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IAHR 7th International Symposium on Ice, Proceedings, 1, pp. 39-47, 1984

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A Procedure to account for machine stiffness in uni-axial compression tests

Timco, G. W.; Frederking, R. M. W.

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Ser / 3 _q&J-

N21d National Resea& Conseil national

0.

1294

Division of Division des

Building Research recherches en batiment

A Procedure to Account for Machine Stiffness in Uni-Axial

Compression Tests

by G.W. Timco and R.M.W. Frederking

ANALYZED

Reprinted from IAHR

7th

International Symposium on Ice

Hamburg, W. Germany, August 27 -31,1984 Proceedings. Vol. I. p. 39-47

(DBR Paper No. 1294)

Price $1.00

NRCC 24681

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I1 est bien connu que la rigidit6 des machines d'essai peut fausser les resultats des essais de compression uniaxiale de la glace. Cela provient du fait que les machines d'essai de compression conventionnelles ne sont pas suffisanment plus rigides que 116chantillon de glace soumis aux essais. I1 en resulte donc un processus complexe d'interaction entre la machine et la glace. Cette communication presente un modele simple de ce processus et les equations deterninantes. On obtient ainsi une formule correctrice qui pernet de tenir compte de la rigidite de la machine. Le nodele est verifie avec des echantillons de glace columnaire d'eau douce et de glace granulaire d'eau de mer en conparant les valeurs des resistances corrigees pour trois machines d'essai different&

avec celles obtenues en utilisant une machine d'essai circuit

ferm6 de forte capacite.

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LIHR Ice Symposium

1984

Hamburg

A PROCEDURE TO ACCOUNT FOR MACHINE STIFFNESS

I N UNI-AXIRL CaMPRESSION TESTS

G. W. Timco and R. F r e d e r k i n g N a t i o n a l Research C o u n c i l Canada Research O f f i c e r s

ABSTRACT

I t is w e l l e s t a b l i s h e d t h a t t e s t machine s t i f f n e s s c a n i n f l u - e n c e t h e r e s u l t s i n u n i - a x i a l compression t e s t s on i c e . T h i s comes about because t h e c o n v e n t i o n a l compression machines a r e n o t s u b s t a n t i a l - l y s t i f f e r t h a n t h e p i e c e of i c e under t e s t ; hence t h e t e s t becomes a c o m p l i c a t e d i c e - s t r u c t u r e i n t e r a c t i o n p r o c e s s . I n t h i s n o t e , a s i m p l e model o f t h i s p r o c e s s is o u t l i n e d and t h e d e f i n i n g e q u a t i o n s a r e e s t a b - l i s h e d . T h i s y i e l d s a c o r r e c t i o n formula which a c c o u n t s f o r t h e s t i f f - n e s s o f t h e t e s t machine. The model is checked f o r both columnar f r e s h - water i c e and g r a n u l a r s e a i c e by comparing t h e c o r r e c t e d s t r e n g t h v a l u e s f o r t h r e e d i f f e r e n t t e s t machines w i t h t h o s e measured using a h i g h - c a p a c i t y c l o s e d - l o o p t e s t machine.

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INTRODUCTION

I n r e c e n t g l a c i o l o g i c a l l i t e r a t u r e , t h e r e has been d i s c u s s i o n on t h e i n f l u e n c e of t h e t e s t machine s t i f f n e s s on t h e u n i - a x i a l compres- s i v e s t r e n g t h of i c e which has been measured using c o n s t a n t cross-head r a t e t e s t machines (Aaynes, 1979; Sinha and F r e d e r k i n g , 1979; S i n h a 1981a, 1981b. 1982; Frederking and Timco, 1983, 1984). B a s i c a l l y this problem a r i s e s because t h e s e c o n v e n t i o n a l t e s t machines a r e not c o n s i - d e r a b l y more r i g i d t h a n t h e i c e specimen being t e s t e d . Because o f t h i s , t h e t e s t machine i t s e l f can deform e l a s t i c a l l y a s i g n i f i c a n t amount d u r i n g t h e t e s t . T h i s deformation of t h e t e s t machine r e s u l t s i n a lower a p p l i e d s t r a i n r a t e on t h e sample t h a n t h e nominal s t r a i n r a t e . S i n c e t h e t e s t r e s u l t s a r e u s u a l l y i n t e r p r e t e d i n terms of t h e s t r a i n r a t e , and t h e compressive s t r e n g t h o f i c e is s t r a i n - r a t e dependent, t h i s l e a d s t o an i n a c c u r a t e i n t e r p r e t a t i o n of t h e t e s t . Thus, a t e s t o f i c e s t r e n g t h made on a machine which is not s i g n i f i c a n t l y more r i g i d t h a n t h e i c e sample w i l l r e s u l t i n a lower s t r e n g t h t h a n w u l d occur f o r a t r u e s t r a i n r a t e e q u a l t o t h e nominal r a t e . It has been shown, i n f a c t , t h a t f o r t h e same nominal s t r a i n r a t e , t h e a p p a r e n t s t r e n g t h of i c e i n c r e a s e s with i n c r e a s i n g t e s t system s t i f f n e s s ( S i n h a , 1981a).

