Deformation mechanisms in ice

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Deformation mechanisms in ice

Gold, L. W.

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Ser

TH1

N21r2

no.

193

c.

2

BLDG

NATIONAL

RESEARCH

COUNCIL

C A N A D A

DIVISION O F BUILDING RESEARCH

DEFORMATION MECHANISMS IN ICE

BY L. W. GOLD

R E P R I N T E D BY P E R M I S S I O N F R O M I C E A N D SNOW.

PROCEEDINGS O F A CONFERENCE HELD FEBRUARY 12-16, 1962 EDITED BY W. D. KINGERY.

COPYRIGHT 1963 BY

THE MASSACHUSETTS INSTITUTE O F TECHNOLOGY.

PUBLISHED BY

THE M. I. T. P R E S S , MASSACHUSETTS, INSTITUTE O F TECHNOLOGY.

RESEARCH PAPER NO. 193

OF THE

DIVISION O F BUILDING RESEARCH

PRICE 2 5 CENTS BL!IL!?II\-i<; R!ISL~LlRCH 1 1 !-" 7

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1 NATlljS;\L i:15i;:;ii: C O U N C I L A U G U S T 196- -.-,

T h i s p u b l i c a t i o n i s b e i n g d i s t r i b u t e d by the D i v i s i o n of Building R e s e a r c h o f the N a t i o n a l R e s e a r c h Council. It should not be r e p r o d u c e d in whole o r in p a r t , without p e r m i s - s i o n of t h e o r i g i n a l p u b l i s h e r . T h e Division would be glad t o be of a s s i s t a n c e i n obtaining s u c h p e r m i s s i o n .

P u b l i c a t i o n s of the D i v i s i o n of Building R e s e a r c h m a y b e o b t a i n e d by m a i l i n g the a p p r o p r i a t e r e m i t t a n c e , ( a B a n k , E x p r e s s , o r P o s t Office M s n e y O r d e r o r a c h e q u e m a d e p a y - a b l e a t p a r in O t t a w a , to the R e c e i v e r G e n e r a l of C a n a d a , c r e d i t National R e s e a r c h Council) to the N a t i o n a l R e s e a r c h Council, Ottawa. S t a m p s a r e not a c c e p t a b l e .

A coupon s y s t e m h a s b e e n i n t r o d u c e d t o m a k e p a y - m e n t s for p u b l i c a t i o n s r e l a t i v e l y s i m p l e . Caupons a r e a v a i l - a b l e i n d e n o m i n a t i o n s of 5 , 2 5 a n d 50 c e n t s , a n d m a y be o b - t a i n e d by m a k i n g a r e m i t t a n c e a s indicated above. T h e s e coupons m a y be u s e d f o r the p u r c h a s e of a l l N a t i o n a l R e s e a r c h Council p ~ b l i c a t i o n s including s p e c i f i c a t i o n s of the C a n a d i a n G o v e r n m e n t S p e c i f i c a t i o n s B o a r d .

Chapter 2

DEFORMATION MECHANISMS IN ICE*

L. W . Gold

N u m e r o u s o b s e r v a t i o n s o n the c r e e p of i c e and i t s dependence on t e m p e r a t u r e and s t r e s s have b e e n published i n r e c e n t y e a r s ( 1 - 4 ) . Attention h a s b e e n d i r e c t e d , p r i m a r i l y , t o d e t e r m i n i n g the dependence of t h e steady- s t a t e c r e e p r a t e i n the s e c o n d a r y c r e e p s t a g e to the c o n s t a n t applied load. Some i n v e s t i g a t o r s '

have c o n s i d e r e d d e f o r m a t i o n p r o c e s s e s and t h e i r possible r e - l a t i o n to the o b s e r v e d c r e e p b e h a v i o r . Glen a t t r i b u t e s the a c - c e l e r a t i o n t h a t o c c u r s i n the t e r t i a r y s t a g e to r e c r y s t a l l i z a t i o n ( 2 , 5 ) ; and S t e i n e m a n n h a s shown t h a t r e c r y s t a l l i z a t i o n will t a k e p l a c e i n thin s e c t i o n s of g r a n u l a r i c e t h a t h a s b e e n s t r a i n e d m o r e t h a n 2%. It h a s b e e n r e p o r t e d t h a t the a v e r a g e g r a i n s i z e of i c e t h a t h a s b e e n s e v e r e l y s t r a i n e d i s s m a l l e r than t h e a v e r a g e g r a i n s i z e b e f o r e the load w a s applied ( 5 ,

6 ) .

T h e s e o b s e r v a t i o n s a r e s i m i l a r t o t h o s e m a d e o n m e t a l s d e f o r m e d a t h i g h t e m p e r a t u r e s .

Shoumsky d e s c r i b e s f o r i c e s i x m e c h a n i s m s of d e f o r m a t i o n and a s s o c i a t e s e a c h m e c h a n i s m with t h e applied load and a c c o m p a n y - ing c r e e p r a t e ( 7 ) . The f i r s t f o u r m e c h a n i s m s , which b e c o m e i m p o r t a n t i n t u r n a s the c r e e p r a t e i n c r e a s e s , a r e b a s a l s l i p i n the s i n g l e c r y s t a l ; s l i g h t d i s t u r b a n c e s of l a t t i c e , g r a i n g r o w t h , and g r a i n - b o u n d a r y m i g r a t i o n ; d i s t o r t i o n of the c r y s t a l l a t t i c e , polygonization and p r i m a r y r e c r y s t a l l i z a t i o n ; i n t e r c r y s t a l l i n e sliding a c c o m p a n i e d by r e d u c t i o n i n g r a i n s i z e a n d quite s e v e r e d i s r u p t i o n of the o r i g i n a l f a b r i c . At h i g h e r r a t e s of s t r a i n , f r a c - t u r e along p r e f e r r e d p l a n e s and p e r h a p s m e l t i n g will o c c u r .

During the c o u r s e of e x p e r i m e n t s o n c r a c k f o r m a t i o n i n i c e s u b j e c t to a c o n s t a n t c o m p r e s s i v e l o a d , s o m e i n f o r m a t i o n w a s obtained o n the d e f o r m a t i o n m e c h a n i s m s t h a t o c c u r r e d . It i s the p u r p o s e of t h i s p a p e r to d e s c r i b e t h e s e m e c h a n i s m s , r e l a t e t h e m to s i m i l a r o b s e r v a t i o n s t h a t h a v e b e e n m a d e on i c e and o t h e r m a t e r i a l s , and d i s c u s s t h e i r s i g n i f i c a n c e with r e s p e c t to the

Xc T h i s p a p e r i s a c o n t r i b u t i o n f r o m the D i v i s i o n of Building R e s e a r c h of the National R e s e a r c h Council of C a n a d a and i s published with the a p p r o v a l of the D i r e c t o r of t h e Division.

d e f o r m a t i o n b e h a v i o r of i c e . T h i s will b e done i n four s e c t i o n s . The f i r s t s e c t i o n c o n t a i n s a d e s c r i p t i o n of t h e i c e and the e x - p e r i m e n t s . In t h e second s e c t i o n the d e f o r m a t i o n m e c h a n i s m s o b s e r v e d a r e d e s c r i b e d and d i s c u s s e d b r i e f l y . The r e s p o n s e of a g r a i n to the a p p l i e d load and t h e r o l e t h a t t h e d e f o r m a t i o n me- c h a n i s m s play in d e t e r m i n i n g t h i s r e s p o n s e a r e d i s c u s s e d i n the t h i r d s e c t i o n . F i n a l l y , d e f o r m a t i o n m e c h a n i s m s a r e d i s - c u s s e d with r e s p e c t to the o b s e r v e d c r e e p b e h a v i o r , and s o m e g e n e r a l i z a t i o n s o n t h e behavior of i c e i n c e r t a i n e n g i n e e r i n g p r o b l e m s a r e p r e s e n t e d .

D e s c r i p t i o n of Ice a n d E x p e r i m e n t s

The i c e u s e d i n t h e e x p e r i m e n t s was m a d e f r o m d e a e r a t e d tap w a t e r i n a g a l v a n i z e d t a n k about 26 i n c h e s i n d i a m e t e r and 2 4 i n c h e s d e e p . Two b a l l o o n s w e r e placed u n d e r a weighted p l a t - f o r m a t the b o t t o m of t h e t a n k and filled with a i r . T h i s a i r was m a i n t a i n e d a t a c o n s t a n t p r e s s u r e by c o n n e c t i n g the b a l l o o n s to

a tube s u b m e r g e d i n a c o l u m n of ethylene g l y c o l . When cooled sufficiently, t h e w a t e r was s e e d e d with fine- g r a i n snow s p r e a d d e n s e l y enough t o c o v e r the s u r f a c e c o m p l e t e l y . A s t h e w a t e r f r o z e , the change i n volume f o r c e d a i r f r o m t h e balloons i n t o t h e c o l u m n of g l y c o l . Jn t h i s way the w a t e r f r o z e a t a l m o s t con- s t a n t p r e s s u r e , t h e r e being only a s l i g h t i n c r e a s e with t i m e be- c a u s e t h e t e n s i o n i n the r u b b e r of t h e balloons d e c r e a s e d a s they d e f l a t e d .

