Mode I Concrete Characterization using Rebar Induction Heating

Transcription

1 Mode I Concrete Crcteriztion using Rebr Induction Heting Fokw Didier #, F. Ngpgue *, T. Nsongo * M. Mpess #4, T. Tmo Ttietse #4 # GRMS, Deprtment of Civil Engineering, ENSET, University of Doul PO Box 87, Doul Cmeroon # didier_fokw8@otmil.com * IUT of Bndjoun, University of Dscng * University of Brzzville, Republic of Congo #4 ENSP, University of Youndé I, Cmeroon Abstrct: Reinforced concrete is composite mteril consisting in rebr embedded in concrete mtrix. Te structurl equilibrium depends of te qulity of bond between te two mterils s well s te intrinsic qulity of ec of te components. Wen te structure is submitted to eting, crcking cn occur due to te difference in terml expnsion properties between te two mterils. In te present work, teoreticl pproc, correlting rebr expnsion rte under eting process, to te frcture properties of concrete is proposed. Te vlidting test consists in Double Cntilever concrete Bem, wit n initil crck lengt, rebr embedded t distnce from te crck tip. Te rebr is eted troug n induction process nd its expnsion induces crck opening displcement t te level of te concrete. Te deformtion of te concrete due to te rebr expnsion induces t te level of te crck tip, displcement s well s stress field, leding to te crck propgtion. In order to follow te development of te displcement field t te level of te crck front, digitl cmer is used to cpture pictures of tt zone t vrious steps (two imges per minute) of te eting process. Te imges re ten nlysed wit imge correltion tecniques to obtin te displcement field s well s te strin field, nd ten te time of crck propgtion. Te criticl crck opening displcement, te criticl energy relese nd Stress Intensity Fctor corresponding to te time of crck propgtion, cn be deduced wit good ccurcy. Key words Induction eting, rebr, crck opening displcement, imges correltion, stress intensity fctor, energy relese rte. I. INTRODUCTION Concrete is composite, constituted of mixture of ggregtes, cement, wter, pores nd vrious micro crcks due to srinkges. Its pysicl s well s its mecnicl properties cnges wit time, not only during setting nd rdening periods, but re sensitive to te environmentl weter. In tis wy, since its erly ge, it undergoes mny volume vritions, due to its interctions wit te environment. Tis volume vrition is very often one of te cuses of concrete structurl micro crcking (srinkge). In tis cse, internl stress induced by concrete expnsion is creted nd crcks pper wen te stress in tensile zones is greter tn te locl ultimte stress of concrete or wen te locl criticl stress intensity fctor reces its criticl vlues. Among oters concrete crcking due to it environment, tere is corrosion. Corrosion is progressive trnsformtion of te iron embedded in concrete mtrix into n expnsive rust in presence of umidity, crbon dioxide or cloride ions penetrtion troug concrete cover. As te quntity of rust increses between te iron nd te surrounding concrete, internl pressure increses, leding to concrete crcking [,, ] nd peeling. Beind te difficulty to model corrosion expnsion round te rebr in corrosion process, joint model is sometimes used []. Under ig temperture, due to te difference between concrete nd rebr terml properties, concrete crcking in reinforced concrete is combintion of two effects: te concrete srinkge nd reinforcement terml expnsion [4,5]. Mny investigtions ve been done in order to understnd te interctions between reinforcement nd concrete under ig temperture [4, 5, 6, 7]. Te ide is to replce te rust tickness round te rebr by rigid joint, expnding in te rdil direction, under ypoteticl temperture vrition. It ppers from tose vrious nlysis, tt te knowledge of te reltion between frcture prmeters nd environmentl effects is useful for good modelling [8, 9, ], s well s te numericl simultion[,,,] of concrete crcking under mecnicl loding nd its vrious interctions wit te environment. At tis end, mny experimentl tecniques re often used to cpture crcking properties of concrete in mode I loding [8,,,, 4]. Te present work proposes new wy, consisting in te use of rebr induction eting expnsion, to crete mode I loding on DCB specimen, from wic frcturing properties of concrete cn be deduced. ISSN : Vol 4 No Apr-My 7

