Viscoelastic Properties of Fiber-Reinforced Plastics - ACS Symposium

19 Viscoelastic Properties of Fiber-Reinforced Plastics HARUO YOSHIDA

Downloaded by RUTGERS UNIV on May 29, 2018 | https://pubs.acs.org Publication Date: August 28, 1980 | doi: 10.1021/bk-1980-0132.ch019

O s a k a M u n i c i p a l T e c h n i c a l R e s e a r c h Institute, 1-1, Ogimachi-2, K i t a k u , O s a k a 530, J a p a n

The most typical f o r m of t h e c o m p o s i t e materials is t h e fiber reinforced plastics composed of glass or c a r b o n fibers and resins. The r e i n f o r c e m e n t s s u c h a s glass or c a r b o n fibers may be elastic, b u t resins must be r e g a r d e d a s viscoelastic materials(1). When t h e s e c o m p o s i t e materials are subjected to various loads, t h e y show viscoelastic c o m p l i c a t e d b e h a v i o r c a u s e d b y t h e mechanical properties of t h e fiber a n d resin, specially by the internal viscosity o f resin a n d t h e friction a t the interface (2) of fiber and resin. Then t h e strain of t h e s e c o m p o s i t e materials is n o t proportional to the stress, and t h e stress-strain d i a g r a m becomes t h e curved line affected b y t h e t i m e scale. T h i s phenomenon is t h e characteristic property of the reinforced plastics and becomes the special merit in practical uses. U n d e r t h e r e p e a t e d loads, t h e stress-strain diagram draws hysteresis loops. C o r r e s p o n d i n g t o t h e a r e a o f t h e loop, t h e strain e n e r g y is consumed in t h e material a t e a c h alternating stress. T h i s e n e r g y loss affects t h e fatigue of t h e material and t h e other h a n d i s e f f e c t i v e t o d a m p i n g t h e v i b r a t i o n o r s c r e e n i n g the a c o u s t i c emission. I n t h i s r e s e a r c h , t h e dynamic v i s c o e l a s t i c p r o p e r t i e s o f the f i b e r r e i n f o r c e d p l a s t i c s w e r e s t u d i e d by m e a s u r i n g t h e c o m p l e x moduli of e l a s t i c i t y of the m a t e r i a l s w i t h the t e c h n i c s of the v i b r a t i n g r e e d method Experiments

and

Discussions

The m e a s u r i n g a r r a n g e m e n t s c o n s i s t o f t h e c o m p l e x m o d u l u s a p p a r a t u s , t h e o s c i l l a t o r , t h e a m p l i f i e r and t h e l e v e l r e c o r d e r . The t e s t s a m p l e i s c l a m p e d a t one end and t h e o t h e r end i s f r e e . Two l i t t l e i r o n d i s c s a r e bonded on t h e sample b a r o p p o s i t e t o t h e t r a n s d u c e r s t o be r e s p o n s i v e t o t h e m a g n e t i c f o r c e . The f r e e end i s e x c i t e d a t t h e f r e q u e n c y f r o m 20 t o 20000 Hz b y t h e e x c i t e r t r a n s d u c e r , then t h e bending v i b r a t i o n o f t h e sample b a r o c c u r s and t h e p i c k - u p t r a n s d u c e r d e t e c t s t h e d e f l e c t i o n a m p l i t u d e

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

RESINS FOR

248

AEROSPACE


o f t h e sample b a r . The s a m p l e s t e s t e d a r e a s f o l l o w s : Sample(a); P o l y e s t e r r e s i n laminates r e i n f o r c e d w i t h g l a s s f i b e r roving cloths. Table I . Sample(b); Epoxy r e s i n l a m i n a t e s r e i n f o r c e d w i t h carbon f i b e r s . S a m p l e ( c ) ; H y b r i d l a m i n a t e d c o m p o s i t e s . One o f t h e r e i n f o r c e m e n t s i s g l a s s m a t ( M ) , a n o t h e r i s c o m b i n e d woven c l o t h w i t h g l a s s f i b e r s and carbon f i b e r s i n w a r p s ( C ) . R e s i n i s epoxy. The c o m p l e x m o d u l i o f e l a s t i c i t y o f t h e m a t e r i a l s m e n t i o n e d above were measured. T a b l e I . C o n s t i t u t i o n s and d i m e n s i o n s o f p o l y e s t e r r e s i n laminates reinforced with glass f i b e r roving cloths. Sample's Mark

