MICROPLASTICITY OF ICE IH STUDIED BY VERY LOW FREQUENCY INTERNAL FRICTION MEASUREMENTS

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MICROPLASTICITY OF ICE IH STUDIED BY VERY LOW FREQUENCY INTERNAL FRICTION

MEASUREMENTS

J. Tatibouet, J. Perez, R. Vassoille

To cite this version:

J. Tatibouet, J. Perez, R. Vassoille. MICROPLASTICITY OF ICE IH STUDIED BY VERY LOW

FREQUENCY INTERNAL FRICTION MEASUREMENTS. Journal de Physique Colloques, 1983,

44 (C9), pp.C9-799-C9-803. �10.1051/jphyscol:19839121�. �jpa-00223358�

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JOURNAL DE PHYSIQUE

Colloque C9, suppl6ment a u n012, Tome 44, d k e m b r e 1983 page C9-799

MICROPLASTICITY OF I C E IH STUDIED BY VERY LOW FREQUENCY INTERNAL FRICTION MEASUREMENTS

J. Tatibouet, J. Perez and R. Vassoille

Groupe drEtudes de Me'taZZurgie Physique e t de Physique des Mat&riam, (CNRS LA 3 4 1 ) , I.N.S.A. de Lyon, Bat. 502, 69621 ViZZembanne Cedex, France Resum6

-

Le f r o t t e m e n t i n t e r n e 2 haute temperature de l a glace e s t 6 t u d i e 2 l a f o i s p a r des mesures 2 t r P s basses frequences (10-$-1 Hz) e t p a r micro- f l u a g e . Deux mecanismes de mouvement de d i s l o c a t i o n s sont a i n s i mis en 6 v i - dence s u i v a n t l a temperature.

A b s t r a c t

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The h i g h temperature i n t e r n a l f r i c t i o n o f i c e i s s t u d i e d b o t h by v e r y l o w frequencies (10-4-1 Hz) i n t e r n a l f r i c t i o n measurement and microcreep experiments. Two mechanisms o f d i s l o c a t i o n movement are p u t

i n evidence, depending on temperature.

I

-

INTRODUCTION

A t h i g h temperature ( h i g h e r than 200 K), i . e . above t h e r e l a x a t i o n peak, t h e r i s e i n i n t e r n a l f r i c t i o n o f i c e has been s t u d i e d b y some o f t h e present authors /1/

b u t f o r a v e r y r e s t r i c t e d range o f frequencies around 1 Hz. I n s i n g l e - c r y s t a l s , t h i s r i s e has been a t t r i b u t e d t o t h e movement o f d i s l o c a t i o n s induced by t h e c y c l i c s t r e s s /2,3/.

A previous model, based on t h e assumption o f a n o n - c r y s t a l l i n e core o f d i s l o c a - t i o n s , has been developped by PEREZ e t a1 /3/. I n order t o improve t h i s model we have extended high-temperature i n t e r n a l f r i c t i o n measurements t o very-low f r e - quencies (10-'+-I Hz). Some r e s u l t s have been p r e v i o u s l y obtained w i t h pure i c e /4/.

The purpose o f t h e present work i s on one hand t o consider HF-doped i c e ; on an o t h e r hand a comparison i s done w i t h microcreep experiments performed i n t h e same range o f temperature w i t h t h e same apparatus used f o r i n t e r n a l f r i c t i o n measurements.

