JOURNAL OF TEXTILES AND POLYMERS, VOL. 6, NO. 1, JANUARY

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1 JOURNAL OF TEXTILES AND POLYMERS, VOL. 6, NO., JANUARY 08 9 Visoelasi Modeling o he Reovery Behavior o Cu Pile Carpe Aer Sai Loading: A Comparison Beween Linear and Nonlinear Models Sahar Jaari * and Mohammad Ghane Absra- In his work, he reovery propery o mahinemade arpe was invesigaed using he visoelasi models. Visoelasi modeling o exile maerials are usually perormed wih presening dieren ombinaion o spring and dashpo. Two dieren mehanial models inluding linear and nonlinear Jeery s mehanial model were analyzed and ompared. Sai loading was applied o he samples or a erain ime. The load was hen removed and reovery behavior was invesigaed. The experimenal daa were hen adaped o he heoreial daa using urve iing based on leas square mehod. The resuls showed ha here was a reasonably good agreemen beween he Jerey s models and experimenal daa. The reason is ha hese wo models are no ompleely elasi showing seondary reep. No signiian dierene was observed beween linear and nonlinear model. The speed o reovery a he removal o he sai loading was also analyzed. The resuls show ha he nonlinear Jeery s model indiaes less value o speed o reovery a zero ime in omparison o he linear model. The reovery o u pile arpers shows some permanen reep and is explained by nonlinear and linear Jeery s model aepably. Keywords: u pile arpe, sai loading, reovery, visoelasi models, hikness loss I. INTRODUCTION Sanding and walking are dieren oresand deormaions ha applied o Carpe piles during suh human daily aiviies. Axial ompression, bending, laening, and exension and also sai and dynami pressure are some examples o hese deormaions []. Furhermore, he ompression behavior and mehanial reaion inluene on he piles hikness lossin he arpe. The reovery behavior o he pile arpe aer sai loading S. Jaari and M. Ghane Deparmen o Texile Engineering, Isahan Universiy o Tehnology, Isahan 83, Iran. Correspondene should be addressed o Sahar Jaari ???? is imporan or he qualiy, perormane and lieime o he piled arpe aer sai loading []. The abiliy o arpe pile o reurn o is original sae aer deormaion is denoed as Reovery or Resilieny. For modeling he mehanial behavior o he exile maerials, Dieren ombinaions o spring and dashpo sysems are usually onsidered. The visoelasi models are usually onsised o wo elemens i.e. visous dashpos whih obey Newon s law and springs whih obey Hooke s law [3]. However Non-Newonian dashpos or nonlinear springs are also involved o explain he dieren aspes o he maerials properies. Meng and Wu [4] sudied he sress relaxaion o membrane sruures in he pre-sress sae by onsidering visoelasi properies o oaed abris. The validiy o he suggesed analyial mehod is examined by omparing he numerial resuls wih experimenal daa o model ess. Shim e al. [5] sudied dynami mehanial properies o abri armor. The resuls show ha he proposed onsiuive equaion, based on a linear visoelasi model is able o desribe reasonably auraely he experimenal sress-srain response over a range o srain raes.vangheluwe [6] applied sandard nonlinear model o haraerize he relaxaion and inverse relaxaion o yarns aer dynami loading. The resuls show ha he model an alulae he residual ore a ininie ime in a relaxaion es or he ensile urve o spun yams. There seems o be good orrelaion wih he resuls o ess made using his mehod. Manih e al. [7] sudied he Ee o proessing and wearing on visoelasi modeling o polylaide/wool and polyeser/wool woven abris subjeed o bursing. The visoelasi behavior o he abris when mulidireional exended was simulaed and modeled using a modiied nonlinear Maxwell model. Asayesh e al. [8, 9] esimaed he reep and aigue behaviors o plain woven abris. They used he Eyring s model and he sandard linear model o desribe he abri behavior. Hashemi e al. [0] and Ardakani e al. [] sudied he inluene o wo bar warp-knied sruure on he abri

