INTERNAL FRICTION OF GLASSY POLYCARBONATE DURING PLASTIC FLOW

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INTERNAL FRICTION OF GLASSY

POLYCARBONATE DURING PLASTIC FLOW

J. Parisot, J. Astier, Arnaud Fernandez, O. Rafi

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque CS, supptdment au nO1O, Tome 4 2 , octobre 1981 page CS-569

INTERNAL FRICTION OF GLASSY POLYCARBONATE DURING PLASTIC FLOW

J. Parisot, J. Astier, A. Fernandez and 0. Rafi

EcoZe NationaZe SupQrieure de M&canique e t dlA&rotechnique, Laboratoire de Mdcanique e t Physique des Matdriaux, Equipe de Recherche Associd au C.N.B.S. n0123, 86034 Poitiers Cedex, France

A b s t r a c t .

- We have measured i n t e r n a l f r i c t i o n o f p o l y c a r b o n a t e

i n t o r s i o n , d u r i n g i ) a c o n s t a n t s t r a i n - r a t e t e n s i l e t e s t ; i i ) a d i f f e r e n t i a l s t r a i n - r a t e t e s t ; i i i ) s e v e r a l r e l a x a t i o n t e s t s . We show t h a t i n t e r n a l f r i c t i o n i s s t r o n g l y dependent on s t r a i n r a t e

,

b u t i n d e p e n d a n t on s t r a i n and s t r e s s . P o l y c a r b o n a t e b e h a v i o u r shows some a n a l o g i e s w i t h m e t a l s : t h e r e f o r e i n t e r p r e t a t i o n of t h e r e s u l t s i s b a s e d upon t h e a s - sumption t h a t d e f o r m a t i o n i n due t o d e f e c t s m o t i o n s . I n t h i s v i e w , i n t e r n a l f r i c t i o n c a n p r o v i d e means f o r e s t i m a t i n g i n t e r - n a l s t r e s s .

1. Experiment. - Measurements o f i n t e r n a l f r i c t i o n were performed du-

r i n g t e n s i l e t e s t s , a t a b o u t 1 Hz, on a t o r s i o n a l pendulum s e t a l o n g t h e v e r t i c a l a x i s o f a t e n s i l e machine.

The sample, t o o k from a "Makrolon" s h e e t , p r e s e n t s an i n i t i a l s e c t i o n o f 3 X 4 mm2 a n d t h e i n i t i a l l e n g t h a c t u a l l y s t r a i n e d ( b e t - ween h e a d s ) i s L.

-

38 mm. I t i s f i x e d between t h e c r o s s - h e a d o f t h e

t e n s i l e machine a t i t s lower p a r t , and t h e i n e r t i a b a r o f t h e pendulum a t i t s t o p . The i n e r t i a b a r i s hanged t o t h e l o a d - c e l l by a

2

s t r i p - i r o n , t h e s e c t i o n of which i s 30 x0.3 mm

.

T o r s i o n motion i s r e c o r d e d by an o p t i c a l d e v i c e and damping i s

measured by a f r e e decay method :

I n t e r n a l f r i c t i o n of t h e sample, A

,

i s deduced from A1 by t h e r e l a t i o n / l / :

where A~ i s t h e s t r i p - i r o n damping, measured by r e p l a c i n g t h e sample by a t h i n s t r i p - i r o n , t h e t o r q u e r i g i d i t y o f which is n e g l i g i b l e ;

W and W1 a r e t o r s i o n a l e l a s t i c e n e r g i e s r e s p e c t i v e l y s t o r e d i n

2

t h e upper s t r i p - i r o n and i n t h e whole system d u r i n g an o s c i l l a t i o n ; i t can be s e e n t h a t W2/W1 = ( f / f 1 2 , f l b e i n g t h e measured f r e q u e n -

2

1

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C5-570 JOURNAL DE PHYSIQUE

cy o f t h e whole s y s t e m , and f 2 t h e f r e q u e n c y measured i n t h e same c o n d i t i o n s a s b 2 ; f 2 and A 2 a r e load-dependent.

2. R e s u l t s .

2.1.

-

C o n s t a n t s t r a i n - r a t e t e n s i l e t e s t .

-

F i g . 1 shows t h e s t r e s s c u r v e U = F/S v e r s u s t i m e , f o r an e l o n g a t i o n r a t e d L / d t = 0 . 5 mm/mn

( t h a t i s

;

= :/Lo

.

d L / d t = 0 . 2 2 . 1 0 - ~ S-').

