Theoretical and Experimental Estimation of the Stored Energy of Plain Knitted Fabrics Using Yarn Pullout Test

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1 Thortical and Exprimntal Estimation of th Stord Enrgy of Plain Knittd abrics Using Yarn Pullout Tst Azita Asaysh Ph.D., Elahh Niazkhani, Ali Asghar Asgharian Jddi, Amirkabir Univrsity of Tchnology, Thran, Thran IRAN Corrspondnc to: Ali Asghar Asgharian Jddi mail: ABSTRACT Th yarn pullout tst is a suitabl mthod for invstigating th intrnal mchanical proprtis of th fabric structur hich is stablishd during th aving or knitting procss. In this study, a thortical modl is prsntd to stimat th stord nrgy of plain-knittd fabrics hich is dtrmind using yarn pullout. Th modl can prdict th stord nrgy in th fabric, basd on th fabric dimnsional proprtis of stitch lngth and yarn contact angl using forc balanc analysis. Morovr, in ordr to valuat th suggstd modl, thr typs of plainknittd fabric from cotton, cotton/polystr and cotton/nylon ith thr diffrnt stitch lngths r producd and subjctd to pull-out tsts. Comparison btn xprimntal and thortical rsults, dmonstrats a rasonabl prdiction. Th rsults sho that th cotton/polystr fabric has th maximum stord nrgy, bcaus of its highr yarn to yarn friction cofficint. It as also found that, th incras in fabric's loop lngth lads to a dcras in th fabric's stord nrgy. Kyords: Yarn pull-out tst, stord nrgy, plainknittd fabric, stitch lngth, thortical modl INTRODUCTION Among various mthods to valuat a fabric's mchanical charactristics, th yarn pull out tst is a practical mthod to invstigat th fabric's intrnal dformations causd by th constitunt yarns. On of th important assumptions in such loading is to considr th fabric as a composit of yarns. Pullout tst is also a mthod, providing usful information about fabric taring, its ability to absorb nrgy spcially in ballistic applications, finishing fficincy, bnding and sharing hystrsis of th fabric, and finally th frictional bhavior of th fabric. In this tst, a forc is applid to on nd of a singl yarn of th fabric to pull it out. This sort of loading is not a novl procdur and scholars hav applid such tsts to xamin mchanical bhaviors of fabrics []. Th main usag of th yarn pullout tst is to achiv a bttr stimation of th rlaxation stat of cotton ft knittd fabrics confrring minimum intrnal nrgy du to rlaxation tratmnts. Whras, th lost yarn pullout forc can b attributd to th minimum intrnal nrgy of fabric []. Thrfor, a full stability of fabric dimnsions is accompanid by th lost yarn pullout forc. Taylor [3] studid fabric tar strngth through a yarn pullout tst, and rprsntd a thory basd on th yarn intractions. Upon his vi, th applid load ovrcoms th frictional forc in crossovrs and causs th thrad to b pulld out of th fabric av. Whn th applid load incrass, it tars th fabric, bcaus it bcoms mor than yarn braking strngth. Sbastianb t al. [4] usd th yarn pullout tchniqu to valuat th ffct of a softning agnt on fabric prformanc, and thy proposd a simpl modl to calculat pullout load and th influnc of yarns crossing ovr. Sbastianb t al. [5] and Motamdi t al. [6] dvlopd physical modls basd on spring junction's assumptions, to invstigat frictional bhavior of yarns ithin th fabrics. In th fild of fabric failur, Ralff t al. [7] and So t al. [8] focusd on th rol of yarn-to-yarn friction and th slippag of yarns in crossovrs hn th ovn fabric is applid by a forc. Thy pointd that bfor fabric failur, th yarn pullout is occurrd. Pan and Young [9] mphasizd on gomtrical and mchanical proprtis of fabric and th yarns. Thir modl as abl to prdict th maximum pullout forc, and found maningful rlations btn th pullout forc and som important proprtis of fabrics such as th bnding hystrsis, and th tnsil complianc. Journal of Enginrd ibrs and abrics Volum 7, Issu 0

