''"* Xac djnh he so dan hoi cua vai ky thuat tiF thi nghiem
;< thoi phong ong mang mong
J l Determination of the elastic coefficients of a technical fabric from the inflation test of Si an air tube
J'ii Ngay nhan bai: 13/10/2014 Ngay sula bai: 9/10/2015 Ngay chap nhan dang: 10/12/2015
Nguyen Quang Tung, Le Khanh Toan
T6m tat
Nghien ciiu nay dl xuSt mpt phitOng phap thi nghifm m6i dl xAc djnh cac tinh chat ca \y cua vat heu vii ky thuat Cd sd \f thuylt cixa. philcJng phdp Ik bii todn thoi phong ong tni tr6n. Cdc phiiong trinh cd ban dUdc xay dilng trong khuon khfi bien dang Wn vi diiOc phat trien thanh m6t he phUdng trinh phi tuyIn, cho ph^p tinh toan bien dang cua 6ng mdng m6ng khi bi thoi ph6ng. Ap dyjig h? phUOng trinh phi tuyen nay, mot phep phdn tich ngilqfc di((?c thdc hi|n nham xdc dinh cac tinh chat cd ly ciia vat heu. Cdc ket qud thu dd(?c trong nghiln ci3u nay rat phu hdp vdi cac sd h|u thu thap difijc tif cac nhom nghien ctiu khac tren the gi6i.
TU khoa: ong thoi phong; biln dang Idn; thi nghiem thoi ph6ng; he s6 dan hoi; vai ky thuat.
Abstract
This paper proposes a new method for determining the mechanical properties of the technical fabrics. The theoretical basis of this method is the inflation problem of the cylindrical tube. The formulation is contributed in the framework of large deformations. A system of non-lmear equations is derived, giving the deformations and the geometries of the tube. Applying this set of non-linear equations, an inverse analyse method is proposed to determine the material coefflcients. The obtained results in this study are shovm to agree very well with those of another studies m the world.
Key words: mflatable tubes; finite deformation; orthotropic membranes; inflation tests; material coefficients.
Nguyen Quang Tung -Ll Khinh Toin
Khoa Xay di/ng DD&CN, Tnldng Dai hpc Bach Khoa, Dgii hpc Ba NSng
£[iiait: ngtiin^(iBdut.und.vn - [email protected]
1 . Gidi thl^u chung
K i t cau m^ng mdng 3h xuat hl^n trong c^c cong trlnh xay ddng t d khodng hem 50 nam t r d 1^16hy. Nhd trpng litpng hin than nhe, c6 khd nang tao hinh da ciang va miu sSc phong p h i j nen l o | i k i t cSu nhy thudng ddcfc sCrdung n h d cac k i t c i u bao che. Ngay nay, cCing vdi sif
| x § y d i r n g , ^ ^ c ket^^u mang n
a) DSm thoiphonc) [I] b) Vom thoi phnng [2]
Hinh 1; Kft c3ii mSng ming thiSl phong
Cac k i t cau nay t h i i d n g dddc c i u tao t d vat lieu vdi ky thuat, Trong do, cac sol vdi ddOc det theo hai phuong vudng goc nhau de ddm bdo khd nang chiu ldc, va ddi^ic bao bpc bdi m d t Idp PVC cd tdc dung chdng t h i m cung nhir bda vi cic sa\ vdi khdi cdc tdc nhdn gdy gai ciia mdi trddng. Vat lieu vdi ky thuat nay c6 quy luat iing x d trdc giao va tuan theo gid thiet iing suat phdng. Mdl quan he glCia iing s u i t crva bien dang E dupc t h i hiin bdi phuang tr'inh sau
trong do, E,. E, lan lUcTt Id md-dun dan hdi theo phddng ngang vi dpc cCia tam vdi; v,, la h& s6 Poisson vd G,t la m6-dun chdng cdt cua tam vdi.
