Effects of different curing conditions on slow crack growth in cement paste

CEMENT and CONCRETE RESEARCH. Vol. 4, pp. 953-965, 1974. Printed in the United States.

Pergamon Press, Inc

EFFECTS OF DIFFERENT CURING CONDITIONS ON SLOW CPJ~CK GROWTH IN CEMENT PASTE Sidney Mindess Department of Civil Engineering University of B r i t i s h Columbia John S. Nadeau Jacqueline M. Hay Department of Metallurgical Engineering University of B r i t i s h Columbia Vancouver 8, B r i t i s h Columbia (Communicated by Z. P. Bazant) (Received August 30, 1974) ABSTRACT Portland cement paste was prepared in the following five ways: (I) cured in fresh water, (2) made with fresh water, cured in sea water, (3) made and cured in sea water, (4) low-pressure steam cured, (5) high-pressure steam cured. The water-cement r a t i o was 0.4 in all cases. Slow crack growth was studied by the double torsion method, and plots were made of crack v e l o c i t y versus stress intensity. Fracture toughness and the modulus of e l a s t i c i t y were also measured by flexural beam methods. The steam cured specimens had lower fracture toughness and were somewhat more sensitive to s t a t i c fatigue than the room-temperature cured specimens. There was evidence that crack growth is aided by the presence of water in the environment or by increased water-cement r a t i o . Le ciment Portland hydrat~ a ~t~ pr~par~ d'apr~s les cinq m~thodes suivantes: (I) t r a i t ~ dans l'eau frafche, (2) pr6par~ avec de l'eau fra?che, t r a i t ~ dans l'eau de mer, (3) pr~par~ et t r a i t ~ dans l'eau de mer, (4) t r a i t ~ avec de la vapeur d'eau ~ basse pression, (5) t r a i t ~ avec de la vapeur d'eau ~ haute pression. Dans chaque cas la proportion eau/ciment ~ t a i t 0.4. La lente propagation de la fissure ~ ~t~ 6tudi~e d'apr~s la m6thode de la double torsion et la vitesse de propagation de la fissure ~ ~t6 repr~sent~e graphiquement en fonction de l ' i n t e n s i t 6 de torsion. La r~sistance ~ la rupture et le module d ' ~ l a s t i c i t 6 ont aussi ~t~ mesur~s d'apr~s la m~thode de flexion des poutres. Les ~chantillons t r a i t ~ s avec de la vapeur d'eau avaient une r~sistance inf~rieure ~ la rupture et ~taient un peu plus susceptibles & l a f a t i g u e statique que les ~chantillons t r a i t ~ s ~ temperature ambiante. II semble que la propagation de la fissure est aid~e par la presence de l'eau dans l'environment ou par une augmentation de la proportion eau/ciment. 953

954

Vol. 4, No. 6 S. Mindess, J. S. Nadeau, J. M. ~,ay Introduction Slow growth of cracks in b r i t t l e

materials under stress is the pheno-

menon that d i c t a t e s t h e i r long-term strength. designed f o r long l i f e ,

the i n i t i a l

Since structures are usually

strength of a material

is of much less

importance than i t s strength a f t e r long exposure to stress. the long time strength can be as l i t t l e

as 20% of the i n i t i a l

With glass, strength.

There is ample evidence that cement and concrete are subjected to slow crack growth or " s t a t i c f a t i g u e " , resembles t h a t of glass.

and in several respects the behavior

Hansen (1) observed the slow growth of tension

cracks along the axis of specimens under uniaxial compressive load.

The

time during which crack growth occurred was s i x or seven hours at 90% of the normal breaking load.

Wittman and Zaitsev (2) studied the e f f e c t s of a sus-

tained t e n s i l e stress on hardened cement paste, and proposed that the c r i t i cal crack length could be reached as a r e s u l t of creep of the cement in the region of the crack t i p .

They also noted a strengthening e f f e c t under sus-

tained t e n s i l e load, which they a t t r i b u t e to a r e d i s t r i b u t i o n of stress concentrations at the crack t i p s due to creep.

Husak (3) subjected mortar

beams to bending stresses and observed the time to f a i l u r e as a function of r e l a t i v e humidity.

As with glass, the time to f a i l u r e decreased with in-

creasing humidity.

Shah and Chandra (4) tested saturated and a i r - d r i e d con-

crete specimens in compression and found t h a t the moist specimens f a i l e d q u i c k l y while the dried specimens did not f a i l allowed.

