Significance of microhardness of porous inorganic materials

CEMENT and CONCRETERESEARCH. Vol. 2, pp. 717-729, 1972. Pergamon Press, Inc. Printed in the United States.

SIGNIFICANCE

OF

MICROHARDNESS

INORGANIC

OF

POROUS

MATERIALS

P.J. S e r e d a Division of Building Research, National R e s e a r c h Council of Canada, Ottawa, C a n a d a

(Communicated by R. E. Philleo)

ABSTRACT M i c r o h a r d n e s s w a s m e a s u r e d of porous and nonporous s a m p l e s of halite and selenite and it has b e e n s h o w n that the relationship between m i c r o h a r d n e s s and porosity m a y be e x p r e s s e d by the e m perical relation H = H e-bP. T h e significance of the m i c r o h a r d o hess m e a s u r e m e n t s as applied to porous materials is discussed f r o m the standpoint of the disturbed zone of crystals or micro-units, including the p r o b l e m of " w o r k hardening" w h e n p o w d e r e d s a m p l e s are compacted. T h e effect of m o r p h o l o g y on m i c r o h a r d n e s s is also discussed with regard to a series of g y p s u m samples. R e f e r e n c e is m a d e to the effect of humidity on m i c r o h a r d n e s s of porous glass and the conclusion d r a w n that the m i c r o m e c h a n i c s of failure in m i c r o h a r d n e s s are similar to flexure strength. SOMMAIRE O n a m e s u r 4 la m i c r o d u r e t 4 d'4chantillons p o r e u x et non p o r e u x d'halite et de s414nite et on a observe que la relation entre la m i c r o d u r e t 4 et la porosit4 peut %ire repr4sent4e par la relation empirique H = Hoe-bP. L'auteur 4tudie l'importance des m e s u r e s de m i c r o d u r e t 4 appliqu6es aux m a t 4 r i a u x poreux, du point de rue de la zone troubl4e de cristaux et de m i c r o - 4 1 4 m e n t s , y c o m pris le p r o b l ~ m e de "l'4crouissage" lorsque les 4chantillons pulv4ris4s sont compact4s. L'auteur 4tudie 4 g a l e m e n t l'effet de la m o r p h o l o g i e sur la microduret4, pour ce qui regarde une serie d'~chantillons de gypse. II m e n t i o n n e l'effet de l'humidit4 sur la m i c r o d u r e t 4 du verre p o r e u x et conclut que la m i c r o m 4 c a n i q u e de ruine dans la m i c r o d u r e t 4 est semblable ~ la force de flexion.

717

718

Vol. 2, No. 6 MICROHARDNESS, POROSITY, MATERIALS Introduction Indentation

hardness

has been used as a measure

metals

(1), a n d a s a m e a s u r e

(2, 3).

It has been shown that microhardness

as load per unit area has satisfied property

of t h e s t r e n g t h

is e q u a l to t h r e e

of m e t a l s

times

of m i c r o h a r d n e s s

was begunin

Research

C o u n c i l of C a n a d a ,

of p a p e r s

involving gypsumplaster paper

presents

discussion

and its limitations.

of i t s m e r i t s

developed

although it is similar

to i n o r g a n i c

results

portland

porous

cement.

work re-

materials

and a

It will not deal with the cone

by Rehbinder

to t h e m i c r o h a r d n e s s

will be dealt with in a separate

National

of t h e d e v e l o p m e n t

to i n o r g a n i c

porous

(4, 5, 6) r e p o r t

and hydrated

a summary

of t h i s t e c h n i q u e

technique

mechanical

or micro-areas.

measurements

l a t i n g to t h e a p p l i c a t i o n

penetration

T h i s , in p a r t ,

t e s t of a n i m p o r t a n t

and a number

rocks

expressed

1966 a t t h e D i v i s i o n of B u i l d i n g R e s e a r c h ,

of s u c h m e a s u r e m e n t s The present

and rocks

layers

of

crystalline

the yield strength.

a n d o n e t h a t c a n b e a p p l i e d to s u r f a c e

materials

subject

of n o n p o r o u s ,

the need for a non-destructive

The application

of s t r e n g t h

and his co-workers

technique

in s o m e

in U S S R ,

respects.

