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Deformation mechanisms in ice

Gold, L. W.

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Ice and Snow, Proceedings of a Conference held February 12-16, 1962, pp. 8-27,
1963-08-01

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Ser
TH1
N21r2
no. 193
c. 2

BLDG NATIONAL
RESEARCHCOUNCIL
CANADA

DIVISION O F BUILDING RESEARCH

DEFORMATION MECHANISMS IN ICE

BY

L. W. GOLD

R E P R I N T E D BY PERMISSION FROM ICE 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. PRESS, MASSACHUSETTS, INSTITUTE O F TECHNOLOGY.

RESEARCH PAPER NO. 193

OF THE
DIVISION O F BUILDING RESEARCH

BL!IL!?II\-i<; R!ISL~LlRCH
1 !-" - ",.
7
1 %\(

i
SEF- 5 i963
OTTAWA
1 NATlljS;\L i:15i;:;ii: COUNCIL
PRICE 2 5 CENTS AUGUST 196- -.-,
 T h i s publication i s being 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 of the National 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 the 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 Division of Building R e s e a r c h m a y

b e obtained 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 Bank,
E x p r e s s , o r P o s t Office Msney O r d e r o r a c h e q u e m a d e p a y -
able a t p a r in Ottawa, to the R e c e i v e r G e n e r a l of Canada,
c r e d i t National R e s e a r c h Council) to the National R e s e a r c h
Council, Ottawa. S t a m p s a r e not acceptable.

A coupon s y s t e m has been i n t r o d u c e d to m a k e pay-

m e n t s for publications 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 -
able i n denominations of 5, 2 5 and 50 c e n t s , and m a y be ob-
tained 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 National R e s e a r c h
Council p ~ b l i c a t i o n sincluding s p e c i f i c a t i o n s of the Canadian
Government Specifications B o a r d .
 Chapter 2

DEFORMATION MECHANISMS IN ICE*

L. W . Gold

Numerous o b s e r v a t i o n s on 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 recent 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 determining
the dependence of the steady- s t a t e c r e e p r a t e i n the secondary
c r e e p s t a g e to the constant applied load. Some i n v e s t i g a t o r s '
have considered 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 -
lation 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 ac-
c e l e r a t i o n that o c c u r s i n the t e r t i a r y stage to r e c r y s t a l l i z a t i o n
( 2 , 5); and Steinemann h a s shown that r e c r y s t a l l i z a t i o n will t a k e
place i n thin s e c t i o n s of g r a n u l a r i c e that h a s b e e n strained m o r e
than 2%. It h a s b e e n r e p o r t e d that the a v e r a g e g r a i n s i z e of i c e
that h a s been 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 before the load was 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 those m a d e on m e t a l s deformed a t high 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 deformation and
a s s o c i a t e s each m e c h a n i s m with the applied load and accompany-
ing c r e e p r a t e ( 7 ) . The f i r s t four m e c h a n i s m s , which become
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 single c r y s t a l ; slight 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 growth,
and grain-boundary 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 accompanied by reduction i n g r a i n s i z e and 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 higher 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 planes and p e r h a p s melting 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
subject to a constant c o m p r e s s i v e l o a d , s o m e information 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 that o c c u r r e d . It i s
the p u r p o s e of t h i s paper to d e s c r i b e these 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 that have been 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 significance with r e s p e c t to the

Xc T h i s paper i s a contribution f r o m the Division of Building

R e s e a r c h of the National R e s e a r c h Council of Canada 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 behavior 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 contains 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 applied load and t h e r o l e t h a t the deformation 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 section. Finally, 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 engineering
problems a r e presented.

Description of Ice and E x p e r i m e n t s

The i c e used 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

water i n a galvanized tank 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 deep. Two balloons w e r e placed u n d e r a weighted p l a t -
f o r m a t the bottom of the t a n k and filled with a i r . T h i s a i r was
maintained a t a constant p r e s s u r e by connecting the balloons to
a tube s u b m e r g e d i n a column of ethylene glycol. 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 to c o v e r the s u r f a c e completely. As the 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
the column of glycol. 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 slight i n c r e a s e with t i m e be-
c a u s e the t e n s i o n i n the r u b b e r of the balloons d e c r e a s e d a s they
deflated.
A i r - f r e e i c e p l a t e s up to 6 i n c h e s t h i c k could be produced with-
out difficulty. B e c a u s e the 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 , the long a x i s of the g r a i n s being
p a r a l l e l to the 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 to the 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.

