Indian Jou rn al of Fibre & Textil e Research Vol. 27. Dt::ccmber 2002. pp. 3X8-392

A geometric model of woven geotexti le tape fabric to predict tensile property

Subhas Ghosh" & Meli ssa M Koeni g

In stitute of Textile Tec hno logy, Charloll esv ill e, Virgi nia 22903-46 14, USA

/?1' Cl' il 'l'iI 3 Jll iv 20UI ,' rl'l'ised recei l'{'(l ({lid ({cc{'pled 15 DC/ober 200 1

A geometr ic model has been prese nteci to prcdict the strengt h and st retch behavior 01' woven IJpe fabr ics that are usually ut ili zed in gcotcx til e appl ications. Mode l input parameters inclucie rabri c geo metri c parameters, tape bending c lTect, conso li dations. ancitensilc properti es . It is poss ihle to pred ictthc strengt h or the commcrcia l gcotcxtilt:: rabric within 10'76 or the cxpc rimentally determ incd va lues in most of thc cascs . Somc discrc pancics havc bec n notcd that arc probah ly cl uc to the hi gh variation in tape tensilc propertics and es timati on in the anglc 8 1,

Keywords: Geomctrie parameters. Geotex ti le, Tensile propert ics

1 Introduction Geotcxtile fabrics are used in civ il engllleenng

app licati ons, such as structural and envi ronmental processes. These fabrics can be woven , nonwoven or composite that ex hibit certain properti es including permeability and high tensile strength . The important factors in manufacturing geotext il es arc fiber (polymer) type and fabric design. At present, a major usc of geotext iles is w ithin foundati on components or load supporting parts of a structure which include build ings, embankments, roads and railways, and hence the strength of these fabri cs is very i I11portant. The woven geotex til es used in our study had a plain weave constructi on that was produced from poly­propylene tapes. The geometry of a fabri c has signi j'i cant effects on fabric 's mechanica l and phys ica l behavior. The study of woven fabric geometry started wi th Piercet who assumed yarns as fl ex ible circular cy linders interwoven in a regularl y recurring pattern to fo rm fabri c. Pierce t deve loped a geometri ca l model to determine the var ious fabric parameters; however, considerati on was not given to the intern al forces. A lthough Pierce's model has been found to be va luable for very open structures. the assumpti on of the circular cross-secti on, fl ex ibility and incompres­sibility was found to be unrea li stic, which limited the application of thi s mode l. It was rea li zed that in more tightl y woven fabrics , the inter-thread forces set up

" To wholll al l thc correspondence should be add resscd. Preselll addrcss : Professor. HUlllan , Environlllental and Consumer Resources , Eastcrn Mich igan Uni ve rsit y. 2 10 Roosevel t l-h,lI. Ypsil anti. Mi chi ga n 48197. USA E-Illai I: Subhas.Ghosh@banya n.cmich .eclu

during weav ing cause considerabl e ri atlening of the thread. In order to avo id complex ity of the elliptica l yarn secti on, Pierce used an approximation treatment =' . In the approximation, the ori ginal equat ions deri ved from the circular cross-secti ons were used by repl ac ing the diameter of the circula r cross-sec ti on yarn with the minor diameter (axis) of the appropriate elliptic sec ti on. Pierce' s approximation was adeq uate for open weave fab rics, but could not be applied to j ammed structures.

Grosberg' descri bed the tensi le property of the woven fabri c as an ani sotropic phenomenon, which makes the prediction of tensi Ie properti es more complex. Lack of symmetry in the fabri c causes a difference in modu lus between the warp and weft direc ti ons. The variati on in modu lus becomes larger when the ex tension of the fabric takes place at an angle and also involves a different mechani sm of deformati on'. Kawabata e l {{I. ~ described a biax ial­deformation theory for plain weave fabrics. In thi s theory, warp and weft yarn s are considered perfectly fl ex ible and the forces due to yarn bending are neg l igible. The theory in troduced th e comprcssi bi I ity of the yarn ca used by a lateral compressi ve fo rce. It was shown that the compressi ve properti es of the yarn s had an effect on the tensi Ie properties of the fabr ic. The model developed by Kawabata el 01.5 has been shown to predict the ten sile behavior of the fabrics th at is in agreement with the experimental resu lts ; however, the model did not include the bend ing of the yarn that wou ld have all effect on the tensile property of th e fabri c.

GHOSH & KOENIG: GEOMETRIC MODEL OF WOV EN GEOTEXTILE TAPE FAB RIC 389

In the uniaxial-deformati on theory of plain weave fabrics, Kawabata ef 01. 5 ass umed that the ya rn in the direction of the applied force is perfect ly flexibl e and also considered the effect of bending on the transverse yarn. The sa me theory used to solve the problem of biaxial tension was not app li cable to thi s situati on because no tension was appl ied to the transverse yarns in the case of uniaxial load ing. The uniaxial­deformat ion model proposed by Kawabata ef al .

