Evaluation of Mode-I Inter Laminar Fracture Toughness for Fiber Reinforced Composite Materials

8/4/2019 Evaluation of Mode-I Inter Laminar Fracture Toughness for Fiber Reinforced Composite Materials

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Composites Science and Technology 43 (1992) 49-54 C " , ,

E v a l u a t i o n o f M o d e - I i n t e r l a m i n a r f r a c t u r et o u g h n e s s f o r f i b e r - r e i n f o r c e d c o m p o s i t emater ia l s

Lin Y e *Department o f Engineering Mechan ics, Xian J iaotong U niversity, Xian, Shaanxi 710049, People's Republic of China

( R ece i ved 6 June 1990 ; r ev i s ed ve r s i on r ece i ved 29 A ugus t 1990 ; accep t ed 4 O c t obe r 1990)T he bas i s f o r t he cha r ac t e r i za t i on o f i n t e r l ami na r c r ack g r ow t h i n compos i t ema t e r i a l s i s d i s cus sed . Mode- I i n t e r l ami na r c r ack g r ow t h i n a un i d i r ec t i ona lT 3 0 0 / 6 3 4 . D D S c a r b o n - f i b e r / e p o x y c o m p o s i t e w a s st u d ie d . A s i m p l e m o d e l i sp r oposed t o e s t i ma t e t he o r t ho t r op i c co r r ec t i on f ac t o r o f t he s t r e s s - i n t ens i t yf a c t o r f o r t h e D C B i n t e r l a m i n a r f r a c t u r e m o d e . I t w a s f o u n d t h a t , f o rc o m p o s i t e m a t e r ia l s ( i n v o lv i n g t h e r m o s e t a n d t h e r m o p l a s t ic c o m p o s i t e s ), t h ei n t e r r e l a t ionsh i p be t w e en t he i n t e r l ami na r f r ac t u r e t oughn es ses G ~c and K ~ccan be co r r e l a t ed on t he bas i s o f l i nea r - e l a s t i c - f r ac t u r e mechan i c s , a l t hought he spec i a l i n t e r l ami na r - f r ac t u r e mechan i sms can d i s t u r b t he r e l a t i onsh i p .Keywords: i n t e r l ami na r f r ac t u r e , f r ac t u r e t oughnes s , C FR P, t he r mopl as t i cma t r i x

1 I N T R O D U C T I O N

A major obstacle to efficient application offiber-reinforced composite materials is theirtendency to delaminate. Delamination is themost predominant and life-limiting failure mech-anism in composite structures. A knowledge ofdelamination growth behavior is thus essentialfor materials development, for selection, and fordesign and life-prediction studies. Consequently,characterization of improved delamination resis-tance and, in turn, more damage-tolerantcomposite structures, has been a major goal ofmaterials-development activities. 1A popular approach2-5 to the characterizationof delamination growth has been through theapplication of linear elastic fracture mechanics(LEFM), which enable the critical energy releaserate or fracture energy, Go, to be deduced.However, from fracture mechanics anotherwell-known parameter, namely, the criticalstress-intensity factor, Kc, is commonly utilized.* Pr esen t addr es s : I n s t i t u t ft i r V e r bu ndw er ks t o f f e G m bH ,U ni ve r s i t y o f K a i s e r s l au t e r n , E r w i n - Schr 6d i nge r - S t r . , Pos t f -ach 3049 , 6750 K a i se r s l au t e r n , FR G .

Composites Science and Technology 0266-3538/91/$03.50( ~ 1991 E l sev i e r Sc i ence Pub l i she r s L t d .49

Both parameters are used to measure fractureresistance in engineering materials. From theclassical linear-fracture mechanics for isotropi-cally homogeneous materials, the strain-energyrelease rate, G, and the stress intensity factor, K,could be related. The interrelation between Gand K is one essential basis of LEFM. Moreimportantly, if K or G is known, the otherparameter can be estimated. However, theprecise relationship between the strain energy-release rate, G, and the stress intensity factor, K,for a heterogeneous system such as a fiber-reinforced composite, is not known and cannoteasily be obtained analytically.6,7 Hence someresearchers believe that the estimation of one ofthe parameters when the other is known is notstraightforward for composite materials and maybe questionable.8

The primary objective of this work is to studythe validity of the orthotropic fracture modeldeveloped by Sih and his co-workers9'1 for thecharacterization of interlaminar delaminationgrowth in fiber-reinforced composite materials.In addition, the common DCB test method isused to investigate the Mode-I interlaminarfracture behavior in a carbon-fiber/epoxy com-posite system. On the basis of the results,together with some others from the open


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5 0 Lin Yel i t e ra t u r e , t h e in t e r r e l a t i o n s h i p b e t w e e n G a n d Kis a s se s se d .

