Self-Stress-Enhanced Water Migration in Composites - American

31 Self-Stress-Enhanced Water Migration i n Composites N. R. FARRAR and K. H. G. ASHBEE Downloaded via UNIV OF TEXAS AT ARLINGTON on July 15, 2018 at 01:14:02 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

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H. H. Willis Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 1TL, England

The resin swelling that accommodates w a t e r u p t a k e "by fibre reinforced plastics is strongly inhomogeneous. A fillet o f resin b e t w e e n three closely p a c k e d fibres ( F i g u r e 1A) w o u l d , if uncon strained b y the p r e s e n c e of the fibres, u n d e r g o t h e shape change illustrated in Figure 1(B). The concentration of w a t e r r e a c h e s saturation in the resin a d j a c e n t to the external s u r f a c e a n d a well defined region of saturated swelling b e g i n s to move i n w a r d s a s indicated in Figure 1(c). However, the resin is not free to a d o p t t h e s e shape changes b e c a u s e of fibre constraint a n d , a s a result, the swollen resin experiences compression and, correspond ingly, the unswollen resin e x p e r i e n c e s tension. These m e c h a n i c a l constraints a r e exerted radially in the core a n d circumferentially in the flanges of the fillet. The tensile stresses so g e n e r a t e d attract a b s o r b e d w a t e r t h e r e b y giving rise to enhanced migration rates. In order to s t u d y this phenomenon in a s p e c i m e n g e o m e t r y representative o f the thin flange s e c t i o n b e t w e e n a d j a c e n t f i b r e s , samples o f p o l y e s t e r r e s i n a n d s a m p l e s o f epoxy r e s i n m e a s u r i n g -10 ym i n t h i c k n e s s a n d c o n t a i n i n g e n t r a p p e d a i r b u b b l e s , were c a s t between g l a s s c o v e r s l i p s , c u r e d i n s t r i c t accordance w i t h r e c o m m e n d a t i o n s b y t h e r e s p e c t i v e m a n u f a c t u r e r s a n d immersed i n w a t e r . R a t e s o f w a t e r u p t a k e a t 100° C. w e r e m e a s u r e d b y n o t i n g t h e t i m e s a t which water d r o p l e t s appeared i n s i d e t h e entrapped a i r b u b b l e s w h i c h were c o n v e n i e n t l y d i s t r i b u t e d a t v a r i o u s r a d i a l d i s t a n c e s f r o m t h e edge o f e a c h r e s i n l a y e r . The d a t a s o o b t a i n e d , i n d i c a t e water d i f f u s i o n c o e f f i c i e n t s o f -ΙΟ" cm s " i n p o l y e s t e r s a n d - 1 0 " c m s"" i n e p o x i e s , i . e . d i f f u s i o n c o e f f i c i e n t s which a r e over an o r d e r o f magnitude g r e a t e r t h a n v a l u e s p u b l i s h e d f o r water d i f f u s i o n i n t h e r e s p e c t i v e b u l k r e s i n s . S u b s e q u e n t w o r k , d e s c r i b e d h e r e , c o n c e r n s measurements o f t h e s t a t e s o f s t r e s s and s t r a i n g e n e r a t e d i n t h i n l a y e r s o f m e c h a n i c a l l y c o n s t r a i n e d r e s i n during water uptake. 4

7

2

2

1

1

1

C u r r e n t a d d r e s s : Department o f M a t e r i a l s S c i e n c e a n d E n g i n e e r i n g , C o r n e l l U n i v e r s i t y , B a r d H a l l , I t h a c a , New Y o r k l U 8 5 3 USA. 0-8412-0567-l/80/47-132-435$05.00/0 © 1980 American Chemical Society May; Resins for Aerospace ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

436

Figure 1.

RESINS F O R A E R O S P A C E

Swelling of resin fillet in fiber reinforced composite

t-p FILTER 1 = 1 GROUND GLASS

Figure 2. Experimental arrangement for Newton's rings experiment. (8)

OPTICAL FLAT SPECIMEN

May; Resins for Aerospace ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31.

