A new mathematical model describing a plain knitted fabric is proposed in this paper.One major feature of this model is that the yarn in the fabric can be naturally curved with nonlinear mechanical properties. The new model is able to describe the dimensions and also the low stress mechanical properties of a plain knit. Based on an energy analysis, the inadequacy of the classic k -values is explained. Complex dimensional behavior and problems associated with relaxation of knitted fabric are discussed. A more precise prediction of fabric dimensions is possible by including the degree of set as one of the parameters. The paper also explains why most of the studies of knitted fabric dimensional properties in the past have been empirical.Fabrics knitted from cotton are a very popular, and thus very important to the textile industry. Cotton, being a nonthermoplastic fiber, is unable to be heat set. This category of knitted fabrics will relax naturally after knitting, resulting in changing fabric dimensions. Due to the nature of the knitting process, the fabric is knitted under high stress and extension. Therefore, grey cotton fabrics off the machine will exhibit large and varied amounts of shrinkage. Measurements of shrinkage in grey fabrics are therefore of little value to fabric finishers. What is of value is the reference state of the fabric. This reference state acts as a target of the norm for assessing fabric dimensional behavior.In attempts to understand the dimensional behavior of knitted fabrics, the key element is the geometry of the knitted loop. Pierce [21 ], Shinn 1271, Leaf [ 13, 14, 15], Doyle [4, 51, Munden 120], Postle 122, 23], and recently Demiroz et al. [3] have all significantly contributed to the geometric analysis of plain knitted fabrics. In particular, Leafs geometric model [15] has aroused the interest of composite engineers [24]. The success of that model is due to its simplicity and a good description of the actual fabric. Recent innovative work (3J on loop geometry has used spline curves to represent the loop, which is especially useful in the visual display of knitted fabrics on a CAD system. Yarn jamming in a knitted fabric has long been identified as a major factor determining its the dimensional and mechanical properties. Knapton et al. III) ] concluded . 1 1 -that the stability of a cotton loop is reached when yarn bulking is restricted by yarn jamming. Alternatively, the dimensional properties of knitted fabrics were studied by some researchers [8. 23, 25] using the force method. In the theoretical models of Postle et al. [23], Shanahan et al. [25], and Hepworth et al. [8], yarn was treated as an elastica [ 18] that is naturally straight. MacRory et al. [ 19) and Hepworth [91 attempted to tackle the biaxial load-extension problem of knitted fabrics. MacRory's model emphasized slippage between loops and the biaxial load case with the loop elements being straightened, while Hepworth's model concentrated on the effect of yarn jamming. &dquo;Extensive experimental works have been accom...

No abstract

To illustrate the importance of cationic groups within hard segments on shape memory effect in segmented polyurethane (PU) cationomers, the shape memory polyurethane (SMPU) cationomers composed of poly(e-caprolactone) (PCL), 4,4 0 -diphenylmethane diisocyanate (MDI), 1,4-butanediol (BDO), and N-methyldiethanolamine (NMDA) or N,N-bis(2-hydroxyethyl)isonicotinamide (BIN) were synthesized. The comparison of shape memory effect between NMDA series and BIN series was made. The relations between the structure and shape memory effect of the two series of cationomers with various ionic group contents were investigated. It is observed that the stress at 100% elongation is reduced for these two series of PU cationomers with increasing ionic group content. Especially for NMDA series, the stress reduction is more significant. The fixity ratio and recovery ratio of the NMDA series can be improved simultaneously by the insertion of cationic groups within hard segments, but not for the BIN series. Characterizations with DSC and DMA suggest that the crystallibility of soft segment in SMPU cationomers was enhanced by incorporation of ionic groups into hard segments, leading to a relative high degree of soft segment crystallization; compared with the corresponding nonionomers, incorporation of charged ionic groups within hard segments can enhance the cohesion force among hard segments particularly at high ionic group content. This methodology offers good control of the shape memory characteristic in thin films and is believed to be beneficial to the shape memory textile industries.

The mechanical behavior, including the tensile and torsional properties, of bulky wool singles yarn, which has an initial fiber packing density that is non-uniform along yarn radial direction, is modeled in this paper. The theoretical analysis is based on discrete-fiber-modeling principles by which the yarn is considered as an assembly of a large number of discrete fibers. The movement of fibers during deformation and their final positions after deformation are determined by their need to minimize tensile strain, which is the so-called the shortest-path hypothesis. Energy method is employed to calculate the applied force. Taking the nonlinear behavior of fiber at large strain into account, the contributions to yarn external force due to fiber tension, fiber bending and fiber torsion can all be derived. Comparing with the experimental data, our theoretical model gives a reasonably accurate prediction of yarn behavior at small deformation.

It is the first attempt to reveal the effect of reversible phase crystallization process on shape memory effect in shape memory polyurethane (PU) ionomer. Thereof the cyclic tensile testing was conducted with various cooling time to fix the temporary deformation for assessing shape memory function. The crystallization process of the reversible phase, poly (ε‐caprolactone) (PCL) in shape memory PU ionomers composed of different ionic group contents, 1,4‐butanediol, 4,4′‐methylenebis(phenyl isocyanate) and PCL, was investigated by using isothermal crystallization kinetics under the thermal routine similar to that for the cyclic tensile testing. The results demonstrate that the ionic groups within hard segments significantly slow down the crystal growth of the reversible phase. When the physical crosslink is strong enough, the crystallization rate would be a predominant factor determining the shape fixity ratio after various cooling time. Instead, when physical crosslink is weakening, the influence of crystallization rate is much less on the cooling time dependence of fixity. Copyright © 2007 John Wiley & Sons, Ltd.