Fig. 1. T h i n s e c t i o n s cut n o r m a l
( a ) and 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 grained
ice.

It had b e e n hoped t h a t seeding 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 the 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 tendency 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 to the 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% had t h e i r c - a x i s b e t w e e n 85" and 9 0 " to the
growth d i r e c t i o n , 2970 h a d t h e i r c - a x i s between 7 5 " and 85" , and
the 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 the 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 in the p l a n e p e r p e n d i c u l a r
to the 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 slightly t a p e r e d , and the 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 the 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 technique 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 and
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 blocks of two s i z e s :
5-by- 1 0 - b y - 2 5 - c m and 2 . 5 - b y - 5 - b y - 1 5 - c m . The b l o c k s w e r e
cut s o t h a t the 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 . All the 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 upper 2 c e n t i m e t e r s con-
taining 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 tech-
nique had b e e n r e m o v e d .

Experiments

T h e a u t h o r h a s shown t h a t when a c o m p r e s s i v e s t r e s s i s ap-

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
multigrained i c e , the cracking activity that r e s u l t s depends on
the 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 di-
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 and a c o m p r e s s i v e load 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 to 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 out, with l o a d s b e t w e e n 5 and 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 to a s
the "kerosene experiments. 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 load w a s
applied to t h e 5-by- 1 0 - c m f a c e s of t h e 5-by- 10-by- 20- c m b l o c k s ,
just 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 sectioned p a r a l l e l to the 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 using H i g u c h i ' s technique ( 9 ) . Although
t h e s e e x p e r i m e n t s gave i n f o r m a t i o n o n the dependence of c r a c k
formation on crystallographic orientation, their primary pur-
p o s e w a s to i n v e s t i g a t e the dependence 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 the f i r s t c r a c k s .
In t h e second 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 gauge length of 15 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 units. The 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 on 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
the 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 the 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 out 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 that d e s c r i b e in d e t a i l the
o b s e r v a t i o n s of t h e dependence of c r a c k f o r m a t i o n on t i m e and
on 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 Bands

The 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 , the 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 the application of a load of
'about 5 . 5 k g / c m Z . At this t i m e t h e s t r a i n did not exceed 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.

Fig. 2. Evidence of s l i p
on p r i s m a t i c planes. Note
c r a c k a t t r i p l e point.

,Near 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 hexagonal sym-

m e t r y usually d e f o r m by s l i p on 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 ) , and Glen and P e r u t z (12) 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. Grain-boundary 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 application
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 application of the 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 that l i t t l e o r no evidence h a s b e e n found of s l i p on t h e

p r i s m a t i c planes. T h i s conclusion i s supported 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 ,
evidence 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 that
glide on 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-
ject to a load of about 8 k g / c m 2 . F i g u r e 2 shows one of t h e s e
s u r f a c e f e a t u r e s , photographed about 30 h o u r s a f t e r the applica-
tion of t h e load. Notice that t h i s f e a t u r e i s confined to the 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 and s l i p - l i n e
d i s t o r t i o n , suggesting 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 (13) f o r t h e o c c u r r e n c e
of s l i p on 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 . The second evidence
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 the load w a s r e m o v e d , on a face
p a r a l l e l t o the long a x i s of the g r a i n s . The second 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 the f i r s t , but t h e r e w a s
evidence 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 conditions
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 , that the s l i p l i n e s define t h e t r a c e of
the b a s a l plane a t the i c e s u r f a c e . The s l i p b a n d s c a n thus b e
used to d e t e r m i n e t h e plane containing 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 the a n g l e between t h i s d i r e c t i o n and the i c e
surface.
In F i g . 2 , only t h e f e a t u r e s r a i s e d above the i c e s u r f a c e a r e
c o n s i d e r e d evidence 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 -
sociated 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 and will
b e d i s c u s s e d f u r t h e r under subboundary formation.

