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Publisher’s version / Version de l'éditeur:

Scripta Metallurgica, 17, pp. 1269-1273, 1983

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Does the strength of ice depend on grain size at high temperatures?

Sinha, N. K.

https://publications-cnrc.canada.ca/fra/droits

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National Research

Conseil national

$

Council Canada

de recherche Canada

DOES THE STRENGTH OF ICE DEPEND ON GRAIN SIZE AT

HIGH TEMPERATURES?

by

N.K. Sinha

ANALYZED

Reprinted from

Scripta Metallurgica,

Vol. 17,1983

p. 1269

-

1273

DBR

Paper No. 1166

Division of Building Research

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Des mesures d e l a r e s i s t a n c e d e l a g l a c e

Q

l a t r a c t i o n s o n t analys'ees d e nouveau a f i n d ' i l l u s t r e r que l e s p r e m i e r s r e s u l t a t s d e s e s s a i s ne r e v g l a i e n t p a s l ' i n f l u e n c e r h l l e d e l a g r a n u l o d t r i e . On montre q u e l a forme i n p r o p r e du sp'ecimen, l a d i f f l c u l t ' e que pose l e c o n t r a l e du t a u x d e d'eformation e t du t a u x de c o n t r a i n t e pendant les e s s a i s a i n s i que l a prBsence d'un grand nombre d ' i n c l u s i o n s dans l e mat'eriau o n t lnfluenc'e l e s r i 5 s u l t a t s .

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S c r i p t a METALLURGICA V o l . 1 7 , p p . 1 2 6 9 - 1 2 7 3 , 1 9 8 3 P r i n t e d i n t h e U.S.A.

Pergamon P r e s s L t d . A l l r i g h t s r e s e r v e d

DOES THE STRENGTH OF ICE DEPEND ON GRAIN SIZE AT HIGH TEMPERATURES?

N.K. Sinha

Division of Building Research, National Research Council Canada, Ottawa, Canada, KIA OR6 ( R e c e i v e d F e b r u a r y 1 6 , 1 9 8 3 )

( R e v i s e d S e p t e m b e r 8 , 1 9 8 3 ) I n t r o d u c t i o n

C u r r i e r and Schulson [ l ] confirmed a n e a r l i e r p r o p o s a l of Michel and Drouin

[z,

3 1 t h a t t e n s i l e s t r e n g t h , o f , of p o l y c r y s t a l l i n e i c e d e c r e a s e s w i t h i n c r e a s i n g g r a i n s i z e , d , a c c o r d i n g t o t h e Hall-Petch r e l a t i o n . A l l t h e measurements were made a t a h i g h homologous temperature of 0.96 Tm (-10°C), where Tm is t h e m e l t i n g p o i n t i n Kelvin. C u r r i e r and Schulson, however, r e p o r t e d a n i n c r e a s e i n t e n s i l e s t r e n g t h of about 50 p e r c e n t f o r a d e c r e a s e i n g r a i n s i z e from 7.3 t o 1 mm, whereas Michel and Drouin r e p o r t e d one of about 300 p e r c e n t f o r t h e same range of g r a i n s i z e s . Muguruma t o o h a s proposed a Hall-Petch t y p e of r e l a t i o n f o r t h e upper y i e l d s t r e s s of i c e under compression [ 4 ] , but Jones and Chew [ 5 ] found t h a t g r a i n s i z e h a s no s i g n i f i c a n t e f f e c t on upper y i e l d s t r e s s . There i s c l e a r l y r e a s o n f o r f u r t h e r d i s c u s s i o n .

