Fracture Mechanics for Failure of Concrete

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    Annu. Rev. Mater S 99:933Copyight by nnual Riws Inc ighs vd

    FRAUR MHAN RFAUR NR

    S. P. S C. gNl S F C A C-Ml N Uy Ill 0208

    K WORDS:

    INTRODUTION

    Fl ly y g . Ug g y gg

    for deeoping ne cementased materias Recent pucations (1 2) haeshon that racture mechanics has no een estashed as a undamentaapproach that can expan certan nonnear aspects o concrete ehaor,l l l gg I l T l lmcrostructure of concrete; the concept of stran ocazation hich is atypica eature o concrete ehaior; the principes o inear eastc fracturemechanics EFM) racture processes and toughening mechanisms in l l R-. W y menta phenomena associated ith faiure of concrete such as size eecton tensie strength and ritteness o hgh strngth concrete can e interpreted y racture mechancs

    INTN TUTUR ND TRIN

    OIZTION OF ONRTConcrete is an anisotropic and heterogenous materia consisting o cementne aggregate coarse aggregate and ater. he cement hydrates hen it

    29008400/94/080029$0.00

    Annu.Rev.

    Mater.Sci.1994.2

    4:293-320.

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    294 HAH & OANG

    s x h os h x o og. Wh h x lls h sp og gggs hg os h ogh o o oolh o.

    Physlly, ol, o os ohs lossg o h x h ggg. Hov, l vos ggp o s lls s y g s oh o opo o h h o. Ths os l pos s ks x-ggg , shkg ks Thss ly o ol o h hl ho o o.

    Pos h s sly lss s gl os llyos Th gl os, gg ppoly o 0 o 10 s, g s p o l-sl-hy CS-H), hs h

    lly ooss, yg o 00 o 0 s, h so -ll sps h xs h lly hy gs.

    Th x h ggg o ogh h . Slg o sggo slly os o sh o, so kso h h h ggg h ho s h. h oh h s h h ols o lsy, h hl xso o spos o hg o os o, h l so o

    h x h ggg o hs o vos s ko o h lk ()

    Hg o sh o s op y h loss o os h s, hh ss shg o h o. Shkgoly hs h h s. Shkg s s slly oo o o s s h loss o os s o h s o h o p o h o h ohh, shg h s s slly s y gggs oy oos o h s g sg oh h o-o

    so o h shkg s h ss o h gggs h oy oos lo vl o sl sss so s o h o hh y s shkg ks olog Slly, oh o g hg s sos os hl kg

    Th os o o y s hl oss o, o oss, hh h y h s l os s Ho, oly h o l s o hl pos o s

    ls s sss h. Ss o ooss hh h osss ops, p o vos l ss ols. Hhy o posss s ls s

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    FRACTURE MECHANIC FOR CONCRETE 95

    pesened in igue . Since micsucue f cemen pase is in scae fnanmees as shwn in igue a facue pcesses in cemen pases aeinuenced by paices and vids in sae scae e nena sucue f

    ma is shwn in igue 1b Use f sands ne aggegaes esus invids in mas up scae f micmees. As a esu facue pcessesin mas may pimaiy invve iniiain and ppagain f inenavids in he scae f micmees. nefacia cacks and weak zne in scaef miimees ae maj defecs f ncee wih case aggegaes asshwn in igue c Teefe facue pcesses in cncee may pimaiy depend n he sabiiy f ee inefacia cacks. Aug cncee is an anispic and heegens maeia cnsising f maix andaggegaes i is geneay acceped ha cncee may be geneay eaed

    as a unifm maeia befe cacking if he minimum dimensin f cncee sucues is geae an ve imes he maximum size f aggegaesused

    Many exerimena echnques such as quaniae acusc emissin(igue a) and eecnic specke paen inefemey (igue b) havebeen used bseve cack ppagain in cncee. n cnas a ineaeasc maea (ideay bie) swn n igue a cncee s a uasibie maeia and a subsania nnineaiy exiss befe e maximumsess as swn in gue b. Recen expeimena bsevains (5) made

