Fratur Mhani of Conrt Conrt Strutur - Amnt, Durability, Monitoring Rtrofitting of Conrt Strutur- B. H. Oh, t al. (d) 2010 Kora Conrt Intitut, Soul, ISBN 978-89-5708-181-5 Dtrmination of fratur paramtr of onrt intrfa uing DIC S. G. Shah & J. M. Chra Kihn Dpt. of Civil Enginring, Indian Intitut of Sin, Bangalor 560012, India ABSTRACT: Th fratur proprti uh a mod I mod II fratur toughn th ritial train nrgy rla rat for diffrnt onrt-onrt jointd intrfa ar xprimntally dtrmind uing Digital Imag Corrlation thniqu. Intrfa bam pimn having diffrnt ompriv trngth matrial on ithr id of a ntrally plad vrtial intrfa ar prpard ttd undr thr-point bnding in a lod loop rvo-ontrolld tting mahin undr rak mouth opning diplamnt ontrol. Digital imag ar apturd bfor loading (undformd tat) at diffrnt intan of loading. Th imag ar orrlatd th urfa diplamnt ar omputd from hih th urfa train, rak opning diplamnt, loadpoint diplamnt, rak lngth rak tip loation ar omputd. It i n that th CMOD vrtial load-point diplamnt omputd uing DIC analyi math ll ith tho maurd xprimntally. It i hon that th digital imag orrlation thniqu an b vry uful for dtrmination of fratur paramtr. 1 INTRODUCTION Currntly, th rarh toard undrting of fratur bhavior of bi-matrial intrfa ha bn a major ara. Undrting th bhavior of an intrfa formd btn old n onrt i vry important in ordr to prdit th prforman of a rpaird trutur. In ompoit trutur matrial, th akt part i oftn th intrfa btn diffrnt matrial (Waltr t al. 2005). An intrfa appar hn a rpair matrial i applid to an infratrutur ytm aftr rhabilitation. Uually th intrfa i rlativly akr than th matrial on ithr id of it, in a rpaird ytm. Th prforman of th rpaird ytm undr loading i trongly dpndnt on th prforman of th intrfa. Compatibility btn rpair matrial ubtrat onrt i rognizd to b important for prvntion of raking but rliabl quantifiation of th rquird paramtr i laking (Mangat & O Flahrty 2000). Furthr, in ordr to prott onrt ontrution, quit oftn layr of onrt or mnt bondd matrial ar ud thrby forming an intrfa (Thgg & Stanzl 1991). Th bonding at intrfa in onrt trutur i important for afty durability (Kunida t al. 2000). Th han of failur by raking along th intrfa ar highr bau of tr onntration rapid hang of tr lvl along th intrfa. Conrt i a htrognou matrial, hrin it fratur bhavior i ompliatd th quantifiation of fratur paramtr bom diffiult. To obtain miroopi information on th failur pro in onrt, a robut full-fild maurmnt mthod i rquird (Choi & Shah 1997). Dirt obrvation of th fratur pro i diffiult bau of th mall al at hih th miro-trutural fatur intrat ith th failur pro. A mor robut mthod for tudying th fratur pro i th Digital Imag Corrlation (DIC), hih ha bn ufully applid to dtt rak in onrt othr matrial. Uing DIC, fullfild urfa diplamnt an b maurd ith high auray for pimn ith multipl rak at inrmntd lvl of fratur. Thi thniqu an b ud to monitor th tting of a id rang of pimn iz undr diffrnt loading ondition (Lalr & Shah 2002). Only a f xprimntal ork hav bn rportd rgarding th bhavior of an intrfa btn old n onrt. Thgg Stanzl (Thgg & Stanzl 1991) hav maurd th adhiv por of bond btn old n onrt by man of a ubi pimn ith a rtangular groov a tartr noth a plit by dg-load quipmnt at th intrfa of to matrial. Thgg o-orkr (Thgg t al. 1993) hav introdud intrfa ith high lo adhion btn old n onrt for tudying thir fratur bhavior. Kunida o-orkr (Kunida t al. 2000) hav valuatd th bond proprti at th intrfa btn old n onrt uing th tnion oftning diagram. Chra Kihn Rao (Chra Kihn & Rao 2007) hav xprimntally invtigatd th fratur bhavior of onrtonrt tranvr jointd intrfa pimn. Hovr, not muh ork ha bn rportd in th litratur on th dtrmination of fratur proprti, uh a th mod I mod II fratur toughn fratur nrgy for onrt-onrt intrfa. Th proprti ar rquird in linar nonlinar fratur mhani bad finit lmnt analyi of trutur having joint intrfa. Propr haratrization of th intrfa i nary for
