A STUDY OF CRACKS IN POLYCRYSTALLINE ICE UNDER UNIAXIAL COMPRESSION

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A STUDY OF CRACKS IN POLYCRYSTALLINE ICE UNDER UNIAXIAL COMPRESSION

S. Hallam, P. Duval, M. Ashby

To cite this version:

S. Hallam, P. Duval, M. Ashby. A STUDY OF CRACKS IN POLYCRYSTALLINE ICE UNDER UNIAXIAL COMPRESSION. Journal de Physique Colloques, 1987, 48 (C1), pp.C1-303-C1-311.

�10.1051/jphyscol:1987143�. �jpa-00226289�

A STUDY OF CRACKS I N POLYCRYSTALLINE ICE UNDER UNIAXIAL COMPRESSION

S.D. HALL AM'^), P. DUVAL and M.F. ASH BY(^)

CNRS, Laboratoire de Glaciologie et GBophysique de 1'Environ- nement, B.P. 96, F-38402 St-Martin-d'Heres Cedex, France

RESUHE - Des e s s a i s en compression u n i a x i a l e o n t b t b r b a l i s b s dans l e b u t d ' 6 t u d i e r l a n u c l b a t i o n e t l a p r o p a g a t i o n des f i s s u r e s en f o n c t i o n de l a d g f o r m a t i o n e t de d b t e r m i n e r l ' o r i e n t a t i o n , l a longueur, l a p o s i t i o n , e t l a d e n s i t b , de ces f i s s u r e s . La f o r m a t i o n de "wing c r a c k s " a pu S t r e observbe. Ceci i n d i q u e que pour des

c o n t r a i n t e s blevbes ( l o r s q u e l e s c a r a c t b r i s t i q u e s du comportement f r a g i l e dominent l a r u p t u r e ) l a p r o p a g a t i o n e t 1 ' i n t e r a c t i o n des f i s s u r e s peuvent condui r e .5 l a r u p t u r e . ABSTRACT - U n i a x i a l compression t e s t s were c a r r i e d o u t w i t h t h e aim o f s t u d y i n g c r a c k n u c l e a t i o n and e x t e n s i o n as a f u n c t i o n o f s t r a i n and o f measuring c r a c k o r i e n t a t i o n s , l e n g t h s , p o s i t i o n s and d e n s i t i e s . Some examples of c r a c k s w h i c h had extended t o f o r m

" w i n g c r a c k s " were seen. T h i s i s an i n d i c a t i o n t h a t a t h i g h e r s t r e s s l e v e l s (when b r i t t l e e f f e c t s dominate f a i l u r e ) c r a c k e x t e n s i o n and i n t e r a c t i o n may be t h e mechanism o f f a i l u r e .

1. INTRODUCTION

O i l r i g s and s t r u c t u r e s i n o f f s h o r e A r c t i c w a t e r s have t o be designed t o r e s i s t t h e f o r c e s e x e r t e d b y m o b i l e sea-ice. A t l o w i c e movement r a t e s t h e i c e deforms by a creep mechanism b u t a t h i g h e r speeds i t i s f r a c t u r e d and i t i s t h i s f r a c t u r e process w h i c h l i m i t s t h e u l t i m a t e l o a d t h a t t h e i c e can e x e r t [ l ] .

The u n d e r s t a n d i n g o f compressive h r i t t l e f r a c t u r e i s poor. I n i c e , t h e r e a r e two s t a g e s i n v o l v e d .

( i ) crack n u c l e a t i o n - on l o a d i n g , s t r e s s e s a r e s e t up w i t h i n t h e g r a i n s which cause c r a c k s w i t h a s i z e about equal t o one g r a i n f a c e t t o f o r m e i t h e r across t h e g r a i n ( t r a n s g r a n u l a r ) o r i n t h e ? r a i n horlndaries

( i n t e r g r a n u l a r ) .

( i i ) c r a c k p r o p o g a t i o n and l i n k a g e - shear s t r e s s e s on a n g l e d c r a c k s produce t e n s i l e s t r e s s e s a t t h e crack t i p s ( F i g . l a ) , w i n g c r a c k s ( F i g . l b ) can grow i n t o t h e s e r e g i o n s and grow p a r a l l e l t o t h e a p p l i e d compressive s t r e s s . The growth of w i n g c r a c k s i s s t a b l e and t h u s i n c r e a s i n g l o a d s a r e r e q u i r e d t o make them extend. F a i l u r e o c c u r s when a c r a c k extends t o f r e e s u r f a c e s o r when c r a c k s i n t e r a c t t o f o r m an i n s t a b i l i t y .