    using e mehds shwn in igue ave indicaed a a sess-engain eainsip f a cncee subjeced uniaxia ensin may bedivided in fu sages as shwn in igue b ( 5) The s sage isbefe pin A which is abu 0% f he peak ad. Ppagain finna ds s ngiib duin s sa. Th snd sag is fmpin A pin B which is abu 80% f he peak ad. nena vidsppagae duing is sage. ese cacks ae isaed and andmy disibued ve he specimen vume and he disibuin f ensie sainin he ading diecin is appximaey unifm e e spece eghe hid sage is bewen pin B and pin . Te nena cacks sa caie in a maj cack wic ppagaes w ineasing ad.is phenmenn is ten efeed as damage caizain saincaizain When sain caizain ccus he disibuin f ensiesin in ing dicin is n ng unif v spcimnn. ak ppagain is sab un pak ad (pin ) Sabcack gw means a e cac ppagaes ny wen e adnceases. Te cack eng a e peak ad is efeed as e cca

    cack eng The fu sage is ate he peak ad The maj cackcninuusy ppagaes even hugh e ad deceases The ensie sainf e maeia wihin he caized damage band cninuusy nceasesweeas unading may ccu f he maeia uside he damage band.

    Annu.R

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    SHAH & OUANG

    Hierachy of actur pocess in cmen-basd maeals.

    Annu.Rev.Mater.

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    RACUR MCHANIC OR CONCR 29

    c 5mm

    igur (iud)

    t cn e deduced fo the oe discusson tht filue of concete is

    chcteid y stin loclition hich y odld y cocck. Thus flue of concee cn e sulted y fcue echncsconsidetion hch povdes poeul ool to desce popgton of cck.

    NR T RTR N

    cs cn e clssed nto ode openn ode) ode (shenode) d ode (tei ode) y ode ctue i dicued it cpte. Si piciple c e exeded o e oe o ode ofcue I cn e deved o eicity t te elic te eld in hevicnty o cck tp cn e expessed s

    Annu.R

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    298 HAH & OUA

    Qv

    igur Experimental techniques fo detecting stain localization. () Quantitative acousticemission b Electonic seckle atten intreometry

    Annu.Rev.

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    RCTR MCHCS OR COCT

    Enain

    a) inaai i) aia

    f, stanlzoEnain

    in n n nin

    Figure Sts-ogato cv fo a na-ac mata and a conc cmn

    K 3y 1/COS 1+SIn: Sl2

    K 3Txy = (2nr)1/SI:coscs'

    whee is te distane t th cack tip an the stess itensity act mde cack K is

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    00 S & O

    K[ /b

    were te aled tre on te tructure, te crac lengt, b teze o te tructure te eometr actor tat can e otanedrom a lnear elatc racture mecanc M andoo

    Accordng to te elatc tre eld gen uaton te trearoace nnt at a crac t were r tend to zero T enomenon termed a te tre ngulart a te t o an elatc crac Snce nntetre cannot deelo n real materal, a certan range o nelatc onemut ext at te crac t Te alue o K[ ndcate te ntent o tetre eld n te negorood o te cract, and a uncton o loadecmen eometr and ze, oundar condton and crac lent Te

    re ntent actorK

    [ can ere a a racture crteron A crac roagate weneer K[ eual to a treold alue, e

    3

    were K[ te crtcal re ntent actor or mode I crac Te alueo K[ regarded a a materal racture arameter n lnear elatc racturemecanc

    Alternatel uaton 3 can e eree n term o racture energ:

    G G[4.

    were G K[/ te tran ener releae rate, and G[ K[J/ te crtcal tran ener releae ate, were or te lane trecondton, / l or te lane tran condton, and Poonrato

    RTUR RO IN ONRT

    nce an nelatc regon alwa reent at te cract n a real materaltree do not ecome ngular T regon oen called te ractureroce one Te EM oluton can tll e aled wen te one mall enoug comared to te dmenon o te tructure

    It a een reorted tat te acture roce zone n concrete notmall 7) Te reence o a zeale racture roce zone ma e attrutedto te nerent materal eterogenet o concrete Man mecanm tatare reonle or te racture roce zone ae een reorted Some otee tougenng mecanm are ncated n gure 4 urng racture,

    te g tr tate near te crac-t caue mcro cracng at aw Tenomenon, nown a mro crac eldn, a own n ure 4a,conume ome o te energ nut to te ecmen te aled load

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    RCR MCHCS OR COCR 30

    Main crack Microcracks-,. - 1- -:: -":-.

