SPRINGBACK ANALYSIS OF SHEET METAL LAMINATES AFTER U-BENDING

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1 ozov po ahostm Czh publ U SPINGBACK ANALYSIS OF SHT TAL LAINATS AFT U-BNDING Ham ADIBI a ohamma Hoss ASADIAN ADAKANI a Bja OLLAI DAIANI a a Amkab Uvsty o Thology 44 Haz Av Tha Ia Abstat -mal ass: h_ab@aut.a. I pst stuy th spgbak o two-ply sht mtal lamats s vstgat thotally a xpmtally. Th ut mol whh s bas o o-quaat Hll ylg to a pla sta oto taks to aout ts o thkss thg o ah lay a omato hstoy o th sht spgbak. xpmtal tsts w out to vy th aalytal sults. U-bg xpmts o two-ply lamats osstg o pu alumum (JIS Al) a stalss stl (JIS SUS34) w pom. Th sults show that spgbak o sht mtal lamats s t om moolth shts. Stgth btw th ompots th latv posto o lays (layup) a th thkss ato o ah lay a makabl atos that at spgbak o sht mtal lamats as wll as th stthg o. Wh th stog matal s loat outs o th bt lamat th t o stthg o o spgbak otol s mo tha th vs posto o lays. It s mostat that th aalytal sults a goo agmt wth xpmtal sults. Kywos: Lamat shts Spgbak S wall ul. INTODUCTION I t yas two-lay shts whh osst o ssmla mtall ompots hav b wly us vaous usts. xllt mhaal a utoal popts ooso ssta a t ltal outvty o ah lay a th ma avatags o two-lay shts [-3]. Spgbak s a ommo phomo sht mtal omg posss that s th lastally-v hag o shap o a pat at omg. Numous stus hav b out o ths phomo moolth shts wh subjt to stth-bg stth-ubg to pt th al shap o pats [4-]. Howv w paps hav b publsh o spgbak o mult-lay shts so a. Complx omato mhasms o two-lay shts ompa wth a moolth sht u to t mhaal popts a omablty o ah lay s th pmay ulty ay stuy o spgbak th two-lay shts. Fo moolth shts t s wll kow that th hgh th stthg o th small th spgbak. Howv o sht mtal lamats osstg o ssmla mtal ompots th spgbak bhavo s muh mo omplat tha o moolth shts []. Ho t al. [] pot out om th umal smulatos o uom stth-bg that hgh stthg o os ot always u th spgbak o sht mtal lamats. I ut pap th spgbak bhavou o two-ply mtall lamats at U-bg poss s vstgat though thotal a xpmtal aalyss. A thotal mol bas o stss aalyss s vlop to pt spgbak. Th ts o omato hstoy a thkss thg o lays o th spgbak o two-ply stps a tak to aout th pst aalyss. U-bg xpmts u vaous stthg o w pom o two-ply lamat stps osstg o

2 ozov po ahostm Czh publ U pu alumum (A) a stalss stl (SUS34); at poss th o agls a sual uvatus o s wall u to spgbak w masu. Th ts o stthg o stgth btw th ompots latv posto o stog/wak lays (layup) a thkss ato o ompots o spgbak a suss ths pap bas o xpmtal a aalytal sults. Wth osg th abov-mto atos th aalytal mol pst ths pap a b us to tm th optmum otos o poss paamts a to pt th spgbak.. THOTICAL APPOACH I U-bg th sht omato a puh o go a b os as sht stth-bg. Th ollowg assumptos a appl: Th stthg o p ut wth ah lay s os to b uom though thkss. Howv t s t o ah lay. It auss sht thg a utal sua shtg. Staght ls ppula to th utal sua ma staght ug poss. 3 Th sta th wth to z s zo. 4 Th tasvs stss ah lay s glt. 5 Th ah o th two lays s pt so th s o sta sotuty two lays ta. 6 Volum osvato s kpt ug stth bg poss... Wh a a th tagtal a tasvs sta sptvly. z. Thg o ah lay Cosg assumptos (3) a (6) th oss-sto aa mas ostat ah lay a lgth o utal sua L s ostat ug two-ply sht stth bg poss ollowg quatos a obta o ah lay: L t L t () m Wh L m t a t a th a lgth o ml sua tal a al thksss o th lay sptvly. It s obvous om gomty o Fg. : L m m L () Fg.. Th sta stbuto a utal sua splamt sht stth bg