A i r - f r e e i c e p l a t e s u p to 6 i n c h e s t h i c k could be p r o d u c e d with- out difficulty. B e c a u s e t h e f r e e z i n g was u n i d i r e c t i o n a l , t h e ice had a c o l u m n a r g r a i n s t r u c t u r e , t h e long a x i s of the g r a i n s being p a r a l l e l to t h e d i r e c t i o n of f r e e z i n g . Thin s e c t i o n s cut n o r m a l and p a r a l l e l t o t h e d i r e c t i o n of f r e e z i n g a r e shown in F i g . l a and b.

F i g . 1. T h i n s e c t i o n s c u t n o r m a l ( a ) a n d p a r a l l e l ( b ) to the d i r e c - tion of f r e e z i n g of c o l u m n a r g r a i n e d i c e .

It had b e e n hoped t h a t s e e d i n g t h e w a t e r with snow would en- s u r e a r a n d o m d i s t r i b u t i o n i n t h e o r i e n t a t i o n of the c r y s t a l l o -

g r a p h i c c - a x i s of t h e g r a i n s ; but b e c a u s e i c e g r o w s m o r e r e a d i l y p e r p e n d i c u l a r to t h e c - a x i s than p a r a l l e l to i t , t h i s r a n d o m d i s - t r i b u t i o n w a s not o b t a i n e d . Within 2 c e n t i m e t e r s of t h e s e e d e d s u r f a c e t h e r e w a s a m a r k e d t e n d e n c y f o r the c - a x i s t o b e p e r - p e n d i c u l a r t o t h e d i r e c t i o n of g r o w t h . O b s e r v a t i o n s o n 100 g r a i n s of a s p e c i m e n c u t a t l e a s t 5 c e n t i m e t e r s f r o m t h e s e e d e d sujrface showed t h a t 40% h a d t h e i r c - a x i s b e t w e e n 8 5 " a n d 9 0 " t o t h e g r o w t h d i r e c t i o n , 2970 h a d t h e i r c - a x i s b e t w e e n 7 5 " a n d 8 5 "

,

a n d t h e r e m a i n d e r b e t w e e n 6 0 " and 7 5 " . T h e b a s a l p l a n e had t h e r e - f o r e a p r e f e r r e d o r i e n t a t i o n p a r a l l e l t o t h e long a x i s of t h e co- l u m n a r g r a i n s , but a r a n d o m o r i e n t a t i o n i n t h e p l a n e p e r p e n d i c u l a r to t h e f r e e z i n g d i r e c t i o n . B e c a u s e of t h e p r e f e r r e d d i r e c t i o n of g r o w t h , t h e g r a i n s w e r e s l i g h t l y t a p e r e d , and t h e a v e r a g e g r a i n s i z e i n c r e a s e d g r a d u a l l y i n t h e d i r e c t i o n of g r o w t h . Ice p r e p a r e d by t h i s t e c h n i q u e h a s a n a v e r a g e g r a i n d i a m e t e r b e t w e e n 1.50 a n d 7 . 0 m i l l i m e t e r s . O b s e r v a t i o n s w e r e m a d e o n r e c t a n g u l a r b l o c k s of two s i z e s : 5 - b y - 1 0 - b y - 2 5 - c m a n d 2 . 5 - b y - 5 - b y - 1 5 - c m . T h e b l o c k s w e r e c u t s o t h a t t h e long a x i s of t h e g r a i n s w a s p e r p e n d i c u l a r to e i t h e r the 1 0 - b y - 2 5 - c m o r t h e 5- by- 1 5 - c m f a c e . A l l t h e t e s t p i e c e s w e r e p r e p a r e d f r o m i c e f r o m which t h e u p p e r 2 c e n t i m e t e r s con- t a i n i n g t h e t r a n s i t i o n r e g i o n a s s o c i a t e d with t h e f r e e z i n g t e c h - nique h a d b e e n r e m o v e d . E x p e r i m e n t s T h e a u t h o r h a s s h o w n t h a t w h e n a c o m p r e s s i v e s t r e s s i s a p - plied p e r p e n d i c u l a r to t h e long a x i s of t h e g r a i n s i n c o l u m n a r m u l t i g r a i n e d i c e , t h e c r a c k i n g a c t i v i t y t h a t r e s u l t s d e p e n d s o n t h e a p p l i e d s t r e s s and t h e s t r u c t u r e ( 8 ) . B e c a u s e of the d e g r e e of d e f o r m a t i o n t h a t o c c u r r e d d u r i n g t h e e a r l y e x p e r i m e n t s , no c o n c l u s i o n s could b e s t a t e d r e g a r d i n g t h e d e p e n d e n c e of the d i - r e c t i o n of t h e c r a c k o n t h e c r y s t a l l o g r a p h i c o r i e n t a t i o n of t h e g r a i n i n which i t f o r m e d . Two s e t s of e x p e r i m e n t s w e r e d e s i g n e d to i n v e s t i g a t e t h i s d e p e n d e n c e . In o n e s e t , t h e 2.5- by- 5- by- 15- c m b l o c k s w e r e s u b m e r g e d i n k e r o s e n e i n a h o r i z o n t a l p o s i t i o n a n d a c o m p r e s s i v e l o a d w a s applied to t h e 2 . 5 - b y - 5 - c m f a c e s . S u r f a c e f e a t u r e s t h a t would n o r m a l l y b e r e m o v e d by e v a p o r a t i o n if e x p o s e d t o a i r w e r e p r e - s e r v e d i n t h i s way. O b s e r v a t i o n s w e r e m a d e o n t h e i c e with a m i c r o s c o p e d u r i n g d e f o r m a t i o n . T h r e e e x p e r i m e n t s of t h i s kind w e r e c a r r i e d o u t , with l o a d s b e t w e e n 5 a n d 9 k g / c m 2 applied f o r 6 0 to 100 h o u r s . T h e s e e x p e r i m e n t s will be r e f e r r e d t o a s t h e " k e r o s e n e e x p e r i m e n t s . I ' In t h e s e c o n d s e t of e x p e r i m e n t s , a c o m p r e s s i v e l o a d w a s a p p l i e d to t h e 5 - b y - 1 0 - c m f a c e s of t h e 5-by- 1 0 - b y - 2 0 - c m b l o c k s ,

j u s t long enough f o r about 10 c r a c k s to f o r m . The i c e w a s then r e m o v e d and s e c t i o n e d p a r a l l e l to t h e 10-by- 20- c m f a c e . The c r y s t a l l o g r a p h i c o r i e n t a t i o n of t h e g r a i n s i n which the c r a c k s f o r m e d w a s d e t e r m i n e d u s i n g H i g u c h i ' s t e c h n i q u e ( 9 ) . Although t h e s e e x p e r i m e n t s g a v e i n f o r m a t i o n o n t h e d e p e n d e n c e of c r a c k f o r m a t i o n o n c r y s t a l l o g r a p h i c o r i e n t a t i o n , t h e i r p r i m a r y p u r - p o s e w a s to i n v e s t i g a t e t h e d e p e n d e n c e o n t h e applied s t r e s s of t h e t i m e to f o r m a t i o n of t h e f i r s t c r a c k s . In t h e s e c o n d s e t of e x p e r i m e n t s c r e e p w a s m e a s u r e d w i t h a s p e c i a l e x t e n s o m e t e r with a g a u g e l e n g t h of 1 5 c e n t i m e t e r s and s e n s i t i v i t y of about 2.5 X s t r a i n u n i t s . T h e c r e e p t h a t oc- c u r r e d d u r i n g t h e s e t e s t s w a s a l w a y s l e s s t h a n 0.170. O b s e r v a t i o n s o n t h e d e f o r m a t i o n m e c h a n i s m s w e r e m a d e during t h e c o u r s e of t h e e x p e r i m e n t s j u s t d e s c r i b e d and t h e e a r l i e r ex- p e r i m e n t s by Gold. All t h e e x p e r i m e n t s w e r e c a r r i e d o u t a t a t e m p e r a t u r e of - 9 . 5

*

0.5' C . P a p e r s t h a t d e s c r i b e i n d e t a i l the o b s e r v a t i o n s of t h e d e p e n d e n c e of c r a c k f o r m a t i o n on t i m e and o n c r y s t a l l o g r a p h i c o r i e n t a t i o n a r e being p r e p a r e d . D e s c r i p t i o n of t h e D e f o r m a t i o n M e c h a n i s m s S l i p B a n d s T h e f o r m a t i o n of s l i p b a n d s r e q u i r e s a l i t t l e c o m m e n t b e c a u s e i t i s s u c h a f a m i l i a r f e a t u r e of t h e d e f o r m a t i o n of s o l i d s , p a r - t i c u l a r l y of m e t a l s . In t h e k e r o s e n e e x p e r i m e n t s , t h e b a n d s be- c a m e v i s i b l e within 1/2 h o u r a f t e r t h e a p p l i c a t i o n of a l o a d of 'about 5 . 5 k g / c m Z . At t h i s t i m e t h e s t r a i n d i d not e x c e e d 0.5 by With t i m e , t h e b a n d s b e c a m e m o r e d i s t i n c t . T y p i c a l ex- a m p l e s c a n b e s e e n i n F i g s . 2 and 3. F i g . 2. E v i d e n c e of s l i p o n p r i s m a t i c p l a n e s . Note c r a c k a t t r i p l e point. , N e a r t h e i r m e l t i n g points s i n g l e c r y s t a l s with h e x a g o n a l s y m - m e t r y u s u a l l y d e f o r m by s l i p o n t h e b a s a l a n d p r i s m a t i c p l a n e s . Nakaya ( l o ) , S t e i n e m a n n ( 1 I ) , a n d Glen and P e r u t z ( 1 2 ) h a v e o b s e r v e d t h a t f o r i c e , s l i p o c c u r s p r e d o m i n a n t l y on t h e b a s a l