The second o f t h e s e has been t h e s u b j e c t of a r e c e n t i n v e s t i g a t i o n [ 2 ] . The c u r r e n t work was c a r r i e d o u t as p a r t o f t h i s s t u d y t o t r y and observe f l a w s w i t h w i n g c r a c k s and t o s t u d y a r e a l c r a c k p o p u l a t i o n i n terms o f c r a c k d e n s i t y , l e n g t h , p o s i t i o n s and, most i m ~ n r t a n t o f a l l , o r i e n t a t i o n s .

("BP petroleum Development Ltd., Britannic House. Moor Lane, GB-London ECZY 9BU. Great-Britain t 2 ) ~ e p a r t m e n t of Engineering. University of Cambridge. Trumpington Street. GB-Cambridge. CB2 1PZ.

Great-Britain

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987143

JOURNAL DE PHYSIQUE

Fig. 1 (a) Shear stresses cause tensile zones at tips of angled crack.

(b) Wing cracks grow into tensile zone and extend parallel to compressive stress.

C y l i n d r i c a l samples o f pure p o l y c r y s t a l l i n e i c e were loaded t o 3MPa a t -lO°C. A f t e r l o a d i n g t o d i f f e r e n t l e v e l s o f s t r a i n t h e samples were sectioned p a r a l l e l and perpendicular t o t h e l o a d i n g a x i s t o a l l o w a d e t a i l e d study o f t h e cracks t h a t formed. The cracks were observed t o form a t a s t r a i n as low as 0.07% and t o n u c j e a t e w i t h a maximum frequency a t 0.1% s t r a i n . The cracks were h i g h l y o r i e n t a t e d i n t h e v e r t i c a l plane, had a l e n g t h approximately equal t o one g r a i n facet, and were e q u a l l y l i k e l y $0 be t r a n s g r a n u l a r o r i n t e r g r a n u l a r . The crack d e n s i t y was measured t o be 0.14/mm i n a s e c t i o n o f i c e s t r a i n e d t o 0.44%. The r e s u l t s a r e i n general agreement w i t h t h e more extensive work o f Cole [3].

A few exampfes o f wing crack f o r m a t i o n were observed b u t damage i n i c e ( a t t h i s s t r e s s and temperature) i s mainly due t o t h e n u c l e a t i o n o f new g r a i n - s i z e d cracks, r a t h e r t h a n t h e propagation o f those which have already nucleated.

2. EXPERIMENTAL PROCEDURE

P r e p a r a t i o n o f Samples The technique used t o produce bubble-free p o l y c r y s t a l l i n e i c e w i t h randomly o r i e n t a t e d g r a i n s was developed from Le Gac [41. Pure d i s t i l l e d water was b o i l e d t o remove d i s s o l v e d gases, sealed, pumped down t o 0.1 t o r r , and cooled t o about - l ° C (supercooled

-

Supercooled Distilled De-aerated

Sections

Vertical Section

Fig. 2 Schematic diagram of ice sample preparation Fig. 3 Sectioning of ice sample

Fig,

JOURNAL DE PHYSIQUE

system was p l a c e d i n an a d j a c e n t c o l d room a t -18OC f o r 24 hours t o f r e e z e . T h i s produced a c a s t i n g w i t h a r e g u l a r g r a i n s i z e o f between 1 and 2 mm. The c a s t i n g s were t u r n e d on a l a t h e t o produce s o l i d c y l i n d r i c a l samples about 50 mm i n d i a m e t e r and up t o 130 mm i n l e n g t h , w i t h a c c u r a t e l y p a r a l l e l ends. F i n a l l y , t h e s u r f a c e s were p o l i s h e d w i t h e t h a n o l t o g i v e c o m p l e t e l y c l e a r , t r a n s p a r e n t samples.

