dynamic crack intiation

8/22/2019 Dynamic Crack Intiation

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E L S E V I E R Mechanics of M ateria ls 23 (1996) 229-239

IIKIlU IC6OFItll

A n investigation of dynam ic crack initiat ion in PM M AD . R i t t e l a , *, H . M a i g r e b

a Facu lty o f Me cha nical Engineering, Technion, 3200 0 Haifa, Israelb Labora to i re de M~canique des So l ides , URA 317 CNR S Eco le Po ly techn ique , F-91128 Pa la i seau Cedex, Fran ce

Received 1 D ecember 1995; revised version received 1 Ap r i l 1996

Abs t r a c t

T h e r e c e n t l y d e v e l o p e d c o m p a c t c o m p r e s s i o n s p e c i m e n ( C C S ) - - H i n t e g r a l te c h n i q u e i s ap p l i e d to t h e c h a r a c t e ri z a t io no f t h e d y n a m i c f r a c t u r e t o u g h n e s s o f P M M A u n d e r t r a n s i e n t l o a d i n g . T h e f o r c e s a n d d i s p l a c e m e n t s o n t h e b o u n d a r i e s o f ac r a c k e d C C S a r e a p p l i e d a n d d e t e r m i n e d u s i n g a K o l s k y a p p a r a t u s . T h e p a t h - i n d e p e n d e n t H - i n t e g r a l i s t h u s c a l c u l a t e d b yf o r m i n g a c o n v o l u t i o n p r o d u c t b e t w e e n e x p e r i m e n t a l a n d r e f e r e n c e d a t a . T h e e v o l u t i o n o f b o t h t h e m o d e I a n d m o d e I Is t r e s s i n t ens i t y f ac t o r s i s de t e rmi ned by so l v i ng l i nea r convol u t i on equa t i ons . T he re fore , t he h i s t o ry o f t he s t r e s s i n t ens i t yf a c t o r s i s a s s e s s e d f r o r a t h e o n s e t o f l o a d i n g u n t i l e a r l y c r a c k p r o p a g a t i o n d e t e c t e d b y a f r a c t u r e g a g e . D y n a m i c f r a c t u r et o u g h n e s s i s t a k e n a s t h e v a l u e o f t h e m o d e I s t r e ss i n t e n s it y f a c t o r a t f ra c t u r e t i m e . E x p e r i m e n t a l r e s u lt s c o m p a r e w e l l w i thp r e v i o u s l y r e p o r t e d v a l~ a es w h i l e e x t e n d i n g t h e r a n g e o f a p p l i ed l o a d i n g r a t e s . T h e f r a c tu r e t o u g h n e s s i s o b s e r v e d t o i n c r e a s em a r k e d l y w i t h t h e s t r e ss i n t e n s it y r a t e. T h i s o b s e r v a t i o n i s d i s c u s s e d i n t h e l i g h t o f f ra c t o g r a p h i c e x a m i n a t i o n s h o w i n g t h eex i s t ence o f a cha rac t e~ f i s t i c r ough zone d i r ec t l y ahead o f t he no t ch- t i p o f dynami ca l l y f r ac t u r ed spec i mens .K e y w o r d s : Dyn am ic fracl~are oughne ss; Stress intensity factor; Comp act compression specim en; H-integral; Mixed m ode fracture; PM MA ;Kolsky bar

1 . I n t r o d u c t i o nE s t i m a t i o n o f d y n a m i c m e c h a n i c a l p r o p e r ti e s o f

m a t e r i a l s i s i m p o r t a n t t o t h e d e s i g n e r s i n c e t h e s ep r o p e r t i e s , s u c h a s th e y i e l d s t r e n g t h , c a n b e q u i t ed i f f e r e n t f r o m t h e i r s t a ti c c o u n t e r p a r t s . R e g a r d i n gf r a c t u r e p r o p e r t i e s , w h e r e a s t h e s t a t i c f r a c t u r e t o u g h -n e s s K i t i s n o w a s s e s se d u s i n g s t a n d a r d p r o c e d u r e s( e .g . A S T M , 1 9 9 3 ) , t h e d y n a m i c fr a c t u r e t o u g h n e s sK ~d i s s t il l e v a l u a t e d i n a v a r i e t y o f e x p e r i m e n t a lp r o c e d u r e s ( f o r a r e v i e w , s e e K o b a y a s h i , 1 9 8 7 ;K a l t h o f f , 1 9 9 0 ) .