prforming failur raking analyi of trutur having intrfa joint pially, in th a of path rpaird onrt trutur hih u onrt ovrlay, rpaird onrt pavmnt, old joint in ma onrt trutur (dam) t. In thi papr, DIC thniqu i mployd for mauring urfa diplamnt rak lngth in onrtonrt intrfa pimn, hih ar furthr ud for omputation of fratur proprti uh a mod I mod II fratur toughn ritial nrgy rla rat. 2 DIGITAL IMAGE CORRELATION Digital imag orrlation (DIC) i an optial nonontat maurmnt thniqu i adoptd to analyz th diplamnt on th urfa of an objt of intrt. In digital imag orrlation, th urfa imag bfor aftr th dformation ar takn by a digital amra from hih th diplamnt at any point of th imag i omputd. DIC i xtnivly ud to tudy a vry larg rang of matrial, in idly diffrnt rang of al. Originally dvlopd in th ighti (Sutton t al. 1983, 1986) th DIC-bad mthod thir fild of appliation hav bn groing tadily du to th thnologial progr affordability of digital imaging ytm. DIC i bad on th folloing prinipl: th imag of th body i dribd by a dirt funtion rprnting th gry lvl of ah pixl. Th gry lvl i a valu btn 0 255 of it gry lvl ith th lot valu rprnting blak, hight valu hit, valu in btn rprnting diffrnt had of gray. Th orrlation alulation ar arrid out for a t of pixl, alld a pattrn. Th diplamnt fild i aumd to b homognou inid a pattrn. Th initial imag rprnting th body bfor ditortion i a dirt funtion f(x, y) i tranformd into anothr dirt funtion f*(x*, y*) aftr ditortion or diplamnt. Th thortial rlation btn th to dirt funtion an b rittn a (Touhal t al. 1997): (1) hr, u(x, y) v(x, y) rprnt th diplamnt fild for a pattrn a hon in Figur 1. Figur 1. Initial Dformd Pattrn. Imag orrlation Jno D ( bom h, T ) h a job of omparing ubt of numbr btn th to digital imag. A typial ro orrlation Th proportionality offiint hih offiint maur ho ll ubt moitur math prmability i givn by it i a nonlina D(h,T) of th rlativ humidity h tmpratur & Najjar 1972). Th moitur ma balan that th variation in tim of th (2) atr ma volum of onrt (atr ontnt ) b q divrgn of th moitur flux J hr f(x, y) i th gray lvl valu at oordinat (x, y) for initial imag f*(x*, y*) i th gray lvl J valu at point (x*, y*) t of th dformd imag. Th oordinat (x, y) (x*, y*) ar rlatd by th dformation hih ha ourrd Th atr btn ontnt aquiition an b of xprd th a to imag. If th of motion th vaporabl of th objt atr rlativ (apillary to th a amra i paralll vapor, to th imag adorbd plan, thn atr) thy ar rlatd by; n (Mil th non- (hmially bound) atr Pantazopoulo & Mill 1995). It i ra aum that th vaporabl atr i a fu rlativ humidity, h, dgr of hydration dgr of ilia fum ration,, i.. ag-dpndnt orption/dorption (3) (Norling Mjonll 1997). Undr thi aum by ubtituting Equation 1 into Equati obtain hr u v ar th diplamnt for th ubt ntr in th x y dirtion, rptivly. Th h trm x y ar th ditan from th & ubt + & + h t h ntr to point (x, y). By prforming imag orrlation, th valu of oordinat (x, y), diplamnt hr (u, v), thir drivativ /h i th lop of th orption/ an b dtrmind iothrm (alo alld moitur apa (Touhal t al. 1997, Bruk t al. 1989). Th ar in govrning quation (Equation 3) mut b turn ud for furthr analyi, for xampl, in th by appropriat boundary initial onditi omputation of fratur Th paramtr. rlation btn th amount of atr rlativ humidity i alld iothrm if maurd ith inraing 3 FRACTURE AT humidity BI-MATERIAL dorption INTERFACE iothrm in th a. Nglting thir diffrn (Xi t al. Unlik fratur in th homognou folloing, matrial orption hrin iothrm th ill b mod I mod rfrn II tr intnity to both orption fator ar funtion of th normal dorption By th har ay, tr if th rptivly, hytri of th fratur of rak iothrm btn ould a bi-matrial b takn intrfa into aount, i to mixd-mod vn rlation, though vaporabl th gomtry atr i ymmtri v rlativ humi ith rpt to th b rak ud aording loading to i th ithr ign of of pur th varia mod I or mod II. rlativity Th tr humidity. intnity fator Th in hap mod of th I mod II rprntd iothrm by for KHPC 1 i Kinflund 2 rptivly, by many p ar funtion of both pially th normal tho that har influn tr. xtnt hmial ration, in turn, dtrm trutur por iz ditribution (atrratio, mnt hmial ompoition, SF uring tim mthod, tmpratur, mix t.). In th litratur variou formulatio found to drib th orption iothrm onrt (Xi t al. 1994). Hovr, in th papr th mi-mpirial xprion pro Norling Mjornll (1997) i adoptd b Figur 2. Crak at Bi-matrial Intrfa. Proding of FraMCoS-7, May 23-28, 2010