The a u t h o r s u g g e s t s t h a t t h e r e s u l t s r e p o r t e d by Muguruma [ 4 ] f o r a g r a i n s i z e range of 2 t o 6 mm a r e misleading because h i s specimens were unacceptably small (5 x 20 x 25 mm); t h a t t h e y a r e a n example of a r e a s o n a b l e conclusion drawn from d a t a of q u e s t i o n a b l e value. T h i s was a l s o t r u e of Michel and Drouin's hypothesis of a g r a i n s i z e e f f e c t based on s t r e n g t h measurements of t h r e e d i f f e r e n t t y p e s of ice: congealed f r a z i l s l u s h , S-4 i c e w i t h g r a i n s i z e of about 1.5 mm; g r a n u l a r T-1 i c e of g r a i n s i z e 2 t o 3 mm; and t r a n s v e r s e l y i s o t r o p i c S-2 i c e of g r a i n s i z e i n t h e range 5 t o 9 mm ( s e e c l a s s i f i c a t i o n s i n Ref. 6). Although t h e t y p e s of i c e d i f f e r e d

s i g n i f i c a n t l y i n average s t r e n g t h , t h e r e w a s no apparent dependence on g r a i n s i z e f o r t h e r e s u l t s f o r e i t h e r T-1 i c e o r S-2 i c e .

A l l t h e t e s t s c a r r i e d o u t by C u r r i e r and Schulson [ I ] were performed under a t r u l y

c o n s t a n t , closed-loop, c o n t r o l l e d cross-head displacement r a t e , x, o r under a nominally c o n s t a n t s t r a i n r a t e ,

in

=

;(/a,

where 11 i s t h e e f f e c t i v e specimen length. F o r t h e chosen

j, = 2.3 x 10- and 11 = 231 mm f o r t h e c y l i n d r i c a l specimens, t h e nominal s t r a i n

rate

in

was 1 x

s-q

The r e p o r t e d discrepancy of one o r d e r of magnitude b e t een nominal s t r a i n r a t e of 1 x s-I and t h e measured specimen deformation r a t e of 1 r 10

-'

8

'

(between end caps) is i n d i c a t i v e of a compliant t e s t i n g machine [ 7 ] and r a i s e s many q u e s t i o n s [8, 91.

P r i m a r i l y , how c o n s t a n t was t h e r a t e d u r i n g a g i v e n t e s t ? Were a l l t h e specimens deformed a t t h e

'/'

same r a t e ? These a r e v i t a l q u e s t i o n s . S t r e n g t h of i c e a t such a high temperature (0.96 Tm) f a 1 1

r a t e s e n s i t i v e [7

-

91. Loading c o n d i t i o n s and temperature m a t be c o n s t a n t i f t h e e f f e c t of g r a i n s i z e on s t r e n g t h i s t o be c l e a r l y defined.

Analysis

If l o a d i n g r a t e i s c o n s t a n t , a s claimed [ I ] , and f r a c t u r e s t r e n g t h , of, v a r i e s

systematically w i t h g r a i n s i z e , t h e f r a c t u r e time, t f , ehould also e x h i b i t a s y s t e m a t i c v a r i a t i o n w i t h grain s i z e , d. CurrLer's [lo) o b s e r v a t i o n s (Pig. I ) do n o t i n d i c a t e any s y s t e m a t i c p a t t e r n , s u g g e s t i n g t h a t t h e l o a d i n g c o n d i t i o n s f o r t h e a e r i e s r e p o r t e d

[ I ]

might be f a r from i d e a l . T h i a

La conflrmed i n Fig. 2 , which i l l u s t r a t e s t h e dependence of t e n s i l e s t r e n g t h on average s t r a i n r a t e t o f r a c t u r e I l l ] ,

6

e f / t f , where cf i s t h e measured a t r a i n

a t

f r a c t u r e f o r t h e t e te- c a r r i e d o u t by C u r r i e r

[ f ~ ] .

Thus t h e s p e c h e n s t r a i n

r

t e s were n o t conat n t - t 1 %

lo-'

s

',

but v a r i e d o v e r a wide range (600 p e r c e n t ) from 6 I B-' t o 3.6 r 10% a

I.

Note t h e two necked-down samples (N) e x h i b i t i n g h i g h e r s t r a i n rates. T h i s i s t o be

expected [9]. The necked-down samples had a d i a m e t e r o f 69 mm, whereas o t h e r c y l i n d r i c a l samples were 91 mm i n diameter. The two samples, w i t h about 50 per c e n t r e d u c t i o n i n c r o s s - s e c t i o n a l a r e a , were s i g n i f i c a n t l y s o f t e r t h a n o t h e r samples i n r e l a t i o n t o t h e s t i f f n e s s of t h e system. The machine could t h e r e f o r e t r a n s f e r h i g h e r deformation r a t e s t o t h e s e specimens f o r t h e same cross-head r a t e .