Barrick (5) found that the f a i l u r e

at all

in the t e s t period

time of mortars decreased with

increasing r e l a t i v e humidity and with increasing temperature.

Recently,

Nadeau, Mindess and Hay (6) observed the slow growth of cracks in saturated cement plates and obtained plots of crack v e l o c i t y versus stress i n t e n s i t y . The slopes of the plots were s i m i l a r to t h a t of soda-lime glass in moist air. Concrete structures are usually designed to minimize t e n s i l e stresses. Where they are unavoidable, as in beams, the t e n s i l e stresses are expected to be borne e n t i r e l y by steel r e i n f o r c i n g bars.

Nevertheless, the e f f e c t s

of slow crack growth or s t a t i c f a t i g u e in concrete can be serious.

Rapid

exposure of the reinforcement to the atmosphere by cracking of the concrete can lead to premature f a i l u r e of the s t r u c t u r e .

A thorough understanding

of the phenomenon of s t a t i c f a t i g u e in concrete, and i t s r e l a t i o n to s t r u c ture and cement chemistry could lead to the development of measures f o r i t s control.

Vol. 4, No. 6

955 CURING, CRACK PROPAGATION, CEMENT PASTE

A recently developed way of studying s t a t i c f a t i g u e is to determine the V-K I p l o t (7,8). sity.

A typical

This is a p l o t of crack v e l o c i t y versus stress i n t e n -

p l o t for soda-lime glass in toluene is shown in Fig. 1 (9).

Extensive studies of soda-lime glass have led to a f a i r l y

clear understand-

ing of the s t a t i c f a t i g u e process and i t s r e l a t i o n to the V-K I p l o t ( I 0 ) . When glass is loaded so t h a t cracks in i t

have an i n i t i a l

stress i n t e n s i t y

in stage I of the curve shown in Figure I , the cracks grow, usually with increasing stress i n t e n s i t y , u n t i l and f a i l u r e occurs.

I f the i n i t i a l

they reach the c r i t i c a l

stress i n t e n s i t y

stress i n t e n s i t y is known, the time to

f a i l u r e can be calculated by i n t e g r a t i o n of the V-K I p l o t (7).

The i n t e g r a -

t i o n is quite simple even f o r a three stage curve as in Figure 1 because the

KI C

:/

FIG. 1 V-K I ~ l o t for soda-lime glass in toluene (9).

'1"

Z

0 _J

LOG K L crack spends most of i t s time at low v e l o c i t i e s .

Thus, i t is usually s a t i s -

f a c t o r y to consider only the lower part of the p l o t and to t r e a t the r e l a t i o n between V and KI as; V

=

AK~

(I)

where log A is the i n t e r c e p t and n is the slope of the log-log p l o t . The p r i n c i p a l

aim of the present research was to determine V-K I plots

f o r cement pastes cured in several d i f f e r e n t environments.

Other f r a c t u r e

mechanical properties such as f r a c t u r e toughness and modulus of rupture were also determined.

956

Vol. 4, ~.~c. 6 S. Mindess, J. S. Nadeau, J. M. Hay Experimental Procedure

Production of Specimens The cement paste specimens were made from Type I l l s t r e n g t h ) p o r t l a n d cement.

Six d i f f e r e n t

under the c o n d i t i o n s shown in Table I .

(high-early

types of specimens were prepared,

The specimens were cast in brass

molds, each 228 x 76 x 13 mm., using the procedure p r e v i o u s l y described (6). TABLE 1 Mixing and Curing Conditions ~pecimen Designation

Mix Water

Curin 9 Conditions

Storage

m,m.

Fresh Water

Fresh Water at T = 23°C

Fresh Water

F.W.S.W.

Fresh Water

Fresh Water at T = 23°C f o r 28 days

Sea Water* Sea Water*

S.W.

Sea Water*

Sea Water* at

H.P.S.

Fresh Water

Autoclaved at T = 105°C (17.5 psia) f o r 2~ hours

Fresh Water

Autoclaved at (106 p s i a ) ' f o r

Fresh Water

Fresh Water

L.P.S. Dry#

Fresh Water

T = 23°C

T = 167°C 24 hours

Fres~ Water at T = 23°C

Fresh Water, then in a i r

* S u b s t i t u t e Ocean Water, prepared according to Reference I I . A l l specimens were prepared from Type I l l an i n i t i a l water/cement r a t i o of 0.4. Storage temperature:

p o r t l a n d cement, with

23°C.

