EFFECTIVENESS AND OPTIMIZATION OF FIBER BRAGG GRATING SENSOR AS EMBEDDED STRAIN SENSOR

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1 EFFECTIVENESS AND OPTIMIZATION OF FIBE BAGG GATING SENSO AS EMBEDDED STAIN SENSO Xiaoming Tao, Liqun Tang,, Chung-Loong Choy Institut of Txtils and Clothing, Matrials sarh Cntr, Th Hong Kong Polythni Univrsity Dpt. of Enginring Mhanis, Traffi and Communiations Collg, South China Univrsity of Thnology SUMMAY: Th strain fild of a host with an mbddd opti fibr is analyd undr a uniform thr-prinipal strain load on th host in ordr to study th masurmnt fftivnss of fibr Bragg grating snsor (FBGS) as mbddd strain snsor. Thr indiators ar dfind to dpit th strain masurmnt fftivnss of a fibr Bragg grating snsor mbddd in a host. Th numrial rsults rprsnt th strain distributions in th host, oating and opti fibr as funtions of th lasti modulus of oating and th gomtrial paramtrs of th host. Th ffts of ths paramtrs on th masurmnt fftivnss indiators ar also studid and th optimal valus of ths paramtrs ar suggstd. KEYWODS: fibr Bragg grating snsor, fftivnss, optimiation, smart matrials. INTODUCTION Th fibr Bragg grating snsors (FBGSs) now hav attratd mor and mor attntion as mbddd snsors to monitor or masur th intrnal strain of omposit struturs [-6]. By using FBGS, th strain is dtrmind by masuring th shift of th Bragg wavlngth of th rfltiv wav pak from th gratings in th opti fibr, λ, whih is dirtly rlatd with th axial strain, ε, of th opti fibr. Whn mbddd in a host, th FBGS an b usd to masur th intrnal strain of th host. Prvious analysis [-5] showd that th snsitivity fator f btwn λ and ε is not a onstant but a funtion of th ratio of th transvrs strain ovr th axial strain. Without onsidring tmpratur fft, th rlationship an b xprssd blow: λ = fε () λ and n ε f = [ P + ( P + P ) υ ], υ = () ε whr ε is th transvrs strain of th opti fibr whn th strains in th two transvrs dirtions ar uniform; P, P ar th strain-opti onstants of opti fibr; and υ is th fftiv Poisson ratio (EP).

2 If thr is no rstrition in th transvrs dirtion of th opti fibr, thus υ is qual to th Poisson ratio (P)υ of th fibr, thn f is a onstant whih has th valu rommndd by many FBGS s manufaturrs. Howvr whn mbddd in a host, an opti fibr may b subjtd to for/dformation in its transvrs dirtions. Th fftiv Poisson ratio, υ, may not b takn as th Poisson ratio of opti fibr or vn a onstant [5]. On may assum that th opti fibr s axial strain is qual to that of host in th opti fibr dirtion, whih implis that th prsn of th mbddd FBGS has no or littl fft on th strain distribution of th host and what th snsor masurs should b th strain of th host without th snsor. In ral situations, thrfor, thr ar thr issus ritial to th masurmnt fftivnss of an mbddd FBGS: ()whthr th fft of mbddd opti fibr on th initial host strain fild is ngligibl; () whthr th opti fibr s axial strain is los nough to that of host in th opti fibr axial dirtion; and () whthr EP υ an b rgardd as a onstant during th masurmnt. If EP is a onstant but not qual to υ, it is nssary to alibrat th snsor in ordr to dtrmin th valu of f aftr it is mbddd into a host. Many authors studid th strss onntration indud by th mbddd fibr opti snsors [7-] whr th optimal paramtrs, suh as th oating s modulus and thiknss, wr onsidrd for th rdution of th onntration in th fibr ross stion plan. Most of th qustions on th masurmnt fftivnss rmain unanswrd. Hn, this papr is intndd to addrss th thr issus of th masurmnt fftivnss of mbddd FBGS for both th axial and transvrs strains.. THEE-LAYE COMPOSITE AND NUMEICAL MODELING A as study was ondutd by applying a uniform thr-prinipal load to a host with mbddd fibr snsor, thn xamining th masurmnt fftivnss of mbddd FBGS by solving th strain fild of th omposit omprising host, oating and opti fibr. For a homognous and isotropi matrial, th simpl way to apply a uniform thr prinipal load on th matrial is to apply a thrmal load on it, and th prinipal strain of th matrial is qual to th thrmal xpansionary strain. Hr it is should b mphasid that th thrmal load is applid to th host only. Th opti-fibr-host systm an b illustratd as a omposit omprising a ylindrial fibr and two onntri shll layrs, with fibr, oating and host arrangd from th ntr to th out surfa (Fig.). Th hight of th omposit ylindr is H, th radius of fibr is, whih is also th intr radius of oating, is th outr radius of oating and th intr radius of host, is th out radius of th host. Th following basi assumptions hav bn mad so that th as an b simplifid as an axial-symmtri problm: () Th optial fibr, oating of fibr and host ar linar lasti and isotropi; () Th thrmal xpansion offiints of fibr, oating and host ar onstants; () Thr is no disontinuity in th displamnts at th intrfas of fibr and oating, oating and host undr th loading ondition; (4) Thrmal load is uniform in th whol ylindrial shll host.

