Creep of columnar-grained ice at low stress

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Creep of columnar-grained ice at low stress

Gold, L. W.

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S e r

T H ~

National Research

Conseil national

~ 2 1

_d

a

9

Council Canada

de recherches Canada

no.

1123

c. 2

CREEP OF COLUMNAR-GRAINED ICE AT LOW STRESS

by L.W. Gold

ANALYZED

L I B R A R Y

Reprinted from

Annals of Glaciology

Vol. 4, 1983

p. 73

-

78

DBR Paper No. 1123

Division of Building Research

Ð SUM^

On a e n t r e p r i s une 6 t u d e du f l u a g e d e l a g l a c e columnaire s o u s c o n t r a i n t e s d e compression c o n s t a n t e s d e 98 e t 49 W a a f i n d ' g t e n d r e l a r e l a t i o n observ'ee e n t r e l e t a u x d e d 6 f o r m a t i o n e t l a c h a r g e dans l a r 6 g i o n d e s f a i b l e s c o n t r a l n t e s . U n e c o n t r a i n t e a t a p p l i q u s e p e r p e n d i c u l a i r e m e n t a u p l u s l o n g axe d e s grains. On a e f f e c t u i des o b s e r v a t i o n s pour d e s temp*eratures v a r i a n t

e n t r e -5*C et -40°C.

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d6forrnation a v a i t tendance b dependre l i n h i r e m e n t de l a

c o n t r a i n t e pour moins de 49 kPa e t que p l u s d'un p r o c e s s u s d e d i s l o c a t i o n a v e c d e s v a l e u r s d i f f g r e n t e s p o u r l ' e x p o s a n t de c o n t r a i n t e p e u t c o n t r i b u e r d'une mani'ere

i m p o r t a n t e b l a d6formation pour d e s c o n t r a i n t e s p l u s

6lev6es. Une 6 n e r g i e d ' a c t i v a t i o n d e 63 kJ mol-' e s t e n

a c c o r d a v e c l a v a r i a t i o n observ'ee du t a u x d e d6formation

e n f o n c t i o n de l a temp'erature. @former l a g l a c e j u s q u ' g

une d6formation donn'ee s o u s une c o n t r a i n t e d ' e n v i r o n

0 , 3 MPa pour e n s u i t e r 6 d u i r e l a charge p o u r r a i t s 1 a v 6 r e r u n e m a n i & r e p r a t i q u e d ' 6 t u d i e r l a c o n t r a i n t e , l a d e f o r m a t i o n e t l a v a r i a t i o n du t a u x de dgformation e n f o n c t i o n de l a teiuperature pour de f a i b l e s c o n t r a i n t e s . I

I

1

1

-

A n n a l s of G l a c i o l o g y

4

1983

a

I n t e r n a t i o n a l Glaciological S o c i e t y

CREEP OF COLUMNAR-GRAINED ICE AT LOW STRESS

L.

W.

Gold

(Division of B u i l d i n g Research, N a t i o n a l Research C o u n c i l Canada, Ottawa, O n t a r i o K I A OR6, Canada)

