MODELING AND CHARACTERIZATION OF HONEYCOMB FRP SANDWICH BEAMS IN TORSION. Abstract

Transcription

1 MODELING AND CHARACTERIZATION OF HONEYCOMB FRP SANDWICH BEAMS IN TORSION Justin Robinson, WVU, Morgantown, WV Julio F. Davalos, WVU, Morgantown, WV Pizhong Qiao, U of Akron, Akron, OH Abstract Fibr rinforcd plastic (FRP) cllular panls hav bn incrasingly usd in highway bridgs, both in nw construction and rhabilitation and rplacmnt of xisting bridg dcks. Rcnt applications hav dmonstratd that honycomb FRP panls can b ffctivly and conomically usd for highway bridg dck systms. Howvr, thir mchanical proprtis and bhaviors hav not bn fully xplord. Thus, th objctiv of this study is to conduct a combind xprimntal and analytical invstigation of honycomb FRP sandwich bams subjctd indpndntly to bnding and torsion loads. Th mphasis of this papr is on torsion xprimnts and finit lmnt modling. Th sandwich panl considrd in this study has a sinusoidal cor gomtry in th plan xtnding vrtically btwn fac laminats, as shown in Figur 1. Th analyss of th honycomb structur and componnts includ: (1) constitunt matrials and ply proprtis, (2) fac laminat and cor wall nginring proprtis, and (3) quivalnt cor matrial proprtis. A homognization procss is usd to obtain th quivalnt cor matrial proprtis for th honycomb gomtry with sinusoidal wavs. Timosnko s bam thory combind with lamination thory is usd to analyz th bams in bnding, and finit lmnt modls of th tst sampls using layrd shll lmnts ar usd to corrlat rsults with bnding analytical prdictions and xprimntal rsults in bnding and torsion. To vrify th accuracy of th analytical and numrical solutions, svral honycomb sandwich bams with sinusoidal cor wavs ithr in th longitudinal or transvrs dirctions ar tstd in bnding and torsion. Th prsnt analysis and charactrization procdurs can b usd in dsign applications and optimization of honycomb structurs and to obtain quivalnt matrial proprtis of honycomb FRP bams with svral cor gomtris. Kywords: Honycomb FRP sandwich panl, Torsion, Finit lmnt modling Introduction Whil honycomb structurs ar commonly usd in th automotiv and arospac industris, thr ar only fw applications in civil infrastructur. Howvr, th rcnt fast growing intrst in composit matrials for th rhabilitation and nw construction of bridg dcks provids an xcllnt opportunity for dvlopmnt and implmntation of honycomb structurs. In gnral, bcaus of th rlativly low stiffnss of polymr composits (E-glass fibrs and polymr rsins), FRP structurs usually xhibit larg dformations, and thrfor, thir accurat rspons prdictions undr various loading conditions ar important. In particular, honycomb fibr-rinforcd plastic (HFRP) structurs hav bn succssfully applid in bridg construction, but thir mchanical proprtis hav not bn fully xplord. Th concpt of a lightwight and havy-duty FRP panl with a sinusoidal cor configuration in th plan xtnding vrtically btwn fac laminats (Figur 1) was introducd for highway bridg dcks by Plunktt (1997). Sinc thn, svral othr uss, including fish racway tanks (Davalos t al., 1

