1975,Orange, TW - Fracture Testing With Surface Crack Specimens

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  • 8/12/2019 1975,Orange, TW - Fracture Testing With Surface Crack Specimens

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    T W Orange

    Fracture Testing with Surface rack Specimens

    REFERENCE: Orange, T. W., F r a c t u r e Te s t i n g w i t h S u r f a c eC r a c k S p e c i m e n s , o u r n a l of Testing and Evaluation JTEVA,Vol. 3, No. 5, Sept. 1975, pp. 335-342.

    A B S T R A C T: This paper is a report of ASTM Task GroupE24.01.05 on Part-Through Crack Testing. It includes recom-mendations for the design, preparation, and static fracture testingof surface crack specimens based on the current state of the art.The recommendations are preceded by background information in-cluding discussions of stress intensity factors, crack opening dis-

    placements, and fra cture toughness v alues associated with surfacecrack specimens. C yclic-load and s ustaine d-load tests ar e discussedbriefly. Recommendations for further research are included.

    K E Y W O R D S : fracture tests, surface defects, cracks, fractureproperties, fracture strength, toughness, mechanics

    Ear ly in 1920, A. A. Griff i th repo rted [1] tha t In the courseof an invest igat ion of the effect of surface scratches on themecha nical s t re ngth of sol ids , some general conclusions werereached which appear to have a d i rec t bea r ing on the p rob lemof rup tu re . . . . A l though he was o r ig ina l ly concerned wi thprob lems o f su r face de fec t s , Gr i ff i th used the more t r ac tab le

    ana ly t i ca l mode l o f a th rough- th ickness c rack to deve lop h istheory. As amend ed by I rwin [2] and Orowan [3 ], th i s theorybecame the founda t ion o f modern l inea r e l as t i c f r ac tu re me-chanics .

    In 1959 an AS TM special commit te e was formed [~i] o ass is t inso lv ing f rac tu re p rob lems invo lv ing h igh s t r eng th so l id rocke tmotor cases . Al though these f rac tu res were o f t en t r aceab le tosmall surface cracks, the commit tee , l ike Griff i th near ly 40years ea r l i e r, t u rned to more t r ac tab le ana ly t i ca l mode l s andtest specimens. Since 1959 the ten-m emb er special comm it tee hasbecome ASTM Commi t t ee E 24 on Frac tu re Tes t ing o f Meta l sand has deve loped severa l AST M tes t me thods and recom mendedprac t i ces . The commi t t ee has a l so fo rmed Task Group 5 onPar t -Through Crack Tes t ing o f Subcommi t t ee 1 on Frac tu reMechan ics Tes t Method s to deve lop gu ide l ines fo r the eva lua t ionof f r ac tu re cha rac te r i s t i c s o f ma te r i a l s th rough t ens ion t e s t s o fspec imens con tain ing pa r t - th rough c racks . Th i s i s a r epor t o ftha t t a sk g roup .

    The p r imary purpose o f th i s r epor t i s to p ropose un i fo rm pro-cedures for the design and s ta t ic tes t ing of surface crack speci-mens based on the cur ren t s t a t e o f the a r t . Th i s r epor t i s a l soin tended to no te the a reas where fu r the r sys temat ic r e sea rch i sneeded to more fu l ly unders tand the p rob lem and to deve lopmore de f in i t ive t e s t me thods . A secondary purpose i s to en -courage the t ak ing o f exper imenta l measurements which a re

    Chairman of ASTM Task Group E24.01.05 on Part-Through Crack

    Testing and research engineer, NASA Lewis Research Center, 21000Broo kpark R d., MS 49-3, Cleveland, Ohio 44135:

    not direct ly useful now but which are expected to be so in thenear future .

    The scope o f th i s r epor t wi l l be l imi ted to the res idua l s t r eng thtes t . The ob jec t o f such a t e s t i s to de te rmine the res idua l t ens i les t r eng th o f a homogeneous shee t o r p la te spec imen con ta in ing asemiel l ipt ical surface crack of specif ic dimensions or, b y means ofa ser ies of such tes ts , to d eterm ine residua l s t rength as a funct ion

    of c rack s i ze and shape . T he spec imen and in s t rumen ta t ion tobe descr ibed wil l be usable (within cer ta in l imitat ions) forcycl ic- load or sustain ed-loa d tes ts as wel l , but these wil l bediscussed only br ief ly.