2 M A T E R I A L A N D T E S T IN G

T h e m a t e r i a l u s e d w a s a (O16) u n i d i r e c t i o n a lT 3 0 0 / 9 3 4 . D D S c a r b o n - f i b e r e p o x y c o m p o s i t e .T h e p a n e l w a s p r e p a r e d b y a c o m p r e s s i o n -m o l d i n g t e ch n i q u e . T h e s p e c i m e n s w e r e c u t f r o mt h e p a n e l a l o n g t h e f i b e r d i r e c t i o n . T h e d e t a i l e dg e o m e t r y is s h o w n i n F ig . 1 . A s h a r p k n i f e a n d ab l u n t w e d g e w e r e u s e d c a r e f u l ly to m a k e a' n a t u r a l ' c r a c k i n t h e m i d p l a n e o f t h e s p e c i m e n sw i t h a n i n i t ia l le n g t h o f 3 0 m m . T h e h i n g e d e n dt a b s w e r e u s e d f o r g r i p p i n g t h e s p e c i m e n s d u r i n gte s t ing .

,20rnm 2.Smm~ . ~ H i n g e C r a c k ~ ~ .

Fibre direct ion

~ 23Cmm

F i g . 1 . D C B s p e c i m e n d i m e n s i o n s .A l l t e s t s w e r e c o n d u c t e d o n a n M T S - 8 8 0 -

1 0 0 K N s e r v o h y d r a u l i c t e s t m a c h i n e i n s t r o k ec o n t r o l . T h e c r o s s h e a d s p e e d w a s m a i n t a i n e d a t2 m m / m i n . A n X-Y p l o t t e r w a s a t t a c h e d t o t h eM T S m a c h i n e to r e c o r d t h e l o a d - d e f l e c t i o nr e s p o n s e . A t y p i c a l l o a d - d e f l e c t i o n r e s p o n s e i ss h o w n i n F i g . 2 . T o m o n i t o r t h e p o s i t i o n o f t h e

Y

x

~2

Fig . 3 . S t r e s s f i e l d a round c r ack t i p i n an o r t ho t rop i c so l i d .

i n t e r l a m i n a r c r a c k t i p , b o t h s i d e s o f t h es p e c i m e n s w e r e c o a t e d w i t h t y p e w r i t e r c o r r e c t i o nf l u i d . T h e ' a c t u a l ' i n t e r l a m i n a r c r a c k l e n g t h i nt h e t e s t s p e c i m e n w a s o b t a i n e d b y a v e r a g i n gc r a ck l e n g t h s o n b o t h s i d es .

3 O R T H O T R O P IC F R A C T U R E M O D E LT h e o r t h o t r o p i c f ra c t u r e m o d e l w a s f o r m u l a t e db y S i h et al . 9 '1 f o r a g e n e r a l l y a n i s o t r o p i cm a t e r i a l i n w h i c h t h e d i r e c t i o n o f c r a c kp r o p a g a t i o n i s c o p l a n a r w i t h t h e o r i g i n a l c r a c k .F o r t h i s c a s e , t h e s y s t e m i s f r e q u e n t l y r e f e r r e d t oa s ' o r t h o t r o p i c ' a n d t h e s t r e s s f ie l d i n t h e v i c i n i t yo f a M o d e I c r a c k t i p ( F i g . 3 ) i s e x p r e s s e d a s :

