INELASTIC PROPERTIES OF ICE Ih AT LOW TEMPERATURES AND HIGH PRESSURES

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INELASTIC PROPERTIES OF ICE Ih AT LOW TEMPERATURES AND HIGH PRESSURES

S. Kirby, W. Durham, M. Beeman, H. Heard, M. Daley

To cite this version:

S. Kirby, W. Durham, M. Beeman, H. Heard, M. Daley. INELASTIC PROPERTIES OF ICE Ih AT

LOW TEMPERATURES AND HIGH PRESSURES. Journal de Physique Colloques, 1987, 48 (C1),

pp.C1-227-C1-232. �10.1051/jphyscol:1987131�. �jpa-00226277�

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JOURNAL DE PHYSIQUE

C o l l o q u e C 1 , s u p p l 6 m e n t au n o 3 , Tome 48, m a r s 1987

I N E L A S T I C PROPERTIES OF I C E I , AT LOW TEMPERATURES AND HIGH _PRESSURES

S.H. KIRBY, W.B. DURHAM*, M.L. BEEMAN**, H.C. HEARD* and

M.A. DALEY

U.S. Geological Survey, 345 Middleroad MS 977, Menlo Park, CA 94025, U.S.A.

" ~ a w r e n c e Livermore National Laboratory, Livermore, CA 94550, U.S.A.

X *

Dept. Materials Science, Cornell University; Ithaca, NY 14853, U.S.A.

Resum6

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Le b u t d e n o t r e programme d e r e c h e r c h e e s t d 1 6 t u d i e r l e comportement r h e o l o g i q u e d e g l a c e s s o u m i s e s a u x mgmes c o n d i t i o n s q u e c e l l e s e x i s t a n t &

l t i n t 6 r i e u r de s a t e l l i t e s d e s ' p l a n e t e s e x t e r i e u r e s a f i n d e c o n n a i t r e l e u r s l o i s d e d e f o r m a t i o n . Pour c e l a , nous a v o n s e f f e c t u e 100 e s s a i s d e compression & v i t e s s e de d e f o r m a t i o n c o n s t a n t e p o u r d e s p r e s s i o n s a l l a n t j u s q u t g 5 0 0 HPa e t p o u r d e s t e m p h r a t u r e s a u s s i b a s s e s que 77 K. P o u r P

>

30 MPa, l a g l a c e Ih s e f r a c t u r e p a r i n s t a b i l i t 6 d e c i s a i l l e m e n t p r o d u i s a n t d e s f a u t e s d a n s l a d i r e c t i o n du maximum d e c o n t r a i n t e de c i s a i l l e m e n t e t l a c o n t r a i n t e de f i s s u r a t i o n e s t i n d e p e n d a n t e d e l a p r e s s i o n . Ce comportement i n h a b i t u e l p e u t - 8 t r e . a s s o c i i 2 d e s t r a n s f o r m a t i o n s d e p h a s e s l o c a l i s e e s d a n s l e s z o n e s d e c i s a i l l e m e n t .

La r e s i s t a n c e e n r e g i m e s t a t i o n n a i r e s u i t d e s l o i s r h e o l o g i q u e s t h e r m i q u e m e n t a c t i v 6 e s d 6 c r i t e s p a r d e s l o i s d e p u i s s a n c e , a v e c d i f f e r e n t s p a r a m e t r e s d t 8 c o u l e m e n t d e p e n d a n t d e s g a m e s d e t e m p e r a t u r e s 6 t u d i B e s . L e s l o i s d 1 6 c o u l e m e n t s e r o n t d i s c u t e e s e n r e l a t i o n a v e c l e s d i v e r s m d c a n i s m e s d e d e f o r m a t i o n d e d u i t s d e s i n i c r o s t r u c t u r e s o b s e r v e e s o p t i q u e m e n t e t en comparaison a v e c d t a u t r e s t r a v a u x . A b s t r a c t

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The aim o f o u r r e s e a r c h programme is t o e x p l o r e t h e r h e o l o g i c a l b e h a v i o r of Hz0 i c e s under c o n d i t i o n s a p p r o p r i a t e t o t h e i n t e r i o r s o f t h e i c y s a t e l l i t e s o f t h e o u t e r p l a n e t s i n o r d e r t o g i v e i n s i g h t i n t o t h e i r d e f o r m a t i o n . To t h i s end, we have performed o v e r 100 c o n s t a n t - s t r a i n - r a t e compression t e s t s a t p r e s s u r e s t o 500 MPa and t e m p e r a t u r e s as low a s 77 K.