J Th D ( rak h, T ) flank h diplamnt at a ditan r (Fig.(1) 2) from th rak tip for plan train i givn by (Smlr Th 1979, proportionality Carlon & Praad offiint 1993): D(h,T) i alld moitur prmability it i a nonlinar funtion of th rlativ humidity h tmpratur T (Bažant & Najjar 1972). Th moitur ma balan rquir (4) that th variation in tim of th atr ma pr unit volum of onrt (atr ontnt ) b qual to th hr, divrgn E 1 of th E moitur 2 ar lati flux J modulu of matrial 1 2 on ithr id of th intrfa, rptivly. K 1 K 2 ar Jopning liding mod tr intnity (2) fator t x y ar th opning liding diplamnt of to initially oinidnt point on th rak Th urfa atr ontnt bhind th an rak b xprd tip, rptivly. a th um ε i a of bi-matrial th vaporabl paramtr atr knon (apillary a an oillatory atr, atr indx vapor, i dfind adorbd by atr) th non-vaporabl (hmially bound) atr n (Mill 1966, Pantazopoulo & Mill 1995). It i raonabl to aum that th vaporabl atr i a funtion of rlativ humidity, h, dgr of hydration,, (5) dgr of ilia fum ration,, i.. (h,, ) ag-dpndnt orption/dorption iothrm hr (Norling β Mjonll i of 1997). Dundr Undr lati thi aumption mimath paramtr by ubtituting (Dundr Equation 1969), hih 1 into for Equation plan train 2 on i givn obtain by: h + h t ( D h) & + & + & (6) n (3) h hr µ, ν /h i a th ar lop th har of th modulu, orption/dorption Poion ratio iothrm rak (alo lngth, alld rptivly, moitur apaity). ubript Th 1 govrning 2 rfr quation to th matrial (Equation abov 3) mut blo ompltd th intrfa, by appropriat rptivly boundary (Touhal initial t al. ondition. 1997, Bruk t al. Th 1989, rlation Rthor btn al. 2005). th amount W not of that vaporabl both β atr ε vanih rlativ hn humidity th matrial i alld abov adorption blo iothrm intrfa if ar maurd idntial. ith Th inraing rlation rlativity btn rak humidity flank diplamnt dorption iothrm tr intnity th oppoit fator givn a. Nglting Equation thir 4 an diffrn b furthr (Xi olvd t al. to 1994), obtain th xprion folloing, orption for mod-i iothrm mod-ii ill b tr ud intnity rfrn fator to a: both orption dorption ondition. ith By th ay, if th hytri of th moitur iothrm ould b takn into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to th ign of th variation of th (7) rlativity humidity. Th hap of th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt rat of th hmial ration, in turn, dtrmin por (8) trutur por iz ditribution (atr-to-mnt ratio, Th mnt abov Equation hmial ar ompoition, ud for omputing SF ontnt, th bi-matrial uring tim tr mthod, intnity tmpratur, fator for mix th additiv, intrfa pimn t.). In th by knoing litratur th variou diplamnt. formulation Th nrgy an b rla found to rat, drib G, for th xtnion orption of iothrm rak of along normal th intrfa onrt for (Xi plan t al. train 1994). i Hovr, givn by (Smlr in th prnt 1979, Carlon papr th & mi-mpirial Praad 1993): xprion propod by Norling Mjornll (1997) i adoptd bau it xpliitly aount for th volution of hydration ration SF ontnt. Thi orption iothrm (9) rad 4 EXPERIMENTAL ( h,, ) G (, PROGRAM ) 1 + 1 10( g ) h 1 Th xprimntal program onit of prparation (4) tting of intrfa pimn. 10 Th intrfa ( g ) h pimn ar prpard K (, ) uing 1tard Portl 1 mnt having pifi gravity of 3.15, rivr 1 paing through 4.75 mm iv, having pifi gravity hr th firt finn trm modulu (gl iothrm) of 2.67 rprnt 2.37, th rptivly phyially bound ruhd (adorbd) granit atr ton having th ond maximum trm iz (apillary of 12 mm iothrm) pifi rprnt gravity th of 2.78. apillary Th dimnion atr. Thi xprion of th pimn i valid ar only 810 for mm lo ontnt lngth, 304 of SF. mm Th dpth offiint 50 G mm thikn a hon in 1 rprnt th amount of Figur atr pr 3. unit volum hld in th gl por at 100% rlativ humidity, it an b xprd (Norling Mjornll 1997) a G (, ) k + k 1 vg vg Figur 3. Dtail of pimn gomtry. Th matrial paramtr k vg k vg g 1 an b Th alibratd pimn by having fitting xprimntal a pan of 760 data mm rlvant ar ttd to undr fr (vaporabl) thr-point atr bnding. ontnt All th in onrt bam ar at variou ag (Di Luzio & Cuati 2009b). nothd ith an initial noth iz (a 0 ) of 60.8 mm noth idth of 2 mm. Tabl 1 ho th mix proportion 2.2 Tmpratur lati volution proprti of th diffrnt mix Not that, of onrt. at arly ag, Th in intrfa th pimn hmial ration ar prpard aoiatd follo. ith mnt On day hydration on, th firt-half SF ration of th bam ar xothrmi, i atd ith th tmpratur mix A. On fild day to, i not th uniform intrfa for non-adiabati i l ith ytm a atr vn jt if th i nvironmntal kpt xpod for tmpratur 24 hour. i A ontant. noth i introdud Hat ondution at th intrfa an b during dribd th ating onrt, pro at itlf lat by for inrting tmpratur a oodn not trip xding of 2 mm 100 C thikn. (Bažant On & day Kaplan thr, th 1996), ondhalf Fourir of th la, bam hih i atd rad by mix A, B, C D. by Thi rat an intrfa btn to mix of onrt at th mid-pan. On day four, th pimn (7) q λ T ar dmouldd kpt in atr for uring. Whil hling hr q th i pimn, th hat grat flux, ar T i i takn th abolut to prvnt tmpratur, falling or impat. λ i th Th hat dignation ondutivity; of th bam in thi ith ithout th intrfa i givn in Tabl 2. 1 (5) hr k vg k vg ar matrial paramtr. From th maximum amount of atr pr unit volum that an fill all por (both apillary por gl por), on an alulat K 1 a on obtain K (, ) 1 g 1 0.188 + 0.22 G 1 0 1 g 1 1 (6) Proding of FraMCoS-7, May 23-28, 2010
