Fabric Geometry 5l2g38

FABRIC GEOMETRY Configuration of fabric and orientation of yarns, so called fabric Geometry , play vital role to simulate fabric behavior under shear defomarmation. However determination of fabric geometry needs special equipment and the process is time consuming. The attempt of this invistegation is to estibilish a model to simulate change in fabric geometry and yarn deformation during shear deformation . Geometrical characteristics are the nature of the basic reinforcing unit in the fabric (yarn) and the various geometries by which these yarns are combined together in the fabric (weft insertion warp knitted, short weft warp knitted, and woven fabrics). It was found that the geometry of a given fabric could enhance the bonding and enable one to obtain strain hardening behavior from low modulus yarn fabrics. On the other hand, variations of the geometry in a fabric could drastically reduce the efficiency, resulting in a reduced strengthening effect of the yarns in the fabric relative to single yarns not in a fabric form. The improved bonding in low modulus yarn was found to be mainly the result of the special shape of the yarn induced by the fabric. Therefore, in cement composites, the fabrics cannot be viewed simply as a means for holding together continuous yarns so that they can be readily placed in the matrix

The objectives of fabric geometry : 1. Prediction of the maximum sett (density) of fabric and fabric dimensions; 2. Find out relationship between geometrical parameters (picks and ends); 3. Prediction of mechanical properties by combining fabric and yarn properties; 4. Understanding fabric performance (handle and surface effect). Geometry Theories Approach 1. In conventional approaches, the general character of fabrics was idealized into simple geometrical forms (circle, ellipse, rectangle) 2. They treated the micro-mechanics of fabrics on the basis of the unit-cell approach, ie fabrics are considered as a repeating network of identical unit cells in the form of crimp weaves and constant yarn cross-section in the woven structure. 3. By combining this kind of geometry with or without physical parameters (material), mathematical deductions could be obtained.

Fabric Geometry Models : •

By using circle, ellipse, rack-track approaches, four fabric geometrical models are formed 1. Pierce model 2. Modified model (ellipse) 3. Kemp’s race track model (rectangle & circle) 4. Hearle’s lenticular model

Mathematical Notation for each model

Pierce’s Model (Classical Model) •

In this model, a two-dimensional unit cell of fabric was built by superimposing linear and circular yarn segments to produce the desired shaped.

•

The yarns were assumed to be circular in cross-section and highly incompressible, but perfectly flexible so that each set of yarns had a uniform curvature imposed by the circular cross-sectional shape of interlacing yarns.

•

Geometrical parameters such as thread spacing (p), weave crimp, weave angle and fabric thickness (h) can be found.

Pierce’s Model Results

Pick spacing (p1) and end spacing (p2), warp thickness (h1), weft thickness (h2) can be found from this model Pierce’s Model Limitations •

This model is convenient for calculation and is valid for open structure (loose density)

•

However, the assumptions of circular cross-section, uniform structure along the longitudinal direction, perfect flexibility and incompressibility are all unrealistic.

Pierce’s Elliptic Model •

In more tightly woven fabrics, however, the inter-thread pressures setup during weaving cause considerable thread flattening normal to the plane of cloth.

•

Pierce recongized this and proposed an elliptic section theory as shown in Fig 3.2

•

Because such model would be too complex and laborious in operation, he adopted an approximate treatment, which involved merely replacing the circular thread diameter in his circular-thread geometry with minor diameter as shown in Fig 3.2

•

This modified model is good for reasonable open fabric but cannot be applied for very closed jammed fabric.

Kemp Model (Race-track section) : •

To overcome the jammed structure, Kemp proposed a racetrack section to modified crosssection shape.

•

The model consisted of a rectangle enclosed by two semi-circular ends and had the advantage that it allowed the relatively simple relations of circular-thread geometry, already worked out by Pierce, to be applied to a flatted threads.

Fig : A rectangle and semi-circular cross section of Kemp Model Kemp Model Results :

Hearle’s Model •

Using energy method for calculations in fabric mechanics, a lenticular geometry was proposed by Hearle as shown in Fig 3.5

Fig : Energy approach for Hearle’s model Hearle’s Model Results

Limitations Fabric Geometry Models 1. Firstly, fabrics are complicated materials that do not conform even approximately to any of the ideal features suggested by these four fabric models. 2. Secondly, the measurement of geometrical parameters is not easy in practice. 3. Thirdly, the relationship between fabric mechanic (tensile, elongation, bending) to fabric geometry is not fully explored. References •

Structure and mechanics of woven fabrics by Jinlan HU

•

Chapter 3 Structural properties of fabric pp61-89