ABSTRACT

An i n v e s t i g a t i o n was undertaken o f t h e creep of coluinnar-grained i c e under constant compressive s t r e s s e s of 98 and 59 kPa i n o r d e r t o extend t h e observed r e l a t i o n s h i p between s t r a i n - r a t e and s t r e s s f u r t h e r i n t o t h e l o w - s t r e s s region. S t r e s s was a p p l i e d p e r p e n d i c u l a r t o t h e l o n g d i r e c t i o n o f t h e g r a i n s . Observations were made f o r temperatures between -5 and -40'C. The steady-state creep r a t e f o r secondary creep was n o t y e t a t t a i n e d f o r s t r a i n of 1.4% and s t r e s s of 98 kPa. An i n i t i a l y i e l d was observed a t t h a t s t r e s s i n t h e s t r a i n range o f 0.2 t o 0.3%. S i m i l a r t o t h a t seen a t h i g h e r s t r e s s . The o b s e r v a t i o n s showed t h a t t h e s t r a i n - r a t e tended t o a l i n e a r dependence on s t r e s s below 49 kPa and t h a t more t h a n one d i s l o c a t i o n process w i t h d i f f e r e n t values f o r t h e s t r e s s exponent may c o n t r i b u t e t o t h e s t r a i n a t h i g h e r stresses. An a c t i v a t i o n energy o f 63 kJ mol-' was c o n s i s t e n t w i t h t h e observed tempera- t u r e dependence of t h e s t r a i n - r a t e . S t r a i n i n g i c e t o a g i v e n s t r a i n under a s t r e s s o f about 0.3 MPa and then reducing t h e l o a d may be a convenient way t o study t h e s t r e s s , s t r a i n and temperature dependence o f t h e s t r a i n - r a t e a t low stress.

P

INTRODUCTION

Observations on t h e s t r e s s dependence o f t h e creep r a t e o f columnar-grained i c e have been con- f i n e d t o a f a i r l y narrow range o f compressive s t r e s s . The upper l i r n i t i s determined by t h e r a p i d breakdown of t h e i c e s t r u c t u r e by crack f o r m a t i o n f o r s t r e s s g r e a t e r t h a n about 3 MPa, and t h e lower l i m i t , about 200 kPa, by t h e l e n g t h o f t i m e r e q u i r e d t o s t r a i n t h e i c e more t h a n

12.

A t t h e lower end, i t t a k e s more than 50 days t o d e f o r ~ n p o l y c r y s t a l l i n e i c e a t -lO°C beyond t h e i n i t i a l t r a n s i e n t o r primary creep Pa""-

,

I t i s considered t h a t t h e viscous creep o f i c e over t h i s s t r e s s range i s c o n t r o l l e d by t h e movement o f basal-plane d i s l o c a t i o n s o u t of t h e i r s l i p plane i n t h e grain-boundary region. T h i s model p r e d i c t s a power-law dependence o f t h e s t r a i n - r a t e on s t r e s s . I t has been p o s t u l a t e d t h a t f o r small s t r e s s ( l e s s than 100 kPa) t h e Nabarro-Herring process should con- t r o l t h e creep behaviour, r e s u l t i n g i n a l i n e a r dependence o f s t r a i n - r a t e on stress.

A creep t e s t was c a r r i e d o u t a t a s t r e s s o f

98 kPa t o a s t r a i n o f 2% t o extend t h e observed r e l a t i o n s h i p f o r t h e s t r e s s dependence o f t h e s t r a i n - r a t e f u r t h e r i n t o t h e l o w - s t r e s s range. T h i s r e q u i r e d t h a t t h e l o a d be m a i n t a i n e d f o r 35 500 h ( s l i g h t l y over f o u r years). A second experiment was t h e n c a r r i e d o u t t o determine i f t h e s t r a i n - r a t e f o r a

specimen s t r a i n e d t o about 1.4% under a constant conrpressive s t r e s s o f 300 kPa was t h e same as f o r t h e f i r s t specimen a t t h a t s t r a i n when t h e s t r e s s was reduced t o 98 kPa. When t h i s was found t o be t h e case, t h e s t r e s s was reduced t o 49 kPa. T h i s paper r e p o r t s t h e r e s u l t s of t h e s e measurements.

EXPERIMENTAL PROCEDURE

The speciinens were made from columnar-grained, t y p e S2 i c e prepared i n a nlanner described by Gold (1965, 1972Cbl). For t h i s t y p e of i c e t h e c r y s t a l l o - g r a p h i c C-axis tends t o be 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 t h e l o n g d i r e c t i o n o f t h e columnar g r a i n s and t o have a random o r i e n t a t i o n . A c h a r a c t e r i s t i c of t h i s i c e , o f t e n t h e p r i n c i p a l one i n i c e covers, i s t h a t t h e deformation i s e s s e n t i a l l y two-dimensional f o r s t r e s s a p p l i e d p e r p e n d i c u l a r t o t h e l o n g d i r e c t i o n o f t h e g r a i n s , w i t h t h e s t r a i n i n t h e plane normal t o t h e d i r e c t i o n o f t h e g r a i n s being much g r e a t e r t h a n t h a t 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 .

