Role of transient creep in high temperature tensile failure of ice

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Role of transient creep in high temperature tensile failure of ice

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Ser

T-a

N21d

3 .

1240

C ,

2 National Research

Conseil national

3LDG

*

Council Canada

de recherches Canada

ROLE OF TRANSIENT CREEP I N HIGH TEMPERATURE

TENSILE FAILURE OF ICE

by

N.K. Sinha

Reprinted from

Scripta Metallurgica

Vol. 18, 1984

p. 777

-

782 DBR Paper No. 1240

Division of Building Research

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ABSTRACT

The s t r e s s - s t r a i n r e l a t i o n s h i p t o f r a c t u r e f o r p o l y c r y s t a l l i n e

i c e i n t e n s i o n h a s been shown t o b e governed by e l a s t i c a n d

d e l a y e d e l a s t i c d e f o r m a t i o n w i t h n e g l i g i b l e v i s c o u s flow.

Delayed e l a s t i c i t y , a s s o c i a t e d w i t h g r a i n boundary s l i d i n g ,

d o m i n a t e s t h e d e f o r m a t i o n p r o c e s s a s t h e g r a i n s i z e d e c r e a s e s

l e a d i n g t o an a p p a r e n t t r a n s i t i o n f r o m b r i t t l e t o d u c t i l e w i t h

t h e d e c r e a s e i n g r a i n s i z e .

La r e l a t i o n contrainte-d'ef ormation jusqu'

B

r u p t u r e d e l a g l a c e

p o l y c r i s t a l l i n e e n t e n s i o n s ' e s t r'ev'el'ee d e n a t u r e 6 l a s t i q u e

i n s t a n t a n k e t

Cl

a s t i q u e d i f f'er'ee

a v e c 6coulement v i s q u e u x

n ' e g l i g e a b l e .

La d'ef o r m a t i o n 6 l a s t i q u e d i f f'er'ee associ'ee a u

g l i s s e m e n t d e s g r a i n s l e s u n s s u r

l e s

a u t r e s

e s t pr'epondkante

l o r s q u e l a t a i l l e d e s g r a i n s diminue, c o n d u i s a n t

2 une p'eriode

t r a n s i t o i r e a p p a r e n t e de l ' k t a t f r a g i l e

3 l ' g t a t d u c t i l e .

(4)

S c r i p t a

M E T A L L U K G I C A

V o l . 1 8 , p p . 7 7 7 - 7 8 2 , 1 9 8 4 P r i n t e d i n t h e U.S.A.

Pergamon P r e s s L t d . A l l r i g h t s r e s e r v e d

ROLE OF TRANSIENT CREEP I N HIGH TEMPERATURE TENSILE FAILURE OF ICE Nirmal K. S i n h a

D i v i s i o n of B u i l d i n g Research, National Research Council Canada, Ottawa, Canada, KIA OR6 ( R e c e i v e d March 1 2 , 1 9 8 4 )

( R e v i s e d May 1 5 , 1 9 8 4 ) I n t r o d u c t i o n

The e f f e c t of g r a i n s i z e on t h e s t r e n g t h of p o l y c r y s t a l l i n e i c e a t a h i g h homologous temperature of 0.96 T, (-IO°C), where T, is t h e m e l t i n g p o i n t i n Kelvin, h a s been i n v e s t i g a t e d e x p e r i m e n t a l l y by a number of i n v e s t i g a t o r s [l-61. A review o f t h e s e r e s u l t s showed t h a t a l l

t h e s e t e s t s , however, have been a f f e c t e d by c h o i c e of improper specimen geometry, t h e p r e s e n c e of l a r g e number of i n c l u s i o n s i n t h e m a t e r i a l s and by u n d e s i r a b l e i n t e r a c t i o n between t h e t e s t i n g machine and t e s t specimens 171. Consequently i t a p p e a r s t h a t t h e dependence of s t r e n g t h on g r a i r s i z e f o r p u r e i c e i s s t i l l n o t k n w n w i t h c e r t a i n t y . The i n v e s t i g a t i o n s c a r r i e d o u t by C u r r i e r e t a l . [ l - 3 1 a r e t h e b e s t among a l l t h e s e r e p o r t s because t h e y documented t h e e x p e r i m e n t a l

c o n d i t i o n s w e l l , which o t h e r s f a i l e d t o do, and because t h e y a r e t h e o n l y p e o p l e who measured t h e specimen d e f o r m a t i o n d u r i n g t h e t e s t s .