K~ Re (Fo (0, /z~ , /~2) ) ( i , j = 1 , 2) (1)o- 2Vyw h e r e K ~ i s d e f i n e d a s t h e s t r e s s - i n t e n s i t y f a c t o r ,E~ a r e t h e c o m p l e x f u n c t i o n s o f 0 ( t h e a n g l eb e t w e e n t h e r a d i u s v e c t o r a n d t h e d i r e c t i o n o ft h e c ra c k p l a n e ), a n d t h e c o m p l e x p a r a m e t e r s , / t la n d / ~ 2 , a r e t h e r o o t s d e t e r m i n e d f r o m t h ec h a r a c t e r i s t i c e q u a t i o n :

a l l / ~ 4 + ( 2 a 1 2 + a66)/z2 + a22 = 0 (2 )

8 0706 o

A 5 0~- 40

3O2O10

- - Loading~ Unloading

y ~ " - _

Opening displaceme nt ( mm )1 ~ . 2 . T y p i c a l l o a d - d e f l e c t io n r es p on s e f r o m D C B t e s ti n g .


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E v a l u a t i o n o f M o d e - I i n t e r l a m i n a r f r a c t u r e t o u g h n e s s 51wh ere a 0 a re the e las t ic compl iances re la t ive tothe c rack-p lane sys tem. Forhave :

1 v12a n - E11 a12 ---- E11

1 v23a22 ~ a23E22 E22

1 1a ~ = G12 a33 E33

p lane s t ress , we

(3 )

and , fo r p lane s t ra in , we have :a~ = a o - a'2aj---2 (i, j = 1, 2, 6) (4)a33

I t i s a c o m m o n u n d e r s t a n d in g a m o n g r e s e a r c h -e rs wi th an accep ted v iew tha t the s t ress - in tens i tyfac to r can be used to charac te r ize the b r i t t l ef rac tu re in meta ls and o the r i so t rop ic eng ineer ingm a te r i a l s . H e n c e , m a n y s tu d i e s h a v e b e e nund er tak en to eva lua te the s t ress - in tens i ty fac to rfo r i so t rop ic so l ids wi th va r ious geom etr ies . HH o w e v e r , o w in g t o t h e i r m a th e m a t i c a l c o m -p lex i ty , the re a re on ly a few so lu t ions fo r thes t ress - in tens i ty fac to r fo r o r tho t rop ic so l ids .Some resea rchers found tha t the s t ress - in tens i tyfac to rs fo r o r tho t rop ic mate r ia l s a re iden t ica l tothose for isotrop ic one s, ~2a3 exce pt for a smallmodi f ica t ion o f the o r tho t rop ic co r rec t ion fac to r .Th is modi f ica t ion accoun ts fo r the in te rac t ionb e tw e e n t h e p r in c ip a l m a te r i a l o r i e n t a t i o n a n dthe c rack ex tens ion , a s we l l a s the ex te rna lb o u n d a r i e s o f t h e s p e c im e n s . Re c o g n iz in g t h eimpo r tance o f th i s , Kon ish 14 inves t iga ted a g roupof mid-p lane symmetr ica l f ibe r -compos i te lamin-a tes wi th d i f fe ren t lay -up , th ickness , andp ly -mate r ia l p roper t ie s . The resu l t s ind ica ted tha tthe o r tho t rop ic co r rec t ion fac to r co r respond ingto t h e o r th o t r o p i c h o m o g e n e o u s m a te r i a l m o d e l si s no rm al ly wi th in the range o f 1 .0 - l -10% andcan ac tua l ly be neg l ig ib le in some cases .In the case o f cop lanar c rack ex tens ion , thes t ress - in tens i ty fac to r , Kx can be re la ted to thes t ra in -energy- re lease ra te , G~ . The in te r re la t ion -sh ip be twee n KI and G~ fo rms o ne essen t ia l bas i so f LEFM . In an ana lys is o f v i r tua l c rackex tens ion , the re la t ion b e twe en G~ and K~ i s :9

g ~ a " a 2 2 ) l / 2 ~ ( a 2 2 ~ l / 2 q - 2a~q-a66 / l '2 ( 5 )G x = " \ 2 / [\a11/ 2a11 J

fo r the p lane-s t ress cond i t ion . Hence , once thes t ress - in tens i ty fac to r Kt i s known, the energy-

re lease ra te G~ can be de te rm ined f rom e qn (5 )and vice versa .