FARRAR

AND

ASHBEE

Water

Migration

437

1

Use o f N e w t o n s R i n g s t o M o n i t o r S w e l l i n g The d i s p l a c e m e n t n o r m a l t o a t h i n l a y e r o f r e s i n b e t w e e n two a d h e r e n d s c a n be m o n i t o r e d d u r i n g s w e l l i n g c a u s e d b y w a t e r u p t a k e a t i t s e d g e , b y o b s e r v i n g changes i n t h e p a t t e r n o f Newton's r i n g s c r e a t e d b e t w e e n one o f t h e a d h e r e n d s , a n d a r e f e r e n c e f l a t . A r e g u l a r 150 ym t h i c k m i c r o s c o p e c o v e r s l i p s e r v e s a s an a d h e r e n d w h i c h i s t h i n and f l e x i b l e s u c h t h a t i t f o l l o w s t h e d e f o r m a t i o n of t h e r e s i n f i l m . A s l a b o f m e t a l i s u s e d as t h e o t h e r a d h e r e n d . The e x p e r i m e n t a l a r r a n g e m e n t i s shown i n F i g u r e 2. Filtered l i g h t , o f w a v e l e n g t h λ, f r o m a m e r c u r y v a p o u r l a m p i s d i r e c t e d t h r o u g h t h e o p t i c a l f l a t t o w a r d s t h e c o v e r s l i p , and i n t e r f e r e n c e b e t w e e n i n c i d e n t and r e f l e c t e d beams o c c u r s w i t h i n t h e v a r i a b l e t h i c k n e s s gap l o c a t e d b e t w e e n t h e two. The Newton's r i n g s a r e p h o t o g r a p h e d u s i n g l i g h t r e f l e c t e d i n t o a 35 mm c a m e r a b y t h e half silvered mirror. I n i t s s i m p l e s t f o r m , t h e p a t t e r n o f New t o n ' s r i n g s i s a c o n s e q u e n c e o f i n t e r f e r e n c e b e t w e e n j u s t two beams, n a m e l y t h e i n c i d e n t beam and t h e r e f l e c t e d beam. The f r i n g e c o n t r a s t i s c o n s i d e r a b l y enhanced b y s i l v e r i n g t h e u p p e r s u r f a c e o f t h e c o v e r s l i p and h a l f s i l v e r i n g t h e l o w e r s u r f a c e o f t h e o p t i c a l f l a t i n o r d e r t o p r o d u c e m u l t i p l e r e f l e c t i o n s and h e n c e m u l t i p l e beam i n t e r f e r e n c e . To e n s u r e t h a t changes i n t h e p a t t e r n a r i s e o n l y from d i s t o r t i o n o f t h e cover s l i p caused by r e s i n s w e l l i n g , i t i s e s s e n t i a l t h a t e a c h e x p e r i m e n t be c a r r i e d out w i t h o u t d i s t u r b i n g t h e s p e c i m e n / o p t i c a l f l a t assembly. A l l o f t h e components a r e s e t up o n an o p t i c a l b e n c h a n d , f o r h o t w a t e r t e s t s , i t has b e e n n e c e s s a r y t o d e v e l o p a r i g w h i c h a v o i d s c o n d e n s a t i o n o n t o t h e o p t i c a l components. A d j a c e n t r i n g s o f t h e same c o l o u r ( b l a c k o r w h i t e ) a r e l o c i of p o i n t s f o r w h i c h t h e o p t i c a l p a t h l e n g t h , i n t h e space between c o v e r s l i p and o p t i c a l f l a t , d i f f e r s b y one w a v e l e n g t h . By t h e same t o k e n , a d i s p l a c e m e n t i n t h e p a t t e r n o f Newton's r i n g s b y a n amount e q u a l t o one r i n g w i d t h c o r r e s p o n d s t o a change i n p a t h l e n g t h e q u a l t o one w a v e l e n g t h . By o b s e r v i n g changes i n t h e num b e r o f r i n g s b e t w e e n f i x e d m a r k e r s , s u c h as e n t r a p p e d a i r b u b b l e s , d i s p l a c e m e n t s n o r m a l t o t h e j o i n t d u r i n g w a t e r u p t a k e c a n be m e a s u r e d t o an a c c u r a c y o f λ A . I f r e q u i r e d , displacements which a r e a t l e a s t a s s m a l l as λ/10 c a n be m e a s u r e d b y s u p e r i m p o s i t i o n o f images i n o r d e r t o c r e a t e M o i r e p a t t e r n s . Experimental Materials. Long t e r m e x p e r i m e n t s have been c a r r i e d out u s i n g CIBA-GEIGY MY 750 DGEBA epoxy r e s i n m i x e d w i t h t h e m a n u f a c t u r e r ' s recommended p r o p o r t i o n s o f m e t h y l t e t r a h y d r o p h t h a l i e a n h y d r i d e hardener and triamyl-ammonium phenate a c c e l e r a t o r . The m i x i s c a s t between a degreased and n i t r i c a c i d c l e a n e d t h i n g l a s s c o v e r s l i p a n d a b l o c k o f 99-99% p u r i t y a l u m i n i u m c l e a n e d b y s u c c e s s i v e d e g r e a s i n g , d e - o x i d i s i n g and a n o d i s i n g p r o c e d u r e s . The r e s i n f i l m t h i c k n e s s i s a b o u t 15 ym and i s c o n t r o l l e d b y t h e mass o f r e s i n


