Ghane M., Sheikhzadeh M., Khaburi S., Ghaeli I.; Investigation on the Ratio of Bending Rigidity of Fabric to Yarn for Low Twist Filament Yarn FIBRES & TEXTILES in Eastern Europe 2009, Vol. 17, No. 3 (74) pp. 51-53. 51 as a result of the analysis given, satisfac- torily explained. The above-mentioned works were mainly focused on staple yarns, which are usu- ally assumed to be incompressible. The main aim of this work is to investigate the application and accuracy of classical theories to predict the bending behaviour of plain woven fabrics consisting of low twist flament weft yarn. n Theory Leaf et al. used the energy salvation method based on the saw tooth model and presented the following Equations [3]: B 1 = b y1 ×P 2 /P 1 (L 1 - 2c 1 ) (1) B 2 = b y2 ×P 1 /P 2 (L 2 - 2c 2 ) (2) Where, B is the bending rigidity of the fabric, b y is the bending rigidity of the weft (warp), c is contact length of the yarn at the crossover points, L is the mod- ular length of the weft (warp) and P is the thread spacing. Indices 1 and 2 refer to the warp and weft, respectively. Considering the thread density n = 1/P, equations 1 and 2 can be written in the following form; B 1 /n 1 = b y1 ×P 2 /(L 1 - 2c 1 ) (3) B 2 /n 2 = b y2 ×P 1 /(L 2 - 2c 2 ) (4) Replacing the bending rigidity of the fab- ric per thread, b, in Equations 3 and 4, we obtain: b 1 /b y1 = P 2 /(L 1 - 2c 1 ) (5) b 2 /b y2 = P 1 /(L 2 - 2c 2 ) (6) To calculate the contact length, c, the contact angle, θ, is needed. This can be calculated using Equations 7 and 8; Investigation on the Ratio of Bending Rigidity of Fabric to Yarn for Low Twist Filament Yarn M. Ghane, M. Sheikhzadeh, S. Khaburi, I. Ghaeli Department of Textile Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran E-mail address: m-ghane@cc.iut.ac.ir Abstract The ratio of bending rigidity of fabric to yarn in the case of low twist flament weft yarn was studied. Samples of fabrics with different weft densities were prepared; their other parameters were identical. After steam setting treatment, the bending rigidity of the fabrics was measured. The results showed that the rigidity of the fabric per thread in the weft di- rection decreases as the weft density increases. However, the theoretical equations suggest an inverse trend. To explain the difference, the thickness of the fabric was considered. It was shown that the reduction in fabric bending rigidity was due to the decrease in fabric thickness. The fxed end beam theory for the defection of weft yarns as well as the fattening effect of low twist flament weft yarns were used to explain the reduction in fabric thickness when the weft densities increase. It was concluded that in the case of low twist flament weft yarn, Leaf’s theoretical equations could not be used to predict the ratio of the bending rigidity of fabric to yarn. Key words: low twist flaments, bending rigidity, weft density, fattening effect. n Introduction bending behaviour is of importance in the study of cloth properties such as han- dle, drape, and crease resistance. Bend- ing rigidity, and shear rigidity introduce the damping ability of fabric, of which the latter affect the handling, deforma- tion, crease resistance, buckling behav- iour and crimp maintenance ability [1]. The bending behaviour of yarn is affect- ed by its mechanical properties as well as the arrangement and interaction between its constituent fbers and yarn geometry [2]. Leaf et al. [3] discussed the relation between the fexural rigidity of a plain woven fabric and the fabric and yarn parameters, such as thread spacing and crimp, yarn fexural rigidity, etc. Wei and Chen [4] outlined a theoretical analysis that leads to a concise formula for calculating the bending behaviour of set plain woven fabrics. The formula shows reasonable agreement with ex- perimental results and good consistency with Grosberg’s [5] conclusion, which is drawn from data computation. Abbott et al. [6] presented two models for a plain woven fabric in which the yarn cross sections are incompressible so as to obtain the predicted relationship between the couple applied and the cur- vature of the fabric. They concluded that the predicted bending resistance does not agree with the behaviour of actual fabrics owing to the diffculty of defning the ra- dius of the yarn in the fabric; however, many puzzling qualitative aspects of the bending behaviour of woven fabrics are, Table 1. Properties of fve samples. Properties Samples A B C D E Warp density, cm -1 25.6 25.6 25.6 25.6 25.6 Weft density, cm -1 14.0 16.5 17.4 23.5 27.9 Fabric weight, g/m 2 72.5 76 78.8 90 99.5 Fabric thickness, mm 0.277 0.246 0.235 0.222 0.178 Table 2. Fabric parameters calculated using Pierce equations. Properties Samples A B C D E C y1 , % 8.685 9.892 10.308 12.200 12.951 C y2 , % 1.150 1.468 1.762 2.508 3.567 L 1 , cm 0.077 0.067 0.063 0.047 0.041 L 2 , cm 0.039 0.039 0.040 0.040 0.040 θ 1 , R 0.545 0.582 0.594 0.646 0.666 θ 2 , R 0.198 0.224 0.245 0.293 0.349