I 1

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EXPERIMENTAL RESULTS

2.1

-

Experimental procedure

I n t e r n a l f r i c t i o n measurements a t very-low-frequency were performed by t h e use o f an i n v e r t e d t o r s i o n a l pendulum /5/ w i t h a v e r y weak i n e r t i a l moment. This pendulum works i n subresonant f o r c e d o s c i l l a t i o n . The t o r q u e i s t r a n s m i t t e d t o t h e specimen (8 x 2 x 50 mm3) by t h e i n t e r a c t i o n between a magnet and a magnetic f i e l d produced by Helmholtz c o i l s . S t r a i n i s detected b y mean o f d i f f e r e n t i a l photovolta'ic c e l l s . S t r a i n and s t r e s s s i g n a l s are b o t h sent t o a c a l c u l a t o r i n which t h e i n t e r n a l f r i c t i o n and a parameter p r o p o r t i o n a l t o t h e modulus are computed. E i t h e r s t r e s s o r s t r a i n can be regulated, so creep o r s t r e s s r e l a x a t i o n experiments are a l s o p o s s i b l e i n t h e domain o f m i c r o p l a s t i c i t y . The specimens are mechanically c u t from s i n g l e - c r y s t a l s grown by t h e Bridgman method i n t h e l a b o r a t o i r e de G l a c i o l o g i e i n Grenoble. T h e i r o r i e n t a t i o n s were determined by X-ray Laue diagrams. Some o f t h e specimens were HF-doped by d i f f u s i o n .

2.2

-

^Results

F i g u r e 1 shows t h e i n t e r n a l f r i c t i o n vs temperature f o r a freshlygrown non deformed specimen. The i n t e r n a l f r i c t i o n increases r a p i d l y when t h e frequency i s decreased

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19839121

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C9-800 JOURNAL

DE

PHYSIQUE

and a t con.stant frequency t h i s i n t e r n a l f r i c t i o n i s v e r y temperature dependent.

F i g . 1 shows a l s o t h e v a r i a t i o n s o f t h e modulus.

S h e a r

2 0 0 2 5 0 K

S h e a r t 3 x t o 3 M o d u l u s

[ a r b i t r a r y hunits]

F i g . 1

-

I n t e r n a l f r i c t i o n and F i g . 2

-

I n t e r n a l f r i c t i o n and shear modulus vs temperature shear modulus vs temperature

non-deformed specimen. deformed specimen (~p=1.8%)

A f t e r p l a s t i c deformation ( F i g . 2) a v e r y i m p o r t a n t increase i n i n t e r n a l f r i c t i o n can be n o t i c e d

.

-

^4.5

5 0 0 -

4001

3 0 0

200-

As high-temperature i n t e r n a l f r i c t i o n i s amplitude dependent a l l t h e experiments were done a t constant amplitude ( E max = 4 x l o - = ) . The experiments were apparently performed a t constant d i s l o c a t i o n density, s i n c e we have v e r i f i e d t h a t a f t e r every measurement a t and Hz we found e x a c t l y t h e i n i t i a l obtained a t 1 Hz.

100-

2 0 0 2 5 0 K

>ll.s

I n t e r n a l f r i c t i o n measurement were a l s o made on others types o f specimens : aged and HF-doped i c e . F i g u r e 3 shows i n t e r n a l f r i c t i o n vS temperature f o r

an HF-doped specimen. I n t h i s case we can n o t i c e d t h a t t h e r i s e i n i n t e r n a l f r i c t i o n begins a t lower temperature. Microcreep experiments were a l s o p e r - formed on every specimen. F i g u r e s 4 and 5 show such r e s u l t s obtained r e ~ p e c t i v e l l y ~ f o r deformed aged- i c e and HF-doped. S t r a i n r a t e E i s measured a f t e r 20 s o f s t r e s s a p p l i c a t i o n because d i f f i c u l t i e s i n determining E a t t i m e zero. I n every case E becomes n o n - l i n e a r w i t h s t r e s s a t temperature higher than 220-235 K. The comparison between d i f f e r e n t specimens i s n o t v e r y easy because d i s l o c a t i o n d e n s i t y could v a r y f r o m one specimen t o an o t h e r .

F i g . 3

-

I n t e r n a l f r i c t i o n vs temperature.

-HF-doped specimen.

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F i g . 4

-

Creep experiments on deformed aged-ice ( ~ p = 1

.a%)

F i g . 5

-

Creep experiment on HF-doped i c e .