4 D C B I N T E R L A M I N A R - F R A C T U R EM O D E LT h e m o s t c o m m o n s p e c im e n g e o m e t r i e s f o r t h ec h a r a c t e r i z a t i o n o f M o d e - I i n t e r l a m in a r c r a c kg r o w th h a v e b e e n t h e d o u b le - c a n t i l e v e r - b e a m( D C B) s p e c im e n lo a d e d b y a p p ly in g s y m m e t r ic a lopen ing tens i le fo rces a t the ends o f the beams(F ig . 4 ) . For the DCB geometr ies , the s t ress -in tens i ty factor , K, is g iven by : 15

P a ( 3 . 2 6 + 2 . 8 2 8 h )K=H - B - - (6)where H i s the o r tho t rop ic co r rec t ion fac to r andequa l to un i ty fo r an i so t rop ic ma te r ia l body .O n th e o th e r h a n d , t h e g lo b a l e n e r g y r e l e a s era te , G, fo r a c rack to ex tend can be eva lua tedd i rec t ly f rom the de r iva t ion o f the s t ra in energyc o n ta in e d i n t h e s p e c im e n a n d t h e w o r kp e r f o r m e d b y t h e e x t e r n a l l o a d s ,~ 6 w h ic hf requen t ly i s re fe r red to as the ' compl iance 'm e th o d :

p2 0CG = 2 - - B a - ~ (7 )

where C i s the compl iance ( the reverse o f thes t if fness ) o f the spec imen , g iven by :6c P (8 )

w h e r e ~ i s t h e d i s p l a c e m e n t c o r r e s p o n d in g t o aload P . I f the c rack f ron t is rem ote f rom thec o n s t r a in e d e n d o f t h e c a n t i l e v e r b e a m a n d t h ec rack leng th , a , i s su f f ic ien t ly long com pared wi thh , the va lue o f the com pl iance , C, i s g iven f rom

tPI ~ B - i

Fig. 4. DCB interlaminar fracture model.


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5 2 L i n Y es i m p l e b e a m t h e o r y b y : 2

6 2a 3C - - - - (9)P 3 E l l Ia n d I = B h 3 / 1 2 . W e t h u s h a v e :

8 a 3C - - - (1 0 )E n B h 3w h e r e E I ~ i s t h e l o n g i t u d i n a l m o d u l u s , a n d I i st h e m o m e n t o f i n e r t i a o f t h e b e a m c r o s s - s e c t i o n .H e n c e , f r o m e q n s ( 7 ) a n d ( 1 0 ) , w e h a v e :

12PZa 2G = (11)E n B Z h 3F o r i s o t ro p i c m a t e r i a l s , E n - - E . F r o m l i n e a r-

e l a s ti c - fr a c t u re m e c h a n i c s , w e h a v e :P aK = V G E = 3 .4 6 4 Bh3/--- (12)

B y c o m p a r i s o n w i t h e q n ( 6 ), i t c a n b e s h o w nt h a t t h e t w o s o l u t i o n s o f t h e s t r e s s - i n t e n s i t yf a c t o r a r e a l m o s t i d e n t i c a l if t h e c r a c k l e n g t h , a ,i s s u f f i c i e n t l y l o n g c o m p a r e d w i t h h . I t i s a c t u a l l ym o r e p r a c t i c a l t o u s e t h e s o l u t i o n o f e q n ( 6 )w h e n t h e c r a c k l e n g t h i s s h o r t . H o w e v e r , f o r t h eo r t h o t r o p i c m a t e r i a l s , w e h a v e :

/ a a \ - 1 / 4 / / a \ 1 / 2 2a |2 + a66)-1 /4K G n 22 22v - i - r - ) +e a l ( a l l a 2 z ) - ' / ' ( ( a 2 2 ) 1'2= 3 . 4 6 4 - ~ { - ~ n \ 2 / \ \ a n ~

2a E + a66~-' /4} (13)-1- 2 a ll / )