I t w i l l be s h w n i n t h i s p a p e r t h a t t h e mechanical r e s p o n s e of t h e specimens u s e d by C u r r i e r e t a l . i s c o n s i s t e n t w i t h a p r e v i o u s l y f o r m l a t e d h i g h t e m p e r a t u r e c o n s t i t u t i v e e q u a t i o n

[8-I01 p r i m a r i l y d e s c r i b i n g t r a n s i e n t and s t e a d y - s t a t e creep. S i n c e t h i s model c o n t a i n s a number of m a t e r i a l parameters t h a t a r e r e l a t e d t o micromechanical p r o c e s s e s [91, t h e a n a l y s i s a l s o p r o v i d e s a n i n s i g h t i n t o t h e mechanics i n v o l v e d i n t e n s i l e f a i l u r e . The p a p e r i n t r o d u c e s new c o n c e p t s i n t h e mechanics of deformation and f a i l u r e t h a t c o u l d p r o v i d e f o o d f o r thought and p o s s i b l e e x p e r i m e n t a l d i r e c t i o n t o t h e i n v e s t i g a t o r s i n v o l v e d i n u n d e r s t a n d i n g t h e h i g h t e m p e r a t u r e f a i l u r e mechanisms of p o l y c r y s t a l l i n e m a t e r i a l s i n g e n e r a l .

Experimental R e s u l t s and P r e l i m i n a r y A n a l y s i s

The t e s t s r e p o r t e d by C u r r i e r e t a!. [1-31 were c a r r i e d o u t under ,a c l o s e C l o o p c o n t r o l l e d c o n s t a n t cross-hea d i placement r a t e , x, o r u n d e r a nominally c o n s t a n t s t r a i n r a t e ,

i

= j / t = 1 x LO-' i 8 , w h e r e t i s t h e e f f e c t i v e specimen l e n g t h . Under t h e s e t e s t c o n d i t i o n s , t g e t e n s i l e s t r e n g t h , o f , d e c r e a s e d w i t h t h e i n c r e a s e i n g r a i n s i z e , d ( i n t h e r a n g e o f 1.0 t o , 7.3 mm),according t o t h e Hall-Petch e x p r e s s i o n a = a + k d -112 £ 1 (1) -2 -312 where a i = 0.6 MN-• and k = 0.02 MN-m

.

-2 If E i s Young's modulus (E = 9.5 GN-m [ a ] ) , t h e n e q u a t i o n (1) g i v e s t h e e l a s t i c s t r a i n a t f r a c t u r e a s i k -112 r f ( e l a s t i c ) =

+

d = 6.3 i lo-'

+

2.1 x d-l12 ( 2 )

F i g u r e 1 shows t h a t e q u a t i o n (2) u n d e r e s t i m a t e s t h e s t r a i n a c t u a l l y measured, and t h a t t h e d e v i a t i o n i n e l a s t i c r e s p o n s e depends g r e a t l y on g r a i n s i z e . The a u t h o r s [2-31 a l s o e s t i m a t e d t h e f r a c t u r e s t r a i n a s

cf (nominal) =

b

tf (3

where tf is t h e observed f a l l u r e time, and n o t e d a l a r g e d i s c r e p a n c y between t h i s and t h e measured s t r a i n s a s shown i n Fig. 1. Consequently t h e measured s t r a i n r a t e s were n o t o n l y a b o u t one o r d e r of magnitude lower b u t v a r i e d o v e r a wide range (600%). The f o l l o w i n g a n a l y s i s w i l l show t h a t e x p e r i m e n t a l o b s e r v a t i o n s c a n b e e x p l a i n e d q u a n t i t a t i v e l y u s i n g stress r a t e d u r i n g l o a d i n g a s t h e b a s i s of a n a l y s i s .

7 7 7

0 0 3 6 - 9 7 4 8 / 8 4 $ 3 . 0 0 + . O O

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TRANSIENT CREEP IN

ICE

Vol.

1 8 ,

NO.