I11

-

DISCUSSION

I n p r e v i o u s papers /2,3/ t h e h i g h temperature i n t e r n a l f r i c t i o n has been a t t r i b u t e d t o t h e movement o f d i s l o c a t i o n s induced by c y c l i c s t r e s s . A model based on t h e assumption o f a n o n - c r y s t a l l i n e core o f d i s l o c a t i o n s was developped /3/ and a t h e o r e t i c a l v a l u e o f high-temperature i n t e r n a l f r i c t i o n was proposed. F o r low s t r e s - ses, which i s t h e case i n a l l our experiments, t h e i n t e r n a l f r i c t i o n was expressed by :

where G = shear modulus, u = frequency o f c y c l i c s t r e s s , pd = d i s l o c a t i o n d e n s i t y , b = B u r g e r s ' v e c t o r o f d i s l o c a t i o n s and T, = T~ exp (2/3)(E/kT)2 = mean d u r a t i o n o f t h e movement o f a Hz0 molecule i n t h e core, l e a d i n g t o t h e g l i d e o f t h e d e f e c t

( E = hydrogen bond energy i n t h e c o r e ) .

T h i s equation i m p l i e s t h a t than # i s p r o p o r t i o n a l t o v - '

A c t u a l l y , thanks t o t h e frequency range used i n t h i s work, i t i s p o s s i b l e t o show t h a t i t i s n o t t h e case. I n t h i s model, t h e s t r a i n r a t e

i

i s supposed time-inde- pendent when t h e s t r e s s o i s constant (Maxwellian f l o w ) . This can be assumed f o r experiments done a t frequencies f o r which t h e c y c l i c s t r e s s i s a p p l i e d d u r i n g a s h o r t t i m e (1

Hz).

F o r experiments performed a t v e r y low frequencies t h i s i s no longer t h e case as we have n o t i c e d i n t h e creep experiments done i n t h e domain of m i c r o p l a s t i c i t y . F o r example i n experiments a t Hz, corresponding t o a creep t i m e

l o 3

s, t h e s t r a i n r a t e does vary, i l l u s t r a t i n g a more complex v i s c o e l a s t i c behaviour o f t h e m a t e r i a l .

This type o f non p r o p o r t i o n a l i t y between t a n an v - l , can be described by using a phenomenological expression derived f r o m t h e r e l a t i o n corresponding t o a stan- dard l i n e a r w i t h a d i s t r i b u t i o n o f . t h e values o f t h e parameters. I n t h e case of i c e we can suggest t h a t t h e d i s l o c a t i o n network presents a d i s t r i b u t i o n concerned m a i n l y by t h e r e s t o r i n g f o r c e s on d i s l o c a t i o n s . Using t h i s assumption, t h e i n t e r n a l

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C9-802 JOURNAL DE PHYSIQUE

f r i c t i o n a t constant temperature can be g i v e n by : 1 (ex.

- $

( 6 1 . ~ ) ~ t a n & =

C1 (-1

₌_C2

v

The d e t e r m i n a t i o n o f E i s p o s s i b l e by p l o t t i n g I n u vs

-

1 a t t a n & = constant ( a ) . We can a l s o obtained E f i by using t h e p l o t I n t a n & vs T 2

1

a t v = constant ( b ) . A d i r e c t determination o f n can be obtained from our experimental r e s u l t s by ;iT p l o t t i n g I n t a n & vs I n v _{( c ) .}

Values obtained from d i f f e r e n t experimental r e s u l t s are summarized i n t h e t a b l e I.

E(eV) ~ f i ( e V ) n c o r r e c t e d E

(a) (b) ( c ) ^from ^{( b )}

non deformed 0.094

*

^0.003 ^0.062

*

^0.004 ^0.40 0.098 ? 0.007

(aged)

deformed(aged) 0.090*0.003 0 . 0 8 5 0 . 0 1 0.83 0 . 0 9 2 2 0 . 0 7

HF doped 0.083 t 0.001 0.056

*

^0.02 ^0.50 ^0.079

*

^0.004

The values o f E obtained from (a) and f r o m (b) a f t e r c o r r e c t i o n w i t h t h e values o f n deduced fom ( c ) are i n good agreement, Showing a s e l f c o n s i s t e n t treatment o f data. The values o f E f o r pure i c e are i n agreement w i t h those determined p r e v i o u s l y /2/. The d i f f e r e n c e w i t h doped i c e r e s u l t s probably from t h e n a t u r e broken hydrogen bonds e x i s t i n g i n t h e core o f d i s l o c a t i o n . A d i f f e r e n c e i s a l s o found between t h e n values f o r deformed and non deformed specimen i n d i c a t e s t h a t t h e d i s t r i b u t i o n i n t h e parameters i s v e r y large; t h e l a r g e d i s l o c a t i o n d e n s i t y i n t h e deformed specimen leads t o anarrower d i s t r i b u t i o n .