Grain- Boundarv Migration

Grain-boundary 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 the grain-boundary configuration. An e x a m p l e of this i s shbwn
i n Fig. 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 photographs. The f i r s t evidence of boundary
movement was o b s e r v e d about 1/2 hour a f t e r t h e application of
the load, when the 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 etch i n s u c c e s s i v e positions
shows that m i g r a t i o n m u s t o c c u r quite rapidly, and that boundaries
r e m a i n stationary 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
the m i g r a t i o n of b o u n d a r i e s under s t r e s s (14).
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 the 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 that w e r e completely consumed
by t h e i r neighbors, 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
the kerosene experiments.

F i g . 4. Small- angle boundary.

( a ) 5 h o u r s a f t e r application
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 long
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 , 25
m i n u t e s a f t e r the application
of the load. Shadow i n u p p e r
right -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 shown
i n Fig. 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 had 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 to t h e s l i p b a n d s d u r i n g the
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 the 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 that 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 the
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 the 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 with a hexagonal 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 bending m o m e n t , t r a n s v e r s e
to the 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 -
mation a r e absorbed a t the small-angle boundaries separating the
bands. This c a u s e s a slight difference between the orientation
of t h e g r a i n s on e i t h e r s i d e of the 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 shown i n F i g . 4 , w h e r e t h e a p p l i e d load w a s
9 kg/cm2.
G e r v a i s a n d o t h e r s ( 18) h a v e shown t h a t i n high- p u r i t y a l u m i -
num t h e p l a n e of kinking b i s e c t s the 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 the kink b o u n d a r y , a n d t h a t the l i n e of i n t e r -
s e c t i o n of t h e lcink plane and 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
the 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 the 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 line
of i n t e r s e c t i o n would tend to be 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 . Subboundary 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 -
ably involve 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
the 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 , with p o l a r i z e d l i g h t ,
thin 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 long a x i s of t h e g r a i n s f r o m
the 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 . Since t h e r e i s a slight 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 kinking, 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. Higuchi' 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) to
the 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 long a x i s
of t h e g r a i n s .
technique was used t o show that t h e boundaries of the bands a r e
approximately perpendicular to the b a s a l plane.
In Fig. 5 i t may be s e e n t h a t i n s o m e c a s e s the kink band fea-
t u r e s a r e continuous and c a n be t r a c e d through a number 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 mode of deformation of one g r a i n
c a n b e strongly influenced by t h a t of i t s neighbor.
In s o m e g r a i n s , t h e bending moment was not relieved 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 , the r e g i o n
of c u r v a t u r e often 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 line f e a t u r e s perpendicular 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 line 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 boundaries.

Distortion of G r a i n B o u n d a r i e s

A s the 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 Figs.
4b and 6a and b. S e v e r e d i s t o r t i o n of the 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 . Suiter and Wood
(19) and R a m s e y (20) c o n s i d e r e d that the continuous background
that they 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 magnesium and
and z i n c , r e s p e c t i v e l y , was due to such d e b r i s . The upper and
l o w e r boundaries of the c e n t r a l g r a i n in Fig. 6 a do a p p e a r t o be
i n a fragmented 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 )
Photograph taken 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) photograph taken 33
h o u r s and 45 minutes a f t e r
application of load of
9 kg/cm2.
 Close examination of s o m e d e f o r m e d boundaries 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 sllplines and subboundaries with subsequent relative r o -
tation. At s o m e s i t e s the s l i p planes o n two a d j a c e n t g r a i n s
were s o orientated that 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
boundaries had a n a r r o w r e g i o n that a p p e a r e d to b e highly d i s -
turbed ( F i g . 6 ) . F o r the t e m p e r a t u r e , deformation r a t e s , and
duration of load u s e d in the e x p e r i m e n t s , the s l i p planes and
subboundaries o b s e r v e d retained t h e i r identity d u r i n g deforma-
tion. No s u r f a c e evidence of r e c r y s t a l l i z a t i o n was observed.

Crack Formation

One of the i n t e r e s t i n g deformation f e a t u r e s o b s e r v e d was that

of c r a c k formation. E a r l i e r work had shown that for 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 , and 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 propagate i n the d i r e c t i o n of the long a x i s of the grain; and
t h e i r plane tends 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 that the t i m e to formation
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 the applied s t r e s s ; that 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
that 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 where 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 dependent, the
c r a c k s nucleate a t s i t e s where 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 dislocations 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 . Since the m o v e m e n t of dis-
locations i s along p r e f e r r e d planes 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
orientation, 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 this hypothesis. An e x c e l l e n t review 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
International Conference on F r a c t u r e held i n Swampscott, 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 sectioned 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- seven 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 and 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 the s u r f a c e t r a c e of t h e b a s a l plane; that
of 15% was perpendicular to the t r a c e of the b a s a l plane; that of
9% was either perpendicular o r p a r a l l e l ; t h a t of 12% was neither.
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.