A t P 30 MPa, i c e I h f a i l s by a s h e a r i n s t a b i l i t y p r o d u c i n g f a u l t s i n t h e maximum s h e a r s t r e s s o r i e n t a t i o n and f a i l u r e s t r e n g t h t y p i c a l l y is independent o f p r e s s u r e . T h i s u n u s u a l f a u l t i n g b e h a v i o r i s t h o u g h t t o be connected w i t h phase t r a n s f o r m a t i o n s l o c a l i z e d i n t h e s h e a r zones. The s t e a d y - s t a t e s t r e n g t h f o l l o w s r h e o l o g i c a l laws o f t h e t h e r m a l l y - a c t i v a t e d power-law t y p e , w i t h d i f f e r e n t f l o w law p a r a m e t e r s depending on t h e r a n g e o f t e s t t e m p e r a t u r e s . The flow l a w s w i l l be d i s c u s s e d w i t h r e f e r e n c e t o t h e o p e r a t i n g d e f o r m a t i o n mechanisms a s deduced from o p t i c a l - s c a l e m i c r o s t r u c t u r e s and comparison w i t h o t h e r work.

1. I n t r o d u c t i o n . - Ice f l o w s p l a s t i c a l l y under t h e f o r c e of g r a v i t y on a l a r g e s c a l e on t h e E a r t h ' s s u r f a c e and i n t e r e s t i n t h i s n a t u r a l phenomenon h a s m o t i v a t e d a l o n g h i s t o r y of r e s e a r c h on i c e r h e o l o g y a t t h e h i g h t e m p e r a t u r e and low p r e s - s u r e s , c o n d i t i o n s a p p r o p r i a t e t o t h e n a t u r a l t e r r e s t r i a l environment. It i s now a r g u a b l y t h e b e s t c h a r a c t e r i z e d c r y s t a l l i n e E a r t h m a t e r i a l as f a r a s i t s r h e o l o g y u n d e r n a t u r a l c o n d i t i o n s . H20 i c e s a l s o e x i s t i n abundance i n t h e o u t e r s o l a r s y s t e m and of p a r t i c u l a r i n t e r e s t i s t h e f a c t t h a t t h e H 2 0 ices e x i s t i n t h a t e x o t i c environment a t t e m p e r a t u r e s a* low as 35 K a n d p r e s s u r e s as h i g h a s s e v e r a l GPa [I]. Not o n l y a r e t h e s e c o n d i t i o n s f a r removed from p r e v i o u s e x p e r i m e n t a l and t e r r e s t r i a l f i e l d e x p e r i e n c e , o t h e r h i g h - p r e s s u r e forms of i c e a r e e x p e c t e d t o b e s t a b l e i n t h e i n t e r i o r s of t h e s e i c y moons and p l a n e t s . Many i n t e r n a l p r o c e s s e s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987131

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Cl-228 JOURNAL DE PHYSIQUE

connected wlth t h e t h e r ~ n o m e c l l a n ~ c a ~ e v o l u t ~ o n of t h e s e :ioclies involve t h e f r a c t u r e and flow p r o p e r t i e s of H20 i c e and hence we were motrvated t o e x p l o r e t h e i n e l a s - t i c p r o p e r t i e s of t h i s compound a t t e m p e r a t u r e s and p r e s s u r e s f a r removed from previous work i n o r d e r t o provide some of t h e t o o l s f o r i n t e r p r e t i n g t h e s u r f a c e f e a t u r e s t h a t stem from t h e s e i n t e r n a l processes. A companion paper [2] r e p o r t s t h e flow p r o p e r t i e s of i c e 11, I11 and V. This paper f i r s t e x p l o r e s t h e f a i l u r e p r o c e s s e s t h a t dominate a t l a b o r a t o r y time s c a l e s a t t e m p e r a t u r e s below about 165 K. Second, we review t h e important e f f e c t s of temperature and deformation r a t e s on t h e s t e a d y - s t a t e p l a s t i c s t r e n g t h of p l y c r y s t a l l i n e i c e Ih and demon- s t r a t e t h a t t h e r h e o l o g i c a l laws determined a t high temperatures f o r i c e a r e an i n a d e q u a t e d e s c r i p t i o n of t h e flow b e h a v i o r a t lower temperatures. L a s t l y , we d e s c r i b e some p r e l i m i n a r y o p t i c a l t h i n s e c t i o n t e x t u r e s and s t r u c t u r e s t h a t a r e r e v e a l i n g of t h e o p e r a t i n g p l a s t i c deformation mechanisms.

