Microfracture mechanisms of fibre-reinforced aluminium composites

Microfracture mechanisms of fibre-reinforced aluminium composites

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Microfracture mecharfisms of fibre-rehlforced aluminium composites B. J. Weng, S. 'T'. C h a n g

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Abstract 'The m.cr,flraclure mechamsm,s ,~1 alummlum malnx c.~mposlleS re,nh~rced w,lh Sl( ' hased hbres are examined such Ihal Ihe e,,enls ,~1 crack mlrlallon and pr,~papal,m .',re rec.,rded ill ~'llll in ~.~scanning eleclron microscope. The specimens are h~aded hv an eleclr,m~callv eonlr.flled dewce hu which IOlJl d.Herenl Ioadmp. c,mdmons are o.mstdered Iongfludmal tens,m, hmg.lud.nul o~mpress,m. Iran,;verse lens,m and Iransverse compress.m Under hmg, udmal lens..m cracks inilialed al an mlerlace laver helween Ihe fibre and malnx, while hm~.Vludmal compres,s,m gave way I., deh, mdml..,,ot Ihe hhre near Ihe specimen edge, leadmp I,~ m.vr,~huckling ol Ihe hhres and Iurlher deb, mding Imlial m,er,~cracks near Ihe ,,pev~men edf.,.e as u resull ,~1 maehm.ng lend I.~ enhance hhre sphll.ng .n a z.gzag pallern when ,slrelched m Ihe Iransverse d~reel.on 'Transverse o,mpress,Jn led h~ cravkm~, ~1 Ihe malnx, where severe d~slon,m was ,d~served Failure caused hv fihre deh, mdm~, and cruslnng appear,, I,~ c,,nc.Je wtlh Ihe plane ,,I ma~mum shear

I. Introduction (."~mlinu~ms hbre-remh~rced melal malrlx c o m p o s ties have been used exlens=vely tn a e r o s p a c e struclures l l - 3 ] T h e y possess atlraclive m e c h a m c a l properlies such as high specfl~c sltHness and slrenglh in addfli~m h~ being Ioleranl I~ envlrtmmental changes A m o n g Ihe p~lenltal apphcatl~mS are aircraft, hehc~)plers, missiles, gun barrels and pn~leclile mumli~ms In response t~ Ihe high d e m a n d h~r racial malrtx c~mposiles, much has been d~me ~n c~.nblmng c a r b o n fibres wilh a l u m m l u m Vari~us a p p r o a c h e s 14-'7] have been a p p h e d I~ opl~mize Ihe chemical, physical and mechanical behav,~ur ~1 Ihese composfles, wilh particular emphasis given h~ lhe c o n d f l , m s al Ihe mtertace l I, ~l T h e malerialo . ~ I r ~ l h n g parameters, however, canm)l he idenlthed wilh(ml a c o m p r e h e n s i v e u n d e r s l a n d m g ~1 Ihe detorm a l . m and m~cr~flracture m e c h a m s m s ~t the c ~ m p ~ s lie under loading, say lensum and c o m p r e s s , m I~, I1)1. T'he I'aflure hehav,~ur ol Ihe racial matrix ~s afl'ecled by lhe mechamcal pr~pert~es ol Ihe c o n s m u e n l s , Ihe h~mdmg c~mdtli~ms helween the fihre and matrix and Ihe ge~melr~c c~mliguralt~m. In parlu.'ular, inlerfuce condm~ms can have a s~.t.~Hhcant Inlluence on Ihe overall hehavuJur ~t Ihe composfles. C h e m i c a l eHet'ts belween Ihe hbre and malrtx can create mechanical delecls ~n Ihe hbre surtace, leading h~ severe d e g r a d a I,_m ~1 Ihe hhre strenglh. 'T'hts can m lurn altecl the h~ad Iransler characlertsltcs ol Ihe constfluenls and Ihe p e r l o r m a n c e ot Ihe c~mp~stle While crack mflml~m and propagati~m in racial malr~x c~mp~s~les have been I)~-~2I "~l)t~t/~2/'~,"~ ()()

sludted 11-3l, Ihe microtraclure mechanisms ~I alummium alloy mulrlX comp~sHes are n~l well under sh~()d II(), I II 'There ts a need I~ l-urlher examine the mtcriffraclure delails l'ri~m pohshed specimens by appllcalion ~1 scanning eleelr~m micn~scope Irac tography. M~re specfl~cally, the presenl study uses a mtmature lest specimen m the scan.rang eleclron rmcroscope such Ihal Ihe sequence of latlure by crack mitml~on and growth can be r e c o r d e d ut sire as Ihe lensile or c o m p r e s s i v e loads are increased incremenlally