B y c o m p a r i s o n w i t h e q n ( 1 2) , i t c a n b e s h o w nt h a t t h e o r t h o t r o p i c c o r r e c t i o n f a c t o r f o r t h eo r t h o t r o p i c D C B s p e c i m e n i s :

l ( a l la 22 ] - l /4 ( (a2 2) 1/2n =

2a1_2 + a6 6) - ' ' 4+ 2a1~ / (14)

I t m a y b e e x p e c t e d t h a t t h e o r t h o t r o p i cc o r r e c t i o n fa c t o r f o r t h e D C B m o d e l w i l l b eh ig h ly d e p e n d e n t o n m a t e r i a l p r o p e rt i e s a n d m a yb e f a r f r o m u n i t y . F o r e x a m p l e , t h e o r t h o t r o p i cc o r r e c t i o n f a c t o r f o r t h e T 3 0 0 / 6 3 4 . D D S c a r b o n -f i b e r / e p o x y c o m p o s i t e t o b e d i s c u s s e d l a t e r i s a sl o w a s 0 . 2 7 7 . H e n c e i t i s v e r y i m p o r t a n t t oc o n s i d e r t h e e f fe c t o f t h e o r t h o t r o p i c f a c t o r w h e nt h e s t r e s s - i n t e n s i t y f a c t o r i s u s e d t o c h a r a c t e r i z et h e i n t e r l a m i n a r f r a c t u r e o f c o m p o s i t e m a t e r i a l s .

5 D A T A A N A L Y S I S A N D D I S C U S S I O NO F R E S U L T ST h e e l a s t i c p r o p e r t i e s o f t h e u n i d i r e c t i o n a lT 3 0 0 / 6 3 4 . D D S c o m p o s i t e a r e gi v e n i n T a b l e 1 .

T ab le 1 . E la s t ic p rope r t i e s o f" 1" 300 /634- DD S compositeE n (G Pa ) E 22(GPa) G , 2 (GPa) v12

133 7.7 4.2 0.33

I n o r d e r t o e v a l u a t e G ~c b y t h e ' c o m p l i a n c e 'm e t h o d ( e q n ( 7 ) ) , a p l o t o f C a g a i n s t c r a c kl e n g t h , a , w a s f i r s t c o n s t r u c t e d . T h e p l o t o f Ca g a i n s t a w a s t h e n c u r v e - f i t t e d b y u s i n g t h em e t h o d p r o p o s ed b y H a s h e m i et al . 17 a n dd i f fe r e n t ia t e d . T h e n , f r o m a k n o w l e d g e o f th ev a l u e s o f t h e c r i t i c a l l o a d , P c , a n d t h e d i f f e r e n t i a ld C / d a a t a g i v e n c r a c k l e n g t h , t h e i n t e r l a m i n a rf r a c t u r e t o u g h n e s s , G ~ c, a t a n y c r a c k l e n g t h w a se v a l u a t e d b y u s i n g e q n ( 7) .

T h e v a l u e s o f G~c s o d e t e r m i n e d f o r a t y p i c a ll o a d - d i s p l a c e m e n t t r a c e a s s h o w n i n F i g . 2 a r eg i v e n i n T a b l e 2 . T h e c r i t i c a l f r a c t u r e t o u g h -n e s s e s , K ~ c , e v a l u a t e d f r o m e q n ( 1 3 ) a r e a l s ol i s t e d i n t h e t a b l e . F o r c o m p a r i s o n , t h e v a l u e s o fK g , e v a l u a t e d f r o m e q n ( 1 2 ), a r e a l s o i n c l u d e d int h e t a b l e . I t c a n b e s e e n t h a t t h e e v a l u a t i o n o ft h e c r i ti c a l f r a c t u r e t o u g h n e s s f r o m e q n ( 1 2 ) , i .e .b y n o t t a k i n g a c c o u n t o f t h e o r t h o t r o p i cc o r r e c t i o n f a c to r , w i l l l e a d t o a n o v e r e s t i m a t e o fgtc .