    (a) Crack helding

    Aggregate

    d>(c) Aggregate bdging

    AggregateMai n crack lt :

    (b) rack deflecion

    Frition between

    (d) rack suace roughnes-nduced closure

    Fire Som oughng mchnsms th rctu ocss zon

    8). Crc deecn ccur wen e le rence run relel rn rcle r ln we nerce ue b Tmecnm been ue n el b ber En 9 er mrn ugenn rcee n cncree re grn brdn wn ngure 4c Brdgng ccur wen e crc dnced end n ggree cnnue rnm ree cr e crc untl t ruurer ulle u Al durng grn ullu r e enn ruucrc, ere m e me cnc r nerlc beween e ce ure4 T cue ener tn trug rcn nd me rdgngcr e cc

    Mn negn e cued n zne, eecll ze nd cnuen 11. Reul e een nuence cnerbl medlg, n nrmn meme een cnrcr urng eerc r cnenu, ne reuen uen weer e rcurerce zne uld be n rn e crc r bend wn bTule 1 b rce re eulen r rucurl nl cncerned e rdng nd dme ne m e cndere euen,

    u n g deren cl ng Bed n er ern ungler lgrc nterermer, CrMner e l 1 rere e rcure rce zne cne we zne ben e erecrc-t nd zne n rn te Te we rce ne ncreed

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    0 S & O

    with cac xtnion, wha th font zon maind imai contantin iz Sinc iz of th wak zon wa much la than that of th fontzon th concludd that mot of h touhnin in conct occu inth wak zon Thi fact ut hat th incai iz of th wakoc zon ath than th contant iz of th cackt oc zoeol e pmly epole fo e o Re eo oee. ml oe e ee epoe em (4, ). uin a d-ntation mthod, watz & Go (16) found that th factuoc zon ai alon cimn thickn. A imila ult ha nalo dtctd uin acoutic mon tchniu (iu 5) (17)

    Sinc th wok of alan (8), my attmt ha bn ad to al

    A

    mm (15 in. A

    k

    (b) Ditribtio auic emision vn oghe kne m pigur Mcrcck ccr m c y cc m c.

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    RACUR MCHANC OR CONCR

    facue mehanics cncee Hwee he pesence f he sizeaefacue pcess zne hindes he appicain f inea easic facueechanics cncee (9. heefe nninea facue echanics

    shud e used f mdeing cncee facue.

    NONLINEAR FRACTURE MECHANICS FOR

    CONCRTE

    Fue ehvi f cncee is geay inuenced y he eiey agefacue pcess ne. he dicuies f using inea eaic facuemechnics f fiue f cncee incude he cck pah in cncee isuus and(b i is dicu deemne he cack ip in cncee ecausef paices idging and viain f he facue pcess ne ng hehickness diecin An ccue descipin f cncee faue shudcue he ouous cc ph nd he heedmensn specs f hecack pe s we as he ineasic maeia espnse wihin he facuepcess ne. n de appy facue mechanics he faie fcncee ms cueny aaiae des emp simuae mde cncee facue wih n eecive ine cack. he vaiin f he facuepcess ne acss he hickess widh is usuay negeced. The ineasic

    facue espnse due he pesence f he fcue pess ne y eken in accun y a chesive pessue acing n he cack faces.An eecie uasi-ie cck is shwn in igue , whee an iniia

    cack and he ssciaed facue pcess ne ae pesened y an eecivecack wih engh . he ughening mechanisms in he facue pcessne ae mdeed y a chesive pessue acing n he cc sfces hechesive pessue w is a mnniy deceasing funcin f cacksepaain dispacemen w he aue f w is eua maeia ensieseh o w 0 he e o he cue ocess oe hs cohesvepesse ends cse he cck nd is he funcin f he cck peningdispacemen w When a cncee sucue wih he eecive uasi-biecack is sujeced ding he appied d esus in n enegy eeaseae G a he ip f he eecive uasiie cack. he enegy eease aeG my e se eua esisance cak ppagain ha can e dividedin w pins: he enegy ae cnsumed duing maei fcuingin ceaing w sufaces (he maeia suface enegy) and b he enegyae euied vecme he chesive pesse w in he sepaing fhe sufces. heefe he enegy eese e f mde sie

    cack G may e expessed as rCTODG G+ J o w 5

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    SHAH & OUYANG

    Appledlod,p

    t t t t t t t t t t t t

    Initial crack

    I aa :

    igur Mg a ra nr

    ee G e ee e o cee o e cc fce fomoe cck () he om co pee h he fo occk opeg pceme ho Fge , heogl cckp opeg pleme. cck me o e le o 5. To ype of eegy po mecm fo e fcepoce ve ee oce o . Te -I eeypo mechm epeee ozeo e e co

    he e-Bel eey po mechm epeeey e co em Hoeve oe my ppomely e moel oye gle fc egy po ec ee eGh- mechm y mg ) o he eBel mecm y mg O