2. Experimental details A cq~mmercial SiC-based hbre-reinh)rced alu mlntum malrtx cump()sile was used The fibre ts 1,4(t p m m dtarneler w,th u c~mcentrlc carbon core 32 itm m d,ameler IIs cross-sectum has hve layers, with an mleHace layer ~n Ihe oulstde (see Fig 3) 'The I,bre has a lensfle slrenglh ifl' 352() MPa, a lensile modulus ~fl' 41)6 GPu and a densIly ol 312, cm-~ [12, 131. Auger eleclr4m speclrosc~py (AE',S)-mduclively coupled plasma (IC'P) analysls shows lhal lhe h(lh), alummtum alloy malnx has u nominal compusil,.m of I)43"/,, St, (). l 3'%, Cu, () 5 I'%~ Mg, (I 2'7% Fe, ()()2'Y,, Mn, 1)()I 7% C'r and ().()13'%, 'T'n (weighl per ~.'enl) The alununium c~mp~snle ns reinh~rced unndnrecl,mally wlth SIC' based fibres (~,()"/,, w~lume Iracllon) and cured by lhe vacuum h~l press dnl=fusum b~mdnng lechnique 14,

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Invesllgalnons ol the mncrolraclure mechann.sms ~I lensnle and t'~mpresslve specnmens were peHormed ~.~Im-~2- E,l,,evier,%ec]uqua ,All nl~hl,, re~,ep,'ed

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with an eleclronically conlrolled h~ading device mounled in a Phflips 515 scanning electrun rrucro scope al a ra~e ~t' (L()I mm rain -~. 'The wst specimens were ul~ras(mically machined lu Ihe dimens,)ns shuwn in F~gs. la and Ih, relerring respectively lu Ihe sehe mal~c drag;Tams of Ihe tensile and compressive specimens. Since nu more Ihan 1() fibres oecupy Ihe width uf the specimen, lhe composile ~s highly nun-hom~) geneous. The resulls uf flus sludy are sig-nihcanfl~/ mlluenced hy the specimen geomelry and size. Therefi~re they should n(d be extrapolated Io ~.~ve dala for large size composfles which have the same fibre w.)lume Iradion. ']"his is simply because the physieal boundaries ~)r free surlaee will have a much larger influence on the failure of speetmens with ~)nly a few fibres.

3. Results and discussion

3 1 1 Longtn.h.,H/en.w,m Figures 2a-21 dlustrale how I'raelure spreads pru gressively I'()r the S=C based i=bre/alummium compus =le under Iont..,~itudmal lension Imlmlly, cracking uecurs al the mterlaclal layer. It Ihen exlends m a z.igz.a~ lashi~m As Ihe h~ad is hJrlher increased, the fihre cracks locally, exlendmg Ihe process ml,~ the matrix ']"his is repeated al ,~everal h)eaUons m a secuon where