438

RESINS

FOR

AEROSPACE

used f o r bonding, the cover s l i p being allowed t o s e t t l e under i t s own w e i g h t . A f t e r t h e m a n u f a c t u r e r ' s recommended c u r i n g s c h e d u l e a r e f l e c t i v e c o a t i n g i s vacuum d e p o s i t e d on t h e c o v e r s l i p and t h e sample exposed t o d i s t i l l e d w a t e r . T e s t s have been c a r r i e d out a t room t e m p e r a t u r e and a t t h e b o i l i n g p o i n t o f w a t e r . Good f r i n g e c o n t r a s t r e q u i r e s a w a t e r r e s i s t a n t r e f l e c t i v e c o a t i n g and m i n i m i s a t i o n o f t h e number o f h i g h l y r e f l e c t i n g a i r / g l a s s i n t e r f a c e s or the use o f t r a n s m i t t i n g c o a t i n g s o f i n t e r m e d i a t e r e f r a c t i v e index. Observations. F i g u r e 3 shows a t y p i c a l s e q u e n c e o f Newton's r i n g s p a t t e r n s observed a f t e r p r o g r e s s i v e l y longer exposure times i n room t e m p e r a t u r e w a t e r . One c h a r a c t e r i s t i c f e a t u r e i s t h e inward m i g r a t i o n o f a c i r c u m f e r e n t i a l l o c u s of k i n k s i n the i n d i v i d u a l f r i n g e s ; t h e k i n k s a r e b e s t r e s o l v e d a t p o i n t s s u c h as B, where t h e f r i n g e o r i e n t a t i o n i s s u c h t h a t a p r o m i n e n t k i n k i s p r o d u c e d . The k i n k s d e l i n e a t e an a b r u p t c h a n g e i n r e s i n f i l m thickness. The w a t e r c o n c e n t r a t i o n , and h e n c e t h e s w e l l i n g a s s o c i a t e d w i t h w a t e r u p t a k e , s a t u r a t e s and g i v e s r i s e t o a shoulder s e p a r a t i n g f u l l y s a t u r a t e d from l e s s t h a n f u l l y s a t u r a t e d r e s i n and t h i s s h o u l d e r p r o g r e s s i v e l y moves i n w a r d f r o m t h e r i m o f t h e s p e c i m e n . T h i s i s shown s c h e m a t i c a l l y i n F i g u r e 1+A-B. A s e c o n d c h a r a c t e r i s t i c f e a t u r e i s t h e o c c u r r e n c e and g r o w t h o f an edge c r a c k l y i n g p a r a l l e l t o t h e i n t e r f a c e s and g i v i n g r i s e to c i r c u m f e r e n t i a l i n t e r f e r e n c e f r i n g e s . To m a i n t a i n c o n t a c t w i t h the outer annulus o f u n i f o r m l y swollen r e s i n (Figure ^ C ) , t h e adherends would need t o bend w i t h c u r v a t u r e o p p o s i t e t o t h a t i n s i d e the shoulder. F a i l u r e t o a d o p t s u c h "S" w i s e b e n d i n g m a n i f e s t s i t s e l f as t h e o b s e r v e d i n t e r f a c i a l c r a c k . A n a l y s i s o f M e a s u r e m e n t s f r o m Newton's R i n g s E x p e r i m e n t s . D i s p l a c e m e n t , n o r m a l t o t h e s p e c i m e n p l a n e , o f one q u a r t e r o f a w a v e l e n g t h i s r e v e a l e d as a r e v e r s a l o f c o n t r a s t i n t h e p a t t e r n o f Newton's r i n g s . Thus t h e b r i g h t -* d a r k c h a n g e a t t h e f r i n g e i n d i c a t e d b y a r r o w A i n F i g u r e 3 ( a ) -> ( c ) i n d i c a t e s a d i s p l a c e ment o f 136.5 nm (λ = 5^-6.1 run f o r t h e g r e e n l i g h t e m i t t e d b y t h e m e r c u r y vapour lamp u s e d i n t h e p r e s e n t e x p e r i m e n t s ) a t a p o i n t 6 mm i n f r o m t h e r i m a f t e r o n l y two weeks e x p o s u r e t o room t e m perature water. A c r o s s t h e l o c u s o f k i n k s i n F i g u r e 3, t h e f r i n g e d e v i a t i o n amounts t o a p p r o x i m a t e l y two r i n g w i d t h s , i . e . a n o r m a l d i s p l a c e m e n t o f λ ( 0.5*+6l ym) i n an a n n u l a r r i n g w i d t h o f a p p r o x i m a t e l y 0.8 mm. A l o c a l t h i c k e n i n g o f t h e 15 ym t h i c k r e s i n f i l m b y 0.5^61 ym c o r r e s p o n d s t o a l i n e a r s w e l l i n g o f a l m o s t k% w h i c h i s c l o s e t o t h e v a l u e e x p e c t e d f o r s a t u r a t e d s w e l l i n g , as d e t e r m i n e d i n p r e v i o u s t e s t s . Using previously measured v a l u e s o f r e s i n modulus t h i s s t r a i n i n d i c a t e s normal s t r e s s e s o f a b o u t two k i l o b a r s i n t h e s a t u r a t e d r e s i n . T i m o s h e n k o s (1) f o r m u l a f o r t h e a x i a l s t r e s s σ p r o d u c e d b y an a x i a l l o a d ¥ on a t h i n p l a t e c l a m p e d a t i t s r i m i s 1


31.

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AND ASHBEE

Water

Migration

439

Figure 3. Swelling and debonding of an epoxy layer during water uptake at its edge (8). The changing pattern of Newtons rings is produced by the gap between an optical flat and a flexible cover slip (see text); 20° C water. Patterns recorded after (a) 0, (b) 116, (c) 356, (d) 1008, (e) 2329, and (f) 3043 hr, viewing from left to right and top to bottom.

y/77777777777/Z^ ΥΖΖΖ7Ζ7ΖΖΖ7ΖΖΖΖΔ

r-

-η

(B)

VmZZZ2ZZZZZZa Figure

4. Inhomogeneous swelling an x ticipated for a layer of resin during water uptake at its edge (8). LES without any mechanical constraint; RHS with me chanical constraint due to presence of adherends.