1 2 6 9

0 0 3 6 - 9 7 4 8 . 8 3 $ 3 . 0 0 + . O O C o p y r i g h t ( c ) 1 9 8 3 Pergamon P r e s s L t d .

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STRENGTH OF

ICE

AT

HIGH TEMPERATURES

Vol.

17,

No. 1 1

t

4

FIG. 1 0 2 4 6

*

I n t e r d e p e n d e n c e between g r a i n s i z e a n d G R A I N S I Z E . d , m m f r a c t u r e t i m e o b s e r v e d by C u r r i e r [ l o ] Hawks a n d M e l l o r [ 1 2 ] c o n d u c t e d t e n s i l e t e s t s o n d u m b b e l l s h a p e d s a m p l e s o f g r a n u l a r T-1 i c e of a v e r a g e g r a i n s i z e of 0.7 rmn a t -7'C (0.97 T,). They u s e d q u a s i - c o n s t a n t c r o s s - h e a d r a t e s a n d d i s c u s s e d t h e d e p e n d e n c e o f s t r e n g t h a s a f u n c t i o n o f

En,

m e a s u r i n g t h e d i s p l a c e m e n t b e t w e e n e n d c a p s and e s t i m a t i n g t h e s t r a i n i n t h e g a u g e s e c t i o n by u s i n g a c o r r e c t i o n f a c t o r . T h e i r t a b u l a t e d r e s u l t s a l s o showed a d i s c r e p a n c y ( a b o u t two o r d e r s o f m a g n i t u d e ) b e t w e e n

En

a n d t h e e s t i m a t e d v a l u e s . A l t h o u g h t h e y d i d n o t d i s c u s s s t r e n g t h s i n t e r m s of measured s t r a i n r a t e s , t h e i r d a t a p r o v i d e d a n e x c e l l e n t o p p o r t u n i t y t o compare t h e i r r e s u l t s w i t h r e c e n t o b s e r v a t i o n s . The d e p e n d e n c e o f of on

E f ,

t a b u l a t e d i n Ref. 1 2 , i s a l s o shown i n F i g . 2. The b a r s a t t a c h e d t o e a c h p o i n t i n d i c a t e t h e maximum a n d minimum v a l u e s t a b u l a t e d f o r e a c h g r o u p o f s a m p l e s .

The s t r e n g t h v a l u e s o b t a i n e d by Hawks a n d M e l l o r [ 1 2 ] w e r e s i g n i f i c a n t l y h i g h e r t h a n t h o s e of C u r r i e r a n d S c h u l s o n [ l , 1 0 1 f o r a b o u t t h e same

4 ,

i n s p i t e o f t h e f a c t t h a t t h e t e m p e r a t u r e was h i g h e r . It would be p r e m a t u r e , however, t o c r e d i t t h e s e h i g h e r s t r e n g t h s t o d i f f e r e n c e s i n g r a i n s i z e a l o n e w i t h o u t f i r s t e x a m i n i n g t h e d i f f e r e n c e s i n t h e m i c r o s t r u c t u r e o f t h e s a m p l e s a n d t h e r e s p o n s e of t h e t e s t system. D e t a i l s a r e n o t a v a i l a b l e , b u t t h e i c e u s e d by Hawks a n d M e l l o r [ 1 2 ] was d e s c r i b e d as b u b b l y . The b u b b l e ( a i r o r w a t e r v a p o u r ) d e n s i t 3 i n t h e ice u s e d by C u r r i e r and S c h u l s o n [ l , 101 was r e p o r t e d t o be i n t h e r a n g e of 2 x 10 m-3 and 3.5 x lo8 m-3 f o r f i n e - a n d c o a r s e - g r a i n e d ice, r e s p e c t i v e l y . The number o f a i r b u b b l e i n c l u s i o n s v a r i e d g r e a t l y w i t h g r a i n s i z e . Moreover, a l m o s t e v e r y g r a i n seems t o h a v e had a few b u b b l e s a t t a c h e d t o i t . T h e q u e s t i o n a r i s e s , what i s t h e e f f e c t o f t h e s e i n c l u s i o n s o n s t r e n g t h ?