Oe xac d m h cdc he sd ddn hdi ndy, cdc nhdm nghien ciihj trdn t h i gidi da xdy dung n h i l u phuong phap thf nghidm khdc nhau. Peng va Cao [3), VysochJna [4], va nhdm nghien ciJtu cua Quaglini [5] da tien hanh cdc t h i n g h i f m keo m d t true n h i l u mdu vdi de xdc djnh khd ndng chju life theo mdt phdong cho trUdc. l/u diem chlnh cua phi/dng phap nay la qud trlnh t h i nghiem d p n gidn, cdc md-dun ddn hoi theo hai phUdng cua vdt lidu cd t h i dddc udc luong nhanh chdng. Tuy nhidn, d o trang thai iJmg suat
91
trong mau vdi tht nghiem (keo m d t chieu) Idiong g i d n g vcri trang thai dng suat cua t i m vdi trong k i t d u thdc (keo hai chieu) nen cac ket qud d o
dUdc cd dd t i n cay khdng cao. ' De khac phuc han che cua phuong phap keo mdt chieu, Galliot va
Ludianger [6], n h d m nghidn ciiU cua Boisse [71 Bridgens [8] va cua Can/elli [9] da t h i ^ hien cdc t h i nghiem keo phang theo 2 tmc cua mau vdi. Do trang thdi iJiYig suat frong m l u vdi t h i nghiem kha gidng so vdi trang thai lam viec thuc ciia tam vdi ndn cdc he sd ddn hdi thu dUdc t d phep do nay cd dd i^n cay cao hdn so vdi phddng phap thi nghiem keo mdt chUu.
Trong nghidn cdu ndy, tac gia de xuat m d t phuong phdp t h i nghidm kdo hai true mdl. £ ) l tao ra trang thai dng suat keo 2 t m c , cac mau vdi t h i nghidm sd ddpc tao hinh thanh cac ong tru tron va duoc t h o i phdng n h d ap suat khdng khi. Trang thai dng suat cua mau vdi trong t h i nghiem dng thoi phdng la hodn toan gidng so v6i sif Idm viec thuc te. Do d d , phUOng phdp t h i nghiem ndy hiJa hen se cho cac k i t qud toi Uu hem so vdi cdc phucfng phdp t h i nghidm keo 2 true t m y l n t h d n g
Cd sd 1^ thuyet cua phucmg phdp ndy Id hai bai toan thuan - nghjch ciia viec thdi phdng dng t n j trdn ddoc cau tao tif vdt lidu vdi ky thuat.
Trong bai toan thuan, cac tlnh chat cd ly ciia vat lieu dUdc gid t h i l t la da b i l t . Cac phuong tnnh cP bdn dupc xdy ddng trong khudn khd bien dang Idn va dupe phdt t r i l n thanh m d t he phuong trinh phi t u y I n , cho phep tinh toan bien dang cua dng mang mdng khi b| thdi phdng. Trong bai todn nghieh. he phUdng trinh phi t u y I n sd ddpc phat Uien theo hUdng phdn tich ngdpe, cho phep xdc dinh cdc tinh chat co ly cua vat lieu ti^cac ket qud do b i l n dang eua dng thdi phdng.
Cdc md-dun ddn hdi ciia vat lieu t h u ddpc t i l bdi toan nghjch se dUoc sd d u n g d l tinh todn l^i bien dang eda dng thdi phdng bdng bai todn thuSn. C3c gid tri b i l n dang cua ong thdi phong thu dupc tir ly thuyet va thdc nghidm sd dupc so Scinh d l danh gid miJc d d hpp ly cua phuong phSp t h i nghidm.
2. Bdi t o d n t h u d n - Hd p h d d n g t r i n h xac d i n h b i l n d a n g c£ia d n g m d n g m d n g 6 t r a n g t h d i t h d i p h d n g
2.1. Datv^nde
Trong muc ndy, tdc gid chd y l u nghien ciiu sd thay ddi kich thudc hinh hpc cua dng tru trdn, dude cau tao t d vat lieu vdi ky t h u | t , va bi thdi phdng bdi dp s u i t p.
