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Bagging in TextilesN. G. Şengöz

Online Publication Date: 01 January 2004

To cite this Article: Şengöz, N. G. (2004) 'Bagging in Textiles', Textile Progress,36:1, 1 — 64

To link to this article: DOI: 10.1533/jotp.36.1.1.59475URL: http://dx.doi.org/10.1533/jotp.36.1.1.59475

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BAGGING IN TEXTILES

N.G. Sengoz*

1. OVERVIEW

1.1 Introduction

Bagging is a three-dimensional residual deformation, seen in used garments, which causes a

deterioration in the appearance of the garment. The places it is seen during wear are elbows,

knees, pockets, hips, and heels. The common factor in all of these parts of garments is the

force exerted on that area of the fabric from the moving parts of the body. When the fabric

covering that part of the body feels this force for a long time and feels it repeatedly, the

fabric deforms and starts to take the form the force is trying to give to it. The force coming

from the human body is in the transverse direction to the fabric’s plane and the deformation

which occurs is spatial. This prolonged and repeated deformation causes the fabric to

change its shape, and it usually takes a dome shape, like a part of a sphere, so it is a three-

dimensional complex deformation that is very different from the other kinds of deformation

seen in textile materials.

In the dictionaries, in its simplest meaning, deformation is defined as a change in form.

When a deformation has to be studied, factors such as the amount of the deformation, the

extreme point of the deformation, the recoverability of the deformation, the residual amount

of the deformation, and the mechanism of the deformation should be investigated. This

means that parameters such as bagging height, volume, shape, and anisotropy are the main

characters of fabric bagging behaviour where no structural breakdown occurs. Since now,

these factors have mostly been the main subjects of fundamental engineering experiences.

From the engineering point of view, deformation is studied in any kind of material, textiles

being our concern. Since all these materials meet human needs in daily life, a wide range of

research, from spacework to foods, are all included in the fundamental engineering

investigations, and research were done in the past and will continue to be done in the future.

When we take a closer look at the deformation research done in textile materials, we see

that it has been carried out for a long time on fibres, yarns, fabrics and all of the semi-

finished forms of them in the production state, and also the garment form that is the final

form of usage. Even though many important points have been elucidated, there are still

many things to be worked on. With the help of developments in the fundamental theories,

the definition of the problems has become easier, and with the help of improvements,

especially in computer technology, the solution of the complex problems has become robust,

eventually research showing a rapid development.

1.2 Importance of Bagging

All fabrics (apparel, medical, technical) are subjected to various forces during their use

in daily life. These forces may be in the form of pressure, stress, impact, puncture, etc.

Fabrics can absorb these forces up to a certain extent in their composition and, when the

force is lifted, the fabric can recover and take its original shape if the force has acted in

*Author’s Current Address: Afyon Kocatepe University Usak Engineering Faculty, Textile Engineering

Department, Bir Eylul Kampusu 64100, Usak-TURKEY sengozgonul@hotmail.com.

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the elastic deformation region of the fabric. Since the elastic recovery of fabrics decreases

with time, and since fabrics possess viscoelastic properties and show creep-relaxation

behaviour, in some cases, they are prevented by these factors from recovering, cannot

overcome the deformation and cannot revert to their original shape. As a result, a

permanent or plastic deformation in the fabric occurs.

1.3 Positive Perspectives

In some cases, a deformation is a requirement, as in a felted hat – the shape is what we would

call a deformed shape when compared with a flat fabric. In a hat made from woven fabric, the

fabric is cut and sewn to take the shape of the head, and in a knitted hat, it is easier because the

yarns can move relative to each other to make the knitted fabric take the shape of the head.

Also, in some technical usages, three dimensional fabrics are produced just in the shape

in which they will be used. This is important for the end-use mechanical performance of

some industrial fabrics. Possessing a special shape may be regarded as some kind of a

deformation in our understanding of fabric. Since these are not our concern, they will not be

dealt with here. The purpose of mentioning them is to show that, in some cases, a deformed

shape is needed; it is not a fault, but it will be regarded as a fault in the rest of the text.

The important thing is that no force is involved in the above explanations. In the meaning

of bagging, the application of an external force is necessary, and that is why a change in the

form happens.