5

appeared to predict the fabri c's tensile behav ior we ll except for hi gh and low extension reg ions where di screpancies have been observed between the experimental and theoreti cal predi ctions. Realll c f 01.6 have reported a mi cromechani ca l model to describe the tensile behav ior of woven fab ri cs. The inputs of thi s modd' included ori ginal fabric geometry, ex perimentally determined bending behav ior, con sol idation response, fl atleni ng response and tensil e response of the yarns. This model has been used to describe the load versus fabr ic strain curve. and al so the normal force versus fabric strain curve at the crossover points. The vari ous models to predict the tensile behav ior of wove n fab rics, proposed by the different researchers l.6, were based on cy lindri ca l yarns. In the present work , a model has been developed foll owing the similar approaches of both Kawabata e l 0 /.

5 and Realff' and using Pierce'sl original geometric parameters for geotexti Ie fabr ic produced from the rectangular tape ya rns. The primary objec ti ve of the study was to develop a geometri c model of a woven tape fabric to predi ct tensile strength .

2 Model Development

The model was deve loped to predict the tensile behavior of the geotex tile fab ric through the anal ys is of fabric geo metry, and the interaction of the geometric elements to the appl ied stress on the fab ric. The tape parameters considered were deni er, tape width , tape thickness. tape strength. tape elongat ion and fl ex ural rigidity. The fabric parameters were warp density , weft density, and warp and weft crimp. Geotex tile fabric s produced from polypropylene tape ya rn were co llected from di fferent industrial locat ions to va lidate the model. These fabri cs had a ran ge of warp and weft densi ty and tensi Ie properti es as fo llows

Warp density, ends per inch 12-28 Weft density, picks per inch 11 - 18 Warp breaking load , g 1519-479 1

Weft breaking load, g Warp elongation , % Weft elongation, %

1887-9055 29.5- I 1.8 27.8-8.6

One of the maj or differences in our model ari ses from the rectangu lar cross-section of the tape ,vi th negligible thickness in all practical purposes. This difference in cross-sec tion yields different propert ies such as modulus and moment of inert ia . Flattening of ya rn was not considered because the original thickness was so small (in microns), whi ch wou ld have a negli gible effect on the ultimate predi cti on model.

3 Inputs and Outputs of the Model

The model inputs include the ori gin al fa bric geometry I.5.!>. tape bending behavior, conso lidat ion response of the tapes and tensi Ie response of the tape. The outputs of the model are the fabr ic load. fab ric strain and normal force at the crossover points.

4 Incompressible Tapes and Fabric-No lamming Situation

4.1 Fahric Structural Parameters

The tapes in the loaded direction of the fabri c are strai ghtened at a low strain region, which is the crimp interchange section. Normal forces that are perpendicul ar to the loading direction act on the tapes at the crossover poi nts (F ). These forces can be determined from the bending ri gidity of the tape and the amount of tape deflection ca used by these forces. The amount of defl ec ti on (h) can be measured from the unit ce ll geometry of deformati on used by Kawabata e f al ." and Realff Cf al.6 as illustrated in Fig. I. The woven geotex tiles that were modeled here had plain weave s7ructu re and , hence, the Kawabata's" deformation geometry was, in genera l, applicable. Tn Fig. I, the solid line represents the initial geometry, while the dotted line is the fab ri c geometry afte r deformation . The XI and X2 are the axes in the warp and weft di rec ti ons respec ti vely. The defl ect ion distance II is calculated considering the so lid li ne and dotted-line tri angles as in Fig. I b. We can obtain II = /111/1 - (11 11/ 1 - hi ) from Fi g. lb. Us i ng the trian gles to solve /111/1 and (hili I - h i) and utili zing the geomet ri c relat ionship in Fig. I, the fo ll ow ing eCfLlati on (l is obtain ed:

... ( I)

390 INDIAN J. FIBRE TEXT. RES .. DECEMBER 2002

( a) t I ,

, , , ,

~ ____ ~~ ________ ~~ ____ -J

'" ~~~' .. ,-~ ~--------- ~I ------~~

( bl

Irm 1 ~ Maximum tape deflection

hi = T:iptl deflection

101 = Initial unit length of tape (Fig 2)

0 0 1 -initial angle between the warp tape axis and the a;,< i~ along the ultersectioll of the warp and weft tape5

o I = Angle between tile warp tape axis and tile axis along tlll~ intersectiun of the warp and weft yarns after defolTnatiOI1

), - Length in the stretched state/length in the unstretched

stat~ = 1 + strail!

Fig. I-Unit cc ll gcometry of deform cd structure-lJ,.