440

RESINS FOR

AEROSPACE

[(ΐ + ν ) ( 0 Λ 8 5 I n f" + 0.52) + 0.U8]

σ = ~

"

1—

h

where h i s t h e p l a t e t h i c k n e s s a n d 2a i s i t s d i a m e t e r , νi s Poisson*s r a t i o . The a x i a l d i s p l a c e m e n t i s g i v e n "by L o v e (2)

ω

as

16 π R

where R

12(1 - v ) 2

Ε i s Young's m o d u l u s . S u b s t i t u t i n g Ε = 6.3 x 1 0 dynes cm" , ν = 0.25 a n d h = 150 ym, f o r t h e g l a s s c o v e r s l i p i t i s f o u n d t h a t D = ~10 e r g s , 2a = 19 mm, h e n c e , ω = 136.5 nm g i v e s ¥ = ikk d y n e s a n d σ = 2.33 b a r s . T h i s e s t i m a t e f o r σ assumes t h a t t h e c o v e r s l i p i s r i g i d l y clamped a t i t s r i m but i s o t h e r w i s e f r e e t o undergo a u n i f o r m c u r v a t u r e d e f o r m a t i o n u n d e r t h e a c t i o n o f t h e a x i a l l o a d ¥. I n f a c t , t h e cover s l i p i s bonded over t h e whole o f i t s a r e a o f con t a c t w i t h t h e r e s i n and t h e d e f o r m a t i o n i s s t r o n g l y inhomogeneous, b e i n g c o n c e n t r a t e d i n t h e v i c i n i t y o f t h e s h o u l d e r between r e s i n which i s f u l l y s a t u r a t e d and r e s i n which i s l e s s than f u l l y saturated w i t h d i f f u s e d water. From g e o m e t r i c c o n s i d e r a t i o n s the f a c t t h a t t h e cover s l i p deformation i s concentrated over a 0.8 mm a n n u l u s l e a d s t o a 600 f o l d i n c r e a s e i n t h e c u r v a t u r e o f t h e s l i p over t h e v a l u e used i n t h e s t r e s s c a l c u l a t i o n (based on p l a t e d i a m e t e r ) . Thus i t i s e x p e c t e d t h a t t h e s t r e s s r e q u i r e d t o p r o d u c e t h e o b s e r v e d b e n d i n g d e f o r m a t i o n i s o f t h e same o r d e r as t h e normal s t r e s s e s t i m a t e u s i n g r e s i n modulus. Additional experiments u s i n g samples o f r e s i n c a s t between two g l a s s a d herends a l l o w e d o p t i c a l s t r e s s - b i r e f r i n g e n c e measurements t o be made d u r i n g s w e l l i n g . T h e s e t e s t s c o n f i r m t h a t t h e l o c a l s t r e s s e s a t t h e d e f o r m a t i o n s h o u l d e r a r e i n d e e d a b o u t t w o k i l o b a r s (3.). 1 1

2

5

O r d e r o f M a g n i t u d e E s t i m a t e f o r S t r e s s E n h a n c e d ¥ater M i g r a tion. An e s t i m a t e o f t h e s t r e s s r e q u i r e d f o r s t r e s s i n d u c e d d r i f t o f w a t e r m o l e c u l e s t o be a s i m p o r t a n t a s d i f f u s i o n i n a c o n c e n t r a t i o n g r a d i e n t may b e made a s f o l l o w s . The r e s p e c t i v e fluxes are J

drift

= - y c ? φ

where y i s t h e d r i f t m o b i l i t y , c i s t h e w a t e r c o n c e n t r a t i o n and V φ i s t h e p o t e n t i a l energy g r a d i e n t a r i s i n g from t h e t e n s i l e s t r e s s a t t h e c e n t e r o f t h e s p e c i m e n s k e t c h e d i n F i g u r e h, a n d


31.

FARRAR AND

Water

ASHBEE

441

Migration

i . = - D V c ^diffusion where D i s t h e w a t e r d i f f u s i o n c o e f f i c i e n t a n d V c i s t h e w a t e r concentration gradient.

u

^drift . diffusion

μ c V φ D V c

c V c

V φ k Τ

u s i n g t h e N e r n s t - E i n s t e i n r e l a t i o n s h i p μ = D/kT. a r e cm f o r c/Vc a n d e r g cm" f o r V* φ. H e n c e ,

The d i m e n s i o n s

1

i s a q u a n t i t y o f e n e r g y , s a y Δ φ, i . e . j

drift

_ Δ φ

^diffusion

k

1 6

T

* 1

k = l.k χ 10" e r g K" s o , f o r t h e f l u x e s t o h e e q u a l a t room t e m p e r a t u r e , Δ φ w o u l d h a v e t o b e o f t h e o r d e r o f h.2 χ 1 0 " erg. Assuming t h a t water m o l e c u l e s m i g r a t e s i n g l y and cause s w e l l i n g Δν e q u a l i n m a g n i t u d e t o t h e n a t u r a l v o l u m e o f t h e w a t e r m o l e c u l e , i.e. l î f

= 30 χ 1 0 '

=

2 k

3

cm ,

6 χ 10** 2H

9

t h e n Δ φ = ρΔΥ = k.2 χ 10~ e r g s a n d ρ = l . h χ 1 0 d y n e s cm" ~ 1 k b a r . Hence, t h e observed s t r e s s e s a r e c e r t a i n l y g r e a t enough t o s i g n i f i c a n t l y enhance w a t e r m i g r a t i o n .