To overcome t h i s problem, r e c e n t t e s t s of i c e s t r e n g t h have been performed on "closed-loop" t e s t machines. I n t h e s e t e s t s , t h e r a t e o f d e f o r m a t i o n o f t h e sample is measured and i n s t a n t a n e o u s l y fed back t o t h e c o n t r o l system. T h i s , i n t u r n , a d j u s t s t h e cross-head r a t e so a s t o m a i n t a i n a t r u e c o n s t a n t s t r a i n r a t e of t h e sample d u r i n g t h e t e s t . Using a t e s t machine of t h i s t y p e , it i s p o s s i b l e t o i n v e s t i g a t e t h e s t r e n g t h of i c e a s a f u n c t i o n of t r u e c o n s t a n t s t r a i n r a t e ; i.e. t h e i n f l u e n c e of t h e t e s t machine s t i f f n e s s is e l i m i n a t e d . In any s t u d y i n v e s t i g a t i n g t h e p h y s i c s o r mechanisms o f i c e f a i l u r e , a machine of t h i s type should be used, i f a t a l l p o s s i b l e . Closed-loop machines, however, have s e v e r a l drawbacks s i n c e t h e y a r e q u i t e expensive, w r y l a r g e and not e a s i l y d e p l o y a b l e for use i n t h e f i e l d . For many e n g i - n e e r i n g a p p l i c a t i o n s , t h e r e f o r e , a c o n v e n t i o n a l t e s t machine is used.

Most of t h e i n f o r m a t i o n i n t h e l i t e r a t u r e An t h e s t r e n g t h o f i c e h a s been o b t a i n e d using such t e s t machines. I t w u l d be h i g h l y d e s i r a b l e , t h e r e f o r e , t o f i n d a t e c h n i q u e which would a l l o w a l l t h i s i n f o r m a t i o n t o be compared by e l i m i n a t i n g t h e i n f l u e n c e o f t h e machine s t i f f n e s s . T h i s t e c h n i q u e would a l s o f a c i l i t a t e f i e l d t e s t i n g s i n c e l i g h t e r and more

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e a s i l y d e p l o y a b l e t e s t machines w u l d s t i l l g i v e r e s u l t s which c o u l d be i n t e r p r e t e d i n terms o f s t r a i n r a t e .

I n t h i s note, a simple model is p r e s e n t e d f o r t h e s t i f f n e s s o f a c o n v e n t i o n a l test machine. T h i s y i e l d s a c o r r e c t i o n formula which a c c o u n t s f o r t h e machine s t i f f n e s s . The model is checked by comparing s t r e n g t h v a l u e s which were o b t a i n e d f o r both columnar f r e s h w a t e r i c e and g r a n u l a r s e a i c e using t h r e e d i f f e r e n t t e s t machines and c o r r e c t e d using t h i s formula, with t h o s e measured using a high c a p a c i t y c l o s e d - l o o p machine.

DEFINING EQUATIONS

The model f o r t h e system o f an i c e sample i n a t e s t machine is shown i n F i g u r e 1. It c o n s i s t s o f a s e r i e s combination o f two i n d i v i d u - a l e l e m e n t s which r e p r e s e n t t h e machine s t i f f n e s s and t h e i c e s t i f f n e s s .

L a n n CELL-

C O M P L I A N T c D E F L E C T I O N

P L A T E N S

L O A D I N G S Y S T E M

E5

?