2 . Experimental d e t a i l s . - C l e a r i s o t r o p i c p o l y c r y s t a l l i n e aggregates of i c e Ih were prepared by a s t a n d a r d molding technique 141, r e s u l t i n g i n a polygonal g r a i n t e x t u r e , uniform g r a i n s i z e of 700 v m ( l i n e a r i n t e r c e p t method [3] ) , and sample s i z e 25.4 mm diameter and 62 mm l e n g t h . The specimens were j a c k e t e d i n indium and s h o r t e n e d a t c o n s t a n t r a t e s i n a h i g h - p r e s s u r e gas a p p a r a t u s designed t o deform i c e a t low t e m p e r a t u r e s 141. The d i f f e r e n t i a l s t r e s s 0 = o l

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o3 ( o l and o3 a r e t h e maximum and minimum p r i n c i p a l compressive s t r e s s e s ) and e n g ~ n e e r i n g s t r a i n E were c a l c u l a t e d from t h e f o ~ c e and displacement t r a n s d u c e r r e c o r d s and t h e r e s u l t - i n g e f f e c t s of s t r a i n r a t e E , a b s o l u t e t e m p e r a t u r e T, and c o n f i n i n g p r e s s u r e P- on

..

t h e s t r e s s - s t r a i n c u r v e s were determined. See our e a r l i e r p u b l i c a t i o n s [4, 131 f o r f u r t h e r d e t a i l s .

3. Experimental r e s u l t s . - 3.1. P r e s s u r e e f f e c t s T a t 2 165 K.-

--- --- - -- --- -

Four f a i l u r e processes a r e important a t low t e m p e r a t u r e s : ( 1 ) Axial s p l i t t i n % a t c o n f i n i n g p r e s s u r e s n e a r 0.1 MPa. This p r o c e s s i n v o l v e s t h e production, growth and coales- cence of t e n s i l e microcracks o r i e n t e d p a r a l l e l t o t h e specimen compression a x i s and normal t o t h e l e a s t p r i n c i p a l compressive s t r e s s and i s a common mode of f a i l - u r e of b r i t t l e m a t e r i a l s under n e a r - u n i a x i a l compression c o n d i t i o n s 163.

( 2 ) B r i t t l e s h e a r f r a c t u r e on i n c l i n e d f a u l t s where t h e f a i l u r e s t r e n g t h of i n c r e a s e s s t e e p l y with i n c r e a s i n g p r e s s u r e ( s e e Fig. 1 ) . Again, t h i s i s a very

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Fig. 1.- F a i l u r e s t r e n g t h s of of i c e a t low t e m p e r a t u r e s (T < 165 K ) and e l e v a t e d p r e s s u r e s [from unpublished d a t a and 41 ^b

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Fig. 2.- V a r i a t i o n of t h e s t r e n g t h of i c e with c o n f i n i n g p r e s s u r e a t T =

195 K.

common f a i l u r e mode of rocks and ceramics a t e l e v a t e d c o n f i n i n g p r e s s u r e [6] and i s thought t o develop from t h e production, growth and i n t e r a c t i o n of t e n s i l e microcracks [71. F a i l u r e s t r e n g t h i s r e l a t i v e l y i n s e n s i t i v e t o temperature and

s t r a i n r a t e [ 4 ] . ( 3 ) F r i c t i o n a l s l i d i n g along p r e e x i s t i n g f r a c t u r e s . A f t e r a s h e a r

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f a u l t h a s formed, t h e r e s i s t a n c e t o f r i c t i o n a l s l i d i n g i s l e s s t h a n t h a t r e q u i r e d tc form a f a u l t ( F i g . 1 ) and hence subsequent deformation t a k e s place by s l i d i n g