Tabl 1. Dtail of matrial & mix proportion. J ) D ( h, T h Figur 4. Exprimntal t-up. Th proportionality offiint D(h,T) moitur prmability it i a nonlina of th rlativ humidity h tmpratur & Najjar 1972). Th moitur ma balan that th variation in tim of th atr ma volum of onrt (atr ontnt ) b q divrgn of th moitur flux J J 5 RESULTS AND DISCUSSIONS t Tabl 2. Dignation of intrfa bam. Th atr ontnt an b xprd a Th digital imag takn during th xprimnt for of th vaporabl atr (apillary a all th pimn ar orrlatd uing a od (Ebrl vapor, adorbd atr) th non- 2006) rittn ithin (hmially th framork bound) of mathmatial atr n (Mil pakag MATLAB. Pantazopoulo Th rult obtaind & Mill from 1995). th DIC It i ra analyi of intrfa aum bam that diffrnt th vaporabl tag of loading atr i a fu ar prntd rlativ diud. humidity, A quar h, grid dgr pattrn of of hydration 5 pixl in ah of x dgr y of dirtion ilia fum ar ration, ltd uh, i.. that th intrfa fall ag-dpndnt ithin th ntr orption/dorption of grid a hon in Figur 5, (Norling hih i Mjonll ud for 1997). furthr Undr analyi. thi aum by ubtituting Equation 1 into Equati obtain h h t h & + & + Intat bam (AI) ithout any intrfa ar alo atd to ompar it bhavior ith th bam having an intrfa. Th intrfa pimn ar ttd in a lod loop rvo-ontrolld tting mahin having a apaity of 500 kn. A pially alibratd 50 kn load ll i ud for mauring th load. Th load-point diplamnt i maurd uing a linar variabl diplamnt tranformr (LVDT). Th CMOD i maurd uing a lip gag loatd aro th noth. All th tt ar prformd undr CMOD ontrol ith th rat of rak opning bing 0.0005 mm/. Th rult of load, vrtial diplamnt, CMOD tim ar imultanouly aquird through a data aquiition ytm. For digital imag orrlation, th pkl pattrn i to b mad on th pimn. Th pimn ar initially hit ahd a pkl pattrn i prpard ovr it uing a tard blak pray paint. Th imag of th intrfa pimn ar apturd bfor loading during variou tag of loading uing a digital amra mountd on a t a hon in Figur 4. A rmot ontrol i ud for apturing th imag to avoid any vibration alo to kp th ditan btn amra ln th pimn unhangd. hr /h i th lop of th orption/ iothrm (alo alld moitur apa govrning quation (Equation 3) mut b Figur 5. Grid Pattrn by ud appropriat for DIC analyi. boundary initial onditi Th rlation btn th amount of 5.1 Surfa diplamnt atr & rlativ train humidity i alld iothrm if maurd ith inraing DIC analyi provid humidity th urfa dorption diplamnt iothrm of in th th ah point of th a. pkl Nglting pattrn. thir Figur diffrn 6-8 ho (Xi t al. th urfa diplamnt th folloing, train orption obtaind iothrm from ill b DIC analyi for ltd rfrn imag. to both Th orption figur ho dorption ho th pattrn of By rak th propagation ay, if th undr hytri diffrnt of th tag of loading. iothrm Th imag ould hon b takn in Figur into 6 aount, ar to ud for alulation rlation, of rak vaporabl lngth atr rak v tip rlativ loation ud humi b for ud quantifying aording th to rak th ign opning of th varia rlativity humidity. Th hap of th diplamnt hih i diud latr on. iothrm for HPC i inflund by many p pially tho that influn xtnt hmial ration, in turn, dtrm trutur por iz ditribution (atrratio, mnt hmial ompoition, SF uring tim mthod, tmpratur, mix t.). In th litratur variou formulatio found to drib th orption iothrm onrt (Xi t al. 1994). Hovr, in th Figur 6. Diplamnt papr th raking mi-mpirial pattrn obtaind xprion from pro DIC (ltd imag). Norling Mjornll (1997) i adoptd b Proding of FraMCoS-7, May 23-28, 2010