Bdi todn dddc thiet l | p trong khudn khd bien dang Idn, d o d o can phdi phdn bidt trang thdi t d nhien vd trang thai thdi phdng ciia dng. De xay dtmg cdc phuong trinh tinh toan, tdc g\h sis d u n g he truc toa dp tru ( e , , e g , e ^ ) , vdi ep,eg vde,, lan lupt la cac vectP chi phuong, dinh hddng theo bdn kinh, ehu vi vd theo true eda dng,
Vj tri eua mdt phan t d eCia dng d trang thdi thdi phdng sd dUpc ky hieu Id X vd ddOC xSc dinh bSng cSc toa d d tru n h u r , 6 , x , nhU vSy, X = re, (0) + xe^ . d tr^ng thai thdi phdng nhy, cdc vectd chi phUOng tai p h i n t d (hay cdn gpi Id vi tri) x phu thudc vao gid trj cua 3 ,
Phucmg tnrc giao
[ H i n h 2).
f t o n g nghien cOtu nay, vat lieu vdi ky thuat dUoc m d hinh nhu mil t i o n g dan hoi trUc giao vai cac vecto chi phuang trUc giao e, va e ^ n lacft dupc dinh hudng theo phuang ngang va dpc cua cac sai vi\.
Gdc tao boi cac vecto e, va e^ d u o c g o i l a g d c d i n h huangvakyhieuli 0 < <18i
i2,2, SUvgndgng
b i d t h i l t rang cac tiet dien ngang cua dng mang mdng sau khi thoi a phang va vuong goc vdi true Oe^ cua ong, n h u vay dng vjn I CO dang hinh tru keca d t r a n g thai t u nhien va trang thai thoi phong l a n d o n g ciia ong cd the duoc the hidn bdi quan he gifla cac toa 6b d trang thai thdi phong va R,0,X 6 trang thdi tU nhien nhu sau;
r = |<gR O = 0 + p x - k ^ X Q) p r o n g do, cac he so \CQ, k^, lan luat la eac he sd bieu hien sUthaydoi
inh, chieu dai ciia dng, va p = k|iXthe hien gde xoay ciia tiet dien ngang c j a dng
2.3. SU bien doi - Bien dgng
ToadocLia phan t i i x d t r a n g thai thdi phdng dUOc xac dinh theo toa dp ciia no a trang thai t u nhien:
x = r c o s ( 5 . e , ( G ) ^ r s i n p . e o ( 0 ) - x e , (3|
^ ^ ^ M a tran eua t e n - x o E b i e u dien cac bien dang tir trang thai li/nhiOT
^ ^ R trang thai thoi phong dUpc viet nhU sau:
( ' • » ) - '
m-
0 rkfikark[5k||
, + r Ku - I
14)
^ ^ 2 . 4 . ifngsucit
^ H M O I quan he gifla flng suat va bien dang ciia mang mdng tore giao
^ ^ | c o the duac viet nhiT s<
• •^•^
^ ^ trong do E la ten-xo bien dang Green - Lagrange; C la ten-xO dp mem
^ ( n g u o c VOI ten-xo dan hoi) ciia vat lieu, va T i a ten-xa flng suat Pioia-
iB|hhoff
^ ^ ^ D o c h i e u d a y c u a m a n g m o n g r a t be, thanh phan Ling suat phap theo phuang chieu day nay khdng dang ke so vdi cac thanh phan flng sual phflong true dng va chu vi dng. Ma tran ten-xa flng suat dUdc viet
p R f i pR pR Rkgkp
* H 2H k .
ih 2: Kkh thudc hinh hoc ban diu ciia £ng
V\ tri cua phdn t d d o d tr^ng thai tU nhien, chua thdi phdng se dude ky hidu a X vd se ddoc xac dinh bdng cdc toa 66 n h d R,Q.X - n h d vay, X = B e r ( © ) + X e , Tuong t u n h d d t r a r > g thdi thdi phdng, cac vecto chi phddng t^i vi t n X sd p h u thudc vao gia tri ciia O.
6ng cd kich thudc ban ddu vdi bdn kinh R, chieu day mang mdng H vd cd chieu ddi t , ddpc khdp kin tai cac t i l t dien cd toa dp X= 0 vd X~ L.
2H k^ *
^ p R R k ^ pR k | 2H k , 2 H k , Ket hop phuang trinh {4) va (6] vao trong phuang trinh (5), ta di/Oc
p R R ^ (61
+ (Rkekp) 2Rk^kn
^xxeo ^xxxx ^xxxO .*^exee ^xxx ^exxe.