* Corresponding aathol. Tel .: + 972-4-8293261; fax: + 972-4-8324533; e-mail : merit [email protected] .

B u i a n d M a i g r e ( 1 9 8 8 ) i n t r o d u c e d t h e p a t h - i n d e -p e n d e n t d y n a m i c H - i n t e g r a l w h i c h r e l a t e s t h e s t r e s si n t e n s i ty f a c t o r s t o t h e e x t e r n a l l y a p p l i e d l o a d s a n dd i s p l a c e m e n t s . T h i s c o n c e p t w a s f u r t h e r d e v e l o p e da n d i m p l e m e n t e d e x p e r i m e n t a l l y u s i n g t h e c o m p a c tc o m p r e s s i o n s p e c i m e n ( C C S ) ( B u i e t a l ., 1 9 9 2 ; R i t te le t a l. , 1 9 9 2 ) . T h e e v o l u t i o n o f t h e m o d e I s t r e s si n t e n s it y f a c t o r w a s d e t e r m i n e d o n a st e e l s p e c i m e nf r o m t h e o n s e t o f l o a d in g u n ti l e a rl y c r a c k p r o p a g a -t i o n d e t e c t e d b y a s i n g l e - w i r e f r a c t u r e g a g e ( R i t t e l e ta l ., 1 9 9 2 ) . T h e p r o c e d u r e w a s e x t e n d e d t o a p p l y t ot h e s i m u l t a n e o u s c h a r a c te r iz a t io n o f m o d e I a n dm o d e I I S I F ' s ( M a i g r e a n d R i t te l , 1 9 9 3 ) . I n a d d i t i o nt o t h e i n f o r m a t i o n p r o v i d e d b y t h e f r a c t u r e g a g e s , t h eo n s e t o f c r a c k p r o p a g a t i o n w a s c h a r a c te r i z ed b y

0167 -6636/96/$1 5.00 Copy right 1996 Elsevier Science B.V. All r ights reservedP I I SO 1 6 7 - 6 6 3 6 ( 9 6 ) 0 0 0 1 4 - 2


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2 3 0 D. R i tt el , H . M aigre / Mechan ics o f Mater ia l s 23 (1996) 22 9-2 39t ak ing advan tage o f the r ec ip roc i ty be tw een the m ea-s u red fo rces and d i s p lacemen ts on the boundary o fthe s pec imen . R ec ip roc i ty imp l ie s tha t the evo lu t ionso f the s t re s s in tens i ty f ac to r s fo rmu la ted in t e rms o fe i the r fo rces o r d i s p lacemen ts s hou ld be iden t i ca lunt i l f racture occurs (Maigre and Ri t te l , 1995) .

There fo re , the f r amew ork cons i s t ing o f the H - in -t eg ra l and the compac t compres s ion s pec imen i squi te convenient for the tes t ing of a re la t ively larges ample s i ze w i th m in imu m exper imen ta l and numer i -cal inves tm ent (Ri t te l and Maigre , 1993) .

Br i t t le po lyme rs have o f t en been s tud ied as mode lmate r i a l s in dynamic f r ac tu re s tud ies . H ow ever thesample s ize is general ly re la t ively smal l whi le d if fer -en t r e s ea rche r s u s e d i f f e r en t f rame w orks ( theo re t i ca land exper imen ta l ) . I t has been obs e rved tha t thedyna mic f r ac tu re toughnes s inc reases w i th the s t r e ssin tens i ty r a t e (Rav i -Chand ar and K nau s s , 1984 ;W ada , 1992) bu t the mec han i s m s under ly ing th i sdependence a r e no t c l ea r . F u r the rmore f ew a t t emptshave been m ade to co r r e la te and com pare the r e s u lt sob ta ined by d i f f e r en t r e s ea rche r s u s ing d i f f e r en tt echn iques .Cons eq uen t ly , th i s pape r r epo r t s and ex tend s r e -s u l t s on dynamic c r ack in i t i a t ion in commerc ia lP M M A u s i n g t h e c o m p a c t c o m p r e s s i o n s p e c i m e ntechn ique . The p res en t r e s u l t s a r e compared w i th