(k]. S e p a r a t e t e s t s on samples w i t h p r e c u t and ground a r t i f i c i a l f a u l t s i n d i c a t e t h a t i c e Ih d i s p l a y s a f r i c t i o n a l law of t h e form

T = 8.5 MPa + 0.2 o (MPa)

f ( 1 )

where .rf i s t h e s h e a r s t r e s s n e c e s s a r y t o overcome s t a t i c f r i c t i o n and on i s t h e normal s t r e s s on t h e s l i d i n g s u r f a c e a t t h e time t h a t s l i d i n g o c c u r s [ 9 ] . F r i c t i o n i n i c e a t t h e s e c o n d i t i o n s i s u n s t a b l e , producing r a p i d s t r e s s drops t h a t can t a k e p l a c e r e p e a t e d l y u p n r e l o a d r n g i f t h e j a c k e t does not r u p t u r e . The s l i d i n g s t r e n g t h g e n e r a l l y i n c r e a s e s with e v e n t number, r e a c h i n g an a p p a r e n t p l a t e a u a f t e r s e v e r a l c y c l e s . The f r i c t i o n law of eq. ( 1 ) i s r e l a t i v e l y i n s e n s i t i v e t o t e m ra- t u r e s over t h e range 77 t o 115 K and s l i d i n g v e l o c i t i e s r a n g i n g from 3 x 10-'to 3 x mm s -1 and normal s t r e s s e s from 20 t o 250 MPa. The micromechanical mechanisms c o n t r o l l i n g i c e f r i c t i o n under t h e s e c o n d i t i o n s a r e ' unknown. ( 4 ) High- p r e s s u r e s h e a r i n s t a b i l i t y . Above a c o n f i n i n g p r e s s u r e of 30 MPa a t T < 165 K, i c e e x h i b i t s an unusual form of s h e a r f a i l u r e . It i s unusual because p r e s s u r e does n o t i n c r e a s e t h e f a i l u r e s t r e n g t h o f ; of i s e i t h e r independent of PC o r of d e c r e a s e s with i n c r e a s i n g PC ( F i g . 1 ) . These f a u l t s form i n t h e maxunum s h e a r s t r e s s o r i e n - t a t i o n ( 4 5 0 t o t h e compression d i r e c t i o n ) and i n t h e one t e s t i n which t h e j a c k e t d i d n o t l e a k a f t e r f a i l u r e o c c u r r e d , a subsequent f a i l u r e o c c u r r e d a t about t h e same o f , i n d i c a t i n g t h a t cohesion was n o t reduced during t h e f i r s t event, i n c o n t r a s t with o r d i n a r y s h e a r f r a c t u r e . Kirby [ l o ] proposes t h a t t h i s s h e a r

i n s t a b i l i t y i s connected w i t h t h e l o c a l i z a t i o n i n t h e f a u l t of a polymorphic phase change t o i c e I1 and c i t e s an example of a n o t h e r non-metallic compound t h a t e x h i b i t e d n e a r l y i d e n t i c a l behavior.

3.2. g g g s g z g _ e f f e c t s _at ^{T _ _ X}152 &.- A t h i g h e r temperatures, i c e Ih e x h i b i t s a t y p i c a l b r i t t l e - d u c t i l e t r a n s i t i o n with i n c r e a s i n g c o n f i n i n g p r e s s u r e which depends upon temperature and s t r a i n r a t e . A t p r e s s u r e s l e s s t h a n about 10 MPa a t

195 K, o r d i n a r y s h e a r f r a c t u r e o c c u r s w i t h of i n c r e a s i n g s t e e p l y with i n c r e a s i n g PC (Fig. 2 ) . A t i n t e r m e d i a t e p r e s s u r e s , t r a n s i t i o n a l b r i t t l e - d u c t i l e behavior occurs. A t PC a 50 MPa, t h e samples deform by e s s e n t i a l l y homogeneous p l a s t i c deformation and t h e s t e a d y - s t a t e s t r e n g t h os ( e x p l a i n e d below) s l i g h t l y d e c r e a s e s with i n c r e a s i n g PC. This p r e s s u r e e f f e c t i s c o n s i s t e n t with a n e g a t i v e a c t i v a t i o n volume f o r c r e e p of -13 x m3/inole ( s e e flow law d i s c u s s i o n below).