+ pRk^
pRki
2 k^
pR Rkettp
t r o n g 06, cdc sd hang cua ma trdn cua ten-xo d p m I m [Q dudc xdc djnh tCr cdc hd sd ddn hdi cua vat lieu:
.2,2
.2c2 .2.2 - c ^ s ^
2c^s^
c V c V c ^ + s "
-2cs^ 2c^s 2c2s^ c^s^
c" s" 2c^s^ c V -2c^s 2cs^ 2c^s-2c5^ c ^ s - c s ^ 4c^s^ 4c^s^ - 8 c V ( c ^ - s ^ y
E,H 1 EtH
E(H
2.5. HiphifOng trinh phi tuyen
Phdt t r i l n p h d d n g trinh ma trdn ndy, ta ddpc m d t hd phdong trinh phi tuyen b a i n (8):
=•^[CeeeelR'^k^k^ + 2 k ^ ) + C ^ k l - Cee^eRkikp 1
ki-1
^ ^ R ' ' ' B k ^ 1 = ^ [ c « e e ( R ' k i k ^ 2 k ^ ) - H C , , ^ k i - c ^ e R k i k p ] {g)
2Rkgkp =0Ce,ee(R'kg^+2k^)+Ce^,kg-CB^eRkikp]
Vdi cdc sd lidu dau vdo da cho n h d bdn kinh ficua dng d t r a n g thdi t d nhien, cdc gid t n md-dun dan hdi cOa mang mdng (E,H,EtH,GrtH,Vrt), gdc dfnh hddng cCia mdng m d n g vd gid trj cCta dp s u i t thdi phdng p, he phUdng trinh phi t u y I n (8) cd the dUOc gidi bdng phdcmg phdp lap Newton-Raphson. Cdc phdp kiem chiing cung n h u phdn tich sd hoc v l iihg xCr cOa I n g mdng m d n g t h d i p h d n g ddoc trinh bdy trong nghidn cuiu eCia Nguyen [10],
3. PhUtfng p h d p xdc d i n h t i n h c h i t ctf l y cila v d t l i e u v d i Icy t h u d t 3.i:casirl^thuyit
TC? hd phUdng trinh phi t u y I n (7), tdc gid d l xuat mdt phudng phap xdc djnh cdc t i n h chSt co \y ciia vdt lidu bdng phddng phap phdn tich i V g U l ^ Nguydn l# ciSa bdi toan phan tich ngupe ndy thifc chat la b i l n ddi K§ phuong trinh phi t u y I n (7) thanh m d t hd phuong trinh t u y I n tinh (9) md cac I n sd Id m6-dun dan hdi cua vat lidu {EfH,E[HGf,l-|,Vfl.).
M, 1 - c^s^ + 2Rkpcs' + (R^k^ + 2 ^ ) s ' *
M,2 =(R2k| + 2 ^ ) c ' ' - 2 R k p c ^ s + c V
ivli3—fikp(2cs3-2e^s) + ( c ' ' + s ' ' ) + 2 ( R \ ^ + 2 ^ ) c V
M , 4 — R k p ( c s 3 - c ^ s ) + ( R ^ k g + 2 ^ - l ) c V kg M3, = c" + 2RkpC^ + {R\1 + 2 i ^ ) c ^ s ^
ke M j 2 = ( R 2 k ^ + 2 ^ ) c ^ S ^ - 2 R k p C S ^ + s ' '
ke
M 2 3 - ( R ^ k ^ + 3 - ' y K c ' ' + s ' ' ) + R k p ( 2 c s ^ - 2 c ^ ) + 2 e V ke
Mz4 = - ( R ^ k ^ + 2 % - 1 ) c V + R k p ( c s 3 - c 3 s ) ke
M31 —2c^s-4RkpC^S^-2(R^kg+ 2 ^ ) c s 3 kg 1^32 =2(R^k^ + 2 ^ ) c ^ 5 - 4 R k p c V + 2 c s ^
ke
J V l 3 3 = ( R \ ^ + 2 ^ - 1 ) ( 2 c s ^ - 2 c ' s ) + 8Rkpc2s^
kg
M 3 4 = { R ^ k ^ + 2 ^ - l ) ( c s 3 - C ^ ) + R k p ( c 2 - S = ) 2 ke
He phuong trinh t u y & i tinh (9) cd 3 phudng trinh va 4 I n sd, do vdy neu chicds6lieucCiamdtbpba (k9,kx,kp) I d k h d n g d d d l g i d i h e p h u o n g t r i n h C l n n & 2 b d ba ndy de gidi q u y l t bdi todn, iJng vdi moi b d b a (kg,k^.kp) thu thdp diWc tiJthi nghiem, ta thdnh l|ip dude mdt hd phuong trinh tuyen tinh.
