BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVI (LX), Fasc. 1, 2010 SecŃia TEXTILE. PIELĂRIE MODELING THE FORCE-ELONGATION CURVE OF SINGLE YARNS BY IONUł NEAGU*, DORIN AVRAM* and PASCAL BRUNIAUX** Abstract. Broadly stated, the scope of this paper is to simulate a mathematical model for the force-elongation curve. This model is for single yarns and the implementation of an algorithm in order to describe the properties of textile products. The model obtained is compared to the force-elongation curve resulted from the practical tests, thus the model input data are represented by the features of the practical curve. Key words: fibre-to-yarn, simulation interfaces, model design, virtual reality, Computer Aided Design. 1. Introduction As already known, software simulation poses many problems, among which: a) Many research papers deal in detail with yarn simulation but it is no criticism of such texts to say that they fail to put forward both a generalized model and a model based on hierarchical structures [1]. b) Tracking and correcting errors become extremely difficult if we try to model a product starting from fibres. Consequently, submodel simulation is introduced avoiding thus error accumulation while passing from one submodel to another. The steps taken are fibre-to-yarn, yarn-to-tissue and tissue-to- product. As a result, the modelling of force-elongation curve was chosen for the fibre-to-yarn submodel. A useful yarn model is certainly a valuable tool for yarn technologists involved in the process of product development. Much effort and time can be saved by avoiding the trial and error approach. Moreover, the reduced human involvement is associated with a higher level of productivity. This can be done based on a theoretical structure which, due to the introduced assumptions, can create the conditions for the mathematical transposition of the phenomena, with a view to analyzing the influence coefficients.
40 IonuŃ Neagu, Dorin Avram and Pascal Bruniaux 2. The State of the Art It must not be forgotten that the research theme has already been approached by a series of engineers, among which: Legrand who produced a representation model of the practical curve by taking into account a number of dynamical components such as the hysteresis and viscoelasticity phenomena and the yarn relaxing process, the inconvenient being that the parameters used depended on the traction speed [2]. Zhong Cai s proposition is a model that arises from the comparison between a metallic and a textile yarn, emphasizing thus the viscoelasticity effect [3]. Zurek combines a rheological model that integrates share rate, mass and time with a Kelvin-Voigt model dealing with elasticity [4]. Vangheluwe s model consists in a model concatenation based on Maxwell s concept: Hooke module serially connected to a viscous element [5]. Manich parallels Vangheluwe s and Zurek s models in view of integrating the interfibrous forces into the yarn. He also modifies Zurek s and Vangheluwe s models, the latter by introducing a non-linear term. Ghith was the first to produce a model that divided the traction curve into two distinct areas [6]. The first area ranges between 3 8% of elongation and can be compared to a line; this is the area corresponding to fiber parallelization upon traction. The second elasticity area is perfectly linear as far as the breaking point of the yarn [7]. 3. The Modeled Curve The force-elongation curve can be identified by designing an algorithm based on the parameters described in Fig. 1. The model was carefully chosen so as to avoid subsequent errors generated by the distribution method other than the submodel one. In modelling the simulated curve, the starting point is represented by the identification of the parameter vectors of the practical curve. Consequently, the first step consists in dividing the practical model into three areas displayed in Fig. 1. Fig. 1 The curve-elongation model.
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 1, 2010 41 The next step entails the localization of the second linear area in order to determine the F1, A1, F2, A2 parameters by means of the mathematical analysis of quadratic curve information. Then we identify the ζ slope angle formed between F1, A1 and F2, A2 m; eq. 1 is used to this purpose: (1) T 2 T1 ζ = E2 E1 Young s module is used in order to determine the F max and A max parameters. The a, d and c represent the empirically-established sensitivity parameters of the model. The following equations are used for the representation of the three submodels: ( ( )) ( ) (2) 1 F1 2F1 F = ζ A1 A ζ F F F1 ζ A1 + + ζ A1 (3) F = ζ ζ F F1 + F1 F1 F F2 F ( ) ( ) (4) F = ζ 1 a+ d exp x A A2 + F2 F F2 c We chose the Bruniaux s [8], [9] model because was the best suited to model our curve. If, after comparing the two curves, the result is unsatisfactory the program restarts the procedure from the beginning, following the same steps until it determines the superposition of the two curves. 4. The Practical Curve 4.1. Method Used The force-elongation curve was determined as follows: All tractions were performed on the MTS 2M dynamometer (Fig. 3), the resulting data being taken and processed by TestWork4 (Fig. 2). To perform the test, the following procedural steps were undertaken in accordance with methodology rules: the 1kN load cell was fitted, the dynamometer was connected to a power source, and the contact jaws were fixed, the minimum distance being of 15 mm according to gripping device specifications. The distance between the two jaws was measured and adjusted by means of buttons so as to prevent subsequent errors. Once the dynamometer was checked and turned on a series of six tests consisting of ten samples were undertaken. The yarn was inserted between the
42 IonuŃ Neagu, Dorin Avram and Pascal Bruniaux jaws and cut off the reel only when the jaws were tighten. Fig. 2 User interface. Fig. 3 MTS 2M Dynamometer. Since the dynamometer was connected to a computer, the purpose of TestWork was to digitally collect data. The appropriate method was chosen: fiber/10n, yarn/10n-1kn, and tissue/1kn-10kn (our option was TP1tractionfil1kN). The steps undertaken in order to configure the sensor by means of the software menu: Configuration>Peripheral>select the desired sensor (1kN in our case) and then press calibrate, end, OK. The test speed was set in mm/min and pretension force at 0.013 N. Before stating the test, force was reset to 0, where after tests were performed.