Ihe h~ad Iransler is hlghesl unUI Ihe hwal cracks merge I(~ damage a sul-llcienlly large reg.i(m, exhauslmg Ihe specimen mlegrity. Five dislinel sleps of lallure can be observed (1) Cracks appear in Ihe mlerface layer in Ihe h~ading direcll~m and lead h) deb~)ndmg. (2) L.~walized dlsh)rlion ~eeurs ar~und Ihe t'rack lips in Ihe malrlx (3) Inlerl,'lee layer cracking, {urns mh~ Ihe fibre in a dlrecll~m perpendicular I~)Ihe load (4) [)eb~mdmg. ~)1 the fibre increases wilh cracking. ~)1 Ihe interlace layer ahmg Ihe fibre. (5) Mulliple libre and matrix cracking resull in separal,m ol the composlle spee=men. The mlerographs clearly reveal the etteel ol ehemi cal reacl,~ns Ihal have ~ceurred between Ihe hbre and malrix 'T'hls gjves rise I(~ an mlerlace layer which has heen Identfl'ied wflh Ihe properHes ol alummmm carhide (AI4(.'~)Iq, 1()1 F'lgure 3 ph)ls Ihe Vwkers hardness (ff Ihis la~,'er agamsl dislance, wflh a max,hum (~1 4X()()+ I(l(J() Hv Indeed, Iraelure was i~bserved I~) milmle al Ihis mlerlace het'ause ~t' ils relalively h)w Iraelure slrenglh as sh~wn m F'ig. 2a The load {o millale mlerlaee cracking is aflecled by chemical h(mdmg and mechameal residual stress ]11 The h~rmer is e~mIr~lled by the hbre surlace chemlslry and malrix e~m p~Ml,m, lhe laller by mismalch ol the t'oeHwlenls ~1 lhermal expans, m (CTE)(~r a w)lume change as a resull ()1 phase Iransh~rmalion ~)t lhe malr~ when =1 =s c,),)led Ir~m h=gh lemperalure =n pr~wessmg ~r sublecled li~ ~ubsequenl heat Irealmenl. Because lhe O(ih3 alummium malrix =s m(~re duclde than Ihe hbre, =l can readdv dist,~rh 'T'h=s can be seen hy Ihe exlenswe d=sI(~rt,.m of Ihe matrix =n F=g 2b In parl=eular, Ihe crack ~)pen=ng m Ihe fibre ot appr~)x~malely '7 t~/~m =n Fig 2e =s increased I,~ I I pm =n F'~g ,-I This change =s relalwely large =n c~)mpar=son w=lh lhe z~)ne ()f d=slorl,_)n ahead i~l'lhe crack m the mulrt~ N¢~le Irl)m F'~gs 2c and-I thai Ihe spreading ul' micrilcracks =n Ihe radml d=rect=un d,~es not change appreciably AI relalively h~w load level the m{)rph,~h_)gy i~l' Ihe local craek=ng, =s ml]uenced more by the initial =mperteelil)ns and/or variance of Ihe fibre. This effecl tends Io d=minish as Ihe load =s increased F'=gures 2c-2e shrew Ihe d=serele nalure ,~1' Ihe hbre and malr~x cracking, while F~g 21 reveals a dominant plane ~1 e,)mp¢~Mte damage directed normal to the direel,.m ol maximum lens,m, allhough s,)me ~1' the fibres were cracked only al ,~ne h~c,'di,m away tr~m IhLs plane. The mrluenee ol hbre Imperleclion due h) mechameal and chemical eH'eet,~ wdl c~mpele wilh Ihe dominance ~II h~ad Iran.sler h~r lailure mHmUon and growlh. This =s why Ihe failure pallern in a e~mpoMte will nol he regular (_)nlv a general Irelld can he eslabhshed. As can be seen by Ihe scanning eleclron m,.'roscopy (SEM) meth~)d, multiple hbre breakage ()o.'urred

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vary qunckly, while ~ther',; had only a ,'smg,le Iraclure belore Ihu malenal laded complelely. Fngure,_,s~a and .~h ,,,;how Ihe tensile Iraclure ,,,;urt'ace ~1 Ihe SIC" based librt'/h()¢-~,'~ alumimum cq~mp~),,,ale Baltic hbre I'raclure was ~ph~erved, with hmnted I'tbre pull-~ut. F'ibre-malnx deb~mdmg us pre.,sent al the tracture ,surface as ,,,;hown m F'ng. 5b 'The debonding Ioeal,.m was I'~und t~ be along Ihe hbre and mlertace layer 'The cracked nnterlace

layer sllll adhered ,,,tronL~,lyI~ Ihe matrtx, mdicalmg thai Ihc hondmg belwc'en Ihe mluHace layer and muln.x was slrong, 3 I 2 Fiml,~ve~,,,'elemmm 'The h~w transverse len,',;ile streng, lh ol unndnrecmmal lammales repre.,,.enl,~ a weak hnk nn the de,_,sE_mo1' lamlnated c~mp~),,,;il¢' ~tructure,s. AIIhl~u.gh hhre,,,; can he

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designed h_~ he parallel It, the exlernal h_~ad, the presence ~)I' Iransver~e stresses can lead h_~ premalure I'anlure ()1 Ihe lammale ']"here is n(~ stmple ec]ualit~n h) predi¢l Ihe transverse strength. LJnlnke the h)n~.,filudmal tenstle ,,.,Irenglh, whteh is delermined almt.~st enlirely by a single I'aeh_)r, i ~'. the t'il'~re strength, the transverse len