2 II.THEORETICAL BACKGROUND OF THE MODEL A. Te bsic ide One of te more importnt problems deling wit reinforced concrete structure is its beviour under ig temperture. In fct, reinforced concrete is composite wic components re ggregtes, cement pste, wter nd reinforcement. Ec of tose components is crcterized by its pysicl intrinsic properties. Te vlues of te coefficient of terml expnsion rnges between. -6 C - to.9-6 C - for concrete nd is influenced by te qulity nd te proportion of corse ggregtes in te mix. For te steel, te coefficient of terml expnsion depends on te mount of crbon in its metllurgicl structure. It rnges is between to. -6 C - for low steel lloy nd 6 to. -6 C - for ustenitic steel. For concrete s well s well s for steel under ig temperture, te coefficient of terml expnsion increses. Te bsic ide of te present study is to correlte te steel expnsion rte under ig temperture to te frcture properties of te concrete. Tis cn be done troug double cntilever bem (DCB) test, in wic te well known mode I force P (figure ) is replced by te pressure of rebr trnsversl expnsion under induction eting. Te double cntilever bem is crcterized by its tickness b, lengt L, eigt, wit n initil crck. At distnce from te end of te specimen, rebr wit dimeter is embedded, representing concrete reinforcement. Te crck lengt is mesured from te centre of te iron to te distnce inside te specimen. During eting process, te pressure t te interfce between rebr nd concrete, due to te rebr expnsion, increses, inducing crck opening displcement, wic cn be mesured troug LVD sensor. If te pressure round te reinforcement is denoted p, nd since its dimeter, its lengt re respectively nd b, te equivlent terml induced force P is given s function of te pressure s, () P S p nds S E s n Tds were n is te positive norml to te concrete t te level of its contct wit te rebr, S is te concrete re under te rebr pressure due to its expnsion. S cn be computed s te rebr dimeter times te tickness of te specimen, is te rebr coefficient of terml expnsion, E s te rebr Young modulus nd T te temperture increse under eting. P b P Figure : Principle of DCB test in clssicl frcture mecnic test b b L Figure : Detil of te induction eting frcture test ISSN : Vol 4 No Apr-My 7

3 B. Termodynmic pproc of crck problem Frcturing test in clssicl elstic frcture mecnics consists in pplying force P s sown in (figure) nd mesuring te corresponding crck opening displcement in te imposed force pproc, or imposing displcement crck opening displcement nd reporting te corresponding force in te cse of displcement imposed loding. In ec of tose cses, wit te ypotesis tt te mteril remins elstic, if W, U, K nd Us re respectively te totl work done by te system, te strin energy, te kinetic energy nd te surfce energy, te globl distribution of te energy of te system is given by te reltion E T = U el -W+U s () were E T is te totl free energy of te system. Wit te ypotesis of qusi sttic loding, kinetic energy K s well s te oters forms of strin energy (non elstic), cn be neglected, nd te eqution is terefore reduced to E T = U-W+U s =+U s () were is te mecnicl potentil of te system. Under equilibrium conditions, te totl free energy is independent of te crck lengt leds to: det d( U s) (4) d d (5) dus d( ) And GI d d were G I is te energy relese rte in mode I frcture. G I, for ctul system is given s function of te force P, by te reltion C (6) G I were C is te complisnce of te bem of bem, wit = / = CP (7) te deflection of te lf bem under te loding force P. ere represents te trnsversl rebr expnsion effect on te concrete, tt mens its expnsion over te initil rebr rdius. Now, if we consider te lf specimen s bem wic lengt is denoted, embedded t te level of te crck tip nd submitted to n ypotetic force P, representing te effect of expnding rebr pressure on te concrete (figure ), te deflection is given ccording to te bem teory nd te Cstiglino s teorem by P (8) EI were E nd I re respectively te elstic modulus nd te qudrtic moment of te concrete specimen section. From te bove reltion, one cn deduce te expression of te complince of te concrete section s C (9) EI Te vrition of te complince wit bem lengt cn be expressed s dc () d EI nd terefore te expression of te energy relese rte is given from () by te following reltion G I P () EI In te present experimentl pproc, since te vlue of te force P is unknown, becuse no direct force is pplied to te specimen, te only mesured prmeter is te crck opening displcement, representing te effect of rebr expnsion. Wit te ypotesis tt te mteril remins elstic until te beginning of crck propgtion, nd te ypoteticl force P is proportionl to te displcement CP, te vrious frcture prmeters involved in te frcturing process re s function of te displcement given by: P E P b 4 () ISSN : Vol 4 No Apr-My 7