PE

PE8G

PE8GV PE8GH PE12G

Plies

0

8

8 ( * l ) 8(*2)

1.18

1.60

1.14

1.39

1.83

31*5

17.5

16.2

48.6

Specific

gravity

Glass content (volume %)

0

12

( * l ) Warps o n l y , (2*) Woofs o n l y S p e c i m e n : L e n g t h 210, W i d t h 22, T h i c k n e s s 5.5 R e i n f o r c e m e n t : G l a s s r o v i n g c l o t h (EWR55) R e s i n : P o l y e s t e r (EPOLAC N317)

mm

The c o m p l e x m o d u l i o f e l a s t i c i t y o f t h e s a m p l e s ( a ) a t t h e v a r i o u s t e m p e r a t u r e f r o m -10 t o 110 d e g r e e C a r e shown i n F i g u r e 1. The c o m p o s i t e s w h i c h h a v e t h e g r o s s c o n t e n t o f g l a s s f i b e r s s u c h a s t h e s a m p l e PE12G a n d PE8G o b t a i n e d t h e h i g h e r v a l u e s o f t h e d y n a m i c m o d u l u s o f e l a s t i c i t y and k e p t t h e e l a s t i c i t y a t t h e e l e v a t e d t e m p e r a t u r e . The s a m p l e PE h a s n o t t h e f i b e r a n d i s r e s i n o n l y , t h e n t h e dynamic modulus o f e l a s t i c i t y d e c r e a s e d a t t h e t e m p e r a t u r e o f 110 d e g r e e C. The l o s s f a c t o r s o f t h e same s a m p l e s a r e shown i n F i g u r e 2. The l o s s f a c t o r s o f t h e s a m p l e s PE a n d PE8GH i n c r e a s e d r e m a r k a b l y i n a c c o r d a n c e w i t h t h e r i s e o f t e m p e r a t u r e . The s a m p l e PE8GH h a s n o t t h e w a r p s . A s t h e r e s u l t s , i t c o u l d be f o u n d t h a t t h e m a t e r i a l s w h i c h c o n t a i n e d much v o l u m e o f g l a s s f i b e r s were heat r e s i s t a n t . V a r i o u s k i n d s o f c o m p o s i t e m a t e r i a l s w e r e l a m i n a t e d a n d some h y b r i d c o m p o s i t e s w e r e c o n s t r u c t e d a s shown i n F i g u r e 3· The com p l e x modulus o f e l a s t i c i t y o f t h i s h y b r i d composite m a t e r i a l E* i s t h e o r e t i c a l l y expressed i n the e q u a t i o n ( l ) as the f u n c t i o n o f t h e i n d i v i d u a l complex modulus o f e l a s t i c i t y Eg o f each l a y e r .

Ε*Ι=ΣΕΪΙ

Κ

(1)

I a n d I K a r e r e s p e c t i v e l y t h e moment o f i n e r t i a o f t h e c r o s s



YOSHiDA

-10

Fiber-Reinforced

0

J

20

L

Temperature

j_J_ -10

0

20

249

Plasties

Figure 1. Complex moduli of elasticity of reinforced polyester resin hminates

80 {*C )

Figure 2. Loss factors of reinforced polyester resin hminates: (Φ) PE12G, (Q) PE8G, ((D) PE8GV, (Q) PE8GH, (Ο) PE

JU

Temperature

(2) jk)

mi

E; I„ En

In

Figure 3. Laminations of composite materials (see text for explanation of variables)



250

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

() (α)

t Figure 4. Theoretical relationship be tween the modulus of elasticity and the reinforcement content (see Equations 6, 7, and 8)

Figure 5. Theoretical refotionship between the loss factor and the reinforcement content (see Equations 6, 7, and 8)

LU

uî"

hi (b)

ÊfÏÏT


19.

YOSHiDA

Fiber-Reinforced

251

Plastics

s e c t i o n c o n c e r n i n g t h e n e u t r a l a x i s o f t h e h y b r i d c o m p o s i t e . The s y m b o l s w i t h s u f f i x k mean t h a t t h e y b e l o n g t o t h e k ' t h l a y e r . G e n e r a l l y Ε * * Ε - Κ Ε , ( £= \P1 ), E * i s t h e c o m p l e x m o d u l u s o f e l a s t i c i t y , E i s t h e dynamic modulus o f e l a s t i c i t y , E " i s t h e l o s s m o d u l u s o f e l a s t i c i t y . From t h e e q u a t i o n ( l ) t h e f o l l o w i n g e q u a t i o n s a r e introduced, d i s the l o s s f a c t o r . !