3 ozov po ahostm Czh publ U So om () a (): t t m Wh m s bg aus o ml sua o th lay a s th bg aus o utal sua.. Calulato o stthg o Th tagtal a tasvs sta stbutos though thkss o ah lay a: l t l t Wh s th bg aus o th o a. Aog to plast low ppl o-quaat Hll ylg quato a th assumptos (3) a (4) th tv stss tm o tagtal stss a b wtt as ollows:.. Wh s th tagtal stss a whh s lat to th tasvs asotopy pla sta oto a omb hag ot obta as [4]: ( m ) ( ) m m m So th stbuto o tagtal stss a b obta as: k l l -ν Plast zo last zo Gally th possbl stss stats last ompssv a tsl plast mght vlop though ah lay thkss. Aog to Fg. 3 a a th -ooats o as at whh th last/plast tastos (ompssv a tsl sptvly) ou. (3) (4) (5) (6) (7) (8)

4 ozov po ahostm Czh publ U Fg.. Posto o stss tasto as So th stbuto o stss th lay u stuy a b xpss as: b k -ν a k l l l (9) I th abov quato th matal popts o lat lay shoul b us. Th t o aoss ah lay s: b a k l - k F l l ν () Tho th stthg o o two-ply sht s: F F ().3 Th bg momt alulato Th bg momt o two-ply shts s: () p (3) Wh s last momt a p s plast momt o th th lay that a b alulat as ollows: ( ) h h l (4) ( ) ( ) K K h b h h a h p l l (5)

5 ozov po ahostm Czh publ U h s bg aus o th utal sua wthout stthg o F that a b tm om qulbum quato a h a b obta by plag wth h q. (9)..4 Two-ply sht vs-bg It s assum that sht vs stth bg (a) ah lay th stthg o s uom a kps ostat a (b) th sht thkss mas uhag. Dug puh movmt th sht s tally stth a bt aou th aus th ubt u to lavg th otat sua. Dug vs bg poss aog to assumptos (a) th utal sua posto s uhag. Th hag o tagtal stss a bg momt a latv to matal hag ul u to th omplat omato hstoy. Cosg sotop hag ul th stbuto o tagtal stss hag though thkss a b xpss as ollows o th th lay: Y b a k l o l (6) k l (7) h h h (8) H h a b alulat om q. (6). Th hag o bg momt o th th lay s: ( ) ( ) ( ) K K h b h Y h h h a h Y l l l (9) A o two-ply sht th total hag o bg momt s: Total () Tho th stbuto o tagtal stss though sht thkss * a th bg momt o oss-sto * at sht vs stth bg a b xpss as ollows: o * () Total * ()