^K,3 S P E C I M E N a1 L O A D I N G M A C H I N E b l T E S T S Y S T E M

FIGURE 1 SCHEMATIC OF ( a ) COMPRESSION W I N G MACHINE AND (b) EQUI VALENP STIFFNESS ELEMENTS

I t has p r e v i o u s l y been d i s c u s s e d by Frederking and Timco (1983). I n b r i e f , t h e l o a d i n g system s t i f f n e s s K i s is d e f i n e d a s

where AP is a load increment, 6j is t h e c o r r e s p o n d i n g d i s p l a c e m e n t increment o f t h e screw jack, and 6s is t h e r e s u l t i n g d e f o r m a t i o n increment o f t h e sample. 6, is d e f i n e d a s

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where E is t h e e l a s t i c modulus of t h e specimen, 1 i s t h e l e n g t h and A its c r o s s - s e c t i o n a l a r e a . Combining t h e s e e q u a t i o n s and s e t t i n g t h e sample s t i f f n e s s Ks = EA/1, y i e l d s (per u n i t t i m e )

T h i s e x p r e s s i o n r e l a t e s t h e d i s p l a c e m e n t r a t e o f t h e sample (6,) t o t h e displacement r a t e of t h e cross-head o f t h e machine ( 6 j ) . S i n c e t h e r e s u l t s of compression t e s t s a r e u s u a l l y d i s c u s s e d i n terms o f t h e

. .

s t r a i n r a t e ( E ) o f t h e sample and ^E= 6/E, e q u a t i o n (3) y i e l d s a r e l a - t i o n s h i p between t h e s t r a i n r a t e i n t h e sample ( E s ) and t h e nominal s t r a i n r a t e o f t h e t e s t ( E n ) a s

T h i s e q u a t i o n shows t h a t t h e sample s t r a i n r a t e is l e s s t h a n t h e nominal s t r a i n r a t e , and t h a t a s t h e l o a d i n g system s t i f f n e s s becomes w r y l a r g e compared to t h e i c e s t i f f n e s s , Es approaches En, a s expected. To use t h i s e q u a t i o n , both t h e l o a d i n g system s t i f f n e s s and t h e i c e s t i f f n e s s must be known. The former is o b t a i n e d by l o a d i n g a specimen o f known c o n s t a n t e l a s t i c i t y and measuring t h e l o a d , movement of t h e screw jack, and l o a d frame d e f l e c t i o n ( F r e d e r k i n g and Timco, 1983). The r e s u l t s f o r t h r e e d i f f e r e n t t e s t machines which t h e a u t h o r s have used ( I n s t r o n , T T ~ - L , 0.1 w c a p a c i t y ; ~ r i - t e s t 50, 0.06 MN c a p a c i t y ; S o i l t e s t CT-405, 0.05 W c a p a c i t y ) a r e shown i n F i g u r e 2. Note t h a t t h e machine s t i f f - ness is not a c o n s t a n t , but a f u n c t i o n of l o a d a t low l o a d s , and f o r a g i v e n t e s t machine, t h e s t i f f n e s s is g r e a t e r for s t e e l p l a t e n s t h a n for compliant p l a t e n s . For t h e a n a l y s i s i n t h i s paper, t h e l o a d dependence o f t h e machine s t i f f n e s s w i l l not be t a k e n i n t o account i n a r i g o r o u s f a s h i o n ; i n s t e a d , it is approximated a s t h e average v a l u e o f t h e machine s t i f f n e s s up to t h e l o a d l e v e l a t which t h e i c e y i e l d s . With r e g a r d t o t h e i c e s t i f f n e s s , t h i s is a l s o not a c o n s t a n t f o r t h e s e t e s t s s i n c e t h e specimen is loaded t o its y i e l d p o i n t . For low l o a d s , t h e i c e s t i f f n e s s is g i v e n by EA/L where E is t h e e l a s t i c modulus o f t h e i c e . With i n - c r e a s i n g l o a d , t h e i c e s t i f f n e s s d e c r e a s e s such t h a t , by d e f i n i t i o n , it is z e r o a t t h e y i e l d p i n t . S i m i l a r t o t h e machine s t i f f n e s s , t h i s l o a d