J ) D ( h, T h Figur 7. Surfa diplamnt from DIC (ltd imag). J (2) ag-dpndnt orption/dorption iothrm Figur 8. Surfa train from DIC (ltd imag). (Norling Mjonll 1997). Undr thi aumption by ubtituting Equation 1 into Equation 2 on 5.2 obtain Crak lngth Th mthod mployd for dtrmining rak opning diplamnt h (δx), rak tip loation & + & + & th ditan n (3) h of t h rak tip (r) from th digitally prod imag i hon in Figur 9. hr /h i th lop of th orption/dorption iothrm (alo alld moitur apaity). Th govrning quation (Equation 3) mut b ompltd by appropriat boundary initial ondition. Th rlation btn th amount of vaporabl atr rlativ humidity i alld adorption iothrm if maurd ith inraing rlativity humidity dorption iothrm in th oppoit a. Nglting thir diffrn (Xi t al. 1994), in th folloing, orption iothrm ill b ud ith rfrn to both orption dorption ondition. By th ay, if th hytri of th moitur Figur iothrm 9. Crak ould tip b CMOD takn into maurmnt aount, from to DIC. diffrnt rlation, vaporabl atr v rlativ humidity, mut b Th ud rak aording lngth to ar th omputd ign of th for variation all th imag of th rlativity ar plottd humidity. againt Th load hap a hon of in th Figur orption 10. From iothrm thi for figur, HPC it i an inflund b n that by many th rak paramtr, ha not propagatd pially tho until that th loading influn tag xtnt orrponding rat of th to imag hmial numbr ration four. Th, load in turn, orrponding dtrmin to por imag trutur four i about por 85 iz to ditribution 90 % of th (atr-to-mnt pak load. It i alo ratio, n mnt that thr hmial i a dpartur ompoition, from SF linarity ontnt, at 85 uring to 90% tim of pak mthod, load. Thi tmpratur, i du to mix th additiv, dvlopmnt t.). of In miro-rak th litratur in variou th fratur formulation pro an zon b that found form to drib ahad of th th tration orption fr iothrm rak hih of normal i a proprty onrt of (Xi quai-brittl t al. 1994). matrial. Hovr, in th prnt papr Aording th mi-mpirial to th thory xprion of linar lati propod fratur by mhani, Norling Mjornll u th (1997) onpt i of adoptd fftiv lati bau rak it lngth, dfind a th rak lngth that i longr than Proding of FraMCoS-7, May 23-28, 2010 (1) Th proportionality offiint D(h,T) i alld moitur prmability it i a nonlinar funtion of th rlativ humidity h tmpratur T (Bažant & Najjar 1972). Th moitur ma balan rquir that th variation in tim of th atr ma pr unit volum of onrt (atr ontnt ) b qual to th divrgn of th moitur flux J t Th atr ontnt an b xprd a th um of th vaporabl atr (apillary atr, atr vapor, adorbd atr) th non-vaporabl (hmially bound) atr n (Mill 1966, Pantazopoulo & Mill 1995). It i raonabl to aum that th vaporabl atr i a funtion of rlativ humidity, h, dgr of hydration,, dgr of ilia fum ration,, i.. (h,, ) xpliitly aount for th volution of hydration ration SF ontnt. Thi orption iothrm rad 1 ( h,, ) G (, ) 1 + 1 10( g ) h 1 10( g ) h K (, ) 1 1 1 (4) Figur hr 10. th Load firt vru trm rak (gl lngth. iothrm) rprnt th phyially bound (adorbd) atr th ond th trm tru (apillary rak but iothrm) hortr than rprnt tru rak th apillary plu th fratur atr. Thi pro xprion zon a i hon valid in only Figur for lo 11, ontnt dfin of SF. ritial Th offiint rak lngth G 1 a rprnt th rak th lngth amount orrponding atr pr to unit pak volum load a hld hon in th in gl Figur por 10. at 100% of rlativ humidity, it an b xprd (Norling Mjornll 1997) a G (, ) k + k 1 vg vg (5) hr k vg k vg ar matrial paramtr. From th maximum amount of atr pr unit volum that an fill all por (both apillary por gl por), on an alulat K 1 a on obtain K (, ) 1 g 1 0.188 + 0.22 G 1 0 1 g 1 1 (6) Th matrial paramtr k vg k vg g 1 an Figur b alibratd 11. Conpt by of fitting fftiv xprimntal rak lngth. data rlvant to fr (vaporabl) atr ontnt in onrt at Furthrmor, variou ag (Di th Luzio proprti & Cuati that ar 2009b). rquird for linar lati fratur mhani analyi ar omputd at thi ritial rak lngth. Th ritial rak lngth 2.2 Tmpratur volution obtaind for diffrnt intrfa pimn ar litd in Not Tabl that, 3. at It arly i n ag, that in a th diffrn hmial ration btn th aoiatd ompriv ith mnt trngth hydration of th onrt SF on ration ithr id ar xothrmi, of intrfa th tmpratur inra, th fild ritial i not lngth uniform dra, for non-adiabati hih ho ytm th inra vn if th in th nvironmntal brittln tmpratur i ontant. Hat ondution an b of th intrfa pimn hih hav highr mimath of proprty on ithr id of th intrfa. dribd in onrt, at lat for tmpratur not xding 100 C (Bažant & Kaplan 1996), by Thi fatur of obtaining th rak tip loation Fourir la, hih rad dtrminination of rak lngth mak th DIC thniqu q λvry T attrativ a it i vry diffiult to obtain (7) th paramtr through othr mthod. Thniqu uh a dy pntration for dtrmination of th hr q i th hat flux, T i th abolut rak lngth hav bn rportd in th litratur tmpratur, λ i th hat ondutivity; in thi ar diffiult in trm of uag in addition to bing xpniv too.