Age of specimens at t e s t i n g :

4 - 6 months.

fReference 6, w/c = 0.5.

Because of the long c u r i n g period and the use of Type I I I

cement, i t was

assumed t h a t the f r a c t u r e behavior would not be s e n s i t i v e to small d i f f e r ences in the age of the specimens. Before t e s t i n g , thickness of lO mm.

the specimens were ground on a surface g r i n d e r to a

They were then grooved along t h e i r l e n g t h with a t h i n

diamond saw to a depth of 5 mm. groove with the same saw. out under water.

All

A notch was introduced at one end of the specimen

p r e p a r a t i o n and t e s t i n g was c a r r i e d

Vol. 4, No. 6

957 CURING, CRACK PROPAGATION, CEMENT PASTE

Double Torsion Tests The load relaxation method was used on double torsion specimens (9,12) to determine the r e l a t i o n between crack velocity and stress intensity.

The specimen and loading f i x t u r e are shown in Figure 2.

The load was

applied by a universal testing machine* at a cross-head speed of about 0.005 n~n/min. The load was increased until a crack formed at the t i p of the machined notch.

This was signalled by a sharp load drop as the specimen

became suddenly more compliant.

The cross-head was stopped and the load (A)

(B)

CROSS - H E A O

I

CROSS -

HE,=D

SPECIMEN

LOAO

LO#,D

CELL

CELL

FIG. 2 (A,B) Apparatus and (C) specimen for double torsion tests.

(C)

I

continued to f a l l

[

t

slowly as the crack grew at a decreasing rate.

w

4

Each

point on the resulting load-time curve corresponded to a d i f f e r e n t crack v e l o c i t y and stress i n t e n s i t y . single load relaxation curve.

Thus, a V-K I plot could be obtained from a The velocity depends upon the slope of the

relaxation curve and the load (12), V :

i.e.,

[(AiPi)/P z] dP/dt

where Ai and Pi are the i n i t i a l

(2)

crack length and load, and P is the load at

any point along the relaxation curve. with an uncracked specimen in place.

The background relaxation is measured This background relaxation, which in-

cludes relaxations in the machine, loading f i x t u r e , *SATEC Systems, I n c . , Grove City, Pennsylvania

load cell and specimen

958

Vol. 4, No. 6 S. Mindess, J. S. Nadeau, J. M. Hay

is subtracted from the load relaxation curve resulting from crack growth. As a control, the background relaxation has been measured with a s t i f f metal plate in place of the cement specimen. The relaxation curve was the same as that of the uncracked cement specimen, indicating that all of the background is due to the machine and fixture. The stress intensity depends only upon the load and the specimen dimension (12), i . e . , KI

=

PWm (3(l+~)/Wt3tn)½

(3)

where ~ is Poisson's r a t i o and the other parameters are defined in Fig. Ic. In a t y p i c a l experiment, two or three load r e l a x a t i o n s were made and then the specimen was loaded q u i c k l y to obtain KIC, the c r i t i c a l

stress i n -

tensity. Modulus of Rupture and Notched Beam Tests The broken double t o r s i o n specimens were sliced i n t o square bars having the dimensions 37.0 x I0.0 x I 0 . 0 mm. on 400 g r i t

Some of these bars were abraded

s i l i c o n carbide to produce a standard surface and then the bars

were broken in three point bending.

Other bars were s l o t t e d on a 0.015 cm.

t h i c k diamond saw and tested according to the method of Brown and Srawley (13) to obtain KIC.

The r a t i o of notch depth to specimen depth was 0.5.

No attempt was made to produce a sharp crack at the t i p of the notch. Modulus of E l a s t i c i t x ,

E.

Beams having the dimensions 228 x I0 x I0 mm. were also cut from the double t o r s i o n specimens.

They were loaded in 3 - p o i n t bending and the de-

f l e c t i o n was measured with an LVDT. Young's modulus was calculated from the slope of the load-deformation curve. Poisson's r a t i o was not determined d i r e c t l y ,

but was assumed to be

= 0.26, on the basis of data reported by Helmuth and Turk (14). Density, Porosity and Pore Size D i s t r i b u t i o n Saturated surface dry d e n s i t i e s were determined for small bars cut out of the double t o r s i o n specimens.