3 H r Fig. : Gomtry and FE modl of th thr-layrd omposit. Th finit lmnt (FE) analysis was applid by using a ommrial program ABAQUS. Four-nod bilinar lmnts (CAX4) wr usd to gnrat mshs. Baus of th symmtry to th r axis, only half of th ylindr was onsidrd for th strain analysis. Th boundary onditions ar u r= = and v = =, whr u, v ar th displamnts along th r, dirtion rsptivly. Th matrial onstants and dimnsions ar listd in Tabl : Tabl : Th matrial onstants and dimnsions usd for omputation Paramtr Fibr Coating Host E (GPa) , υ α ( -6 / C).8 (mm).6 (mm). (mm).-,. H (mm) -9, E, υ and α ar th lasti modulus, Poisson s ratio and thrmal xpansion offiint rsptivly, subsripts h,, f rprsnt fibr, oating and host, rsptivly. Th host paramtrs ar thos of polystr. Th valus with ar th dfault valus, som of thm wr providd by ommrial supplirs.. NUMEICAL ESULTS AND ANALYSIS A thrmal load of T =5 C was applid to th host only. Without th mbddd fibr, th strain fild should b uniform in th host and qual to: ε = α h T =.5 () Th strain in th fibr axial dirtion, ε, is th most important trm in our disussion and its normalid trm,, will b usd in th rst of this stion unlss statd, whih is givn by: = ε / ε (4). Distributions of normalid strain and EP Figurs, and 4 illustrat th normalid strain distributions in th fibr, host and oating, rsptivly. Th strains, alulatd by using th dfault valus in Tabl, ar in th fibr axial dirtion and xprssd as funtions of radius r as wll as th omposit half hight. Fig. shows that th normalid strain of fibr dlins with th inrasing lngth. As th middl part of th opti fibr is rstritd mor than th parts nar two nds, th strain of middl opti fibr is losr to that of th host without mbddd fibr snsor ( = ). Th

4 strain distribution urvs ar idntial rgardlss th radial position in th fibr, thus th strain of fibr an b rgardd as a funtion of only. Fig. shows rvrs trnds of strain distribution in th host along th hight dirtion. Th strain lvl of th middl host is lowr than that of th host nar th boundary, whih is baus th middl host is rstritd mor by th fibr and th hosts nar boundary an xpans mor frly undr a thrmal load. Th normalid strain valus of th host ar vry los to (.995 < < ), whih implis that th host with mbddd fibr snsor has a strain fild vry los to that without mbddd opti fibr. Baus of its lowr lasti modulus in this as, th strain distribution of th oating is signifiantly afftd by both th (mm) (mm) 8 Fig. Distribution of fibr s axial strain. Fig. Distribution of host s axial strain. fibr and host, as shown in Fig.4. Th strain distribution along th is similar with that of th fibr whn r approahs, and th strain nar th outr surfa of oating varis littl along lik that of host. Th distribution of EP is shown in Fig.5, whr EP, υ, is plottd against with r as a paramtrs. Th EP has littl variation insid of th opti fibr (mm) υ (mm) Fig.4: Distribution of oating s axial strain. Fig.5: Distribution of fibr s fftiv Poisson s ratio along th fibr lngth.. Thr indiators of th masurmnt fftivnss of FBGS In ordr to dpit th thr issus of th masurmnt fftivnss quantitativly, in this stion, w will introdu thr indiators. Th rlativ rror, th fftiv fibrhost strain ratio β, and th fftiv Poisson s ratio EP-P ratioυ ar dfind as follow: () Max rlativ rror is dfind as th imum rlativ rror of th strain of th host