    Hlleo e l (2) popoe coev me K O Bz(22) evelope cc moe g ml cocep I oe y m ome compo ececy my e ccomphe.Hoeve he gle geBe eey po mechm

    my oly cheve lol eey lce y eec moel pmee.Some c fee oce h cc popo c he cckpoe comp e o e pe coeve moel, o o mc oe epemelly mee ( 1).

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    RACTR MCHACS OR COCRT 0

    The frcure proce e cocree c e moee y le GrhIr eery mechm y um () O A eecve elc crcoere y M crer c e rouce he euvlece

    eee he cu he correpo eecve crc c e precreeplcly he moel Sce le crc eeo efore he pe o pee cocree, he crcl eecve crc eh fure of hemer ere from he crc eh To prec flurecoo of he merl o coo mu e o eerme hecrcl o he correpo crc eh Mo of hee eecvecrc moe ue o or more frcure prmeer o ee he ecfrcure proce

    Sce he crc eecve crc leh h ee epermelly fou

    o e pecme ze eomeryepee co recly erve he frcure crero U he cocep of he eecve el cc Je& Shh () propoe he oreer frcure moe ho ure 7 her moel he o epee mer frcure properere he crcl re ey fcor he crc crc oeplceme D hch re ee erm of he eecve elccrc The frcure crer for ule crc re

    a

    T(_ T

    a

    a

    (

    TOD= TOD

    a a

    X

    K K.

    x

    Figu 7 Tw m rr md, rr r: K/ Kfe d CTOD CTODe.rsis 1) d 2) rs d szs srs

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    06 SHH & O

    crOD CrODe> 6.

    here KJ an CrOD are the tre intenity factor an the crack-tipopenin iplacement, repectively Both parameter can e calclateae on linear elatic fractre mechanic perimental etemination ofto material ractre parameter Ke an CrODe are ice elo. nthe to-parameter fractre moel the eective crack ehiit a complianceeal to the nloain compliance of the actal trctre arihaloo &Nallathami have propoe a imilar eective crack moel.

    n ation , the o-calle toparameter fractre moel, the valeof K an CrOD are fnction of the applie loa, trctre eometry,

    an ize, a ell a the crack lenth, herea the critical tre intenityfactor Kl an the critical cracktp openin iplacement CrOD are thefractre parameter only epenin on the material A a relt ation6 provie to conition neee to etermine the critical fractre loaan the critical crack lenth of a trctre.

    t may be orthhile to explain the phycal inicance o OThe exitence of rOD can e tie from the fact that all materialave ome ort of initial a Thi i epecially tre for concrete Whenthe material i ecte to an external loa thee a ill open propa

    ate, an ometime coalece ith other crack. The openin iplacementof thee a can e irectly linke to the vale of CrOD. A the crticalfractre loa, the crack openin iplacement at the initial crack-tip cane ene a rOD. or airittle material ch a concrete, thetale crack extenion occr efore the critical fractre loa Since rODi ene at the tip of the initial crack, it may primarily accont or theroin ize of the ake proce zone.

    Bae on fractre mechanic, ractre propertie o a material are relateto it rface fractre enery For the ame type o material, rohneof fractre rface may provie a mean to characterize fractre propertieA typical threeimenional imae for a fractre rface of cement patei hon in ire 8 (26) Thi imae a otaine in a tanem canninconfocal microcope, hich ha the nie aility to provie an imae ofan iolate ocal plane Bae on thi imae, the rface rohne of amaterial may e ecrie y a rohne nmer ene a theratio of actal rface area to proecte rface area. The actal rfacearea i etimate y trianlatin the rface area eteen aacent pixel

    an mmin all element Srface rohne of cement pate an mortarpecimen a correlate to fractre propertie etemine from threepoint notche eam tet The relationhip eteen the critical cracklenth, etermine from the toparameter fractre moel, an the

