Tensile Behavior Simulation of Woven Fabric with Different Weave Pattern Based on Finite Element Method

Transcription

1 34 JOURNAL OF TEXTILES AND POLYMERS, VOL. 3, NO. 1, JANUARY 2015 Tensle Behavor Smulaton of Woven Fabrc wth Dfferent Weave Pattern Based on Fnte Element Method Majd Tehran-Dehkord and Hooshang Nosraty Abstract The propertes and structure of the yarns wthn the fabrc generate a complex mechansm of deformaton. Although many lteratures are avalable on mechancal propertes of woven fabrcs, lttle mcro-mechancal nformaton have become publc on tensle behavor of such materals. In ths study, the tensle behavor of woven fabrcs wth dfferent weave patterns s smulated by usng fnte element method. Yarn geometry parameters are measured wth the help of mcroscopy and mage processng technques. Three-dmensonal geometrcal models are smulated by use of fabrc geometry data. To evaluate the proposed model, the numercal results are compared to the expermental measurements. The results show that by usng the three dmensonal modelng of fabrc and precsely mpartng the yarn propertes n the fnte element program, the tensle propertes of fabrc wth dfferent weave patterns can be reasonably predcted. Keywords: Smulaton, fnte element method, tensle behavor, woven fabrc, weave pattern M I. INTRODUCTION echancal propertes of woven fabrcs can be characterzed n terms of yarn propertes and fabrc structures. Many studes have been made on the determnaton of mechancal propertes of woven fabrcs [1]. Attempts of modelng of woven structures trace back to the begnnng of the twenteth century. The man goal of the mechancal modelng conssts n a descrpton of the nature of the efforts exerted wthn the pattern and ther dstrbuton on the contact area between two threads. The reported mechancal models wthn the lterature can be classfed nto three dfferent categores,.e. the geometrcal models gve an essentally geometrcal descrpton of the structure [2-7], the mechancal models deal wth the descrpton of the efforts exerted on a fabrc sample and ther relatonshp to the fabrc deformaton [8-10], whle energetc models handle the consttutve behavor of the fabrc as an energy mnmzaton problem [11-13]. The geometrcal studes of Perce [2] provded the bass for the frst approach, whch ts modfcatons were subsequently ntroduced [3-5]. Perce s paper [2] contans a mechancal model for determnng the shape of elastc yarns n a plan weave fabrc subject to equal and opposte M. Tehran Dehkord s wth the Department of Carpet, Shahrekord Unversty, Shahrekord, Iran. H. Nosraty s wth the Department of Textle Engneerng of Amrkabr Unversty of Technology, Tehran, Iran.. Correspondence should be addressed to M. Tehran Dehkord (emal: mtehran@lt.sku.ac.r). lateral pressures at ther contact pont. Olofsson [6] extended the mechancal approach to nclude external tensons and bendng moments. More recently, de Jong and Postle [14-15] developed a model of fabrc structure based on energy relatons rather than force equatons [7, 16]. In the early stages of computers age, fnte element (FE) were rapdly mplemented to smulate the mechancal behavor of plan weave structure, provdng a more accurate nsght on ths subject. FE method provdes the detaled shape assumed by the yarn axs for each of the yarn systems n the fabrc such as crmp heght, crmp angle, and yarn-spacng [17, 18]. The ablty of the FE method to predct the detaled shape of the yarn axes as well as the yarn dameters provde the possblty to nclude the geometrcal aspects of jammng wthn the analyss and nvestgate the condton when the nterlaced yarns are n contact over a contnuous regon rather than smply at a pont. Several researchers nvestgated the mechancal behavor of woven fabrcs usng FE method. Among the publcatons n ths area, Shen et al. [19] smulated the tensle behavor of plan weave woven fabrcs usng fnte element method. Hou and hs coworkers [20] nvestgated the numercal smulaton of the mpact tenson behavors of 3-D orthogonal woven fabrc under hgh stran rates and compared the results to those obtaned under quas-statc tenson. Wang et al. [21] analyzed the tongue-tearng behavors of plan and twll woven fabrc based on the mcrostructure model. Jeong and Kang [22] proposed a computer model for analyzng the compresson deformaton behavor of a woven fabrc n the three-dmensonal vewpont. To mprove