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snle slren~,lh can be aHected t',y many lack)rs. These include Ihe prt)perlies ()1' Ihe fibre and matrLx, Ihe inlerlactul b(_mding slrenglh, the vt.~id distnbultt.ln, Ihe micrt)crackmg ~_~tIhe hbre and Ihe mternal sire,,,;,,,;and slrain dlslrtbutit)n due It) l.'Jr~.~cesstng. The most clearcut fealure of' the transverse tensnle strength is thai nl us usually less Ihan the ,,,;tuen~h t_~l Ihe parenl matrix, st_) that, nn c~nlra,st I~ the p(~sntnve eltect (.)1 tnbres ~)n Ih¢' Iransverse modulus, the I'nbres have a negalive reinl'~)rcing eft'eel durnng transverse lensicm ]15]. F'ngure t)a displays the mtcrtlcracks at the libre edge whtch are presena even when a dnam~.pnd culler ()r an ullrasoruc drtll ts used. FLout ~_)1'Ihe dt~minanl leatures ,.}1 ela~.'knng under transverse lensile h)adlng are' (1) cracks directly penelraling the hbre, resulting in h~ngiludinal I'ibre splitlmg as sh~)wn m F'tg. t~h; (2) crack prt.)pagaltt)n thai kdl~.)ws h~)lh Ihe tnlertaee layer and Ihe hbre, as sht)wr! m F'i.~, tJc, (3) crack prt~pagalit_)n running, alung ht)lh the mler lace layer and the rnalrtx as sh~wn i.n F'tg. hd; (,-1) crack prt.)pag,attt)n I'tflh_~wmg, u zigzag pallern ah_~ng, the inlerfaee layer as shtlwn m F'tg t~l' ~_prslraymg away horn Ihe layer and Ihen ert),,,,sin~, t.~ver the fibre

and running, tnl~ the ~_)lher ,,,,tde ~_~l mledace layer a.,.; ',;h¢~wn m Fng. t~e. F ~ u r e 7 shrews a lypical transverse len.',;tle I'raelure ,,;urtace ¢~1 the e~mp~,',;ile II t',; eharaclertzed by a Ilal Iraclured surface where lthre splnltmg and hbre-nlalrLx deh~ndmg are ~)bserved. T h e mtertaenal del)¢~ndinff, palh mamly h_dh~wed Ihe inlertaL'e layer and Ihe I'tl~re

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damage during machining. The resulting pallern i~l crack propagation can be regarded as a cumbmatiim ~I lhe hmr types m F,gs. 6 b - h l Because italy a few fibres prevad m lhe specimen crtlss seclatm, lhe loregoing results tm failure under Iransverse h)ad,ng will be ease specdk" and may nt~l m general he exlrapolaled ttl large-size composites even Ihough lhe hi'ire volume fraction is fixed. This is simply because Ihe physical boundaries clr Iree surlace wdl have a much larger influence on the ladure of specimens wllh truly a few fibre,.,, Fibre d~str~but,m effects have been examined analytically by Brockenbr(mgh el

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S~mdar Io the case (d transverse tensum, tadure by h.mglludmal e~mpressu.m is c(.nplex since ~1 revolves many variables such as lhe hbre and matruf properhes, Ihe mterlaeml bonding slrenglh and the void distnbu Itim. F'anlure mlldes are parllcularly sensitive Itl Ihe fibre v(dume Iraeli~ln and malrix prciperlies F'lgures ~a-8t summanze the Iour dislincl steps ~ll' Si(?-hl)h 3 alumimum eomposHe ladtire (I) The libres closest Io the speeHnen edge are debcmded helween the interlace layer and hbre as shilwn m F'ig 8a. (2) The ,nterlace layer chlsesl h_)the specimen edge is susceptible lu mierobucklmg under ctlmpressl(m (F,g. llb) 'T'his layer breaks under lhe tens,m mlro duced by mlerobueklmg arid faciblate,s crack propagalatin inhl the adlacenl matrix as shtlwn in Fig lie 'The specimen edge, m ctmtael wHh the hmding device, debonds alcmg the hbre and inlerlace layer (F'ig, 8d). (~) As loading mlensihes, lhe hbre under lens,tin debcmds Irtim ils surrounding malrix; also, cracks Marl h_)c~lalesce (Fig. Be).