Μ

1

E'=if*E' κ·ιΐ

(2)

K

E»s£!* .t

(3)


E

«4

(4)

I f t h e m a t e r i a l o f r e i n f o r c e m e n t i s o n l y one k i n d a n d u n i f o r m l y d i s t r i b u t e d i n t h e composite, t h e f r a c t i o n o f volume con tent β o f the reinforcement i s expressed a s f o l l o w .

β"ϊ*

(5)

Then t h e e q u a t i o n s ( 2 , 3 , 4 ) a r e r e w r o t e a s f o l l o w s . E«=SE^.(l-p)E

(6)

m

(7)

f,

E =i3E|+(l-P)E» βΕ'ά.+(ΐ-β)Ε·(1

The s y m b o l s w i t h s u f f i x f and m mean t h a t t h e y b e l o n g t o t h e r e inforcement ( f i b e r ) and t o the m a t r i x ( r e s i n ) r e s p e c t i v e l y . The t h e o r e t i c a l r e l a t i o n s o f t h e d y n a m i c a n d t h e l o s s modu l u s o f e l a s t i c i t y and t h e l o s s f a c t o r t o t h e content o f t h e r e i n forcement expressed i n t h e equations(6,7,8) a r e d i s p l a y e d i n F i g u r e s 4 , 5 · The d y n a m i c a n d t h e l o s s m o d u l u s o f e l a s t i c i t y a r e r e s p e c t i v e l y p r o p o r t i o n a l t o the content o f f i b e r s but the l o s s f a c t o r has the h y p e r b o l i c r e l a t i o n s h i p t o the content o f f i b e r s . The e x p e r i m e n t a l r e s u l t s c o n c e r n i n g t h e r e l a t i o n b e t w e e n t h e complex modulus o f e l a s t i c i t y o f p o l y e s t e r r e s i n l a m i n a t e s r e i n forced w i t h g l a s s r o v i n g cloths(Sample(a)) and t h e content o f g l a s s f i b e r s a r e shown i n F i g u r e s 6 , 7 . T h e s o l i d b a r s e x p r e s s t h e r a n g e o f t h e v a l u e s f r o m t h e minimum t o t h e maximum a t t h e tem p e r a t u r e f r o m -10 t o 110 d e g r e e 0. I n F i g u r e 6, e x c e p t PE8GH a n d PE8GV, t h e e n d p o i n t s ( i n t h e c a s e o f Ε · , t h e u p p e r e n d p o i n t s a r e t h e v a l u e s a t -10 d e g r e e C, t h e l o w e r e n d p o i n t s a r e t h e v a l u e s a t 110 d e g r e e C, i n t h e c a s e o f E , t h e u p p e r s a r e a t 110, M



252


Figure 6. Experimental relationship be tween the complex modulus of elasticity of reinforced polyester resin laminates and the glass fiber content

Glass content

X

β

(vol.%)

>

ο ο 00 CD

Figure 7. Experimental relationship be tween the loss factor of reinforced poly ester resin laminates and the glass fiber content

0

10

20

30

Glass content

0

40

50

(vol.%)



19.