Because o f t h i s symmetry, r e c t a n g u l a r specimens 25 x 10 x 5 cm i n size, prepared w i t h a m i l l i n g machine, were used. The l o n g d i r e c t i o n o f t h e g r a i n s was p e r p e n d i c u l a r t o t h e 25 x 10 cm face. Average g r a i n s i z e increased from about 2.5 mm a t one face t o 3.5 mm a t t h e other. A f t e r t h e specimens had been wrapped i n a p o l y v i n y l f i l m t o prevent s u b l i m a t i o n , l o a d s were a p p l i e d t o t h e 10 x 5 cm ends t h r o u g h metal p l a t e n s u s i n g a dead-weight l e v e r system. T o t a l deformation was measured u s i n y two d i a l gauges a t t a c h e d t o t h e upper p l a t e n on e i t h e r s i d e of t h e specimen. The d i v i s i o n s on t h e gauge d i a l c o r r e s - ponded t o a displacement o f 2.5 x cm o r a s t r a i n o f about 2.5 x 10-5.

The t e s t s were c a r r i e d o u t i n a room f o r which t h e temperature c o u l d be c o n t r o l l e d w i t h an accuracy of O.lDC over l o n g p e r i o d s o f time. Observations were made f o r temoeratures between -5 and -4n°C.

RESULTS

The t i m e dependence of t h e s t r a i n i s presented i n F i g u r e 1 f o r t h e f i r s t t e s t and i n F i g u r e 2 f o r t h e second. Times of temperature and s t r e s s changes and f e a t u r e s of i n t e r e s t a r e i n d i c a t e d by numbered l i n e s . The temperature and s t r e s s changes o r o t h e r rernarks corresponding t o these times a r e presented i n Table I f o r specimen 1. I t was found t h a t t h e s t r a i n - r a t e , a l s o shown i n Table I , was e s s e n t i a l l y c o n s t a n t over t h e r e l a t i v e l y l o n g p e r i o d s between l i n e s . I n p r e p a r - i n g F i g u r e 1 and Table I , s t r a i n s due t o a change i n temperature were ignored.

The change i n s t r a i n - r a t e w i t h s t r a i n f o r t h e l o n g - t e r m t e s t i s presented i n F i g u r e 3. I t was found t h a t t h e s t r a i n - r a t e had a maximum i n t h e s t r a i n

Gold: Creep of oolumr-grained ice

TIME, h

Fig.1. Time dependence of s t r a i n f o r s t r e s s of 90 kPa and v a r i o u s temperatures. See Table I f o r i n f o r m a t i o n r e l e v a n t t o numbered l i n e s . 1 . 2

"C

-

-

_-

REMARKS 0 5 10 15 20 25 30 35 40 45 50 55 60 6 5 x TIME, h 0-1 294 -10 1-2 37.8 294 -10 2-3 1.83 98 -10 3-4 0.347 49 -10 4-5 49 -10 NO MEASUREMENT 5-6 49 <-20 6-7 49 -29 NO OBSEF 7-8 0.389 49 -10 8-9 49 -10 SPECIMEN UNLOADED 10-11 1.157 49 -10