4 p G I P E b EI 4 8 EGI E K I.6 ( ) ( ) P, p, G I, K I being respectively, te equivlent force t te level of te rebr, te locl equivlent pressure, te energy relese rte nd te stress intensity fctor t te level of te vicinity of te crck. Te energy relese rte G I represents te energy stored in te mteril becuse of te presence of te initil stble crcknd te stress intensity fctor is n indiction on te effect of te discontinuity on te stress field t te level of te crck vicinity. Tese reltions become respectively, P c, p c, G Ic nd K Ic wen te crck is bout to propgte nd correspond to te criticl crck opening displcement vlue. Over tt vlue, te crck lengt increse wit te crck opening displcement, nd terefore nonlinerity ppers between te ypoteticl force P nd te crck opening displcement. It ppers from tese reltions tt te knowledge of te Poisson s rtio, te Young modulus nd te geometry of te specimen togeter wit te mesurement of te criticl crck opening displcement induced by rebr expnsion, enble us to determine vrious mecnicl crcking properties of concrete. Te prmeters KIC nd GIC, crcterize te mteril. Te first crcterize te bility of te mteril to resist to crck propgtion nd te second, its bility to store elstic energy before crck propgtion. C. Correltion between rebr terml expnsion rte nd frcture properties of concrete Let been te rebr dimeter nd T te vrition of its temperture during time t. Te deflexion of te lf bem (figure ) under rebr expnsion is correlted to te vrition of temperture T by te following reltion: T (6) Te temperture vrition T rte nd vrious crcking prmeters cn be correlted s follow: nd K I G I p EI P EsT 8 P b EsT 8b T 8 E T EGI.6 ( ) 4 ( ) 4 T 4 T.E ( ) Eventully, te criticl time corresponds to te crck propgtion, nd tis time will be defined troug te nlysis of te displcement nd strin field t te level of te crck tip given by digitl imges correltion. D. Digitl imges correltion Digitl imge correltion is non contct wy of cpturing full field surfce displcement nd te corresponding strin on zone of structure under loding. Te fundmentl difference between tis tecnique nd te clssicl guge is tt, since tere is not ny contct between te specimen nd te cmer, te test is not disturbed by te mesuring system nd te mesurement cn be done in zone wic ccess is not esy. Te principle developed since erly 98 consist in tken N pictures of te zone of study wit frequency t, te first, before te loding, being tken s reference. Te imges re in te first step digitized, tt mens trnsformed from continuous signl into discrete one (pixels) nd stored in computer. Ec of te N- () (4) (5) (7) (8) (9) () ISSN : Vol 4 No Apr-My 74

5 pictures is ten compred to te reference imge. Te difference between te reference nd given imge gives n ide on te modifiction of displcement field during te period of time n*t, n corresponding to te sequence number of te picture by nlysing te picture, it cn be known pproximtely te time t wic crck propgtes. Tis nlysis s been crrying out using specific progrm, clled CORRIELI_LMT. Zone of displcement field observtion b Figure : Zone of cmer observtion E. Rebr induction eting Induction eting is non contct wy of providing fst, consistent et for vrious pplictions suc s: joining, metl treting. It consists in using ig frequency electricity to et electriclly conductive mterils. Its principle is s follow: ig frequency current is used to crete n lternting current troug coil. Te pssge of te lternting current genertes n intensive nd lternting mgnetic field. Te lternting mgnetic field genertes ccording to Frdy s lw n induced current (eddy currents) in te conductive mteril, wic in tis cse beve like sort circuit, generting loclized nd fst incresed et witout ny pysicl contct between te coil nd te work piece. Te temperture s well s te rte of eting depends on te intensity of te lternting current nd te initil power s well s te frequency of te current. Mgnetic mterils re esier to et tn non-mgnetic, due to te effects of ysteresis eting. Mgnetic mterils nturlly resist te rpidly cnging mgnetic fields witin te induction coil. Te resulting friction produces its own dditionl et ysteresis eting in ddition to eddy current eting. A metl wic offers ig resistnce is sid to ve ig mgnetic "permebility". Permebility cn vry on scle of to 5 for mgnetic mterils; non-mgnetic ve permebility of. Hysterisis eting occurs t tempertures below te "Curie" point te temperture t wic mgnetic mteril loses its mgnetic properties. III. EXPERIMENTAL PROCEDURE A. Experimentl setup Te figure 4 sows te globl setup used to perform te present test. It is composed of: LVD sensor for te mesurement of te crck opening displcement d; A termocouple for te mesurement of te temperture of te rebr; A CDD cmer for te cpturing of te imges of te zone of interest; A coil connected to ig frequency lterntive current genertor, nd generting t te level of te rebr n inductive current inducing temperture rise; A computer is used to collect nd nlyse ll informtions from te mesurements. Computer Specmien CDD cmer Coil LVD guge Figure 4 : Globl setup ISSN : Vol 4 No Apr-My 75