2 2002), hav bn xplord. Aftr valuating th favorabl charactristics of sandwich panls for bridg dcks and othr applications, svral studis for tsting and fild installations wr succssfully compltd. Howvr, th dsign modling and optimization of th HFRP structur was not rigorously undrtakn, partially du to th complx cor gomtry. In this study, an ovrviw of an approximat analytical solution vrifid by finit lmnt modling and xprimntal tsting of bam sampls in bnding is prsntd, and a dtaild xamination of bam sampls in torsion is givn, basd on finit lmnt analyss and xprimntal valuations. Transvrs Dirction, (y) Longitudinal Dirction, (x) Figur 1. Configuration of Honycomb FRP Sandwich Panl Modling Of Honycomb FRP Sandwich Panl In this sction, th gomtry and charactristics of th honycomb FRP sandwich panl ar prsntd. Equivalnt proprtis of fac laminats ar obtaind using micro/macromchanics modls, whil th ffctiv orthotropic proprtis of th honycomb cor ar obtaind from a homognization procss using combind nrgy mthod and mchanics of matrials approach (Davalos t al., 2001). Th HFRP panl considrd in this study was dvlopd by Kansas Structural Composits, Inc. (Plunktt, 1997), and th sandwich structur consists of two fac laminatd plats co-curd with a cor of sinusoidal configuration (Figur 1). This cor gomtry was concivd to incras th stiffnss and buckling capacity of th panl by continually supporting th fac laminats with th cor lmnts. Th cor gomtry consists of closd honycomb-typ clls, formd by a rptitiv combination of a flat componnt and a wavd componnt, which is dfind by a sinusoidal function (Figur 1). Th wavd componnt of th cor is manufacturd by forming FRP shts into a corrugatd mold. A plan viw of th cor is shown in Figur 2. For th sampls usd in this study, both th fac and cor laminats wr producd from E-glass fibrs and polystr rsin, and th total thicknss of th panl was approximatly fiv inchs. 2

3 4" Cor Sinusoidal Wavs t = 0.09" t 4" Cor Flats Figur 2. Plan Viw of Honycomb Sinusoidal Cor Modling of Fac Laminats Th nginring proprtis for th fac laminats ar obtaind from a micro/macromchanics approach. Using micromchanics, th stiffnss proprtis of ach layr, or ply, of th laminat can b prdictd, and basd on th ply proprtis and lay-up, th apparnt stiffnss of th laminat can b found using classical lamination thory (Davalos t al., 1996). Th fibr architctur of th top and bottom fac laminats is symmtric about th mid-plan of th sandwich panl. Each fac laminat includs th following typs of layrs: (1) a 0 /90 bidirctional stitchd fabric (CM-3205) togthr with continuous strand mat (ContSM), (2) a unidirctional layr (UM-1810) and a ContSM, and (3) a choppd strand mat (ChSM) bonding layr at th intrfac of th cor. Th lay-up for th fac laminat usd in this study, starting at th intrfac, consists of on ChSM bond layr, a CM-3205/ContSM layr, six layrs of th UM-1810/ContSM, and a final layr of CM-3205/ContSM. Th total fac panl thicknss is approximatly 0.43 inchs. Th layr stiffnss valus ar summarizd in Tabl 1, and furthr dtails can b found in Davalos t al. (2001) and Robinson t al. (2001). Tabl 1. Layr Stiffnss Proprtis Ply typ Orintation E 1,msi E 2,msi G 12,msi G 23,msi ν 12 ν 23 ChSM Bond Layr Random CM / CSM a Random Um CSM a Random Not: a rfrs to CSM layr attachd to prvious fabric. Th quivalnt lastic proprtis of th fac laminats ar computd from classical lamination thory. Using th ply proprtis found by micromchanics, a st of quivalnt laminat proprtis (E x, E y, G xy, ν xy ) can b dfind. Ths constants rprsnt an quivalnt orthotropic plat that bhavs in th sam mannr as th actual laminat undr in-plan loading. Th quivalnt lastic proprtis of th laminat ar summarizd in Tabl 2. 3