1

Fig.2. Time dependence of s t r a i n f o r specimen 2. 0 . 2

0

range of 0.2 t o 0.3% as observed a t h i g h e r s t r e s s 0.79% f o l l o w e d an i n c r e a s e i n temperature from -20 t o IKrausz 1963, old 1965, 1972[aI). S i m i l a r behaviour _{-10'C. Although a s i m i l a r i n c r e a s e was n o t observed} was observed f o r g r a n u l a r i c e by M e l l o r and C o l e _{immediately a f t e r t h e p e r i o d between l i n e s 16 and 17} (1902). who used a v e r y s t i f f t e s t i n g machine. The _{a t -19.0eC, t h e r e were r a p i d increases i n s t r a i n a t} numbers above each p l o t t e d p o i n t i d e n t i f y t h e s t r a i n - _{l i n e s 18, 19 and 20, as w e l l as a s l i g h t tilting at} r a t e and s t r a i n range i n Table I. _{l i n e 20 ( T a b l e I ) . These r a p i d changes i n s t r a i n ,}

Some i n t e r e s t i n g and p o t e n t i a l l y s i g n i f i c a n t _{which occurred over 2- t o 10-day periods, were} i r r e g u l a r i t i e s were n o t i c e d i n t h e long-term creep _{r e g i s t e r e d by b o t h d i a l gauges. The s t r a i n - r a t e} behaviour (see F i g s . 1 and 3 ) . The h i g h creep r a t e _{between p o s i t i o n s 19 and 20, p l o t t e d a t a s t r a i n of}

between l i n e s 12 and 13 p l o t t e d a t a s t r a i n o f _{1.56%. was a l s o g r e a t e r than would have been expected}

-

-

--

I

Gozd: Creep of eoLu?rmar-grained ice TARLE 1. INFORMATION ON TIME, TEMPERATURE, STRAIN AND STRAIN-RATE FOR SPECIMEN 1

( s t r e s s i s 98 kPa)

Time Numbered 1 in e s Temperature Strain-range S t r a i n - r a t e Comments

"

( ~ o . o f hours) Fig.1 Fig.3

("C)

( % ) (S-1 x 10'0 )

Temperature change Temperature change Temperature change Temperature change Temperature change Temperature change Temperature change Temperature change S l i g h t hardening e f f e c t S l i g h t hardening e f f e c t Temperature change Temperature change S t r a i n s o f t e n i n g o f 10-q S t r a i n s o f t e n i n g of 0.7 x 10-4 S t r a i n s o f t e n i n g of 1.47 x 10-9 Temperature change Temperature change Temperature change Temperature change Temperature change

from t h e e a r l i e r trend. I t appeared t h a t i n t h e s t r a i n range of 1.3% t o 1.8% t h e i c e was going through p e r i o d s o f s t r u c t u r a l i n s t a b i l i t y . The I markedly l a r g e s t r a i n - r a t e s p l o t t e d a t s t r a i n s

I

o f 1.97 and 2.03% occurred a t -1O0C, immediately a f t e r a p e r i o d a t -39.6'C and a t -29.8-C. I n t h e second t e s t t h e specimen was unloaded a t about 5 250 h and r e l o a d e d a t 5 540 h. I t was found t h a t even by 6 050 h t h e s t r a i n - r a t e s t i l l had n o t

decreased t o i t s v a l u e between l i n e s 6 and 7. I n F i g u r e 4 a r e p l o t t e d t h e r e s u l t s o b t a i n e d on t h e s t r e s s dependence of t h e s t r a i n - r a t e f o r s t r e s s Up t o 0.98 MPa, temperature o f -104C and s t r a i n of

1.4 t o 1.5%. The observations a t stresses o f 0.59, 0.78 and 0.98 WPa a r e t h e average of s i x t e s t s ( G o l d 1972[aI). The i n i t i a l y i e l d behaviour over t h e s t r a i n range of 0.10 t o 0.30% was observed i n a l l cases.

1

Gotd: C r e e p

of

_{cotwnnar-grninad}

_ice

1.0 1 1 1 1 1 1 1 ( 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0. 5 1 . 0 1. 5 2 0 2. 5

STRAIN, %

Flg.3. S t r a i n dependence of s t r a l n - r a t e . 0: specimen 1,

+:

specimen 2, T: - l O ° C . See Table I f o r i n f o r l n a t i o n

I

r e l e v a n t t o numbered 1 i nes.

t h e usual power-law dependence, i .e.