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 1, 2010 43 4.2. Results Test performance determined the six pairs of values together with the curve-plotting displayed in Fig. 4 including the after-breakage region. Subsequent data processing was undertaken in view of eliminating the abovementioned region, resulting thus the six curves in Fig. 5. Fig. 4 Curves before data processing. Fig. 5 Curves after data processing.
44 IonuŃ Neagu, Dorin Avram and Pascal Bruniaux Another statistical analysis of the determined values was achieved for the purpose of tracing a single median curve, obtaining the median curve in Fig. 6. 5. Comparing the Two Curves The practical curve parameters act as input parameters of the simulation model. With a view to simplifying the determination of model parameters, a simulation program was developed in C++. The superposition of the two models was achieved automatically by the software program. Table 1 Aspects of the Modelled Curve Force F, [cn] Elongation A, [%] Area1 0.015 0 Area2 0.16 1.5 Area3 0.989 8 Max 1.23 16.8 Table 1 contains data obtained as a result of curve modelling used for tracing the two curves, the first in Office excel (Fig. 7), the second by means of the software program. Fig. 6 Median curve and simulated curve. Fig. 7 Curves obtained as a result of software simulation.
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 1, 2010 45 6. Conclusions Although the research theme is not new in specialty literature, the paper distinguishes itself by the non-linear way of working so that any yarn curve can be modelled by means of the algorithm presented above. For the time being we intend to carry out the research concerning this subject and determine the factors influencing the model so that they could be automatically implemented. The integration of the hysteresis phenomenon represents another main factor requiring special attention. Test speed represents one of the main disadvantages having a major influence on the data range; our future purpose is to eliminate this type of error. Also in the future we want to analyze the first part of the curve in order to characterize the trajectory of the curve. Received: October 12, 2009 * Gheorghe Asachi Technical University of Iaşi, Department of Technology and Design of Textile Products e-mail: davram@tex.tuiasi.ro **ENSAIT-Ecole Nationale Supérieure des Arts et Industries Textile, Roubaix, France R E F E R E N C E S 1. Hearle J.W.S., Chen X., Potluri P., Jiang Y., Ramgulam R., From Biological Macromolecules to Drape of Clothing: 50 Years of Computing for Textiles. Manchester, 2004. 2. Bruniaux P., Legrand X., Vasseur C., Yarn and Fabric Model Inter-Connected. Journal of Advanced Materials, Vol. 37, 4, 60 69 (2006). 3. Gutowski T.G, A Resin Flow/Fiber Deformation Model for Composite. SAMPE Quaterly, Vol. 16, 4, 1985, 58 64. 4. Zurek W., Aksan S., A Rheological Model of Viscose Rayon. Journal of Applied Polymer Science, Vol. 19, 3129 3137 (1975). 5. Vangheluwe L., Relaxation and Inverse Relaxation of Yarn After Dynamic Loading. TRJ, Vol. 63, 9, September 1993, 552 556. 6. Ghith A., Contribution à la simulation du comportement dynamique des tissus textiles. Ph. D. Diss., Université des sciences et technologies de Lille, 1998. 7. Serwatka A., Bruniaux P., Frydrych I., New Approach to Modelling the Stress-Strain Curve of Linear Textile Products. I. Theoretical Considerations. Fibres & Textiles in Eastern Europe, Vol. 14, 1(55), 30 35 (2006). 8. Serwatka A., Bruniaux P., Frydrych I., New Approach to Modelling the Stress-Strain Curve of Linear Textile Products. II. Simulation of Real Stress-Strain Curves. Fibres & Textiles in Eastern Europe, 60 62 (2007).
46 IonuŃ Neagu, Dorin Avram and Pascal Bruniaux MODELAREA CURBEI FORłĂ-ALUNGIRE PENTRU FIRELE SIMPLE (Rezumat) Lucrarea de fańă îşi propune să simuleze un model matematic al curbei forńăalungire pentru firele simple. Modelul propus se referă la fire simple şi la introducerea unui algoritm care descrie proprietăńile produselor textile. Modelul obńinut prin simulare este comparat cu curba forńă-alungire obńinută în urma testelor practice, astfel modelul are ca date de intrare caracteristicile curbei practice.