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    FRACRE MECHANCS FOR CONCREE 0

    iur Tpgpc p f cee p nd eedml epee

    oe me oe e o e ee e le of a oe e o e wopmee fce moe ceeow. e aue o increases wit increasng te aue o

    o me oey e elc fce mecc oe pmee

    Annu

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    SHH & OUYN

    00

    00

    09

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    (a)

    P. --

    RACTURE MECHANICS OR CONCRTE 309

    I

    Ball

    Unngat pe d

    CMOD

    - I. CO: 1CMO

    b

    Figur 10 sn cmn n c o mn h vl f K, n D

    Annu.Rev.Mater.Sci.1994.24:293-320.D

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    310 SA & OAG

    shud be ntred by a nstant rate inrement D suh thatthe peak ad s reahed n abut mn

    he beam shud be mntnay aded up the maxmum adhe apped ad s hen manua redued (as ermed unadng) whenhe ad passes he maxmum ad and s wihn 9% he maximumad as shwn in gure Ob When he appied ad s rdued zerreadng s apped

    CUsing the measured urve D as a untin ad he wingquaniies an be auated as shwn bw th mduus astiity he ritia stress intensiy atr KL and the riia raktip pening

    dispaement Dhe mduus eastiiy is auated rm

    7.

    where Co is the initial cmpliance calculated frm the lad-CMOD curve,

    as shwn n igure Ob and g

    3 066go .762.28o+3.87o2.04o ()

    8.

    where o (o+)/() and and are dened nFigue Oa

    An eeiveeasti ritia ra ength may be dened in suh a waythat it resus n he unading mpane, within 9% the peak adbased n inear east rature mehans herere he mduus l l ll

    I e9.

    where s the unadng mpane wthn 9% he peak ad auaed rm the adD urve as shwn in Fgure Ob and thegemetria untn () s based n quatin 9 but (+)/(+ ) instead shud be used.

    By equating quatins 7 and the vaue the eetiveeasti ritiarak engh r a tesed materia an be sved. hen the rita stress

    ntensiy ar is auaed using h quain

    s ()j Pc+0 W 2 2 '

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    FRCUR MCHNICS FOR CONCR were P s te peak ad W WoS/, and Wo s te se-wegt tebeam.

    e t k-tp penng dspement s ten auated usng teequatn

    6(P+05 W)Sag(ab)CTOD

    Eb2t

    x [-)2+1.0811.149 (Po-P6)T2, 11.wee P aoan andg(ab) s based n Equatn 8 but o sd beepaed by ab

    A age und-bn test pgam was nduted by te RILEM mmttee 89 (28). It was swn tat te vaue K} evauated at te tp te eetve east rak was essentay ndependent te dmensns nted beams. A smar extensve mparsn s nt avaabe rCTOD' Sne CTOD s a sma uantty and dut t measueaddtna veratn s needed t nrm tat t s ndeed a materaprperty

    A -CUV BASD O WOAAM

    AC MODL

    Appatn ad t a struture wt an nta ak sze ao prduesstran energy U e rate stran energy reease wt respet t rakengt , s dented by and s termed te stran energy reease rate. nte ter and te rak prpagatn at te rak tp needs t nsumesme energy W e rate ange W wt respet t rak engt ,s dented b and s teed te atue esstane e ak ppagates

    wen te wng ndtn s satsedG . 12.

    F a btte atea s a atea nstant an ppagatn tenta aw may mean atastp aure te struture. Hwever duet te estene rak arrest meansms su as aggegate brdgng nnrete te rak steady prpagates unt a send ndtn s assatsed (see Fgure )

    Ra a' 1.

    In de use Equatns 12 and 3 t smuate rakng nete

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    32 SHH & OUYANG

    Falur cra:G= RG R = \ oncrete

    Brtl matrx

    Cack Lngth

    igur -curves or erent maeras

    bth G-uvs and Rurvs shuld b knwn h Guvs dpndn gmt spimns bunda nditins and natu applidlading h xpssins th G-uvs an b divd m LFMnsidatns

    Basd n quatins 2 and 3 uyang & Shah (29) divd a dintialquatin gvning Ruvs as givn blw

    O dn) r )nL n - -c+ =O,n I n d -I 14wh aao is th ak xtnsin r is dnd as ac/ao, and is thitial ak lngth nl up t snd d tms n 2) ansidd th llwing R-uv an b divd

    d _ 1 rl [ r- (r1)2JI/I- -+- .2 2 r '

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    FRACTURE MCHAICS FOR COCR 33

    were te tw cnstants ( and can e determned rm Kle and CTODeas

    ERCTOD 32 KS / + I Jand

    [E!fCTODJ32 s ) /2 + I J

    = (K)aoao)d2( d2(-( ) 'E -c d-+

    6

    7

    Nte were! and!

    depend n te gemetry te specmens. r tetreepnt end eam ! .2 and! .5 t s nted tat te R-curve gven y Equatn 5 s an envelp Gcurves wt derent szesut t same ntc and gemetry.

