Influence of Fiber Length Distribution on Strength Efficiency of Fibers in Yarn

Abstract

The tensile and tear strengths and hence the durability of a cotton fabric are greatly influenced by the length and strength of cotton fibers in addition to the fabric structure. This is so because fiber length to a large extent determines yam strength, which ultimately contributes to fabric strength. Also, fiber length and its distribution affect fiber processing and hence yarn performance during subsequent mechanical processing, including knitting and weaving. Therefore, fiber length distribution and its ultimate effect on the yarn strength are important. To better understand the length-strength relationship in cotton fibers, we have tried to model the strength of fibers assemblies in a yarn, based on some simple assumptions. In this model, we address an important issue of friction among adjacent fibers in a yarn structure and also introduce and derive a new parameter called the "strength efficiency" of fibers in a yarn, which may contribute to an understanding of the yarn failure mechanism. The paper should be helpful to the scientific community involved in improving the properties of cotton fibers, yarns, and fabrics.Although fiber migrations and the resulting entanglements are very important in yarn formation, fiber length, fineness, and strength and their respective distributions/ consistencies are even more critical parameters in determining the effectiveness of the ultimate fibrous assembly (yarn). For decades, textile scientists worldwide have been studying the mechanics of flexible fiber assemblies and investigating the effect of fiber properties on yarn properties, especially tensile properties [1][2][3][4][5][6][7][8][9][10][11]. Several models have been developed to understand the mechanics of yarn formation and failure [2,5,8,10, 111. For example, a semi-empirical expression developed from work by Grosberg and Smith on worsted rovings to predict the breaking strength of low-twist woolen-spun yarn reveals the relative importance of the contribution of fiber length and fiber strength to estimated yarn strength [ 10]. They examined the effect of carbonizing in altering fiber strength and entangling and showed that fiber length has the most marked influence on yarn strength. Tests have also shown that fiber slippage is an important part of the yarn failure mechanism. Van Luijk et al. developed a model for the long-gauge behavior of staple-fiber yarns based on Hearle's work incorporating fiber migration and slippage [ 11 ]. The tensile strength of the model stems from frictional forces, which are calculated using the Grosberg theory of fiber-withdrawal force from a sliver. The governing equations of the staple fiber/yarn model have been formulated and solved using the finite element method.Since fiber length and strength greatly influence yarn , strength, we have tried to develop a model to express yarn strength as a function of the accumulated strengths of the individual fibers in the yarn cross section. In this research approach, we use the following simplifying assumptions: First, the fibers are quasi...

Generation of Length Distribution, Length Diagram, Fibrogram, and Statistical Characteristics by Weight of Cotton Blends

“…The upper half mean length is calculated by using (8). For the blends USA2 (medium)/Brazilian (medium) and Egyptian (long)/USA1 (long), the variation of UHML is nearly linear expressed by a DUHML variation close to zero.…”

“…Other studies were conducted to generate fibre length parameters and to study the relationships between these parameters and their effects on the other fibre characteristics and on the end product quality [8,9].…”

Estimation of yarn strength based on critical slipping length and fiber length distribution

“…It is known that if yarn breaks, fibers may break or slip in the yarn breaking section, which is decided by critical slipping length. 12–16 Assume all constituent fibers are completely straight and parallel to the yarn axis, and take one fiber in the yarn that is subjected to tensile load for consideration. It is assumed that the fiber is subjected to uniform lateral compressive stress q during the yarn stretching process.…”

“…Based on this, Zeidman and Sawhney 13 developed a yarn strength model that took fiber length distribution into consideration. Yarn strength F could be expressed as where p f = fiber breaking strength; N¯ = the average number of fibers in the yarn cross-section; L¯ = mean fiber length; W(x)=∫x ∞∫s ∞∫t ∞f(L)dLdtds = an integral of distribution density function of fiber length f ( L ).…”

“…However, there still exists the parameter q which is hard to test or calculate in both equations (3) and (4). Yan and Yu 16 calculated l c based on Zeidman and Sawhney’s analysis, 13 which was expressed as …”