3.3. g~~g~_s_t~gu&p~& _ i _ n t r p r e t a t i o g _qf e_e_

.sxs&~

s_sl_n~ryzs.- A l l of t h e t e s t s i n t h e d u c t i l e regime e x h i b i t l i n e a r q u a s i - e l a s t i c behavior a t low s t r e s s e s , followed by macroscopic y i e l d a t 0 a peak r n t h e s t r e s s - s t r a i n curve a t om followed by s t r a i n s o f t e n i n g and tK6n s t e a d y - s t a t e s t r e n g t h as t o s t r a i n s of about 0.20 where b a r r e l i n g of t h e samples becomes t o o pronounced t o make meaningful measurements of s t r e s s and s t r a i n . Thin s e c t i o n s of samples t a k e n t o v a r i o u s s t r a i n s a l o n g a s t r e s s - s t r a i n curve a t T = 213 K , E = 3.5 x s - I and PC = 100 MPa i n d i c a t e t h e f o l l o w i n g e v o l u t i o n of i n e l a s t i c processes: ( A ) A t low s t r a i n s where s t r e s s e s a r e between a and a,,,, samples show p l a s t i c deformation f e a t u r e s i n t h e o r i g i n a l g r a i n s a s i x d i c a t e d by v a r i a b l e e x t i n c t i o n ( o p t i c a l o r i e n t a t i o n changes) i n i n d i v i d u a l g r a i n s . (B) A t s t r a i n s j u s t beyond new r e c r y s t a l l i z e d g r a i n s appear f o r t h e f i r s t time and no o p t i c a l - s c a l e ev%ence f o r p l a s t i c deformation i n o r i g i n a l o r r e c r y s t a l l i z e d g r a i n s i s seen. ( C ) A t s t r a i n s s u f f i c i e n t l y high t h a t s t e a d y - s t a t e flow s t r e n g t h i s a t t a i n e d , t h e r e c r y s t a l l i z e d g r a i n s i z e s t a b i l i z e s t o v a l u e s l e s s t h a n t h o s e observed i n t h e s t r a i n - s o f t e n i n g p a r t of t h e s t r e s s - s t r a i n curve. There i s no evidence f o r s i g n i f i c a n t g r a i n f l a t - t e n i n g a t any s t a g e of t h e s t r e s s - s t r a i n curve. We conclude t h a t t h e s t r a i n - s o f t e n i n g s t a g e s a r e a s s o c i a t e d w i t h t h e o n s e t of r e c r y s t a l l i z a t i o n and t h a t t h e a t t a i n m e n t of s t e a d y - s t a t e flow i s connected with t h e s t a b i l i z a t i o n of r e c r y s - t a l l i z e d g r a i n s i z e . I n t h e d i s c u s s i o n below, we e x p l o r e t h e s y s t e m a t i c e f f e c t s of T, E and PC on as.

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3 - 4 - E_f_fects_ of tempe_r_ature~ s t r a h gate and_ pyes_s=_e gte_a_dy:_state _st:en$h.-

For t h e purposes of d i s c u s s i o n , we p l o t t h e s t e a d y - s t a t e s t r e n g t h s on a l o g 0, v e r s u s l/T(K) b a s i s f o r f o u r d i f f e r e n t s t r a i n r a t e s ( F i g . 3 ) . I f i c e Ih f o l l o w s a flow law of t h e g e n e r a l form

t h e n t h e d a t a should p l o t l i n e a r l y with s l o p e s equal t o Q*/2.303 nR. In e q u a t i o n ( 2 ) . A, n and Q* a r e m a t e r i a l c o n s t a n t s t h a t depend u p n deformation mechanism. Q*

i s t h e a c t i v a t i o n energy f o r s t e a d y - s t a t e flow which c o n t a i n s an e f f e c t of pres- s u r e P: Q* = H* + PV* where H* i s t h e a c t i v a t i o n e n t h a l p y and V* i s t h e a c t i v a t i o n volume. The d a t a i n d i c a t e t h r e e d i s t i n c t regimes of flow: ( 1 ) Regime A a t t h e h i g h e s t t e m p e r a t u r e s which d i s p l a y s t h e l a r g e s t e f f e c t of t e m p e r a t u r e on as. I n Figure 3 we a l s o p l o t t h e u n i a x i a l as d a t a of MelLor and Cole [ l l ] which c l e a r l y shows t h a t our flow d a t a converges w i t h d a t a c o l l e c t e d f o r g l a c i o l o g i c a l purposes a t h i g h e r t e m p e r a t u r e and room p r e s s u r e . The l e a s t - s q u a r e s f i t s t o t h i s d a t a s e t ( T a b l e 1 ) i n d i c a t e n = 4.0