(,4) Buckling induced cracks in Ihe llbres and irller c(mneclmg cracks ,n the malrlx prt~pagate towards Ihe centre t~t Ihe speomen and cause hnal ctlmpc)mle trac ture as displayed m Fig. 81 Debonding accompanied by cracking is seen tin Ihe hhre chlsest to Ihe specimen edge The buckhng reslslante m such a regi~m =s less Ihan Ihat predicted for a unihlrmlv btmded arrangemenl II";I Failure milialed by ctlmpresslon is thus hlund hi dt~minate. Moretlver, hbres ch_isesl hi the specimen edge were hmnd ttl debtmd mtlre easdy, occurring between Ihe interlace and hbre. In general, debonded libres buckle more readily than well b(mded hbres Exhibited in F'lg qa is a specimen under Ionglludinal ctlmpressi(in showing the Iranslllon I'rtlm lension Io c¢tmpress,m thai ctlrrespcmds I o m plane buckling i~l the fibre II 5J. II is along Ihe planes AA and C'C Ihal buckhng and crack iniliulion are hkely ttl ltecur. (.-'racking spreads t~)ward Ihe cenlre, forming the fraelure paltern as shown in Fig. qb. Figure I1)displays Ihe h.mgfiudinal eompress,ve Iraeltire surlace uf Ihe c¢lmposile. Siheon carbide llbres lad m a briille tashion m the regl~ln under lenslcm (marked T), hdh.~wed by crushing ~)r shear haclure m the ctlmpressive reglcm (marked (?) The lensile and etlmpresMve regitlns m Ihe hbre are readily dlslinguishable by their differences in I'raelure mt~rphldogy (Fig II)) 3 2, 2 ']'talt,~'l'ers(' rooilort',~;~'totl Figures I l a - l i d shllw Ihe transverse conlpresswe mlerotraelure mechanisms ill' the SR? based hbre/h(lh t altimmmm comptlsile. The general prtleess tll crack inillal,m and propagatu.m in Ibis composlle can be summarized as hdh_lws. (1) The matrix dist(irt,on and delachmenl ill Ihe inlerlace laver are shilwn m Fig. I la. ('2) Lt)ealized non uniform deformaliqm ol Ihe malrtx exerls a ctlinbmed Ic)cal lensl~m and shear hl crack Ihe fibre as dlustraled m Fig. I lb, (3) Multiple fibre crushing and malrlx cracking are displayed in Fig. I le. (,4) The malnx is forced to prtllrude and lad (F'ig. lid) II is seen l'rtlm F'ig 12 lhal hbre splilimg is lhe d~llninanl characlenslic ill lhe fractured surlace Fibre-malnx debondmg and fibre dishwalu.m due Io shear are exhibiled m Fig. l'2a.The debcmding hwatiun is l't)und along the hbre and interlace layers The cracked inlerluce layer remains allached to lhe matrix, indlcallng, a slrlmg blind between the mlerl'ace layer and matrix A large amtmnl ill shear del'ormallon is alstl observed m lhe alum,nium malrtx. Figure 12b shi~ws hilw the fibres are crushed and deb(mded. The maxHnum shear plane and hbre orlenlalum relalwe tt~ a.xml ctlmpress, m are indlealed in Fig,. 1t Although

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F'np, I(). Seannmp, ¢leclr~m rmcro/~raph ~1 Ihe Iraelure nudace ~1 .Sn(.' h;J,,ed hhre/¢~()¢~'~ ahJlTiinlum c~mp~),~He .,,h~v,'mp, u hhre bw.'k hnl_.,, m~=de hJHure ~Hh I¢'n,.;iOrl ~11 q~n(.' MalL' ;Jrld c~)mpt~.=,~M,m ,)rl Ihe ~lhe; iJrldc'r d h ~n~.,,lllJdlrId] ~.'~)ml.~lL"~,l~lrl