F i g . 3. G r a i n - b o u n d a r y m i - g r a t i o n . ( a ) O b s e r v e d 5 1/2 h o u r s a f t e r the a p p l i c a t i o n of a c o m p r e s s i v e load of 5 k g / c m 2 . (b) S a m e s i t e 61 h o u r s , 40 m i n u t e s a f t e r the a p p l i c a t i o n of t h e load. I n s e r t A l o c a t e s a r e a shown i n F i g . 3a.

plane and t h a t l i t t l e o r no e v i d e n c e h a s b e e n found of s l i p o n t h e p r i s m a t i c p l a n e s . T h i s c o n c l u s i o n i s s u p p o r t e d by o b s e r v a t i o n s m a d e i n the k e r o s e n e e x p e r i m e n t s . In one e x p e r i m e n t , h o w e v e r , e v i d e n c e o b s e r v e d a t t h e s u r f a c e of two g r a i n s s u g g e s t e d t h a t glide o n p r i s m a t i c p l a n e s had o c c u r r e d . The s p e c i m e n w a s sub- j e c t to a load of about 8 k g / c m 2 . F i g u r e 2 s h o w s one of t h e s e s u r f a c e f e a t u r e s , photographed a b o u t 30 h o u r s a f t e r t h e a p p l i c a - tion of t h e l o a d . Notice that t h i s f e a t u r e i s confined to t h e t r i p l e - point r e g i o n and a s s o c i a t e d with g r a i n - b o u n d a r y a n d s l i p - l i n e d i s t o r t i o n , s u g g e s t i n g a high l o c a l s t r e s s . A s i m i l a r a s s o c i a - tion h a s b e e n found by H a u s e r and o t h e r s ( 1 3 ) f o r t h e o c c u r r e n c e of s l i p o n p r i s m a t i c p l a n e s i n m a g n e s i u m . T h e s e c o n d e v i d e n c e of p r i s m a t i c s l i p w a s t h e s a m e a s t h e f i r s t , e x c e p t that i t w a s o b s e r v e d i m m e d i a t e l y a f t e r t h e l o a d w a s r e m o v e d , o n a f a c e p a r a l l e l t o the long a x i s of t h e g r a i n s . The s e c o n d f e a t u r e w a s not a s s o c i a t e d with a t r i p l e point a s w a s t h e f i r s t , but t h e r e w a s e v i d e n c e of d e f o r m a t i o n n o r m a l to t h e s u r f a c e .

It would a p p e a r t h a t n e a r the m e l t i n g point the loading c o n d i t i o n s r e q u i r e d to c a u s e p r i s m a t i c s l i p i n i c e m u s t be v e r y s p e c i a l . It w a s a s s u m e d , t h e r e f o r e , t h a t t h e s l i p l i n e s define t h e t r a c e of t h e b a s a l plane a t the i c e s u r f a c e . T h e s l i p b a n d s c a n thus b e u s e d to d e t e r m i n e t h e plane c o n t a i n i n g t h e c r y s t a l l o g r a p k c c- d i r e c t i o n but not t h e a n g l e b e t w e e n t h i s d i r e c t i o n a n d the i c e s u r f a c e .

In F i g . 2 , only t h e f e a t u r e s r a i s e d above t h e i c e s u r f a c e a r e c o n s i d e r e d e v i d e n c e of p r i s m a t i c s l i p . The s h o r t l i n e s not a s -

s o c i a t e d with a r a i s e d f e a t u r e w e r e o b s e r v e d quite often a n d will b e d i s c u s s e d f u r t h e r under subboundary f o r m a t i o n .

G r a i n - Boundarv M i g r a t i o n

G r a i n - b o u n d a r y m i g r a t i o n was one of t h e f i r s t signs of change i n t h e g r a i n - b o u n d a r y configuration. An e x a m p l e of t h i s i s shbwn i n F i g . 3a; the d i r e c t i o n of c o m p r e s s i v e s t r e s s i s p a r a l l e l to the long d i r e c t i o n of t h e p h o t o g r a p h s . The f i r s t evidence of boundary m o v e m e n t w a s o b s e r v e d about 1/2 hour a f t e r t h e a p p l i c a t i o n of t h e l o a d , when t h e c r e e p s t r a i n was l e s s t h a n 0.05%.

The d e g r e e to which b o u n d a r i e s e t c h i n s u c c e s s i v e p o s i t i o n s shows t h a t m i g r a t i o n m u s t o c c u r quite r a p i d l y , and t h a t b o u n d a r i e s r e m a i n s t a t i o n a r y i n t h e i r new positions f o r s o m e t i m e . T h i s ob- s e r v a t i o n i s i n a g r e e m e n t with t h a t made o n o t h e r m a t e r i a l s on t h e m i g r a t i o n of b o u n d a r i e s u n d e r s t r e s s ( 1 4 ) .

P r a c t i c a l l y e v e r y boundary o b s e r v e d showed evidence of mi- g r a t i o n . In s o m e c a s e s t h e b o u n d a r i e s b e c a m e v e r y i r r e g u l a r ( F i g . 4b). In e x p e r i m e n t s on t h e c r e e p of i c e b e a m s , K r a u s z (15) h a s o b s e r v e d c a s e s of g r a i n s t h a t w e r e c o m p l e t e l y c o n s u m e d by t h e i r n e i g h b o r s , although no e x a m p l e of t h i s was o b s e r v e d i n t h e k e r o s e n e e x p e r i m e n t s . F i g . 4. S m a l l - angle b o u n d a r y . ( a ) 5 h o u r s a f t e r a p p l i c a t i o n of load of 9 k g / c m 2 . C o m p r e s - s i v e s t r e s s p a r a l l e l to l o n g d i r e c t i o n of photograph. ( b ) The s a m e a r e a 70 h o u r s , 2 5 m i n u t e s a f t e r t h e a p p l i c a t i o n of t h e load. Shadow i n u p p e r r i g h t -caused by i n t e r n a l c r a c k . Note s m a l l s u r f a c e c r a c k s . I n s e r t A l o c a t e s a r e a s h o w n i n F i g . 3a.

S m a l l - Angle B o u n d a r i e s , Kink B a n d s S m a l l - a n g l e b o u n d a r i e s w e r e o b s e r v e d t o f o r m i n the k e r o s e n e e x p e r i m e n t s b e f o r e d e f o r m a t i o n h a d e x c e e d e d 17'0, T h e s e bound- a r i e s w e r e a l w a y s p e r p e n d i c u l a r t o t h e s l i p b a n d s d u r i n g t h e e a r l y s t a g e s of d e f o r m a t i o n . A s t h e d e f o r m a t i o n i n c r e a s e d , i t b e c a m e c l e a r t h a t i n s o m e c a s e s t h e y w e r e a s s o c i a t e d with t h e f o r m a t i o n of kink b a n d s . Kink b a n d s , f i r s t r e p o r t e d by O r o w a n ( 1 6 ) , a r e a f a m i l i a r f e a t u r e i n t h e d e f o r m a t i o n of s o m e m e t a l s , p a r t i c u l a r l y t h o s e w i t h a h e x a g o n a l s y m m e t r y ( 1 7 ) . T h e i r f o r - m a t i o n i s a m e c h a n i s m by which a b e n d i n g m o m e n t , t r a n s v e r s e t o t h e s l i p d i r e c t i o n , c a n b e r e l i e v e d i n c r y s t a l s w i t h only o n e o r two p o s s i b l e s l i p d i r e c t i o n s . D i s l o c a t i o n s g e n e r a t e d by the d e f o r - m a t i o n a r e a b s o r b e d a t t h e s m a l l - a n g l e b o u n d a r i e s s e p a r a t i n g t h e b a n d s . T h i s c a u s e s a s l i g h t d i f f e r e n c e b e t w e e n t h e o r i e n t a t i o n of t h e g r a i n s o n e i t h e r s i d e of t h e b o u n d a r y , t h e d i f f e r e n c e i n - c r e a s i n g with d e f o r m a t i o n . An e x a m p l e o b s e r v e d i n the k e r o - s e n e e x p e r i m e n t s i s s h o w n i n F i g . 4 , w h e r e t h e a p p l i e d l o a d w a s 9 k g / c m 2 . G e r v a i s a n d o t h e r s ( 1 8 ) h a v e s h o w n t h a t i n high- p u r i t y a l u m i - n u m t h e p l a n e of kinking b i s e c t s t h e a n g l e b e t w e e n t h e s l i p p l a n e s o n e i t h e r s i d e of t h e k i n k b o u n d a r y , a n d t h a t t h e l i n e of i n t e r - s e c t i o n of t h e lcink p l a n e a n d t h e s l i p p l a n e s i s p e r p e n d i c u l a r to t h e s l i p d i r e c t i o n . R o t a t i o n a s s o c i a t e d with t h e c h a n g e i n o r i e n - t a t i o n a c r o s s the p l a n e of kinking i s a b o u t t h e l i n e of i n t e r s e c t i o n . B e c a u s e of t h e c o l u m n a r s t r u c t u r e of t h e i c e u s e d i n the e x p e r i - m e n t s and t h e b i a s i n t h e c r y s t a l l o g r a p h i c o r i e n t a t i o n , t h i s l i n e of i n t e r s e c t i o n would t e n d t o be p a r a l l e l t o t h e long a x i s of t h e g r a i n s . S u b b o u n d a r y a n d lcink b a n d f o r m a t i o n , t h e r e f o r e , p r o b - a b l y i n v o l v e t h e whole g r a i n and not j u s t the p a r t o b s e r v e d a t t h e s u r f a c e . T h i s w a s p r o v e d by o b s e r v i n g , w i t h p o l a r i z e d l i g h t , t h i n s e c t i o n s c u t p e r p e n d i c u l a r t o t h e l o n g a x i s of t h e g r a i n s f r o m t h e c e n t e r of a d e f o r m e d t e s t p i e c e . S i n c e t h e r e i s a s l i g h t c h a n g e i n o r i e n t a t i o n a t t h e p l a n e of k i n k i n g , t h e kink b a n d s show u p v e r y c l e a r l y u n d e r p o l a r i z e d l i g h t , a s m a y b e s e e n i n F i g . 5. H i g u c h i ' s F i g . 5 . Thin s e c t i o n s p e r p e n - d i c u l a r ( a ) and p a r a l l e l (b) t o t h e l o n g a x i s of c o l u m n a r g r a i n e d i c e d e f o r m e d about 6 % by a c o m p r e s s i v e load of 9 k g / c m 2 . Note e v i d e n c e of kink b a n d f o r m a t i o n i n s e c t i o n p e r p e n d i c u l a r t o t h e l o n g a x i s of t h e g r a i n s .