8

Bigh Temperature Rheology of P o l y c r y s t a l s

Creep deformation i n p o l y c r y s t a l l i n e m a t e r i a l s a t high t e q e r a t u r e s c a n b e expressed phenomenologically (81 by

€ = € + E d + € " (4) v h e r e ce is t h e pure e l a s t i c deformation, e is t h e recoverable, delayed e l a s t i c s t r a i n , and $

i s t h e viscous o r permanent deformation. ( h e t e r n "viscous' w i l l b e used i n a general s e n s e t o d e s c r i b e flow l e a d i n g t o permanent deformation. The term " p l a s t i c " is avoided h e r e because i t is comaonly used t o d e s c r i b e b o t h permanent and delayed e l a s t i c deformation.)

Under c o n d i t i o n s where g r a i n boundary d i f f u s i o n a l processes d o n o t play a dominant r o l e and where t h e m i c r o s t r u c t u r e h a s not d e t e r i o r a t e d by t h e formation of i n t e r n a l voids and c r a c k s , u n i a x i a l c o n s t a n t s t r e s s c r e e p i n previoualy undeformed, pure, randomly o r i e n t e d , p o l y c r y s t a l l i n e m a t e r i a l s can be expressed i n terms of s t r e s s , a, and time, t , f o r a m a t e r i a l w i t h an average g r a i n diameter of d a t a g i v e n t e q e r a t u r e T, by 191

- .

I n t h i s equation t h e t h r e e t e r n s correspond t o t h e t h r e e s u c c e s s i v e t e r n s i n equation (4). E i s Young's modulus; aT, b, c l , n and s a r e constants; dl is t h e u n i t of g r a i n diameter; and

kv

1

is t h e viscous s t r a i n r a t e f o r u n i t s t r e s s

2 .

The constant a= is t h e i n v e r s e of r e l a x a t i o n t i m i a t temperature T i n Kelvin; n i s t h e s t r e s s exponent f o r viscous flow; and s is t h e s t r e s s exponent f o r delayed e l a s t i c i t y . Both

+

and cv. vary w i t h temperature according t o an Arrhenius

- 1

equation with t h e same a c t i v a t i o n energy, Q. Numerical values of t h e s e material c o n s t a n t s f o r i c e determined from previous c r e e p experiments [ a ] and subsequent a n a l y s i s [ 9 ] a r e given i n Table 1. Note t h a t s=l f o r i c e although i t may b e d i f f e r e n t i n o t h e r m a t e r i a l s 191.

A simple f o r m l a t i o n f o r p r e d i c t i n g s t r a i n corresponding t o a n a r b i t r a r y monotonically i n c r e a s i n g s t r e s s h i s t o r y and hence t h e s t r e s s - s t r a i n r e l a t i o n h a s been developed 1101 on t h e b a s i s of equation (5) f o r p o l y c r y s t a l l i n e m a t e r i a l s l i k e i c e , i.e., f o r s = l

.

T h i s theory h a s been t e s t e d s u c c e s s f u l l y u s i n g information obtained from u n i a x i a l unconfined compressive s t r e n g t h t e s t s on i c e i n t h e t e n p e r a t u r e range of -5 t o -30°C [ l o ] .

For l o a d i n g c o n d i t i o n s of constant s t r e s s - r a t e ,

i,

i t i s shown (10) t h a t equation (5) t a k e s t h e following form f o r t h e s t r a i n a t time t a f t e r t h e beginning of loading:

1 C1 dl Nt1

b n+l

€ = Q + -

(r)

1

Aa [ l

-

exp [ - ( a T [ ~ + l l l ~ )

I ]

+

-

v1

(5)

(6)

111 a(n+l) a

where a a

k

= NAa =

N G A ~ .

Note t h e u s e of a numerical i n t e g r a t i o n method f o r f o r m l a t i n g t h e

second, delayed e l a s t i c term. This term, however, r a p i d l y converges a s A t i s decreased [ 101.

Experimental o b s e r v a t i o n s (111 shared t h a t a c o n s t a n t cross-head displacement r a t e induces a monotonically i n c r e a s i n g s t r a i n r a t e r a t h e r t h a n t h e c o n s t a n t s t r a i n r a t e given by

k

.

