Dynamic response of laminated glass under blast loading: effect of negative phase

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1 ic resose of lie glss uer ls loig: effec of egive se L. R. ri & J. Wei ere of Mecicl Aerosce Egieerig Egieerig Mecics Uiversi of Missouri-Roll U.S.A. Asrc Mos of e rece suies ve esize e effec of e osiive se of ls loig ile eeriig e srucurl resose. Te effec of e egive se o e ic srucurl resose s ee igore. Tis reserc focuses o e effec of e egive se of ls loig o e ic resose of rciecurl lie glss. A close-for soluio se o e clssicl le eor is eveloe e e resuls re core i -iesiol olier ic fiie elee lsis. Resuls iice e egive se of ls loig s sigific effec o e ic resose of e lie glss el. I riculr i-s el eflecio sress ue o egive se ressure re los oule e corresoig quiies ue o osiive se. Tis e if e glzig oes o fil i e osiive loig urio u i o so i e egive loig se ecuse of iger ic sresses urig is ler se. Keors: ls lo lie glss egive se close-for soluio fiie elee lsis lier elsici lier visco-elsici. 1 Iroucio I is esie e jori of ofl ijuries fro o lss resul fro irore glss frges fro rciecurl glzig. Te use of lie rciecurl glss s ee so o iige is zr. Te elosive ls ve s iseous rise ri ec relivel sor osiive se urio. Te ressure-ie isor for elosive ls ve is e overressure fro osiive se ros o zero e ros elo zero i egive se ii fiie ie. Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X

2 18 Srucures Uer Sock Ic VIII Mos of e rece suies ve esize e effec of e osiive se of ls loig ile eeriig e srucurl resose. Te effec of e egive se o e ic srucurl resose s ee igore [1-5]. Tis is rue e use for e ree srucure resose u o rue for e glzig els. Si e l. [6] reore e lie glzig ull ou of e fre ie fll i oe iece ousie e srucure urig e elosio ess for ceri cofigurio cses. I e e egive se of e ls loig cuses e lie glss el filure. Bse o suc oservio Kruer Aleerg [7] suie e effecs of egive se of e ls lo o e roili of glss el filure. I is er eiricl qusi-eoeil for s ee eee o escrie e elosive ls ve for o osiive egive se. Te effecs of e egive se of ls loig o e ic resose of rciecurl lie glss el ere suie. A close-for soluio se o e clssicl le eor is eveloe e e resuls re core i -iesiol olier ic fiie elee lsis. Bls lo crcerizio A icl ressure-ie isor curve for ls ve is so i figure 1. A eiricl qusi-eoeil for s ee use o escrie e ve Kie [8] α 1 / / e 1 ere is e iseous overressure ie is e ek overressure oserve e is zero α is e ec fcor is e osiive overressure urio. Bse o e ule give Kie [8] ri e l. [5] resee e folloig ree equios for e ree reers i eq 1. 5 Pressure P Posiive Pse lo i g u rio Fro forul Fro es 5 Negive Pse Tie Sec. Figure 1: A icl ressure-ie curve for elosive ls. Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X

3 Srucures Uer Sock Ic VIII /5 s α ere is e scle isce s is e scle osiive overressure urio efie elo. B es of e sclig l eqs - c e lie o oer elosio cses. For grou elosio o fr fro e elosio ceer e scle isce is eresse s Kie [8] 1 5 ere is e TNT equivle of elosive eerg relese i e elosio o e escrie is of referece elosio l or 98 kg is cul isce fro elosio ceer. Te cul osiive ressure urio is oie s 1. 6 s Te ec reer α is o iself scle so i c e oie irecl fro eq roerl scle isce fro eq 5. We ls ve ecouers e uilig surfce i ill e reflece ere lifig e overressure. Furerore if ls source is lce o or er reflecig surfce suc s e grou e e surfce urs ers o ve 1 o ies e source eerg s e ls i free-ir. Terefore scle fcor eee o correc e ifferece eee e clculio i free-ir ls usig forule 1-6 e eeriel esure of grou ls. Te scle fcors for e ek overressure eee e es e clcule re oie i η.6 ri e l. [5]. Terefore e ls ve geere grou elosio ioses ic lo o ojecs give η 7 ere is e lie sock ressure o e lie glss. Oce e TNT equivle of elosio e isce fro e elosio ceer re ko e overressure e osiive se urio ie e ec fcor c e clcule usig eqs -. I ese equios e U.S. ui sse soul e use 1 l.5 kg 1 f.5 1 si 69 P. A colee ressure-ie isor iclues o e osiive e egive se c e loe usig eqs 1-7. For 7 kg TNT equivle 51.8 reice resuls fro 1-7 re resee i figure 1. Also resee i figure 1 re e corresoig es resuls of Si e l. [6]. Sice greee eee e reice es is goo eq 1 c e use o siule o e osiive e egive ses of overressure fro Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X