technique w a s u s e d t o show t h a t t h e b o u n d a r i e s of the b a n d s a r e a p p r o x i m a t e l y p e r p e n d i c u l a r to t h e b a s a l plane.

In F i g . 5 i t may b e s e e n t h a t i n s o m e c a s e s t h e kink band fea- t u r e s a r e continuous and c a n b e t r a c e d through a n u m b e r of g r a i n s , c l e a r l y d e m o n s t r a t i n g how t h e m o d e of d e f o r m a t i o n of one g r a i n c a n b e s t r o n g l y influenced by t h a t of i t s n e i g h b o r .

In s o m e g r a i n s , t h e bending m o m e n t w a s not r e l i e v e d by t h e f o r m a t i o n of s m a l l - a n g l e b o u n d a r i e s o r kink bands. In t h e s e c a s e s t h e s l i p plane developed a m a r k e d c u r v a t u r e , t h e r e g i o n of c u r v a t u r e o f t e n having a rough a p p e a r a n c e , with n u m e r o u s s h o r t l i n e f e a t u r e s p e r p e n d i c u l a r to the c u r v e d s l i p l i n e s . E x - a m p l e s of c u r v e d s l i p l i n e s and s h o r t l i n e f e a t u r e s c a n b e s e e n i n F i g s . 2 , 3b, and 6. The s h o r t l i n e s a p p e a r t o be s h o r t s m a l l - angle b o u n d a r i e s . D i s t o r t i o n of G r a i n B o u n d a r i e s A s t h e d e f o r m a t i o n i n c r e a s e d , t h e b o u n d a r i e s of m o s t g r a i n s b e c a m e s e v e r e l y d i s t o r t e d . E x a m p l e s of t h i s a r e shown i n F i g s . 4b and 6a and b. S e v e r e d i s t o r t i o n of t h e g r a i n boundary r e g i o n s h a s b e e n c o n s i d e r e d evidence of f r a g m e n t a t i o n . S u i t e r and Wood (19) and R a m s e y (20) c o n s i d e r e d t h a t t h e continuous background t h a t t h e y o b s e r v e d i n t h e i r X r a y s of d e f o r m e d m a g n e s i u m a n d and z i n c , r e s p e c t i v e l y , w a s due to s u c h d e b r i s . The u p p e r and l o w e r b o u n d a r i e s of the c e n t r a l g r a i n in F i g . 6 a do a p p e a r t o be i n a f r a g m e n t e d condition. Fig. 6 . E x a m p l e s of g r a i n - boundary d i s t o r t i o n . ( a ) P h o t o g r a p h t a k e n 30 h o u r s and 45 m i n u t e s a f t e r appli- cation of l o a d of 9 k g / c r n 2 . (b) p h o t o g r a p h t a k e n 33 h o u r s and 45 m i n u t e s a f t e r application of load of 9 k g / c m 2 .

C l o s e examination of s o m e d e f o r m e d b o u n d a r i e s i n the k e r o - sene e x p e r i m e n t s showed c e l l f o r m a t i o n by the orthogonal s y s - t e m of s l l p l i n e s and s u b b o u n d a r i e s with subsequent r e l a t i v e r o - t a t i o n . At s o m e s i t e s the s l i p p l a n e s o n two a d j a c e n t g r a i n s w e r e s o o r i e n t a t e d t h a t the boundary developed s t e p s and had the a p p e a r a n c e of a s t a i r c a s e . At o t h e r s i t e s , the c o n s t r a i n t s a t the boundary w e r e s u c h that s m a l l c r a c k s developed. Some b o u n d a r i e s had a n a r r o w r e g i o n t h a t a p p e a r e d to b e highly d i s - t u r b e d ( F i g . 6 ) . F o r the t e m p e r a t u r e , d e f o r m a t i o n r a t e s , and d u r a t i o n of load u s e d i n the e x p e r i m e n t s , the s l i p p l a n e s and s u b b o u n d a r i e s o b s e r v e d r e t a i n e d t h e i r identity d u r i n g d e f o r m a - tion. No s u r f a c e e v i d e n c e of r e c r y s t a l l i z a t i o n was o b s e r v e d .

C r a c k F o r m a t i o n

One of the i n t e r e s t i n g d e f o r m a t i o n f e a t u r e s o b s e r v e d was t h a t of c r a c k f o r m a t i o n . E a r l i e r w o r k h a d shown t h a t f o r the i c e s t r u c t u r e s y m m e t r y , t e m p e r a t u r e , a n d load g e o m e t r y u s e d , t h e s e c r a c k s c a n be e i t h e r i n t e r c r y s t a l l i n e o r t r a n s c r y s t a l l i n e ; they p r o p a g a t e i n the d i r e c t i o n of t h e long a x i s of t h e g r a i n ; and t h e i r plane t e n d s to b e p a r a l l e l to the d i r e c t i o n of s t r e s s ( 8 ) . Subsequent o b s e r v a t i o n s have shown t h a t the t i m e to f o r m a t i o n of the f i r s t c r a c k s h a s a n a p p r o x i m a t e l o g a r i t h m i c dependence upon t h e applied s t r e s s ; t h a t c r a c k f o r m a t i o n i s r a r e during the p r i m a r y c r e e p s t a g e f o r s t r e s s e s below about

6

k g / c m 2 ; and t h a t the t r a n s c r y s t a l l i n e c r a c k s tend to b e e i t h e r p a r a l l e l o r p e r - pendicular to the b a s a l plane.

Many i n v e s t i g a t o r s now c o n s i d e r t h a t for a l l c a s e s w h e r e c r a c k f o r m a t i o n i s t i m e dependent a s well a s s t r e s s d e p e n d e n t , t h e c r a c k s n u c l e a t e a t s i t e s w h e r e the moving d i s l o c a t i o n s a s s o c i a t e d with the c r e e p p r o c e s s a r e blocked. At t h e s e s i t e s the s t r e s s r e s u l t i n g f r o m blocked d i s l o c a t i o n s i n c r e a s e s until i t e x c e e d s the l o c a l s t r e n g t h of the m a t e r i a l . S i n c e the m o v e m e n t of d i s - l o c a t i o n s i s along p r e f e r r e d p l a n e s i n the c r y s t a l , i t i s to be ex- pected that c r a c k f o r m a t i o n will be r e l a t e d t o c r y s t a l l o g r a p h i c o r i e n t a t i o n , T h e r e i s now c o n s i d e r a b l e e x p e r i m e n t a l evidence supporting t h i s h y p o t h e s i s . An e x c e l l e n t r e v i e w of c u r r e n t think- lng on c r a c k f o r m a t i o n c a n b e found i n the P r o c e e d i n g s of t h e I n t e r n a t i o n a l C o n f e r e n c e o n F r a c t u r e held i n S w a m p s c o t t , M a s s a - c h u s e t t s (2 1 ) .