This type of loading, however, g i v e s a n e a r l y l i n e a r s t r e s s r a t e during i n i t i a l l o a d i n g perfods. S t r e s s r a t e a n a l y s i s should t h e r e f o r e be a p p r o p r i a t e f o r t h e t e s t s under consideration. Also, a s w a s discussed i n [ 7 ] , i t is l e s s ambiguous because both load (and hence s t r e s s f o r t h e small

s t r a i n involved i n t h e p r e s e n t s e r i e s of t e s t s ) and time c a n b e measured a c c u r a t e l y . Moreover, i t provides an opportunity t o examine t h e a p p l i c a b i l i t y of equation (6) t o independent

experimental o b s e r v a t i o n s under a t e n s i l e mode of loading. Application of Theory

The t e s t r e s u l t s r e p o r t e d i n a t a b u l t t e d form i n [2,3] a r e presented h e r e i n Fig. 2 i n terms of average s t r e s s r a t e t o f a i l u r e , af = af

It

.

The s t r a i n a t f r a c t u r e time was c a l c u l a t e d using m a t e r i a l c o n s t a n t s i n Table 1 and equation

( 6 )

w i t h

b

=

P

f o r each t e s t and g r a i n s i z e i n Fig. 2. The r e s u l t s a r e compared with t h e measured values i n Fig. 3. The agreement between theory (open c i r c l e s ) and experiment ( s o l i d c i r c l e s ) i s considered e x c e l l e n t s i n c e no

modification was made i n e i t h e r t h e method of c a l c u l a t i o n o r t h e numerical values of t h e m a t e r i a l c o n s t a n t s determined s e v e r a l y e a r s ago [ 8 ] from c r e e p t e s t s on pure inclusion-f r e e ice. One of t h e f a c t s supporting t h e v a l i d i t y of t h e proposed model i s t h a t i t can account f o r t h e

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Vol.

18,

No.

8

TRANSIENT CREEP IN ICE

It s h o u l d be n o t e d t h a t t h e p r e d i c t e d s t r a i n s a r e , i n g e n e r a l , somewhat l o w e r t h a n t h e measured v a l u e s . T h i s was a n t i c i p a t e d (71 b e c a u s e t h e deformation of t h e specimens was measured by i n s t a l l i n g gauges between t h e t o p and t h e bottom end c a p s (1-31. The measured s t r a i n s t h e r e f o r e r e p r e s e n t e d t h e sum of t h e d e f o r m a t i o n s of t h e gauge s e c t i o n and t h e c o n p l i a n t g r a i r r r e f i n e d end zones of e a c h specimen [ 2 , 3 ] i n which t h e g r a i n s were s m a l l e r t h a n t h o s e i n t h e gauge s e c t i o n . For t h e same a p p l i e d s t r e s s r a t e and l o a d i n g time i t was p r e d i c t e d i n a n independent s t u d y (121 t h a t a f i n e r g r a i n e d m a t e r i a l w i t h more grain-boundary s u r f a c e a r e a s would deform more t h a n a c o a r s e g r a i n e d one.

The c o n s i s t e n c y between t h e e x p e r i m e n t a l o b s e r v a t i o n s and t h e t h e o r y i s f u r t h e r

i l l u s t r a t e d i n Fig. 4, which r e p r e s e n t s t h e maximm s p a n i n

trf

i n which t h e e x p e r i m e n t s were conducted. Computed r e s u l t s a r e based on e q u a t i o n (6).

D i s c u s s i o n

Measurements of t o t a l s t r a i n a l o n e d o n o t n e c e s s a r i l y l e a d t o a n u n d e r s t a n d i n g o f t h e f a c t o r s c o n t r o l l i n g t h e deformation behaviour of a m a t e r i a l . P u r e l y e m p i r i c a l c o n s t i t u t i v e r e l a t i o n s , though extremely u s e f u l from a p r a c t i c a l p o i n t of view, d o n o t n e c e s s a r i l y p r o v i d e i n f o r m a t i o n on b a s i c m a t e r i a l p r o p e r t i e s e i t h e r . Equation ( 5 ) , however e m p i r i c a l i t may appear t o be, was developed (91 by g i v i n g c o n s i d e r a t i o n t o deformation b e h a v i o u r (81 and t h e

micromechanics of deformation through s e p a r a t i n g t h e e l a s t i c , d e l a y e d e l a s t i c and v i s c o u s components. The e l a s t i c component i s a s s o c i a t e d w i t h t h e d e f o r m a t i o n of t h e l a t t i c e . It i s assumed t h a t t h e delayed e l a s t i c i t y component i s a s s o c i a t e d w i t h g r a i n boundary s l i d i n g and t h a t t h e v i s c o u s c r e e p i s l i n k e d p r i m a r i l y t o i n t r a g r a n u l a r c r e e p due t o d i s l o c a t i o n motion.