There a r e t r e e p a r t s i n t h i s s t r e s s c u r v e . The f i r s t p a r t (OA) c o r r e s p o n d s t o a r e c o v e r a b l e and homogeneous d e f o r m a t i o n : i n t e r n a l - 3 f r i c t i o n i n c r e a s e s from A = 30.10 b e f o r e l o a d i n g , t o A A = 120. I O - ~ . The second p a r t ( A B ) i s a P i o b e r t - L u d e r s p l a t e a u w i t h a L P 50 MPa. P l a s t i c s t r a i n i n g ( e = 55 %) i s l o c a l i z e d on one o r L

two f r o n t s which move a l o n g t h e sample. T h i s h e t e r o g e n e i t y o f t h e de- f o r m a t i o n makes d i f f i c u l t t h e a n a l y s i s o f i n t e r n a l f r i c t i o n measurements i n t h i s p a r t o f t h e t e n s i l e c u r v e . The t h i r d p a r t o f t h e c u r v e ( B C ) c o r r e s p o n d s t o a homogeneous d e f o r m a t i o n up t o t h e r u p t u r e which o c c u r s by c r a c k - p r o p a g a t i o n ( e R = 9 3 % ) . I n t e r n a l f r i c t i o n i n c r e a s e s from A = 1 1 0 . 1 0 - ~ t o B = 2 0 0 . 1 0 - ~ . 2 . 2 . D i f f e r e n t i a l s t r a i n - r a t e t e n s i l e t e s t .

-

The c u r v e s t r e s s v s t i - me o f t h e f i g , 2 a h a s been o b t a i n e d by t a k i n g t u r n s w i t h two s t r a i n r a t e s : 0 . 5 and 0 . 0 5 mm/mn. The p a r t B C o f t h e c u r v e shows s t r e s s

Fig.l

m

a ) Tensile curve.: s t r e s s vs time Influence of strain-rate (Strain-rate L = 0.5 m/m) a ) on the s t r e s s

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d r o p s 6 0 = 8 . 3 MPa. F i g . 2b shows t h e d r o p s o f i n t e r n a l f r i c t i o n c o r - r e s p o n d i n g w i t h s t r a i n - r a t e d e c r e a s e s . Theses d r o p s a r e i m p o r t a n t i n t h e B C p a r t o f t h e s t r e s s c u r v e ( 6 8 = 1 0 0 . 1 0 - ~ f o r t h e f i r s t o f them) ; t h e y a l s o e x i s t i n t h e OA p a r t . When t h e s t r a i n r a t e i s i n c r e a s e d a g a i n , t h e s t r e s s - c u r v e shows a t r a n s i e n t i n c r e a s e 6 5 a s i n m e t a l s s u b j e c t t o a g i n g e f f e c t s . Then i n - t e r n a l f r i c t i o n does n o t immediately r e a c h t h e s t e a d y - s t a t e v a l u e a s measured i n t h e i n i t i a l c o n s t a n t s t r a i n - r a t e c o n d i t i o n s . 2 . 3 . S t r e s s - R e l a x a t i o n t e s t s . - The t e n s i l e s t r a i n i n g t e s t i s sudden- l y s t o p p e d a t t h e s t r e s s o o ( = 58 MPa), c o r r e s p o n d i n g t o a deforma- t i o n e o ( = 66 % ) . There a r e t h r e e p o s s i b i l i t i e s .

i ) The c r o s s - h e a d i s k e p t immobile. Under t h e a c t i o n o f t h e s t r e s s o o t h e specimen c o n t i n u e s t o e l o n g a t e v e r y s l o w l y , and t h e s t r e s s d e c r e a s e s f o l l o w i n g a l o g a r i t h m i c f u n c t i o n o f time : t h a t i s t h e r e l a x a t i o n ( F i g . 3 a ) . During t h e d e c r e a s e o f o

,

t h e i n t e r n a l f r i c t i o n d e c r e a s e s a l s o and t e n d s towards a l i m i t c l o s e t o i t s i n i - t i a l v a l u e measured on t h e s t r a i n e d m a t e r i a l ( F i g . 3 b ) .

i i ) The cross-head i s r a p i d l y moved b a c k and i s s t o p p e d as t h e s t r e s s i s z e r o . Then t h e specimen c o n t r a c t s w i t h a d e c r e a s i n g s t r a i n r a t e and t h e s t r e s s i n c r e a s e s , 6 > 0 : t h a t i s t h e a n t i - r e l a x a t i o n

( F i g . 4 a ) . The i n t e r n a l f r i c t i o n i s immediatly r e d u c e d , t h e n i t de- c r e a s e s w i t h time a s ;r

,

t e n d i n g a g a i n towards i t s i n i t i a l v a l u e ( F i g . 4 b ) .

Fig.3

Evolution of the Internal Friction (b) during stress-relaxation ( a ) .

v:F/So MPa

C l

-

Fig.4

Evolution of the Internal Friction (b)

during antirelaxation after total. un-

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CS-572 JOURNAL DE PHYSIQUE

i i i ) The t h i r d p o s s i b i l i t y i s t o move back t h e c r o s s - h e a d and s t o p i t a f t e r a p a r t i a l u n l o a d i n g a t a s t r e s s d < U

.