2 0 JOURNAL OF TEXTILES AND POLYMERS, VOL. 6, NO., JANUARY 08 ensile sress relaxaion. They examined dieren abri sruure and analyzed dieren visoelasi models. The experimenal resuls showed ha he abri sruure aes he ensile sress relaxaion signiianly. They also onluded ha he hree-omponen model wih he parallel-onne nonlinear spring shoed he bes agreemen wih he experimenal relaxaion o he analyzed abris. Khavari and Ghane [] sudied he ompression and reovery behavior o u pile arpes under onsan rae o ompression by mehanial models. Maxwell mehanial model, he sandard linear and nonlinear models were employed or simulaing he ompression behavior and reovery o he arpe samples. The resuls showed ha he sandard nonlinear models an desribe he ompression behavior o more signiianly in ompression o Maxwell and sandard linear models. Jaari and Ghane [3] sudied he reovery behavior o u pile arpe aer sai loading by mehanial models. Jeery s model and sandard linear model was used or simulaing he reovery behavior. The sandard linear model showed poor regression or he reovery properies o u pile arpes aer sai loading. The reason was ha he sandard linear model was ompleely elasi. Jaari and Ghane [4] also sudied he ee o UV radiaion on he reovery properies o pile arpe aer sai loading hrough analyial and visoelasi modeling. They ound ha he hikness loss and he maximum ompression were boh higher a longer UV exposure imes. The aim o his work is o invesigae he he oreial and experimenal reovery behavior o he u pile arpes. In his sudy, wo well-known mehanial models i.e. he linear and nonlinear Jeery s model were analyzed. To ind he bes model semi empirial urve iing mehod based on he leas square mehod was used. II. MECHANICAL MODELING Dieren mehanisms are involved when a u pile arpe is exposed o ompressive ore. The irs one is avisoelasi deormaion. The deormaion is reoverable wih a reardaionime. The seond mehanism involves a plasi or non-reoverable deormaion. This is due o dispassion o energy beween he pile yarns and plasi deormaion o he onsiuen ibers. I seems ha mehanial models onsising o dieren ombinaion o spring and dashpo an be used o represen he elaso-plasi behavior o he arpe under ompressive sai load. The aim o his paper is o analyze and ompare dieren visoelasi models in order o explain he mehanial behavior o arpe piles aer a shor-erm sai loading. For his purpose, wo models were presened or simulaion Fig.. Visoelasi models or he reovery behavior o u pile arpe: (a) linear Jeery s model and (b) nonlinear Jeery s model. o reovery behaviors o arpe pile yarns inluding; a) linear Jeery s model [5], b) quadrai nonlinear Jeery s model. Shemai diagrams o wo models are presened in Fig.. The ompressive ore is applied o he model. Erepresens he spring onsan or linear model (N/m) and b is he spring onsan or nonlinear model and η is he dashpo onsan (N.s/m). The governing dierenial equaion or he linear visoelasi model is ound o be: In his modeling a onsan load ( ) is applied o he model. Thus, o ind he x- equaion or he nonlinear model, we an separae wo par o exension. () x = x + x We an alulae plasi deormaion x p and elasi deormaion x e separaely and hen add hem ogeher. In plasi par we have: = η dx d p In he ase o onsan load ( ), we have: x η E a) + + (Ex +η x) = 0 η η p e = η The governing deerenial equaion in elasi par is: = bx x +ηx e e e In he ase o onsan load i beomes: bx x +η x = 0 p e e e For he elasi par we have he ollowing boundary () (3) (4) (5) (6)