Tabl 3. Critial rak lngth omputd from DIC. J ) D ( h, T h Th proportionality offiint D(h,T) moitur prmability it i a nonlina of th rlativ humidity h tmpratur & Najjar 1972). Th moitur ma balan that th variation in tim of th atr ma volum of onrt (atr ontnt ) b q divrgn of th moitur flux J t J 5.3 Crak mouth opning diplamnt Th advantag of DIC thniqu i that an dtrmin th rak opning diplamnt at any poition along th rak a hon in th Figur 9, hih i not poibl ith othr xprimntal nor uh a, a lip gag, unl mount a numbr of thm along th rak. Th atr ontnt an b xprd a Figur 13. Load vru tr intnity fator. of th vaporabl atr (apillary a vapor, adorbd atr) th non- (hmially bound) atr n (Mil Pantazopoulo & Mill 1995). It i ra aum that th vaporabl atr i a fu rlativ humidity, h, dgr of hydration dgr of ilia fum ration,, i.. ag-dpndnt orption/dorption (Norling Mjonll 1997). Undr thi aum by ubtituting Equation 1 into Equati obtain h h t h Figur 14. Load vru nrgy rla rat. & + & + Figur 12. Load vru CMOD. For validation of th rult obtaind from DIC, th CMOD omputd for all th imag uing DIC analyi ar plottd ompard ith tho maurd xprimntally uing lip gag, a hon in Figur 12. It i n that thr i a vry lo math btn th to. Hovr, on drabak of DIC analyi n i that th maurmnt of CMOD during th initial loading portion i diffiult in th rak do not gt initiatd a n from th rult of imag 1 to 4. 5.4 Fratur proprti of onrt intrfa Th mod I mod II fratur toughn of th intrfa bam ar dtrmind by ubtituting th valu of rak opning diplamnt (δx) rak liding diplamnt (δy) omputd at th ritial rak lngth poition in to Equation 7 8, rptivly. hr Sin, th fratur toughn /h i th lop of th orption/ ar linar lati fratur mhani paramtr, th ar obtaind at th iothrm (alo alld moitur apa govrning quation (Equation 3) mut b ritial rak lngth hih in thi ork i aumd by appropriat boundary initial onditi to hav ourrd at Th th maximum rlation btn load lvl. th Figur amount of 13 ho th plot atr of mod-i rlativ mod humidity II tr i intnity fator omput iothrm from if DIC maurd for diffrnt ith inraing im- alld ag. Th mod humidity I fratur toughn dorption (K IC iothrm ) omputd for diffrnt a. intrfa Nglting ar hon thir diffrn in Tabl 4. (Xi t al. in th Th valu obtaind th folloing, by uing orption th Rilm iothrm mthod ill b (RILEM 1990) hih rfrn i bad to both on th orption iz fft dorption la of Bazant (Bazant By 1984) th ar ay, alo if hon th in hytri thi tabl of th (Shah 2009). In addition, iothrm th ould valu b rportd takn into for aount, diffrnt intrfa to rlation, in Rfrn vaporabl (Rao 2006) atr v obtaind rlativ humi b ud aording to th ign of th varia uing th omplian mthod ar alo hon. It i rlativity humidity. Th hap of th n that th mod I fratur toughn omputd iothrm for HPC i inflund by many p uing DIC agr ll ith tho obtaind uing th pially tho that influn xtnt Rilm mthod. It may hmial b notd ration that th, Rilm in mthod turn, dtrm rquir only th trutur maximum load por obtaind iz ditribution for go-(atrmtrially imilar ratio, pimn mnt of hmial diffrnt iz ompoition, SF th modulu of latiity. uring tim mthod, tmpratur, mix Th valu of t.). mod In II th fratur litratur toughn variou omputd for diffrnt found intrfa to drib ar rportd th orption in Tabl iothrm 5. formulatio For omparion onrt th valu (Xi rportd t al. 1994). in Rfrn Hovr, in th (Rao 2006) ar alo papr hon. th mi-mpirial Th valu rportd xprion in pro Rfrn (Rao 2006) Norling ar for Mjornll intrfa (1997) ith onrt i adoptd b trngth diffrnt from Proding of FraMCoS-7, May 23-28, 2010
Tabl J D 4. ( Comparion h, T ) h of K IC Valu. Tabl Th 5. Comparion atr ontnt of K IIC Valu. an b xprd a th um hr /h i th lop of th orption/dorption th on ud in thi tudy. It i providd hr only for th iothrm (alo alld moitur apaity). Th ak of omparing th rang in hih th rult fall. It govrning quation (Equation 3) mut b ompltd may by appropriat b notd hr boundary that du to th initial diffrn ondition. in th lati proprti Th rlation of onrt btn on ithr amount id of of th vaporabl intrfa, mod atr II omponnt rlativ i humidity prnt although i alld th adorption har tr along iothrm intrfa if maurd i ngligibl. ith Only inraing mod I rlativity valu of fratur humidity toughn dorption an b obtaind iothrm uing th th oppoit Rilm mthod a. Nglting in it i drivd thir diffrn for ingl (Xi homognou