2

Summary o f O t h e r Newton's R i n g s E x p e r i m e n t s . V e r y s i m i l a r r e s u l t s h a v e b e e n o b t a i n e d f r o m changes i n t h e p a t t e r n o f New ton's r i n g s observed during water uptake by supported adhesive films. T h a t i s , d i s p l a c e m e n t s r e m o t e f r o m t h e edge o f t h e j o i n t occur a f t e r s u r p r i s i n g l y short exposure t i m e s , l a r g e d i s p l a c e ments a n d c o r r e s p o n d i n g l y l a r g e s t r e s s e s s t r a d d l e t h e boundary between f u l l y s w o l l e n and l e s s t h a n f u l l y s w o l l e n a d h e s i v e , and debonding a t t h e r i m f o l l o w s attainment o f f u l l water s a t u r a t i o n . These c o n c l u s i o n s a r e t r u e f o r j o i n t s manufactured between a g l a s s c o v e r s l i p a s one adherend and a l u m i n i u m , b o t h w i t h and w i t h o u t a n o d i s i n g t r e a t m e n t s , as t h e o t h e r adherend. Use o f h o t w a t e r r a t h e r t h a n c o l d w a t e r a s t h e e x p o s u r e medium a c c e l e r a t e s t h e i n c i d e n c e o f a l l t h e s e phenomena. F i g u r e 5 shows a c o m p a r i s o n o f t h e d e b o n d i n g r a t e s f o r e p o x y r e s i n j o i n t s t e s t e d a t room t e m p e r a t u r e a n d 1 0 0 C, a n d a


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Figure 5.

Debonding of epoxy resin joints at (%) room temperature and 100°C and ( Q ) polyester resin joint at room temperature (3)

Figure 6. Migration of ( Q ) the kink in a Newtons ring and (O) of a point on the debonding crack; 20° C water. Data taken from Figure 8(8)

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p o l y e s t e r r e s i n j o i n t t e s t e d a t room t e m p e r a t u r e . The h i g h e r t e m p e r a t u r e t e s t r e s u l t s i n a ^-0 f o l d i n c r e a s e i n d e b o n d i n g r a t e f o r e p o x y r e s i n , w h i c h y i e l d s an a c t i v a t i o n e n e r g y o f a b o u t 10 k c a l mole"" f o r t h e p r o c e s s , a s s u m i n g i t t o be t h e r m a l l y a c t i v a t ed. As e x p e c t e d , due t o i t s more p o l a r s t r u c t u r e , t h e p o l y e s t e r r e s i n i s l e s s w a t e r r e s i s t a n t t h a n e p o x y r e s i n a t t h e same t e m p e r a t u r e , by a f a c t o r o f -13. 1

Discussion K i n e t i c s o f t h e V a r i o u s P r o c e s s e s d u r i n g Water Uptake. The s p a t i a l p o s i t i o n s o f t h e l o c u s o f k i n k s i n t h e p a t t e r n o f Newton's r i n g s , t h e edge o f t h e d e b o n d i n g c r a c k and t h e w a t e r d r o p l e t s i n s i d e e n t r a p p e d a i r b u b b l e s a r e a l l v e r y w e l l d e f i n e d and have b e e n m e a s u r e d as f u n c t i o n s o f t i m e . The d a t a o b t a i n e d f r o m t h e e x p e r i m e n t r e p o r t e d i n F i g u r e 3 a r e p r e s e n t e d i n F i g u r e 6. To t e s t w h e t h e r any o f t h e d a t a f i t t h e s o l u t i o n t o F i c k ' s l a w f o r t h e case o f a p l a n a r i n t e r f a c e between i n f i n i t e l y l o n g b a r s o f s o l u t i o n and s o l v e n t , p u b l i s h e d b y B a r r e r (U) , f o r e x a m p l e , t h e measurements a r e p l o t t e d as f u n c t i o n s o f ( t i m e ) / . M i g r a t i o n o f the shoulder d e f i n i n g the extent of water s a t u r a t i o n i s e v i d e n t l y not c o n t r o l l e d by a t / law. M i g r a t i o n o f t h e c r a c k e d g e , howe v e r , does a p p r o x i m a t e r e a s o n a b l y w e l l t o t ' behaviour. The k i n k m o n i t o r e d i n o r d e r t o c o n s t r u c t F i g u r e 6 d i d n o t f a l l on a r a d i u s where d e b o n d i n g i n i t i a t e d , i . e . t h e two s e t s o f d a t a i n F i g u r e 6 a r e f o r d i f f e r e n t r a d i i and t h e c r o s s - o v e r does n o t i n d i c a t e t h a t t h e c r a c k edge has o v e r t a k e n t h e s h o u l d e r . The d a t a shown i n F i g u r e 7 a r e f o r a s p e c i m e n m a n u f a c t u r e d b e t w e e n two g l a s s components ( a c o v e r s l i p and m i c r o s c o p e s l i d e ) , u s i n g t h e same CIBA-GEIGY epoxy r e s i n s y s t e m and e x p o s e d t o b o i l ing water. I n t h i s experiment t h e appearance o f penny-shaped p r e s s u r e f i l l e d c a v i t i e s , c r e a t e d by d i s s o l u t i o n o f w a t e r s o l u b l e i m p u r i t i e s (5.), was a l s o u s e d t o d e t e c t t h e a d v a n c e o f a b s o r b e d water from the f r e e s u r f a c e . Straight lines, i.e. t ' l a w s , may be drawn t h r o u g h t h e t h r e e d a t a s e t s a l t h o u g h b o t h p l o t s o f a b s o r b e d w a t e r i n g r e s s change s l o p e a t t / = 6.5· The t i m e d e p e n d e n c e shown i n b o t h F i g u r e s 6 and 7 i s u n e x p e c t e d f o r an amorphous g l a s s y p o l y m e r b e l o w i t s g l a s s t r a n s i t i o n t e m p e r a t u r e , T. A s s u m i n g t h a t p h y s i c a l s o r p t i o n and a c t i v a t e d d i f f u s i o n a r e t i e permeation processes i t i s expected t h a t polymer segmental motion i s the r a t e c o n t r o l l i n g step i n the m i g r a t i o n of water molecules. The s t r o n g p o s i t i v e t e m p e r a t u r e d e p e n d e n c e o f t h e r a t e o f i n g r e s s i n d i c a t e s t h a t t h e p r o c e s s i s one o f d i f f u s i o n r a t h e r t h a n c o n v e c t i o n , and t h e l a c k o f e v i d e n c e f o r w a t e r f l o w i n channels or c a p i l l a r i e s supports t h i s c o n c l u s i o n . However, there are s e v e r a l e f f e c t s which could i n f l u e n c e the k i n e t i c s of water uptake. In p a r t i c u l a r i t i s expected that the d i f f u s i o n c o e f f i c i e n t be s t r o n g l y c o n c e n t r a t i o n d e p e n d e n t , a l t h o u g h n e a r l y F i c k i a n b e h a v i o u r i s o f t e n observed at low l e v e l s o f s o r p t i o n . The anomalous p r o p e r t i e s o f t h e w a t e r m o l e c u l e due t o i t s s m a l l 1

