitride in which cavitation is a major component in the

^ . 12 tensile creep detormation.

The radius of the deformation zone may be derived from the stress

distribution ahead of the crack tip, i.e.

a = K/Zlifc ( 3 )

by inserting the appropriate stress and solving for distance ahead of the

crack tip(r)

1 ''ic

'pt 2-rr pi

(4)

Note that this analysis relies on the assumption that the stress field

outside of the small plastic zone is described by K. The above distance

(r^^) is then added to the crack length used in the highest strain rate

measurement of (a=5.02 mm). is then recalculated from Eqn. 1

using the new crack length and the original load at fracture for the

high rate K (471 N) . This is the predicted K corresponding to the

XL/ strain rate at which a , was measured. pi

To carry this procedure out for the present data, the strain rate was

determined from the displacement rate in a bend test.^^ The relation

used is:

e max

6 (W-a) A

(5)

where e is the strain rate in the outer fiber, A is the displacement

rate, and 2.^^ are the major and minor spans, and (W-a) is the ligament

width. The assumption is made here that the strain rate at the crack tip

- 14 -
is equal to the outer fiber strain rate in an elastic bar having a width

equal to the remaining ligament width. Since most of the bar is

deformed elastically, Eqn. 5 seems more appropriate than an equation which

assumes a creeping or perfectly plastic material. At longer times than were

studied here, however, creep deformation occurs on a scale comparable to

the specimen’s dimensions and other relations would have to be used. In

this regime, however, the validity of measuring K would also be questionable.

In Table 2, the strain rates at which the tests were carried out are

listed in decreasing order in the first column. In the second column, the

corresponding yield stresses calculated from Eqn (5) are shown. These

yield stresses are then used (Eqn. (4)) to determine the plastic zone size.

Finally the corrected K is calculated from the highest rate K by altering

XU

the effective crack length by an amount equal to the extent of the

deformation. These values may be compared with the experimentally determined

ones in the last column. This comparison is shown graphically in Fig. (7).

The agreement between the predicted and experimental toughness is as good

as the scatter between the experimental values. The predicted line tends

to be below the experimentally determined points. This could be due to

the measurement of the creep stress in compression rather than in tension.

Creep should occur more readily at lower stresses in tension. This would

tend to shift the predicted line upward and give better agreement.

The effect of the deformation or plastic zone on the toughness decreases

with time after unloading as shown in Fig. (5). It takes about 1 hour at 1400°C.

to recover fully. The effect can be frozen in by cooling to room temperature

under load. This is additional evidence that it is the time dependent

deformation which is responsible for increasing the apparent by

reducing the crack tip stress field intensification. The delay time

- 15 -
Table

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IT3 r— crv o to C7> LT3 LO CM

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- 16 -
Fig. Measured and Predicted K as a Function of Crack Tip Strain

Rate.

-17-
effect could be explained as follows: on loading, a zone of tensile

creep deformation develops around the crack tip. On unloading, the

predominantly elastic specimen puts the deformed region into compression

and tends to reverse the deformation that has occurred at the crack tip.

The time required to return to the low toughness state depends on the

creep rate of the material and how fast the stress falls off as the

deformation is reversed (that is, the elastic modulus).

It is possible to rule out oxidation and microstructural instability,^^

to some extent, as causes of the above effects. Oxidation could either blunt or

sharpen the crack. If it sharpened the crack, then toughness should go

down the longer the specimen was held at temperature. This might explain

the delay time reloading tests, but it cannot explain the increase in

toughness with decreasing strain rate. Alternatively, if oxidation blunted

the crack, then it could explain the rate effect but not the delay time

effect

.

With regard to the microstructural instability, a general degradation

14

of properties in NCX34 is frequently noted after thirty minutes at 1400°C.

This has been associated with a volume change in the grain boundary phase causing

* cracking. With longer exposures, there is only a slow change in properties

after the first hour. Since the specimens used here were heated up

slowly and equilibrated at temperature before testing, they spent more

than an hour at a temperature high enough to reach a relatively stable state.

To verify that the microstructure was indeed stabilized, some specimens

were kept in the furnace while other tests were run. Later, these specimens

themselves were tested. Although these specimens had been at 1400°C for

- 18-
f

several hours, no appreciable change in fracture properties was noted

when they were compared to the specimens that were tested at room temperature or

heated and tested immediately. Also, the microstructural instability cannot

simultaneously explain the delay time effect and the strain rate effect.