previous ly repor ted resul ts on a s imilar mater ia l .F rac tog raph ic cha rac te r i za t ion o f the s pec imens i scar r ied out and features which are character is t ic ofdynamic c r ack in i t i a t ion a r e r epo r ted and r e la ted tothe m eas u red f r ac tu re pa ramete r s.The p aper is organized as fo l lows: f i r s t , we b r ief lyrecal l the bas ic pr incip les of the approach and i tsexper imen ta l app l i ca tion . N ex t s pec i f ic exper imen ta la s pec t s o f th i s s tudy a r e add res s ed . Then w e p res en tthe r es u l ts ob ta ined on 17 P M M A s pec im ens , namelythe dynam ic f rac tu re toughnes s and the r e s u l ts o f thef r ac tog raph ic cha rac te r i za t ion o f the s pec imens .These resul ts are d iscussed in the l ight of previous lyrepor ted resul ts.

2 . T h e H - i n t e g r a l a n d t h e c o m p a c t c o m p r e s s i o ns p e c i m e n

The H - in teg ra l i s a pa th - independen t in teg ra lwhich re la tes forces (_T) and d isp lace me nts (u and _v)on the ex te rna l boundar ie s S o f a c r acked s o l id(crack length a) to the s t ress in tens i ty factors K~ andK H (Bui a nd M aigre , 1988). T his con cep t appl ies to2D l inear-e las t ic media . In th is in tegral the t imedependence i s exp l i c i t ly t aken in to accoun t th rough

( a ) [~

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7 0 m m ~ 1-I. . . . . . . . . 2 0 m m

~ - 3 5 m m - - m "

1 6 . 5 m r n

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T- r -

( b ) I L i aCOSS t r ik e r I n c id e n t b a r f ~ T r a n s m i t t e r b a rr - ll j I I jS t r a i n g Fac e I Fac e 2

Fig . I . ( a ) T h e c o m p a c t C o m p r e s s i o n S p e c i m e n ( C C S ) . ( b ) E x p e r i m e n t a l s e tu p : t h e C C S i s i n se r te d b e t w e e n t w o i n s t ru m e n t e d b a r s ( K o l s k yb a r ) . T r a n s i e n t s i g n a l s a r e r e c o r d e d o n t h e t w o s t r a i n g a g e s U ) d e t e r m i n e i n t e rr a c i a l ( f a c e 1 a n d f a c e 2 ) f o r c e s a n d d i s p l a c e m e n t s .


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D. Ritte l, H. Maigre / Mechanics of Materials 23 (1996 )22 9-2 39 231c o n v o l u t i o n p r o d u c t s ( n o t e d * ) . T h e g e n e r a l e x p r e s -s ion fo r H i s as fo l lows :H ( , ) : = - - - . u a s

0 a a a1 - v 2

- - - / ~ d * K ~ d a = I , I I ( 1 )EA s i mp l e r e x p r e s s i o n i s o b t a i n e d b y a s s u mi n g c o n -s t a n t a p p l i e d f o r c e s w i t h r e s p e c t t o t h e c r a c k l e n g t hv a r i a t io n . L e t t h e s u b s c r i p t r e f d e n o t e r e f e r e n c e d a t a(ca lcu la ted numer ica l i ly ) , wh i l e ex p i n d i c a te s e x p e r i -m e n t a l da t a. W i t h E a n d v d e n o t i n g Y o u n g ' s m o d u -l u s a n d Po i s s o n ' s r a t i o r e s p e c t i v e l y , H c a n b e w r i t -t en as fo l lows :

au ref 1 - v 2H ( - r ) = l f T e x P . _ : ~ d S = _ _ trexp,,ad* "~ctdk"ref2 J s - a a Eo t = I , I I (2 )