These bars were then dried at I05°C

for f i v e days and the dry d e n s i t i e s determined.

The p o r o s i t y was assumed

to be the d i f f e r e n c e between the saturated and dry weights, divided by the dry weight. In a d d i t i o n , s i m i l a r small specimens were tested in a 15,000 psi mer-

Vol. 4, No. 6

959 CURING, CRACK PROPAGATION, CEMENTPASTE

cury porosimeter.

These specimens were dried at I05°C for 24 hours p r i o r to

testing. Experimental Results Mechanical and Physical Properties The modulus of e l a s t i c i t y , modulus of rupture, saturated and dry dens i t y , and porosity are given in Table I I .

There was r e l a t i v e l y l i t t l e

dif-

ference between the three sets of specimens prepared at room temperature, TABLE I I Mechanical and Physical Properties

Modulus of Elasticity (1010Nm-2)

Modulus of Rupture (IO T Nm-2 )

S.S.D. Density (gm/cm 3)

Dry Density (gm/cm3)

Porosity (cm31gm)

R,T,

2.06

l .40

2.09

l .69

0.234

F.W,S.W.

2.08

l .41

2.10

l .71

0.233

S.W.

2.03

l .28

2.11

l .70

0.243

L.P.S.

1.46

l .37

2.07

l .65

0.255

H.P.S.

1.26

0.99

2.08

l .64

0.271

Specimen Designation

regardless of whether they were in

contact with fresh water or sea water.

However, the steam cured specimens had lower values of E and higher porosities than specimens cured at room temperature. The modulus of rupture of the H.P.S. specimens was substantially lower than that of the other types. The mercury porosimetry data is consistent with the above results. I t can be seen from Figure 3 that the three materials cured at room temperature had very similar pore size distributions in the range studied. However, the steam cured specimens had a much greater fraction of their total porosity in pores with a diameter above 0.013 lUm. Critical Stress Intensity Factors, KIC The values of KIC determined by both the notched beam and the double torsion method are given in Table I l l .

The double torsion measurement was

always made on a sharp crack, i . e . , one that had been extended from a machined notch.

No attempt was made to produce sharp cracks in the notched

beam specimens. Thus, the difference between the two methods reflects the greater d i f f i c u l t y of starting a crack from the t i p of a machined notch. I t i s , therefore, significant that there was no difference between the two

960

Vol. 4, No. S. Mindess, ~..~ S. Nadeau, J. M. Hay D:PORE DIAMETER (~ICRONS) io

o ~

3 4

o 2

~

34

~"

O2

3,

~C ~

/ f

•

_

//

wsw

~--LmS

/

"

FIG. 3

l

Pore volume d i s t r i b u t i o n s by mercury porosimetry.

C.} OlO~ U

•

i

f

.Y

o oOE

006

0O2

OOC, ~OO

I,O00 P=ABSOLUTE

IO,OOO PRESSURE,PSI

TABLE Ill Fracture. Toughness,

KIC,

(MNm-3/2) Notched Beam

Double Torsi on

R.T.

O. 46

0.36

F.W.S.W.

0.48

0.35

S.W.

0.48

0.33

L.P.S.

0.37

0.31

H.P.S.

0.33

0.37 0.31

Dry

for the steam cured samples. V-K I Plots Typical load relaxation curves are shown in Figure 4.

The highest

velocity observable is determined by the a b i l i t y of the recorder to follow the load drop. The lowest velocity is determined by the uncertainty in the background relaxation of the loading system.

Lower v e l o c i t i e s can be ob-

tained by deadweight loading and visual observation of the crack position but such data were not obtained in the present experiments.

Vol. 4, No. 6

961 CURING, CRACK PROPAGATION, CEMENT PASTE

3E

u~ "~

32 RT

FIG. 4

O

Typical load-relaxation curve ~ 28 for cement specimens.

HP.S

J (bockgroundl

R T

24

20

-E

' -,'o

'

6

;

~

'

~o

TIME

,go

,40

'

200

240

(sec)

The V-K I plots shown in Figure 5 represent approximately the mean values for each material.

Slopes and intercepts were obtained for the

straight portions of the curves by least squares analysis and the mean values of these parameters are l i s t e d in Table IV.