*

^{0 . 6} ^and^Q*⁼⁹¹⁺2 kJ mol-l, v a l u e s very c l o s e t o t h o s e r e p o r t e d by o t h e r s i n . t h i s t e m p e r a t u r e r a n g e ( s e e review by Weertman [I21 ).

Samples deformed i n t h i s regime a r e unusually c l e a r and t h i n s e c t i o n s c u t from them show evidence f o r g r a i n boundary m o b i l i t y i n t h e form of g r a i n growth and g r a i n boundary bowing. ( 2 ) Regime B i n which r e c r y s t a l l i z e d g r a i n s a r e polygonal i n shape and n e i t h e r g r a i n shape changes nor i n t e r n a l p l a s t i c deformation f e a t u r e s a r e observed a t t h e o p t i c a l s c a l e i n t h e deformed samples. Although t h e s t r e s s exponent n i s e s s e n t i a l l y t h e same a s i n regime A, Q* i s markedly lower a t 61 f 2 kJ mold'. ( 3 ) Regime C , i n which p a r t i a l r e c r y s t a l l i z a t i o n h a s o c c u r r e d b u t e v i d e n t l y h a s n o t kept pace with i n t e r n a l deformation, judging from t h e p l a s t i c deformation f e a t u r e s (bending and k i n k i n g ) t h a t a r e prominent i n many of t h e g r a i n s . The n = 4.7 f. 0.2 and Q* = 36 f 5 kJ mol-' a r e both s i g n i f i c a n t l y d i f f e r - e n t t h a n a t h i g h e r t e m p e r a t u r e s and lower s t r e s s e s . I t should be emphasized t h a t t h e flow-law parameters c h a r a c t e r i z i n g regime C a r e t h e l e a s t - w e l l determined of

TEMPERATURE. K

1 0 0 0 2 8 0 260 2 4 0 220 2 0 0 180 160 140 125

Y I I I I I I I

-

5 0 0

- -

-

m

-

a \

2 - \ -

\ SHEAR INSTABILITY LIMIT

- - - -

-

- -

STEADY-STATE FLOW DATA. ICE ih Confining pressure 5 0 MPa- Imposed axial strain r a t e 1

\

\ 0 3.5 x 10-4 s-1 1

u

-

U- A 3.5 x 10-5 S-1

0 3.5 x 10-6 s-1

-

o 3.5 x 10-7 s-1

I I I

4 5 6 7 8

INVERSE TEMPERATURE I O ~ / T ( K )

Fig. 3 . - V a r i a t i o n of s t e a d y - s t a t e flow s t r e s s as w i t h temperature T a t f o u r d i f f e r e n t s t r a i n r a t e s p l o t t e d on a l o g l o a s v e r s u s 1/T(K) b a s i s . The i n t e r p l a t e d d a t a of Mellor and Cole [ I l l i s shown a s f l l l e d symbols. The s l o p e s of t h e c u r v e s a r e p r o p s r t i o n a l t o t h e a c t i v a t i o n energy Q* and t h e s e p a r a t i o n between t h e d a t a a t v a r i o u s s t r a i n r a t e s r e f l e c t s t h e s t r e s s exponent n. Note t h e d i f f e r e n t flow r e q i x e s t h a t e v i d e n t l y r e f l e c t chanqes i n deformation mechanisms.

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t h e t h r e e because of t h e narrower s t r a i n r a t e range i m p s e d by t h e high-pressure f a u l t i n g i n s t a b i l i t y and t h i s flow law may be contaminated by s u b t l e t r a n s i t i o n a l behavior toward t h e f a u l t i n g behavior.