Fig. 7. C r a c k s during deformation. ( 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 the b a s a l plane. The
e t c h pits w e r e f o r m e d using t h e technique of Higuchi. (b)
Example 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 observed
6 1/2 h o u r s a f t e r the application 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 as Fig. 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 in-
volving a combination of g r a i n s and g r a i n boundaries.
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 the long d i m e n s i o n of the
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 possible t o o b s e r v e t h e
c r a c k s during deformation. F i g u r e 7b i s a n example 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 plane and
i n t h e second, 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 subboundaries that h a v e f o r m e d i n a s -
sociation with the deformation. 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 grain-boundary sliding h a s
o c c u r r e d . A c c o m m o d a t i o n between 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 along 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 dependence 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
deformation.
Many c r a c k s involved only one g r a i n . In t h e s e c a s e s one edge
of the c r a c k would often be a t t h e g r a i n boundary. If the c r a c k
involved m o r e than 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 the g r a i n boundary 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 the b a s a l plane. 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 not to p r o p a g a t e
v e r y f a r i n t o that g r a i n and 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 tendency t o c u r v e into t h e b a s a l plane.
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 quite 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 dependence of
c r a c k formation on crystallographic orientation c a n be observed
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 Fig.
7d, w h e r e t h e c r a c k h a s propagated along t h e g r a i n boundary
and into t h r e e neighboring 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
photographs 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 .

Cavities

A d e f o r m a t i o n f e a t u r e that 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 , 23). 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 the 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 begin 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 evi-
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 the 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 about 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 the i n t e r -
s e c t i o n of s l i p p l a n e s and sub-
boundaries. Sometimes cavity
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 continuous column. Such
F i g . 8. Cavity 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
multigrained ice. 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 and 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 evidence 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 , and p e r i o d s
o f loading u s e d i n t h e e x p e r i m e n t s , evidence 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 had 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 had 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 the 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 had 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 2.570).

g r a i n b o u n d a r i e s a n d polygonization 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 the g r a i n i n t h e l o w e r left-hand c o r n e r .
The 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 and 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 -
tion. 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 the 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 the 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 one. F i g u r e 5 s h o w s a l s o that 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 show 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 the evidence
for recrystallization b e a r s the s a m e relationship to conditions
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.

Unusual C r e e ~
Behavior

Gold o b s e r v e d t h a t f o r t h e i c e and c o n d i t i o n s of loading 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 initial increasing 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 load and 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 studied 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
ice beams.
Similar behavior h a s b e e n reported for i c e single c r y s t a l s
( 1 1 2 , 24). 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 effect i s a s -
s o c i a t e d with 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 loading
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 . On 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 type. With r e p e a t e d
loading 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 loading c o n d i t i o n s a r e
identical and c e r t a i n r e s t r i c t i o n s a r e placed o n the recovery
t i m e . An 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 the 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.