From the ori ginal geometr/ (Fig. 2), 10 1 and YUI are known and, hence, eOI can be determined as follow s:

. YOI SlIl eo, = - (2) 111I

where YOI is the initial tape spactng ( lithread per inch)

4.2 Bcnding Effects in thc Model

A beam model was utili zed to determine the normal forces on the tapes at the crossover points. The beam model was applicable for thi s model because of the rectangular cross-sec tion of the beam and the zero slopes at the wall s and at the center of the beam. The slopes match those of the tapes at the crossover points in the fabric , which is al so the reason for Realff el 01 .0 to use thi s model. Using the approach of Gere and Timoshenk07 for a pri smatic beam and a beam that defl ects a distance 211, the following relati onship can be derived:

211 = FN (2/ o2 ).1 orF = 192£1 .2h 192 £1 N ( 2/02)'

... (3)

where F N is the normal force; £1, the flexural ri gidity ; 102 , the initi al unit length (Fig. 2) of the weft tape; and /7 , the tape defl ecti on.

This equ ati on was used to calculate the bending coeffici ent (Be) which is similar to the procedure used by Kawabata el 0 1.4 to calculate their constants.

(ol (b)

Fig. 2- Unit structure or plain weave rabric by Kawabata (' / (/1. 4.

However, they considered bending of fibers instead of the yarn. Realff el 01.0 measured the bending responses experimentally using a four-point bcnding tester. In thi s study, the bending coefficient (Be) was calculated using the followin g rel ationship:

Bc= 192£~ . .. . (4) (21m ) .

4.3 Consolidation Effect

After crimp interchange and in the moderate strain region, the tapes in the loading directi on are ex tended. I n thi s region , tapes undcrgo consol idation or a reduction in width whi le the length increases. Thi s increase in length and reduction in width is assoc iated

GHOS II & KOEN IG: GEOMETRIC MO DEL OF WO VEN GEOTEXT ILE TAPE FABR IC 39 1

with an increase in normal force. This increase in normal force takes into account the width before and after consolidation and the flex ural rigid ity. Realff ef a f. (, used a similar equati on where yarn diameter was used instead of the tape width to calculate the normal force due to consolidati on [F N(consolid"!ion)] as fo llows:

F N (consolid,,!iun ) = 41 EI [~~I - ;1 I 02 Ad 0 J

... (5)

where 101 is the in iti al unit length of warp tape; 1,,2, the initi al unit length of weft tape; W i-yl, the tape width after consoli dation; and Wo , the tape width before conso lidation.

4.4 Fabric Response to Extension- No Jamming

A tape within the fabric fa il s when it reaches its average extension, whi ch is determined by an indi vidual tape tensi Ie test. Three equati ons for the plain weave tape fa bric breaking load (F), stretch (AI) and normal fo rce (F N) at the crossover points are proposed here th at are similar to the models proposed by Kawabata et ars and Rea lff ef a16

. Tapes L1 sed in these fab ri cs are generally very thin ; consequent ly, the effect of fl attening due to the normal fo rce becomes negligible. Therefore, the effect of fl attening was not considered in the foll owing model for the plain weave tape fa bri c.

1- [ IOlcos 801 )" \'

4g 1 (A "I) + BJolA d .

end per inch x l " . .. (6)

... (7)

... (8)

where AI is the fabric stretch ( I + stra in); and Ayl. the tape stretch ( I + strain ).

5 Fabric Breaking Load and Stretch (Experimental vs Model P red icted) Results Severa l commercial tape fab ri cs (pl ain weave)

we re co ll ected fro m diffe rent producers to compare the va lues of model predi cted fabri c strength with the ex perimentally determin ed resul ts. The tape's tensile testing was perfo rmed on an Instron Single-end Tester at a constant rate of ex tension ( 10 inches/min) using a 5-inch gauge length. An average breaking load of the tapes from each fabri c was determined. A grab tensile tes t was performed on the tape fabrics according to the ASTM Standard 0 5034 on a MTS All iance RT/5 Tensile Tester. Bending coefficient (Be> was

T able I- Experimcnla l and pred icled values of fabric load and slreleh

Fabric Fabri c load, g Fabric slrelch No. Ex peri Ille III a I Pred icled C/n DilTere llcc Ex peri lllelHal Pred icled % Diflc rcnce

I 48, 126 48,496 0 .77 1.201 6 1.206 0.44

2 42.290 39.999 -5.43 1. 16 10 1.303 10.90

3 40,075 46.778 16.73 1.1503 1.273 9.6-+

4 47 ,883 43.23 1 -9.72 1.lns 1.2X I 8.06

5 5 1.809 49. 187 ·5.06 1.2053 135 1 10.78 6" 145.240 157.097 8. 16 1.1 5 17 1. 155 0 .29

7 90,278 9 1.924 1.82 1.0860 1. 163 6.62 8' 96,524 95.39 1 - 1.1 7 1.1 458 1.140 -0.50

9 49.287 49.377 0 . 18 1.2341 1.237 0.23 10 49.280 48.672 - 1.23 186 1 1. 179 ·0.60 II 46. 194 45.557 - 1.38 1676 1. 17 1 0. 29 12 46. 157 49 .285 6.78 1698 1. 199 2.4 13 5 1,787 51.2·P - 1.04 1690 1. 173 0.34 14" 128 .749 124.4 16 -3 .40 1.1 9 10 179 - 1.02 15 35.934 34. 3 14 -4.5 1 1.1 00 1 I. 15 I 4.42

"T hese Cabrics were produccd wilh do uhl e tape (2- ply) .