This

publication.

Experimental Materials Natural Fitzroy

selenite

Harbour,

Ontario

tained as a core from Saskatchewan

single crystals

Power

H.M.

a Saskatchewan Commission);

obtained as commercial samples

(courtesy

products

showed impurities

were

obtained from

Woodrooffe);

salt deposit

pottery

plaster

(courtesyU.S.

Kingdon Mine,

natural

(courtesy

R.

halite was obHanson,

and a hemihydrates Gypsum).

Analyses

were of

below 0.01%.

Equipment Both Tukon and Leitz microhardness and both Knoop and Vickers indenters

gave similar

To measure material almost

values

For the samples

under

of t h e i n d e n t a t i o n

of a s a m p l e

to m o d i f y t h e l i g h t i n g s o t h a t a b e a m

to t h e i n d e n t e d

were

used,

study both

of m i c r o h a r d n e s s .

the diagonal

it was necessary parallel

indenters.

testing machines

surface

and highlighted

of a p o r o u s of l i g h t p a s s e d

the boundary

of t h e i n -

Vol. 2, No. 6

719 MICROHARDNESS, POROSITY, MATERIALS

dentation.

T h e diagonal w a s m e a s u r e d

vided with the m i c r o h a r d n e s s Microhardness to 5 0 %

RH

by m e a n s

of the optical s y s t e m pro-

instruments.

measurements

were made

in either a r o o m

conditioned

or a gloved box w h e r e relative humidity w a s maintained at dif-

ferent levels.

Compacts

of p o w d e r e d

s a m p l e s w e r e p r e p a r e d by the technique

of dry c o m p a c t i o n in a steel m o l d (4) . E x a m i n a t i o n of m i c r o s t r u c t u r e the apex of an indentation w a s m a d e

with S E M

under

( C a m b r i d g e Stereoscan) on a

fractured surface. What Does Microhardness Measure? T h e question of w h a t m i c r o h a r d n e s s

measures

fully with regard to n o n p o r o u s materials (i, 7, 8). technique of testing by A S T M

Committee

has been discussed

A review in 1966 of this

E-4, Subsection

V, led to the con-

clusion that h a r d n e s s is still relatively undefined and little understood.

It is

valid to ask the basic question with regard to the application of the technique to porous materials such as hydrated c e m e n t and g y p s u m

plaster.

F o r n o n p o r o u s materials it has been s h o w n that m i c r o h a r d n e s s

is in-

dependent of load (7, 9). A similar conclusion w a s reached for porous m a terials b a s e d on m e a s u r e m e n t s

of c o m p a c t e d

salt.

A twenty-fold variation

in load did not p r o d u c e a variation in the values of rnicrohardness b e y o n d the normal

scatter within the a c c u r a c y limits of the m e a s u r e m e n t . P o r o u s materials tend to have a heterogeneous microstructure in-

volving a wide range of particle sizes and pore sizes. measurement reason,

If m i c r o h a r d n e s s

is to be representative of the bulk material it must,

include a statistically significant n u m b e r

for this

of particles and pores.

F o r n o n p o r o u s materials Atkins et al (8) concluded that the d e f o r m e d zone r e s e m b l e s

radial c o m p r e s s i o n

approximately a hemisphere

and practically unaffected by the detailed shape

of the indentation itself. A s s u m i n g porous systems,

and that the elastic/plastic b o u n d a r y is

that this conclusion is applicable to the

the depth to which the microstructure is disturbed at the

apex of the indentation should be the radius of the h e m i s p h e r e ed zone (Fig.

la).

of the d e f o r m -

720

Vol. 2, No. 6 MICROHARDNESS, POROSITY, MATERIALS 400~m ,

v'iCKER

1 \

l

nD

/

/

,\ oo \

\

A.3.o ~e --~--

FIG. Microhardness

indentation

(2)

(1) M i c r o g r a p h of undisturbed microstructur e outside deformed zone.

la and

Micrograph of d i s t u r b e d microstructure in d e f o r m e d

lb

of g y p s u m p l a s t e r b e l o w SEM micrographs of V i c k e r ' s m i c r o h a r d n e s s indent sample

zone

zone.