Ghdp n hd phuong trinh t u y I n tlnh ndy lai, ta dupc mdt hd phuong trinh t u y I n tinh tdng qudt gdm 3n phudng trinh vd 4 a n sd:
BitfflBBii'gttiSngniBngiWflclhlnghleiTi bjSflflSflinlifiiSi^^^figmSng Hinh 3: (Sng mang ming Suae thi nghiem Cdc t h d n g s d v l sU thay ddi kich thUdc hinh hoc cung nhU gdc xoay
n h d tham sd ddu vdo cOa bdi toan va sd ddpc t h u thdp ti^ cdc phep d o t h v t t l . Cdc sd hang eda ma triln [M(3,4)] dUdc viet nhdsau:
pRki
pRk§ M[3,4)
[ 1
EfH
E,H EfH [GaH
=
L
(ke-l)k, ( k ; + R ' k | k | - l ) k ^
2Rk|kpk,
j - 1 ) k <
( k i + R 2 k | k | - 1 ] k , 2 R k | k j k , G i i i h# phuong trinh (10) nSy bdng p h u a n g phap HouseHolder cho ph^p x^c djnh duoc cac thdng $6 vi ti'nh chat co ly cOa vdt lieu ( E , H , E , H , G „ H , v „ ) .
3.2. Thi nghiem xdc Xnhc^e thdng so Sin Iwi ciia vat iiiu 32.1. 6ng mang mdng tnjcgiao thai phdng duac thi nghiem Loai vdi ky thuat duoc thi nghi&m Id Ferrari precontraint* F302. Trong
nghidn cdu ndy, 4 dng mdng mdng thdi phdng c6 kich thude hinh hoc gidng nhau (bdn kinh R = 7.6Scm, e h i l u dai I. = 1.8m) da ducK che tao. SU k h ^ nhau cua cdc dng ndy dupc t h i hidn d goc dinh hudng (a = 0°,30'',4S°,90'') cua tdm vdi (xem Hinh 3).
3.22. M6 hinh thinghifm (xem Hinh 4}
Qe do cac bien dang cOa dng khi b\ thdi phdng, mdt gia d d bdng nhdm da dupc t h i l t k l vd ldp di/ng, Khung ndy dupc lidn k i t cung vao mdt bdn dd de ddm bdo si/ dn djnh ciia hd khung khi t i l n hdnh do dac.
M a t i n g d l kJm loai cd dddng kinh ngodi xap xl vdidifdng kinh dng mdng mdng dupc Idp vdo khung nhdm. Mdt van hoi dupc b d tri trdn dng kim loai ndy d l cung edp cung n h u xd khi ndn trong qua trinh thi nghidm.
6ng mang mdng se dupc Iudn ngodi dng d l kim loai vd dupc cd djnh bdi n loai,
I c h i ndn ddpc dUa vdo trong dng se duoc k i l m sodt va dUpc h bi d o dp sudt. S u t h a v d d i bdn kinh curm n h d chieu dai o bdi cdc cdm b i l n do i
g se OMC xic djnh bdng mdt I
qud gidi tfch, cdn nhflng d i l m rdi rac b i l u d i l n cdc sd lieu t h u duoc tir thi nghiem (xem Hinh 5), SU phO hop cOa hai b i l u dd da chi ra rdng phuong phdp xac dinh cdc tinh chat co ty eda vat lieu nay la cd t h e dp dung dupe.