Compression T e s t i n g The samples were f r o z e n t o t h e l o a d i n g p l a t e n s o f a s i m p l e l o a d - c o n t r o l l e d , l e v e r t y p e , compression c r e e p machine c o n t a i n e d i n a c o l d room a t -IO°C. They were l o a d e d i n i n c r e m e n t s o f 0.5 MPa a t i n t e r v a l s o f a p p r o x i m a t e l y one m i n u t e t o t h e maximum s t r e s s o f 3 MPa. The compressive s t r e s s o f 3 MPa was chosen

f o r t h e p r e s e n t experiments because t h e c r e e p e f f e c t s were as s m a l l as p o s s i b l e w i t h o u t r i s k i n g an immediate c a t a s t r o p h i c b r i t t l e f r a c t u r e . Creep displacement was measured u s i n g a l i n e a r v a r i a b l e d i f f e r e n t i a l t r a n s d u c e r mounted between t h e l o a d i n g p l a t e n s . Displacement - t i m e c u r v e s were r e c o r d e d r e m o t e l y on a c h a r t r e c o r d e r . One t e s t , number S2, was t a k e n t o a s t r a i n o f 1.4% and appeared t o be v e r y c l o s e t o f a i l u r e . Two o t h e r t e s t s , S9 and S12 were stopped a t l o w e r s t r a i n s o f 0.69% and 0.44% t o compare c r a c k d e n s i t i e s .

A s e r i e s of photographs was t a k e n d u r i n g t h e l o a d i n g t o r e c o r d t h e i n i t i a t i o n o f c r a c k s w i t h time. The samples were i l l u m i n a t e d f r o m t h e s i d e w i t h an i n t e n s e l i g h t source so t h a t l i g h t r e f l e c t e d f r o m t h e c r a c k s was r e c e i v e d by t h e camera. It was found t h a t i t was i m p o s s i b l e t o see and c o u n t e v e r y c r a c k which formed, e s p e c i a l l y when t h e c r a c k d e n s i t y was high.

Thin S e c t i o n P r e p a r a t i o n A f t e r u n l o a d i n g and removal . f r o m t h e p l a t e n s , t h e sample ( i n a c o l d room) was c u t i n t o t h r e e s e c t i o n s , t h e m i d d l e o f which was t h e n c u t i n a v e r t i c a l p l a n e ( t h a t i s p a r a l l e l t o t h e l o a d i n g a x i s ) (see Fig. 3). The a p p r o p r i a t e s u r f a c e was smoothed on a f i n e emery paper and t h e n pressed o n t o p l a t e s o f warmed glass. T h i s caused a t h i n l a y e r o f i c e t o m e l t and r e - f r e e z e making t h e i c e s t i c k t o t h e p l a t e . A s l i c e o f i c e about 5 mm t h i c k was t h e n c u t o f f w i t h a bandsaw, and t h i n n e d u s i n g a microtome. One v e r t i c a l and one h o r i z o n t a l s e c t i o n were reduced i n t h i c k n e s s t o about one h a l f t h e g r a i n s i z e ( o r about 0.5 mm).

The t h i n n e r s e c t i o n s were photographed u s i n g b o t h p o l a r i s e d and u n p o l a r i s e d t r a n s m i t t e d l i g h t . The photographs i n normal l i g h t showed t h e p a t t e r n o f cracks.

Those i n p o l a r i s e d l i g h t r e v e a l e d b o t h t h e c r a c k s and g r a i n s . W i t h b o t h s e t s o f photographs, i t was p o s s i b l e t o see and measure t h e p o s i t i o n s , l e n g t h s and

o r i e n t a t i o n s o f t h e c r a c k s . The numerical s t u d y was c o n f i n e d t o a c e n t r a l p o r t i o n o f 30 mm d i a m e t e r i n t h e h o r i z o n t a l s e c t i o n , and 30 mm square i n t h e v e r t i c a l s e c t i o n . The c r a c k o r i e n t a t i o n s were measured r e l a t i v e t o t h e l o a d i n g a x i s i n t h e v e r t i c a l s e c t i o n and r e l a t i v e t o an a r b i t r a r y a x i s i n t h e h o r i z o n t a l ( p e r p e n d i c u l a r t o t h e l o a d i n g a x i s ) s e c t i o n . I f a c r a c k was curved, i t s d i r e c t i o n was assumed t o be d e f i n e d by t h e l i n e j o i n i n g i t s t i p s .

The t h i c k e r , 2 mm, s e c t i o n s o f i c e were photographed i n normal t r a n s m i t t e d l i g h t t o i l l u s t r a t e t h e v e r y h i g h c r a c k d e n s i t y .