P r a c t i c a l l y , t h e d e t e r mi n a t i o n o f K ~d a mo u n t s t os o l v i n g a l i n e a r c o n v o l u t i o n e q u a t i o n , o n c e H h a sb e e n e s t i m a t e d ( f r o m t h e f o r c e s a n d d i s p l a c e m e n t s )a n d t h e c o r r e s p o n d i n g r e f e r e n c e s c a l c u l a t e d . T h ec o n t r ib u t io n o f e a c h c r a c k o p e n i n g m o d e c a n n o w b ea s c e r t a i n e d t h e f o l l o w i n g w a y : H i s s e p a r a t e d i n t oi t s p u r e m o d e I a n d m o d e I I c o m p o n e n t s u s i n gr e f e r e n c e d a t a c o r r e s p o n d i n g t o e a c h mo d e . F i n a l l y ,t h e r e q u i r e d S I F i s d e t e r mi n e d b y s o l v i n g t h e c o r r e -s p o n d i n g ( I o r I I ) l i n e a r c o n v o l u t i o n e q u a t i o n .

E x p e r i m e n t a l l y , w e u s e a s p l i t H o p k i n s o n b a r( K o l s k y b a r ) t o a p p l l y d y n a mi c l o a d s a n d me a s u r ei n t e rf a c i a l d i s p l a c e me n t s ( Fo l l a n s b e e , 1 9 8 5 ). A c o n -v e n i e n t s p e c i m e n g e o m e t r y i s p r o v i d e d b y t h e C C Sw h i c h c a n b e i n s e r t e d b e t w e e n t h e b a r s a n d l o a d e dwi thou t ex t ra dev ice :g to tu rn compress ion in to t en -s ion (Fig . 1 , Ri t t e l ~rad M aigre , 1993) . The on se t o fc r a c k p r o p a g a t i o n i s d e t e c t e d b y s i n g l e w i r e f r a c t u r eg a g e s . I t c a n b e n o t e d t h a t t h e g e o me t r y o f t h e CCSi s s y mme t r i c , b u t l o a d s a r e a p p l i e d o n o n e s i d e o n l y .Co n s e q u e n t l y , o n e c a n a s s u me t h a t mo d e I i s t h ep r e d o m i n a n t c r a c k o p e n i n g m o d e k e e p i n g i n m i n dt h a t a c e r t a i n a mo u n t o f mo d e I I i s p r e s e n t . Fo r ag i v e n s e r i e s o f e x p e r i m e n t s , o n e h a s t o g e n e r a t e ac o u p l e o f r e f e re n c e d a t a ( m o d e I a n d m o d e I I ) f o rany c r a c k l e n g t h b e t w e e n a a n d a + d a . T h i s w a y ,t h e c o n t r i b u t i o n o f e a c h mo d e c a n b e a s s e s s e d q u a n -t i t a t i v e l y u n t i l f r a c t u r e t i me ( Ma i g r e a n d R i t t e l ,

Table 1Measured mechanical properties of the commercial PMMA usedin this study

Young's modulus Pois son' s ratio(GPa)

Static 3.70 0.42Dynamic 5.76 0.42

1 9 9 3 ) . T h e me t h o d i s s i mp l e t o i mp l e me n t e x p e r i -me n t a l l y . Fu r t h e r mo r e , s i n c e t h e s e t o f r e f e r e n c e smu s t b e g e n e r a t e d o n l y o n c e f o r a s e r i e s o f e x p e r i -me n t s , a l a r g e s a mp l e s i z e c a n b e t e s t e d .