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dependence w i l l not be t a k e n i n t o account i n a r i g o r o u s f a s h i o n ; in- s t e a d , t h e ice s t i f f n e s s is approximated a s t h e a v e r a g e of t h e i c e s t i f f n e s s d u r i n g t h e t e s t (assuming a l i n e a r d e c r e a s e with l o a d to y i e l d ; i.e. Ci = EA/2I1 where E is t h e e l a s t i c m d u l u s of t h e i c e for low l o a d s ) . It s h o u l d be noted t h a t w i t h i n c r e a s i n g l o a d , t h e s t i f f n e s s o f t h e t e s t machine i n c r e a s e s whereas t h e s t i f f n e s s o f t h e i c e specimen d e c r e a s e s . Thus, t h e p r e s e n t approach g r e a t l y s i m p l i f i e s a complex i n t e r a c t i o n problem by using a v e r a g e v a l u e s i n a l i n e a r system t o r e p r e s e n t t h e s i t u a t i o n . With t h i s approximation, t h e r e a d e r is c a u t i o n e d not t o i n t e r p r e t

n o t h e c o r r e c t e d s t r a i n r a t e

- ES a s t h e t r u e s t r a i n r a t e

100 - -

o f t h e t e s t . To v e r i f y t h e

+

-

+ a l . ~ l s f f 1 I I I L PL**ENf) x

- 8 0

-

IWEftlOY [ S T E E L PLhfZ"3l

-

a p p l i c a b i l i t y o f e q u a t i o n

( 4 )

,

it was used to c o r r e c t

1911. T F l T I t l l Y I & I * * l . L h I I Y I I

s t r e n g t h measurements f o r two d i f f e r e n t c a s e s . F i r s t , £or measurements on columnar S2 f r e s h w a t e r i c e which were

o 10 2 0 3 0 - 0 so so ro made using a c o n v e n t i o n a l

L O A D I K N I

machine with s t e e l p l a t e n s under c a r e f u l l y c o n t r o l l e d FIGURE 2 l a b o r a t o r y c o n d i t i o n s ; and LOADING SYSTE4 STIFFNESS second, on g r a n u l a r s e a i c e WRSUS LOAD FOR THREE made i n t h e f i e l d using two COMPRESSICN TEST MACHINES d i f f e r e n t t e s t machines w i t h both s t e e l and c o m p l i a n t p l a t e n s . The c o r r e c t e d v a l u e s were compared t o t h e l a b o r a t o r y measurements on t h e same t y p e o f i c e using a c l o s e d - l o o p t e s t machine. I n both c a s e s , t h e t e s t d a t a was t a k e n from p r e v i o u s l y p u b l i s h e d t e s t r e s u l t s .

FRESEWATER ICE

The i n f o r m a t i o n on f r e s h w a t e r i c e was t a k e n from t h e p u b l i s h e d work o f Sinha (1981a) who compared t h e r e s u l t s o f compression t e s t s by s e v e r a l i n v e s t i g a t o r s using a number of t e s t machines. For t h i s

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a n a l y s i s , t h e r e s u l t s o f h i s t e s t s u s i n g t h e c o n v e n t i o n a l I n s t r o n t e s t machine a r e compared t o h i s c l o s e d - l o o p t e s t r e s u l t s . These r e s u l t s were p r e s e n t e d i n t h e form o f a b e s t - f i t r e g r e s s i o n l i n e t h r o u g h h i s d a t a and t h e y a r e shown i n F i g u r e 3. I n o r d e r t o a p p l y e q u a t i o n (4) t o h i s r e s u l t s , t h e l o a d i n g system s t i f f n e s s and e l a s t i c m d u l u s o f t h e i c e must be known. The former is shown i n F i g u r e 2. An a p p r o p r i a t e v a l u e f o r t h e e l a s t i c m d u l u s o f t h e i c e f o r a g i v e n s t r a i n r a t e was t a k e n from t h e r e s u l t s of T r a e t t e b e r g e t a l . (1975) which g i v e s t h e s t r a i n r a t e dependence o f t h e m d u l u s f o r both g r a n u l a r and columnar S2 f r e s h - water i c e . Using t h e s e v a l u e s , t h e t e s t r e s u l t s o f S i n h a were re-analy- s e d u s i n g e q u a t i o n ( 4 ) , and t h e r e s u l t is shown i n F i g u r e 3. T h e r e is e x c e l l e n t agreement between t h e s t r e n g t h o b t a i n e d u s i n g t h e c o n v e n t i o n a l and t h e c l o s e d - l o o p machine.