In the e x p e r i m e n t s w h e r e load w a s applied only long enough for about 10 c r a c k s to f o r m , and t h e n the i c e s e c t i o n e d and the c r y s t a l l o g r a p h i c o r i e n t a t i o n of the g r a i n s d e t e r m i n e d by the technique of Higuchi, 132 c r a c k s w e r e studied. Sixty- s e v e n

qc

of the c r a c k s w e r e t r a n s c r y s t a l l i n e a n d the r e m a i n d e r i n t e r - c r y s t a l l i n e . The s u r f a c e t r a c e of 3170 of the c r a c k s was ob-

s e r v e d to be p a r a l l e l to t h e s u r f a c e t r a c e of t h e b a s a l p l a n e ; that of 15% was p e r p e n d i c u l a r to t h e t r a c e of the b a s a l plane; t h a t of

9% was e i t h e r p e r p e n d i c u l a r o r p a r a l l e l ; t h a t of 12% was n e i t h e r .

F i g u r e 7 a i s a n e x a m p l e of a c r a c k whose s u r f a c e t r a c e i s p a r a l l e l to the b a s a l plane.

F i g . 7. C r a c k s d u r i n g d e f o r m a t i o n . ( a ) E x a m p l e of c r a c k whose s u r f a c e t r a c e i s p a r a l l e l to t h e b a s a l plane. The e t c h p i t s w e r e f o r m e d using t h e technique of Higuchi. (b) E x a m p l e of t r a n s c r y s t a l l i n e c r a c k f o r m a t i o n o b s e r v e d

6

1/2 h o u r s a f t e r t h e a p p l i c a t i o n of a c o m p r e s s i v e load

of 9 k g / c m 2 . D i r e c t i o n of load p a r a l l e l to long edge of

photograph. ( c ) S a m e s i t e a s F i g . 7b, 45 h o u r s l a t e r . I n s e r t A l o c a t e s a r e a shown i n F i g . 7b. ( d ) C r a c k i n - volving a c o m b i n a t i o n of g r a i n s and g r a i n b o u n d a r i e s . C o m p r e s s i v e s t r e s s p a r a l l e l to t h e long d i m e n s i o n of t h e photograph. In t h e k e r o s e n e e x p e r i m e n t s i t w a s p o s s i b l e t o o b s e r v e t h e c r a c k s d u r i n g d e f o r m a t i o n . F i g u r e 7b i s a n e x a m p l e of a c r a c k involving two g r a i n s . In one i t i s p a r a l l e l to t h e b a s a l p l a n e and i n t h e s e c o n d , p e r p e n d i c u l a r . F i g u r e 7c i s t h e s a m e c r a c k 45

h o u r s l a t e r . Note t h e s u b b o u n d a r i e s t h a t h a v e f o r m e d i n a s - s o c i a t i o n with t h e d e f o r m a t i o n . Note a l s o t h a t although the c r a c k h a s opened c o n s i d e r a b l y , l i t t l e if any g r a i n - b o u n d a r y s l i d i n g h a s

o c c u r r e d . A c c o m m o d a t i o n b e t w e e n g r a i n s i s a s s o c i a t e d r a t h e r with s l i p a l o n g b a s a l p l a n e s and g r a i n - b o u n d a r y m i g r a t i o n . Fig- u r e 7 c i s a good e x a m p l e of how t h e i n i t i a l d e p e n d e n c e of c r a c k f o r m a t i o n o n c r y s t a l l o g r a p h i c o r i e n t a t i o n c a n b e m a s k e d by the d e f o r m a t i o n .

Many c r a c k s involved only o n e g r a i n . In t h e s e c a s e s one e d g e of t h e c r a c k would o f t e n be a t t h e g r a i n b o u n d a r y . If the c r a c k involved m o r e t h a n one g r a i n , i t would u s u a l l y c h a n g e d i r e c t i o n a b r u p t l y a t t h e g r a i n b o u n d a r y s o a s to be e i t h e r p a r a l l e l o r p e r - p e n d i c u l a r t o t h e b a s a l p l a n e . If t h e c r a c k w a s not e i t h e r p a r a l - l e l o r p e r p e n d i c u l a r to t h e b a s a l p l a n e , i t tended n o t to p r o p a g a t e v e r y f a r i n t o t h a t g r a i n a n d w a s u s u a l l y i r r e g u l a r , s o m e t i m e s showing a t e n d e n c y t o c u r v e i n t o t h e b a s a l p l a n e . In s o m e c a s e s t h e c r a c k g e o m e t r y w a s q u i t e c o m p l e x , involv- ing a n u m b e r of g r a i n s . F o r e v e n t h e s e c a s e s , a d e p e n d e n c e of c r a c k f o r m a t i o n o n c r y s t a l l o g r a p h i c o r i e n t a t i o n c a n b e o b s e r v e d f o r m o s t of t h e g r a i n s involved. An e x a m p l e i s s h o w n i n F i g . 7d, w h e r e t h e c r a c k h a s p r o p a g a t e d a l o n g t h e g r a i n b o u n d a r y and i n t o t h r e e n e i g h b o r i n g g r a i n s . In one c a s e t h e c r a c k i s p e r - p e n d i c u l a r to t h e b a s a l p l a n e , i n a s e c o n d , p a r a l l e l . In a l l t h e p h o t o g r a p h s shown i n F i g . 7, t h e c r a c k i s viewed a p p r o x i m a t e l y p a r a l l e l to i t s plane and n o r m a l to t h e s h o r t d i r e c t i o n . C a v i t i e s A d e f o r m a t i o n f e a t u r e t h a t h a s r e c e i v e d a t t e n t i o n l a t e l y i s t h e f o r m a t i o n of i n t e r n a l c a v i t i e s ( 2 2 , 2 3 ) . T h e s e c a v i t i e s a r e u s u a l l y o b s e r v e d a t g r a i n b o u n d a r i e s o r a t t h e i n t e r s e c t i o n of s l i p p l a n e s o r s l i p p l a n e s and s u b b o u n d a r i e s of m e t a l s d e f o r m e d i n t e n s i o n . One p o s s i b l e m e c h a n i s m of t h e i r f o r m a t i o n i s con- s i d e r e d to b e t h e c o a l e s c e n c e of m i c r o s c o p i c h o l e s e i t h e r i n t h e m a t e r i a l to b e g i n with o r g e n e r a t e d d u r i n g c r e e p . T h e r e i s e v i - d e n c e t h a t c a v i t i e s c a n s e r v e a s n u c l e i f r o m which c r a c k s c a n develop. C a v i t i e s w e r e e a s i l y v i s i b l e a t a m a g n i f i c a t i o n of about 10

-

X b e f o r e t h e c r e e p s t r a i n h a s ex- c e e d e d 3% u n d e r a c o m p r e s s i v e load of a b o u t 8 k g / c m 2 . The c a v i t i e s w e r e i n t h e r e g i o n of g r a i n b o u n d a r i e s , g r a i n - bound- a r y t r i p l e p o i n t s , a n d t h e i n t e r - s e c t i o n of s l i p p l a n e s and s u b - b o u n d a r i e s . S o m e t i m e s c a v i t y f o r m a t i o n w a s g r e a t enough t o f o r m a c o n t i n u o u s c o l u m n . S u c h F i g . 8. C a v i t y f o r m a t i o n i n a c o l u m n , with c a v i t i e s i n t h e m u l t i g r a i n e d i c e . _{b a c k g r o u n d i s s h o w n in Fig. 8.}

R e c o v e r y a n d R e c r y s t a l l i z a t i o n Although t h e r e w a s no s u r f a c e e v i d e n c e of r e c r y s t a l l i z a t i o n d u r i n g d e f o r m a t i o n f o r the t e m p e r a t u r e , c r e e p r a t e s , a n d p e r i o d s o f l o a d i n g u s e d i n t h e e x p e r i m e n t s , e v i d e n c e of r e c o v e r y a n d r e - c r y s t a l l i z a t i o n w a s o b s e r v e d t o o c c u r a t t h e s u r f a c e and i n t e r n a l l y a f t e r t h e load h a d b e e n r e m o v e d . F i g u r e 9 s h o w s f o r t h e s a m e r e g i o n shown i n F i g . 3 t h e g r a i n - b o u n d a r y r e a r r a n g e m e n t t h a t o c c u r r e d a f t e r tho l o a d h a d b e e n r e m o v e d . Note t h e i r r e g u l a r F i g . 9 . R e c r y s t a l l i z a t i o n and poly- g o n i z a t i o n a t t h e s a m e s i t e a s i n F i g . 3. T h e r e a r r a n g e m e n t of g r a i n bound- a r i e s o c c u r r e d a f t e r t h e load h a d b e e n r e m o v e d ( t o t a l d e f o r m a t i o n a b o u t 2 . 5 7 0 ) . g r a i n b o u n d a r i e s a n d p o l y g o n i z a t i o n a s s o c i a t e d with t h e s e i r - r e g u l a r i t i e s ; note a l s o t h e s u b b o u n d a r y t h a t t e r m i n a t e s a t a s l i p p l a n e f e a t u r e i n t h e g r a i n i n t h e l o w e r l e f t - h a n d c o r n e r . T h e i c e w a s e t c h e d by i m m e r s i n g i n k e r o s e n e . T h i n s e c t i o n s c u t f r o m i c e d e f o r m e d 70 o r m o r e h o u r s u n d e r l o a d s b e t w e e n 5 a n d 10 k g / c m z showed e x t e n s i v e r e c r y s t a l l i z a - t i o n . T h i s m a y b e s e e n by c o m p a r i n g F i g s . 1 and 5. T h e thin s e c t i o n s c u t p a r a l l e l to t h e long a x i s of t h e g r a i n s show c l e a r l y a t e n d e n c y f o r t h e c o l u m n a r s t r u c t u r e to b e t r a n s f o r m e d i n t o a g r a n u l a r o n e . F i g u r e 5 s h o w s a l s o t h a t r e c r y s t a l l i z a t i o n a p p e a r s t o b e p r i m a r i l y a s s o c i a t e d with t h e g r a i n - b o u n d a r y r e g i o n . No e v i d e n c e w a s o b t a i n e d t o s h o w t h a t r e c r y s t a l l i z a t i o n o c c u r r e d d u r i n g o r a f t e r d e f o r m a t i o n . It i s quite p o s s i b l e t h a t t h e e v i d e n c e f o r r e c r y s t a l l i z a t i o n b e a r s t h e s a m e r e l a t i o n s h i p t o c o n d i t i o n s d u r i n g d e f o r m a t i o n a s F i g . 9 d o e s to F i g . 3. U n u s u a l C r e e ~ B e h a v i o r Gold o b s e r v e d t h a t f o r t h e i c e a n d c o n d i t i o n s of l o a d i n g u s e d i n c o m p r e s s i v e c r e e p e x p e r i m e n t s a n i n i t i a l i n c r e a s i n g c r e e p r a t e with t i m e w a s s o m e t i m e s o b s e r v e d ( 8 ) . T h i s o b s e r v a t i o n h a s b e e n c o n f i r m e d by s u b s e q u e n t e x p e r i m e n t s on c r e e p u n d e r c o m p r e s s i v e l o a d a n d by i n v e s t i g a t i o n s by K r a u s z ( T h e c r e e p of i c e i n bending. R e p o r t i n p r e p a r a t i o n ) , who h a s s t u d i e d s o m e