6 B. Mterils Te mteril used for te present test is mortr mde wit te mix weigt proportion of /.5/. respectively for te cement, wter nd snd, wit mximum ggregte size of 5mm Te initil crck ws obtined troug very tin plstic seet introduced in te formwork during te csting. Te mortr is crcterized by Young modulus E=GP, nd Poisson rtio =. nd =mm. Te rebr is crcterized by lengt b=mm corresponding to te tickness of te specimen, dimeter =mm, yield stress y = 5MP nd Young modulus E= GP. Te lengt of te initil crck is =55mm. C. Loding procedure A displcement is imposed to te concrete ccording to te figure, troug rdil expnsion of rebr embedded in te mortr. Te rebr expnsion is creted by imposing ig frequency current to te rebr troug coil. Tis ig frequency current cretes n inductive current inside te rebr wic is tis cse beve like sot circuit, inducing rpid increse of te temperture ccording to Frdy s induction lw. Te vrition of te temperture of te rebr induces vrition of its dimeter nd terefore te pressure t te level of te interfce between te rebr nd te concrete. Tis pressure is te only mecnicl lod involved in te test. Te plot of te crck opening displcement s function of time, gives n ide on te rte of vrition of te pressure on te concrete. D. Crck front pictures Te imges of te crck front re tken using CDD ultr rpid cmer wit frequency of one picture ec tirty seconds. Te sequence of imges depends of te estimted durtion of te test nd te cpcity of te computer rd disc. An incresing number of imges increses te time of imge correltion computtion nd needs evy memory spce. Figure 5 sows scemtic representtion of te zone of interest on te wole specimen. Figure 6 sows poto of zone of interest, tken before te beginning of te terml loding. Tis picture togeter wit te roller enble to convert numericl dimensions (pixels) nd usul metric units. It sows for tis prticulr cse tt 4 pixels correspond to 9.4mm mening tt one pixel equl to 7.8m. At ec imge tken corresponds vlue of crck opening displcement nd te time t wic it s been tken. It will ten be esy to nlyse te vrious pictures nd determine te criticl time tt mens te time of crck propgtion. Before tt time, energy under rebr expnsion pressure is elsticlly store in te concrete, nd te lengt of te crck, remins constnt, but te stress intensity fctor s well s te energy relese increses. Tis time correspond to te criticl vlues of te mteril crcking properties K IC nd G IC nd te pressure pc. Zone of displcement field observtion b Figure 5: Zone of cmer observtion Figure 6 : poto of te zone of interest ISSN : Vol 4 No Apr-My 76

7 4. RESULTS AND DISCUSSION Figure 7 sows for te first column te mes of te zone of interest, for te second, te strin field, nd te tird te displcement field of te zone. Te first line corresponds to stte of te zone before eting tt men undeformed field (see on figure 6). It is not possible to distinguis even en te position of te existing crck. Te second line corresponds to te stte t wic crck begin to propgte. Te time of crcking ere, correspond to 4 seconds. Figure 8 nd 9 sow respectively te mesured rte of eting nd te corresponding vrition of te mesures displcement during te experiment. Tose criticl vlues corresponds respectively to 6 C nd 5. - m. Wen te mximum cpcity of energy storge of te concrete is reced, crck propgtes. Te cpcity to stock elstic energy before crck propgtion depends on te mteril properties. Te elstic energy stored is trnsformed into crck extension. During te pse of crck propgtion, te crck opening displcement continues to increse under rebr expnsion, but no elstic energy is stored, but trnsformed into new surfce. Te reltion between te crck opening displcement, te crcking prmeters nd crck lengt become non liner. Figure 7 : Mes, strin field nd displcement field of te zone of interest Before loding nd t crck propgtion Figure 8 : Rte of eting during te test ISSN : Vol 4 No Apr-My 77

8 Figure 9 : Rte of displcement On figure nd re sown respectively te vrition of stress intensity fctor nd te corresponding energy relese rte, computed from mesured vlues of time nd displcement, togeter wit equtions (9) nd (). Te vlues obtined re in te order of mgnitude of te ones usully founded in te literture[,4,5 ].Figure nd sow respectively te evolution of te resultnt force nd te contct pressure round te rebr, computed from eqution () nd () togeter wit te mesured vlue of te displcementnd te time. As te temperture rises, te pressure round te rebr increses leding to mode I loding. Tble summrize te vrious criticl vlues obtin from te present test. Prmeter Time to Crcking(s) Tble : Vrious prmeters obtined from te test Temperture t crcking( C) Displcement t crcking (m) GIC (J/m) KIC MP m Pc (N) Pc (MP) Vlue ISSN : Vol 4 No Apr-My 78