4 Tabl 2. Stiffnss Proprtis Of Fac Laminats E x, x10 6 psi E y, x10 6 psi ν xy G xy, x10 6 psi Modling of Honycomb Cor Th lastic quivalnc analysis of th sinusoidal-wavd honycomb cor structur (s Figurs 1 and 2), as givn by Davalos t al. (2001), is basd on a homognization concpt combind with an nrgy mthod and a mchanics of matrials approach. Th homognization procss of th priodic cor structur rquird dfining a Rprsntativ Volum Elmnt (RVE), for which th global proprtis wr obtaind by invoking priodic conditions and approximations. Th honycomb cor was producd from ChSM, with a thicknss of t=0.09 (s Figur 2), and its quivalnt proprtis ar givn in Tabl 3, whr th in-plan coordinats x-y ar shown in Figur 1. Whil xact solutions ar obtaind for Young s moduli using mchanics of matrials approach, th valuation of shar stiffnsss usually involv complx analyss with uppr and lowr bounds drivd from an nrgy mthod, but as shown in Tabl 3, th bounds for out-of-plan shar moduli ar within a narrow rang, and thrfor, th lowr bound can b consrvativly usd. Tabl 3. Elastic Equivalnt Proprtis For Honycomb Cor Cor wall proprtis: E s 1 = E s 2 = 1.71 x 10 6 psi; G s 12 = x 10 6 psi Young s Moduli E x E y E z s E x10-5 s E 1 s E 2 Shar Moduli G xy G xz G yz Uppr bound 5.98x10-5 s E 1 s G 12 s G 12 Lowr bound 5.98x10-5 s E 1 s G 12 s G 12 Poisson s Ratios v xy v xz v yz x10-4 Not: rfrs to quantitis with quivalnt proprtis; s rfrs to quantitis of cor matrial proprtis. 4

5 Ovrviw Of HFPR Bams In Bnding An ovrviw of rsponss and prdictions for HFRP bam sampls in bnding is prsntd in this sction. Comparisons of finit lmnt and analytical rsults with xprimntal valuations ar usd to validat th quivalnt matrial proprtis givn in th prcding sction. Tabls 4 and 5 prsnt comparisons of midspan dflctions and tnsil strains for longitudinal and transvrs bam sampls undr thr- and four-point bnding. Furthr information and dtails about th bnding study ar givn by Robinson t al. (2001), Davalos t al. (2001) and Robinson (2001). Th finit lmnt and analytical prdictions of displacmnts compar wll with th xprimntal valus, with th transvrs sampls showing smallr diffrncs. Th rang of prcnt diffrnc from xprimntal valus for th longitudinal sampls is btwn 6 to 20%, with th actual gomtry finit lmnt modls showing smallr discrpancis. Th transvrs sampls show a lowr prcntag diffrnc from xprimntal dflction valus, with a maximum diffrnc of 10%. Th prdictions of th midspan tnsil strains show largr prcntag diffrncs than thos of th dflctions. Th most favorabl prdictions for th longitudinal sampls wr found using th actual gomtry finit lmnt modl. Howvr, for th transvrs bams, ach of th numrical and analytical modls prdictd th strains wll. Tabl 4. Comparison of Midspan Dflctions for HFRP Bam Sampls Cor Span, Width, Bnding Dflction, in./kip Orintation ft inchs Typ Exp. FE Modl Analytical Actual 1/2 % 1/2 % 1/2 % from Span Span Exp. Span Exp. Span Exp. 15.0' 12" 3-point point " 3-point point ' 12" 3-point point Longitudinal 8" 3-point point ' 12" 3-point point " 3-point point ' 12" 3-point " 3-point ' 12" 3-point point Transvrs 8" 3-point point ' 12" 3-point " 3-point

6 Tabl 5. Comparison of Midspan Tnsil Strains for HFRP Bam Sampls Cor Span, Width, Bnding Midspan, microstrain/kip Orintation ft inchs Typ Exp. FE Modls Analytical Actual Equivalnt Strain Strain % from Strain % from Strain % from Exp. Exp. Exp. 15.0' 12" 3-point point " 3-point point ' 12" 3-point point Longitudinal 8" 3-point point ' 12" 3-point point " 3-point point ' 12" 3-point " 3-point ' 12" 3-point point Transvrs 8" 3-point point ' 12" 3-point " 3-point A possibl rason for th diffrncs btwn xprimntal valus and analytical and numrical prdictions for th longitudinal sampls may b du to discontinuitis at th intrfac bond btwn th cor and fac shts. Also, an xamination of th data for th longitudinal sampls lads us to conclud that th prdiction of quivalnt longitudinal out-of-plan shar stiffnss nds furthr rfinmnt. This problm plays a mor significant rol in th torsion rsponss, as discussd furthr in th following sction. Charactrization Of HFRP Bams In Torsion Analytical modls ar valuabl for dscribing rsponss of th HFRP bam sampls considrd in this study. Howvr, du to th complx gomtry of th sandwich panl, a closd-form solution for torsion is not availabl at this tim. Thus, an xprimntal study is prsntd, supplmntd by a finit lmnt analysis to valuat th rspons of th sampls in torsion. Exprimntal Study Exprimntal tsting of bam sampls is conductd to vrify finit lmnt rsults. Longitudinal and transvrs sampls ar instrumntd and loadd in torsion, as dscribd blow. Th machin usd to xprimntally tst sampls in torsion was dsignd by a formr graduat studnt at Wst Virginia Univrsity, who providd dsign dtails in his thsis (Brokaw, 1992). A diagram of th torsion machin 6