of t h e f e a t u r e s of t h i s b e h a v i o r m a n i f e s t i n t h e d e f o r m a t i o n of i c e b e a m s . S i m i l a r b e h a v i o r h a s b e e n r e p o r t e d f o r i c e s i n g l e c r y s t a l s ( 1 1 2 , 2 4 ) . F o r s i n g l e c r y s t a l s t h e e f f e c t e x t e n d s o v e r d e f o r - m a t i o n of s o m e 1 0 t o 20%; f o r m u l t i g r a i n e d i c e t h e e f f e c t i s a s - s o c i a t e d w i t h t h e p r i m a r y c r e e p s t a g e , and i s c o m p l e t e d b e f o r e d e f o r m a t i o n h a s e x c e e d e d 0.570 u n d e r t h e c o n d i t i o n s of l o a d i n g u s e d . T h e u n u s u a l b e h a v i o r i s i r r e v e r s i b l e . O n s u b s e q u e n t r e - l o a d i n g , t h e c r e e p c u r v e i s of t h e n o r m a l t y p e . W i t h r e p e a t e d l o a d i n g a n d a s s o c i a t e d d e f o r m a t i o n , t h e o b s e r v e d c r e e p c u r v e b e c o m e s m o r e r e p r o d u c i b l e a s long a s l o a d i n g c o n d i t i o n s a r e i d e n t i c a l a n d c e r t a i n r e s t r i c t i o n s a r e p l a c e d o n t h e r e c o v e r y t i m e . A n e x a m p l e of t h e u n u s u a l c r e e p b e h a v i o r a n d t h e c r e e p b e h a v i o r o b s e r v e d o n s u b s e q u e n t r e l o a d i n g i s s h o w n i n F i g . 10. I I I L O A D : 6 . 9 K G / C M '

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0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 T I M E , M I N F i g . 1 0 . U n u s u a l c r e e p b e h a v i o r of i c e . R e s ~ o n s e of a G r a i n t o a n Applied L o a d T a y l o r ( 2 5 ) h a s p o i n t e d out t h a t t h e d e f o r m a t i o n o f a c r y s t a l c a n b e c o m p l e t e l y d e t e r m i n e d by m e a s u r i n g t h e s t r a i n i n s i x i n d e p e n d e n t d i r e c t i o n s . If t h e v o l u m e r e m a i n s c o n s t a n t d u r i n g d e f o r m a t i o n , t h e s e r e d u c e t o f i v e . F r o m t h i s h e d e d u c e s t h a t a c r y s t a l c a n b e d e f o r m e d a t c o n s t a n t v o l u m e i n t o a n y a r b i t r a r y s h a p e a s l o n g a s s l i p c a n o c c u r i n f i v e i n d e p e n d e n t d i r e c t i o n s . It would be e x p e c t e d t h a t a n a g g r e g a t e of s u c h c r y s t a l s could b e d e f o r m e d a n d c o n t a c t m a i n t a i n e d b e t w e e n t h e c r y s t a l s without i n t r o d u c i n g m a j o r d i s o r d e r i n t h e b o u n d a r y r e g i o n s . If t h e n u m - b e r of o p e r a t i v e i n d e p e n d e n t s l i p d i r e c t i o n s i s l e s s t h a n f i v e , l o c a l s t r e s s e s t h a t o p p o s e the a p p l i e d s t r e s s w i l l d e v e l o p owing t o t h e c o n s t r a i n t s i m p o s e d b y n e i g h b o r s . T h e s e c o n s t r a i n t s a r e p r o b a b l y t h e m a i n s o u r c e of t h e i n c r e a s e i n t h e r e s i s t a n c e t o d e - f o r m a t i o n of a n a g g r e g a t e o v e r i t s c o n s t i t u e n t c r y s t a l s .

F o r t h e e x p e r i m e n t - s o n m u l t i g r a i n e d i c e d e s c r i b e d i n t h i s p a p e r , t h e l o a d w a s a p p l i e d p e r p e n d i c u l a r to t h e long a x i s of the g r a i n s . T h e r e w a s a s t r o n g p r e f e r e n c e f o r t h e b a s a l p l a n e s of t h e g r a i n s t o b e p a r a l l e l t o t h i s a x i s . T h i s r e s u l t e d i n d e f o r m a - t i o n t h a t w a s p r e d o m i n a n t l y t w o - d i m e n s i o n a l , t h e c r e e p i n t h e d i r e c t i o n of t h e l o n g a x i s of t h e g r a i n s b e i n g m u c h s m a l l e r t h a n t h a t p e r p e n d i c u l a r t o i t ( 8 ) . F o r t w o - d i m e n s i o n a l d e f o r m a t i o n of t h i s c h a r a c t e r , t h e r e q u i r e m e n t p o s t u l a t e d b y T a y l o r of f i v e i n d e p e n d e n t d i r e c t i o n s i n w h i c h s l i p c a n o c c u r i s r e d u c e d t o two, t h e s e b e i n g i n t h e p l a n e o f t h e d e f o r m a t i o n . I c e h a s o n l y o n e e f f e c t i v e s l i p p l a n e , a n d r e s i s t a n c e t o s l i p w i t h i n t h i s p l a n e i s i n d e p e n d e n t of d i r e c t i o n ( 1 1 , 1 2 , 2 6 ) . T h e r e i s , t h e r e f o r e , o n l y o n e s l i p d i r e c t i o n a v a i l a b l e t o e a c h c o l u m n a r g r a i n f o r t h e l o a d i n g c o n d i t i o n s u s e d . A s t h e i c e i s d e f o r m e d , t h e i n a b i l i t y of the g r a i n s t o c o n f o r m t o t h i s d e f o r m a t i o n m u s t r e s u l t i n l o c a l s t r e s s e s b e t w e e n g r a i n s . T h e d e f o r m a t i o n m e c h a - n i s m s t h a t h a v e b e e n d e s c r i b e d a r e the w a y s b y which a g r a i n r e s p o n d s to t h e s e l o c a l s t r e s s e s . T h e y r e p l a c e the s e c o n d in- d e p e n d e n t s l i p d i r e c t i o n t h a t a c o l u m n a r g r a i n r e q u i r e s to u n d e r - go a n a r b i t r a r y c h a n g e i n s h a p e i n t h e p l a n e p e r p e n d i c u l a r t o i t s long d i r e c t i o n . T h e f i r s t r e s p o n s e of i c e t o a n a p p l i e d s t r e s s i s a n e l a s t i c d e f o r m a t i o n t h a t a p p a r e n t l y i n v o l v e s t h e m o v e m e n t of d i s l o c a - t i o n s . E v i d e n c e f o r t h i s c a n b e found i n t h e o b s e r v a t i o n s of B r y a n t a n d M a s o n ( 2 7 ) a n d Gold ( 2 8 ) . T h i s i s followed by non- r e v e r s i b l e s l i p w i t h a s s o c i a t e d m o v e m e n t of d i s l o c a t i o n s , c r e a - t i o n of d i s l o c a t i o n g e n e r a t i n g s o u r c e s , a n d e s t a b l i s h m e n t of s l i p z o n e s o r b a n d s . T h e i m p e r f e c t i o n s p r e s e n t i n i t i a l l y i n t h e s t r u c - t u r e , o r g e n e r a t e d s u b s e q u e n t l y , w i l l m i g r a t e i n s u c h a d i r e c - t i o n a s t o r e d u c e t h e l o c a l s t r e s s e s d e v e l o p e d i n g r a i n s by t h e c o n s t r a i n i n g a c t i o n of n e i g h b o r s . In c a s e s w h e r e t h e a p p r o p r i a t e b e n d i n g m o m e n t i s e s t a b l i s h e d , s u b b o u n d a r i e s and k i n k b a n d s w i l l b e f o r m e d . If t h e d i s l o c a t i o n s a r e not a b s o r b e d a t t h e sub- b o u n d a r i e s a n d a r e not b l o c k e d i n t e r n a l l y , t h e y will m i g r a t e into t h e g r a i n - b o u n d a r y r e g i o n . O b s e r v a t i o n s i n d i c a t e t h a t s l i p a n d s u b b o u n d a r y , kink b a n d f o r m a t i o n o r b e n d i n g a r e s u f f i c i e n t to a l l o w t h e c e n t r a l p a r t of a g r a i n , but not t h e b o u n d a r y r e g i o n , to c o n f o r m t o t h e i m p o s e d d e f o r m a t i o n . T h e s o m e t i m e s e x t e n s i v e r e o r g a n i z a t i o n of t h e s t r u c t u r e t h a t o c c u r s i n t h i s r e g i o n s u g g e s t s t h a t m o s t of t h e a c c o m m o d a t i o n t h a t m u s t b e m a d e b e t w e e n g r a i n s d u r i n g d e f o r - m a t i o n t a k e s p l a c e h e r e . T h c f i r s t s i g n of t h i s r e o r g a n i z a t i o n i s e r a i n - b o u n d a r y m i g r a t i o n . T h e c o m b i n a t i o n of g r a i n - b o u n d a r y m i g r a t i o n a n d s l i p i s o f t e n s u f f i c i e n t i n i t i a l l y t o s a t i s f y t h e d e f o r - m a t i o n r e q u i r e m e n t s of s o m e b o u n d a r i e s f o r t h e i c e u s e d ( F i g . 3 ) . A s d e f o r m a t i o n i n c r e a s e s , g r e a t e r r e o r g a n i z a t i o n s u c h a s c e l l f o r m a t i o n i s r e q u i r e d . If t h e m a t e r i a l i n t h e b o u n d a r y r e g i o n