A n o t h e r i m p o r t a n t f a c t s h o u l d b e mentioned. The s t r a g n r a t e a c t u a l l y imposed i n t h e "gauge s e c t i o n " o f e a c h s p e c i m e n u s e d by C u r r i e r a n d S c h u l s o n [ l , 1 0 1 c o u l d b e e v e n l o w e r t h a n Qf e s t i m a t e d from t h e measurements of t o t a l s t r a i n between t h e e n d c a p s , t h a t is f r o m t h e sum o f t h e d e f o r m a t i o n o f t h e g a u g e s e c t i o n a n d t h e c o m p l i a n t "end zone" o f e a c h s p e c i m e n i n w h i c h t h e g r a i n s a r e s m a l l e r t h a n t h o s e i n t h e g a u g e s e c t i o n [ 1 3 ] . T h u s , t h e r e s u l t s i n F i g . 2 f o r R e f s . 1 a n d 1 0 would move t o w a r d s t h e l o w e r s t r a i n r a t e ( a n d h e n c e c l o s e r t o t h o s e o f R e f . 12) when t h e s t r a i n r a t e i n t h e g a u g e s e c t i o n was measured. Making t r a n s p a r e n t c o l u m n a r g r a i n e d i c e i s ( r e l a t i v e l y ) s i m p l e r t h a n making b u b b l e f r e e g r a n u l a r i c e . I t i s p o s s i b l e t o p r e p a r e b u b b l e - f r e e , t r a n s v e r s e l y i s o t r o p i c S-2 ice

[ a ] ,

b u t n o t e n s i l e s t r e n g t h d a t a w i t h i n f o r m a t i o n o n of a n d tf a r e a v a i l a b l e . T h e r e i s a v a i l a b l e , however, i n f o r m a t i o n r e g a r d i n g t h e r a t e s e n s i t i v i t y of s t r e s s , of,, f o r t h e f o r m a t i o n o f t h e f i r s t l a r g e i n t e r n a l c r a c k s u n d e r u n i a x i a l c o m p r e s s i o n , w i t h l o a d a p p l i e d p e r p e n d i c u i a r t o t h e columns [14]. The d a t a a r e a l s o shown i n F i g . 2 a s a f u n c t i o n o f a v e r a g e s t r a i n r a t e , E~~ = E~

I t f c ,

w h e r e a n d t f c a r e t h e c o r r e s p o n d i n g s t r a i n and t i m e , r e s p e c t i v e l y . S t r a i n s were a c t u a f l y m e a s u r e d by

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V o l . 1 7 , N o . 11 STRENGTH OF I C E AT H I G H TEMPERATURES

gauges mounted d i r e c t l y on t h e samples. The c o a r s ~ g r a i n e d i c e samples were completely f r e e of bubbles [ 8 ] ; t h e f i n e r - g r a i n e d samples a l s o were t r a n s p a r e n t , b u t n o t s t r i c t l y bubble-free. Elongated a i r bubbles a b o u t 0.1 mm i n d i a m e t e r and 0.5 t o 1.0 mm i n l e n t h were d i s t r i b u t e d

4

uniformly i n t h e f i n e r - g r a i n e d i c e , w i t h a number d e n s i t y of 8 x 10' m

.

F i g u r e 2 does n o t show any g r a i n s i z e dependence of t h e s t r a i n r a t e s e n s i t i v i t y of of,. It i s worth n o t i n g a l s o t h e a p p a r e n t correspondence between t h e s e r e s u l t s and t h o s e o f Hawks and M e l l o r [12].

As t h e i n i t i a l l o a d i n g p a t h s a r e n e a r l y l i n e a r f o r c o n s t a n t cross-head r a t e t e s t s [ 8 , 9, 141 and l o a d and time can be measured f a i r l y a c c u r a t e l y , s t r e s s r a t e a n a l y s i s could be a p p r o p r i a t e f o r t e n s i l e f r a c t u r e s . A l l t h e r e s u l t s shown i n Fig. 2 a5e p r e s e n t e d i n Fig. 3 i n terms of t h e c o r r e s p o n d i n g a v e r a g e r a t e t o f r a c t u r e o r f i r s t c r a c k s , of = o f / t and

= t

.