It is important to note that the range of strain rates over which

the plastic zone correction is applicable is limited. At very high strain

rates, the zone is so small that it makes a negligible correction to the

and the toughness there should be independent of rate. At very low

strain rates, the creep deformation extends throughout the whole • specimen

so that the correction would give effective crack lengths equal to or

greater than the specimen width. In such a case, no longer describes

the crack tip stress field and it might be better to evaluate J in order

X c* to predict the K that would be obtained in larger bodies.

Xu

5. CONCLUSION ^

At temperatures where creep becomes an important component in the

deformation of silicon nitride, the apparent depends on the

rate at which the fracture test is carried out. This toughening is due

to the relaxation of crack tip stress intensification by high temperature,

time dependent plasticity rather than oxidation or microstructural

effects. It has been shown here that, when the extent of this deformation

is small, its effect on the toughness may be estimated by making a

plastic zone correction to the crack length.

Acknowledgments: The authors thank P. L. Land of Air Force Materials

Laboratory, Wright-Patterson AFB and R, deWit for helpful advice and

useful discussions.

-- 19 -
References

1. A.G. Evans and S.M. Wiederhorn, J. Mater. Sci. ^ (1974) 270.

2. T.D. Ketcham and R.M. Cannon, Amer . Ceram. Soc. Bui. (1979) 343.

3. M. Srinivasan and R.H. Smoak, Amer. Ceram. Soc. Bui. (1979) 347.

4. D.G. Miller, C.A. Anderson, S.C. Singhal, F.F. Lange, E.S. Diaz, and

R. Kossowsky, AMMRC 76-32, ARPA Order No. 1849, Project Code No IDIO,

Agency Accession No. OD 4733, December 1976.

5. M.G. Mendiratta, J. Wimmer , and J. Bransky, J. Mater. Sci. 2^ (1977) 212.

6. S.T. Gonczy and D.L. Johnson, "Fracture Mechanics of Ceramics, Vol. 13," edited

by R. C. Bradt, D.P.H. Hasselman, and F.F. Lange (Plenum Press, New York,

1978) p. 495.

7. J.J. Petrovic and L.A. Jacobson, J. Amer. Ceram. Soc. ^ (1976) 34.

8. S.T. Rolfe and J.M. Barsom, "Fracture and Fatigue Control in Structures;

Applications of Fracture Mechanics," (Prentice-Hall, Englewood Cliffs,

N.J., 1977).

9. G.R. Irwin, Appl. Mater. Res. 3_ (1964) 65.

10.. H. Tada, P.C. Paris, and G.R. Irwin, "The Stress Analysis of Cracks Handbook",

(Del Research Corp., Hellertown, PA., 1973).

11. W.F. Brown, Jr. and J. Srawley, "Plane Strain Crack Toughness: Testing

of High Strength Metallic Materials", ASTM-STP 410 (Amer. Soc. Testing and

Mater., Phila; PA., 1966).

12. F.F. Lange, Met. Trans, (to be published).

13. S.W. Freiman, private communication.

14. N.J. Tighe and S.M. Wiederhorn, Air Force Mater. Lab. Tech. Rpt.,

AFML-TR-78-83 (1978) .

15. P.L. Land, J. Mater. Sci. (to be published).

16. G.W. Hollenberg, G.R. Terwilliger, and R.S. Gordon, J. Amer. Ceram.

Soc. 54 (1970) 196.

17. F.F. Lange, S.C. Singhal, and R. C. Kuznicki, J. Amer. Ceram. Soc. ^

(1977) 249.

- 20 -
NBS-n4A (REV. 9- 78 )

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 79-1960 M (DoE

No.

. .... ' .. ReciBtait’s Accession No,

4. TITLE AND SUBTITLE

EFFECT OF STRAIN RATE ON THE FRACTURE TOUGHNESS OF

SILICON NITRIDE AT 1400°C

5. Publication Date October 1980

S. Performing Organization Code

7. AUTHOR(S)

R. J. Fields, N. J. Tighe, E. R. Fuller, Jr.

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS rSfreer, City, stdfe, ZIP)

Department of Energy

Washington, D.C.

13. Type of Report & Period Covered Interim

15. SUPPLEMENTARY NOTES

I

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

16. ABSTRACT (A 200~word or leas tactual summary of moat aignificant information. If document includes a significant bibliography or

literature survey, mention it here.)

The critical stress intensity factor for fracture, was measured in

Si^N^ at 1400°C as a function of strain rate. It was found that increased

with decreasing rates of bending of notched bars. This effect could be

approximately predicted using a time dependent plastic zone correction to Kj^.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper nam»5 separated by semicolons)

Crack growth; creep fracture; high tenperature fracture; silicon nitride;

strain rate effect; toughness.

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