t al. 1994), matrial. th folloing, Hn, th orption mod II fratur iothrm toughn ill b uing ud ith th in Rilm rfrn mthod to both i not orption rportd in dorption Tabl 5. ondition. By th ay, if th hytri of th moitur Tabl iothrm 6. Comparion ould b of takn G C Valu. into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to th ign of th variation of th rlativity humidity. Th hap of th orption iothrm for HPC i inflund by many paramtr, pially tho that influn xtnt rat of th hmial ration, in turn, dtrmin por trutur por iz ditribution (atr-to-mnt ratio, mnt hmial ompoition, SF ontnt, uring tim mthod, tmpratur, mix additiv, t.). In th litratur variou formulation an b found to drib th orption iothrm of normal onrt (Xi t al. 1994). Hovr, in th prnt papr th mi-mpirial xprion propod by Norling Th nrgy Mjornll rla (1997) rat, G i hih adoptd i dfind bau a th it nrgy rquird for rating a rak of unit ara, i Proding of FraMCoS-7, May 23-28, 2010 (1) Th proportionality offiint D(h,T) i alld moitur prmability it i a nonlinar funtion of th rlativ humidity h tmpratur T (Bažant & Najjar 1972). Th moitur ma balan rquir that th variation in tim of th atr ma pr unit volum of onrt (atr ontnt ) b qual to th divrgn of th moitur flux J t J (2) of th vaporabl atr (apillary atr, atr vapor, adorbd atr) th non-vaporabl (hmially bound) atr n (Mill 1966, Pantazopoulo & Mill 1995). It i raonabl to aum that th vaporabl atr i a funtion of rlativ humidity, h, dgr of hydration,, dgr of ilia fum ration,, i.. (h,, ) ag-dpndnt orption/dorption iothrm (Norling Mjonll 1997). Undr thi aumption by ubtituting Equation 1 into Equation 2 on obtain h + h t ( D h) n (3) h & + & + & omputd xpliitly by aount ubtituting for th valu volution of KI of hydration KII in Equation ration 9. Figur SF ontnt. 14 ho Thi th plot orption of nrgy iothrm rla rad rat vru load for diffrnt imag. Tabl 6 ho th nrgy rla rat valu omputd for diffrnt intrfa. Th valu obtaind from Rfrn (Rao 2006) ar alo hon for 1th ak of omparing th valu 1undr hih th prnt rult fall. ( h,, ) G (, ) 1 + 10( g ) h 1 (4) 6 CONCLUSIONS 10( g ) h K (, ) 1 1 1 Th bi-matrial fratur toughn in mod I (KI) mod II (KII) th ritial nrgy rla rat (G) hr ar th xprimntally firt trm (gl dtrmind iothrm) for rprnt a onrtonrt phyially jointd bound intrfa (adorbd) pimn atr uing th digital ond im- th ag trm orrlation (apillary thniqu. iothrm) Th rprnt onrt-onrt th apillary intrfa atr. pimn Thi xprion ar ttd i valid undr only thr for point lo bnding ontnt in of a SF. lod Th offiint loop rvo-ontrolld G 1 rprnt tting th amount mahin of undr atr pr rak unit mouth volum opning hld in diplamnt th gl por at ontrol. 100% Th rlativ imag humidity, of th intrfa it an pimn b xprd ar apturd (Norling during Mjornll variou 1997) tag a of loading uing a digital amra. Uing orrlation mthod, th imag ar analyzd th urfa diplamnt, urfa train, G (, ) k + k (5) rak 1 mouth vgopning vgdiplamnt, rak liding diplamnt rak lngth ar omputd. It i n hr that k thr i vry good agrmnt in th vrtial vg k vg ar matrial paramtr. From th diplamnt maximum amount of rak atr mouth pr unit opning volum diplamnt fill all por omputd (both through apillary DIC por tho gl por), maurd on that an uing an alulat LVDT K 1 a lip on gag, obtain rptivly. It an b onludd that th impl DIC thniqu an b a vry uful an onomial ubtitut againt g train gag, lip gag LVDT. 1 Furthr, 0.188 + 0.22 G th 1 0 1 maurmnt of rak tip loation rak lngth (6) an K ( b, don ) fftivly uing DIC thniqu hih 1 ar vry diffiult g xpniv 1 for onrt lik 1 matrial uing traditional nor. Th matrial paramtr k vg k vg g 1 an b alibratd by fitting xprimntal data rlvant to REFERENCES fr (vaporabl) atr ontnt in onrt at variou ag (Di Luzio & Cuati 2009b). Bazant Z. P. 1984. Siz fft in blunt fratur: Conrt, rok, mtal. Journal of Enginring Mhani 110: 518 535. Bruk H. A., MNill S. R., Sutton M. A. & Ptr W. H. 1989. 