the comprehenson of woven fabrc behavor, Drd et al. [23] developed an orthotropc hyper-elastc contnuum model of woven fabrc. The model covered the nfluence of the rato between shearng and tensle rgdtes of woven fabrc on stress and stran felds. Ln [24] employed a geometrcal modelng based on slce array model to predct the elastc property (.e. ntal Young s modulus) of plan weave woven fabrc. Zouar et al. [25] employed the numercal tensle analyss n seven drectons of plan weave woven fabrc to ensure ther homogenety. In order to better understand the drape phenomenon of fabrcs, Kang and Yu [26], Hedf and hs coworkers [27] and Mngxang et al. [28] smulated the macro-mechancal three-dmensonal drape shapes of a woven fabrc by usng the non-lnear FE code. Khadamalhossen and hs colleagues [17] developed a computatonal model to smulate the effect of sewng

2 TEHRANI DEHKORDI. AND NOSRATY: TENSILE BEHAVIOR SIMULATION OF WOVEN FABRIC WITH DIFFERENT WEAVE 35 Fabrc pattern Plan Twll Satn TABLE I RESULTS OF KEMP S MODEL PARAMETERS FOR DIFFERENT FABRIC WEAVE PATTERN Test drecton Fabrc densty (cm -1 ) Crmp of yarn (%) a (mm) b (mm) p (mm) l (mm) l ' (mm) θ (degree) h (mm) Warp Weft Warp Weft Warp Weft machne needle mpact on woven fabrcs. Although many lteratures such as the aforementoned models are avalable on the mechancal propertes of plan weaved woven fabrcs, a very few reports on mcromechancal nformaton are avalable about the tensle behavor of other weave patterns. In ths study, the tensle behavor of some weave patterns (plan, twll, satn) was smulated n three-dmensonal vewpont usng FE method. The valdty of model was examned by the results of experments obtaned from cotton woven fabrcs. II. NUMERICAL MODEL A. Fabrc structure parameters Woven fabrcs were produced by nterlacng two orthogonal sets of yarns, warp and weft. Dependng on the type of nterlacement, a varety of weaves patterns ncludng plan, twll and satn would be produced. The cross-sectonal shapes and the centerlne confguratons of the consttuent yarns manly determne the fabrc geometrc structures. The cross-sectonal shapes of the yarns wthn the fabrcs may be crcular, ellpsodal, or racetrack. In fact, based on the weave patterns, the tghtness of constructon, the fnshng treatment and the cloth constructon they could be vared quckly. Perce [2] frst presented a rather ntensve analyss of woven fabrc structure by consderng the geometrc form of the yarn confguraton. In ths model, he assumed that the cross-sectonal shapes of woven threads are crcular. Wth normal knds of woven fabrcs, t can fnd that the assumpton of a crcular thread cross-secton s nvald. To overcome ths dffculty, Kemp [5] modfed the shape of yarn cross-secton wthn a fabrc. As Fg. 1 shows, he adopted the shape called racetrack secton whch encloses a rectangle between semcrcular ends. In ths study, the Kemp s model was used to smulate the structure of plan, twll 3/1 and satn 8 fabrcs usng Abacus software. Detals of yarns and fabrcs parameters for dfferent weave patterns are summarzed n Table I. In ths table, the crmp of yarns was obtaned from the extenson n yarns that was measured by an Instron tensle tester. Dameter of yarns were measured wth provde of fabrc cross-sectons and usng mcroscopy mages. The fabrc densty was obtaned wth the standard countng lens. To obtan the fabrc geometry, the Kemp equatons [5] were solved by usng yarn crmp, yarn dameters and fabrc densty. The employed equatons are: l = l a + b (1) D = b 1 + b 2 (2) p = a b + (l Dθ + Dsn θ ) (3) j j h = (l Dθ )sn θ + D(1 cos θ ) (4) where, θ and l are the angle and half-length of yarn n undulaton secton of each wave repetton. The subscrpts of and j are used to denote the warp and weft drecton, respectvely. Other symbols are shown n Fg. 1. The results of Kemp s equatons are gven n Table I. j Fg. 1. Confguraton of yarns n Kemp s model [5]. Fg. 2. Interlacng of warp and weft yarns n fabrcs wth (a) plan, (b) twll 3/1 and (c) satn 8 weave patterns. To estmate l n Equaton 1, the yarns were assumed straght except n undulaton sectons. Fgure 2 shows the nterlacng of warp and weft yarns n fabrcs wth dfferent weave pattern. In ths fgure, A denotes the wave repetton. Accordng to ths fgure, Equatons 5 to 7 can be used for calculatng the value of l n plan, twll 3/1 and satn 8 fabrcs, respectvely.