An o t h e r i n t e r e s t i n g p o i n t can be deduced f r o m our experiments e s p e c i a l y microcreep experiments. We have p l o t t e d f o r a l l our experiments l o g b(o) vs (k(o) i s the s t r a i n r a t e e x t r a p o l a t e d a t T'.max = 0 ) . F o r every t y p e o f specimen T f o r example Fig. 6 r e p r e s e n t s t h e p l o t f o r an HF-doped specimen) we can p u t i n evidence two a c t i v a t i o n energies i n d i c a t i n g t h a t two mechanisms occur d u r i n g microcreep. From low temperature t o 240-250 K t h e a c t i v a t i o n energy i s found t o be t h e same as t h a t o f t h e r e l a x a t i o n peak observed a t lower temperature ( i . e . E = 0.24 eV f o r pure and HF-doped ice; E = 0.32 eV f o r aged i c e /4/).

F i g . 6

-

l o g ~ ( o ) vs

1

f o r HF -doped i c e .

T h i s f i r s t mechanism can be a t t r i b u t e d t o a movement of d i s l o c a t i o n thanks t o t h e r e o r i e n t a t i o n o f H 0 molecules w i t h t h e h e l p o f . r o t a t i o n a 1 defects. The second mechanism higher t6an 240-250 K has a l a r g e r a c t i v a t i o n energy w i t h v a l u s between 0.35 and 0.50 eV. This p o i n t i s observed again by p l o t t i n g l o g t a n

&

vs ,

f

f o r t h e same specimen (Fig. 7) and t h e same d i s t i n c t i o n between two mechanisms T can be made.

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F i g . 7

-

l o g t a n

6

vs 1 HF -doped specimen

I V

-

CONCLUSION

Very low frequencies measurements associated w i t h creep experiments i n t h e domain of m i c r o p l a s t i c i t y demonstrate t h a t high-temperature f r i c t i o n i s due t o t h e movement o f d i s l o c a t i o n s .

Our experiments show t h a t t h e model o f n o n - c r y s t a l l i n e core o f d i s l o c a t i o n can described t h e phenomenon a t l e a s t a t h i g h e r temperature by i n t r o d u c i n g a d i s t r i - b u t i o n i n t h e parameters concerning t h e r e s t o r i n g f o r c e s on d i s l o c a t i o n s . As b o t h creep and i n t e r n a l f r i c t i o n experiments suggest t h a t two mechanisms o f d i s l o c a - t i o n movement occur, depending on temperature, i t can be deduced t h a t , under 240-250 K, t h e movement o f l i n e a r d e f e c t s i s l i m i t e d by r e o r i e n t a t i o n o f water molecules as p r e v i o u s l y proposed by GLEN /6/.

REFERENCES

/1/ PEREZ J., MA1 C . , TATIBOUET J. and VASSOILLE R, Nuovo Ciments

BB3

(1976) 86-95.

/2/VASSOILLE R., MA1 C., TATIBOUET J. and PEREZ J., J. G l a c i o l .

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(1978) 375-384.

/3/ PEREZ J., MA1 C., TATIBOUET J and VASSOILLE R., J. G l a c i o l .

2

(1980) 133-149.

/4/ TATIBOUET J., PEREZ J. and vASSOILLE. R., V I e I n t e r n a t i o n a l Symposium on t h e Physics and Chemistry of Ice, R o l l a

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Missouri, U.S.A. (1982) t o be p u b l i s h e d i n J . Phys. Chem.

/5/ ETIENNE S., CAVAILLE J.Y., PEREZ J. and SALVIA M., J. Phys. Colloq. (Orsay

-

France) C5, 42 (1981) 1129-1134.

/6/ GLEN J . W y phys. Condens. Mater.

7

(1968) 43-51.