7 is shown in Figur 3. To sttablish confidnc on th accuracy of th xprimntal rsults, th torsion machin was fist calibratd using an aluminum bar. Location of LVDTs Gag lngth bam sampl Turnbuckl Countr-Balanc Support bam Load fram Torsion grip Hydraulic jack Load bam Figur 3. Torsion Machin Th calibration of th machin had two objctivs: (1) to xprimntally masur th angl of rotation and prdict its valu from St. Vnant s solution, using th applid torqu and publishd shar modulus; and (2) to crat a finit lmnt modl of th aluminum bar and compar its rsponss with th xprimntal rsults for angl of rotation. Th angl of rotation rsults for th aluminum bar at th gaug lngth of L = 36 ar givn in Tabl 6, whr th prcnt diffrncs btwn th analytical and finit lmnt prdictions with th avrag xprimntal rsult ar, rspctivly, 7.5% and 2.7%. Ths small prcnt diffrncs providd confidnc to procd with th FE modling and th xprimntal tsting of th HFRP sampls.. Tabl 6. Summary of Angl of Rotation for th Aluminum Bar Analytical Prdiction Finit Elmnt Prdiction Exprimntal Rsults, Avrag Angl of Rotation, radians/kip-in Th sampls usd in th xprimntal valuation includ thr with longitudinal cor orintation (on 12-inch wid and two 8-inchs wid) that ar tn ft long, and four with transvrs cor orintation (two 12-inchs wid and two 8-inchs wid) that ar nin ft long. Th bams ar instrumntd with two shar strain gags (±45 to rcord shar strain) and with four linar voltag diffrntial transducrs (LVDT s), which ar usd to dtrmin angl of rotation. Two LVDT s ar placd on ach sid of th bam at a distanc of 3-ft from th midspan in th dirction of th nd- 7

8 support, and ach of th two LVDT s is suspndd from a rod xtnding 24 inchs normal to th bam as shown in Figur 4. Th torqu is applid to th sampl by a hydraulic jack, which applis a forc to th load bam, against th raction at th support bam (Figur 3). Th load is transfrrd diagonally to th turnbuckls, which in turn, caus th nds of th bam sampl to rotat opposit to ach othr. Idally, th cntr of th bam sampl would hav absolutly no rotation, thus simulating a fixd boundary condition at th midspan. Th rcordd valus ar load and dflctions, which ar thn convrtd to applid torqu and inducd angl of rotation, rspctivly. Rod Suspnding LVDT S Figur 4. Exprimntal Arrangmnt for HFRP Bam Sampls in Torsion Exprimntal valus of angl of rotation ar givn in Tabl 7, whr ach rsult is obtaind from th tangnt of th avrag angl, which found by taking th avrag of th absolut valus of th four dflctions (two at ach nd) and dividing that numbr by th distanc btwn th cntr width of th bam and th nd of th rod holding th LVDT cor (Figur 4). Rsults ar givn in radians pr kipinch. Shar strain valus ar shown in Tabl 8 as micro strains pr kip-inch. Finit Elmnt Modling Finit lmnt analyss ar prformd to prdict th rsponss of th svral bam sampls usd in th xprimntal study. Th rsults ar thn compard with th xprimntal valus. As with th bams in bnding, thr ar two typs of modls producd for xamination. Th actual gomtry modls ar cratd with appropriat cor orintations and sampl widths using layrd shll lmnts to rplicat th actual gomtry of th sampls. Th lngth of ach modl is thr ft, which is on-half of th gaug lngth usd in th xprimntal tsting. A fixd-fr boundary condition is assumd in th modl, with all of th nods at on nd compltly constraind, whil only th cntr nod at th othr nd is prvntd to translat normal to th gomtric cross-sctional axis. This is to prvnt out-of- 8