5 with mbddd fibr with rspt to that without mbddd fibr, i..: ε ε = Max( ) (5) ε () Baus th axial strain of opti fibr is uniform in its ross stion, as disussd in Stion., lt f b th fibr axial strain, in h b th host strain nar th oating, thn th fibr-host strain ratio an b dfind as: f S fh = (6) in Howvr, S fh varis signifiantly along (Fig. 6) with a similar trnd to th fibr s axial strain. Hn w us a hight H 95 whr th S fh dlins to.95. Th physial maning of H 95 is that only within th rang of < H 95 th strain of opti fibr an rprsnt that of host fftivly, with a imum diffrn of 5%. Using this hight, now th nw fibr-host strain ratio β is dfind by: β = (7) H β rflts th proportion of an opti fibr insid of host suitabl for snsing within th spifid imum diffrn of 5%. () Baus th EP varis littl along, as shown in Figur 5, w simply dfin th ratio of th fftiv Poisson s ratio to Poisson s ratio (EP-P ratio) υ as th EP at = ovr th Poisson s ratio of th fibr, i..: υ ( = ) υ = (8) Following th dfinitions of valus of, β and as wll as highr valus of β and υ. h H 95. Fators influning th masurmnt fftivnss indiators υ υ, an fftiv mbddd FBGS dmands lowr Thr fators hav bn invstigatd inluding th oating lasti modulus thiknss (rlatd ) and hight H of host (lngth of opti fibr insid host). E, host s In ordr to obtain a ompltd pitur of thir ffts on th fftivnss indiators and to idntify th optimal valus of paramtrs, w lt th thr fators vary in thir own rangs as listd in Tabl. Furthrmor, th fft of th host lasti modulus E h on th fftivnss is xamind with othr paramtrs taking dfault valus. Fig.6 Distribution of fibr strain ratio along fibr lngth...8 S.6 fh (m m )

6 .. Maximum rlativ rror Th numrial analysis indiat that th imum rlativ rror is not snsitiv to th host s lngth H (> m), whn th host out radius >. mm. An xampl an b sn in Fig.7 with taking th dfault valu of mm. inrass with th lasti modulus of oating gradually, and dlins rapidly with inrmnt of th thiknss of host spially whn th host is thin (Fig.8) ,,5,,5, -,5 - -,5,5,5 Log( E ) (GPa) Whil smallr than %. Whn Fig.7 : Maximum rlativ rror. E taks its dfault valu (.45GPa), with >mm, th imum rlativ rror is E rahs GPa, with >.7mm, is still smallr than %. Thrfor it am b onludd that th influn of opti fibr on th host strain fild is small and an b ngligibl in gnral ass Log( E ) (GPa) Fig.8 : Maximum rlativ rror... Fibr-host strain ratio β β is indpndnt of th host s thiknss ( >.). An xampl an b sn in Fig.9 with H taking th dfault valu. β inrass with th inrmnt in oating lasti modulus E or host s hight H, as shown in Figur. E = GPa sms a thrshold valu baus aftr that point th urvs rah thir platau and th fft of E on β boms vry small. Th thrshold valu is β >.85 for all th hights, H > mm, undr th urrnt invstigation. If th dfault valu E =.45 GPa is hosn, th hight H has to b mor than 5 mm to nsur β >.85.

7 β Log( E ) (GPa) Fig.9: Fibr-host strain ratio against th oating lasti modulus with outr radius of host as a paramtr β Log( E ) (GPa) Fig.: Fibr-host strain ratio against th oating lasti modulus with hight of host as a paramtr... EP-P ratioυ Having a similar proprty to that of fibr-host strain ratio β, υ drass as th oating lasti modulus inrass but it has a small rlation with th host s thiknss (.) whn H > mm. An xampl an b sn in Fig. with th dfault valus. υ dlins with th inrmnt of th oating lasti modulus E. Th largr E auss mor oupling of th host s strain into th transvrs strain of opti fibr, howvr, th urv varis gntly whn E GPa. Th diffrn btwn th urvs bom largr whn E >GPa. Thn th small ffts of and H on υ bom visibl (Fig., Fig.) υ Log( E ) (GPa) Fig.: EP-P ratio against th oating lasti modulus with outr radius of host as a paramtr. From Figur, with a dfault valu of E =.45 GPa, υ =. This implis that thr is no host s strain to b oupld into th fibr s transvrs strain vn th host s transvrs strain has th sam quantity as th fibr axial strain. Thrfor, w an us th valu of snsitivity fator f, drivd from th thortial prdition, in our masurmnt without orrtion.