    SOM RSS FROM PPYING FRCTUR

    MCNICS O CONCRT

    z E

    Epermental results ave ndcated tat te strengt cncrete usuallydecreass wt ncreasng se structures and ten remans cnstant asswn n gure 2, were nmnal strengt a treepnt end eams equal t ts alure lad (peak la) dvded y ts crss-sectnal area.s sze eect n cncrete strengt may e prmarly eplaned y teracture prcess zne Wen a cncrete structure s laded te stranenergy prduced y appled lad s cnverted t te energy cnsumed tcreate a new racture surace and te energy asred n te ractureprcess zne. r large szed structures, te latter s neglgle cmpared t

    te rmer, wereas r small szed structures, te latter can e cmparalecmpared t te rmer erere, te larger te structure se te lwerte nna strengt wever te cncrete strengt appraces a cnstant when szes cncete structures ecme ver large.

    s sze eect n cncrete tensle strengt can predcted usng teracture mecancs apprac mentned ave. e nmnal stress acncrete structure can e taned drected rm Equatn as

    K

    UN .F!(a/b) 8ang et al 30) und tat te values K and a are determned

    rm te twparameter racture mdel te sze eect n tensle nmnal

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    34 SHH & OY

    5 - 4 0 0 3 -

    $

    2 0

    z b b b Ax 97

    0 I 0 00 400 600 800 1000

    of bas ()igur Snth o conct ms w rnt szs

    strength nrete an be predited by quatin 1 The resuts that theybtained three-pint bend beams are shwn in igure 13 whih shws

    the simiar trend with eperimenta vauesBazant & Peier (31) epained this size eet n nrete strength bytheir size eet mde based n gemetriay simiar strutures.

    Hg Sg CTypl e oee m vey o omp poee elloe eemo efe e oits mpsitin severa the tughening mehanisms und in nrmanrete are absent during the rature press. Mirrakng at inter

    aes aws and vids are inrequent and raks pragate thrugh thearse aggregates instead being deeted by them. arrasqui et a(32) oeve ee eee ole that as its mpressivestrength inreases nrete behaves mre ike a hmgeneus materia.

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    8e Q 6 4

    :;U

    4

    RCR MCNCS OR CONCRT 3

    o

    B Dpth

    =o = mm

    6

    gr 1 pdictd nomina stngt of tpont bnd bams wit dnt dpts

    hs decrease in tughening eads t an ncrease in britteness. esignershave been frced t cnne (i.e. prvde transverse reinfrcement highstrength cncrete wth stee n rder t prevent catastrphc faiureeseciay under seismic adng. biusy a ess britte maeria wudmake desgn mre ecnmica and safer. Fr cncrete r hgh stengthcncrete if ny ne araeter such a K is cnsidered ne bserves tatthe fracture tughness increases wit increasing cmressve strength asshwn in Fgure . Such a ne-parameter representatin s miseading

    since cncrete in fact becmes mre brite as ts cmpressive strengthincreases he mprtance f a twparameter representatn fr hghstrength cncrete is shwn in Figure 15 (25) where the crtca cracketensin cacuated using uatn s tted against mressvestrengt t s seen tat te crtica crack etensin decreases with increasngcmpressive strength. Fr an ideay brtte materia critica crack etensn is zer hus the twparamete fracture mde crrecty smuatesthe bserved britte respnse f high strength cncrete

    T f cSnce the drect tensin test s dcut t perfrm the spttensin testshwn in Fgure 6 is ten used t measure tensie strength f cncrete.

    Annu.Rev.