FIG.

A cast gypsum

deformed

of 52% p o r o s i t y

v e a l e d t h a t t h i s d e p t h of d i s t o r t i o n

and fracture

the apex

examined by SEM has reof t h e c r y s t a l s

under the

a p e x of a n i n d e n t a t i o n is r o u g h l y e q u i v a l e n t to t h e l e n g t h of t h e d i a g o n a l of the indentation using the Vickers t u r e of t h e d e f o r m e d From

and undeformed

these observations

4 0 0 ~ m ( d i a g o n a l of V i c k e r s is c o n t a i n e d b y a h e m i s p h e r e sample

it w a s e s t i m a t e d

total number

indenter.

of c r y s t a l s

Figure

1 b shows the microstruc-

zones.

it m a y b e c o n c l u d e d t h a t a n i n d e n t a t i o n

indentation),

the volume

of t h e d e f o r m e d

of r a d i u s 4 0 0 ~ m o r 134 x 106 ~ m 3.

t h a t t h e r e is a b o u t 0 . 0 1 8 c r y s t a l / ~ m

3,

of

zone,

For this

so that the

a f f e c t e d is a b o u t 2 . 4 m i l l i o n f o r t h e o n e t e s t .

In cement paste most

of t h e m i c r o - u n i t s

or crystals

are much smaller

Vol. 2, No. 6

721 MICROHARDNESS, POROSITY, MATERIALS

t h a n t h o s e in t h e g y p s u m applicable

to t h e h y d r a t e d

microhardness number

sample.

in t h e c e m e n t

pyramidal

system,

would,

TT t h e s e

observations

then an indentation

for the same

porosity,

are

produced

by

involve a larger

and should be valid as representing

a statistically

by any direct

observations

system.

material

barrel-shaped

above.

This cannot be easily verified

According porous

analysed

cement

measurement

of m i c r o - u n i t s

significant

cause

sample

to K i n g a n d T a b o r

(9) m i c r o h a r d n e s s

produces

a plastic

deformation

indentation

resulting

from

faces.

This piling-up

the displaced

material

indentation

of a p o r o u s

of b r e a k i n g

of b o n d s b e t w e e n

companied

by densification,

decreases

this process

a piling-up

is not observed

must

particles as occurs

must

involve,

at the centre

with a porous

materialbeThus the

w h o l l y o r in p a r t ,

in c o m p a c t i o n

the process

of p a r t i c l e s

of p o w d e r s .

replaced

as a

of t h e

in t h e p o r e s .

as well as fracturing

be proportionately

on a n o n -

that can be observed

can be accommodated

material

indentation

ac-

As porosity

b y o n e of p l a s t i c

deformation. Indirect relative

evidence

humidity

hardness on Y o u n g ' s

from

changes

(to b e d i s c u s s e d

of a p o r o u s

material

in m i c r o h a r d n e s s

in a l a t e r

with changes

section) indicates

is representative

that micro-

of i t s f l e x u r e

strength.

modulus

and hardness

of h y d r a t e d

have been combined

and replotted

in F i g . 2 to s h o w t h e r e l a t i o n

these measurements. lated for similar

The results

samples

but their

suggest

in

Data

cement, Soroka and Sereda between

that these properties

significance

(6),

is not apparent

are reat present.

80 60 ~E 40 ~E o ' 30

FIG.

i

---

DATA

•

o COMPACTS ~,, • C O M P A C T E D PASTE • o PASTE objs~ .

~. ~o q

Relation between hardness and Young's modulus for hydrated cement paste and compacts.

d --

~

s

~

6

og/

/ I

I

[

I

I

4

6

8

10

15

E X ]O - 4 ,

KG PER SQ CM

I 3O

722

Vol. 2, No. 6 MICROHARDNESS, POROSITY, MATERIALS

Effect of Porosity Strength and Young's modulus of various materials have been related to their porosity by an empirical relation (i0-14).