L A B O R A T O R Y T E S T S S T E E L P L A T E N S

1 o - ~ 10." l o - =

S T R A I N R A T E ( s - ' )

FIGURE 3 STRENGTH-STRAIN RATE RELATIONSHIP FOR S2 FRESHWATER ICE

SHOWING SINJiA'S RESULTS OBTAINED USING BOTH A CONVENTIONAL

AND CLOSED-LOOP TEST MACHINE. THE DASHED LINE I S TBE

CONVENTIONAL MACHINE TEST RESULTS CORRECTED FOR MACHINE

STIFFNESS USING TBE PROPOSED MODEL SEA ICE

For t h i s t y p e o f i c e , t h e r e s u l t s o f c o m p r e s s i o n t e s t s p e r - formed by t h e a u t h o r s i n t h e f i e l d on g r a n u l a r s e a i c e u s i n g two d i f f e r - e n t t e s t machines ( S o i l t e s t CT-405; T r i - T e s t 50) w i t h b o t h c o m p l i a n t and

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s t e e l p l a t e n s ( F r e d e r k i n g a n d Timco, 1 9 8 3 ; 1 9 8 4 ) viere c o m p a r e d to t h e r e s u l t s o f tests made by Wang ( 1 9 7 9 ) o n t h e same t y p e o f s e a ' i c e u n d e r l a b o r a t o r y c o n d i t i o n s u s i n g a c l o s e d - l o o p t e s t m a c h i n e . I n a l l cases, t h e test t e m p e r a t u r e was a p p r o x i m a t e l y -lOeC, a n d t h e ice was o f com- p a r a t i v e s a l i n i t y . T h e r e s u l t s f o r t h e s e tests a r e p r e s e n t e d i n F i g u r e 4 a . S i m i l a r t o t h e r e s u l t s f o r t h e f r e s h w a t e r ice t e s t s , t h e a s m e a s u r - e d s t r e n g t h o f t h e ice is less t h a n t h o s e f o r c o m p a r a b l e s t r a i n r a t e s o b t a i n e d w i t h t h e c l o s e d - l o o p m a c h i n e . S i n c e t h e elastic m o d u l u s o f t h e ice was n o t m e a s u r e d i n t h e s e tests, a n e s t i m a t e o f it was made by u s i n g t h e r e l a t i o n s h i p b e t w e e n t h e e l a s t i c m o d u l u s (E) a n d t h e b r i n e w l u m e

G R A N U L A R S E A I C E T = - 1 0 ' C

0 F R E D E R K I N G A N D T l M C O ( I 9 8 3 a ) - C O M P L I A N T P L A T E N S - S O I L T E S T P R E S S - -0 F R E D E R K I N G A N D T l M C O ( 1 9 8 3 a ) - S T E E L P L A T E N S - S O I L T E S T P R E S S

-

- - - -

W A N G ( 1 9 7 9 )

I-C L O S E D - L O O P

C O N V E N T I O N A L ( U N C O R R E C T E D )

[ a ] I I I I l 1 1

1 1

_I 1 1 1 1 1 1

-

W A N G ( 1 9 7 9 ) ' C L O S E D - L O O P

0

C O N V E N T I O N A L -

(CORRECTED)

~ r u I , , 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I I 1 1 1 1 1

S T R A I N R A T E ( s - ' 1

FIGURE 4 STRENGTH-STRAIN RATE RELATIONSHIP FOR GEfANULAR SEA ICE

SHOWING WANG'S LABORATORY RESULTS OBTAINED USING CLOSED

LOOP MACHINE AND FREDERKING AND TIMCO'S FIELD RESULTS

OBTAINED USING CONVENTIONAL MACHINES ( a ) UNCORRECTED, ( b ) CORRECTED FOR MACHINE STIFFNESS USING THE PROPOSED MODEL

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( u b ) determined f o r s e a i c e by Mudrey (1977)

,

E = 5.32

-

13% m a . Using t h e s e v a l u e s and e q u a t i o n ( 4 ) , t h e r e s u l t s of t h e t e s t s k r

Frederking and Timco were re-analysed and a r e p r e s e n t e d i n F i g u r e 4 The c o r r e c t e d v a l u e s compare w e l l with t h o s e of Wang.

The method o u t l i n e d i n t h i s n o t e , based on a knowledge o f t h e t e s t system s t i f f n e s s and specimen modulus, a p p e a r s t o p r o v i d e a r e a s o n a b l e f i r s t approximation for c o r r e c t i n g s t r a i n r a t e s i n s t r e n g t h t e s t s . The t e c h n i q u e can be a p p l i e d t o i n t e r p r e t i n g d a t a a l r e a d y i n t h e l i t e r a t u r e i f t h e t e s t machine s t i f f n e s s is known. I t a l s o p r o v i d e s a r a t i o n a l e f o r using c o n v e n t i o n a l t e s t machines i n f i e l d t e s t i n g .