E = Ad', (1)

where e i s t h e s t r a i n - r a t e , o t h e s t r e s s , and A and n a r e constants. The v a l u e o f n was found t o be 4. It was assumed t h a t t h e Nabarro-Herring process c o n t r o l s t h e s t r e s s dependence of t h e s t r a i n - r a t e a t l o w s t r e s s and t h a t

The values o f A 1 and A 2 were determined by t h e o b s e r v a t i o n s f o r o = 50 kPa and 0.4 MPa. The r e s u l t

i s p l o t t e d i n F i g u r e 4; t h e t o t a l s t r a i n i s shown as t h e ' dashed l i n e .

For h i g h homologous temperatures, t h e s t r e s s de~endence o f t h e s t r a i n - r a t e i s sometimes expressed i n ' general by an equation of t h e forin

where T i s t h e temperature i n ti, d t h e g r a i n Size, and 11 t h e c o e f f i c i e n t of d i f f u s i o n g i v e n by

D

=

o0

exp

3

.

(HT)

( 4 ) DO and m a r e constants,

R

i s t h e gas constant, and

q

t h e a c t i v a t i o n energy (Langdon 1973). The p r o d u c t T; i s p l o t t e d i n F i g u r e 5 a g a i n s t 1/T f o r t h e long- term t e s t . A l i n e corresponding t o q-63 kJ mol-' i s drawn t h r o u g h t h e p o i n t

TB

= 4.5 x tis-' and l / T = 3.8 x 10-3 ti-'. It can be seen t h a t t h i s v a l u e f o r

9

i s c o n s i s t e n t w i t h t h e observations.

S T R E S S , ~ . m - ' DISCUSSION

An i n t e r e s t i n g f e a t u r e o f t h e creep behaviour o f Fig.4. S t r e s s dependence of s t r a i n - r a t e . T: -lO°C, columnar-grained i c e i s t h a t t h e s t e a d y - s t a t e o r

s t r a i n : 1.4 t o 1.5%. secondary creep r a t e appears t o be a minimum t h a t 76

cold: Creep of colwnnar-grained ice ~ o

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-

-

-

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4 =

78 k J mol

=-

-

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- _A-

-

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1 0 - l ~ - ~ I

1

,

1

,

I

I

I 3 . 6 3. 7 3 8 3.9 4.0 4 . 1 4.2 4 . 3 ~ l i T . O K - '

Fig.5. Dependence o f TE K s - I on 1/T K-l. S t r e s s : 98 kPa, 0: s t r a i n < 15, A: s t r a i n >I%, t: soecimen 2.

o c c u r s i n a r e l a t i v e l y narrow range o f s t r a i n . I n t h e p r e s e n t study, f o r s t r e s s between 0.1 and 1 MPa and t e m p e r a t u r e o f -lO°C, t h i s range b e g i n s a t about 1.4 t o 1.5%. M e l l o r and Cole (1982) found t h a t t h e minimum f o r g r a n u l a r i c e and s t r e s s between 0.8 and 3.67 MPa o c c u r r e d a t a s t r a i n o f about 1%. The f a c t t h a t t h e s t r a i n a t which t h e minimum o c c u r s i s r e l a t i v e l y con- s t a n t suggests t h a t t h e f u n c t i o n a l form o f t h e s t r a i n dependence o f t h e e f f e c t i v e s t r e s s c o n t r o l l i n g t h e deformation p r o c e s s ( e s ) i s dependent p r i m a r i l y on t h e s t r a i n . I t a l s o i n d i c a t e s t h a t s t r u c t u r a l changes due t o t h e movement o f d i s l o c a t i o n s , f o r example, may be r e l a t i v e l y i n s e n s i t i v e t o s t r e s s l e v e l s below t h o s e a t which c a v i t y and c r a c k f o r m a t i o n occurs. T h i s b e h a v i o u r a l s o suggests t h a t t h e s t r e s s dependence of t h e s t r a i n - r a t e a t l o w s t r e s s m i g h t be be s t u d i e d c o n v e n i e n t l y i n t h e secondary c r e e p r e g i o n by s t r a i n i n g t o t h i s r e g i o n i n i t i a l l y u s i n g a h i g h e r s t r e s s . The r e l a t i v e l y c l o s e agreement between t h e s t r a i n - r a t e s a t 1.4% and s t r e s s o f 98 kPa found f o r t h e two l o a d h i s t o r i e s i n t h e p r e s e n t s t u d y bear t h i s o u t (see Fig.3).