A similar empirical re-

lation has been found for microhardness and porosity of compacts of a n u m ber of crystalline powdered materials as well as hydrated g y p s u m and hydrated

cement

(4, 6).

H = H e -bp

(1)

0

where H and H° are the microhardness p l e s of a g i v e n m a t e r i a l , b = an empirical p = sample The basic

constant,

was carried

Microhardness

measured

of t h e K n o o p i n d e n t e r .

values

respectively,

out using large

of t h e s i n g l e c r y s t a l s

of 2 0 . 4 t o 2 2 . 8 ,

published

by King and Tabor

faces

particular measure

by Kurichina

of t h e s e l e n i t e

and depended

orientation

because

a n d a v a l u e of 17 t o 18,

faces

of t h e t e n d e n c y single crystals

relative

The values

increased

varied

greatly

on At a

it was not possible

of t h e c r y s t a l

was also very

considerably

to

to c l e a v e . sensitive

to

when the relative

hu-

c o n d i t i o n w a s c h a n g e d f r o m 50 to 0%. A number

pestle

well with

of t h e K n o o p i n d e n t e r .

on certain

of s e l e n i t e

midity

of h a l i t e w a s

reasonably

single crystal

The microhardness humidity.

(15),

on t h e o r i e n t a t i o n

of t h e i n d e n t e r

microhardness

of

(9).

The microhardness different

single crystals

A value for Knoop Hardness

( K H N ) of 1 9 . 5 k g / m m 2 w a s o b t a i n e d t h a t a g r e e s

reported

sam-

and

halite and selenite.

Number

and nonporous

porosity.

correlation

by means

of t h e p o r o u s

to pass

ent pressures

of t h e s e

the 200-mesh

single crystals sieve;

i n a m o l d to f o r m

and about 1.3 mm

termined

using the Knoop indenter.

50% r e l a t i v e age values

humidity.

the powder

compacts

diameter

thick.

Ten values

used to plot the logarithm

were

crushed

in a m o r t a r

was then compacted

of v a r y i n g

Microhardness

porosity

along the diameter of m i c r o h a r d n e s s

were made were

at differ-

3.17 cm in

of e a c h c o m p a c t

All measurements

and

was dein a i r a t

taken and aver-

vs porosity.

Figure

723

Vol. 2, No. 6 MICROHARDNESS, POROSITY, ~IATERIALS i00 ~

,

)

,

80 F ~_~

vs

porosity

"\

I io

,

L ,zo

POROSITY.

3 shows the straight-line value for the constant, Effect

relation

confirming

the validity

~

, 3o

PER CENT

of e q u a t i o n

(1).

The

b, w a s f o u n d t o b e 6 . 3 f o r h a l i t e a n d 9, 3 f o r s e l e n i t e .

of C o m p a c t i o n Nonporous

crystal. size,

)

} ~

3

Microhardness of c o m p a c t s .

'

o SELENITE • HALITE m3HALITE (ANNEALED)

601%.

FIG.

I

compacted

This can be attributed

both effects produced

observed

work hardening

with the resulting

of 0 . 5 % ,

Similar

were

a rate

results

of v a r i o u s

by compaction

brought

porosities

were

annealed

The results

t h e e f f e c t of s t r a i n

for which the normal work where

obtained normal when the series

upon microhardness

Brace

of a s i n g l e c r y s t a l ,

values

compacts of h a r d n e s s .

of h a l i t e c o m -

King and Tabor

of a n o n p o r o u s

of 27 k g / m m 2 f o r a h i g h l y s t r a i n e d

100, 000 p s i a n d t h e m i c r o h a r d n e s s

was stressed

(3)

to 6 0 0 ° C a n d c o o l i n g a t

a r e s h o w n on F i g . 3.

a single crystal

compact

rubbing

by heating

of g r a i n

temperature.

He also produced

v a l u e w a s f o u n d to b e 1 7 . 2 .