F o r t h e u p p e r 0 0 v a l u e s of U;, 'O i s n e g a t i v e ; f o r t h e l o w e r v a l u e s o f U' 6 i s p o s i t i - 0 ' v e ( f i g . 5 a ) . There i s a v a l u e o f u ' f o r which 6 i s z e r o , t h i s 0 s t r e s s i s u s u a l l y c o n s i d e r e d a s t h e i n t e r n a l s t r e s s . J u s t a f t e r t h i s p a r t i a l u n l o a d i n g t h e v a l u e o f i n t e r n a l f r i c t i o n i s r e d u c e d ( F i g . 5 b ) . The i n s t a n t a n e o u s v a l u e s o f i n t e r n a l f r i c t i o n a r e p l o t t e d v e r s u s U ' i n f i g u r e 6 . From t h i s f i g u r e i t i s c l e a r t h a t 0 i ) t h e i n s t a n t a n e o u s v a l u e o f A i s a l w a y s h i g h e r t h a n i t s v a l u e be- f o r e s t r a i n i n g , 30. I O - ~ ; i i ) t h e c u r v e shows a minimum o f A f o r t h e s t r e s s a ' = 20 MPa, t h i s s t r e s s i s s m a l l e r t h a n t h e s t r e s s f o r which 6 i s z e r o : 45

MPa.

D i s c u s s i o n . - I n t e r n a l f r i c t i o n o f t h e u n l o a d e d s p e c i m e n , A = 30.103,

c o r r e s p o n d s t o t h e background between t h e two t r a n s i t i o n s or and B o f t h e p o l y c a r b o n a t e which a r e r e s p e c t i v e l y a t 150 O C and -100 O C f o r

1 Hz / 2 / . The i n c r e a s e o f i n t e r n a l f r i c t i o n o b s e r v e d d u r i n g s t r a i n

o=F/So

MPa

L

Fig. 5

a ) Beginning of the relaxation after p a r t i a l unloading

b) Correspondent values of the Inter- nal Friction.

Fig.G

Internal Friction vs stress immediately a f t e r p a r t i a l unloa-

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d o e s n o t seem t o be r e l a t e d t o t h e s e t r a n s i t i o n s b u t more l i k e l y i t i s c o n n e c t e d t o t h e s t r a i n r a t e i

.

T h i s i s c l e a r l y o b s e r v e d on t h e d i f f e r e n t i a l s t r a i n r a t e t e s t ( F i g . 2 ) and on t h e r e l a x a t i o n and an- t i - r e l a x a t i o n t e s t s : e a c h t i m e A d e c r e a s e s w i t h t . I n t h e r e l a x a - t i o n and a n t i r e l a x a t i o n t e s t s , t h e same t i m e i s n e c e s s a r y f o r

b e i n g c l o s e t o z e r o and f o r A r e a c h i n g a g a i n i t s i n i t i a l v a l u e . The

same r e s u l t h a s been o b t a i n e d on a specimen s t r a i n e d up t o r u p t u r e and k e p t a t room t e m p e r a t u r e f o r 48 H : i t shows t h e same damping s p e c t r u m a s undeformed m a t e r i a l from 77 t o 370 K .

I t c a n be s e e n from t h e p r e s e n t r e s u l t s t h a t t h e s t r a i n beha- v i o u r o f p o l y c a r b o n a t e shows s e v e r a l a n a l o g i e s w i t h m e t a l s : s t r a i n - r a t e s e n s i t i v i t y , e x i s t e n c e o f a n i n t e r n a l s t r e s s and e x i s t e n c e of

O 3

a n a c t i v a t i o n volume which h a s been c a l c u l a t e d ( P 1000 A ) b o t h from d i f f e r e n t i a l s t r a i n - r a t e t e s t s and from r e l a x a t i o n t e s t s .

Those a n a l o g i e s s u g g e s t two a s s u m p t i o n s . F i r s t l y , t h e p l a s t i c s t r a i n i n g o f g l a s s y - s t a t e p o l y c a r b o n a t e i s made p o s s i b l e by c r e a t i o n and motion o f d e f e c t s /3/. S e c o n d l y , when t h o s e d e f e c t s a r e moving under t h e a c t i o n o f t h e t e n s i l e s t r e s s , t h e i r motion c a n be m o d i f i e d by a s m a l l t o r q u e : t h i s m o d i f i c a t i o n i s d i s s i p a t i n g e n e r g y , s o t h a t i t p r o d u c e s i n t e r n a l f r i c t i o n when t h e t o r q u e i s s i n u s o i d a l . Using t h o s e two a s s u m p t i o n s , a c o h e r e n t i n t e r p r e t a t i o n o f t h e r e s u l t s c a n be g i v e n . I n a l l t h e t e s t s , a s t r a i n - r a t e d e c r e a s e i s r e - l a t e d t o an i n t e r n a l f r i c t i o n d e c r e a s e ( F i g . 2 , 3 , 4 ) : s o t h e number o f t h e m o b i l e d e f e c t s a l s o d e c r e a s e s .