YOSHiDA

Fiber-Reinforced Plastics

253

the l o w e r s axe a t - 1 0 degree 0) a r e arranged a p p r o x i m a t e l y i n a s t r a i g h t l i n e r e s p e c t i v e l y . This f a c t proves the r e a s o n a b i l i t y of the p r o p o r t i o n a l i t y law expressed i n the equations(6,7). The sample P I 8 G ? h a s n o t w o o f s a n d h a s w a r p s o n l y , t h e n t h e g l a s s c o n t e n t i s s m a l l e r t h a n t h a t o f t h e sample P E 8 G , b u t t h e v a l u e s o f t h e c o m p l e x m o d u l u s o f e l a s t i c i t y i s n e a r l y t h e same a s t h a t o f P E 8 G . I f the c o n s i d e r a t i o n i s r e s t r i c t e d w i t h i n t h e warps o n l y , t h e c o n t e n t o f g l a s s f i b e r s i s t h e same a t P E 8 G a n d PE8GV. T h i s means t h a t o n l y w a r p s w h i c h l i e t o t h e same d i r e c t i o n a s the d i r e c t i o n o f t h e s t r e s s a r e e f f e c t i v e t o improve t h e complex m o d u l u s o f e l a s t i c i t y . The s a m p l e P E 8 G H h a s w o o f s o n l y a n d h a s not warps, then t h e v a l u e o f t h e complex modulus o f e l a s t i c i t y i s t h e same a s t h a t o f t h e r e s i n s a m p l e PE. I n F i g u r e 7» t h e end p o i n t s o f t h e s o l i d b a r s a r e a r r a n g e d on t h e h y p e r b o l i c c u r v e s e x c e p t PE8GV and PE8GH. The v a l u e s o f t h e l o s s f a c t o r o f PE8GV a n d PE8GH a r e r e s p e c t i v e l y t h e same a s t h o s e o f P E 8 G a n d P E b y t h e same t h e o r y c o n c e r n i n g t h e d y n a m i c a n d the l o s s modulus o f e l a s t i c i t y e x p l a i n e d above. The s a m p l e s o f t h e e p o x y r e s i n l a m i n a t e s r e i n f o r c e d w i t h c a r b o n f i b e r s ( S a m p l e ( b ) ) a r e shown i n F i g u r e 8. The l e f t p l a t e i s u n i d i r e c t i o n a l l y r e i n f o r c e d l a m i n a t e (5 p l i e s ) . The r i g h t p l a t e i s c r o s s p l i e d r e i n f o r c e d l a m i n a t e (8 p l i e s ) . The t e s t s a m p l e s were c u t o u t a s shown. The s t r e s s d i r e c t i o n i s t h e l o n g i t u d i n a l d i r e c t i o n o f t h e s a m p l e b a r . Then t h e d i r e c t i o n o f f i b e r s o f t h e s a m p l e CFRP-L a g r e e s w i t h t h e d i r e c t i o n o f t h e s t r e s s , t h e d i r e c t i o n s o f f i b e r s a n d s t r e s s o f t h e s a m p l e CFRP-T a r e p e r p e n d i c u l a r t o e a c h o t h e r . The e x p e r i m e n t a l r e s u l t s a r e shown i n F i g u r e s 9,1Q> The d y n a m i c m o d u l i o f e l a s t i c i t y o f t h e s a m p l e s CFRP-L and CFRP+L were p r e t t y h i g h and a l m o s t d i d n o t be a f f e c t e d b y t h e temperat u r e , b u t t h a t o f t h e s a m p l e CFRP-T e v e n l y d e c r e a s e d i n a c c o r d a n c e w i t h t h e r i s e o f t h e t e m p e r a t u r e . The l o s s f a c t o r s a r e shown i n F i g u r e 9. The v a l u e o f t h e l o s s f a c t o r o f t h e s a m p l e CFRP-T i s h i g h e r t h a n t h a t o f t h e s a m p l e CFRP-L. When t h e d i r e c t i o n o f f i b e r s i s 45 d e g r e e t o t h e d i r e c t i o n o f t h e s t r e s s , f o r example t h e s a m p l e CFBP-45 h a s a p r e t t y h i g h v a l u e o f t h e l o s s f a c t o r . I t i s deduced t h a t t h i s i s caused by t h e s h e a r i n g s t r a i n i n t h e r e s i n among f i b e r s a n d b y t h e f r i c t i o n a t t h e i n t e r f a c e o f r e s i n a n d f i b e r . The m e c h a n i c a l p r o p e r t i e s o f t h e c r o s s p l y l a m i n a t e s s u c h a s t h e s a m p l e s C F R P t L a n d CFRP+T a r e i n f l u e n c e d b y t h e d i r e c t i o n o f t h e f i b e r s e x i s t i n g i n t h e s u r f a c e l a y e r s o f the samples, because o f the bending s t r e s s . To i m p r o v e t h e m e c h a n i c a l p r o p e r t i e s o f t h e c o m p o s i t e mater i a l s , two o r more k i n d s o f r e i n f o r c e m e n t s a r e c o m b i n e d a n d t h e h y b r i d c o m p o s i t e s a r e made. I n t h i s r e s e a r c h , two k i n d s o f r e i n f o r c i n g m a t e r i a l s (M) a n d ( C ) w e r e u s e d , t h e r e s i n i s epoxy(Sample(c)). The s e q u e n c e o f l a m i n a t i n g w i t h t h e s e two k i n d s o f m a t e r i a l s was changed and f i v e k i n d s o f h y b r i d c o m p o s i t e s w e r e s e t a s shown i n F i g u r e 1 1 . The t h e o r e t i c a l v a l u e s o f t h e c o m p l e x m o d u l u s o f e l a s t i c i t y c a l c u l a t e d by t h e e q u a t i o n ( l ) w e l l a g r e e d w i t h t h e experimental r e s u l t s ( 6 ) .