a) M6 hinh thi nghiem flfcgkxDiydiifas Htaih 4: Thi nghi^ do bi$n dang tag thJi phdng
3,2,5. Xdc djnh Unh chdt ca^cua v^t li^u
Che phdp d o sd thay ddi kich thudc hinh hpc sddupc thue hidn vdi cd 4 dng vd vdi 6 dp sudt khdc nhau, Vdi 24 bd ba (ke,kx,kp) t h u duoe tir cdc k i t qud t h i nghidm, hd (10) sd bao g d m 72 phudng trinh va 4 an sd, Gldl hd phdOng trinh ndy, ta dupc cdc h f sd ddn hdi eda loai vdi dupc t h i nghidm nhu sau:
EfH=215035 (Pam) EtH=215962 (Pam) GrtH = 5255 (Pam) v ^ =0.1971 Gid trj cua cdc hd s i ddn hdi xdc djnh dupc Id hop ly khi so vdi k i t qud cCia nhieu nhdm nghidn cdu khdc trdn t h i gidi. Oe kiem chung d o tin cay eCia ede k i t qud thu dupc t d phuong phdp phdn tieh nguoc, tdc gid sd da sir dung cdc tlnh chdt c a i y ciia vdt lidu (EfH,EtH,GnH,v^] vila thu dUPe de t l n h todn t^i c i c hd sd thay ddi k(ch thudc hinh hoe cua dng (kg,kx,kp) bdng hd phddng trtnh (8). Cdc gid trj (kg.k^.kp) ddpc tinh bdng ly thuyet vd dupc d o bdng phdcmg phdp thi/c nghidm sd dupc vd bieu dd, phu thudc vdo ip s u i t thdi phdng. NhOng dddng l i l n net b i l u d i l n cdc k i t
c)GKi(oayditiu6ngp(L)
Hinh 5: So sdnh kft qui ly thuyA v^ thuc nghiem (Ghi chu: diriing lien net bieu dien ket qui gi jl tfch dif m rdi rac bieu dien kft qui thf nghifm)
4 C d c k l t l u ^ n
Bai bdo ndy trinh bdy mdt phuong phdp mdi xac djnh cdc tlnh chat CO ly cua v$t hdu tis che phip do b i l n dang cua dng khi thdi phdng.
Phuong phdp ndy dya trdn bdi todn phdn tieh ngupc cac phuong trinh phi t u y I n da cd tir 1^ t h u y l t Cdc h f so ddn hdi cfla mdt vdt lieu mdng mdng hidn cd trdn thj trUdng dUpc xdc ^ n h . Gia trj eua cac he sd nay hodn todn phCi hpp vdri k i t qud do dUpc da dupc cdng b d .
Cdc nghidn cdu khdc dang duPc thyc hidn Oi xdc djnh cdc iJng xdcila dng mdng mdng thdi phdng dudi tdc ddng cua cdc tdc nhdn gdy udn ngang vd udn doc.
T A I L i l u THAM K H A O
(1ihttps://secufe [fai.com/bbardi/art«les/iv1009_fl_inflatable html (2] http //www.doublet.com/en/UK/eq uipment/inflatabie-donie
{3]X.Q. Peng, I Cao (200S) A contmuum medianks-based non-aithogonal ccmshtulive model for woven compoiite fabrics, CompoOeL Part A. (36), pp, 8 5 9 - 8 7 4 .
|4] K. Vjftochins. Comportement des textiles tedmiiiues soaples dans le domaines des grandes dehrmations IdentHkabondehngidltiendsoiSementplan PhDthesis,UnirersiteClaudeBematd l y o n 1 , 2 0 0 5 .
[5jV.(luaglini,C Coraz;a,andCPoggi. Experimental charaderizatiim of orthotropic technical textiles underitniaxiai and biaxial loading Com(iiK/(«,'Pflff;i,39:1J31-1342,200B.
[6]C.6alliot, R,H. Luchiinger (2010). The shear r a m p i A n e w t e s t method f o r t h e investigation of coated febric shear behaviour - Part II: Experimental validation. Composites: Port A, 41(10), pp 1750-1759.
[7] P Boisse, A. Gasser, and 6 . Hivet Analyses of fabric tensile behawour: detmnination of the biaxial ter«ion-strain surfaces and their use in forming simulations. Composites Part A, 32(10):1395-1414,2001.
[8JB.N Bndgens, P.D. Gosling, and M J,S. Birdiall. Membrane material behaviour concepts, pracbse and devdopments.Sfrudiffo/ffijAieer, 82(14):28-33., 2004.
[9]V, Can/elli, C. Corazza, and C Poggi. Mechanical modelling of monofilament tedinical tertiles Computational Matenals Science. Al:679-&Xim.
[101 Q.T Nguyen,J,C Thomas, and A. Le van An analytical solution f o r a n inflated orthotropic membrane tube w i t h an arbitranly ortenied orthotnjpy basis Engineering Structures. 56:1080- 1091,2013,