Subsequent development of e q u a t i o n ( 6 ) from (5) a l s o involved f u r t h e r c o n s i d e r a t i o n of t h e micromechanisms of deformation (101. These b a s i c s t u d i e s s t r o n g l y i n d i c a t e d t h a t experiments should b e designed n o t o n l y t o s t u d y t h e s t r e s s - s t r a i n r e l a t i o n s b u t a l s o t h e s t r e s s and s t r a i n p a t h and recovery h i s t o r y o n unloading, a s w e l l a s m i c r o s t r u c t u r a l f e a t u r e s .

F i g u r e 4 c l a r i f i e s t h i s idea. Both t h e t h e o r y and t h e experiment c o n s i s t e n t l y show a n o n l i n e a r s t r e s s - s t r a i n response f o r t h e e n t i r e d u r a t i o n of t h e t e s t . The s t r e s s - s t r a i n diagrams i n d i c a t e t h a t c o n s i d e r a b l e n o n e l a s t i c deformation o c c u r r e d b e f o r e f r a c t u r e . The t h e o r y , because of i t s t h r e e p a r t form, b r i n g s a new i n s i g h t i n t o t h e r e l a t i o n between deformation and f a i l u r e f o r t h e t e s t s under c o n s i d e r a t i o n . T h i s i s i l l u s t r a t e d i n Fig. 5 i n which t h e d e t a i l e d

c a l c u l a t i o n s c o r r e s p o n d i n g t o t h e s t r e s s - s t r a i n diagram f o r t e s t No. 54 i n Fig. 4 a r e shown. The n o w l i n e a r time dependence of t h e t o t a l s t r a i n and i t s l a r g e d e v i a t i o n from t h e nominal s t r a i n p a t h a r e p a r t i c u l a r l y n o t i c e a b l e . The t h e o r y s u g g e s t s t h a t t h e v a r i a t i o n i n t h e s t r a i n r a t e d u r i n g t h e t e s t was c a u s e d p r i m a r i l y by t h e t i m e w i s e n o n l i n e a r r e s p o n s e o f t h e d e l a y e d e l a s t i c s t r a i n . Note a l s o t h e p r i m a r i l y e l a s t i c and d e l a y e d e l a s t i c (hence r e c o v e r a b l e ) n a t u r e of t h e t o t a l s t r a i n w i t h v e r y l i t t l e c o n t r i b u t i o n from t h e v i s c o u s t e r m (i.e., permanent s t r a i n ) , e v e n a t t h e time of f r a c t u r e .

The c o n t r i b u t i o n of t h e t h r e e components o f s t r a i n t o t h e t o t a l s t r a i n a t f r a c t u r e (corresponding t o a l l t h e r e s I t s i n Fig. 3 ) a r e p r e s e n t e d i n Fig. 6.

_Y

The c o n t r i b u t i o n of t h e v i s c o u s s t r a i n a t f r a c t u r e , ov, t o t h e t o t a l s t r a i n , of, d e f i n e d a s

4

= of/ zf, i s s m a l l i n a l l t h e t e s t s , i n t h e range of 4 t o 7%. T o t a l s t r a i n , t h e r e f o r e , was dominate$ by t h e e l a s t i c and d e l a y e d e l a s t i c deformation. However, t h e r e l a t i v e importance o f t h e e l a s t i c s t r a i n and t h e delayed e l a s t i c s t r a i n depends on g r a i n s i z e (Fig. 6). For l a r g e g r a i n s , e l a s t i c s t r a i n

dominates whereas t h e d e l a y e & e l a s t i c c o onent dominates f o r f i n e r g r a i n s . The cone i b u t i n o f t h e delayed e l a s t i c s t r a i n a t f r a c t u r e ,

q.