6 ozov po ahostm Czh publ U a o a a out sua aus o sht sptvly..5 Aalyss o sht U-bg Th omato aa o sht U-bg a b v to v gos alog th lgth to as show Fg. 4 a th stthg o a bg momt atg o ah go a show Fg. 4(a) () sptvly. Fg.. Domato gos U-bg go I a V a th lat pats otatg wth th staght gs o puh a sptvly. Fo smplty th bg momt atg o ths two gos s glt although thy shoul hav a uvatu. go II a IV ugos stth bg aou th puh a o sptvly whh th sht thkss stss a sta stbuto a bg momt o oss-sto a alulat by stth bg omulato. go III s th usuppot pat a has ugo omplx omato hstoy. It s tally stth a bt aou o a th ubt to bom swall o U-pat. Th stss a sta stbuto a bg momt a alulat usg sotop hag ul. Baus o th bg momt atg o sht oss-sto th sht ths go shoul also hav a uvatu ug omg poss. But s th laa btw th a puh s a small tha th puh stok sta ths go a b os as staght ug omg poss. Howv at th loag s mov th sht ths go has a latvly lag uvatu baus o spgbak..6 Spgbak o sht U-bg Th o-uom stbuto o stss oss-sto ug omg poss wll hag th pat pol a aus spgbak wh th loag s mov. Fo U-bg spgbak happs oly th gos II III a IV whl th gos I a V ma to b lat bo a at th loag a mov. Assumg that th uloag os ot aus vs ylg th omato spgbak s quvalt to th omato by ag a vs bg momt - ospog go. 3. OVVIW OF XPINTS Fg. 5 shows shmat llustato o U aw-bg poss. I o to xpmtal aalyss th typs o two-ply lamats osstg o pu alumum (JIS A) a stalss stl (JIS SUS34) t thkss atos w ppa. Th total thkss o th two-ply sht was ostat a about. mm. Th matal thkss atos ah stu ass a lst Tabl.

7 ozov po ahostm Czh publ U Fg. 5. Shmat llustatos o th aw-bg tst Tabl. Thkss ato o ah matal omposg a lamat sht ths stuy Cas (І) Cas (IІ) Cas (III) atal Thkss Thkss Thkss t (mm) t (mm) t (mm) ato % ato % ato % A SUS I o to obta mhaal popts uaxal tsl tsts 45 a 9 tos w pom o ah ompot a sults a lst Tabl. Tabl. Th matal popts o ompots. atal Posso ato (υ) (Hag ot) K (Stgth ot) (Pa) Yl Stss (Pa) last oulus (GPa) (asotop ot) SUS A Th U-hal bg a out wth th xpmtal st-up whh s show Fg. 6. I o to stuy th t o paamts v t st o thkss o stps ompos o alumum alloy a stalss stl shts tst aog to Tabl. oov th t o blak hol o a latv posto o lays (layup) w vstgat ths xpmts. Th loas w appl by a hyaul systm a o lubat was us o puh/sht a /sht otat suas. Fg. 7 shows th gomtal paamts o th assmbly. Fg. 6. xpmtal st-up a aw pats. Fg. 7. -D shmat o toolg gomty

8 ozov po ahostm Czh publ U 4. SULTS AND DISCUSSION Th popos thotal mol s appl to aalyz th -D aw bg poblm stu NUISHT 93 [6] as show Fg. 7 a th spgbak paamts o a ρ stu by ths bhmak a show Fg.8. I th spgbak agls th go II III a IV a sw a sptvly th a Fg. 8. a b xpss as: 9 9 sw sw Fo ov layup o lamats a ot by th abbvatos otos AS a SA ot th latv posto o th ompot lays o th spm. AS mas th oto wh th stalss stl lay s loat s o th bt spm a otats a o. O th oth ha u th oto SA th alumum lay s loat s o th bt spm. ts/t stas o th lay-thkss ato. (3) (4) Fg. 8. asu mtho o spgbak Th t o BHF o th sual ul (ρ) o s-wall a o agls ( ) at spgbak all stu ass s pov gus 9 a. Fgu 9(a)-() shows th t o thkss ato o spgbak paamts as t s pt Tabl th ato o wak ompot thkss to total thkss o lamat ass om Cas (I) to Cas (III). So by as thkss ato o stog matal sam layup th t o BHF s mo obsvabl.. th mo BHF th mo otol o o agls a s-wall uvatu. Th smla ty s obsvabl AS layup as s llustat gu (a)-(). Also gus 9 (a) a (a) mostat that sam thkss ato th spgbak o AS layup s mo tha SA layup. Th smla bhavo s obsv o oth stu ass.