    B a c k g r o u n d

    Historical Milestones

    The h i s to ry o f the su r face c rack spec imen inc ludes a number o fmilestones in tes t ing and analysis . These serve to ident i fys ign if i can t s t eps toward the so lu t ion o f the p rob lem and to p lacethem in h i s to r i ca l pe r spec tive .

    The f i rs t surface crack specimen tes ts to be reported wererunindependen t ly and concur ren t ly a t the Nava l Resea rch Labora -

    t o r y [5 6] and a t the Douglas Ai rc ra f t Co . [7 8] around 1960.Randal l [9] in 1966 s tudied the effect of crack s ize and shape onapparen t p lane s t r a in f r ac tu re toughness (K~: ) va lues . He a l soused c rack open ing d i sp lacement measurements a s qua l i t a t iveind ica to r s o f c rack t ip de fo rmat ion phenomena . In 1968 , Corn[10] a t t em pted to cha rac te r i ze the na tu r a l shape t endenc ies o fsurface cracks propagat ing under cycl ic loading. Hal l[11] in1970 compare d app aren t K~o values f rom surface crack speci-mens wi th those ob ta ined f rom o the r spec imen types .

    The ana lys i s o f su r face c rack da ta accord ing to f r ac tu remechanics pr inciples was mad e pos sible by Ir win [12] in 1962.From an ea r l i e r work by Green and Sneddon[13] he de r ived thes t ress in tens i ty f ac to r for an e l l ip t ica l c rack embedded in an

    in f in it e sol id and e s t ima ted th e max imum s t ress in tens i ty f ac to rfor a sere[el l ipt ical surface crack in a p late . P ar is a nd Sih [14] in1964 a t t emp ted to improve the app l i cab i l i ty o f I rwin ' s e s t ima teto plates of f ini te thickness by means of analogies to exis t ingtwo-dim ensional solut ions. In 1966, F. W. Smith[15] solved theproblem of a sem icircular surface crack in a f ini te thickness plateby a numer ica l me thod . Ayres [16] appl ied a f ini te differenceelastopla st ic solut ion to one semiel l ipt ical surface crack geom etryin 1968. In 1970, Miya mo to and Miy oshi[17] a n d L e v y a n dM a r c a l [18] presented f ini te-element analyses , again for specif icgeomet r i e s . Mar r s and Smi th [19] presen ted a me thod o f de te r-min ing s t r e s s in tens i ty f ac to r s in p las t i c mode l s by th ree -dimensio nal photoelas t ic i ty in 1971. In 1972, Cruse [20] ana-lyzed a semic i rcu la r su r face c rack us ing boundary in tegra lequat ions.

    5

    Copyright by ASTM Int'l (all rights reserved); Fri Sep 9 17:36:11 EDT 2011Downloaded/printed byUniversity of Western Ontario pursuant to License Agreement. No further reproductions authorized.

  • 8/12/2019 1975,Orange, TW - Fracture Testing With Surface Crack Specimens

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    3 3 6 J O U R N A L F T E S T IN G N D E VA L U A

    S t r e s s I n t e n s i t y F a c t o rs

    A s y e t t h e r e i s n o e x a c t s t r e s s i n t e n s i t y s o l u t i o n f o r t h e g e n e r a lp rob lem of a semie l l ip t i ea l su r face c rack in a p la te o f f in i t ed imens ions . I rwi n [12] p resen ted a n exac t so lu t ion fo r the e l l ip t i-c a l c r a c k e m b e d d e d i n a n i n f i n i t e s o l i d u n d e r t e n s i o n . H e a l s og a v e a n a p p r o x i m a t e e x p r e s s i o n f o r t h e m a x i m u m s t r e s s i n t e n s i t yfac to r fo r a semie l l ip t i ca l su r face c rac k in a p la te , w hich wasb a s e d o n a n a n a l o g y t o t h e p r o b l e m o f a n e d g e c r a c k i n a h a l fp l a n e . H e a s s u m e d t h a t h i s a p p r o x i m a t i o n w o u l d p r o v i d e ause fu l s t ress in tens i ty es t imate fo r a ~ c and a ~ t /2 , w here ai s c rack de p th , c i s ha l f c rack l eng th , and t i s th ickness ( seeF i g . 1 ) . I n d e e d , h i s e s t i m a t e d i d p r o v i d e f a i r l y c o n s t a n t f r a c t u r et o u g h n e s s v a l u e s f r o m t e s t s o f s m a ll s u r f a c e c r a c k s i n r e l a t iv e l yb r i t tl e , h i g h s t r e n g t h r o c k e t m o t o r c a s e s te e l s[6,21].