The motion o f e a c h d e f e c t i n t h e m a t e r i a l i s opposed by t h e i n - t e r n a l s t r e s s e s . So, t h e e f f e c t i v e s t r e s s a c t i n g on a d e f e c t i s : U = a

-

oiwhere o i s t h e e x t e r n a l a p p l i e d s t r e s s , and 0. i s t h e i n - t e r n a l s t r e s s . C o n s e q u e n t l y when a p p l y i n g a n e x t e r n a l s t r e s s = o i ' t h e e f f e c t i v e s t r e s s o e becomes z e r o and t h e p l a s t i c s t r a i n - r a t e i s a l s o z e r o . I n t h e r e l a x a t i o n t e s t , d e f e c t s c o n t i n u e t o move a s l o n g a s a e > 0 , b u t b e c a u s e t h e sample l e n g t h i n c r e a s e s , t h e s t r e s s d e c r e a s e s a n d t h e p l a s t i c s t r a i n r a t e

Z p

a l s o ; a s t h e d e f e c t s a r e l e s s and l e s s m o b i l e , t h e i n t e r n a l f r i c t i o n a l s o d e c r e a s e s ( F i g . 3 ) . I n t h e a n t i r e l a x a t i o n t e s t , f o r G = 0 , t h e e f f e c t i v e s t r e s s i s o e =

-

a .

-

1 '

t h a t s t r e s s i n d u c e s t h e backward motion of some d e f e c t s and macrosco- p i c a l l y , t h e s t r a i n r a t e

GB

i s n e g a t i v e ; t h e i n t e r n a l f r i c t i o n A i s n o t s e n s i t i v e t o t h e d i r e c t i o n o f t h e d i s p l a c e m e n t o f t h e d e f e c t s , and d e c r e a s e s w i t h

EB

.

I n t h e p a r t i a l u n l o a d i n g t e s t , t h o s e two e f f e c t s a r e i n competi-

. .

t i o n : t h e whole s t r a i n - r a t e i s E = E~

+

E ~ AS . s c h e m a t i c a l l y shown

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C5-5 74 JOURNAL DE PHYSIQUE p l i e d a f t e r u n l o a d i n g . When a p p l y i n g a s t r e s s do = U . t h e p l a s t i c 1' s t r a i n Qp becomes z e r o a n d t h e t o t a l s t r a i n r a t e

;

i s i = k < 0 . But B t h e i n t e r n a l f r i c t i o n A v a r i e s a s 'cp

+

I

C B

I

: c o n s e q u e n t l y , i t p a s - s e s t h r o u g h a minimum when C p becomes z e r o ( F i g . 7 b ) a n d t h e c o r r e s - p o n d i n g v a l u e o f t h e a p p l i e d s t r e s s ( F i g . 6 ) i s t h e m a c r o s c o p i c va- l u e o f t h e i n t e r n a l s t r e s s o i . T h a t v a l u e i s l e s s t h a n t h e s t r e s s f o r which Er = 0 , c o r r e s p o n d i n g t o a t r a n s i e n t e q u i l i b r i u m b e t w e e n t h e p l a s t i c s t r a i n - r a t e and t h e backward s t r a i n - r a t e :

+

_B= 0 ( s a m p l e 2 on f i g . 5 a ) . a ) S c h e m a t i c d r a w i n g o f c p a n d v s t h e s t r e s s i m m e d i a t e l y a f t e r u n l o a d i n g b ) L P

+ l

tgl r

4 . Aknowledgements.

-

The a u t h o r s a r e g r a t e f u l t o P

.

B. E s c a i g and D ~ . J . L . G a c o u g n o l l e f o r h e l p f u l d i s c u s s i o n s and a s s i s t a n c e f o r w r i - t i n g t h e p a p e r .

5 . R e f e r e n c e s .

/ l / G . COLLETTE

-

C . R . Hebd. S h a n c e s Acad. S c i . B

*,

2756, ( 1 9 5 8 ) Mgtaux C o r r o s . I n d .

9,

1 4 3 , ( 1 9 6 4 ) .

/ 2 / N . G . MC CRUM, B.E. READ and G . WILLIAMS,

A n e l a s t i c a n d D i e l e c t r i c E f f e c t s i n P o l y m e r i c S o l i d s . J o h n WILEY and SONS, London.

/ 3 / B. ESCAIG.

D i s l o c a t i o n s e t d g f o r m a t i o n p l a s t i q u e pp.261-286 E c o l e d ' E t 6 d g Y r a v a l s 1979.