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    36

    '

    HH & OUY

    254 , 1 M 15

    4 omv Sgh, xJ psu 1 Relaionship eween he crica sress inensy faco and he compessivesengh.

    h trnd in strngth chang with sz r a spittnsin cyindr is shwnn gur 7 33 3. Th nmnal strngth crass at rst an thnncrass br arachng a mit va r this ty spcmn. ant al that this ty trd th mial strngth th cyidmay b plaind by th twparamtr ractur md. hy appid

    30r ------"31 20I

    oq r 1 t dmnns n inches

    15 inh:254 mm J1 psi: 0.0069 MP1 2 4 , 10 1Comressve strgth f,(X03s)

    Fiu 1 Drease prepeak nonlineari (een of prpeak crck growh) wih increasigcompressive srengh.

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    RAC MCHANIC FOR NCR 7

    gure 1 A spttens tes f measung ese stengh f ee.

    nite eemnt anayi to the cyinde, and Equation 8 wa ued a criterionor aiure o the cyinder. Since the actua oad on the cinder i dtrbuted

    on a certain width a hown in Figre , anae were eormed orthe cyinder ubjected to a concentrated oad and a ditributed oadreectivey he obtined nomina trength or the cyinder ubected tothe ditributed oad with the mm oad ditribution width ( mm) iomaed with that or the onentrated oad in Figure 8 I i een thahe rediced criica nomia re or the ditribued oad how theame rend wih he eerimena data given in Figure 18. he reutobtained here ugget that the oad ditribution width i an imortantarameter or the ittenion cyinder ued to evauae the tenie trength

    o a concree. Ideaizing the actua ditributed oad a the concentratedoad in many reviou tudie may reut in a miinterretation o theeerimenta reut.

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    38 SHH & ONG

    8- ttttt SplitTesion y

    Bazant , 99): t.

    -7 *6- *. =5

    Z

    **

    *

    *

    *

    100 200 300 400 500 600Dieter Cylnder (

    Figu 17 Masud szdpndc f spt-nsn strngth f cncrt

    SMMARY

    A sees tudes n appcat racture mechancs t pdct au cncete have bn ummarid n thi chaptr. pc dicud ncudtr trt f rt rtp tw rk prpt mchanica pn

    fcncrt tran caiatn pncp

    fina

    atic ractur mechanic acte pcesses and tughening mchansmsin cncete nnnea actu mechanics mdes used t dscrib aiu cncret, and dtmnatn mateia actur paamets cnct.Athugh intnsve studi n acu cncrete have been cnducteddung the pat tw decades many undamenta aspects n actur pcsin cncrt ti rman uncar caus htrgnty cncretmatra. Futhr prgr n thi d may primariy dpnd n bradcperatn and devpmnt nw expeimenta technue.

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    RCTR MCHC OR COCRT

    6

    v

    -f 4Q 'E

    v ! !

    '3 !

    i 04 D L 8 (

    )Db

    o" 5mm + ao 5c " b L aomm amm

    0 . 0 0 20 20 2

    Cylinder Radius (mm)Fg Pedcted se-dependence f splensn stength f cncete

    ACKOWLDGMT

    Sort of Natonal Scence ondaton Center for Scence and Tecnolog of Adanced CementBased Mateals (ACBM) gratefllarecated

    Any nnul viw chapter, as we any atce cted in an nnul viw chaperma ucas from nnual Revews Preprns n Rens sevce.

    1-800-347-8007; 415-259-5017 em: @cog

    Ltatu Ctd

    1. hah P wat , eds 1989 Fact0/ Conc an Rock New Yknge-Velg. 4 pp.