For a nonporous

and reduction

at normal

about by surface

and by annealing

salt when they obtained a value

present

to " w o r k h a r d e n i n g "

obtained at DBR/NRC

of 0 . 6 ° C / m i n .

demonstrated

than twice as hard as the single

d o u b l i n g of m i c r o h a r d n e s s .

having porosity

pacts

halite is more

This is confirmed in a c o m p a c t i o n

(9)

rock

specimen in t h e m o l d to

doubled. of s e l e n i t e

the extrapolated

(Ho) m i c r o h a r d -

724

Vol. 2, No. 6 MICROHARDNESS, POROSITY, MATERIALS

ness has a single value that cannot be c o m p a r e d to the range of values obtained for a single crystal.

T h e hardening effect is even m o r e

dramatic in

this case than in halite because the hardness of the single crystal at a particular orientation of the d i a m o n d point is so low that it cannot be m e a s u r e d . In the compact,

the direction of easy fracture disappears b e c a u s e of the

small size of grains and their r a n d o m orientation; the c o m p a c t s by heating.

it is not possible to anneal

It w a s thought the exposure to high humidity would

relieve stress, but this did not happen.

In fact, exposure to humidities of

5 0 % for a period of 10 days caused a considerable increase in microhardness, due possibly to aging (recrystallization),

and resulted in strengthening at

points of contact b e t w e e n crystals. Previous w o r k by Soroka and Sereda (6) has s h o w n that in hydrated c e m e n t the relation of hardness to porosity is the s a m e for c e m e n t paste as for c o m p a c t s of bottle hydrated cement. does not occur in this system,

It is apparent that " w o r k hardening"

possibly owing to the fact that the material is

poorly crystallized and in part a m o r p h o u s . Effect of M o r p h o l o g y Ridge and Surkevicius (16) have s h o w n that different crystal habits of g y p s u m can be obtained by the use of certain admixtures that retard or accelerate set of the hemihydrate.

It w a s of interest to test whether these

changes in habit would be detected as changes in m i c r o h a r d n e s s . T h r e e modifications of the g y p s u m crystals w e r e obtained by hydrating pottery plaster in a rotating polyethylene bottle at a g / w ratio of l: I0, with admixtures of calcium acetate 0.7%,gelatin 0 . 5 % and without admixture. T h e t e m p e r a t u r e w a s controlled at 77°F. RH

T h e crystals w e r e dried at 3 0 %

and c o m p a c t e d at different pressures to provide a range of porosity. T h e s e c o m p a c t s w e r e m e a s u r e d for m i c r o h a r d n e s s and the results

are plotted on Fig. 4 with results for c o m p a c t s of selenite.

T h e results

s h o w clearly that m i c r o h a r d n e s s vs porosity curves are distinct for each preparation, but the significance of this finding is not yet evident.

It is antiei

pated that the crystal habit giving the highest m i c r o h a r d n e s s curve represents the material that will f o r m the strongest s y s t e m at a given porosity.

Vol. 2, No. 6

725 MICROHARDNESS, POROSITY, MATERIALS

100

T

'

100

1

'

80 ° SELENITE (b=9.31 • pptd GYPSUM Ib=l.3) OGYPSUM WITH Ca ACETATE IGYPSUM WITH GELATINE

80

60

oPOTTERY PLA_
\

40

\

2O

o -

EMI HY D R A T [ ' ~ o

iO

z 8

6

[0

L

0

i

10

\i

i

~ o2 \ J

I

I0

POROSITY. PEte CENT

,

I

,

20 POROSITY PER CENT

I

30

FIG. 5

FIG. 4

Microhardness vs porosity c o m p a c t s of h e m i h y d r a t e s .

Microhardness vs porosity for compacts of d i f f e r e n t s a m p l e s

of

of gypsum. Again,

this is not certain,

i n v i e w of t h e p o s s i b i l i t y

of w o r k h a r d e n i n g

d u e to

c ompac tion. As an example

of a v e r y g r e a t c h a n g e in m i c r o h a r d n e s s

changes

in m o r p h o l o g y ,

Fig.

samples

of h e m i h y d r a t e

compacts.

pottery

plaster

and B-Base.

shown by Holdridge Base

(17),

relation

the results

of m i c r o h a r d n e s s

The two samples

According

is mostly

of t w o

8 modification material

and Bconsti-

data do not yield a semi-logarithmic

with porosity.