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Fq.~, I I T'rdrl,,,v,=r,,q ' ~ ,~m|~re,.,,,,iv¢' Ir,JclUre ,~1 ~l(_' b;J,,ed hbk,/~dl/~ ~ ,JhJmlnlum ~.'~nlp¢,!,lle a. m,.llrlX pI,Jhll¢' dch~fmull, m =Jr|d du'l',~ndlrlp, appear in Ihq: rnah'rhll b, dellq mdml.~ and fibre crackml;,, u, mull=pie hhr~.' ~.'uack ml; ,, d, rnalnx prq~lru,,i~m and ,,hear Iraclure

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Ihe Iheuielical ma.%imuni shear ,qress prevails (lit all planes al .J .~'~I~l Ihe compressive a.xi,,, lailure ,ict'urred l.vedulninanllv ~)n planes wilh hbre.~ clqncuding with Ihe plane ABCE) (Fig, I t ) Sheailng ~lil Ihe plane BFIEiF. eann~tl easily take place clwing. I~i inlerterence with the lubre.~ I I ~l F'ri~m Ihe hlre.~,()ln~, discussuln, crack prilrlal~,ali, ln under Iransvelse c(impresMon ¢)t't'urs along the mler lace laver ,)r h_)lh_lw,~ Ihe hbre sphllun.R path In h(llh cases iI coincides wllh Ihe plane ABCI-) in FiQ.. I

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Fip I 2 T'ran~verke t'()lTirtre',,,ivt' Iral.'lure ,,ui|at'e ()1 HI(_' ha,~ed IIl'llt'/(lllf'l t ahJmlrllUlTi t'¢ilTIpiIMle a, trat'liJrt' ,,iJltlll.'l' ,d A m ' r i in P'il.,,, I 1. Ii, ,,uFIiict' d;Ima[.,,c~lri AFl-'t(iln Fil..,' I I

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(I j L.m4qmlchH(H IVH.W()H Failule intliale,~ l=~m the inlertace laver h v crat'klnl7 , hllh_lwed hv dl.~lilililln ill Ihe sulroundllip, malrlX inalerlal Fibre crat'kln.p, Ihen llccurs lil.~,elhel wllh deb~indlnl~ ' (.'lat'ks In Ihe alumi nlum malrlX are hlunled T'ermmal hac'll/rc 4~1 Ihe specimen ix t'LlU,~ed h v mulliple IraclurlnT, and t'~lale~;t'elli.'e i_ll Ihe h~eal cracks (2) I'#'IIII.VI'I'/Vt' /t'll,%/lHI Ple-eXlsllnL2 , inll.'liidelt't'ls near Ihe specimen ed.~,e enhance t'lac'k Inlllali(in al Ihe hi,re F'allule irivl_llvt's Ilhre spIIlllnl7 ,, Inlerl'ace dehlliid In~, and zi~,za.~, cracking 'T'ran,~verse lensile lallure ix ~ensllive h~ hbrc ed~,e ('(~lldili¢)n,~ In cclml.~,)silc's caused hv macilining (~I) / rm~jl/Hdmo/r'rml/uc.s.w(u~ Fraclure ul Ihe t'(~in pilslle is preceded hv debilndinQ ill Ihe hhre i:hl~esl hi Ihe spe¢ilnen edl:x,e. This is Ihen hdhlwed bv inlcr,~ huekhnl? , (tl Ihe inlertaee laver, leadm.p, h) hhre iniclohuckhnl7 , and clacknll? , Fasl crack pll¢lpa.Ral,m ensues when intt'rllc'lat'k,, j(lln h~l),elher wllh lhe d,)rnmanl crack (4) 'T)(/H,~'l'i'L~c' ('(mip#r~'.w(u# Miel~llraclure (it Ihe c'llmpli~ile uccurs hv malrix di,~l(irlilln This is hllh_)wed by dehlindinl~, (_ll Ihe Inierlace laver and lihre F'urlher (Jel'~irmali(in ill Ihe malrix enhance,~ crack lTr()wlh as Ihe hbres are ClLi,~hed in shear Linltl lhe specimen ix liaclLired

4. Conclusions

Aekmm'ledgment,s IN .~m~ experlmenls (in Si(.'-based hhre/6(lh3 alumlmum comp(),dte have heen perh_)rmed i~ e~arnme Ihe haclure I~ehavu_lur hv appltcati(in lit Ihe $ E M melh(_)d Whale Ihe hlcal delecl.s o1' Ihe hbres lend I(l c~mlrcll the initial latlure hehavi(_lur, Ihe eHe¢l (ll' kiad IVpe takes ,)w.'r a,~ lhe load mal..,,mlude as increased. Fi)r Ihe lour cases invesli.Raled the I'~llhlwinT, c(inclusi(ms can be dlawn