, : Caution, however, must be used w i t h t h i s proced-

ure. The i n f o r m a t i o n t o d a t e shows t h a t f o r columnar- g r a i n e d i c e t h e p o s i t i o n o f t h e maximum s t r a i n - r a t e d u r i n g t h e i n i t i a l y i e l d moves from 0.25 t o 0.15% s t r a i n when t h e s t r e s s i s decreased from 0.9 t o

U.6 MPa and r e t u r n s t o about 0.YA a t 90 kPa. F i g u r e 4 a l s o p r o v i d e s evidence t h a t a t v e r y lovr s t r e s s a creep process o f t h e N a b a r r o - H e r r i n g t y p e i s domi- nant. T h i s process !nay n o t b r i n y about t h e s t r u c t u r a l changes t h a t a r e a s s o c i a t e d w i t h d e f o r m a t i o n p r o - cesses a t h i g h e r s t r e s s . At a s t r e s s o f 0.3 MPa t h e s e processes were observed t o cause grain-boundary m i g r a t i o n and p o l y g o n i z a t i o n i n t h e grain-boundary r e g i o n , p a r t i c u l a r l y a t t r i p l e p o i n t s , f o r s t r a i n l e s s t h a n 1%.

None of t h e d i s l o c a t i o n mechanisms l i s t e d by Langdon (1973), which m i g h t be a p p l i c a b l e t o i c e , had a s t r e s s exponent o f 4. T h i s , p l u s t h e f a c t t h a t t h e c a l c u l a t e d c u r v e i n F i g u r e 4 underestimates t h e s t r a i n observed a t 0.1 MPa, i n d i c a t e s t h a t t h e r e may be a t l e a s t t h r e e d e f o r m a t i o n processes f o r i c e . One o f t h e processes may depend on g r a i n s i z e , such as yrain-boundary s l i d i n g due t o a d i s l o c a t i o n process w i t h a s t r e s s exponent of 2, and m i g h t t h u s e x p l a i n t h e d i f f e r e n c e observed f o r t h e exponent f o r g r a n u l a r i c e (about 3) and columnar-grained, t y p e S2 i c e ( a b o u t 4 ) . G r a n u l a r i c e has a s i g n i f i c a n t l y l a r g e r grain-boundary area t h a n columnar-grained i c e o f t h e same nominal g r a i n size.

Gold (1963) a t t r i b u t e d t h e maximum i n t h e s t r a i n - r a t e d u r i n g t h e i n i t i a l t r a n s i e n t creep t o t h e development of modes of d e f o r m a t i o n i n p r e v i o u s l y

Gold: Cmsp of cotwmmi.-grained ice

undefornled i c e . The i n i t i a t i o n o f these modes was considered t o be due t o t h e stresses associated w i t h t h e p i le-up of d i s l o c a t i o n s i n t h e grain-boundary r e g i o n and t o t h e l i m i t e d degrees o f freedom f o r deformation o f i n d i v i d u a l g r a i n s o f i c e . These modes i n c l u d e d s l i p on t h e basal and non-basal planes, f o r m a t i o n o f low-angle boundaries and k i n k bands, grain-boundary m i g r a t i o n , p o l y g o n i z a t i o n , c a v i t y f o r i n a t i o n and, f o r s t r e s s g r e a t e r than about 0.5 MPa, crack formation. The maximum i n t h e s t r a i n - r a t e shown i n F i g u r e 3 f o r a s t r e s s o f 98 kPa i n d i c a t e s t h d t d i s l o c a t i o n processes a r e s t i l l s i g n i f i c a n t a t t h i s s t r e s s l e v e l . . . . -. . .