3, OBSERVATIONS

Compression L o a d i n g A t y p i c a l sequence o f photographs ( f r o m sample SZ), showing crack n u c l e a t i o n w i t h i n c r e a s i n g s t r a i n , i s shown i n Fig. 4. The l o a d i n g a x i s i s v e r t i c a l . The i c e samples were i n i t i a l l y t r a n s p a r e n t and a l m o s t t o t a l l y crack f r e e (4a) and remained c r a c k f r e e u n t i l a s t r a i n o f 0.06% (4b). A t a s t r a i n of 0.07%

crack n u c l e a t i o n s t a r t e d (4c) and t h e r a t e o f c r a c k n u c l e a t i o n i n c r e a s e d t o a maximum (judged b o t h by c r a c k c o u n t i n g and by sound) a t a s t r a i n o f between 0.09 and 0.13%

(4d); t h e r e a f t e r t h e r a t e o f c r a c k n u c l e a t i o n decreased a l t h o u g h t h e t o t a l number o f c r a c k s i n c r e a s e d s t e a d i l y (4e and 4 f ) . T h i s p r o g r e s s i o n i s i l l u s t r a t e d g r a p h i c a l l y i n F i g . 5.

-.-...--...in

-

1.2-

-

I

-

W 0.8

Time t (mins)

Fig. 5 Schematic graphs of crack Fig.6 Strain against time curves o f ice

nucleation against strain. samples S2, S9 and S12.

It i s i m p o r t a n t t o n o t e t h a t a l t h o u g h t h e f i n a l c r a c k d e n s i t y i s v e r y h i g h (of o r d e r one c r a c k p e r g r a i n ) t h e c r a c k s n u c l e a t e i n d e p e n d e n t l y o f t h e i r neighbours, t h a t i s , t h e i n i t i a t i o n o f one c r a c k does n o t t r i g g e r t h e f o r m a t i o n o f o t h e r c r a c k s nearby.

There i s a g r a i n s i z e dependence i n c r a c k n u c l e a t i o n . One sample c o n t a i n e d l a r g e g r a i n s a t one end and s m a l l e r g r a i n s a t t h e o t h e r . Cracks n u c l e a t e d a t t h e l a r g e g r a i ns f i r s t

.

The s t r a i n curves f o r samples S2, S9 and S12 a r e shown i n F i g . 6. The d i s j o i n t e d n a t u r e o f t h e curves i s due t o t h e i n c r e m e n t a l l o a d i n g . The t e r t i a r y c r e e p s t a g e appears t o commence a t a s t r a i n o f about 0.6%.

Thin Sections Figs. 7 t o 9 show t h i n h o r i z o n t a l and v e r t i c a l s e c t i o n s o f sample 512 i n normal and p o l a r i s e d l i g h t , where each i n d i v i d u a l crack c o u l d be i d e n t i f i e d w i t h o u t t o o much d i f f i c u l t y , and t h i c k e r s e c t i o n s (about 2 mm t h i c k ) i n normal l i g h t t o i l l u s t r a t e t h e h i g h d e n s i t y o f cracks. C a r e f u l e x a m i n a t i o n o f t h e t h i n v e r t i c a l s e c t i o n s r e v e a l e d s e v e r a l p o s s i b l e c r a c k s t h a t have extended and formed wing c r a c k s . Examples a r e arrowed i n F i g . 8. It i s c l e a r t h a t a t t h e s e l o w l o a d s (about h a l f t h e f r a c t u r e s t r e s s ) few c r a c k s extend and f o r m w i n g c r a c k s : i n s t e a d , t h e c r a c k d e n s i t y i n c r e a s e s w i t h t i m e . A f t e r 0.5% s t r a i n , t h e c r a c k d e n s i t y i s h i g h , w i t h a c r a c k s e p a r a t i o n o f o r d e r t h e g r a i n s i z e .