An a p p a r e n t correspondence between t h e o b s e r v a t i o n s of Refs. 1 5 and 14 and t h e s i g n i f i c a n t h f f e r e n c e between t h e s e and t h e o b s e r v a t i o n s r e p o r t e d i n Ref. 10 a r e a g a i n a p p a r e n t ( s t r e s s r a t e f o r Ref. 10 v a r i e d over 300 p e r c e n t between 2.2 and 6.6 MN-m-' The h i g h e r s t r e s s r a t e s r e c o r d e d f o r necked-down samples a r e a l s o n o t i c e a b l e .

F i g u r e 3 a l s o shows a l i n e r e p r e s e n t i n g a s t r e s s - r a t e s e n s i t i v i t y o f t e n s i l e s t r e n g t h , proposed by Kubo i n 1941 [ 1 5 ] ,

o = ;,/(6.0 x 10-4

+

0.7 6,)

f (1)

T h i s was f o r c o l u m n a r g r a i n e d n a t u r a l r i v e r i c e a t -lO°C i n t h e e x p e r i m e n t a l s t r e s s r a t e range of 3.3 x t o 3.3 x lo-' MN-m-' s-l. Equation ( 1 ) seems t o s a t i s f y t h e r e s u l t s of Refs. 1 and 1 0 and two f i r s t - c r a c k o b s e r v a t i o n s made i n Ref. 14 on f i n e g r a i n e d S-2 i c e .

D i s c u s s i o n

F r a c t u r e o c c u r s i f c r a c k s , e i t h e r i n h e r e n t i n t h e m a t e r i a l o r n u c l e a t e d d u r i n g

deformation, can p r o p a g a t e under a p p l i e d s t r e s s [16]. P r e - e x i s t i n g f l a w s w i l l be d i s c u s s e d f i r s t . An e s t i m a t e of f l a w s i z e , 2L, c a n be made from of by t h e a p p l i c a t i o n of G r i f f i t h s ' c r i t e r i o n

where

E

i s Young's modulus and y i s t h e e f f e c t i v e s u r f a c e energy.

Goodman's [ 1 7 ] f r a c t u r e toughness measurements f o r f r a c t u r e t i m e s l e s s t h a n a b o u t 20 s i n c o n j u c t i o n w i t h t h e r e s u l t s i n Fig. 3 i n d i c a t e t h a t p l a s t i c work p r i o r t o c r a c k p r o p a g a t i o n i s n o t l a r g e f o r r a t e s of l o a d i n g h i g h e r t h a n about 0.1 ~ ~ * r n - ~ s-l. T h i s s i m p l i f i e s t h e e s t i 2 t i o n of c r a c k s i z e , a t l e a s t f o r h i g h l o a d i n g r a t e s . For y = 0.109 .J*m-' [18] and E = 9.5 GN*m

[19], e q u a t i o n (2) g i v e s c r a c k l e n g t h of 0.2 and 2 mm f o r of of 2.5 and 0.8 r e s p e c t i v e l y . The s t r e s s range, i n f a c t , covers t h e e n t i r e range of t e n s i l e s t r e n g t h v a l u e s i l l u s t r a t e d i n Figs. 2 and 3 and r e p o r t e d f o r a l l t y p e s of i c e i n Refs. 2 and 3. Thus, t h e s i z e of e x i s t i n g f l a w s could determine s t r e n g t h and s c a t t e r . As t h e e n t i r e range of c r a c k s i z e s e s t i m a t e d c o u l d be e a s i l y accommodated w i t h i n t h e g r a i n b o u n d a r i e s of even f i n e r g r a i n e d i c e , t h e e f f e c t o n s t r e n g t h of g r a i n s i z e a l o n e might n o t be d e t e c t a b l e u n l e s s improvements a r e made i n f a b r i c a t i n g f l a w l e s s , o r crack-f r e e , i c e .