2 Pan [0] proposd an analytical modl and analysis of fibr pullout from a bondd fibrous matrix. H dmonstratd that th modl can prdict th bhavior of fibr pullout in ths systms, provid insights on intractions btn fibrs by mans of bonds, charactriz bond proprtis, and rval and stimat important paramtrs. igur shos a typical forc-displacmnt curv, rsulting from yarn pullout tst for ovn fabrics []. Hossini and Toriumi [] dmonstratd that th natur of th stick-slip motion of th dynamicfrictional forc of a pulld-out thrad is priodic and dpnds on th fabric construction. Thy also found high corrlation btn th arp-pullout forc, th intnsity of thrad intraction at th crossing points, th strngth of fabric in th arp dirction and th ft yarn irrgularity. Badrosamay t al. [] introducd an oscillation modl, hich as capabl of anticipating yarn pullout forc-displacmnt profil. Kirkoods t al. [3] studid yarn pullout procss as an nrgy absorbnt and charactrizd th yarn pullout forc and nrgy as a function of pullout distanc through a smi-mpirical modl. Jddi t al. [] invstigatd th dimnsional proprtis of plain knittd fabrics producd from cotton yarn and subjctd to diffrnt rlaxation tratmnts. Thy charactrizd th intrnal nrgy of fabric by using yarn-pullout tst mthod in ultrasonic rlaxation stat and compard it ith othr common mchanical rlaxation tratmnts. Valizadh t al. [] prsntd a thortical modl to prdict variations of th intrnal mchanical paramtrs of ovn fabrics basd on a forcbalanc analysis of yarn pullout tst. To considr th intrnal stord nrgy of plain knittd fabric, hich can b attributd to th intrnal mchanical proprtis, suggstd a thortical modl in this rsarch. This modl can prdict th stord nrgy in th fabric, according to th fabric dimnsional proprtis, stitch lngth, and contact angl of yarns, using forc balanc analysis. THEORETICAL MODEL In ordr to simplify th modl, considrd th folloing assumptions: - Yarn xtnsion during th pullout tst is ngligibl. - Yarn cross sction during th pullout tst is constant. IGURE. Gnral pattrn of forc-displacmnt curv rsulting from yarn pullout from a ovn fabric []. Th stord nrgy in th fabric is calculatd from th undrnath ara of th curv as folloing: W=.d () Whr is th yarn pullout forc, and d is th yarn displacmnt. To distinct rgions ar rcognizabl from igur. In th first rgion, th forc incrass to rach to a maximum valu, hich corrsponds to th maximum static frictional forc ( S ). Th maximum pullout forc is du to pullout of to lgs of th first loop from th nighbor loops. Aftr ovrcoming th friction btn first loop and nighbor loops at cross points, th yarn pullout curv shos a stick-slip oscillation (scond rgion). This rgion corrsponds to th dynamic frictional forc ( K ), hich rmains almost constant. igur shos th yarn pullout tst from plain knittd fabric schmatically. This figur illustrats that during th yarn pullout, th yarns slip in a circular path on ach othr. By assuming that th yarn cross sction is constant during pullout tst, may us Capstan's la to calculat th pullout forc. Capstan's la hich is usd to calculat th friction btn string and pully is as folloing: T T. () Whr T and T ar input and output tnsions rspctivly, is friction cofficint btn to yarns and is th contact angl of to yarns. Journal of Enginrd ibrs and abrics Volum 7, Issu 0