3 36 JOURNAL OF TEXTILES AND POLYMERS, VOL. 3, NO. 1, JANUARY 2015 B l = 2 (5) B 2P l = 2 (6) B 6P l = 2 (7) In these equatons, B s the length of yarn n each wave repetton ( A ). B. Assumptons The followng assumptons for numercal modelng were consdered: The geometry of yarns surface was assumed to be smooth and unform (whch was not smooth really due to the fne hars on the yarn surface). Therefore, the resstance of the fne hars on the yarns surface was gnored. The fabrcs were assumed to be completely relaxed. It means that the fabrcs dd not have any resdual stress wthn tself. The longtudnal geometry of yarns was assumed monotonc wthout any thn and/or thck places. C. Fnte element model The tensle propertes of woven fabrcs wth dfferent weave patterns were smulated based on FE method. For smulaton, some stages such as part, assembly, property, contact propertes, boundary condton, mesh and solve were performed n the Abaqus software verson 6.4 wth followng specfcatons [29]. In the part stage, the yarns were smulated sold, homogenous sotropc and deformable, as shown n Fg. 3. After that, woven fabrc wth dfferent weave patterns were created by nterlacng the smulated yarns n assembly stage. of plastc regon at load-elongaton curves. Fgure 4 shows the defnton of elastc-plastc behavor of yarns n Abacus software. The physcal and mechancal propertes of smulated yarns are summarzed n Table II. The propertes were obtaned from extracted yarns of woven fabrcs, expermentally. Maxmum prncple stress (Maxps damage) crteron was used as strength crteron. In ths strength crteron, longtudnal stress of each element n prncpal materal coordnates must be less than the respectve strength; otherwse, rupture s sad to have occurred on that element [29]. TABLE II THE PHYSICAL AND MECHANICAL PROPERTIES OF YARNS Elastc modulus (Mpa) along 3 Posson rato Densty (kg / m ) Warp Weft Fg. 4. Defnton of (a) elastc and (b) plastc behavors of yarns n Abacus software. The yarns were meshed by C3D8R element type wth the sze of 0.1 mm. Ths type of mesh had unform, 3D sold and brck structure, whch s shown n Fg. 5. Fg. 5. Eght-node brck element. Fg. 3. Models of yarns and fabrcs n abaqus software. The physcal and mechancal parameters of yarns such as tensle behavor, Posson s rato and densty were determned n Abacus software. These parameters were characterzed from Instron tensle tester and reference [30]. Tensle behavor of yarns was determned n the elastcplastc phase. The elastc phase (before yeld pont) was determned wth elastc modulus. The plastc phase (yeld pont up to rupture pont) was determned by some ponts Surface-to-surface contact-element was used to represent the contact between warp and weft yarns. The frcton coeffcent of 0.23 was assumed n all analyses [31]. Before descrbng the boundary condton, several notatons were defned. u x, u y and u z represent the dsplacements n x, y and z drectons, respectvely. In addton, ϕ,ϕ and ϕ are rotatons around the x, y and z- x y z axes. Wth respect to these notatons, the boundary condtons were defned that could be descrbed as follows. The boundary condtons were mposed on the two ends of the fabrcs as shown n Fg. 6. One sde fxed n all drectons, whle the other sde was movable wth constant velocty. It means that u x =u y =u z = ϕ = ϕ = ϕ 0 on a x y z = fxed sde and on the other sde, all degree of freedoms are fxed expect u x and u y.