.

Morland and Spring (1981) have modelled mathe- m a t i c a l l y t h e minimum i n t h e secondary creep r a t e assuming s t r a i n - r a t e t o be a f u n c t i o n of s t r e s s , s t r e s s r a t e and s t r a i n a c c e l e r a t i o n . L i t t l e a t t e n t i o n has been given, however, t o t h e e f f e c t s o f s t r u c t u r a l changes on t h e mathematical d e s c r i p t i o n o f t h e deform- a t i o n behaviour before, d u r i n g and a f t e r t h e minimum, p a r t i c u l a r l y f o r p r e v i o u s l y undeformed i c e . The observations on columnar-grained i c e have c l e a r l y shown t h a t these changes a r e s t r o n g l y s t r a i n - dependent d u r i n g t h e i n i t i a l t r a n s i e n t o r primary creep stage and i n t r o d u c e a dependence on s t r a i n h i s t o r y t h a t may be v e r y d i f f i c u l t t o e s t a b l i s h e x p l i c i t l y . For example, observations have shown t h a t t h e y i e l d e f f e c t d u r i n g t h e i n i t i a l t r a n s i e n t creep i s n o t observed on r e l o a d i n g a f t e r a p e r i o d o f recovery (Krausz 1963, Gold 1965). Smith and Morland (1981) concluded, a f t e r a t t e m p t i n g t o f i t b o t h a 3- and a 4-term polynomial s t r e s s f u n c t i o n t o p u b l i s h e d d a t a on t h e minimum secondary creep r a t e , t h a t " i t i s c l e a r t h a t t h e r e i s no r e a l consistency between t h e v a r i o u s data, w i t h normalized s t r a i n - r a t e s a t f i x e d s t r e s s v a r y i n g by a f a c t o r o f 3". This v a r i a b i l i t y may n o t be p r e s e n t f o r t h o s e s i t u a t i o n s f o r which i c e has been e x t e n s i v e l y deformed, f o r example, i n g l a c i e r s . I n most e n g i n e e r i n g problems, however, i c e has had l i t t l e o r no p r e v i o u s deform- a t i o n and t h e s t r a i n i s u s u a l l y l e s s t h a n 1%. I t may be necessary t o accept t h a t t h e r e i s no simple, s i n g l e r e l a t i o n t h a t s a t i s f a c t o r i l y describes t h e f i r s t

22

s t r a i n f o r i c e under a l l c o n d i t i o n s .

Althouyh t h e observations o f t h e temperature dependence o f TP shown i n F i g u r e 5 are c o n s i s t e n t w i t h an a c t i v a t i o n eneryy o f 63 kJ mol-', t h i s may be more apparent than r e a l , as shown by t h e dashed l i n e s . The r a n e o f Q d e f i n e d by these l i n e s i s 47

9

t o 100 kJ mol-

.

Most observations o f t h e a c t i v a t i o n energy f o r p o l y c r y s t a l l i n e i c e l i e i n t h i s range. I t i s p o s s i b l e t h a t t h e deformation processes i n i c e have d i f f e r e n t a c t i v a t i o n energies; consequently t h e i r r e l a t i v e c o n t r i b u t i o n and accompanying s t r u c - t u r a l changes would be temperature-dependent.

T h i s i s c o n s i s t e n t w i t h t h e conclusions a r r i v e d a t by Smith and Morland (1981) t h a t "present d a t a do n o t p r e d i c t a s i n g l e temperature-dependent r a t e f a c t o r " . l f t h i s i s t h e case, i t would be expected t h a t i t would t a k e t i m e a f t e r a change i n temperature t o e s t a b l i s h t h e expected s t r a i n - r a t e f o r g i v e n stress, s t r a i n and temperature. That i s , t h e deform- a t i o n behaviour f o l l o w i n g a change i n temperature may depend n o t o n l y on t h e s t r a i n but on t h e p r e v i o u s temperature c o n d i t i o n as w e l l .