T a b l e 2 . Va lues o f t h e f n c t u r e t o u g h n es s e s K ~ , G k fo r1 3 0 0 / 6 3 4 . D D S c o m p o s it e mate r i a la ( r am ) K , ( M P a V ~ ) K ~ ( M P a V ~ ) G k ( k J / m 2)

30.0 1.54 5-56 0.6940.0 1.63 5.87 0.6144.8 1.79 6.45 0.6951.5 1-98 7.14 0.7762-3 2-07 7.48 0.7673.9 1.91 6-90 0.6085.3 1.77 6.37 0-4995.0 1.89 6.84 0.53average 1-82 6 .58 0-64

1E---~o=\ 2 / \ \ a , , / 2 g , :


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Evaluation of Mode-I interlaminar fracture toughnessT able 3 . R e la t ionsh ip be tw een Kk and C~c

Materials H K~c Kg Gtc G I c E o / K ~ GIeEo/K~(MPa;~/-m) (MPa~/-m) kJ/m zT300/634 DD S 0.2 77 2.2 8.0 0.8 1.68 0-127

APC -28 0-304 5.85 19.25 s 1.98 0.64 0-059A S4 /PEE K ~s 0"33 ~s 5"2 Is 0"875 is- - 1"9 is0"276 4"35 1" 156

The italic superscript numerals refer to the data from the respective re ferences .

53

I n T a b l e 3 a r e s h o w n t h e a v e r a g e i n t e r l a m i n a rf r a c t u r e t o u g h n e s s e s , K ~ c , KI* , an d G~ f o r t h eT 3 0 0 / 6 3 4 . D D s c o m p o s i t e f o r a l l t e s ts . I n o r d e r t od i s c u ss t h e r e l a t i o n s h i p b e t w e e n K ~ c a n d G x c,s o m e d a t a f r o m t h e o p e n l i t e r a t u r e 8,xs a r e a l s oi n c l u d e d . T h e o r t h o t r o p i c c o r r e c t i o n f a c t o r f o rt h e A S 4 / P E E K c o m p o s it e d e te r m i n e d b y t h ep r e s e n t m o d e l i s s l i g h t l y s m a l l e r t h a n t h a td e t e r m i n e d b y u s in g a p a t h - i n d e p e n d e n t Ji n t e g r a P s i n c o m b i n a t i o n w i t h s t r e s s a n a l y s i s f r o mf i n i t e e l e m e n t s . A c c o r d i n g t o l i n e a r - e l a s t i c -f r a c t u r e m e c h a n i c s , G ~ E o / K 2 c s h o u l d a p p r o a c hu n i t y .

H o w e v e r , a s r e p o r t e d b y m a n y r e s e a r c h e r s , as i g n i f i c a n t a m o u n t o f f i b e r - b u n d l e b r i d g i n gb e h i n d t h e c r a c k t i p w a s o b s e r v e d d u r i n g c r a c kg r o w t h in t h e T 3 0 0 / 6 3 4 - D D S c o m p o s i t e . T h i si m p o r t a n t f r a c t u r e m e c h a n i s m m a y d i s t u r b t h eb a s i c a s s u m p t i o n s i n t h e f o r m u l a t i o n o f e q n ( 5 ) ,i . e . t h e m a t e r i a l i s h o m o g e n e o u s a n d o r t h o t r o p i c ,a n d a s i n g le c r a c k g r o w s i n a s i m i la r m a n n e r . T h em a t e r i a l s u n d e r c o n s i d e r a t i o n a r e i n h e r e n t l yh e t e r o g e n e o u s . I t h a s b e e n r e p o r t e d ~9 t h a t t h e r ee x i s t s a p r o c e s s z o n e w h e r e e x t e n s i v e m a t r i xd e f o r m a t i o n a n d m a t r i x - c r a c k i n g o c c u r d u r i n gc r a c k e x t e n s io n . T h e f i b e r b r i d g i n g c a n o f t e n l e a dt o f r a c t u r e o f f i b e r s . A l l t h e s e s p e c i a l f r a c t u r em e c h a n i s m s f o r th e i n t e r l a m i n a r f r a c t u r e o fc o m p o s i t e m a t e r i a l s m a y c o n t r i b u t e t o d i s t u r -b a n c e i n t h e r e l a t i o n s h i p b e t w e e n G~ a n d Kic.I t c a n b e s e e n t h a t G~cEo/K2 r e a l l y a p p r o a c h e su n i ty f o r t h e A S 4 / P E E K c o m p o s i t e . B u t , f o r t h eo t h e r t w o c o m p o s i t e s , A P C - 2 a n dT 3 0 0 / 6 3 4 . D D S , t h e c o r r e l a t i o n i s n o t v e r y g o o d .I t c o u l d b e e x p e c t e d t h a t o n e r e a s o n f o r t h i sw o u l d b e t h e s p e c i a l i n t e r l a m i n a r f r a c t u r em e c h a n i s m s m e n t i o n e d a b o v e f o r e a c h m a t e r i a ls y s t e m . A n o t h e r r e a s o n m a y b e t h e t h e o r e t i c a le r r o r s o f t h e p r e s e n t m o d e l . A l l o f t h e s e n e e df u r t h e r i d e n t i f i c a t i o n .