3 JAFARI AND GHANE: VISCOELASTIC MODELING OF THE RECOVERY BEHAVIOR OF... ondiions: = = = = b xe 0 a 0 and xe a Solving he dierenial Eq. (6) and applying he boundary ondiion as in Eq. (7) he deormaion o he elasi par under he onsan load is ound o be: b. = xe an h. b η For he nonlinear model he oal exension under he onsan load an be ound by summing Eqs. (4) and (8). The x- equaions or he linear (model a) and quadrai nonlinear model (model b) are shown in Eq. (9): = + + E η η a)x e b. = + η b) x an h. The onsan load,, is applied o he proposed model. The se is ompressed o he exen o x a he ime. The value o x is ound o be as in Eqs. (0): a)x e η = + E η b) x = an h b.. + η (7) (8) (9) (0) I is lear ha he ompression o he whole se is equal o he ompression o boh elasi (x e ) and plasi pars (x p ) i.e. x =x e +x p. Thus, he amoun o ompression or elasi and plasi pars an be deermined separaely as in Eqs. (): a) x e and x η e = p = E η b) x = an h b.. and x = e p η () Aer removing he applied onsan load rom he se, reovery equaions ould be obained. By onsidering he general equaion o he models as well as our ondiion (aer load removal; =0, =0) he reovery dierenial equaions or boh models are ahieved as ollows: dx d x a)e +η = 0 d d dxr d xr r b) bx +η = 0 d d () Solving hese dierenial equaions need boundary ondiions. The ondiions an be provided rom he displaemen equaion where x=x a =0, as well as x = x p a =. For he nonlinear model we onsider x r =0 a =0 and x r =x e a =. Thus, hikness loss-ime equaions obained as in Eqs. (3) or (4): η a) x = xee + xp b) x = x b.x an h. and x = x x e r e r η (3) Or; replaing he boundary values orm Eqs. 0 and gives: η η a)x = e e + E η b. = + b) x an h. η b b. b. x e an h. an h. η η III. MATERIALS AND EXPERIMENT (4) A. Maerials In his work, he 700-reeds mahine woven arpe samples wih densiies o knos were produed. The arpe samples onsis o he oon/polyeser blended yarns wih densiy o 700 per meer as he warp yarns, he jue yarns wih densiy o 800 per meer as he we yarns. Aryli yarn was used as he pile yarn and he pile heigh was adjused o be 0 mm. B. Experimens Digial hikness gauge was used o measure he sample hikness. Iniial hikness o he sample was measured and denoed by x 0. A laboraory saled sai loading apparaus was used o simulae he applying o he sai loading. The appropriae weigh was hanged on he end o he arm o he apparaus so ha he onsan pressure o 700 kpa was applied o he arpe sample. The load was hen removed aer he ime. Two levels o sai loading ( ) were esed i.e. min and h. The hikness o he arpe is measured a his ime (x ) whih is onsidered as zero ime or he

4 JOURNAL OF TEXTILES AND POLYMERS, VOL. 6, NO., JANUARY 08 reovery mode. The ompression o he arpe a he ime (x ) is denoed by x =x 0 -x. The reovery proess was hen moniored and in every min inervals he hikness o he arpe (x ) is measured. This oninues up o 30 min. The hikness loss o he samples a he ime is hen onsidered as x=x 0 -x. IV. RESULTS AND DISCUSSION In his paper, he reovery propery o he pile arpes aer sai loading was invesigaed by presening wo visoelasi models. Analyial approah was used and he reovery-ime equaions were derived. The heoreial equaions were hen adaped o he experimenal daa using bes urve iing based on he leas square mehod. Deerminaion o he bes i equaion allows he exraing he disree visoelasi parameers o he models. The reovery behavior o he pile arpe was invesigaed in wo dieren sai load ime i.e. min and h. In eah level o sai loading, he values o hikness loss (x) were measured in he inerval imes o every min. Fig. shows he experimenal daa and he ied urves or reovery behavior o he arpe pile yarns aer applying min and h sai loading. Fig. reveals ha here is a good orrelaion beween he ied and he experimenal daa or wo Jeery s model. The ied urves show very high R-square o This an provide a suiable explanaion or he reovery behaviors o he arpe. The model is able o explain he non-reoverable deormaion o he arpe piles due o sai loading. The model is also desribes he ee o he ime o he onsan sai loading (See Table I). Eqs. (5a) and (5b) represenhe equaions o he ied urve wih linear Jeery s model and nonlinear Jeery s model respeively mod el (a) hours : x = 0.9e +.66 min ues : x.49e = + mod el (b) hours : x = an h (0.5.) min ues : x = an h (0.9.) (5a) (5b) (a) (b) Fig.. Fied urves vs. experimenal daa or reovery aer h and min sai loading: (a) linear Jeery s model and (b) nonlinear Jeery s model. To alulae he model parameers he onsan load,, is needed. This was alulaed rom he pile densiies and pressure load applied by he laboraory-saled sai loading apparaus. The onsan load,, applied o eah pile was alulaed as.4 N/pile. The model parameers were deermined using ied Eqs. (5a) and (5b) in aordane o Eq. (4). The resuls are shown in Table I. The good agreemen beween he ied urve and he experimenal daa suggess ha wo Jerey s model an predi well he reovery behavior o arpe piles aer sai loading. Analysis and omparison beween wo models revealed ha here was no signiian dierene beween he linear and quadrai nonlinear models in order o jusiy he reovery properies o he u-pile arpe aer removing o he sai loading. I an be onluded ha he Jeery s linear model shows signiian auray and an be proposed o explain he reovery properies o he upile arpes. Anoher ouome o he resuls is ha boh spring onsan and dashpo onsan show less values in longer sai loading. This shows learly ha he ime aes he ine sruure o he ibres. In oher words, he ime auses deerioraion in he rysal regions as well as he amorphous regions. This suggesion needs more ine sruural analysis. VI. SPEED OF RECOVERY The speed o reovery a he sar o reovery proess an

5 JAFARI AND GHANE: VISCOELASTIC MODELING OF THE RECOVERY BEHAVIOR OF... 3 TABLE I ESTIMATED VISCOELASTIC PARAMETERS Model Time R Spring onsan η min N. mm η min N. mm a) linear Jeery s model b) nonlinear Jeery s model min 0.96 E=0.37 (N/mm) h E=.54 (N/mm) min b =0. (N/mm ) h 0.97 b =.75 (N/mm ) be a good rierion o evaluae he ompression properies o he pile arpes. To ind he speed o reovery, he irs derivaion o reovery-ime equaion (Eq. 4) an be alulaed as shown below: η η a)x = e e η b. b. b.x e b) x = xe an h. se h. η η η (6) Applying he values o he parameers in o Eq. (6) he speed o reovery a zero ime or boh linear and nonlinear model were alulaed as an be seen in Table II. The experimenal values o he speed o reovery a zero ime were alulaed orm he slope o angen o he displaemen-ime urves (Fig. ) a zero ime (=0). The resuls o he heoreial and experimenal values o he speed o reovery a zero ime are shown in Table II. As seen in Table II, he speed o reovery a he sar o reovery (zero ime) is less in longer sai loading. The reason may be explained by he deerioraion or degradaion o he ine sruure o he ibers in longer ime o sai loading. The nonlinear model also shows lower reovery speed in min as well as h sai loading. Comparison o he heoreial and experimenal values o he speed o reovery a zero ime reveals ha wo values are reasonably lose o eah oher. Furhermore, he resuls o heoreial values by he nonlinear model are loser o he experimenal values. I an be onluded ha he nonlinear model is more reliable o predi he speed o reovery in omparison o he linear model. The reovery properies o he u pile arpes is aeed by dieren aors inluding he ype and mehanial properies o pile yarn and weigh and duraion o sai load. Finding an appropriae mehanial model and alulaing he visoelasi parameers allows invesigaing on he ee o dieren eeive aors on he reovery properies o he u pile arpes. Finally, we may be able o propose he sruure and maerials o gain opimum reovery properies. VI. CONCLUSIONS The aim o his paper was o ompare wo visoelasi models o desribe he reovery behavior o he pile arpe aer sai loading. Using analyial proedure reovery-ime equaions were derived and ompared o he experimenal daa. Bes ied urves based on he leas square mehod