The t h i n s e c t i o n s show t h a t t h e c r a c k s a r e randomly o r i e n t a t e d i n t h e h o r i z o n t a l d i r e c t i o n (as one would e x p e c t ) b u t i n t h e v e r t i c a l s e c t i o n t h e r e i s an abundance o f c r a c k s a l i g n e d a l o n g t h e l o a d i n g a x i s o r d e v i a t e d a t r e l a t i v e l y s m a l l angles f r o m i t . The r e s u l t s have been grouped i n t o 5 " s e c t o r s f r o m t h e l o a d i n g a x i s and i l l u s t r a t e d i n a b a r c h a r t ( F i g . 10). The a n g u l a r d i s t r i b u t i o n i n t h e v e r t i c a l s e c t i o n i s a p p r o x i m a t e l y normal ( c o r r e l a t i o n c o e f f i c i e n t 0.90) w i t h a mean o f -3.5" and s t a n d a r d d e v i a t i o n o f 23.3O. The mean v a l u e i s n o t s i g n i f i c a n t l y d i f f e r e n t f r o m OD.- t h e expected mean f o r t h i s d i s t r i b u t i o n .

Crack l e n g t h s were measured on t h e photographs o f t h e t h i n s e c t i o n s a t t h r e e t i m e s a c t u a l s i z e . The r e s u l t s , i n measured c r a c k l e n g t h s , a r e p l o t t e d on histogyams i n F i g . 11. The d i s t r i b u t i o n s a r e a p p r o x i m a t e l y normal, b u t have a l o n g ' t a i l due t o o c c a s i o n a l l o n g e r cracks. The h o r i z o n t a l l e n g t h d i s t r i b u t i o n i s grouped about an a c t u a l c r a c k l e n g t h o f about 1.3 mm (a measured c r a c k l e n g t h o f 4 mm) whereas t h e v e r t i c a l d i s t r i b u t i o n i s grouped about a s l i g h t l o w e r v a l u e o f 1 mm (a measured v a l u e of 3 mm). T h i s i s n o t what one would expect b y c o n s i d e r a t i o n s o f t h e c r a c k growth process, t h i s would l e a d t o l o n g e r c r a c k l e n g t h s i n t h e v e r t i c a l s e c t i o n , as t h i s i s t h e d i r e c t i o n o f c r a c k growth. T h i s suggests t h a t when t h e c r a c k s n u c l e a t e , t h e y a r e n o t c i r c u l a r d i s c s b u t e l l i p t i c a l d i s c s w i t h t h e m a j o r a x i s i n t h e h o r i z o n t a l plane.

C1-308 JOURNAL DE _PHYSIQUE

Fig. 7 Horizontal ice sections - normal light (left) and polarised light (right).

The grid squares are Icm.

Fig. 8 Vertical ice sections - normal light (left) and polarised light (right).

The grid squares are lcm.

Fig. 9 2mm thick ice sections - horizontal (left) and vertical (right).

The grid squares are lcm.

s i z e was about one h a l f o f t h e g r a i n s i z e . T h i s i s what i s expected i f t h e c r a c k s a r e one g r a i n f a c e t long.

Observations o f crack p o s i t i o n s , r e 1 a t i ve t o g r a i n boundaries, were made by comparing photographs o f t h e same t h i n s e c t i o n made w i t h p o l a r i s e d , and w i t h normal, l i g h t

(e.g. Figs. 7 and 8 ) . Each c r a c k was denoted t r a n s g r a n u l a r , i n t e r g r a n u l a r , o r b o t h -

a l t h o u g h t h e d e c i s i o n was f r e q u e n t l y s u b j e c t i v e . The general t r e n d s have been shown by shading t h e l e n g t h d i s t r i b u t i o n s h i s t o g r a m ( F i g . 11). I n t h e v e r t i c a l s e c t i o n , 57% o f c r a c k s were t r a n s g r a n u l a r , 41% i n t e r g r a n u l a r and 2% a c o m b i n a t i o n o f b o t h . T h i s compares w i t h c o r r e s p o n d i n g values i n t h e h o r i z o n t a l s e c t i o n s o f 47%, 46% and 7%. Perhaps t h e b e s t c o n c l u s i o n t h a t can be drawn f r o m t h i s i s t h a t i t IS aDout e q u a l l y l i k e l y t h a t a c r a c k w i l l f o r m across a g r a i n o r i n a g r a i n boundary.

c

. 10

rE

. 8 104 cracks

: ⁶

> 4

2 2

" 0

- 9 0 - 6 0 - 3 0 0 3 0 60 9 0

" E ²⁰

5 ^{trans- 8} Inter- granular

2.10 [.I ~ntergranular

h. Iransgranular u

" ⁰

0 2 4 6 8 10 12 14 16 40

Crack Angle to Arbitrary Axis ( O ) Crack Length x 3 (mm)

trans. 8 ~ n t e r - Intergranular

granular

Crack Angle to Loading Axis (') Crack Length x 3 (mm) Fig. 10 Crack angular distributions - Fig. 11 Crack length distributions -

horizontal section (top) - horizontal section (top) -

vertical section (bottom). vertical section (bottom).