Table 1. Flow law parameters f o r i c e a t a c o n f i n i n g p r e s s u r e of 50 MPa

loglOA n Q* V*

Regime [MP~-"s- l ] [ k ~ mol-l] [rn3 rnol-l]

D u c t i l e C -2.8 f 0.6 4.7 f 0.3 36 f 5

--

LOW T

( 5 ¹⁹⁵^K)

D u c t i l e B

I n t e r m e d i a t e T 5.10 f 0.03 4.0 f 0.1 61 f 2 -(13*3) x (-195-240 K)

D u c t i l e A 11.8

*

^0.4 ^4.0 ^{f 0.6} ⁹¹^{f 2}

--

High T

4. I n t e r p r e t a t i o n of t h e d u c t i l e flow regimes.- We have a l r e a d y reviewed i n a n o t h e r paper [I31 t h e probable deformation mechanisms t h a t c o n t r o l t h e r h e o l o g i - c a l laws d i s p l a y e d by i c e Ih. Regime B i s probably t h e b e s t understood. The a c t i v a t i o n energy f o r c r e e p Q* = 61 f 2 kJ mol-' is n e a r l y i d e n t i c a l with t h a t f o r molecular H20 d i f f u s i o n ( 6 6 k 13 k J mole' [14] ) and s o i s s i m i l a r t o many power law m a t e r i a l s deformed a t h i g h t e m p e r a t u r e where d i s l o c a t i o n recovery p r o c e s s e s dominate [12, 15, 161. A l t e r n a t i v e l y , a d i f f u s i o n - c o n t r o l l e d d i s l o c a t i o n g l i d e process may be o p e r a t i n g [12, 181. A t h i g h e r t e m p e r a t u r e s , g r a i n boundary p r o c e s s e s e v i d e n t l y a r e involved s i n c e t h e t r a n s i t i o n i n a c t i v a t i o n e n e r g i e s between regimes A and B do n o t occur i n s i n g l e - c r y s t a l t e s t s 117, 181. L i q u i d a l o n g g r a i n boundaries t h a t f a c i l i t a t e s g r a i n boundary m i g r a t i o n and i n t e r g r a i n i n t e r a c t i o n s h a s been f r e q u e n t l y c i t e d a s c o n t r i b u t i n g t o t h e h i g h e r a c t i v a t i o n energy i n t h i s regime ( s e e reviews i n [I71 and [ 1 8 ] ) . The evidence of enhanced grain-boundary m i g r a t i o n i n our samples i s c o n s i s t e n t with t h i s i n t e r p r e t a t i o n . Regime C i s more d i f f i c u l t t o i n t e r p r e t . Samples deformed under t h e s e c o n d i t i o n s show c l e a r evidence f o r i n t e r n a l deformation, a s we noted e a r l i e r i n t h i s paper.

The h i g h e r 2 v a l u e and lower a c t i v a t i o n energy may be more i n d i c a t i v e of s t r i c t l y g l i d e - c o n t r o l l e d creep. A l t e r n a t i v e l y , t h e apparent flow-law parameters may b e merely t r a n s i t i o n a l t o t h o s e a p p r o p r i a t e t o lower temperatures which we c o u l d n o t e x p l o r e because our t e s t s were t r u n c a t e d by t h e s h e a r i n s t a b i l i t y phenomenon, The l a c k of d e t a i l e d knowledge of d i s l o c a t i o n and p i n t d e f e c t p r o p e r t i e s a t . t h e s e low t e m p e r a t u r e s obviously hampers our understanding of t h e flow p r o p e r t i e s of i c e Ih a t low temperatures.

5. Conclusions.- I c e Ih d i s p l a y s a r i c h v a r i e t y of i n e l a s t i c behavior a t low t o i n t e r m e d i a t e t e m p e r a t u r e s , behavior t h a t stems from a range of deformation p r o c e s s e s t h a t a r e p o r l y understood. These e x p l o r a t o r y experiments a r e only a beginning i n t r y i n g t o b e t t e r understand t h e rheology of t h i s i n t r i g u i n g m a t e r i a l a t low temperatures.

Acknowledgments.- We thank C a r l Boro and Laura S t e r n f o r t h e i r t e c h n i c a l a s s i s t - ance i n a p p a r a t u s c o n s t r u c t i o n and maintenance and sample p r e p a r a t i o n . This work was performed under c o n t r a c t W-7405-ENG-48 w i t h NASA which we g r a t e f u l l y acknowl- edge. Beverly Monroe performed h e r u s u a l magic i n t y p i n g t h e manuscript.

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