2.2 Tmpratur volution Digital imag orrlation uing Nton-Raphon mthod Not of partial that, at diffrntial arly ag, orrtion. in th Exprimntal hmial Mhani ration aoiatd 29:, 261 267. ith mnt hydration SF ration Carlon L. A. & Praad S. 1993. Intrfaial fratur of ih ar xothrmi, bam. Enginring th tmpratur Fratur Mhani fild i 44: not 581 590. uniform Chra for non-adiabati Kihn J. M. & ytm Rao P. S. vn 2007. if Fratur th nvironmntal of old jointd tmpratur onrt intrfa. i ontant. Enginring Hat Fratur ondution Mhani an 74: b dribd 122 131. in onrt, at lat for tmpratur not Choi xding S. & Shah 100 C S. P 1997. (Bažant Maurmnt & Kaplan of dformation 1996), by on onrt ubjtd to omprion uing imag orrlation. Fourir la, hih rad Exprimntal Mhani 37: 307 313. Dundr J. 1969. Edg-bondd diimilar orthogonal lati q dg λ Tundr normal har loading. Journal of Applid (7) Mhani 36: 650 652. Ebrl C. 2006. Digital Imag Corrlation Traking. http:// hr.mathork.om/matlabntral/filxhang/12413. q i th hat flux, T i th abolut Kunida tmpratur, M, Kurihara λ N, i Uhida th hat Y & ondutivity; Rokugo K 2000. in Appliation of tnion oftning diagram to valuation of thi bond
proprti at onrt intrfa. Enginring Fratur Mhani 65: 299 315. Lalr J. S. & Shah S. P. 2002. Fratur pro of quai-brittl matrial tudid ith digital imag orrlation. In: Rnt Advan in Exprimntal Mhani. Klur Aadmi Publihr, Nthrl, pp. 335 344. Mangat P. & O Flahrty F. 2000. Influn of lati modulu on tr rditribution raking in rpair path. Cmnt & Conrt Rarh 30: 125 136. Rao P. S. 2006. Fratur bhavior of jointd onrt intrfa. Ph.D. thi, Dpartmnt of Civil Enginring, Indian Intitut of Sin, Bangalor, India. Rthor J., Gravouil A., Mortin F. Combur A. 2005. Etimation of mixd-mod tr intnity fator uing digital imag orrlation an intration intgral. Intrnational Journal of Fratur 132: 65 79. RILEM draft rommndation. 1990. Siz-fft mthod for dtrmining fratur nrgy pro zon iz of onrt. Matrial & Strutur 23: 461 465. Shah S. G. 2009. Fratur & fatigu bhavior of onrtonrt intrfa uing aouti miion, digital imag orrlation miro-indntation thniqu. Ph.D. thi, Dpartmnt of Civil Enginring, Indian Intitut of Sin, Bangalor, India. Smlr R. E. 1979. Evaluation of tr intnity fator for biomatrial bodi uing numrial rak flank diplamnt data. Intrnational Journal of Fratur 15: 135 143. Sutton M. A., Chng JM., D Ptr ( h, T ) W.H., h Chao Y.J. & MNill S.R. 1986. Appliation of an optimizd digital orrlation mthod to planar dformation analyi. Imag Viion Computing 4: 143 150. Th proportionality offiint D(h,T) Sutton M. A., Woltr moitur W. J., Ptr prmability W. H., Ranon it W. i F. a & nonlina MNill S. R. 1983. of th Dtrmination rlativ humidity of diplamnt h tmpratur uing an improvd digital & Najjar orrlation 1972). mthod. Th Imag moitur Viion ma balan Computing 1: 133 139. that th variation in tim of th atr ma Touhal S.M., Mortin F. & Brunt M. 1997. Variou xprimntal appliation volum of digital of onrt imag orrlation (atr ontnt mthod. ) b q In: Proding divrgn of Intrnational of th onfrn moitur on flux omputational mthod xprimntal maurmnt. Rhod, J Gr, pp. 45 58. Thgg E. K. & Stanzl S. E. 1991. J Adhiv por maurmnt of bond btn t old n onrt. Journal of Matrial Sin 26: 5189 5194. Thgg E. K., Tan D. M., Th Kirhnr atr H. ontnt O. K. & Stanzl an S. b E. 1993. xprd a Intrfaial ubintrfaial of th vaporabl fratur in atr onrt. Ata (apillary mtallurgial matrial vapor, 41: 569 576. adorbd atr) th non- a Waltr R., Otrgaard L., Oln J. F. & Stang H. 2005. Wdg (hmially bound) atr plitting tt for a tl-onrt intrfa. Enginring n (Mil Fratur Mhani Pantazopoulo 72: 2565 2583. & Mill 1995). It i ra aum that th vaporabl atr i a fu rlativ humidity, h, dgr of hydration dgr of ilia fum ration,, i.. ag-dpndnt orption/dorption (Norling Mjonll 1997). Undr thi aum by ubtituting Equation 1 into Equati obtain h h t h & + & + hr /h i th lop of th orption/ iothrm (alo alld moitur apa govrning quation (Equation 3) mut b by appropriat boundary initial onditi Th rlation btn th amount of atr rlativ humidity i alld iothrm if maurd ith inraing humidity dorption iothrm in th a. Nglting thir diffrn (Xi t al. th folloing, orption iothrm ill b rfrn to both orption dorption By th ay, if th hytri of th iothrm ould b takn into aount, to rlation, vaporabl atr v rlativ humi b ud aording to th ign of th varia rlativity humidity. Th hap of th iothrm for HPC i inflund by many p pially tho that influn xtnt hmial ration, in turn, dtrm trutur por iz ditribution (atrratio, mnt hmial ompoition, SF uring tim mthod, tmpratur, mix t.). In th litratur variou formulatio found to drib th orption iothrm onrt (Xi t al. 1994). Hovr, in th papr th mi-mpirial xprion pro Norling Mjornll (1997) i adoptd b Proding of FraMCoS-7, May 23-28, 2010