It h a s been p o i n t e d o u t t h a t c r a c k t i p p l a s t i c i t y p r i o r t o c r ck p r o p a g a t i o n was e x p e c t e d t o i n c r e a s e w i t h d e c r e a s e i n l o a d i n g r a t e below about 0.1 MNDi.m-2s-P, t h e range used i n most experiments. Kubo's e m p i r i c a l e q u a t i o n ( 1 ) i s c o n s i s t e n t w i t h t h i s p o s s i b i l i t y (Fig. 3). A s i m i l a r t r e n d is e v i d e n t i n t h e r e s u l t s of Hawks and Mellor [12]. Kubo's lower s t r e n g t h v a l u e s [ 1 5 ] , i n comparison w i t h t h o s e of Ref. 14 (Fig. 3 ) , c o u l d be due t o l a r g e f l a w s i n t h e n a t u r a l r i v e r i c e he used. The q u e s t i o n a r i s e s whether t h e r e s u l t s o b t a i n e d by C u r r i e r and Schulson

[ I , 101 were a l s o a f f e c t e d by p r e e x i s t i n g f l a w s . Two h i g h s t r e s s - r a t e o b s e r v a t i o n s o n t h e f o r m a t i o n of t h e f i r s t c r a c k i n f i n e - g r a i n e d S-2 i c e a r e c o n s i s t e n t w i t h Kubo's r e s u l t s . It i s p o s s i b l e t h a t t h e c r a c k s i n t h e two t e s t s were g e n e r a t e d by e l o n g a t e d b u b b l e s i n t h i s i c e .

O b s e r v a t i o n s on t h e f o r m a t i o n of f i r s t l a r g e c r a c k s i n c l e a r i c e under compression and i t s r a t e s e n s i t i v i t y have provided i n s i g h t i n t o t h e mechanical behaviour of i c e . High-temperature c r a c k n u c l e a t i o n p r o c e s s e s were c e r t a i n l y o p e r a t i v e i n t h e p r o d u c t i o n of t h e s e c r a c k s i n v i r t u a l l y f l a w l e s s ( m a c r o s c o p i c a l l y ) columnar-grained S-2 i c e [8, 141. T h e i r w i d t h seemed t o depend on c r o s s - s e c t i o n a l g r a i n s i z e , b u t no s i g n i f i c a n t d i f f e r e n c e s were n o t i c e d i n t h e i r l e n g t h : t h a t of t h e f i r s t l a r g e c r a c k s v a r i e d a g r e a t d e a l , from a few mm t o a few cm. Thus, t h e dimensions of t h e n u c l e a t e d c r a c k s were i n d e e d compatible w i t h t h e geometry of t h e c o n s t i t u e n t g r a i n s . Such d i r e c t o b s e r v a t i o n s have important consequences. The l e v e l of s t r e s s shown i n Figs. 2 and 3 and t h e l e n g t h of t h e c r a c k s were s u f f i c i e n t t o s a t i s f y t h e c o n d i t i o n s n e c e s s a r y , a c c o r d i n g t o e a r l i e r c a l c u l a t i o n s , t o p r o p a g a t e c r a c k s under t e n s i l e mode of loading.

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S T R E N G T H OF ICE A T H I G H T E M P E R A T U R E S

Vol. 17, No. 11

3 . 0 I I I

1

H A W K S & M E L L O R (121. 0 . 7 m m , - 7 ' C a 2.5 0 C U R R I E R (101. - 1 0 ° C G R A I N S I Z E A S S H O W N S l N H A ( 1 4 1 . 4 . 5 m m , - 1 0 ° C F I G . 2

-

2 . 0 - Z I "

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b 1 . 5 -

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b Y) Y)

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Dependence of strength and s t r e s s t o f i r s t large cracks on average s t r a i n r a t e

0 S I N H A (141, 2 rnm. - 1 0 " ~

/'*

M-D

-

/ -

-

A /

,*'

/ / /

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4.6 7 I I I 3.0 1 I I

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H A W K S b M E L L O R 1121. 0 . 7 m m . - 1 ' C a 1 0 - ~ A V E R A G E S T R A I N RATE. i f . i f c . 5 - I 0 C U R R I E R ( 1 0 ) . - 1 0 ° C

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G R A I N S I Z E A S S H O W N I N m m S I N H A 114). 4.5 m m . - 1 0 ° C v S I N H A 1141. 2 m m . - 1 0 ° C 8 -