9 plan bnding. Th torqu is applid using a coupld traction loading on th top and bottom dg nods of th fr nd of th modl. Th amount of torqu applid is 1 kip-inch. Th shar strain data can b obtaind at th point of intrst by simply xamining th nodal avrag of th strains. Howvr, th task of finding th angl of rotation is not so simpl. Th latral displacmnts in th width dirction of th cntr nods of th top and bottom plats can b usd to dfin a right triangl, and using small-angl thory, th sum of thir displacmnts can b dividd by thir vrtical distanc to giv th angl of twist (Robinson, 2001). Th valus of intrst ar givn in tabls 7 and 8. A displacmnt contour of a typical actual gomtry modl is givn in Figur 5. Th FE quivalnt plat modl consists of 3-layr shll lmnts with matrial proprtis dfind by th quivalnt orthotropic valus. Th ovrall dimnsions of th modls ar th sam with rspct to th actual gomtry modls, and th sam fixd-fr boundary condition is usd, with th cntr nod at th fr-nd constraind against out-of-plan translations. A torqu of 1 kip-inch is applid by using two coupld, nodal loads at opposit dgs of th fr nd. Th angl of rotation and shar strains of intrst can b dirctly obtaind from th modl at th location of intrst. Th valus of intrst ar also givn in tabls 7 and 8. Discussion of Torsion Rsults Th comparisons for th longitudinal sampls show larg prcnt diffrncs btwn th finit lmnt modls and xprimntal rsults. Thr ar svral possibl rasons for this discrpancy. First, it could b du to tsting inaccuracis. Th torsion tst procdur is difficult to implmnt, and any small rrors could influnc th rsults gratly. Scond, th obsrvd lack of consistncy in th manufacturing quality of th sampls probably affctd th tsting rsults. A srious problm that was obsrvd during th torsion tsts was som dlamination of th fac-sht from th cor. This problm was particularly vidnt for th 12-inch wid and #2 8-inch wid longitudinal sampls; thus th masurd torsional rsponss for ths sampls ar likly to b in rror with rspct to th FE rsults. Anothr possibl sourc of rror in th analysis could b th inaccuracy of th longitudinal outof-plan shar stiffnss. As can b sn in Tabl 7, th actual and quivalnt-plat finit lmnt modls for th longitudinal sampls prdict stiffr rsponss than xprimntally masurd, whil for th transvrs sampls th prcnt diffrncs ar rasonabl. 9

10 Figur 5. Displacmnt Contour for 8 Transvrs Sampl in Torsion Tabl 7. Comparison of FE and Exprimntal Valus of Angls of Rotation Cor Orintation Longitudinal Transvrs Width Sampl Angl of Rotation, radians/kip-in FE FE Exp. Actual Equiv. % Diffrnc of FE Actual and FE Equivalnt % Diffrnc of Exp. and FE Actual 12" # " # # " # # " # # Tabl 8. Comparison of FE and Exprimntal Valus of Shar Strains Cor Orintation Longitudinal Transvrs Width Sampl Shar Strain, microstrain/kip-in. FE Modl Exprimntal Actual Equiv. #1 #2 % Diffrnc of FE Actual and FE % Diffrnc of Exp. and FE Actual Equiv. #1 #2 12" # " 12" 8" # # # # # #