6 C O N C L U S I O N ST h e m o d e - I i n t e r l a m i n a r - f r a c t u r e b e h a v i o r o f aT 3 0 0 / 6 3 4 . D D S c a r b o n - f ib e r / e p o x y c o m p o s i t eh a s b e e n i n v e s t i g a t e d . A n a t t e m p t h a s a l s o b e e nm a d e t o a s s e s s t h e i n t e r r e l a t i o n s h i p b e t w e e n K ~ ca n d G ~ . O n t h e b a s i s o f t h e r e s u l t s , t h e f o l l o w i n gc o n c l u s i o n s m a y b e d r a w n .

( 1 ) A p p l i c a t i o n o f f r a c t u r e m e c h a n i c s t oi n t e r l a m i n a r c r a c k g r o w t h i n f i b e r r e i n f o r c e dc o m p o s i t e m a t e r i a l s a n d t h e c h a r a c t e r i z a t i o n o fi n t e r l a m i n a r f r a c t u r e t o u g h n e s s w i t h t h e D C Bm o d e l a r e o n a s o u n d f o o t i n g .

( 2 ) T h e i n t e r r e l a t i o n s h i p b e t w e e n K ~c a n d G~cf o r c o m p o s i t e m a t e r i a l s d i s c u s s e d h e r e ( i n v o l v i n gt h e r m o s e t a n d t h e r m o p l a s t i c c o m p o s i t e s ) c a n b ee x p l a i n e d o n t h e b a s i s o f l i n e a r - e l a s t i c - f r a c t u r em e c h a n i c s .

( 3 ) C a r e s h o u l d b e t a k e n w h e n t h e s t r e s si n t e n s i t y f a c t o r s o l u t i o n s f o r i s o t r o p i c m a t e r i a l sa r e u s e d t o e s t i m a t e t h o s e o f o r t h o t r o p i c s o li d s ,s i nc e t h e r e s u l ts m a y b e m i s l e a d i n g .

A C K N O W L E D G E M E N T S

T h e a u t h o r i s g r a t e f u l t o P r o f e s s o r Y o n g - Q i uJ i a n g a n d P r o f e s s o r Y a - P e n g S h e n f o r e n -c o u r a g e m e n t d u r i n g t h i s s t u d y .

R E F E R E N C E S1. Sela, N . and Ishai , O . , Interlaminar fracture toug hne ssand tough ening of lam inated composite materials: arev i ew . Composites, 20 (1989) 423-35.2. Devitt, D. F., Schapery, R. A. & Bradley, W. L., Amethod for determining Mode I delamination fracture

toughness of elastic and viscoelastic composite m ate-rials. J. Co mpos. Ma ter., 14 (1980) 270-84.


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54 Lin Ye3. Wilkins, D. J . , Eisenmann , J . R . , Camin , R . A. ,Margol is , W. S. & Benson, R. A. , Character iz ingdelaminat ion growth in graphi te-epoxy. In Damage inComposite Materials (ASTM STP 775) , ed. K. L.Reifsnider , Am erican Socie ty for Test ing and M ater ia ls ,Phi ladelphia , PA , U SA , 1982, pp. 168-83.4 . W hi tney , J . M . , Browning , C . E . & Hooges t eden , W. ,