REFERENCES

F r e d e r k i n g , R.M.W. and Timco, G.W., 1983. u n i - a x i a l Compressive S t r e n g t h and Deformation of B e a u f o r t Sea Ice. Proc. POAC 83, M1. I, p. 89-98, H e l s i n k i , Finland.

F r e d e r k i n g , R.M.W. and Timco, G.W., 1984. Compressive Behaviour o f Beaufort Sea I c e Under k r t i c a l and H o r i z o n t a l Loading. Proc. 3rd I n t . Symp. on Offshore Mech. and A r c t i c Technology, M1. 111, p.

145-149, New O r l e a n s , U.S.A.

Haynes, F.D:, 1979. Temperature E f f e c t on t h e ~ n i - a x i a l S t r e n g t h of I c e . Proc. POAC 79, M1. I, p. 667-681, ~ r o n d h e i m , Norway.

S i n h a , N.K., 1981a. Comparative Study of I c e S t r e n g t h Data. Proc. IABR Symp. on I c e , M1. 11, p. 581-595, Quebec C i t y , Canada.

S i n h a , N.K., 1981b. Rate S e n s i t i v i t y of Compressive S t r e n g t h of' Columnar-Grained I c e . Exp. Mech. 21, No. 6, p. 209-218.

S i n h a , N.K., 1982. Constant S t r a i n - a n d S t r e s s - R a t e Compressive S t r e n g t h o f Columnar-Grained Ice. J. Mat. S c i . 17, p. 785-802.

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S i n h a , N.K. and F r e d e r k i n g , R.M.W., 1979. E f f e c t o f Test System S t i f f - n e s s on S t r e n g t h of I c e . Proc. POX 79, M1. I, p. 708-717;

Trondheim, Norway:

T r a e t t e b e r g , A., Gold, L.W. and F r e d e r k i n g , R.M.W., 1975. The S t r a i n Rate and Temperature Dependence o f Young's Modulus o f I c e . Proc.

3rd IAHR Symp. on I c e , p. 479-486, Hanover, N.H., U.S.A.

M u d r e y , K.D., 1977. Determination o f EYrchanical Sea I c e P r o p e r t i e s by Large-Scale F i e l d Beam Experiments. Proc. POX 77, M1. I, p.

529-543, S t . John's, Canada.

Wang, Y.S., 1979. C r y s t a l l o g r a p h i c S t u d i e s and S t r e n g t h Tests o f F i e l d I c e i n t h e Alaskan Beaufort Sea. Proc. POX 79, M1. I, p.

651-665, Trondheim, Norway.

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T h i s p a p e r , w h i l e being d i s t r i b u t e d i n r e p r i n t form by t h e D i v i s i o n of B u i l d i n g R e s e a r c h , remains t h e c o p y r i g h t of t h e o r i g i n a l p u b l i s h e r . It s h o u l d n o t be r e p r o d u c e d i n whole o r i n p a r t w i t h o u t t h e p e r m i s s i o n of t h e p u b l i s h e r .

A l i s t of a l l p u b l i c a t i o n s a v a i l a b l e from t h e D i v i s i o n ^maybe o b t a i n e d by w r i t i n g t o t h e P u b l i c a t i o n s S e c t i o n , D i v i s i o n of B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l of C a n a d a , O t t a v a , O n t a r i o , K I A OR6.

Ce document e s t d i s t r i b u 6 sou8 forme d e t i r e - i l - p a r t par l a D i v i s i o n d e s r e c h e r c h e 8 e n b l t i m e n t . Les d r o i t s d e r e p r o d u c t i o n s o n t t o u t e f o i s l a p r o p r i € t € d e 1 1 6 d i t e u r o r i g i n a l . Ce d o c u m e n t n e p e u t 8 t r e r e p r o d u i t en t o t a l i t 6 ou en p a r t i e s a n s l e consentement d e l ' i d i t e u r .

Une l i s t e d e s p u b l i c a t i o n s d e l a D i v i s i o n p e u t 8 t r e obtenue en Q c r i v a n t

a

l a S e c t i o n d e s p u b l i c a t i o n s . D i v i s i o n d e s r e c h e r c h e s e n b l t i m e n t , C o n s e i l n a t i o n a l d e r e c h e r c h e s Canada, O t t a v a , h t a r i o . K1A OR6.