392 INDIAN J. FIBRE TEXT. RES., DECEMBER 2002

Tabl e 2- Nol'lnal forcc (F ,.;) at the crossover points near break

Fahric No. Normal force. g

17.12

2 6.84

:1 1.\)8

4 9.:12

5 6.79

7 25 .17

\) ] ] .73

10 2 1.6 1

I I 2 1.61

12 16.04

1:1 11.01

15 457

Norma l force for fabri c Nos. 6. 8 and 14. produced w ith douhle tape, were not calculated.

determined from Eq 4. Flexural ri gidit y (£ X /) was obtained from the modulus of elas ti cit y that was deri ved from the load-elongat ion diagram. The moment of inertia (I ) of the tape was then ca lculated from the fo llow ing equation 7

:

Width x Thickness ' / = ... (9)

12

The initi al angle between the warp tape ax is and th e axis along the intersecti on of the warp and weft tapes was cal culated using Eq 2. The angl e after dcl'ormation (0 1) was approx imated by exa minin g the fabr ics aner deformation under a microscope. In Tab le I, both ex perimenta ll y determined and model pred icted va lu es of fabri c load and stretch are presented . It was poss ible to pred ict fabri c load and stretch within 10% of the experimentall y detennin ed va lues on a tensil e tes ter. In a few cases, however, a larger discrepancy between the ex perimen tal and the model predi cted va lues was found , wh ich is show n in Table I as pos iti ve or negati ve va riations. There arc three poss ible sources th at can be attributed to these di screpancies. Both break in g load and elongat ion of the commercial tapes used in these fabrics were hi ghl y va ri able, whi ch created difficulty in acc urately

determining the tape strength and strain. There may be so me error in esti mati ng 8 1 of the deformed fab ri c in absence of a more accurate method. Some of the va ri ati on may al so be due to the fact that two fab rics caused jamming under load, whi ch was not considered in our mode l. The model shou ld be mod ifi ed for those fabrics that woul d jam during extension, to yie ld better resul ts.

For the various fab ri c geometry anci tape parameters, normal forces at the crossover points nea r break were ca lculated. It is an important parameter because th e normal force near break \-v il l affect the load transfer to the tapes in the area or the break. The normal force va lues presented in Table 2 were not experimentall y verified and were ca lculated based on the beam model as desc ri bed carl ier.

5 Conclusions A geo metric model for predi cting the strength and

stretch of woven tape fabric has been reported . Origi nal fab ri c geometric parameters , bend i ng response and tape co nso l idati on (w idth change effeel due to ex tension) have been ca lcu lated to determ ine tape fabr ic strength and stretch. Model predicted load at break and st retch values were general ly found to be within 10% of the ex perimentall y determined fabr ic load and st retch ; however, some excepti ons were observed. To make the model more uni versa l, the fabric jamming effect needs to be considered. particu larl y fo r li ghtl y woven fab ri cs. It is beli eved th at thi s could prov ide a guidance (0 design tape fabr ics for spec ific app li ca ti on .

Rcfcl'cnccs I Pi erce FT . .I Texl I IISI. 28 ( I \) .)7 ) T45 . 2 I-Iu J, Te.\1 Asia . 26 ( I \)\)5 ) 5X. :1 Grosberg P, in Slmcl llm/ Mec!wllic.\· oj' FiiJe/,.I. Yal'll s ({ lIiI

FaiJrics hy J W S I-I earl e, P Grosbcrg & S Bach . ..: r (John Wi ley & Sons, Inc., New York). I \)6\) , :1:19.

4 Kawabata S. Kawai 1-1 & N iwa M . .1 r e.l"I / IiSI . (A ( 1973) 2 1. 5 Kawabata S, Niwa M & Kawai H . .1 1'e.l"l /".1'1 . 64 ( I \)73 ) 47. 6 RealiI' N L. Boyce M C & Backer S A. Te.rI Nt's J. 67 ( I \)X7)

445. 7 Gere J M & Tililoshellko S P. Mechallics o/Ma/eria/s ( PWS

Pub l ishing CO lllpany. Boston). 1\)97. 6X4.