254


(0,0,0,0,0 )

(0,0,90,90*90,90,0,0)

Fiber

direction

Figure 8. Epoxy resin laminates reinforced with carbon fibers: the left plate is 5-ply, unidirectionally reinforced; the right plate is 7-ply, cross-plied reinforced

-

CFRP+T

. CFRP-45

Figure 9. Dynamic moduli of ehsticity of reinforced epoxy resin laminates

Frequency

( s"

1


YOSHiDA

Fiber-Reinforced

255

Plastics


0.100 0.050

0.005|

J

10 Frequency

Figure 10.

Exp. Theor. Exp. Theor.

10

10

(s" ) 1

Loss factors of reinforced epoxy resin hminates

L L Τ Τ

Journal of the Society of Materials Science

Figure 11. Dynamic modulus of elas ticity and loss factor for several hybrid composite laminates (6): (Φ) experi mental L; (O) theoretical L; (fj^) experi mental T; ( Q ) theoretical Τ


RESINS FOR A E R O S P A C E

256


Conclusions A s t h e k e y t o f i n d i n g t h e v i s c o e l a s t i c p r o p e r t i e s o f t h e com p o s i t e m a t e r i a l s , t h e c o m p l e x modulus o f e l a s t i c i t y o f t h e mate r i a l s were measured. The f o l l o w i n g r e s u l t s w e r e o b t a i n e d . The v a l u e s o f t h e c o m p l e x modulus o f e l a s t i c i t y w e r e n o t a f f e c t e d by t h e v i b r a t i o n mode a t t h e r e s o n a n c e w i t h i n t h e f r e q u e n cy range o f t h i s s t u d y . The d y n a m i c modulus a n d t h e l o s s modulus o f e l a s t i c i t y w e r e r e s p e c t i v e l y p r o p o r t i o n a l to the content o f the reinforcement. The r e l a t i o n b e t w e e n t h e l o s s f a c t o r a n d t h e c o n t e n t o f t h e r e i n f o r c e m e n t was h y p e r b o l i c . W i t h a n i n c r e a s e i n t e m p e r a t u r e i t was g e n e r a l l y o b s e r v e d t h a t t h e e l a s t i c r e s p o n s e d e c r e a s e d , whereas t h e v i s c o u s response increased. The r e i n f o r c e d p l a s t i c s w i t h t h e g r e a t e s t c o n t e n t o f t h e r e i n f o r c e m e n t s w e r e more r e s i s t i b l e a g a i n s t t h e h i g h t e m p e r a t u r e . The d i r e c t i o n o f t h e f i b e r s w e r e i n f l u e n t i a l i n t h e v i s c o e l a s t i c p r o p e r t i e s o f the composite m a t e r i a l s . The t h e o r y t o c a l c u l a t e t h e c o m p l e x modulus o f e l a s t i c i t y o f the h y b r i d composites from the v i s c o e l a s t i c p r o p e r t i e s o f each c o n s t i t u e n t l a y e r was i n t r o d u c e d , t h e n t h e m e c h a n i c a l p r o p e r t i e s o f t h e h y b r i d c o m p o s i t e s a r e a b l e t o be c o n t r o l l e d a t t h e d e s i g n ing process.

Literature Cited 1. 2. 3. 4. 5. 6.

Flugge,W., "Viscoelasticity",Blaisdell Pub.,London, 1967,p.3. Endo,Κ.;Watanabe,M.,Proc.J.C.M.R.,1971,14,120. O n o g i , S . , " K o b u n s h i k a g a k u " , M a r u z e n , T o k y o , 1957,p.308. Nolle,A.W.,J.Appl.Phys.,1948,19,753. Horio,M.;Onogi,S.,J.Appl.Phys.,1951,22,977. Yoshida,H.,J.Soc.Mat.Sci.Japan,1976,25,442.

RECEIVED January 30, 1980.


Viscoelastic Properties of Fiber-Reinforced Plastics - ACS Symposium

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