CONCLUSIONS

The s t e a d y - s t a t e creep r a t e o f columnar-grained, t y p e SZ i c e a t -1O0C i s n o t a t t a i n e d b e f o r e a s t r a i n of 1.4%. S t r a i n i n g t h e i c e r e l a t i v e l y r a p i d l y t o a

columnar-grained i c e has an i n i t i a l y i e l d

i n

t h e s t r a i n range o f 0.2 t o 0.3% when deformed under a constant compressive l o a d o f 0.1 MPa a p p l i e d perpendi- c u l a r l y t o t h e l o n g d i r e c t i o n o f t h e g r a i n s , which shows t h a t d i s l o c a t i o n processes a r e s t i l l s i g n i f i - cant a t t h i s s t r e s s . Although a v a l u e o f 63 k J mol-' f o r t h e a c t i v a t i o n energy i s c o n s i s t e n t w i t h t h e observed temperature dependence o f t h e s t r a i n r a t e f o r a s t r e s s o f 98 kPa, t h e observations were n o t s u f f i c i e n t l y d e f i n i t i v e t o r u l e o u t t h e p o s s i b i l i t y t h a t t h e e f f e c t i v e a c t i v a t i o n energy may be

temperature-dependent. REFERENCES

Gold L

W

1963 Deformation mechanisms i n i c e . In K i n g e r y W

D

( e d ) Ice and snow. Cambridge,

MA,

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Gold L w--i965

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i n i t i a l creep o f columnar- g r a i n e d ice. P a r t I. Observed behavior. Canadian Joumult of Physics 43(8): 1414-1422

Gold L W 1972Lal The f a i l u r e process i n columnar- g r a i n e d i c e . Canada. National Reeeamh Councit. Division o f Buitding Reseamh. Technicat Paper 369 Gold L W 1972rbI The process o f f a i l u r e o f columnar-

g r a i n e d ice. PkilosophicaZ Magaains E i g h t h Ser 26(2): 311-328

Krausz A S 1963 The creep o f i c e i n bending.

Canadian Journat o f Phyeioe 41(1): 167-177 Langdon T G 1973 Creep mechanisms i n i c e . ~n

Whalley E, Jones S J, Gold L W ( e h ) Phyeioe and ahemietry of i c e . Ottawa, Royal Society o f Canada: 356-361

M e l l o r M, Cole D M 1982 Deformation and f a i l u r e of

i c e under c o n s t a n t s t r e s s o r c o n s t a n t s t r a i n - r a t e . Cold Regions Science and Teahnotogy 5 ( 3 ) : 201-219 Morland L W, Spring U 1981 V i s c o e l a s t i c f l u i d

r e l a t i o n f o r t h e deformation o f ice. Cotd R e g i w Science and Teahnotogy 4 ( 3 ) : 255-268

Smith G D, Morland L W 1981 Viscous r e l a t i o n s f o r

t h e steady creep o f p o l y c r y s t a l l i n e ice. c o l d Regions Science and Technotogy 5(2): 141-150

g i v e n s t r a i n and then reducing t h e l o a d may be a convenient way t o study t h e s t r e s s , s t r a i n and temperature dependence o f t h e s t r a i n - r a t e f o r low stresses. Observations o f t h i s dependence f o r s t r e s s down t o 50 kPa i n d i c a t e t h a t a l i n e a r dependence of t h e s t r a i n - r a t e on s t r e s s e x i s t s below t h i s l e v e l a t -1O0C and t h a t more than one d i s l o c a t i o n process w i t h d i f f e r e n t values f o r t h e s t r e s s exponent may c o n t r o l t h e deformation behaviour a t h i g h e r stresses. Type

S2