Because t h e s e c t i o n s had a t h i c k n e s s s m a l l compared t o t h e g r a i n s i z e , i t was r e a s o n a b l e t o assume t h a t v a l i d measurement o f t h e number o f c r a c k s p e r u n i t area c o u l d be made. F o r t h e v e r t i c a l s e c t i o n o f sample S12 (0.44% s t r a i n ) , 130 c r a c k s

', -

were measured i n an a r e a 900 mmL - a d e n s i t y o f 0.144/mZ. F o r t h e h o r i z o n t a l s e c t i o n

- 104 c r a c k s were measured i n an area 707 mm2 - a c r a c k d e n s i t y o f 0.147/mm 2

.

The r e s u l t s , so f a r d e s c r i b e d , r e f e r t o sample S12 w h i c h was deformed t o 0.44%

s t r a i n . The c r a c k d i s t r i b u t i o n s f o r t h e o t h e r experiments (S9 - 0.692, S2 - 1.4%) were v i r t u a l l y i d e n t i c a l . The r e l e v a n t s t r a i n s f o r t h e t h r e e experiments have been shown on t h e schematic graph o f c r a c k n u c l e a t i o n ( F i g . 5 ) . A l l t h e t e s t s were

CI-310 JOURNAL DE PHYSIQUE

t e r m i n a t e d a t s t r a i n s much h i g h e r t h a n t h a t f o r t h ~ ? P A C n u c l e a t i o n frequency which o c c u r r e d a t a s t r a i n o f about 0.1%.

4. DISCUSSION

The r e s u l t s o f t h i s s t u d y h i g h l i g h t t h e problems o f p r e d i c t i n g f a i l u r e s t r e n g t h s which depend on t h e i n t e r a c t i o n o f a c r a c k p o p u l a t i o n . It would be c o n v e n i e n t t o assume t h a t cracks a r e a l l o f t h e same l e n g t h w i t h e i t h e r an e n t i r e l y random, o r a c o n s t a n t , o r i e n t a t i o n . F o r p o l y c r y s t a l l i n e i c e t h e c r a c k s were o r i e n t a t e d a t s m a l l angles t o t h e l o a d i n g a x i s w i t h an a p p r o x i m a t e l y normal d i s t r i b u t i o n and had a d i s t r i b u t i o n o f l e n g t h s grouped around one h a l f o f t h e g r a i n s i z e .

The o b s e r v a t i o n o f a few wing c r a c k s l e n d s s u p p o r t t o t h e t h e o r y t h a t compressive f a i l u r e depends on t h e growth o f s t a b l e c r a c k s t o a p o i n t where t h e y may l i n k . Few examples o f w i n g c r a c k s were observed b u t t h i s can b e e x p l a i n e d by t h e f a c t t h a t t h e s t r e s s was about one h a l f t h e u n i a x i a l f r a c t u r e s t r e s s . T h i s i s about t h e p o i n t i n rocks when d i l a t a t i o n i s f i r s t observed and a c o u s t i c emissions i n c r e a s e [5] -

s u g g e s t i n g t h a t i t i s t h e s t r e s s l e v e l a t which w i n g c r a c k s a r e o n l y j u s t s t a r t i n g t o i n i t i a t e . There a r e a l s o v e r y few c r a c k s w i t h o r i e n t a t i o n a t 30-60° t o t h e l o a d i n g a x i s and i t i s t h e s e c r a c k s s t h a t propagate most e a s i l y i n compression C11.

P o l y c r y s t a l l i n e i c e i s an example o f a m a t e r i a l where l i m i t e d p l a s t i c i t y n u c l e a t e s cracks. The crack d e n s i t y i s a f u n c t i o n o f t h e a p p l i e d s t r a i n a l t h o u g h , a f t e r a s t r a i n o f perhaps 0.2%, i t i n c r e a s e s r e l a t i v e l y s l o w l y . T h i s add-s an a d d i t i o n a l c o m p l i c a t i o n t o t h e a1 ready d i f f i c u l t problem o f p r e d i c t i n g compressive s t r e n g t h , namely a c r a c k p o p u l a t i o n t h a t changes as a f u n c t i o n o f s t r a i n .