3 Substituting Eq. (5) in Eq. (4) ill giv: K T (6) Consquntly, n is calculatd as folloing: IGURE. Schmatic of yarn pullout tst from plain knittd fabric. Th stord nrgy in th fabric during pullout tst quals to summation of rquird nrgis to unravl ach loop. Thrfor: n T n n n (7) In ordr to calculat th stord nrgy in th fabric, using Eq. (3), th valus of and d should b stimatd. W m n. d n (3) n Whr n is th rquird forc to unravl th n th loop, d n is th vrtical displacmnt of th yarn, corrsponds to unravling of th n th loop and m is th numbr of unravld loops. igur 3 shos th yarn pullout procss for th plain knittd loops. During th yarn pullout for th first loop, is th output tnsion ( T ) and is quivalnt to avrag forc in oscillatory rgion ( K ) of forcdisplacmnt curv (igur ) i..: T K Aftr unravling th first loop and dominanc on static friction, th rquird forc to unravl th scond loop is calculatd as folloing: T (4) Eq. (4) xprsss that, quals to summation of rquird forc to dominat th dynamic friction of th scond loop ith undrnath loops ( T ) and rquird forc to unravl th prvious loop ( ). Using Capstan's la, T obtains as folloing: IGURE 3. Loops unravling in th plain knittd fabric during th pullout tst. Estimation Of Th Contact Angl Of To Yarns ( ) As illustratd in igur 3, BB'= = al spacing, and BAB'=L= loop lngth. In ordr to sho th dtail of th yarn path, a part of igur 3 is magnifid in igur 4. Th circls O' and O ar rspctivly, th cross sction of th ndl to pullout th yarn from th fabric and th yarn usd in th fabric. It is assumd that, th yarn lngth btn A and B quals to lngth of th lin that conncts A to B dirctly. T K (5) T Journal of Enginrd ibrs and abrics 3 Volum 7, Issu 0

4 IGURE 4. Magnifid part of igur 3. Rfrring to igur 4, AB ˆ E quals to CO ˆ D and quivalnt to. Oing to th fact that th yarn diamtr is ignorabl against al spacing, thus, it can b rittn: tan( ) AE BE In th nxt stp: d tan( ) 3 inally, d tg tg n is obtaind as folloing: n dn tan( ) (n ) d ( d ( ) 3 dn n tg ( ) (n ) ) (8) (9) (0) Estimation Of Th Yarn Vrtical Displacmnt (d) igur 5 shos to continuous stags of unravling of th first and scond loops. IGURE 5. To continuous stags of unravling of th first and scond loops. In triangl (), th valu of d quals to x c, hr c is cours spacing. rom triangl () and (), th valu of x and x can b obtaind as follos: L ( d) ( x c) () L ) ( x d) (3) ( d () inally, d n is calculatd as folloing: L n) ( x dn ) (n ) (3) ( d By dtrmination of d and in diffrnt stags of yarn pullout, and rplacing thm in Eq. (3) and Eq. (7), th stord nrgy in th fabric ill b calculatd. MATERIALS AND METHODS Thr typs of plain-knittd fabric from cotton, cotton/polystr and cotton/nylon ith thr diffrnt loop lngths r producd using 30 N (0 tx) ring yarn on a circular knitting machin (gaug 8 and diamtr 30 inch). Th fabric charactristics ar givn in Tabl I. Journal of Enginrd ibrs and abrics 4 Volum 7, Issu 0

5 abric Cod C C C3 CP CP CP3 CN CN CN3 TABLE I. abric charactristics. Dscription 00% Mrcrizd Cotton Loop Lngth: 3.8 mm 00% Mrcrizd Cotton Loop Lngth: 3.3 mm 00% Mrcrizd Cotton Loop Lngth: 4.66 mm 33%Polystr Loop Lngth: 3.8 mm 33%Polystr Loop Lngth: 3.3 mm 33%Polystr Loop Lngth: 4.66 mm 33% Nylon Loop Lngth: 3.8 mm 33% Nylon Loop Lngth: 3.3 mm 33% Nylon Loop Lngth: 4.66 mm Cours Spacing (cm) Wal Spacing (cm) Yarn's riction Cofficint Masurmnt To masur th yarn to yarn friction cofficint, from ach bobbin of yarn (cotton, cotton/polystr and cotton/nylon), strings r cut and fixd on to short and long cardboards (igur 6). Th componnts of th usd apparatus (th Instron Tnsil Tstr 5566) includd th