11 In gnral, it is a difficult task to obtain shar strain valus at a point from th FE rsults, du to th complxity of th gomtry, but it can b sn from Tabl 8 that th actual FE modls provid bttr corrlations with xprimntal valus than th quivalnt-plat modls. With th xcption of th #1 8- inch wid longitudinal sampl, rlativly small prcnt diffrncs ar found btwn th actual FE modls and th xprimntal rsults. Howvr, th quivalnt-plat FE modls show largr prcnt diffrncs, spcially for th longitudinal sampls. Again, this could b du to ithr manufacturing irrgularitis or inaccurat stimations of th longitudinal out-of-plan shar stiffnss proprtis. Th quality of manufacturing has an important rol in dvloping intgral bond btwn th top and/or bottom fac plats and th cor, and th strngth of th intrfac bond is much mor critical for a torsion loading condition. It was noticd that som dlamination btwn th cor and fac plats had occurrd prior to as wll as during th torsional loading. This dlamination could caus th torsional stiffnss to dcras. Howvr, th finit lmnt modl assums a prfct contact btwn cor and fac plats, and thus givs a highr stiffnss. It should also b notd that during bnding, th shar ffcts ar small. Evn if som portion of th cor had dlaminatd from th fac plats, th top and bottom fac plats, which act as bam flangs, ar still hld at th sam locations away from th nutral axis, thus still ffctivly carrying th bnding momnt. In contrast, during torsional loading of th HFRP sandwich bams, th dominant proprtis that influnc torsional rigidity ar th in-plan and out-of-plan shar stiffnsss which ar quit snsitiv to dlamination ffcts. Conclusion W prsnt in this papr a combind analytical and xprimntal charactrization of honycomb fibr-rinforcd plastic bams undr bnding and torsion, with mphasis on xprimntal procdurs and numrical modling for torsional loading. Th cor consists of in-plan sinusoidal clls xtnding vrtically btwn top and bottom fac laminats. Whil th xprimntal rsults corrlat rasonably wll with finit lmnt prdictions, rfinmnts in manufacturing quality and prdictions of quivalnt out-of-plan shar stiffnss proprtis could incras th accuracy of th corrlations. Thus, a furthr study of shar ffcts by a closd-form solution and using bttr stimats of shar moduli proprtis is a topic of furthr rsarch by th prsnt authors. Acknowldgmnt Th tst sampls wr gnrously providd by Kansas Structural Composits Inc. (KSCI), and w thank th KSCI's Prsidnt Dr. Jrry Plunktt for his tchnical contributions. Partial financial support for this study was providd by th NCHRP-IDEA program, National Acadmy of Scincs; and th NSF Partnrships for Innovation Program. 11

12 Rfrncs 1. Brokaw, J.T Tst mthods to dtrmin strngth and stiffnss proprtis for strsslaminatd timbr bridg dcks. M.S. Thsis, Wst Virginia Univrsity, Morgantown, WV. 2. Davalos, J.F., Qiao, P.Z., Xu, X.F., Robinson, J. and Barth, K.E Modling and charactrization of fibr-rinforcd plastic honycomb sandwich panls for highway bridg applications, J. Comp. Struct. 52(2001): Davalos, J.F., Robinson, J., Vantaram, A., Viadro, R.C., Smmns, K., Plunktt, J.D., Honycomb Fibr Rinforcd Polymr Sandwich Panls for Fish Cultur Tanks, Procdings of th 3 rd Intrnational Confrnc on Composits in Infrastructur (ICCI 02), San Francisco, CA, Jun (In prss). 4. Davalos, J. F., Salim, H. A., Qiao, P.Z., Lopz-Aid, R. and Barbro, E. J Analysis and dsign of pultrudd FRP shaps undr bnding, Composits: Part B, Enginring J., 27(3-4): Plunktt, J.D. Novmbr Fibr-rinforcd polymr honycomb short span bridg for rapid installation, NCHRP-IDEA Projct Rport. 6. Robinson, J Analytical and xprimntal study of FRP honycomb sandwich panls with sinusoidal cor. M.S. Thsis, Wst Virginia Univrsity, Morgantown, WV. 7. Robinson, J., Davalos, J.F., Xu, X.F., Qiao, P.Z., and Barth, K.E FRP honycomb composit sandwich bams undr bnding, Procdings of th ASC 16 th Annual Tchnical Confrnc, Amrican Socity of Composits (ASC), Blacksburg, VA, Spt (in CD-ROM, Papr#111, 12 pags). 12