3 . M a t e r i a l a n d e x p e r i m e n t a l

T h i s s t ud y w a s c a r r ie d o u t o n c o m m e r c i a l P M M A( p -= 1 1 8 2 k g / m 3 ) w h o s e p r o p e r t i e s ( a s m e a s u r e d i no u r l a b o r a t o r y ) a re l i st e d i n T a b l e 1 . S i n c e P M M A i sa v i s c o u s ma t e r i a l , a t r a n s f e r mo d u l u s w a s d e t e r -m i n e d b y m e a s u r i n g t h e t i m e r e q u i r e d f o r w a v e s t ot r a v e l i n a r o d s p e c i me n ( Z h a o , 1 9 9 2 ) . Su c h t r a n s f e rm o d u l u s ( a l t ho u g h o f l o w e r v a l u e ) w a s a l so e m -p l o y e d b y o t h e r r e s e a r c h e r s i n a s i m i l a r c a s e ( W a d a ,1 9 9 2 ; W a d a e t a l . , 1 9 9 2 ) . Co mp a c t c o mp r e s s i o ns p e c i m e n s w e r e a l l m a n u f a c t u r e d f r o m t h e s a m ep l a t e a n d c a r e w a s e x e r t e d t o h a v e a l l s l i t s o r i e n t e di n t h e s a me d i r e c t i o n . Sh a r p n o t c h e s ( a v e r a g e r o o tr a d i u s 0 . 2 m m ) w e r e m a c h i n e d m e c h a n i c a l l y a n d n oa t t e mp t w a s ma d e t o o b t a i n s h a r p e r n o t c h e s . T h ed e g r e e o f m a t e r i a l i so t r o p y w a s a s s e s s e d b y m e a s u r -i n g u l t r a s o n i c w a v e v e l o c i t y ( a t 1 a n d 0 . 5 MH z )p a r a l le l a n d t h r o u g h t h e t h i c k n e s s w i t h r e s p e c t t o th en o t c h . T h e s e me a s u r e me n t s s h o w e d v e r y l i t t l e d i f f e r -e n c e b e t w e e n t h e t w o d i r e c t i o n s s o t h a t t h e ma t e r i a lc a n r e a s o n a b l y b e c o n s i d e r e d a s i s o t r o p i c , a t l e a s t f o rc o mp u t a t i o n a l p u r p o s e s .

T w o s p e c i me n s w e r e u s e d t o d e t e r mi n e t h e s t a t i cf r a c t u r e t o u g h n e s s o f t h e ma t e r i a l . T h e s p e c i me n sw e r e s l o w l y l o a d e d i n c o mp r e s s i o n . A 2 D f i n i t ee l e me n t mo d e l w a s u s e d t o c a l c u l a t e t h e S I F a tf r a c t u r e ( K ~c ) u s i n g I r w i n ' s f o r mu l a w h i c h r e l a t e st he c r a c k o p e n i n g d i s p l a c e m e n t ( C O D ) t o t h e S I F

8(1 - v ) 2 / rC O D ( r , O = FI ) = K , E- V 21-I " (3 )


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2 3 2 D. Rittel, 1t. Maigre / Mechanics of Materials 23 (1996) 229-239D y n a mi c t e s t i n g w a s c a r r i e d o u t o n 1 6 . 5 mm

d i a me t e r ma r a g i n g s t e e l b a r s . A t o t a l o f 1 5 s p e c i -me n s w e r e t e s t e d . A s i n g l e w i r e c o mme r c i a l f r a c t u r eg a g e ( MM CD 0 2 1 5 A ) w a s g l u e d i n t h e v i c i n i t y o ft h e n o t c h t i p . I n s o me c a s e s , w e u s e d o n e g a g e o ne a c h f a c e o f t h e s p e c i me n . A s t h e c r a c k p r o p a g a t e d ,i t f rac tu red the wi re and t r iggered a pu l se on ther e c o r d i n g s y s t e m. A l l s i g n a l s w e r e s y n c h r o n i z e d w i t ht h e s i g n a ls o f t h e i n c id e n t g a g e a n d s a m p l i n g w a sc a r r i e d o u t a t 1 MH z . T h e d i f f e r e n c e i n p o s i t i o n o ft h e f r a c t u r e g a g e w i t h r e s p e c t t o t h e c r a c k - t i p w a sa s s e s s e d ' p o s t mo r t e m ' . I t w a s n o t e d t h a t t h i s d i f f e r -e n c e r a r e l y e x c e e d e d 0 . 2 m m . G a g e s i g n a l s w e r ec o r r e c t e d f o r g e o me t r i c d i s p e r s i o n a n d p r o c e s s e d t od e t e r mi n e i n t e r f a c i a l f o r c e s a n d d i s p l a c e me n t s u s i n gD A V I D p r o g r a m ( G a r y a n d K l e p a c z k o , 1 9 8 8 ) . T h edura t ion o f the impact , as se t by the l eng th o f thei mp a c t e r , w a s 7 0 o r 3 5 0 i xs . I n a c o u p l e o f c a s e s , w eu s e d a s ma l l s t e e l b a l l t o a c h i e v e a s h o r t e r i mp a c t( a b o u t 3 0 I ~s ). H o w e v e r i n t ha t c a s e t h e i mp a c t p u l sew a s g a u s s i a n r a t h e r t h a n s q u a r e s h a p e d .