8 υ Log( E ) (GPa) Fig.: EP-P ratio against th oating lasti modulus with hight of host as a paramtr. From Eqn, w an driv two spial ass as follow: () No strain oupling: υ = υ, f =. 798, () With strain oupling: υ υ υ =., f =. 78 = whr from Figur, if E = GPa, and H = mm, thn υ =.776. Th matrial proprtis of opti fibr ar givn in Tabl. Tabl : Matrial paramtrs of opti fibr. Strain-opti offiint Indx of rfration Elasti modulus Poisson s ratio P P n E (GPa) υ Th rlativ rror btwn th fator with and without strain oupling is smallr than %. Thrfor E = GPa is a good thrshold valu for all th thr indiators of th masurmnt fftivnss, that is,, β, and υ. Howvr if E = 45Gpa, whih is th sam as that of th host, thn υ =, aording to Fig,. Th snsitivity fator f is qual to.666. In this as how to alibrat th snsor aftr it is mbddd into th host boms an important problm. In prati, it is vry diffiult to us th oating with suh high lasti modulus. But somtims, th host may prmat into th oating during th produr of mbdding th snsor whn th host is in stat of liquid (suh as polystr, poxy), whih will inras th oating s lasti modulus vidntly. 4. CONCLUSION Th prsnt numrial analysis on th strain fild of th thr-layr omposit omprising a host with an mbddd opti fibr draws som onlusions as follow: () A thik host and a larg mbddd lngth of an opti fibr will improv th masurmnt fftivnss of th mbddd opti snsor. () A high lasti modulus E of oating is bnfiial for improving th fftiv fibr-host strain ratio β, but this positiv fft is ount-baland by a high valu of th imum

9 rlativ rror and a larg variation in th EP-P ratioυ valu. By onsidring th thr fftivnss indiators togthr, an optimal valu of th oating lasti modulus, E =Gpa, is rommndd to ahiv th optimal masurmnt prforman of FBGS. () Should th host rsin prmat into th oating during th mbdding produr, th oating lasti modulus of FBGS might inras signifiantly and th FBGS would b usd in a ompliatd strss status. Car should b takn to hoos th suitabl valu of th snsitivity fator f, or it might b nssary to alibrat th mbddd FBGS. (4) Within th rang of th dfault paramtrs usd, th fft of mbddd FBGS on th initial strain fild of a host is ngligibl, xpt that th host s diamtr is vry small (ompatibl with that of oating). Th strain of FBGS annot rprsnt that of th host stion in whih th fibr is mbddd, only at th portion far away from th boundary of host is suitabl for th masurmnt. Th longr th mbddd FBGS is, th largr proportion of th usabl portion of th fibr. Th dfault valu of snsitivity fator f an b usd in this as. Aknowldgmnts W would lik to aknowldg th Hong Kong Univrsity sarh Grant Counil for supporting this work, whih was arrid out at th Hong Kong Polythni Univrsity. frns. Du W. C., Tao X. M., Tam H. Y., Choy C. L. Optial Fibr Bragg Grating Snsors In Smart Txtil Strutural Composit. Prodings of th 4th Intrnational Confrn on Composit Enginring, ICCE/4, Hawaii, USA, 997, Eri Udd. Fibr Opti Snsor Ovrviw. Fibr Opti Smart Struturs, Ed: Eri Udd, John Wily & Sons In, Masurs. M. Fibr Opti Strain Snsing. Fibr Opti Smart Struturs, Ed: Eri Udd, John Wily & Sons In, Jakson D. A., Jons J.D.C. Fibr Opti Snsors. Pot Ata 986,, Tao X. M., Tang L. Q., Du W. C., Choy C. L. Intrnal strain masurmnt by fibr Bragg grating snsors in txtil omposits. Submittd to J Composit Sin and Thnology 6. Buttr C. D., Hokr G P. Fibr Optis Strain Gaug. Appl Opt, 99, 7, Sirkis J. S., Dasgupta A. Optimal Coating for Intllignt Strutur Fibr Optial Snsors. Prodings of th SPIE, 99, 7, Pak Y. E., Dyys V., Shmutr E. S. Miromhanis of Fibr Opti Snsors. Prodings of th ADPA/AIAA/ASME/ SPIE Confrn, 99, Madsn J. S., Jardin A. P., Milunas. J., Tobin A, Pak Y E. Efft of Coating Charatristis on Strain Transfr In Embddd Fibr-Opti Snsors. Prodings of th SPIE, 99, 98, Hadjiproopiou M., d G. T., Hollaway L., Thorn A. M. Optimisation of Coating Proprtis for Fibr Opti Smart Struturs Using Finit Elmnt Analysis. Prodings of th SPIE, 995, 44, 9-.. Hadjiprooplou M., d G. T., Hollaway L, Thorn A M. Optimiation of Fibr Coating Proprtis for Fibr Opti Smart Struturs. Smart Matrials and Struturs, 996, 5(4), Lvin K., Nilsson S. Analysis of th Loal Strss Fild an a Composit Matrial with an Embddd EFPI-Snsor. Prodings of th SPIE, 994, 6: 79-8.

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