long cardboard, fittd horizontally on th bottom ja, th short cardboard ighting 40 gf, an inxtnsibl cord connctd to short cardboard, and a lo friction pully. Th short cardboard is dran at a constant spd (5 cm/min) by th Instron-tstr crosshad. Th principl of th masurmnts as basd on th rctilinar motion of yarns in prpndicular dirction. This xprimnt as prformd 4 tims for ach yarn and th static and dynamic friction cofficints r calculatd as folloing: s, k s, k (4) m 0 n 000 Whr m is th ight of short cardboard and n is th numbr of yarn strings. Th avrag rsults ar shon in Tabl II. TABLE II. Yarns' friction cofficint. Yarn Typ s k Cotton Cotton/Polystr Cotton/ Nylon Yarn Pullout Tst To prform yarn pullout tst, fabric sampls ith 7X7.5 cm dimnsions r cut and unravld in th cours dirction. Th prpard sampl as clampd to a U form fram (igur 7). Th fram as connctd to th lor had of tnsil strngth tstr (Instron 5566). Thn, th middl loop of th sampl as unravld from th knit and connctd to th uppr had of Instron (igur 8). Th uppr had movd up at a vlocity of 0 mm/min and th pullout forc as masurd hil 30 loops r unravld from th knit. or this purpos 30 loops r countd and markd on th fabric bfor pullout tst. During th tst, hn th markd loops r unravld from th knit, th tst as stoppd. rom ach fabric structur, fiv sampls r tstd and th pullout curvs r rcordd by using Instron. igur 9 illustrats a typical yarn pullout curv. IGURE 7. Clampd fabric using th U form fram. IGURE 6. Yarn to yarn friction masurmnt. Journal of Enginrd ibrs and abrics 5 Volum 7, Issu 0

6 It should b notd that, hil th pullout forc incrass to rach to its maximum valu, th static friction cofficint ( s ) should b usd in Eq. (7), and aftrards, th dynamic friction cofficint ( k ) should b usd. Th xprimntal and thortical valus of stord nrgy in th fabrics and th prcntag of th diffrnc btn thm ar shon in Tabl IV. TABLE IV. Exprimntal and thortical stord nrgy in th fabrics. IGURE 8. Modifid tnsil tstr usd to masur th yarn pullout. IGURE 9. Yarn pullout curv from th plain knittd fabric. RESULTS AND DISCUSSION In ordr to calculat th undrnath ara of th xprimntal yarn pullout curv, th Cumtrapz tool of Matlab softar as usd. Also, th stord nrgy in th fabric calculatd thortically, by rplacing n and d n from Eq. () and (4) in Eq. (8) and (3). Sinc th calculatd valus of for diffrnt loops ar vry clos to ach othr, th avrag valus of ar shon in Tabl III for diffrnt fabric structurs. TABLE III. Th avrag yarns contact angl ( ). abric Cod (Dgr) C 59.8 C C CP CP CP CN CN CN According to Tabl IV th maximum diffrnc btn xprimntal and thortical valus is lss than 5%.Thrfor, it can b concludd that th prsntd thortical modl shos a rasonabl prdiction of th stord nrgy in ths fabrics. Th diffrnc btn xprimntal and thortical rsults could b attributd to som xprimntal rrors, and also loos structur of fabrics ith long loop lngth, hich causs misplacing of th fabric in th U form fram. Effct of abric Matrial on th Stord Enrgy in th abric Th ffct of fabric matrial on th stord nrgy in th fabric is shon in igur 0. It is obsrvd that, th cotton/polystr fabric has th maximum stord nrgy, du to its highr yarn to yarn friction cofficint. Cotton/nylon and cotton fabrics ar in th nxt stags rspctivly. It is obvious that, incras in friction cofficint ill incras th frictional forc and th stord nrgy in th fabric consquntly. Journal of Enginrd ibrs and abrics 6 Volum 7, Issu 0