Fo r t h r e e s p e c i me n s ( P6 , P8 a n d P9 ) , t h e ( a v e r -a g e ) i n i t i a l c r a c k v e l o c i t y w a s mo n i t o r e d u s i n g ac o mme r c i a l f r a c t u r e g a g e . T h i s p r o v i d e d a d d i t i o n a ld a t a t o t h e f r a c t u r e t o u g h n e s s .

F i n a l l y , i n o n e c a s e ( s p e c i me n P1 7 ) , w e c a r r i e do u t a n e x p e r i me n t w i t h o u t t h e t r a n s mi t t e r b a r . T h ee x p e r i me n t w a s s u c c e s s f u l , i n t h a t t h e s p e c i me nf r a c t u r e d a s i t h a p p e n s i n o n e p o i n t b e n d e x p e r i -me n t s ( G i o v a n o l a , 1 9 8 6 ) . Fo r a l l s p e c i me n s e x c e p tP1 7 , f r a c t u r e w a s o b s e r v e d t o p r o c e e d a l o n g t h ei n it ia l n o t c h l i n e w h e r e a s f o r s p e c i m e n P1 7 t h e c r a c kp r o p a g a t e d b y f o r m i n g a t a k i n k a n g l e o f a b o u t 4 5 .

F o r e a c h e x p e r i m e n t , t h e a m o u n t o f m o d e I Ic o n t r i b u t i o n w a s a s s e s s e d . A l s o , t h e r a t e o f l o a d i n gw a s s p e c i f i e d a s t h e v a l u e o f t h e mo d e I f r a c t u r et o u g h n e s s d i v i d e d b y t h e t i me t o f r a c t u r e . T i me t of r a c t u r e i s d e f i n e d a s t h e ' a c t i v e ' l o a d i n g t i me d u r i n gw h i c h t h e c r a c k o p e n s e f f e c t i v e l y u n t il f r a c t u r e .

4 . R e s u l t s

4.1. Dynam ic fracture toughnessT y p i c a l e x p e r i me n t a l s i g n a l s ( i n c i d e n t p u l s e , i n -

t e r r a c i a l f o r c e s a n d t i me t o f r a c t u r e ) a r e s h o w n i nFig . 2 (Maigre and Ri t t e l , 1995) . Here , the inc iden t

~ 4 . 0

2. 0

1. 0

oo

- 1 . 0 -

Il F z ( t)

a , ! I . .. .. .. .. .. . In cid en t pu lse

i i0 100 200 ~ 0 400 450 5 0 0I I i

.2.0- "..,,......................................................,...!I f

F i g . 2 . T y p i c a l e x p e r i m e n t a l s i g n a l s ( s p e c i m e n P I 6 ) . I n c i d e n tp u lse ( a rb i t r a ry u n i t s ) an d in te r fac ia l fo rce s . Frac tu re i s d e tec tedb y 2 g ag es . No te th a t f r ac tu re o ccu r red b e fo re co mp le t io n o f th ei n c i d e n t p u l s e .