A double-cant i lever-beam test for charac ter iz ing ModeI de laminat ion of composi te mater ia ls . J. Reinf. Plast.Compos., 1 (1982) 297-313.5 . Ram kumar , R . & Whi t comb, J . D . , Cha rac t er i zingMode I and mixed-mode de l amina t ion g rowth i nT300/5208 graphi te /epoxy. In Delamination and De-bonding of Materials (ASTM STP 876) , ed. W. S.Johnso n. Am erican Socie ty for Test ing and Mater ia ls ,Phi ladelphia , PA, USA, 1985, pp. 315-35.6. Sih , G. C. , Hi l ton, P. D. , Badal iance , R. , Shenberger ,P. S. & Vi l larea l , G. , Frac ture mechanics of f ibrouscomposi tes . In Analysis of Test Methods for HighModulus Fibers and Composites. ASTM STP 521 . ed . J .M. Whi tney , Amer i can Soc i e ty fo r Tes t i ng andMater ia ls , Phi ladelphia , PA, U SA , 197 3, pp. 98-132.7. Sih, G. C., Fracture mechanics of composite materials.In Proceedings of First USA-USSR Symposium onFracture of Composite Materials. ed G. C. Sih and V. P.Tamuzs . S i j tho f f & N oordhof f , Alphen aan den R i jn ,The N ether lands, 1979, pp. 111-130.8. Newaz, G. M ., O n the va l idi ty of or thot ropic f rac turemodel for advanced thermoplast ic composi tes . EngngFract. Mech. 29 (1988) 31-9.9 . Sih , G. C. , Par is , P. C. & Irwin, G. R. , On cracks inrec t i linear ly anisot ropic bodies. Int. J. Fract. Mech. 1(1965) 189-203.10. Sih , G. C. & Liebowitz , H. , Mathemat ica l theor ies ofbrit t le fracture. In Fracture--An Advanced Treatise: I I ,ed. H. Liebowitz . Acad emic Press, New Y orl~, 1968,

Chap te r 2 .11. Sih, G. C., Handbook of Stress-Intensity Factors forResearchers and Engineers, Inst i tu te of Frac ture andSol ids Mechanics, Lehigh Universi ty , Bethlehem, USA,1973.12. Ell is , C. D . & Ha rr is , B. , Th e effec t of specimen andtest ing variables on the f rac ture of som e f ibre-re inforcedepoxy resins. J. Compos. Mater. 7 (1973) 76-88.13. Dha ran, C. K. , Frac ture m echanics of composi tematerials. J. Engng Mater. Technol., 100 (1978),233-47.14. Konish, H . J . , Jr . , M ode I s t ress- intensi ty fac tors forsym metrically-crack ed ortho tropic strips. In FractureMechanics of Composites (ASTM STP 593) , ed. G. P.Sendeckyj . Am erican Socie ty for Test ing and M ater ia ls ,Phi ladelphia , PA, USA, 1975, pp. 99-116.15. Srawley, J. E. & Oro ss, B. , Stress-intensity factors forcrack-line-loaded edge-crack specimens, NAS A TN-03820, 1967, pp. 1-19.16. Brock, D. , Elementary Engineering Fracture Mechanics,Si j tho f f & Noordhof f , Alphen aan den Ri jn , TheNether lands, 1978.

17. Hash emi , S. , Kinioch, A. J . & Wil liams, J . G. ,Correc t ions needed in double-cant i lever beam tests forassessing the interla min ar failure of fiber-composites. J.Mater. Sci. Letters, 8 (1989), 125-9.18. Hine , P. J . , Brew, B. , Ducket t , R. A. & Ward, I . M. ,The frac ture behavior of carbon-f iber-re inforcedpo ly (e the r e the rke tone ) , Compos. Sci. & Technol., 33(1988) 35-71.19. Bradley, W. L. & Cohen, R. N. Matr ix deformat ionand frac ture in graph i te-re inforced epoxies. InDelamination and Debonding of Materials (ASTM STP876), ed. W . S. Johnso n. A merican S ocie ty for Test ingand M a te ri a ls , Ph i l ade lph i a , PA, USA , 1983 , pp .389-410.

Evaluation of Mode-I Inter Laminar Fracture Toughness for Fiber Reinforced Composite Materials

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