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A V E R A G E S T R E S S RATE, 6 , - g t c . M N . m - 2 . s - ' F I G . 3

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V o l . 1 7 , No. 11 STRENGTH OF I C E AT H I G H TEMPERATURES 1 2 7 3

N u c l e a t i o n of t h e f i r s t l a r g e c r a c k s i n t e n s i o n c o u l d a l s o d i c t a t e t h e u l t i m a t e s t r e n g t h o f columnar-grained i c e . A s t h e r a t e s e n s i t i v i t y o f t h e f o r m a t i o n o f t h e c r a c k s (Figs. 2, 3 ) and t h e l e n g t h of t h e f l a w s were n o t a f f e c t e d by c r o s s - s e c t i o n a l g r a i n s i z e , t h e t e n s i l e s t r e n g t h of S-2 i c e w i t h l o a d a p p l i e d normal t o t h e l e n g t h of t h e columnar g r a i n s might n o t show any g r a i n s i z e e f f e c t e i t h e r . T h i s is simply s p e c u l a t i o n , however, a l t h o u g h t h e r e s u l t s p r e s e n t e d i n Refs. 2 and 3 p r o v i d e some e v i d e n c e of i t . The a u t h o r would l i k e t o c a r r y o u t f u r t h e r d i r e c t t e n s i l e t e s t s on p u r e S-2 i c e t o v e r i f y t h i s p o i n t .

V i s i b l e c r a c k s were observed t o form i n S-2 i c e soon a f t e r a few low-amplitude a c o u s t i c e m i s s i o n s were y c o r d e d [14]. F i r s t a c o u s t i c e m i s s i o n s were r e c o r d e d ~ o n l y a f t e r s t r e s s exceeded about 0.4 M N - m

.

T h i s s t r e s s l e v e l c o i n c i d e s c l o s e l y w i t h t h e r e s u l t s of a c o u s t i c e m i s s i o n measurements c a r r i e d o u t s i m u l t a n e o u s l y w i t h t e n s i l e t e s t s on g r a n u l a r i c e [ l o ] , when i t was shown t h a t s t r e s s a t t h e o n s e t of a c d u s t i c e m i s s i o n doe n o t depend o n g r a i n s i z e . The minimm

-1

s t r e s s f o r t h e o n s e t of e m i s s i o n s was 0.44 ? 0.17 MN-m

.

These o b s e r v a t i o n s r a i s e t h e q u e s t i o n of what mechanism of n u c l e a t i o n of a c o u s t i c e m i s s i o n (and p o s s i b l e microcracks) t h e r e might be t h a t would n o t depend on g r a i n s i z e . A new high-temperature c r a c k n u c l e a t i o n c r i t e r i o n , based on a c r i t i c a l grain-boundary s l i d i n g d i s p l a c e m e n t , h a s been proposed [ Z O ] and i s now s u p p o r t e d by experiment w i t h m e t a l s [21].

Conclusions

T e n s i l e t e s t s on fresh-water i c e [l-4, 10, 121 have been a f f e c t e d by choice of improper specimen geometry and by i n t e r a c t i o n between t h e t e s t i n g machine and t e s t specimens. A n a l y s i s s u g g e s t s t h a t t h e u s e of i c e w i t h l a r g e numbers of i n c l u s i o n s c o u l d have played a n i m p o r t a n t r o l e i n p r o p a g a t i n g i n h e r e n t f l a w s i n a l l t h e r e p o r t e d r e s u l t s . The G r i f f i t h c r i t e r i o n f o r f r a c t u r e c o u l d c a u s e a n a p p a r e n t g r a i n s i z e e f f e c t i f s i z e of i n h e r e n t f l a w s o r s i z e of n u c l e a t e d c r a c k s a r e c o n t r o l l e d by g r a i n s i z e . I f t h e e f f e c t on s t r e n g t h of g r a i n s i z e a l o n e is t o be examined, e x p e r i m e n t s s h o u l d be performed on i n c l u s i o r r f r e e i c e under t r u l y c o n s t a n t s t r e s s - r a t e , o r under t r u l y c o n s t a n t s t r a i n - r a t e w i t h t h e gauge mounted on t h e specimen.