9 Figure : Evolution of te Stress intensity fctor wit time of eting Figure : Evolution of te energy relese wit te time of eting ISSN : Vol 4 No Apr-My 79

10 Figure : Evolution of te equivlent force P wit te time of eting t te level of te rebr Figure : Evolution of te pressure p round te rebr wit te time of eting IV. CONCLUSION Using te mgnetic properties of iron togeter wit Frdy s lw of induction eting nd imge correltion nlysis, tis study ve presented new metod to determine frcturing properties of concrete. Tis experimentl pproc enbles to: Correltes concrete frcture properties of concrete wit te expnsion of te rebr expnsion in reinforced concrete structures under eting; Gives n estimtion of te pressure s well s equivlent force cting on te concrete round te reinforcement during fire process; Estimtes te vlue of te criticl energy relese s well s te frcture tougness troug induction eting. ISSN : Vol 4 No Apr-My 8

11 In te usul frcture mecnic test very evy pprtus re used nd one needs generlly mny smples to ve n estimtion of te frcturing properties of concrete. In te present pproc, te smples re very smll in size, te pprtus is very simple nd n order of mgnitude of te mteril cn be obtined from one specimen. One oter dvntge of te metod is te possibility to conduct two or more tests t te sme time from te sme ig frequency genertor if mny cmers nd displcement tools mesurement system re vilble. REFERENCES [] Koisi Mekw, Tessuy nd Tosiru Kisi, Multiscle Modelling of Concrete Performnce, Journl of Advnce Concrete Tecnology, Vol., N, pp. 9-6, July. [] Tn Qung Ngueyen, Etudes expérimentles et téoriques de l effet de l corrosion sur l fissurtion du béton et le comportement globl des structures en béton rmé, PHD tesis, Université de Pris 6, Octobre 6 [] X. H. Wng nd X. L. Liu, Modeling effects of corrosion on cover crcking nd bond of reinforced Concrete, Mgzine of Concrete reserc 56, N 4, pp. 9-99, my 4. [4] Hny Abdll, Concrete Cover Requirements for FRP reinforced Members in Hot Climtes, Composites Structures, 7, pp. 6-69, 6. [5] P.J Sullivn, Deteriortion nd Spling of Hig Strengt Concrete under fire, Offsore Tecnology Report, /74, United Kingdom. [6] Nestore Glti, Bryn Vollintine, Antonio Nnni, Lokeswrpp R. Drni, Mri Antoinett Aiello, Terml effects on bond between FRP rebrs nd Concrete, ttp:// [7] Rdoune M., Ali Zdi nd Ptrick G., Trnsverse Terml Expnsion of FRP rebrs Embedded in Concrete, Journl of Composite in Construction, Vol. 9, issue 5, pp , September-October 5. [8] Andrs Szekrenyes, Josef Uj, Advnced bem model for fibres bridging in unidirectionl composite double cntolever bem specimen, Engineering Frcture Mecnics, 7, pp , 5. [9] Miln Jisek nd Borek Pzk, Models for qusibrittle filure: teoreticl nd computtionl spects, ECCOM-, Europen Conference on Computtionl Mecnics, june 6-9, Polnd [] Yu-Ceng Kn, Kung-Ci Pei, Cien-Lung Cng, Strengt nd Frcture Tougness of evy Concrete wit vrious iron Aggregte Inclusion, Nucler engineering nd Design, 8, pp. 9-7, 4. [] J. Olivier, A. Huesk, M. D. G. Publido nd S. Blnco, Computtionl Modelling of Crcking of Concrete in strong discontinuity setting, Computer nd Concrete, Vol., N, pp. 6-76,. [] T. Suzuki et l., Study on te degrdtion of concrete Crcteristics in te ig Temperture environment, Concrete Under Severe Conditions: Environment nd Loding,. pp. 9-9, E&FN Spon Publisers(995) [] Frnçois Hild nd Stépne Roux, Mesuring Stress Intensity Fctor wit Cmer: Intergreted Digitl Correltion (I-DIC), C.R. Mécnique, 4(6), pp. 8- [4] Yingwu Xu, Pizong Qio nd Julio F. Dvlos, Explortory Evlution of Mode I frcture Tougness of Concrete-composite bonded Interfces, 5 t ASCE Engineering Mecnics Conference, june -5, Columbi University, New York,. [5] Artur Dziedzic, Structurl control on Frcture Tougness(brittle crcking) in Krosnosndstone of Musrz, Soutern Polnd, Geologicl Quterly, 47(), pp. -8,. ISSN : Vol 4 No Apr-My 8