4 TEHRANI DEHKORDI. AND NOSRATY: TENSILE BEHAVIOR SIMULATION OF WOVEN FABRIC WITH DIFFERENT WEAVE 37 All tensle processes were carred out at a constant cross-head speed. The velocty of tensle operaton for dfferent weave pattern along warp and weft drectons s summarzed n Table III. These cross-head speeds were calculated accordng to the dmenson of the analyzed unt cell. The explct solver was used for fnal analyses n Abaqus package. Explct fnte element codes were used to solve non-lnear analyss problems. Ths type of code could be therefore deal for the analyss of fabrc structure where materal behavor can be hghly non-lnear and large deformatons occur [32]. Three-pont gauss method for equatons solvng was used. The results of these analyses summarzed as follow. Fgure 7 shows typcal tensle processes for twll weave pattern along warp drecton. tensle tester equpped wth a 10 kn load cell along the warp and weft drectons. The tests were carred out on rectangular specmens wth a length of 200 mm and a wdth of 50 mm. The tensle tests were performed at temperature of 22 ± 2 c and relatve humdty of 50 ± 2%. All measurements were carred out at a constant cross-head speed on at least eght specmens. The expermental results obtaned for varous woven structures are summarzed n Table IV. TABLE IV EXPERIMENTAL RESULTS OF VARIOUS FABRICS Fabrc pattern Test drecton Maxmum load (N) Tensle stran (%) Warp Plan Weft Warp Twll Weft Warp Satn Weft Fg. 6. The mposed boundary condtons on the two ends of fabrcs. TABLE III THE CROSS-HEAD SPEED OF TENSILE OPERATION FOR DIFFERENT SPECIMENS Weave pattern Test drecton Velocty(µm/s) Plan Warp 69.2 Weft 39.8 Twll Warp 57.1 Weft 42.1 Satn Warp 40.8 Weft 44.3 Fracture load (N) Expermental Numercal Plan Twll Satn Plan Twll Satn Along warp drecton Along weft drecton Fg. 8. Expermental and numercal rupture load for dfferent weave patterns. Fg 7. Tensle processes for twll weave along warp drecton. III. EXPERIMENTAL PROCEDURE To evaluate the smulated model, three types of fabrc wth dfferent woven structures were produced. The cotton yarn was used n the count of 24 Ne at the warp and weft drectons. All sample fabrcs were tested by usng an Instron IV. RESULTS AND DISCUSSION In order to evaluate the numercal results, the rupture load of dfferent weave patterns (plan, twll and satn) were compared wth expermental results n Table V. The obtaned results n ths table show that there s a reasonable correlaton between the numercal and expermental results. It can be realzed that the maxmum dfference between numercal and expermental results s about 20%. The reason of ths dfference s the assumptons that made n modelng secton and expermental errors. To mprove the numercal results and reach the real fabrc model, the mentoned assumptons have to be modfed or even corrected. The expermental and numercal rupture load of dfferent weave patterns along warp and weft drectons are compared n Fg. 8. Ths fgure shows that on both drectons, the plan and satn weave patterns have the TABLE V NUMERICAL AND EXPERIMENTAL RESULTS OF DIFFERENT WEAVE PATTERNS Fabrc pattern Rupture load (N) along warp drecton Rupture load (N) along weft drecton Expermental Numercal Dfference (%) Expermental Numercal Dfference (%) plan Twll Satn

5 38 JOURNAL OF TEXTILES AND POLYMERS, VOL. 3, NO. 1, JANUARY 2015 hghest and least rupture load, respectvely. The satn weave pattern has less undulaton than the plan one. Therefore, the satn weave must have more rupture load respect to the plan one. The frctons between warp and weft yarns caused to varant these results. Among the studed fabrc weave patterns, the plan weave pattern has the hghest frcton load between warp and weft yarns therefore; the hghest rupture load belongs to the fabrc wth plan weave pattern. For the fabrc that used n ths research, the frcton load respect to the yarn undulaton has more nfluence on rupture load. In Abacus package, frctons between the warp and weft yarns were performed usng the surface-to-surface method. Fg. 9. Numercal and expermental curves of load vs. stran for plan weave along warp drecton. Fgure 9 shows the typcal plots of load versus stran for plan weave pattern along warp drecton, obtaned from nstrumented tensle testng and numercal model. As the fgure shows, the numercal curve has a good correlaton wth the expermental curves. The results show that the appled load n each stran can be elgble determned from numercal curve. V. CONCLUSIONS In ths study, a numercal model based on FE method was proposed for predctng the tensle propertes of fabrcs wth dfferent weave patterns. From the results, the followng conclusons can be obtaned: By assumng the straght behavor for yarns (except n undulaton sectons), Kemp s model can be utlzed as a proper model for extracton the ntal nformaton of twll and satn fabrc structures. By usng the three dmensonal modelng of fabrc and precsely mpartng the yarn propertes n the Abacus package, the tensle propertes of fabrc wth dfferent weave patterns can be reasonably predcted. A good correlaton between the numercal and expermental load-stran curves s possble. Therefore, the proposed numercal model can be determned the appled load n each stran. 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