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Figure 8.

Theoretical prediction of the plasticization of epoxy resin by absorbed water at 100°C


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s i z e and h i g h p o l a r i t y o f t e n c o n t r i b u t e t o u n e x p e c t e d b e h a v i o u r . C r o s s l i n k s , c h e m i c a l i n t e r a c t i o n s and o r i e n t a t i o n e f f e c t s a l s o l e a d t o n o n - l i n e a r i t y . The o t h e r c l e a r i n f l u e n c e o n w a t e r m i g r a t i o n i s s w e l l i n g s t r e s s e s w h i c h c e r t a i n l y enhance t h e r a t e o f p e r m e a t i o n , a l t h o u g h t h e e f f e c t o n t h e t i m e dependence i s n o t c l e a r . I n t h e 100°C t e s t , r a p i d r e s i n p l a s t i c i s a t i o n may h a v e o c c u r r e d and a d i f f u s i o n - r a t e c o n t r o l l e d p r o c e s s may t h e n be e x p e c t e d . F i g u r e 8 shows a t h e o r e t i c a l p r e d i c t i o n o f t h e d e c r e a s e i n Tg w i t h a b s o r b e d w a t e r c o n t e n t f o r e p o x y r e s i n . I t i s clear t h a t o n l y 0.02 v o l u m e f r a c t i o n o f w a t e r i s r e q u i r e d f o r T t o be r e d u c e d b e l o w 100°C. H o w e v e r , a b s o r p t i o n o f t h i s amount, e q u i v a l e n t t o a b o u t 2 w t . % t a k e s a b o u t 1*0 h o u r s a c c o r d i n g t o p r e v i o u s m e a s u r e m e n t s o n t h e same r e s i n (3). I n t h i s case t h e slope t r a n s i t i o n i n F i g u r e 7 may be e v i d e n c e f o r an a b r u p t c h a n g e i n d i f f u s i o n c o e f f i c i e n t at T , w i t h apparent F i c k i a n d i f f u s i o n o c c u r r i n g a t a l l e f f e c t i v e t e m p e r a t u r e s . The r e a s o n f o r t h i s i s n o t c l e a r . E f f e c t i v e d i f f u s i o n c o e f f i c i e n t s have been measured from F i g u r e s 6 and 7.^ At^20°C, 7 x 1 0 " < D < 5 x 1 0 " c m s ~ and a t 100°C, 7 x 1 0 " < D < 5 x 1 0 - c m s " . A c o n s t a n t f a c t o r o f 1000 b e t w e e n t h e two t e m p e r a t u r e s w o u l d i n d i c a t e an a c t i v a t i o n e n e r g y f o r ' d i f f u s i o n * o f a b o u t 20 k c a l / m o l e . P r e v i o u s measurement s o n b u l k r e s i n g i v e D - 1 0 " c m s - a t 100°C, w h i c h i s l e s s t h a n t h e l o w e r l i m i t o f t h e p r e s e n t v a l u e s due t o t h e f a c t t h a t c o n s t r a i n e d s w e l l i n g has n o t c r e a t e d t h e s t r e s s e s r e s p o n s i b l e f o r e n h a n c e d migration. The anomalous b e h a v i o u r shown i n F i g u r e 6 i s i n d i c a t i v e o f a r a t e i n c r e a s e over a p r o c e s s dominated by polymer r e l a x a t i o n s . In g e n e r a l , a t i m e e x p o n e n t o f 0.5 i n d i c a t e s F i c k i a n d i f f u s i o n , c h a r a c t e r i s e d b y a more d i f f u s e a d v a n c i n g f r o n t t h a n r e l a x a t i o n c o n t r o l l e d m i g r a t i o n , w h i c h i s c h a r a c t e r i s e d b y a t i m e e x p o n e n t o f 1.0 and a s h a r p s w o l l e n / u n s w o l l e n r e s i n t r a n s i t i o n z o n e . The 0.7 t i m e e x p o n e n t may i n d i c a t e t h a t w a t e r i n g r e s s f o l l o w s a F i c k i a n l a w b u t with a continuously increasing value of diffusion coefficient, i . e . the curve i n F i g u r e 7 i s a s u c c e s s i o n o f s t r a i g h t l i n e s . The s h a r p n e s s o f t h e o b s e r v e d "boundary b e t w e e n s w o l l e n and u n s w o l l e n r e s i n r e q u i r e s f u r t h e r study i n order t o determine the r a t e cont r o l l i n g s t e p i n t h e permeation p r o c e s s . Experiments such as t h o s e o f Thomas and W i n d l e (6), who h a v e u s e d i o d i n e doped s o l v e n t s t o a l l o w m e a s u r e m e n t s o f c o n c e n t r a t i o n p r o f i l e and d i f f u s i o n f r o n t p o s i t i o n d u r i n g s o r p t i o n i n b u l k PMMA, c o u l d be u s e d t o s t u d y t h i s problem i n epoxy r e s i n f l i m s . K w e i and Zupko (7.) h a v e m e a s u r e d t h e t i m e dependence o f t h e s o r p t i o n o f d i f f e r e n t s o l v e n t s in e p o x y s a m p l e s and o b s e r v e t i m e e x p o n e n t s b e t w e e n 0.5 and 1.0 c o r r e s p o n d i n g t o d i f f u s e and s h a r p f r o n t s r e s p e c t i v e l y . However, no e x p l a n a t i o n o f t h e r e a s o n f o r anomalous t i m e d e p e n d e n c e and no c o n c l u s i o n s on s o r p t i o n mechanisms a r e made i n e i t h e r work. F u r t h e r w o r k u s i n g t h e methods o u t l i n e d h e r e w i l l p r o v i d e d a t a on epoxy p r o p e r t i e s p a r t i c u l a r t o t h i n f i l m s e c t i o n s t y p i c a l o f t h e r e s i n f i l l e t s i n c o m p o s i t e s . However, measurement s o n b u l k r e s i n w i l l a l s o p l a y an i m p o r t a n t r o l e i n u n d e r s t a n d i n g s o r p t i o n g