7 IGURE 0. Effct of fabric typ on th stord nrgy in th fabric. Effct of abric's Loop Lngth on th Stord Enrgy in th abric Th ffct of fabric loop lngth on th stord nrgy in th fabric is shon in igur. This figur rvals that, for all fabrics, th incras in fabric's loop lngth lads to dcras in th fabric's stord nrgy, hich is du to loos fabric structur hich causs lss friction btn th loops. IGURE. Effct of fabric's loop lngth on th stord nrgy in th fabric. CONCLUSION In this study, a thortical yarn pullout modl is prsntd to stimat th stord nrgy of plainknittd fabrics. This modl is basd on th fabric dimnsional proprtis i.., stitch lngth, and contact angl of yarns, using forc balanc analysis. Th prcntag of diffrnc btn xprimntal and thortical stord nrgy in th fabrics indicatd that th prsntd thortical modl shos a rasonabl prdiction of th stord nrgy in ths fabrics. Journal of Enginrd ibrs and abrics 7 Volum 7, Issu 0

8 Th ffct of fabric matrial on th stord nrgy in th fabrics as invstigatd. Th cotton/polystr fabric had th maximum stord nrgy, du to its highr yarn to yarn friction cofficint. Cotton/nylon and cotton fabrics r in th nxt stps rspctivly. It is obvious that, incrasing in friction cofficint ill causs incras th frictional forc and th stord nrgy in th fabric. Invstigation of th ffct of fabric's loop lngth on th stord nrgy in th fabrics rvald that, for all fabrics, th incras of fabric's loop lngth lads to dcras in th fabric's stord nrgy. RERENCESS [] Valizadh, M., Ravandi, S. A. H., Salimi, M., and Shikhzadh, M., "Dtrmination of Intrnal Mchanical Charactristics of Wovn abrics Using th orc- Balanc Analysis of Yarn Pullout Tst", J. Tx. Inst., 99, 008, [] Jddi, A. A. A., Mohammadi, V., Rahimzadh, H., Honarvar,., "Knittd abric Rlaxation by Ultrasound and Its Charactrization ith Yarn Pullout orc", ibrs and Polymrs, 8, 007, [3] Taylor, H., M., "Tnsil and Taring Strngth of Cotton Cloths", J. Tx. Inst., 50, 959, [4] Sbastian, S. A. R. D., Baily, A. I., Brisco, B. J. and Tabor, D., " Effct of Softning Agnt on Yarn Pullout orc of a Plain Wav abric ", Tx. Rs. J., 56, 986, [5] Sbastian, S. A. R. D., Baily, A. I., Brisco, B. J. and Tabor, D., " Extnsion, Displacmnts and orcs Associatd ith Pulling a Singl Yarn rom a abric", J. Phys. D. Appl. Phys., 0, 993, [6] Motamdi,., Baily, A. I., Brisco, B. J., and Tabor, D., "Thory and Practic of Localizd abric Dformation", Tx. Rs. J., 59, 989, [7] Ralff, M. L., So, M., Boyc, M. C., Scharz, P. and Bakr, S., "Mchanical Proprtis of abrics Wovn from Yarns Producd by Diffrnt Spinning Tchnologis: Yarn ailur as a unction of Gaug Lngth", Tx. Rs. J., 6, 99, [8] So, M. H., Ralff, M. L., Pan, N., Boyc, M., Schartz, P., Backr, S., "Mchanical Proprtis of abrics Wovn from Yarns Producd by Diffrnt Spinning Tchnologis: Yarn ailur in Wovn abric", Tx. Rs. J., 63, 993, [9] Pan, N., and Young Y., M., "Bhavior of Yarn Pullout from Wovn abrics: Thortical and Exprimntal, Tx. Rs. J., 63, 993, [0] Pan, N., "Thortical Modling and Analysis of ibr Pullout Bhavior from a Bondd ibrous Matrix: Elastic Bond Cas", J. Tx. Inst., 84, 993, [] Ravandi, S. A. H., and Toriumi, K., "Spctral Analysis of th Yarn Pullout orc from Plain Wav abric", J. Tx. Inst., 87, 996, [] Badrossamay, M. R., Ravandi, S. A. H., and Morshd, M., "undamntal Paramtrs Affcting Yarn Pullout Bhavior", J. Tx. Inst., 9, 00, [3] Kirkood, K., M., t al., "Yarn Pullout as a Mchanism for Dissipating Ballistic Impact Enrgy in Kvlar KM- abric", Tx. Rs. J., 74, 004, AUTHORS S ADDRESSES Azita Asaysh Ph.D. Elahh Niazkhani Ali Asghar Asgharian Jddi Amirkabir Univrsity of Tchnology Txtil Enginring Dpartmnt Hafz Av. Thran, Thran 594 IRAN, ISLAMIC REPUBLIC O Journal of Enginrd ibrs and abrics 8 Volum 7, Issu 0