9 ozov po ahostm Czh publ U ( a ) CAS I SA ( a ) CAS I AS ( b ) CAS II SA ( b ) CAS II AS ( ) CAS III SA ( ) CAS III AS Fg. shows th t o thkss ato o lays o sult o agls. As a sult o (ts/t.3) th asg th stog matal (stalss stl) as th spgbak but o mo tha ths ato t t vsly th s a optmum oto (ts/t.3) that th spgbak s th last o both latv postos.

10 ozov po ahostm Czh publ U (a) AS layup BH5KN (b) SA layup BH5 KN Fg.. Pt o lamat sht. I summay th aalytal sults show th sam ty wth th xpmtal os but th a ou som spay btw thm. Th pto oul b mpov by g th osttutv mol spally o th spto o th Baushg t o ompot matals a also by osg th stss stbuto th wth to o a lamat stp. 5. CONCLUSION A w aalytal mol s vlop o pto o o agls a s wall ul o lamat shts u-bg poss lat to spgbak phomo. Th pt sults a goo agmt wth xpmtal os. Bas o both thotal a xpmtal vstgatos th spgbak bhavo o sht mtal lamats s stogly at by th stgth btw th ompot lays o th lamats th latv posto o th lays a th lay-thkss ato as wll as by th stthg o atg o th lamats. U th oto SA wh th puh otat mtal s th stog matal (stalss stl) th stthg o has mo lu o asg th spgbak. It s olu that a sam blak hol o th oto AS has mo spgbak. I sum o tmg th optmum oto o spgbak o lamat stps o shoul pay attto to abov mto atos. Th aalytal appoah pst ths pap woul mak a gat otbuto towa spgbak pto. FNCS [] W.Y.D. Yu A galz soluto o th pto o spgbak lamat stp. Joual o atals Possg Thology 6 (996) [] J. K. Km T. X. Yu Fomg a alu bhavo o oat lamat a sawh sht mtals: a vw Joual o atals Possg Thology 63 (997) [3] F. Yosha Domato a atu o sht mtal lamats plast omg I Pogs o 4th Itatoal Co o Compost gg. (997) [4] Z.T. Zhag S.J. Hu Stss A sual Stss Dstbutos Pla Sta Bg Itatoal Joual o haal Ss 4998 p [5] Z.T. Zhag D. L Dvlopmt o a w mol o pla sta bg a spgbak aalyss. Joual o atals gg a Poma [6] P. Xu T.X. Yu. Chu Thotal pto o th spgbak o mtal shts at a oubl-uvatu omg opato. Joual o atals Possg Thology 89 9 (999) 65 7

11 ozov po ahostm Czh publ U [7] J.T. Gau G.L. Kzl A w mol o spgbak pto whh th Baushg t s os Itatoal Joual o haal Ss 43 () [8] H.. Huag S.D. Lu S. Jag Stss a Sta Hstos o ultpl Bg-Ubg Spgbak Poss. Tas AS 3 () [9]. K. Vma A. Hala t o omal asotopy o spgbak. Joual o atals Possg Thology 9 (7) []. Samul xpmtal a umal pto o spgbak a s wall ul U-bgs o asotop sht mtals. Joual o atals Possg Thology 5 () []. Ho Y. Goto F. Yosha Spgbak o sht mtal lamats aw-bg. Joual o atals Possg Thology 39 (3) [] Z. Dogjua C. Zhsha. Xuyu L. Yuqag A aalytal mol o ptg spgbak a s wall ul o sht at U-bg Computatoal atals S 38 (7) [3] S.W. L Y.T. Km A stuy o th spgbak th sht mtal lag awg. Joual o atals Possg Thology (7) [4] W.D. Ca L.. Gg D.K. atlok.h. Wago asumt o spgbak Itatoal Joual o haal Ss 44 () 79.