9

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phenomena r e l e v a n t t o c o m p o s i t e s . F o r t h i s r e a s o n an i n t e r f e r e n c e t e c h n i q u e u s i n g d o u b l e e x p o s u r e h o l o g r a p h y has a l s o b e e n d e v e l o p e d (9.), -which y i e l d s , s i m u l t a n e o u s l y , a c c u r a t e d e f o r m a t i o n and s o r p t i o n d a t a on e p o x y a d h e s i v e i n t e r f a c e s . General Discussion. I t i s apparent t h a t enhanced w a t e r m i gration occurs i n constrained t h i n r e s i n f i l m s . The a t t r a c t i o n a f f o r d e d b y t e n s i l e s t r e s s i s t h e most l i k e l y e x p l a n a t i o n o f t h i s effect. T h r e e mechanisms c o u l d g i v e r i s e t o s u c h a s t r e s s . C u r i n g s h r i n k a g e i s assumed t o be n e g l i g i b l e , as v i s c o e l a s t i c f l o w a t e l e v a t e d t e m p e r a t u r e s w i l l r e l i e v e any s t r e s s e s , and d i f f e r e n t i a l c o n t r a c t i o n b e t w e e n r e s i n and a d h e r e n d s on c o o l i n g w i l l be p a r t i a l l y r e l i e v e d by s e l f - a d j u s t m e n t o f t h e f i l m t h i c k n e s s . The n o r m a l s t r e s s e s w i l l be i n s i g n i f i c a n t a l t h o u g h l a t e r a l t e n s i o n s may be p r e s e n t . Hence, i t i s thought t h a t s w e l l i n g s t r e s s e s d u r i n g w a t e r a b s o r p t i o n a r e t h e most i m p o r t a n t s o u r c e o f h i g h local stresses. I f water m i g r a t i o n w i t h i n the r e s i n l a y e r i s s i g n i f i c a n t l y enhanced by t h e s e l f - s t r e s s i n g t h a t r e s u l t s f r o m t h e inhomogeneous n a t u r e o f s w e l l i n g , i t f o l l o w s t h a t t h e e f f e c t i v e d i f f u s i o n c o e f f i c i e n t i s a f u n c t i o n o f w a t e r c o n c e n t r a t i o n and processes o c c u r r i n g at r a t e s p r o p o r t i o n a l t o the square r o o t o f t i m e c a n n o t be e x p e c t e d . The s e l f g e n e r a t i o n o f h i g h l o c a l s t r e s s e s d u r i n g s w e l l i n g i s a consequence o f t h e sharp boundary b e t w e e n f u l l y s a t u r a t e d and l e s s t h a n f u l l y s a t u r a t e d r e s i n and a p p e a r s t o be u n a f f e c t e d b y c h a n g i n g t h e m a t e r i a l s u s e d as a d h e r e n d s i n o r d e r t o r e s i s t m e c h a n i c a l f a i l u r e when e x t e r n a l f o r c e s are a p p l i e d t o the composite i t s e l f . Measurements o f t h e s w e l l i n g s t r e s s e s and c a l c u l a t i o n s o f e n h a n c e d m i g r a t i o n i n a s t r e s s - f i e l d show t h a t t h e o b s e r v e d i n c r e a s e s i n d i f f u s i o n c o e f f i c i e n t s may be e x p l a i n e d , a l t h o u g h t h e t i m e d e p e n d e n c e and k i n e t i c s o f t h e o v e r a l l p r o c e s s and t h e r a t e c o n t r o l l i n g mechanisms r e m a i n i n c o m p l e t e l y u n d e r s t o o d . Complete u n d e r s t a n d i n g o f t h e problem w i l l r e q u i r e i n v e s t i g a t i o n o f t h e n a t u r e o f s w e l l i n g and a r e a s o f r e s e a r c h fundamental t o t h i s i n c l u d e i d e n t i f i c a t i o n of the v a r i o u s p h y s i c a l and c h e m i c a l s t a t e s o f d i f f u s e d w a t e r , t h e m e c h a n i s m ( s ) b y w h i c h d i f f u s e d w a t e r p r o m o t e s s o - c a l l e d p l a s t i c i s a t i o n , and t h e p r e c i s e o r i g i n ( s ) o f d i m e n s i o n a l changes a t t r i b u t a b l e t o c u r i n g , water u p t a k e and w a t e r e x p u l s i o n . Abstract S w e l l i n g d u r i n g w a t e r u p t a k e b y f i b r e r e i n f o r c e d r e s i n composi t e s i s s t r o n g l y inhomogeneous. I n p a r t i c u l a r , t h e r e e x i s t s a w e l l d e f i n e d s h o u l d e r b e t w e e n f u l l y s a t u r a t e d and l e s s t h a n f u l l y s a t u r a t e d r e s i n . The p r i n c i p a l s t r e s s e s i n t r o d u c e d as a c o n s e q u e n c e o f t h e m e c h a n i c a l c o n s t r a i n t e x e r t e d by t h e f i b r e s i n c l u d e a n o r m a l c o m p r e s s i v e s t r e s s n e a r t h e f l a n g e s and a n o r m a l t e n s i l e s t r e s s near the core o f a r e s i n f i l l e t . The m a g n i t u d e o f t h e s t r e s s has b e e n m e a s u r e d b y a n a l y s i n g t h e Newton's r i n g s p a t t e r n s p r o d u c e d b e t w e e n a f l e x i b l e t h i n g l a s s c o v e r s l i p , b o n d e d t o a sample t h i n f i l m o f r e s i n s u p p o r t e d on a t h i c k m e t a l a d h e r e n d ^ and an o p t i c a l