References

1. J.H. C u r r i e r and E.M. Schulson, Acta M e t a l l . 30, 1511 (1982).

2. B. Michel and M. Drouin, Report T-19, Dept. of C i v i l Engineering, Lava1 U n i v e r s i t y (1971). 3. B. Michel, Can. J. Civ. Engng. 5, 285 (1978).

4. J. Muguruma, J. Phys., D., Ser. 2, V. 2, 1517 (1969).

5. S.J. Jones and H.A.M. Chew, J. G l a c i o l o g y , 27, p. 517 (1981). 6. B. Michel and R.O. Ramseier, Can. Geotech. J. 8 , 36 (1971).

7. N.K. Sinha, Proc. IAHR I n t e r n a t i o n a l Symposium on I c e , Quebec, Canada, Vol. 2, 581 (1981). 8. N.K. Sinha, Experimental Mechanics, 21, 209 (1981).

9. N.K. Sinha and R.M.W. F r e d e r k i n g , Proc. 5 t h I n t e r n a t i o n a l Conference on P o r t and Ocean Engineering under A r c t i c Conditions, Trondheim, Norway, V. 1 , 708 (1979).

10. J.H. C u r r i e r , M.Sc. T h e s i s , Thayer School of Engineering, Dartmouth C o l l e g e , Hanover, N.H. (1981).

N.K. Sinha, J. Mat. S c i . 17, 785 (1982).

I. Hawks and M. M e l l o r , J. Glaciology, 11, 103 (1972).

N.K. Sinha, Proc. 6 t h I n t e r n a t i o n a l Conference on P o r t and Ocean E n g i n e e r i n g under A r c t i c C o n d i t i o n s , Quebec, Canada, V. 1 , 216 (1981).

N.K. Sinha, Proc. 1982 SESA/Japan S o c i e t y f o r Mechanical Engineers. Honolulu-Maui, Hawaii, P a r t 11, 767 (1982).

Y. Kubo, C o n s t r u c t i o n Bureau, South Manchurian Railway Company Study on R i v e r I c e ( I n J a p a n e s e ) , (1941). P r i v a t e communication. See a l s o U.S. Army, Cold Regions Research and E n g i n e e r i n g L a b o r a t o r y , T r a n s l a t i o n T50, (1955).

L.W. Gold, J . G l a c i o l o g y , 1 9 ( 8 1 ) , 197 (1977).

D.J. Goodman, Proc. Workshop on I c e P h y s i c s , Hokkaido, J a p a n , (1979). (Also p r i v a t e communication).

W.M. Ketchum and P.V. Hobbs, P h i l . Mag. 19, 1161 (1969). N.K. Sinha, Experimental Mechanics, 18, 464 (1978).

N.K. Sinha, Symposium on Deformation and F a i l u r e o f G r a n u l a r M a t e r i a l s , I n t e r n a t i o n a l Union of T h e o r e t i c a l and Applied Mechanics, D e l f t , 31 Aug.

-

3 Sept. 1982, p. 323-330.

T. Watanabe, M e t a l l u r g i c a l Trans. A , 14A, 531 (1983).

T h i s p a p e r i s . a c o n t r i b u t i o n from t h e D i v i s i o n of B u i l d i n g Research, N a t i o n a l Research Council Canada, and i s p u b l i s h e d w i t h t h e a p p r o v a l of t h e D i r e c t o r of t h e D i v i s i o n .

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T h i s paper, w h i l e being d i s t r i b u t e d i n r e p r i n t form by t h e D i v i s i o n of B u i l d i n g

Research, remains t h e copyright of t h e

o r i g i n a l p u b l i s h e r . It should n o t be reproduced i n whole o r i n p a r t w i t h o u t t h e permission of t h e p u b l i s h e r . A l i s t of a l l p u b l i c a t i o n s a v a i l a b l e from t h e D i v i s i o n may be o b t a i n e d by w r i t i n g t o t h e P u b l i c a t i o n s S e c t i o n , 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 , N a t i o n a l R e s e a r c h C o u n c i l of Canada, O t t a w a , O n t a r i o , K I A OR6.

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