pu l se l as t s abou t 350 Ixs . The s igna l t akes typ ica l ly6 0 - 7 0 ~s t o r e a c h t h e c r a c k a n d f o r c e i t s o p e n i n g .F r a c t u r e o c c u r s s o o n a f t e r . A c o mmo n f e a t u r e t o a l lt e s ts i s th a t f r a c t u r e o c c u r s w e l l b e f o r e c o m p l e t i o n o ft h e 3 5 0 I xs . Co n s e q u e n t l y , t h e s p e c i m e n c a n n o t w i t h-s t and the en t i re s igna l , as i t appears on the in te r fac ia li n c i d e n t f o r c e p u l s e . I t c a n t h u s b e c o n c l u d e d t h a t th ef i r s t p a s s a g e o f t h e w a v e c a u s e s f r a c t u r e b e f o r e t h ep u l s e c o u l d l e a v e t h e s p e c i me n t h r o u g h t h e t r a n s mi t -t e r b a r i n t e r f a c e . F r a c t u r e o c c u r s i n a t r u l y d y n a mi cmo d e , i n o t h e r w o r d s t h e t r a n s mi t t e r b a r i s n o t r e a l l yn e e d e d i n t h i s s e r i e s o f e x p e r i me n t s . T h i s o b s e r v a -t i o n w a s c o n f i r me d b y t h e s u c c e s s f u l t e s t i n g o fs p e c i me n P1 7 w h i c h f r a c t u r e d d u e t o i n e r t i a o n l y .F i g . 3 s h o w s t h e a t y p i c a l e v o l u t i o n o f K~( t ) andg i i d ( t ) u n t i l f r a c t u r e . T h e s e r e s u l t s a r e o b t a i n e d b yt h e l i n e a r d e c o n v o l u t i o n p r o c e d u r e . T h i s e v o l u t i o nc a n b e c o n s i d e r e d a s t y p i c a l i n t h e s e n s e t h a t mo d e Iw a s o b s e r v e d t o b e s y s t e m a t i c a l l y d o m i n a n t i n a llt h e e x p e r i me n t s r e p o r t e d h e r e . H o w e v e r , t h e p i c t u r emi g h t b e d i f f e r e n t f o r ma t e r i a l s ( s p e c i me n s ) w h i c hf r a c t u r e i n v e r y s h o r t t ime s a s n o t e d b y K a l t h o f f a n dPo d l e s c h n y ( 1 9 9 2 ) .

I n T a b l e 2 w e h a v e l i s t e d t h e e x p e r i me n t a l v a l u e sof the f rac tu re toughn ess , K~a = Kid ( t ) a t t = tfraca long wi th the s t res s in t ens i ty ra t e K~d These resu l t sa r e p l o t t e d i n F i g . 4 ( a ) . A l t h o u g h v a r i o u s c o n f i g u r a -


5/11

D. R ittel, H. Maigre / Mechanics of Ma terials 23 (1996) 229-239 233

| . co K / / / /

6.4.s. ~ K nt) ( 1 0 4 M P a f m / s . T h i s o b s e r v a t io n i s c o n s is -t en t w i t h p rev i ous r e s u l t s ob t a i ned u s i ng a d i f f e ren tapp roach and i t ex t ends t he r ange o f ava i l ab l e exper -i m en t a l da t a .

T h e v a r i a ti o n s o f t h e d y n a m i c f r a c t u r e t o u g h n e s sco r re l a t e qua l i t a t i ve l y w i t h t he v i s ua l a s pec t o f t hef r ac t u re s u r f aces . A cha rac t e r i s t i c rough zone i s ob -s e rved on t he f r ac t u re s u r f ace i n t he v i c i n i t y o f t hen o t c h f r o n t o f d y n a m i c a l ly l o a d e d s p e c i m e n s . C o n s e -quen t l y , i t i s s ugges t ed t ha t dynam i c c rack i n i t i a t i oni n P M M A o c c u r s b y t h e p o s s i b l e n u c l e a t i o n o f s e v -e ra l m i c roc ra cks a l ong t he no t ch f ron t . In s uch cas e af i n i t e t i m e i s r equ i r ed fo r t he i r coa l es cence du r i ngwh i ch t he s t r e s s i n t ens i t y f ac t o r ( s ) m ay i nc reas em a r k e d l y .