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flat. The o b s e r v e d l o c a l s t r e s s e s o f a b o u t two k i l o b a r s i n t h e sample a r e shown t o b e g r e a t enough t o a c c o u n t f o r enhanced w a t e r m o b i l i t y i n t h e r e s i n and n o n - F i c k i a n d i f f u s i o n e f f e c t s . L i s t o f Symbols λ a

W h R μ:

Φ Τ: Ρ D

wavelength o f l i g h t stress load plate thickness flexural rigidity drift mobility p o t e n t i a l energy absolute temperature pressure diffusion coefficient

v:

2a: ω* Ε 3

c k V t

1

Poisson s ratio p l a t e diameter displacement Young's m o d u l u s flux concentration Boltzmann's constant volume time

Ac knowledgement s T h i s r e s e a r c h was s u p p o r t e d i n p a r t b y t h e US Army ( g r a n t No. DA-ERO-76-G-068) a n d i n p a r t b y t h e US A i r F o r c e ( g r a n t No. AFOSR-

77-3^8). T h i s a r t i c l e was p r e p a r e d w i t h t h e c o o p e r a t i o n o f t h e C o r n e l l M a t e r i a l Science Center which i s funded by t h e N a t i o n a l Science F o u n d a t i o n (DMR 76 81083). Literature Cited 1. 2.

T i m o s h e n k o , S.; "Strength of Materials", 2nd E d . , V a n N o s t r a n d , New Y o r k , 1947. L o v e , Α. Ε . H.; "Treatise on the Mathematical T h e o r y of Elasticity", 4th E d . , Cambridge University Press, Cambridge,

1959. 3. 4. 5.

Farrar, N. R., "Ph.D. Thesis", University of Bristol, 1977. Barrer, R. M.; "Diffusion in a n d through Solids", Cambridge University Press, C a m b r i d g e , 1941. Farrar, N. R., a n d A s h b e e , K. H. G.; J. Physics D, 1978, 11,

6. 7.

Thomas, N. L . , a n d Windle, A. H.; P o l y m e r , 1978, 19, 255. K w e i , Τ. Κ., a n d Z u p k o , N. M.; J. Pol. Sci., 1969, A-2, 7,

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RECEIVED

Farrar, N. R., a n d A s h b e e , K. H. G.; U.S.A.F. Interim Scien tific R e p o r t o n G r a n t Number AFOSR-77-3448, 1978. Farrar, N. R., C o n n e r s , Α. Μ., a n d K r a m e r , E. J.; U n p u b l i s h e d results.

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Self-Stress-Enhanced Water Migration in Composites - American

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