t o t h e t o t a l s t r a i n , r f , denoted by

4

(= z / s f ) , is 73% f o r t h e t e s t w i t h d = 1.0 mm, wh r e a s

_f

i t i s o n l y 26% f o r t h e t e s t w i t h d = 7.3 mm. Bn g e n e r a l , i t is t h e l a r g e v a r i a t i o n of yd w i t h d t h a t d e t e r m i n e s t h e g r a i n s i z e dependence of t h e f r a c t u r e s t r a i n and hence t h e a p p a r e n t i n c r e a s e i n d u c t i l i t y w i t h d e c r e a s e i n g r a i n s i z e .

F i n a l l y , t h i s e x p l a i n s t h e observed dependence between t h e d e c r e a s e i n g r a i n s i z e and t h e r a p i d l y i n c r e a s i n g d e v i a t i o n of t h e t o t a l s t r a i n from p u r e e l a s t i c s t r a i n ( s e e Fig. 1). S nce t h e delayed e l a s t i c s t r a i n i s a s s o c i a t e d w i t h t h e g r a i n boundary s l i d i n g s t r a i n [91,

f

g i v e s a measure of t h e c o n t r i b u t i o n of t h e s l i d i n g t o t h e t o t a l s t r a i n a t f a i l u r e . T h i s b r i n g s i n i n t e r e s t i n g p o s s i b i l i t i e s of i n t r o d u c i n g t h e s u b j e c t of i n t e r g r a n u l a r f r a c t u r e and d i s c u s s i n g t h e above r e s u l t s a c c o r d i n g l y . However, t h i s i s o u t s i d e t h e s c o p e of t h i s paper.

I f a specimen i s unloaded f u l l y and i n s t a n t l y j u s t b e f o r e i t f r a c t u r e s , most o f t h e deformation w i l l be recovered. T h i s p r e d i c t i o n c a n b e i n v e s t i g a t e d r e a d i l y and d i r e c t l y by measuring t h e d e f o r m a t i o n d u r i n g l o a d i n g o f a specimen, u n d e r a s p e c i f i c stress r a t e , t o a r e q u i r e d s t r e s s l e v e l f o l l o w e d by r a p i d u n l o a d i n g t o z e r o stress. A s e r i e s of c o n s t a n t s t r e s s r a t e t e s t s , o v e r a wide r a n g e o f l o a d i n g r a t e s , h a s b e e n conducted t o examine t h e v a l i d i t y o f t h e

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above h y p o t h e s i s u s i n g a 1 MN c a p a c i t y servo-hydraulic closed-loop t e s t system. T e s t procedures d e s c r i b e d i n 1131 were followed. R e s u l t s of t h e s e t e s t s w i l l be p r e s e n t e d elsewhere i n d e t a i l . An example i s s h m h e r e i n Fig. 7 t h a t i s r e l e v a n t t o t h e l o a d i n g c o n d i t i o n s shown i n Fig. 2. It i l l u s t r a t e s t h e r e s u l t s o b t a i n e d on t r a n s p a r e n t , i n c l u s i o n f r e e , t r a n s v e r s e l y i s o t r o p i c c o l u m n a r g r a i n e d S-2 i c e w i t h c o n p r e s s i v e l o a d 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 c o umns. The specimen was loaded t o a stress l e v e l of 1.2 W a a t a c o n s t a n t r a t e of 5 x lo-' U N i 2 8-' a t -lO°C and t h e n unloaded r a p i d l y . The a x i a l s t r a i n was measured by means of a displacement gauge mounted d i r e c t l y on t h e specimen. Note t h e monotonically i n c r e a s i n g s t r a i n r a t e d u r i n g l o a d i n g and t h e s m a l l amount of permanent deformation on unloading.