1i
I I I

LOAD 6 . 9 KG / CM'
:
'
0,4t 2 n d LOADING 2 4 UR AFTER FIRST

0 50 100 150 200 250 300

TIME, MIN

Fig. 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 eof 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 pointed out t h a t the 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 to 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 be deformed a t constant volume into any a r b i t r a r y
shape a s long a s s l i p c a n occur in five independent directions.
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 and c o n t a c t m a i n t a i n e d b e t w e e n the 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 the 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 will d e v e l o p owing
to 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 the 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 the experiment-s on multigrained i c e described i n this
p a p e r , the load w a s applied 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
the g r a i n s to b e p a r a l l e l to 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 -
tion 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 long a x i s of t h e g r a i n s being 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 to 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 which s l i p c a n o c c u r i s r e d u c e d to two,
t h e s e being i n the p l a n e of t h e d e f o r m a t i o n .
I c e h a s only o n e e f f e c t i v e s l i p p l a n e , and r e s i s t a n c e to s l i p
within 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 , only 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 to e a c h c o l u m n a r
g r a i n f o r the loading conditions u s e d . As the 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 to 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
result i n local s t r e s s e s between grains. The deformation mecha-
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 . They 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 applied 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 and M a s o n ( 2 7 ) and 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 with 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
zones o r bands. T h e imperfections p r e s e n t initially in the struc-
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 , will m i g r a t e i n s u c h a d i r e c -
tion 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 the a p p r o p r i a t e
bending 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 kink 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 and a r e not blocked i n t e r n a l l y , t h e y will m i g r a t e into
the grain-boundary region.
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 and 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 to 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
accommodation that must be m a d e between g r a i n s during defor-
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 often s u f f i c i e n t i n i t i a l l y to 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 and r o t a t i o n with-
out 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 available to t h e region is not sufficient
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
cracking c a n produce highly fragmented regions ( F i g . 6a).
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 .
They probably f o r m i n planes t r a n s v e r s e to local tensile 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 which 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 showed 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 points
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 Gifkins ( 2 9 ) . Cavity 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
local tensile s t r e s s e s .
Some g r a i n s a r e so oriented that t h e i r b a s a l plane i s either
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
operative s l i p plane. T h e s e g r a i n s m a y be considered a s h a r d
s i t e s within the 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
away 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 the a p p l i e d
stress.
A g r a i n with 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 di-
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 with 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 enough, a
c r a c k will 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
the 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 the c r a c k h a s f o r m e d , the 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 the 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
plane 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 the 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 during the p r i m a r y c r e e p stage. F o r c r e e p under
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
for s e v e r e deformation s u c h a s i s shown i n Fig. 7 b and c and
c a n b e c o n s i d e r e d a s accommodation^' c r a c k s .
The lower the c r e e p r a t e , the f e w e r a r e the accommodation
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 and 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 the 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 with s l i p , c a v i t y , s u b -
b o u n d a r y , and 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 below 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 the p r i m a r y and 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 the observations on the deformation m e c h a n i s m s

that h a v e been r e c o r d e d in this paper w e r e m a d e during the pri-
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 formation that occurred.
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 i n g e n e r a l a g r e e -
m e n t with the s c h e m e p r o p o s e d by Shoumsky ( 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
cavity formation, and accommodation 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 to t h e a p p l i e d load a n d a s -
sociated c r e e p r a t e . E x p e r i m e n t s suggest t h a t for a given tem-
p e r a t u r e , c r e e p r a t e i s probably the m a j o r f a c t o r in determining
what 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 to t h e ap-
plied d e f o r m a t i o n . At low 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 , kink b a n d , a n d c a v i t y f o r m a t i o n , polygonization,
a n d bending a r e l i k e l y to 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
accommodation cracking during the p r i m a r y c r e e p stage and
g r e a t e r d i s t o r t i o n i n the 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
to 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 and 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 well. T h i s a p p e a r s to 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 the 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 to s l i p on the b a s a l plane 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 to b e t h e s o u r c e of the u n u s u a l c r e e p
behavior observed i n multigrained ice, except perhaps for the
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 the r e s i s t a n c e of t h e b a s a l plane, and 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 the 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 to 2070 s t r a i n .
The 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 within
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 should 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 to 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 the 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 to 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
ways 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 the 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 and 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 the 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 the 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 that 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 and 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
the 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 and 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 Glen (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 the 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 continued 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 only 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 the a c c o m m o d a t i o n c r a c k i n g was 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 to b e a s s o c i a t e d with the 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 sub-
s e q u e n t f a i l u r e along 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 to 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 to 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 and 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 pos-
sible to present s o m e generalizations pertinent to i c e engineer-
ing. F o r s l i p to 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 such a
s t r e s s will 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 , but i t will b e
m a i n t a i n e d only 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
subject to such a s h e a r s t r e s s .
F o r e x a m p l e , when 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
to 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 plane 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 moving l o a d s . If t h e b a s a l planes of
the 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 to the 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 , the s h e a r
s t r e s s o n t h e m will 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 for quite appreciable
p e r i o d s of t ~ m e ,a n d will o f t e n c r a c k when d r i l l e d o r walked upon:
If t h e r m a l s t r e s s e s c a n b e m a i n t a i n e d f o r a p p r e c i a b l e p e r i o d s ,
t h e y c a n h a v e a v e r y s i g n i f i c a n t effect o n t h e b e a r i n g c a p a c i t y of
t h e i c e , p a r t i c u l a r l y f o r i c e t h i c k n e s s e s l e s s t h a n 5 0 c m . Many
of t h e i c e f a i l u r e s t h a t h a v e o c c u r r e d i n t h e n o r m a l o p e r a t i o n of
C a n a d i a n pulp and p a p e r c o m p a n i e s a r e thought to be t h e r e s u l t
of s t r e s s e s o r a s s o c i a t e d c r a c k s f o r m e d i n t h e c o v e r by changing
temperature.
C o n s i d e r a b l e a t t e n t i o n h a s b e e n given i n r e c e n t y e a r s t o v a r i o u s
l a b o r a t o r y a n d field t e s t s f o r d e t e r m i n i n g v a l u e s of t h e p r o p e r t i e s
of i c e r e q u i r e d f o r t h e s o l u t i o n of e n g i n e e r i n g p r o b l e m s . B e c a u s e
t h e d e f o r m a t i o n r e s p o n s e of i c e d e p e n d s o n t h e r e l a t i o n s h i p be-
t w e e n t h e a p p l i e d s t r e s s , t h e g r a i n - b o u n d a r y c o n f i g u r a t i o n 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 t h e g r a i n s , a s well a s t h e
m a g n i t u d e of t h e s t r e s s and t h e t e m p e r a t u r e , t h e r e i s c e r t a i n l y
s o m e q u e s t i o n a s to w h e t h e r n u m b e r s o b t a i n e d f r o m s u c h t e s t s
c a n b e u s e d f o r t h e s o l u t i o n of e n g i n e e r i n g p r o b l e m s involving
i c e u n d e r q u i t e d i f f e r e n t l o a d c o n d i t i o n s . It i s p o s s i b l e t h a t the
s o l u t i o n of s u c h p r o b l e m s will h a v e to b e o b t a i n e d f r o m d i r e c t
field o b s e r v a t i o n s , and t h a t t h e g r e a t e s t u s e f u l n e s s of l o a d t e s t s
w i l l b e t o i n d i c a t e t h e quality of t h e i c e i n v o l v e d .