Effect of humidity Evidence polar species

has been presented

can have a considerable

larly on indentation creep.

(18, 19) t h a t a d s o r b e d

water and other

effect upon microhardness,

In the w o r k n o w p r e s e n t e d ,

as

using the method

It s h o u l d b e n o t e d t h a t t h e B - B a s e to date where

from

have been identified

to D T A a n a l y s e s ,

the pottery plaster

i s c~ m o d i f i c a t i o n .

tutes the only exception

5 shows

resulting

particu-

involving inorganic

726

Vol.

2 , No. 6

MICROHARDNESS, POROSITY, MATERIALS non-metallic materials, it is a significant factor with respect to the value of hardness and as an aging factor in certain porous materials.

B e c a u s e of the

latter it is often difficult to separate the effect of humidity on m i c r o h a r d n e s s because, in conditioning, the s a m p l e undergoes aging.

Comparison

of m i c r o -

hardness values at different humidities is therefore not valid for certain m a terials. F e l d m a n and Sereda (20) have reported the effect of different h u m i d ities on m i c r o h a r d n e s s of porous glass (see Fig. 6).

T h e effects of humidity

on m i c r o h a r d n e s s of porous glass and on flexure strength of portland c e m e n t paste s h o w the s a m e characteristics, suggesting that m i c r o h a r d n e s s is representative of the flexure strength of a porous material.

Additional data are

required to confirm or reject this apparent relation. In s o m e nonporous materials it appears that humidity can have a large effect on m i c r o h a r d n e s s .

Alarge

for m i c r o h a r d n e s s at 0 and 5 0 % R H

single crystal of selenite w a s tested

conditions.

The Knoop microhardness

values obtained on the 010 cleaved face ranged f r o m 13.5 to 31.5 k g / m m

2

for 0 % IZH (depending on the orientation of the indenter) and f r o m 8. i to 9.5 kg/mm

2 for 50°70 condition. 1 .oj~

I

I

I

I

1

- - O ' ~ O - - P O RO U S 0.9

I

I

GLASS

I

I

~

.o

f-30 -- 0 . 9

':,,\T

.

I \',i'-

-F- 0 . 7

LICA

I

.

.

.

----

PORTLAND CEMENT PAS,E
USEO OUART

•

t

--0,7

06

0. 6 --

0. 5 --

--

I

I

I

I

I

I

I

10

20

30

40

50

60

70

RELATIVE

HUMIDITY,

PER

I

I

80

90

CENT

FIG. 6 Effect of humidity on m i c r o h a r d n e s s

and strength

100

.5

~A-

Vol. 2, No. 6

727 MICROHARDNESS, POROSITY, MATERIALS Summary

i.

and Conclusions

It appears that sufficient w o r k has been carried out to support the

conclusion that m i c r o h a r d n e s s m e a s u r e m e n t s

of porous materials provide

meaningful information about m e c h a n i c a l behaviour and that these m e a s u r e m e n t s are as significant for porous materials as they are for nonporous materials.

It is clear that differences in porosity and m o r p h o l o g y of the

s a m p l e can be readily observed. 2.

Microhardness measurements

of porous materials appear to yield the

s a m e characteristic curve as flexure strength w h e n it is related to humidity, indicating that the m i c r o - m e c h a n i c s 3.

of failure are similar in both cases.

A relation exists b e t w e e n m i c r o h a r d n e s s and m o d u l u s of elasticity for

c e m e n t paste.

Similarly, there is a relation b e t w e e n compacting p r e s s u r e

and m i c r o h a r d n e s s w h e n dealing with c o m p a c t s of p o w d e r e d materials. Work

should be done to d e t e r m i n e whether a relation exists b e t w e e n c o m -

pressive strength and m i c r o h a r d n e s s . 4.

Microhardness measurement

is a nondestructive test of m e c h a n i c a l

behaviour and as such offers a useful tool for studying the effect of various microstructural changes in a material with changes in conditions of exposure It is believed that indentation creep m e a s u r e m e n t

can provide information on

creep behaviour of materials.