    A n u m b e r o f i n v e s t i g a t o r s[1~,15,22-29] h a v e a t t e m p t e d t oe x t e n d t h e a p p l i c a b i l i t y o f I r w i n ' s a p p r o x i m a t i o n t o s u r f a c ec r a c k s d e e p e r t h a n h a l f t h i c k n e s s . E a c h m e t h o d i n v o l v e s s o m ek i n d o f a n a l o g y t o a n a l t e r n a t e c r a c k c o n f i g u r a t i o n w h i c h h a ss o m e p h y s i c a l s i m i l a r i t y a n d f o r w h i c h a s o l u t i o n i s a v a i l a b l e .T h e s e a p p r o x i m a t e m e t h o d s d i f f e r o n e f r o m a n o t h e r, a n d i nsom e cases the ca lcu la ted s t ress in ten s i ty fa c to rs d i ffe r con-s i d e r a b l y[29,30].S e v e ra l m e t h o d s h a v e b e e n c o m p a r e d[27-29,31]o n t h e b a s i s o f t h e i r a b i l i t y t o p r o d u c e c o n s t a n t f r a c t u r e t o u g h -n e s s v a l u e s f r o m s e l e c t e d s e ts o f e x p e r im e n t a l d a t a , b u t n o o n ea p p r o x i m a t i o n h a s y e t b e e n s h o w n t o b e c l e a r l y s u p e ri o r.

    A t t e m p t s t o d e v e l o p t h r e e - d i m e n s i o n a l s o l u t i o n s h a v e p r o -d u c e d o n l y l im i t e d r e s u l ts . S m i t h ' s n u m e r i c a l s o l u t i o n s f o r th esemic i rcu la r [15] a n d c i r c u l a r s e g m e n t [ 2 8 ] s u r f a c e c r a c k s a r et h o u g h t t o b e f a i rl y a c c u r a t e ( e x c e p t n e a r t h e i n t e r se c t i o n o f t h ec r a c k a n d t h e c r a c k e d s u r f a c e ). O t h e r n u m e r i c a l m e t h o d s[16-18,20] h a v e t r e a t e d o n l y s p e c i f i c g e o m e t r i e s, a n d t h e i ra c c u r a c i e s a r e r e s t r i c t e d b y c o m p u t a t i o n a l l i m i t a t i o n s .

    M o s t o f th e s o l u t i o n s a n d a p p r o x i m a t i o n s i u s t d i s c u s s e dc o n s i d e r o n l y t h e c r a c k e d p l a t e u n d e r u n i f o r m t e n s il e lo a d . O n l y

    ~ ~ E S ectio n A

    t

    a = c r a c k d e p t hc h a l f c r a c k l e n g t h

    L t e s t s e c t i o n l e n g t ht = t h i c k n e s s

    W = test sectionw i d t hFIG. 1--Typical surface crack specime n grip detai ls omit ted) .

    a few [15,24,26,29]h a v e c o n s i d e r e d t h e c a s e o f l i n e a r ly v a r y i n g( b e n d i n g ) s t r e s s , a n d n o n e h a v e y e t c o n s i d e r e d h i g h e r o r d e rvar ia t ions .

