Composite Reinforcement of Cylindrical Pressure Vessels

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Caren Adams
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1 Comosie einorcemen o Cylindricl Pressure Vessels

Cylindricl Pressure Vessels Cylindricl ressure vessels re in idesred use or vriey o licions SCBA nd SCUBA nks Prone nks Comressed Nurl Gs (CNG) nd ydrogen or

2 Cylindricl Pressure Vessels Cylindricl ressure vessels re in idesred use or vriey o licions SCBA nd SCUBA nks Prone nks Comressed Nurl Gs (CNG) nd ydrogen or Alernive Fuel Veicles Medicl oxygen nks Lborory gs nks Deending on e licion, rimry design considerions include: Weig Cos Pressure cciy Sorge cciy Sey nd durbiliy

3 Design nd Anlysis Considerions Firs, consider mellic, in-lled cylindricl vessel For reliminry design/nlysis, nd or ody s discussion, e ill resric ourselves o e olloing condiions nd ssumions: Vessels re in-lled ( < /0) Sresses re uniorm roug e ll ickness (membrne loding) Sress norml o e ll ickness is muc less n membrne sresses Meril (yiclly seel or luminum) is elsic-erecly lsic von Mises yield crierion lies We ill consider e cylinder orion only y End closures (domes) re beyond ody s scoe Noe e vessel is xisymmeric bou cylinder xis Alied ressure loding is lso xisymmeric ε

4 Equibrium in Hoo nd Axil Direcions Noion Consider slice o leng L:, inernl ressure, rdius, ll ickness, sress, oo direcion Sum orces in orizonl (vericl) direcion: L L 0, xil direcion Sum orces in orizonl direcion: ( π ) ( π ) 0

5 Summry o Sresses Bixil se o sress Norml sress in e oo direcion Norml sress in e xil direcion No ser sress τ 0 y Tereore, nd re rincil sresses y von Mises yield crierion in o dimensions: y y + + y y Filure occurs en lod line reces e von Mises ellise 5

6 Design Equion + + y y + Filure crierion: Subsiue or e oo nd xil sresses, se, nd simliy: 6 y

7 Exmle Given: Tnk Dimensions Dimeer in. Leng o cylinder secion. 6 in. Lod Service ressure 600 si Fcor o sey gins burs.5 Meril is 0 seel E 0 x 0 6 si Poisson s rio, ν 0.5 Pressure ilure: (600) si y y 0.76 in. ( 800)( 6),000 (< /0) Weig o nk (cylinder secion): Yield sress, y,000 si Weig densiy, ρ 0.8 lb/in Deermine e required ll ickness W W W ρv 0.8 lb. ρ( π ) L ( π 6)( 0.76)( 6) 7

8 Some Observions Te oo sress is ice s lrge s e xil sress I e ly reinorcemen in e oo direcion, mybe e cn y educe e nk lod in e oo direcion y Mke oo sress more nerly equl o e xil sress y Enble reducion in nk ll ickness y educe e eig o e nk (imroved srucurl eiciency) Wr e cylinder secion i coninuous iber reinorced comosie meril Common merils re glss or crbon ibers in n eoxy mrix Wi ll reinorcing ibers in e oo direcion, e ill ssume e reinorcemen crries lod in e oo direcion only Assume e comosie is linerly elsic o ilure 8

9 Equilibrium Considerions Noion: subscri denoes e oo-r reinorcemen Equilibrium in e xil direcion is uncnged Equilibrium in e oo direcion: ( + ) L L 0 + Te roblem is no siclly indeermine To deermine o e oo lod is divided beeen e nk nd e r, e need n ddiionl equion: oo srin in nk nd r mus be equl As long s e nk s no yielded, Hooke s l lies: ε ( υ ) ε E E ( E ν ) E 9

10 Soluion o e Elsic Equions + ( E ν ) E E ν E E + ν E nd E + E (equilibrium) (equilibrium) (Hooke s L) Tese equions re vlid s long s e r s no iled: < nd e nk s no yielded: + < eq y 0

11 Folloing Tnk Yield Once e nk s yielded (ssuming e r is sill inc): sill, rom xil equilibrium Bu no e nk oo sress is obined rom e yield crierion y y Solve or e oo sress using e qudric ormul: ( ) + And ge e sress in e r rom equilibrium in e oo direcion: Noe rom e equion or, e vlue inside e squre roo mus be 0: y y 0 ( ) + y + y

12 W s i All Men? y Aer r eq y y Beore r y As e ressure increses u o nk yield, oo sress nd xil sress in e nk, s ell s e sress in e r, increse linerly. Aer e nk yields: Axil sress in e nk coninues o increse linerly (xil equilibrium) Hoo sress decreses, keeing nd on e von Mises ellise (yield crierion) Sress in e r mus increse ser re (oo equilibrium) To ossible ilure modes: Filure o e r (reerred) Filure o e nk

13 Exmle Given: Tnk Dimensions Dimeer in. Leng o cylinder secion. 6 in. Lod Service ressure 600 si Fcor o sey gins burs.5 Meril is 0 seel E 0 x 0 6 si Poisson s rion, ν 0.5 Yield sress, y,000 si Weig densiy, ρ 0.8 lb/in Hoo r i T00 crbon iber/eoxy E x 0 6 si Filure sress 70,000 si Weig densiy, ρ ω lb/in Deermine ickness o nk nd r Minimum nk ickness y Se 0.00 in. ( 800)( 6), in. A burs ressure, ( 800)( 6), 500 si ( 0.00) Tnk s yielded; use os-yield equions or nd burs ressure: W W + y 99, si Weig o nk (cylinder secion): 0.07 in. πl( ρ + ρ ) ( π 6)( 6) (( 0.8)( 0.00) + ( 0.056)( 0.07) ) W 85 lb.

Closing Commens Governing equions re redily enered ino sredsee Exmine e eecs o dieren meril selecions, icknesses, nk geomeries For given nk rdius, meril selecion, nd ressure requiremen ind e

in revious exmle) Addiionl considerions Comre ressure ic nk yields o service ressure (568 si vs.

14 Closing Commens Governing equions re redily enered ino sredsee Exmine e eecs o dieren meril selecions, icknesses, nk geomeries For given nk rdius, meril selecion, nd ressure requiremen ind e icknesses give oimum design (minimum eig) Minimum eig design is cieved by enorcing e condiion bo nk nd r il simulneously e required burs ressure (8 lb. in revious exmle) Addiionl considerions Comre ressure ic nk yields o service ressure (568 si vs. 600 si in revious exmle) Auorege (inenionlly ressurize beyond e elsic limi) o increse e elsic rnge nd imrove igue sreng Terml eecs: nk nd r ve dieren coeiciens o erml exnsion Processing-induced residul sresses due o eleved emerure comosie cure Oerion eleved nd reduced ressures Te nex ses o reduce eig : Fully-red i lod-sring mellic liner Fully-red i lsic liner

Composite Reinforcement of Cylindrical Pressure Vessels. MAE 661 Laminated Composite Materials Spring 2012

Composite Reinforcement of Cylindrical Pressure Vessels. MAE 661 Laminated Composite Materials Spring 2012 Comosie einorcemen o Clindricl Pressure Vessels MAE 66 Lmined Comosie Merils Sring 0 Clindricl Pressure Vessels Clindricl ressure vessels re in widesred use or vrie o licions SCBA nd SCUBA nks Prone nks