4 18 Srucures Uer Sock Ic VIII elosio. I is ieresig o oe Kie [8] resee eq 1 origill for e osiive se of ls loig. P z Figure : o surfce oo surfce o Ouer Glss Pl PVB Ierler i Ier Glss Pl z Sceic igr of recgulr lie glss le sujece o uifor ls loig. Close-for soluio Figure sos i recgulr four eges sil suore lie glss el. Te el is coose of o rciecurl glss lies ere olvil url PVB ierler. Te glss l is oele s lier elsic eril e PVB ierler e oele s lier viscoelsic eril for ic e evioric cooe of sresses is give ri e l. [5] Sij G τe ijτ 8 ere eoes ie e ij is e evioric sri re G is e sress relio oulus ic is ssue o e of e for β G G G G e 9 ere G is e log ie ser oulus G is e sor ie ser oulus β is e ec fcor. Te volueric resose is elsic so e e rosic ressure is coue Kε kk 1 ere K is e ulk oulus. Te sor-ie ser oulus glss oulus G is ou 1 GP giue ile e log-ie ruer oulus ser oulus is ou 1 MP giue. Wii sor ie PVB eves like soli glss eril. Usull e urio of e ls loig is ou ii-seco giue. Terefore o silif e role i e close-for soluio e furer ssue e PVB eril s lier elsic soli vi glss oulus G ulk oulus K s 9KG K G E ν. 11 K G 6K G Accorig o e clssicl eor of i le e sri cooes i e - le c e eresse rsverse eflecio of e le s ε z ε z γ z. 1 Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X

5 Te sri eerg for e le i le sress se is z U V γ τ ε σ ε σ 1. 1 We oi e sri eerg of e lie le eresse e rsverse eflecio s i o U 1 1 ν ν 1 i ic 1 k k k k E ν k o i 11 ν E. Force ork oe is s. 15 Te kieic eerg of e recgulr lie el c e rie s T i i o o ρ ρ ρ Usig Hilo s ricile [9] 1 W U T s δ δ δ 17 e ge e equios of oio for lie le s o e M 1 18 ere i o i g o g M ρ ρ ρ E ν ρ g is Youg s oulus Poisso rio esi of e glss lies resecivel; ρ is esi of PVB ierler. Te sil suore our coiios re 19 e iiil coiios re Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X Srucures Uer Sock Ic VIII 185

6 . 1 To ge e url frequec e se j e W 5 1 si si 1 1 A W i gives M. Te url frequec is M K 5 ere K. Te free virio oe is 15 si si si cos si si 1 1 B A V 6 ere A B re coss o e eerie usig iiil coiios. B usig oule Fourier esio si si A si si e ge e A M A K Te soluio of e force resose of 18 is 5 1 si si si cos f e f f f F α ere Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X 186 Srucures Uer Sock Ic VIII

7 Srucures Uer Sock Ic VIII 187 α α α 16 f1 1; f 1 α ; f 1 ; f. T T T M T Usig coiuous coiios 1 V F V F e ge e free virio oe fer osiive se urio s si 1 cos f f V si 6 cos f f f si si for 1 5 ere α α α e αe α 1 f T ; ; T 6 f ;. 5 T Afer geig F V e c clcule sresses usig e le sress-sri relios. Fiie elee oelig Te role is lso solve uericll usig e coercil ic olier ree iesiol fiie elee coe LS-YNA eveloe Liverore Sofre Tecolog Cororio [1]. Te FEA eses for e squre lie glss le re corresoig o - - z-irecio resecivel. I e FE lsis e PVB ierler is oele s lier viscoelsic eril for ic e evioric cooes re give i Resuls iscussios I e close-for soluio e fiie elee clculio e folloig coss re use: for e glss lies E 7 GP ν.5 ss esi ρ g 5 kg/ ; for e PVB ierler G o. GP G.69 MP K. GP β 1.6 s -1 ρ 11 kg/. Te iesios re: o i Te elosio reers re 7. 7s α f ere f vries fro.5 o 1. o su e effec of e overressure o e ic resose. Sil suore our coiios re lie o e lie glss le. Te lie glss ui is iscreize usig - 8-oe soli elees. Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X