is t o u n d e r g o t h e r e q u i r e d r e l a t i v e t r a n s l a t i o n a n d r o t a t i o n with- o u t s t r u c t u r a l f a i l u r e ( c r a c k i n g ) , s u f f i c i e n t i m p e r f e c t i o n s s u c h a s d i s l o c a t i o n s m u s t b e a v a i l a b l e . If t h e r a t e a t w h i c h t h e s e i m p e r f e c t i o n s a r e m a d e a v a i l a b l e t o t h e r e g i o n i s n o t s u f f i c i e n t to a l l o w t h e l o c a l d e f o r m a t i o n t o c o n f o r m t o t h a t a p p l i e d , t h e l o c a l s t r e s s will i n c r e a s e , a n d m i c r o c r a c k s m a y f o r m . T h i s c r a c k i n g c a n p r o d u c e h i g h l y f r a g m e n t e d r e g i o n s ( F i g . 6 a ) . C a v i t i e s a r e a p a r t i c u l a r l y i n t e r e s t i n g f e a t u r e of d e f o r m a t i o n . T h e y p r o b a b l y f o r m i n p l a n e s t r a n s v e r s e t o l o c a l t e n s i l e s t r e s s e s e s t a b l i s h e d by t h e c o m p r e s s i v e l o a d . Although t h e y m a y a c t a s n u c l e i f r o m w h i c h c r a c k s c a n f o r m , no e v i d e n c e w a s o b t a i n e d t h a t s h o w e d t h a t t h i s w a s s o . T h e i r f o r m a t i o n a t t r i p l e p o i n t s a n d i n t e r s e c t i o n of g l i d e p l a n e s a n d s u b b o u n d a r i e s i s i n a g r e e - m e n t with a m e c h a n i s m s u g g e s t e d by G i f k i n s ( 2 9 ) . C a v i t y f o r - m a t i o n i s a m e c h a n i s m t h a t s h o u l d r e s u l t i n t h e r e d u c t i o n of l o c a l t e n s i l e s t r e s s e s . S o m e g r a i n s a r e s o o r i e n t e d t h a t t h e i r b a s a l p l a n e i s e i t h e r p a r a l l e l o r p e r p e n d i c u l a r t o t h e p r i n c i p a l s t r e s s e s a n d h a v e no o p e r a t i v e s l i p p l a n e . T h e s e g r a i n s m a y b e c o n s i d e r e d a s h a r d s i t e s w i t h i n t h e a g g r e g a t e . T h e i r n e i g h b o r s m u s t d e f o r m a r o u n d t h e m . U n d e r a c o m p r e s s i v e l o a d , m a t e r i a l w i l l t e n d t o flow a w a y f r o m a h a r d s i t e i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e a p p l i e d s t r e s s . A g r a i n w i t h i t s s l i p d i r e c t i o n e i t h e r p a r a l l e l o r p e r p e n d i c u l a r t o t h e a p p l i e d s t r e s s w i l l t h u s b e s u b j e c t to c o m p r e s s i o n i n t h e d i r e c t i o n of t h a t s t r e s s , a n d to t e n s i o n i n t h e p e r p e n d i c u l a r d i - r e c t i o n . It i s t o b e e x p e c t e d t h a t t h e t e n s i l e s t r e s s will t e n d to i n c r e a s e w i t h d e f o r m a t i o n . If t h e i n c r e a s e i s g r e a t e n o u g h , a c r a c k w i l l r e s u l t . T h e f o r m a t i o n of t h e c r a c k m a y b e a i d e d by t h e g r o w t h u n d e r t h e a p p l i e d s t r e s s of p o t e n t i a l c r a c k n u c l e a t i o n s i t e s s u c h a s c a v i t i e s . O n c e t h e c r a c k h a s f o r m e d , t h e g r a i n s a s s o c i a t e d with i t c a n m o r e e a s i l y c o n f o r m t o t h e a p p l i e d d e f o r - m a t i o n . B e c a u s e of t h e d i r e c t i o n of l o c a l t e n s i l e s t r e s s e s , t h e p l a n e of t h e c r a c k s t e n d s t o b e p a r a l l e l t o t h e a p p l i e d c o m p r e s - s i v e s t r e s s . It i s s i g n i f i c a n t t h a t t h e p l a n e a l s o t e n d s to be p a r a l - l e l o r p e r p e n d i c u l a r to t h e b a s a l p l a n e . It i s of i n t e r e s t t h a t t h e s e c r a c k s f o r m d u r i n g t h e p r i m a r y c r e e p s t a g e . F o r c r e e p u n d e r c o m p r e s s i o n t h e y a r e a s t a b l e m o d i f i c a t i o n of t h e s t r u c t u r e , e v e n f o r s e v e r e d e f o r m a t i o n s u c h a s i s s h o w n i n F i g . 7 b a n d c a n d c a n b e c o n s i d e r e d a s accommodation^' c r a c k s . T h e l o w e r t h e c r e e p r a t e , t h e f e w e r a r e t h e a c c o m m o d a t i o n c r a c k s t h a t f o r m a n d t h e l o n g e r i s t h e t i m e r e q u i r e d f o r the f i r s t t o d e v e l o p . F o r s p e c i m e n t e m p e r a t u r e of - 1 0 3 C a n d c r e e p r a t e s c o r r e s p o n d i n g to a n a p p l i e d s t r e s s of a b o u t 6 k g / c m 2 , s u c h c r a c k s a r e r a r e . T h i s s u g g e s t s t h a t p r o c e s s e s that go o n i n t h e b o u n d a r y r e g i o n , s u c h a s g r a i n - b o u n d a r y m i g r a t i o n , c e l l a n d c a v i t y f o r m a t i o n , i n a s s o c i a t i o n w i t h s l i p , c a v i t y , s u b -