R e f e r e n c e s

A o k i , S . ( 1 9 8 8 ), O n t h e m e c h a n i c s o f d y n a m i c f r a c t u re , J S M E I n t.J . , Se t . 1 3 1 ( 3 ) , 4 8 7 - 4 9 9 .

A S T M ( 1 9 9 3 ) , S t a n d a r d t e s t m e t h o d f o r p l a n e - s t r a i n f r a c t u r etoughness o f m e t a l l i c m a t e r i a l s , A n n u a l b o o k o f A S T M s ta n -d a r d s , V o l . 0 3 . 0 1 , A S T M , P h i l a d e l p h i a , P A .

B u i , H . D . a n d H . M a i g r e ( 1 9 8 8 ) , F a c t e u r d ' i n t e n s i t 6 d e s c o n -t ra in te s t i r6 des grandeurs m 6 c a n i q u e s g l o b a l e s , C . R . Acad . Sc .P a r i s , 306 I I , 1213 -1216 .

Bu i , H .D. , H . M a ig re and D. Ri t t e l (1992 ) , A new app roach to thee x p e r i m e n t a l d e t e r m i n a t i o n o f t h e d y n a m i c s t r e s s i n t e n s i t yfac to r , In t . J . So l ids S t r uc t . 2 9 ( 2 3) , 2 8 8 1 - 2 8 9 5 .


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p lanar s i ze and d ynam ic load ing ra te on in i t i a tion and p ropa-ga t ion toughness o f a modera te - toughness s tee l , Eng. Fract.Mech., 47(2) , 249-267 .

Fo l lansbee , P .S . (1985) , The Hopkinson ba r , ASM Metals Hand-book, Vol . 9 , 9 th Ed . , Meta l s Pa rk , OH.Ga ry, G. and J .R. Klep aczko (1988), D AVID: Logiciel ded6poui l l ement de l 'e s sa i i de com press ion pa r ba r res de Hopkin-son , Eco le Po ly techn ique , U nivers i t6 de Metz .

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Ka l thof f , J .F . and R . Po d leschny (1992), On the nonsym met ry o fthe load ing cond i t ion in Izod- type impac t t e s t conf igura t ions ,in: ed. I . Maekawa, Proc. of the Int. Syrup. on Impact Eng.,Senda l , pp . 605-610 .

Klepaczko, J .R. (1990), Dynamic crack ini t ia t ion, some experi-mental methods and modell ing, in: ed. J .R. Klepaczko, CrackDynamics in Metallic Materials, Springer-Verlag, W ien, pp.2 5 4 - 4 5 3 .

Kobayash i , A .S . (1987) , tlandbook on Experimental Mechanics,Pren t ice -Hal l , Eng lewood Cl if fs , NJ .

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Ri t t e l , D . and H. Maigre (1993) , A new approach to dynamicfracture toughness test ing, in: ed. A. Shukla, Novel Experi-mental Techniques in Fracture Mechanics, A S M E - A M D V o l.176 , New York , NY, pp . 173-185 .

Maigre , H . a nd D. R i t t e l (1995), Dynam ic f rac tu re de tec t ion us ingthe force-displac eme nt reciprocity: applicat io n to the com pactcompress ion spec imen , Int. J. Fract., 7 3 , 6 7 - 7 9 .

Ri t t e l , D . , H . Maigre , and H.D. Bui (1992) , A new method fo rdynam ic f rac tu re toughness t e s ting , Scripta Metall. Mater., 26 ,1 5 9 3 - 1 5 9 8 .

Shock ey, D.A., J.F. Ka lthoff and D.C., Erl ich (1983), Evalu at ionof dy namic c rack ins tab i l i ty c r it e r i a , Int. J. Fract., 2 2 , 2 1 7 -229.

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dynamic crack intiation

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