8 188 Srucures Uer Sock Ic VIII.1 1s ek eor osiive lo ol.5 eflecio eor osiive FEA osiive & egive lo & egive lo ek Tie sec. Figure : Mi-s eflecio isor of e lie glss el. We suie o clculig oels. Oe is e osiive se lo ol PPLO ic firs elos eq o clcule e ic resose ill e osiive lo urio e e ic resose is clcule usig eq for e free virio. Aoer is i egive se lo WNPL ic clcules e ic resose i full ls loig erio usig eq. Figure sos i le eflecio-ie isor i-s of e le i overressure fcor f 1.. I ic e s lie is oie close-for soluio usig e PPLO oel ic sos free virio i ieicl liue fer 7.7 s e osiive se lo urio. Te soli lie is fro e close-for soluio usig e WNPL oel oe lie is e se u fro e FEA resul. Te ifferece eee e close-for e FEA seco ek is ue o olier resose of lrge eflecio oie e FEA. I is see e eflecio seco ek is ou oule e corresoig quiies firs ek. Figure sos e iu ricil sress-ie isor i-s of e le. Te s lie is oie closefor soluio o e o surfce usig e PPLO oel e soli lie is e se u usig e WNPL oel. As coriso e FEA resuls oie fro o o oo surfces of e le re eoe e s-o oe lies resecivel. I is so e esile sress seco ek is rou ice s ig s firs ek. If e lie glss le is o o e ge urig e firs ek esile sress e elsic recover force of e le lus e egive se ls lo ill geere iger esile sress o o surfce. Terefore e seco ek esile sress ill e ore gerous o e le e firs esile ek esile sress. To ccou for e effec of e overressure o e ic resose of e le figure 5 6 so e eflecios iu ricile sresses firs seco ek s so i Figures & gis e overressure resecivel. I is see o i-s eflecio sresses fro e close-for soluio coicie ver ell i FEA resuls ii e curre lo regio. Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X

9 Srucures Uer Sock Ic VIII FEA o surfce 1s ek ek eor osiive & egive lo eor osiive lo ol Sresses MP FEA oo surfce Tie sec. Figure : Mi-s iu ricil sress isor of e lie glss el. 6 eflecio FEA 1s ek Teor 1s ek FEA ek Teor ek Pressure P 1/689.8 Figure 5: Effec of e overressure o e i-s eflecio. FEA 1s ek Teor 1s ek FEA ek Teor ek Sress MP Pressure P 1/689.8 Figure 6: Effec of e overressure o e i-s iu ricil sress. Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X

10 19 Srucures Uer Sock Ic VIII 6 Coclusios Te eiricl qusi-eoeil for of ls loig c roiel e use o siule o e osiive e egive se overressure. Te egive se of ls loig s sigific effec o e ic resose of e lie glss el. Te i-s eflecio sress ue o egive se ressure re rou ice s ig s e corresoig quiies ue o osiive se sll eflecio regio. Tis e e lie glss el o fil i e osiive loig urio u i e ge i e egive loig se ecuse of iger ic sresses urig is ler se. To recisel clcule e olier ic resose of lie glss le egive se lo uer iger ls overressure olier soluio is ecessr ill e. Ackolege Tis ork s suore e Uiversi of Missouri Reserc Bor Refereces [1] Buer H.F. Nolier resose of Elsic les o ulse eciios. Jourl of Alie Mecics Trscios of e ASME Mrc [] Bir V. & Ber C.W. Beviour of lie les sujece o coveiol ls. I. J. Ic Egieerig [] Teg T.L. Lig C.C. & Lio C.C. Trsie ic lrge-eflecio lsis of el srucure uer ls loig. JSME Ieriol Jourl Series A [] Turke H.S. & Mecioglu Z. Nolier srucurl resose of lie coosie les sujece o ls loig. AIAA Jourl [5] ri L.R. Wei J. & Ji F.S. Filure lsis of lie rciecurl glss els sujece o ls loig. Srucures Uer Sock Ic VII es. N. Joes C.A. Brei & A.M. Rjer WIT Press: Souo [6] Si J.L. Hll B. & Refroe N. Glzig Hzr Miigio Tecolog. Proecive Glzig Associio: 1 s Aul Euciol Seir Wsigo C Aril [7] Kruer T. & Aleerg A. Negive se ls effecs o glss els. Ieriol Jourl of Ic Egieerig [8] Kie G.F. Elosive Socks i Air Te Mcill Co: Ne York 196. [9] Soeel W. Virios of sells les M. ekker: Ne York [1] Liverore Sofre Tecolog Cororio LS-YNA USER S MANUAL Nolier ic Alsis of Srucures i Tree iesios Srucures Uer Sock Ic VIII N. Joes & C. A. Brei Eiors WIT Press.iress.co ISBN X