The uncertainties

and position are large and considerable additional determine the s t a t i s t i c a l

testing will

in slope

be needed to

significance of the differences between the mat-

erials. The curvature at the top of the V-K I plots suggests a second stage like that in soda-lime glass. Discussion Strength and Fracture Toughness The fracture toughness of cement paste increases with decreasing water-cement r a t i o .

Previous tests (6) on fresh water cured pastes having

10-2

FIG. 5 V-K I plots for cement specimens. KIC values (broken lines) are from the same specimens as the curves.

~ 10-4 E ~

I0"s

I~RT 2 ~ FWSW 3--~- SW 4~-LP$ 5~- Hps 6 ---~- DRY

fi1'T f

1

•

tu i0-~

~3 L ,~ 12

i0 "~

2,

Kz( IOSNm "3/2 }

4

962

Vol. 4, No. 6 S. Mindess, J. S. Nadeau, J. M. Hay

TABLE IV

Slopes and Intercepts of V-K I Plots shown in Figure 5. Cement Type

Slope (Mean)

Log A (Mean)

No. of Specimens

R.T.

76.2

-415.8

4

F.W.S.W.

74.9

-409.7

3

S.W.

76.9

-417.3

3

L.P.S.

69.4

-378.1

3

H.P.S.

45.7

-250.5

2

Dry

64.1

-354

1

a W/C = 0.5 yielded a KIC of 0.29 MNm-3/2.

The fresh water cured paste in

the present experiments having a W/C : 0.4 has a KIC of 0.36 MNm-3/2. The r e l a t i o n between fracture toughness, strength, and flaw size is given by; KIC

=

Y~f A½

(4)

where ~f is in the fracture stress (modulus of rupture) and Y is a geometrical parameter depending upon the loading system and the r a t i o of flaw size to section size.

For specimens containing small flaws, i . e . ,

(flaw size / section size)

<

I00, the value of Y is about 2.0.

where The solu-

tion to Eq. (4) for fresh-water cured paste is A = 0.165 mm. and for H.P.S. paste is

A = 0.35 mm.

Thus, the strength determining flaw size appears to

be twice as large f o r the steam cured material as for the water cured material.

There appears to be no r e l a t i o n between this " G r i f f i t h

the pore structure revealed by mercury porosimetry. will

be needed to i d e n t i f y the fracture i n i t i a t i n g

flaw" and

Fractographic studies flaws.

V-K I Plots and Delayed Failure The V-K I plots shown in Figure 4 affirm the fact that s u b c r i t i c a l crack growth occurs

in cement paste.

The degree of s u s c e p t i b i l i t y of a

p a r t i c u l a r paste depends upon the position and slope of the V-K I plot.

An

approximate expression for the time to f a i l u r e under a constant applied stress ~ a i s ; T

=

K2-n /(n_2)y2 ~2 A li a

(5)

Vol. 4, No. 6

963 CURING, CRACKPROPAGATION, CEMENTPASTE

where Kli is the i n i t i a l stress intensity.

The relative susceptibility of

two materials to static fatigue can be compared by computing their l i f e expectancies from Eq. (5) assuming identical i n i t i a l conditions.

The ratio of

l i f e expectancies of materials A and B is; TA/TB =

K (n i i B-n A )

[(n A - 2) AA/ (nB - 2)AB]

(6)

In order to compare two of the curves in Figure 4 i t is only necessary to know the experimental parameters n and A, and to assume that the applied stress and Kii are the same for each material.

The assumption of

constant Kii is tantamount to assuming that the i n i t i a l flaw size is the same according to the relation; KIiA

= KIiB

= Y°a aA = Y~a aB

(7)

Thus, the two extreme curves of Figure 4, curves 5 and 6, can be compared by calculating the ratio

T6/T5 assuming Kii : 2.5 x 105Nm-3/2.

This i n i t i a l stress intensity is about 67% of the c r i t i c a l stress intensity for the H.P.S. paste and about 80% of that of the dry paste.

This calcula-

tion yields the result; T6/T5 = 4.89 X lO5 Thus, under the conditions specified, the dry paste would survive more than lO5 times longer than the water saturated paste. The r e l i a b i l i t y of the above calculation is severely limited by the uncertainties in the V-KI plots.

Before they can be used for design pur-

poses i t is necessary to obtain a very large number of plots and to ascertain their distribution.

However, for making a rough comparison between

materials, calculations based on Eq. (5) are useful.