b o u n d a r y , a n d k i n k band f o r m a t i o n , a r e a b l e t o m a i n t a i n t h e s t r e s s b e l o w t h e l o c a l f a i l u r e s t r e n g t h . U n d e r t h e s e c o n d i t i o n s c r a c k f o r m a t i o n i s no l o n g e r r e q u i r e d a s a d e f o r m a t i o n p r o c e s s i n t h e p r i m a r y a n d s e c o n d a r y c r e e p s t a g e . D e f o r m a t i o n M e c h a n i s m s a n d C r e e ~ B e h a v i o r P r a c t i c a l l y a l l t h e o b s e r v a t i o n s o n t h e d e f o r m a t i o n m e c h a n i s m s t h a t h a v e b e e n r e c o r d e d i n t h i s p a p e r w e r e m a d e d u r i n g t h e p r i - m a r y a n d s e c o n d a r y s t a g e s o f c r e e p . Only f o r e x p e r i m e n t s with h i g h e r l o a d s did t h e d e f o r m a t i o n i n c l u d e t h e t e r t i a r y s t a g e . In t h e s e c a s e s t h e o b s e r v a t i o n s w e r e only on t h e c h a r a c t e r of t h e c r a c k f o r m a t i o n t h a t o c c u r r e d . T h e d e f o r m a t i o n m e c h a n i s m s o b s e r v e d a r e i n g e n e r a l a g r e e - m e n t w i t h t h e s c h e m e p r o p o s e d by S h o u m s k y ( 7 ) . In a d d i t i o n to t h e m e c h a n i s m s t h a t h e d e s c r i b e s , o t h e r s s u c h a s k i n k b a n d and c a v i t y f o r m a t i o n , a n d a c c o m m o d a t i o n c r a c h n g w e r e o b s e r v e d . S h o u m s k y r e l a t e s t h e m e c h a n i s m s t o t h e a p p l i e d load a n d a s - s o c i a t e d c r e e p r a t e . E x p e r i m e n t s s u g g e s t t h a t f o r a g i v e n t e m - p e r a t u r e , c r e e p r a t e i s p r o b a b l y t h e m a j o r f a c t o r i n d e t e r m i n i n g w h a t m e c h a n i s m s a r e r e q u i r e d f o r a g r a i n t o c o n f o r m t o t h e ap- plied d e f o r m a t i o n . At l o w c r e e p r a t e s g r a i n - b o u n d a r y m i g r a t i o n , s u b b o u n d a r y , k i n k b a n d , a n d c a v i t y f o r m a t i o n , p o l y g o n i z a t i o n , a n d b e n d i n g a r e l i k e l y t o b e s u f f i c i e n t . F o r h i g h e r c r e e p r a t e s a c c o m m o d a t i o n c r a c k i n g d u r i n g t h e p r i m a r y c r e e p s t a g e a n d g r e a t e r d i s t o r t i o n i n t h e g r a i n b o u n d a r y r e g i o n o c c u r . In a d d i t i o n t o c r e e p r a t e , t h e a m o u n t of d e f o r m a t i o n a n d t h e d u r a t i o n of t h e l o a d a r e p r o b a b l y i m p o r t a n t a s w e l l . T h i s a p p e a r s t o b e t r u e f o r t h e u n u s u a l c r e e p b e h a v i o r a n d i s p r o b a b l y t r u e f o r t h e on- s e t of t e r t i a r y c r e e p a s i n d i c a t e d by t h e o b s e r v a t i o n s of S t e i n e m a n n ( 1 ) . Although t h e r e s i s t a n c e t o s l i p o n t h e b a s a l p l a n e of p r e v i o u s l y u n d e f o r m e d s i n g l e c r y s t a l s d e c r e a s e s with i n c r e a s i n g d e f o r m a - t i o n , t h i s i s not c o n s i d e r e d t o b e t h e s o u r c e of t h e u n u s u a l c r e e p b e h a v i o r o b s e r v e d i n m u l t i g r a i n e d i c e , e x c e p t p e r h a p s f o r t h e v e r y f i r s t p a r t of t h e d e f o r m a t i o n . T h i s v i e w i s s u p p o r t e d by t h e o b s e r v a t i o n t h a t r e s i s t a n c e t o d e f o r m a t i o n of t h e a g g r e g a t e i s m u c h h i g h e r t h a n t h e r e s i s t a n c e of t h e b a s a l p l a n e , a n d f o r t h e c o n d i t i o n s of t h e e x p e r i m e n t s , t h e u n u s u a l c r e e p b e h a v i o r i n t h e a g g r e g a t e i s c o m p l e t e d b e f o r e t h e s t r a i n h a s e x c e e d e d 0.570. F o r t h e s i n g l e c r y s t a l the u n u s u a l c r e e p b e h a v i o r e x t e n d s o v e r s o m e 10 t o 2070 s t r a i n . T h e i c e u s e d i n t h e e x p e r i m e n t s \(.as a l w a y s m a i n t a i n e d w i t h i n 1 0 ° C of i t s m e l t i n g t e m p e r a t u r e . It would b e e x p e c t e d t h a t a s long a s the p r e s s u r e i n t h e w a t e r \vas not a l l o w e d to i n c r e a s e while f r e e z i n g , t h e r e s h o u l d h a v e b e e n l i t t l e o r no d e f o r m a t i o n

of g r a i n s i n a s p e c i m e n p r i o r t o t h e f i r s t a p p l i c a t i o n of l o a d . T h e e x p e r i m e n t s s u g g e s t t h a t t h e u n u s u a l c r e e p b e h a v i o r of p r e v i o u s l y u n d e f o r m e d m u l t i g r a i n e d i c e i s r e l a t e d t o t h e v a r i e t y of w a y s b y which a g r a i n will a d j u s t to the d e f o r m a t i o n of i t s n e i g h b o r s . T h e s e w a y s a p p e a r t o b e e s t a b l i s h e d i n t h e p r i m a r y c r e e p s t a g e . T h e i r f o r m a t i o n i s a n i r r e v e r s i b l e p r o c e s s , d e t e r m i n e d b y t h e l o c a l c r y s t a l l o g r a p h i c o r i e n t a t i o n a n d g r a i n b o u n d a r y g e o m e t r y , t h e c h a r a c t e r of t h e a p p l i e d l o a d , t h e r a t e of s t r a i n i n g , and p r e s u m - a b l y , t h e t e m p e r a t u r e . If t h e w a y s by which a g r a i n will d e f o r m a r e e s t a b l i s h e d d u r i n g p r i m a r y c r e e p , t h i s s u g g e s t s t h a t t h e d e - f o r m a t i o n r a t e f o r s e c o n d a r y c r e e p m a y be d e t e r m i n e d by t h e r a t e a t which d i s l o c a t i o n s a n d o t h e r i m p e r f e c t i o n s g e n e r a t e d b y t h e a p p l i e d load w i l l d i f f u s e to t h e c e l l a n d g r a i n b o u n d a r i e s . S t e i n e m a n n ( 1 ) a n d G l e n ( 2 ) s u g g e s t t h a t t e r t i a r y c r e e p i s a s - s o c i a t e d with r e c r y s t a l l i z a t i o n . None of t h e e x p e r i m e n t s with l o w e r l o a d s w e r e c o n t i n u e d to d e f o r m a t i o n s w h e r e t h i s would b e o b s e r v e d . It w a s o n l y f o r l o a d s i n e x c e s s of a b o u t 15 k g / c m 2 t h a t t h e o b s e r v a t i o n s i n c l u d e d t h e t e r t i a r y s t a g e of c r e e p . F o r t h e s e t e s t s t h e a c c o m m o d a t i o n c r a c k i n g w a s v e r y e x t e n s i v e . On- s e t of t e r t i a r y c r e e p a p p e a r e d t o b e a s s o c i a t e d with t h e b r e a k - down of t h e s t r u c t u r e by t h e a c c o m m o d a t i o n c r a c k i n g and s u b - s e q u e n t f a i l u r e a l o n g p l a n e s a p p r o x i m a t e l y p a r a l l e l t o t h e m a x i - m u m s h e a r d i r e c t i o n ( 8 ) . C r a c k i n g of a c h a r a c t e r d i f f e r e n t f r o m t h e a c c o m m o d a t i o n c r a c k i n g w a s a s s o c i a t e d with t h e s e p l a n e s . A p p l i c a t i o n t o I c e E n g i n e e r i n g

Although t h e i c e u s e d i n the e x p e r i m e n t d e s c r i b e d had a u n i q u e g r a i n s t r u c t u r e a n d g r a i n c r y s t a l l o g r a p h i c o r i e n t a t i o n , i t i s p o s - s i b l e t o p r e s e n t s o m e g e n e r a l i z a t i o n s p e r t i n e n t t o i c e e n g i n e e r - i n g . F o r s l i p t o o c c u r o n t h e b a s a l p l a n e s of i c e t h e r e m u s t b e a s h e a r s t r e s s i n t h a t p l a n e . On a p p l i c a t i o n of a l o a d s u c h a s t r e s s w i l l b e p r e s e n t i n i t i a l l y i n m o s t g r a i n s , b u t i t will b e m a i n t a i n e d o n l y f o r t h o s e c a s e s w h e r e t h e l o a d s u b j e c t s the i c e t o a s h e a r s t r e s s . T h e r e a r e a n u m b e r of p r a c t i c a l e x a m p l e s of l o a d i n g w h e r e i t i s q u i t e p o s s i b l e t h a t t h e b a s a l p l a n e s a r e not s u b j e c t t o s u c h a s h e a r s t r e s s . F o r e x a m p l e , w h e n a n i c e c o v e r o n a l a k e o r r i v e r i s s u b j e c t t o a c h a n g i n g a i r t e m p e r a t u r e , t h e p r i n c i p a l t h e r m a l s t r e s s e s t h a t d e v e l o p a r e e q u a l i n t h e p l a n e p a r a l l e l t o t h e s u r f a c e . T h i s i s t r u e a s w e l l f o r a s t a t i o n a r y c o n c e n t r a t e d l o a d , a n d to a f i r s t a p p r o x i m a t i o n f o r s l o w l y m o v i n g l o a d s . If t h e b a s a l p l a n e s of t h e g r a i n s a r e p a r a l l e l o r p e r p e n d i c u l a r t o t h e i c e s u r f a c e , a s i t u a t i o n t h a t c a n o c c u r u n d e r s o m e f i e l d c o n d i t i o n s , t h e s h e a r s t r e s s o n t h e m w i l l be z e r o . T h i s would e x p l a i n why t h e r m a l l y s t r e s s e d i c e c o v e r s c a n r e m a i n s t r e s s e d f o r q u i t e a p p r e c i a b l e