'T'he aulhor.~ are ~,raletul I() ['rllle,~,,or F P (..'hian~,, L.aboratllry hlr Experimenlal Mechantc,~ Research, glule Llniverslly ol New Yclrk al ~l(Iny Br()~ik h)r .~u.~, geslin.g the I(iptc (_)1 lhls sludv and rlr(ividin.R lest material Pr~itessor (.-'hlang's etl(irls are supporled by the LJS (_)fftee ol Naval Research, E'n£.~neering Mechanics Dtwsicln, through granl N~). N()(i()l.-Iql-

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Jl 3X()(Dr Yapa D $ Raiapalsse, Senenlnl'ne C)flwer). Thanks are due I(., Prul'es.~or G C. Snh, Inslilule ~t F'raelure and S~flnd Meehannes, L, ehig, h L.Innver,dlV h~r hus invaluable eommenl.,, and su#,.fl,e.',;Inon.~.

References I .I M "n'an!.,,.~ M Jcnp and (_ I Yanp,..,llm'e~ .~,'~~ I.H,q .L I ~,~' (Iq"+l) I'~', 2 _% M .J(mp,, .I. M 't'an[.,, arid (.' .I Yan[.,, ,~l,#et .~,'~'~ t..n).; A, I ¢,~' (Iqql)lf#-~ _% M .k'u,l.,,..I M. Yani,.,,and (.' I Yanl.,,/tlalet ~,'l~ E~qq ,~, I +,~' (l~Ul)l~l .4 K M I'r~.'w~ a n d K (.i K,und<'r, ,'lh'l+ill ItaH.s, ¢ ( l U 7 2 1 2,2()1 '~ S Yalnma. K (_)kamura, I 'T'unaka and 'T' Hu~'a,,r'. I ,'~late~ .~'
¢~ .~ Yallrnu K (_)kumura, J T',}naka and T'. Haya,,e, .I ,'Ua/er 7 I A (.',)rme. Y M (.'hlan~,. D R Uhlmunn. A Morlensen arid J M (.'1)lh,,,,, (_'en+m EI.II., t)'~ (2) (lUXh) 2~-,~"~ ,~ P Marl,neau. R Padlcr, M L a h a y e a n d R Naslam,.I M,m,r .~,'rl. lU( IqM4 ) ? 7,-lU ~ J Mel:usar (.) LB..J A (.'~)rniL' and K H. Wc'MmaCall, (.'e'vrlIH ['n~:: ,~'~ l ['ro~ , U('7-X)(Iq~X) II)~1 I() (i L~,mhardl. G Wlel4hurdl and H P,_~dle~,ak. ,~lalet ,~',, /~ II,_Ll ,4, I ¢'~ t IqU I ) 2 I 7 I S [4 Wu and R .I Ar,,enuull, ,,ll, m,r .~'~l ErtEI ,4, I I,~'(Iqql) 227 2 _% R Null and F' F, Wa~,nur,,I ,,~lllzlt'r ,.~'l) , ?(J(]qXh) II-)h.ll [' Marlin,.'au, M L.ahaye, R Pmlle,, R Na.slam, M. ('~uzl and F (.'ruc:b,,~', J ,~lul~'t .~,¢'~, lU( I qbl,.I) 2'7 ~lI 14 K (_; Kre,der (ed). r '¢mtp+~.~+l+' /Ih#h'na/.~ V~I .4..,~h'talh~ ,~hm+~ (ompo.~i/+'s. Acad~mzc. New Y~)rk, Iq 74 I ' D Hull, ,.-t~l ht/vo,h,'noH to ( 'OH,pO,~,llt ' .,~hlle'vl~l~, (_'amhrndlz~:

l_rnnv~'r',,nl~,,F'r~"~s,C'amhrndL.,e, I q,",lI I~~ I R Br~..'k~',lhr~.J~.h, S Suru'.,h and H A. Wwn~'ck~'. A~I,+ ;1h'ltl/I ,~ hlh't , CU 1% '1( I q q I ) 7 ~ ",.