A method similar to

the one outlined above, in which V-KI plots are compared to a standard material with a well known V-KI plot has also been proposed (15). standard material is soda-lime glass in water. IOg(TX/TW)

The

The calculation is:

= -4.086 - nx log (0.5 KIC(x)) -log(nx-2) -log Ax

(8)

where the subscript w refers to soda-lime glass in water and the subscript x to the material being indexed. Table V shows values of the parameter log (Zx/Zw) (static fatigue resistance index) for the materials in this study. The table indicates that the H.P.S. paste is considerably more sus-

964

Vol. ~, No. S. Mindess, ~!. S. Nadeau, J. M. Hay

ceptible to s t a t i c fatigue than the other cements in t h i s study.

I t also

shows that the paste previously studied (W/C = 0 . 5 ) , is s l i g h t l y more susceptible than any of the pastes with lower W/C r a t i o s .

The least susceptible

material was the dry paste tested in a i r . TABLE V Index of S t a t i c Fatigue S e n s i t i v i t y of Seven Cement Pastes Material

Index (log TX/T w)

Soda-lime glass i n H20

0

R.T.

9.032

F.W.S.W.

11.25

S.W.

9.94

L.P.S.

11.88

H.P.S.

3.97

Dry

15

W/C = O.5 (6)

8.57

Effects of Environment Because of the extreme d i f f i c u l t y dry specimen was tested.

in drying cement pastes, only one

The r e s u l t was consistent with t h a t for glass.

The dry specimen was much more r e s i s t a n t to slow crack growth than wet specimens.

Similarly,

the specimens made with a higher water-cement r a t i o ,

reported previously (6), were less r e s i s t a n t to slow crack growth than those used in t h i s study.

Thus, the r e s u l t s of t h i s study are consistent

with those of other workers described in the i n t r o d u c t i o n . Conclusion I.

High pressure steam cured cement paste is considerably more susceptible to s t a t i c f a t i g u e than the other pastes tested.

2.

Sea water cured cement is as r e s i s t a n t to s t a t i c f a t i g u e as fresh water cured cements.

3.

Changing the W/C r a t i o from 0.5 to 0.4 improves the resistance to static fatigue.

4.

Slow crack growth in cement paste is enhanced by the presence of water.

Vol. 4, No. 6

965 CURING, CRACK PROPAGATION, CEMENT PASTE Acknowledgements

The authors wish to thank Professor O.J. Whittemore and Kunio Aihara of the University of Washington, Seattle, for the mercury porosimetry r e s u l t s .

Some of the work was supported by grants from the National

Research Council of Canada. References T.C. Hansen, Causes, Mechanism, and Control of Cracking in Concrete, American Concrete I n s t i t u t e Publication SP-20, pp. 43-66, D e t r o i t , 1968.

.

.

F.H. Wittman and Ju. Zaitsev, Mechanical Behavior of Materials, Vol. IV, pp. 84-95, The Society of Materials Science, Japan, 1972.

.

A. Husak, Static Fatigue of Portland Cement Concrete, Doctoral Diss e r t a t i o n , Carnegie-Melon University, 1969.

.

S.P. Shah and S. Chandra, Journal, American Concrete I n s t i t u t e , 67110] 816 (1970).

.

J. Barrick, The Effects of Temperature and Relative Humidity on Static Fatigue of Hydrated Portland Cement Concrete. Doctoral Dissertation, Carnegie-Mellon University, 1972.

.

J.S. Nadeau, S. Mindess and J.M. Hay, J. Amer. Ceram. Soc., 50[2] 51 (1974).

7. .

.

S.M. Wiederhorn, J. Amer. Ceram. Soc., 5(][8] 407

(1967).

S.M. Wiederhorn and L.H. Bolz, J. Amer. Ceram. Soc., 53110] 543 (1970). A.G. Evans, Journal of Materials Science, ~,

1137

(1972).

I0.

A.G. Evans and S.M. Wiederhorn, NBSIR, 73-147

II.

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12.

D.P. Williams and A.G. Evans, Journal of Testing and Evaluation, 1 [4] 264 (1973).

13.

W.F. Brown, Jr., and J.E. Srawley, STP 410, pp. 30-81, American Society for Testing and Materials, Philadelphia, 1966.

14.

R.A. Helmuth and D.A. Turk, Highway Research Board, Special Report 9(], pp. 135-44, 1966.

15.

J.S. Nadeau and J.M. Hay, submitted to Journal of the Canadian Ceramic Society.

(1973).