Summary

P o l y c r y s t a l l i n e , c o l u m n a r g r a i n e d i c e , with the b a s a l p l a n e
of each g r a i n approximately p a r a l l e l to i t s long axis, cannot
d e f o r m u n d e r a n a p p l i e d l o a d without s t r e s s e s being s e t u p i n
t h e g r a i n s d u e to t h e c o n s t r a i n t s i m p o s e d by n e i g h b o r s . T h e s e
s t r e s s e s cause grain-boundary migration, subboundary, kink
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 k i n g . Along
with s l i p on t h e b a s a l p l a n e , t h e s e s t r e s s - i n d u c e d p r o c e s s e s allow
t h e g r a i n to c o n f o r m to t h e a p p l i e d d e f o r m a t i o n . The v a r i o u s
w a y s b y which a g r a i n will d e f o r m d u r i n g a l o a d t e s t a p p e a r to
be established in the p r i m a r y c r e e p stage. The experiments
i n d i c a t e t h a t d e f o r m a t i o n t h e r e a f t e r p r o c e e d s by r e l a t i v e t r a n s -
l a t i o n and by r o t a t i o n a b o u t t h e b o u n d a r i e s a n d a c c o m m o d a t i o n
c r a c k s established during p r i m a r y creep. This suggestion leads
t o t h e h y p o t h e s i s t h a t s e c o n d a r y c r e e p r a t e i s c o n t r o l l e d b y the
r a t e of diffusion of i m p e r f e c t i o n s g e n e r a t e d b y the a p p l i e d load.
T h e d e p e n d e n c e of the d e f o r m a t i o n of i c e o n t h e g r a i n - b o u n d a r y
c o n f i g u r a t i 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 n d the n a t u r e of
the a p p l i e d load s h o u l d b e t a k e n i n t o c o n s i d e r a t i o n i n s o m e en-
g i n e e r i n g p r o b l e m s , p a r t i c u l a r l y t h o s e i n which t h e r e m a y b e
no s h e a r s t r e s s o n t h e b a s a l p l a n e s . It s h o u l d a l s o b e c o n s i d e r e d
when applying r e s u l t s o b t a i n e d f r o m l a b o r a t o r y and f i e l d t e s t s
on i c e , particularly f r o m small- scale tests.
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