5. CONCLUSIONS

Cracks s t a r t t o n u c l e a t e a t s t r a i n s as low as 0.07% and n u c l e a t e w i t h a maximum frequency a t about 0.1% s t r a i n . H e r e a f t e r , t h e n u c l e a t i o n o f new c r a c k s d e c l i n e s w i t h n e g l i g i b l e n u c l e a t i o n a f t e r 0.2% s t r a i n .

The n u c l e a t i o n o f one c r a c k does n o t t r i g g e r a s e r i e s o f o t h e r crack n u c l e a t i o n s i n t h e v i c i n i t y .

A few examples o f wing c r a c k f o r m a t i o n were observed, b u t damage i n i c e ( a t t h i s s t r e s s and t e m p e r a t u r e ) i s m a i n l y by t h e n u c l e a t i o n o f new, g r a i n - s i z e d cracks, n o t by t h e p r o p o g a t i o n o f t h o s e w h i c h have a l r e a d y n u c l e a t e d .

The c r a c k s were o r i e n t a t e d about t h e v e r t i c a l a x i s w i t h a normal d i s t r i b u t i o n o f s t a n d a r d d e v i a t i o n 23'. There were r e l a t i v e l y few c r a c k s o r i e n t a t e d a t angles f a v o u r a b l e f o r t h e f o r m a t i o n o f wing cracks.

The mean c r a c k l e n g t h was measured t o be 1 mm i n t h e s e c t i o n p a r a l l e l t o t h e l o a d i n g a x i s b u t 1.3 mm i n t h e 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 a d i n g a x i s . T h i s d i f f e r e n c e was a t t r i b u t e d t o t h e shape o f a c r a c k b e i n g e l l i p s o i d w i t h t h e m a j o r a x i s i n t h e h o r i z o n t a l plane.

Both t r a n s g r a n u l a r and i n t e r g r a n u l a r c r a c k s were observed i n r o u g h l y equal p r o p o r t i o n s .

The c r a c k d e n s i t y was measured t o be 0.14lmm 2 a t a s t r a i n o f 0.44%.

111 Hallam, S.D., Proc. IAHR Symp. On I c e , Iowa, August 13-22, (1986).

121 Ashby, M.F. and Hallam, S.D., Acta Met. 34 (1986) 497 - 509.

[3] Cole, D.M., The E f f e c t o f G r a i n S i z e on t h e I n t e r n a l F r a c t u r i n g o f

P o l y c r y s t a l l i n e I c e , Master o f Science Thesis, Thayer School o f Engineering, Dartmouth C o l l e g e (1985).

[4] Le Gac, H., C o n t r i b u t i o n A La D e t e r m i n a t i o n Des L o i s De Comportement De La Glace P o l y c r y s t a l l ine, These de T r o t sieme Cycle, U n i v e r s i t y o f Grenoble, CNRS

L a b o r a t o i r e de Gl a c i o l o g i e e t Geophysique de 1 'Environment (1980).

[5] Brace, W.F., Pure Appl. Geophys. 116 (1978) 603-614.

COMMENTS

Remark of S.MURRELL :

A possible explanation for your observation of a preponderance of cracks aligned with the compresion axis in your ice. specimens is that you were observing cracks initiated by a slip process (e.g. by a slip band with dislocation pile-up, perhaps against a grain boundary), which would probables give rise to preferential cleavage or g.b. cracking in planes parallel to the compression axis. This must be contrasted with the process envisaged by Griffith (and in your model expriments) which depends on the pre-existence of cracks (a randomly oriented population in Griffith's case).

Remark of S.KIRBY

I have a comment to amplify the one made by Stan Murrell concerning the tensile crack sources. Shear cracks might not be the sourcesof the tensile cracks observed in your specimens. Any localized shear deformation could generate tensile shear stresses. For example, grain-boundary sliding or intracrystalline slip bands could be tensile crack sources. Perhaps spatial relationships can be sought after between grain boundaries and slip bands on the one hand and tensile cracks on the other.