    . h P, ed 991. Tghning Mhnsms n Qus-Bttl Matl, Dde Kwe. 714 p

    3 Met PK Mnte PJM 1993 nCt Stt Ppt aMatial pp. 3641 nglewd Cs PenteHa. nd ed.

    Gtm V hh P. 198 JAm Cnc. J 82 310235 Z Kn M hh P 993 xMh 33: 8188

    6. ada H, Pas PC wn GR. 1985. Tht nayss 0/ Cacks Handbook ts MO 2nd Ps Pd

    7 h P Oung C 1992 n MatlS Ct ed. ln 3 43. Westeve OH: Am. Ceam

    8. Khnv M 18. In Fatu Tugh a Fatu Eng /t edFH Wttmann, pp. 31. Amstedm:lseve

    9 Fbe KT, vns A 1983 Ata

    Mall 31: 5657610 vn Me M 1991. Cmt C 1 11

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    20 SHH & UY

    11 Mindess S. 1991. In Rouqhning Mchan isms in Quasi-Brittl Matrials ed. SPShah, pp. 27196. Dordrecht Kluwer

    12. Thouess MD. 1988. J AmCram. Soc.

    71: 4081313. Castro-Monero A, Shah SP, Miller

    1990. J Eng Mch 116 246384

    14. Saai M, Yoshimura J, Goto Y,nagaki M. 1988 J Am. Crm So 7160916

    15Homeny J, aughn WL. 1990 J. Am.Cram Soc. 72 206062

    16. Swarz SE, Go CG. 1984 Exp. Mch24 12934

    17 Lands E, Shah SP. 1993 J Nondstructiv Eval. In press

    18 Kapan ME. 1961 J. Am. Conc 58591610

    19 Shah SP, McGarry . 1971. J Eng.Mch. Div ASCE 97 166376

    20 enq S, Shah SP 198. ng Frt.Mch 21 105569

    21Hleorg A, Modeer M, Peesson PE.1976 Cmnt Con. Rs 6 77382

    22. Baan ZP . J. Eng. . ASCE110 51835

    23. Jenq YS, Shah SP. 1985. JEng Mch 1227

    24 Bazant Kazemi MT. 1990 Int Jrat44 11131

    25 Karihaoo BL, Nallahambi P 1986Mag. ConRs. 386776

    26. Lange DA, Jennings HM, Shah SP.993. J. AmrmS 6 5899

    27 ILEM Committee on racure Mhanics o ConceteTest Mehods. 190.Matr. Struct. 23 45760

    28. Karhaloo BL, Nallathambi P. 1991Inrctur Mchanics Tst Mthods orConcrt, ed. SP Shah, A Carpinteri p186 London: Chapman & Hall

    29 Oyang C, Shah SP. 1991. J. AmCramSoc74 28313

    30. Tang T, Shah SP Oyang C. 1992. J.Struct. Eng 18 316985

    31. Bazant P, Peer PA. 1987 ACMatr. J. 8446380

    32. Caaquillo L, Slae FO, Nilon AH.1981. J Am Conc. 78 17986

    33. Hasegawa T, Sho T, Oada 985.ProcJpn. Conc. Inst 7th Cn! pp 30912Jpn. Con Inst.

    . Baan Z aem MT, segawa T,Mazars J. 991AC MtrJ. 88 32532

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    Annual Review of Materials ciencVolume 24, 1994

    CONTENTS

    MATERIALS CIENCE AND NGINEERING, N DUCATIONAL

    ISCIPLINE, Morris E. Fine and Harris L. Marcus

    C ARBON-ARBON OPOSITES, J E Sheehan, K. W Buesking,

    and B. J Sullivan 1

    HE ROBLE OF OPING IN V EICONDUCTORS, D. J Chadi 45

    OLYER OPOSITES, F J McGary 63

    C WHISKER OUGHENING OF ERAICS: ghg hFb d p Pp, Murat Bengisu andOsman T. Inal 83

    ON PLANTATION OF PTICAL MATERIALS, Ch Buchal,S. P. Withrow, C W. White, and D B. Poker 25

    LECTRODEPOSITED MULTILAYER HIN ILS, C A. Ross 15

    ECHNOLOGY OF ELFEINFORCED ILICON ITRIDE, A.

    JPyzikand D F. Carroll 18

    URFACE AND NTERFACE TRESSES, Robert C Cammarata and

    Karl Sieradzki 215

    ARBON ANOTUBES, Thomas W. Ebbesen 235

    EUTRONIFFRACTION ETERNATION OF ESIDUAL TRESSES

    IN DANCED OPOSITES, D S. Kupperman 265

    C RACTURE MECHANICS FOR AILURE OF ONCRETE, S. P. Shah

    and C Ouyang 23 LASTIC LO IN I/L OPOSTESTRENGTNING AND

    UCTILITY, N Shi and R J Arsenault 32

    ROGRESS IN RANSFORATION OUGHENING OF ERAICS,

    M. V Swain and R H J Hannnk 35

    C RDERED NTERETALLICS, E. P. George, M. Yamaguchi,

    K. S. Kumar, and C. T. Liu 409

    TRONGLY EOETRICALLY RUSTRATED MAGNETS,

    A. P Ramirez 453LASTIC AND LASTIC ROPERTIES OF OPOSITIONALLY

    MODULATED HIN ILS, Scott A. Barnett and

    Meenam Shinn 481

    ( i d)

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