    C r a c k O p e n i n g D i s p l a c e m e n t

    E x p e r i m e n t e r s h a v e l e a rn e d t h a t v a l u a b l e i n f o r m a t i o n c a n b eo b t a i n e d f r o m c r a c k o p e n i n g d i s p la c e m e n t ( C O D ) m e a s u r e -m e n t s o n s u r fa c e c r a c k s p e ci m e n s. T h e t e r m C O D i s u s e dh e r e i n t o d e n o t e t h e d i s p l a c e m e n t o f th e c r a c k f a c es o n t h ec r a c k e d s u r f a c e a t t h e m i d p o i n t o f t h e c r a c k ( se e F i g . 2 ) ; t h es a m e t e r m i s s o m e t i m e s u s e d b y o t h e r s t o d e n o t e d i s p l a c e m e n ta t t h e c r a c k t i p . R a n d a l l [ 9] w a s a p p a r e n t l y t h e f i r s t t o m e a s u r es u r f a c e c r a c k C O D . H i s s p e c i m e n s w e r e i n s t r u m e n t e d p r i m a r i l yt o o b s e r v e p o s s i b l e p o p - i n b e h a v i o r, b u t f r o m t h e l o a d - C O Dr e c o r d s h e w a s a b l e t o i n f e r t h e p r e s e n c e o f s i g n if i c a n t c r a c k t i pp l a s t ic f l o w. Ti f f a n y e t a l [ 3 2 ] u s e d C O D m e a s u r e m e n t s a sq u a l i t a t i v e i n d i c a t o r s o f s u b c r i ti c a l c r a c k g r o w t h . C o l l i p ri e s t[33,3~]a n d E h r e t [35] h a v e a t t e m p t e d t o m a k e q u a n t i t a t i v e u s eo f C O D m e a s u re m e n t s , a n d s o m e re c e n t C O D d a t a a r e i n c lu d e d

    i n R e f 36.E x a m p l e s o f C O D t r e n d s f o r s e v e r a l p o s s i b l e f r a c t u r e p h e -

    n o m e n a a r e s h o w n i n F ig . 2 . S t r a i g h t - l in e s e g m e n t s ( O B , D C , G J )ind ica te e las t i c de f lec t ions , and the i r s lopes a re func t ions o fc r a c k s iz e a n d s h a p e . N o n l i n e a r i ti e s ( A C , A F, J L ) m a y b e d u e t oc r a c k g r o w t h , c r a c k t i p p l a s t i c f l o w, o r a c o m b i n a t i o n o f b o t h .T h e c a u s e o f t h e n o n l i n e a r i t y c a n s o m e t i m e s b e d e t e r m i n e d b yu n l o a d i n g t h e s p e c i m e n p r i o r t o f r a c t u r e ; a c h a n g e i n s l o p e( u n l o a d i n g v e r s u s l o a d i n g ) i s i n d i c a t i v e o f a c t u a l c r a c k g r o w t ha n d z e r o o f fs e t i s i n d i c a t i v e o f c r a c k t i p p l a s t ic f l o w. P a t h O B H i nFig . 2 represen t s the c lass ic Gr i ff i th type o f b r i t t l e f rac tu re .Wi t h r e a l m a t e r i a l s , s e v e r a l o t h e r p a t h s a r e p o s s i b l e . C r a c kt i p

    : ~ s ti c fl ow, s u b c r i t i c a l c r a c k g r o w t h , o r a c o m b i n a t i o n o f b o t h

    m a y r e s u l t i n t h e n o n l i n e a r p a t h A C . I f t h e c r a c k i s s u f f i c i e n t l yd e e p a n d t h e m a t e r i a l s u f f i c i e n t l y t o u g h s ot h a t t h e c r a c k t i p

    o a d

    k ,--- , ,

    F B C /

    ; i . . / - / .

    COD

    FIG. 2--~u rface c rack opening displacement CO D) trends for severalpossible ractur e phenomena

    Copyright by ASTM Int'l (all rights reserved); Fri Sep 9 17:36:11 EDT 2011Downloaded/printed byUniversity of Western Ontario pursuant to License Agreement. No further reproductions authorized.

  • 8/12/2019 1975,Orange, TW - Fracture Testing With Surface Crack Specimens

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    ORANGE ON SURFACE CRACK SPECIMENS 7

    plastic zone penetrates the thickness prior to fracture, a pathsuch as AF may result . Or, the crack may pop in (AD) to a newstable shape (DC). Once an instabil i ty point (C, B, or F) hasbeen reached, the crack may then propagate catastrophical ly(CH, BH, or FH) or i t ma...

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