Conclusions

Experimental o b s e r v a t i o n s by C u r r i e r e t alemade on t e n s i l e s t r e n g t h and deformation of p o l y c r y s t a l l i n e i c e a t 0.96 T,have been examined on t h e b a s i s of a proposed h i g h temperature r h e o l o g i c a l model developed s p e c i f i c a l l y f o r d e s c r i b i n g t r a n s i e n t c r e e p and i t s dependence on g r a i n s i z e . The model shows t h a t t h e s t r e s s - s t r a i n r e l a t i o n s h i p is governed by e l a s t i c and delayed e l a e t i c deformation w i t h very l i t t l e permanent deformation due t o v i s c o u s flow. The apparent b r i t t l e t o d u c t i l e t r a n s i t i o n w i t h t h e d e c r e a s e i n g r a i n s i z e , a s i n d i c a t e d by t h e s t r a i n a t f r a c t u r e , is s h a m t o be t h e r e s u l t of t h e conqlementary r e l a t i o n s h i p between t h e e l a s t i c s t r a i n and t h e delayed e l a s t i c s t r a i n . Delayed e l a s t i c i t y , a s s o c i a t e d w i t h g r a i n boundary s l i d i n g , dominates t h e deformation p r o c e s s a s t h e g r a i n s i z e decreases.

Acknowledgement

The a u t h o r i s i n d e b t e d t o J.H. C u r r i e r , E.M. Schulson and W.F. St. Lawrence. It vould have been impossible t o develop t h e concept proposed i n t h i s paper without t h e a v a i l a b i l i t y o f t h e experimental d a t a o b t a i n e d by them.

T h i s paper i s a c o n t r i b u t i o n from t h e D i v i s i o n of B u i l d i n g Research. National Research Council of Canada, and i s published w i t h t h e approval of t h e D i r e c t o r of t h e Division.

References

1. J.H. C u r r i e r and E.H. Schulson, Acta Metall. 30, 1511 (1982).

2. J.H. C u r r i e r , H.Sc. T h e s i s , 'Ihayer School of Engineering. Dartmouth College. Hanover, N.H. (1981).

3. J.H. C u r r i e r , E.M. Schulson and W.F. S t . Lawrence, US A r m y , Cold Regions Research and Engineering Laboratory, Hanover. N.H., Report 83-14 (1983).

4. J. Muguruma, J. Phys.,

D.,

Ser. 2, V.2. 1517 (1969). 5.

B.

Michel, Can. J. Civ. Engng. 5, 285 (1978).

6. S.J. J o n e s andH.A.M. Chew, J. Glaciology. 27, p. 517 (1981). 7. N.K. Sinha, S c r i p t a Metall. 17, 1269 (1983).

8. N.K. Sinha, Experimental Mechanics, 18, 464 (1978). 9. N.K. Sinha, Phil. Mag., 40, 825 (1979).

10. N.K. Sinha, Cold Regions S c i . Technol., 8 , 25 (1983). 11. N.K. Sinha, Experimental Mechanics, 21, 209 (1981).

12. N.K. Sinha, Proc. 6 t h I n t e r n a t i o n a l Conference on P o r t and Ocean Engineering under A r c t i c Conditions, Quebec, Canada, V.1, 216 (1981).

13. N.K. Sinha, J. Mat. S c i . , 17, 785 (1982). TABLE 1

Creep Parameters f o r I c e Obtained from E a r l i e r Creep Experiments [8,9

1.

E = 9.5 G N * ~ ' ~ ; G = 3.8 G N - ~ - ~ ; Q

-

67 Wlmol c l = 9; d l

-

1 mm; s = 1; n = 3; b = 0.34; aT (T = 263 K) = 2.5 x s'l;

2. -

1.76 x 1 0 ' ~ 8-1; al = 1 U N ~ I I - ~ , T = 263 K. 1

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T I M E . I. I

FIGURE 5

GRAIN SIZE, d, rnrn

FIGURE 6

FIG. 5 Computed s t r a i n components and the t o t a l s t r a i n f o r t e s t No. 5 4

FIG. 6 Grain s i z e dependence of the contribution of e l a s t i c s t r a i n , delayed e l a s t i c s t r a i n and viscous s t r a i n t o the t o t a l s t r a i n a t fracture

2

-

2.5 UNLOADED IN < 0.5 r 0

-

2 . 0 '=

-

1.5 263 K i

-

i r - 5 x 1 0 ~ 3 ~ ~ . m ~ 2 ~ ~ i - 1 , 0 5-2 ICE

-

VI - _{0 . 5} 1 , I . I . : 0 0 100 200 300 100 500 TIME. t. r FIGURE 7