**1. Introduction**

There are many ways of making fabrics from textile fibers. The most common and most complex category comprises fabrics made from interlaced yarns. These are the traditional methods of manufacturing textiles. The great scope lies in choosing fibers with particular properties, arranging fibers in the yarn in several ways and organizing in multiple ways, interlaced yarn within the fabric. This gives textile designer great freedom and variation for controlling and modifying the fabric. The most common form of interlacing is weaving, where two sets of threads cross and interweave with one another. The yarns are held in place due to the inter-yarn friction. Another form of interlacing where the thread in one set interlocks with the loops of neighboring thread by looping is called knitting. The interloping of yarns results in positive binding. Knitted fabrics are widely used in apparel, home furnishing and technical textiles. Lace, Crochet and different types of Net are other forms of interlaced yarn structures. Braiding is another way of thread interlacing for fabric formation. Braided fabric is formed by diagonal interlacing of yarns. Braided structures are mainly used for industrial composite materials.

Other forms of fabric manufacture use fibers or filaments laid down, without interlacing, in a web and bonded together mechanically or by using adhesive. The former are needle punched nonwovens and the later spun bonded. The resulting fabric after bonding normally produces a flexible and porous structure. These find use mostly in industrial and disposable applications. All these fabrics are broadly used in three major applications such as apparel, home furnishing and industrial.

The traditional methods of weaving and hand weaving will remain supreme for high cost fabrics with a rich design content. The woven structures provide a combination of strength with flexibility. The flexibility at small strains is achieved by yarn crimp due to freedom of yarn movement, whereas at high strains the threads take the load together giving high strength. A woven fabric is produced by interlacing two sets of yarns, the warp and the weft which are at right angles to each other in the plane of the cloth (Newton, 1993). The warp is along the length and the weft along the width of the fabric. Individual warp and weft yarns are called ends and picks. The interlacement of ends and

Modeling of Woven Fabrics Geometry and Properties 3

Irregular weaves are commonly employed when the effect of interlacement is masked by the coloured yarn in the fabric. Such weaves are common in furnishing fabric. In such structures the prediction of mechanical properties is difficult. Examples of some of the common

The firmness of a woven fabric depends on the density of threads and frequency of interlacements in a repeat. Fabrics made from different weaves cannot be compared easily with regard to their physical and mechanical properties unless the weave effect is normalized. The concept of average float has been in use since long, particularly for calculating maximum threads per cm. It is defined as the average ends per intersection in a unit repeat. Recently this ratio termed as weave factor (Seyam, 2002; Weiner, 1971) has been

It is a number that accounts for the number of interlacements of warp and weft in a given

Fig. 2. Regular weaves

**1.2.2 Irregular weaves** 

Fig. 3. Irregular weaves

**1.3.1 Weave factor** 

irregular weaves are given in figure 3.

**1.3 Mathematical representation of different weaves** 

repeat. It is also equal to average float and is expressed as:

used to estimate tightness factor in fabric.

picks with each other produces a coherent and stable structure. The repeating unit of interlacement is called the weave (Robinson & Marks, 1973). The structure and properties of a woven fabric are dependent upon the constructional parameters as thread density, yarn fineness, crimp, weave etc.

The present chapter establishes some interesting mathematical relationships between these constructional parameters so as to enable the fabric designer and researcher to have a clear understanding of the engineering aspects of woven fabrics. This is an attempt to transform from an experience based designing into an engineered approach to model woven fabric constructions.