Acknowledgements T h e crystals of selenite w e r e f r o m the K i n g d o n Mine, Harbour,

Ontario, and w e r e obtained by M r .

H.M.

M i n e r a l Processing Division, D e p a r t m e n t of Mines,

Fitzroy

Woodrooffe,

Chief,

E n e r g y and Resources;

the halite s a m p l e w a s obtained f r o m a core taken f r o m a S a s k a t c h e w a n salt deposit, obtained through the courtesy of M r . Power

Corp.

R. Hanson,

Saskatchewan

T h e author is grateful for these s a m p l e s without which the

w o r k could not have been done. T h e author also wishes to a c k n o w l e d g e the contribution of M e s s r s . D . E . Kennedy, mental work.

E.G.

Quinn and N. D a r b y for assisting with the experi-

728

Vol. 2, No. 6 MICROHARDNESS, POROSITY, MATERIALS This paper is a contribution f r o m the Division of Building Research,

National Research Council of Canada,

and is published with the approval of

the Director of the Division. References Clarendon P r e s s

I.

D. Tabor,

2.

H. Winchell, A m e r .

3.

W.F.

4.

5. Soroka and P.J. Sereda, J. A m e r .

5.

D. Chandra, P.J. Sereda, and E.G. Swenson, (64) 131-136 (1968).

.

The hardness of metals. Oxford,

Brace,

Mineral. 30, 583-595

3. Geophys.

Res. ~

(1951).

(1945).

(6)1773-1788 (1960). C e r a m . Soc. 51(6) 337-340 (1968). Mag.

Concr. Res. 2___0

5. Soroka and P.J. Sereda, Proc. Fifth 5nt. Syrnp. C h e m . Part Ill, VollII, 67-73 (1968).

Cem.

Tokyo,

7.

B . W . Mort, Micro-indentation hardness, Publications, London (1956).

Butterworth Scientific

8.

A . G . A t k i n s, A. Silverio and D. Tabor, J. 5nst. Metals 94__, 369-378

(1966). 9.

R.F. King, and D. T a b o r ,

P r o c . R o y . Soc. L o n d o n , Sec. A223,

225-238 (1954). I0.

W. D u c k w o r th, J. A m e r .

11.

F.P.

K n u d s e n , 3. A m e r .

C e r a m . Soc. 4 2 ( 8 ) 3 7 6 - 3 8 7

12.

R.M.

Spriggs, J. A m e r .

Ceram.

13.

F.P. Knudsen,

14.

R . B . Martin and R . R .

J. A m e r .

Ceram.

Soc. 36.__,(2) 68 (1953). (1959).

Soc. 44 (12)628-629 (1961).

C e r a m . Soc. 45 ( 2 ) 9 4 - 9 5 (1962).

Haynes,

J. A m e r . C e r a m . Soc. 54 ( 8 ) 4 1 0

(1971). 15.

A.D. Kurichina,

16.

M . J . Ridge and H. Surkevicius, (1960).

17.

D.A.

Holdridge,

Trans. Brit. C e r a m .

Soc. 64 (4)211-231 (1965).

18.

J.H. Westbrook,

and P.J. Jorgensen,

Amer.

{1968).

Zavodskaia Laboratoria,

M o s c o w 16 (4) 5 0 4 - 5 0 6 (1950)

A u s t . J. Appl. Sci. II, (3) 385-398

Mineral. 53, 1899-1909

Vol. 2, No. 6

729 MICROHARDNESS, POROSITY, MATERIALS

19.

R.E. Hannemar~ and J.H. Westbrook, Phil. Mag. 18 (151) 89-99 (19681

20.

R.F. Feldman and P.J. Sereda, Engrg. J. 53, 53-59 (1970).

21.

P.J. Sereda, R.F. Feldman and E.G. Swenson, High. Res. Bd. Special Report 90, 58-73 (1966).

22.

H. LeRoux, Proc. Roy. Soc. London, Sect. A, 289, 390-401 (1965).