were deermined. The models were analyzed and a omparison was made beween he linear and quadrai nonlinear Jery s models. Using he analyial mehods he reovery equaions were derived and he disri visoelasi parameers were deermined and presened. The resul o urve iing proedure showed ha boh linear and nonlinear models i he experimenal daa signiianly. However, no signiian dierene was observed beween wo models. The nonlinear model provided less speed o reovery a he sar o he reovery TABLE II SPEED OF RECOVERY AT ZERO TIME FOR LINEAR AND NONLINEAR MODEL FOR RECOVERY a) linear Model Time Speed o reovery (mm/min) Speed o reoverya =0 (mm/min) Theoreial Experimenal min x = 0.38e Jeery s model b) nonlinear Jeery s model h x = 0.7e min x = 0.8seh (0.9) h x = 0.0seh (0.5)

6 4 JOURNAL OF TEXTILES AND POLYMERS, VOL. 6, NO., JANUARY 08 mode in omparison o he linear model. The resuls o he analysis also revealed ha he model parameers i.e. he spring onsens as well as he dashpo onsans are signiianly less in longer sai loading ime. I may be onluded ha he erm o sai loading aes he inernal sruure o iber. Deerioraion o he inernal sruure an lead o less value o model parameers. More ine sruure analysis is needed o veriy his onlusion. VII. ACKNOWLEDGMENT The auhors would like o express heir sinere hanks o he researh depuy o Isahan Universiy o Tehnology or he inanial suppor. REFERENCES [] Y. Korkmaz and S. DaliKoer, Resiliene behaviors o woven aryli arpes under shor- and long-erm sai loading, J. Tex. Ins., vol. 0, pp. 36-4, 00. [] S.M. Tabaabaei, M. Ghane, A. ZeinalHamadani, and H. Hasani, Modeling he unional ompression properies o hand-knoed arpes using aorial design and response surae mehodology, Fiber. Polym., vol. 5, pp , 04. [3] J.D. Ferry, Visoelasi properies o polymers, 3rd ed. New York: John Wiley & Sons, 980. [4] L. Meng and M. Wu, Sudy on sress relaxaion o membrane sruures in he presress sae by onsidering visoelasi properies o oaed abris, Thin. Wall. Sru., vol. 06, pp. 8-7, 06. [5] V.P.W. Shim, C.T. Lim, and K.J. Foo, Dynami mehanial properies o abri armour, In. J. Impa Eng., vol. 5, pp. -5, 00. [6] L. Vangheluwe, Relaxaion and inverse relaxaion o yarns aer dynami loading, Tex. Res. J., vol. 63, pp , 993. [7] A.M. Manih, R. Miguel, M.J.d.S. Silva, J. Luas, M. Marí, and D. Cayuela, Ee o proessing and wearing on visoelasi modeling o polylaide/ wool and polyeser/wool woven abris subjeed o bursing, Tex. Res. J., vol. 84, pp , 04. [8] A. Asayesh, A.A.A. Jeddi, and P. Ghadimi, Modeling he aigue behavior o plain woven abris Consrued rom exured polyeser yarn, Tex. Res. J., vol. 79, pp.3-, 009. [9] A. Asayesh and A.A.A. Jeddi, Modeling he reep behavior o plain woven abris onsrued rom exured polyeser yarn, Tex. Res. J., vol. 80, pp , 00. [0] N. Hashemi, A. Asayesh, Ali A.A. Jeddi, and T. Ardakani, The inluene o wo bar warp-knied sruure on he abri ensile sress relaxaion par I: (reverse lokni, sharkskin, queens ord), J. Tex. Ins., vol. 07, pp. 5 54, 06. [] T. Ardakani, A. Asayesh, and Ali A.A. Jeddi, The inluene o wo bar warp-knied sruure on he abri ensile sress relaxaion par II: (lokni, sain, loop raised), J. Tex. Ins., vol. 07, No., pp , 06. [] S. Khavari and M. Ghane, An analyial approah or he ompression and reovery behavior o u pile arpes under onsan rae o ompression by mehanial models, Fiber. Polym., vol. 8, pp , 07. [3] S. Jaari and M. Ghane, An analyial approah or he reovery behavior o u pile arpe aer sai loading by mehanial models, Fiber. Polym., vol.7, pp , 06. [4] S. Jaari and M. Ghane, Analysis o he ee o UV radiaion on he reovery properies o pile arpe aer sai loading hrough analyial and visoelasi modeling, J. Tex. Ins., vol. 08, pp , 07. [5] F. Mainardi and G. Spada, Creep, relaxaion and visosiy properies or basi raional models in rheology, European Physial J., vol. 93, pp , 0.