1.4 Negative Perspectives

The phenomenon of bagging, encountered in used garments and seen at elbows, knees,

pockets, hips, and heels, is a good example of permanent spherical deformation of fabrics

under stress during wear. After the application of prolonged static or repeated force from

the moving parts of the human body, the fabric loses its dimensional stability and cannot

recover, and permanent residual deformation takes place in the form of a dome – like part

of a sphere. Because the appearance of the garment is distorted and because this appearance

is important from the aesthetic point of view in the daily use of the garment, such a subject

involves a quality factor and must be studied. Bagging occurs with the loss of elastic energy

of fabric with wear time, so gradually the shape deteriorates, and this deteriorated shape

and the deformed fabric together is perceived as a kind of garment fatigue behavior by

people. On the one hand, we want the fabric to stretch and conform to the body and give

dynamic comfort to the person wearing if when the body moves; on the otherhand, there are

many material and structural factors that prevent the fabric presenting the same behaviour

all the time. Even if there is not any structural breakdown in a garment, bagging detracts

from its appearance during wear in such a way that it is perceived as an unwanted fault.

A fabric’s permanent spatial deformation behaviour depends on the fibre properties of the

material, as well as yarn thickness, fabric density and weave, and also the fabric construction

properties, namely yarn and fabric parameters. The elastic deformation of the fibres, the

viscoelastic deformation of the fibres, stress relaxation due to fibre viscoelastic behaviour,

and the friction between fibres and yarns in the fabric structure are all important in bagging

of fabrics. These can be grouped into three components – elasticity, viscoelasticity

and frictional forces. Permanent spatial deformation behaviour, what we call bagging, can

be characterized by parameters such as bagging height, volume, shape, and anisotropy. In

subjective judgements of bagging, its degree can vary from one person to another, from one

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garment to another, and from one fabric surface pattern to another. These will be explained

later in the text.

2. DEFINITION AND TYPES OF DEFORMATION

2.1 Definition

As stated previously, deformation is a change in form. This form can be in any kind

and there may be many factors affecting it. The purpose of research is to determine

what these factors are and, with the knowledge obtained, to take control of the occasions

and improve the mechanisms of achieving our goal of overcoming or minimizing bagging.

So, knowing the various deformation types and the differences between them are important.

2.2 Deformation Types

Lloyd [40] and Amirbayat and Hearle [3] have grouped the deformations seen in fabrics as

the following cases:

(i) In-plane deformations: These are the kinds of deformation where a fabric, initially

aligned in one plane, is deformed in its own plane. When the force is applied parallel

to the fabric plane, every point in the fabric is affected in the same way by this force

and shape deterioration is the same in every point. Tensile properties in either the

warp or the weft directions are mentioned in this group. No transversal displacement

of the fabric plane is seen in this kind of deformation – see Fig. 1(a).

(ii) Uniaxial bending: The fabric displaces perpendicular to its own plane and bends to

form a curve leading to a circle by the extention of this curve. Good examples for

research in this subject are buckling, drape, the forms that the fabric takes and loses

during daily wear of a garment, the forms that a curtain takes and loses, and the

rolling and opening of a fabric sheet – see Figures 1(b1) and 1(b2).

(iii) Torque in the fabric plane: This is the moment occurring in the fabric sheet when

force couples acting in opposite directions are applied to the fabric sheet from each

side of the sheet and where a twist is also seen in the fabric sheet. In this case, every

point of the fabric feels a different force, is exerted to a different moment, and shows

different inner displacements, in general. Case (iii) is very different from Cases (i) and

(ii) in this sense – see Fig. 1(c).

(iv) Conforming to a spherical surface: This is the case when the fabric is forced to

conform to a spherical surface, and, as a result, bagging occurs. In this case, recovery

is mostly not achieved and some permanent spatial deformation is left on the fabric,

like a part of a sphere. In this kind of deformation analysis, forces are defined as

hydrostatic, which means they are equal in different angles starting from the same

centre. In research, the elbow, knee, pocket, hip, and heel areas of garments, and the

top area before the curvature begins in the drape analysis, are good examples of this

kind of deformation – see fig. 1(d ).

According to Konopasek [36], there are six kinds of continuum models in mechanics of

fibre assemblies, and the deformation in each kind can be written as below:

Fibres and yarns are deformed tensile or torsional (1:1);

Fibres and yarns are deformed bending in their plane (1:2);

Fibres and yarns are deformed bending and torsional in space (1:3);

Fabrics are deformed tensile and shear in their plane (2:2);

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Fabrics are deformed tensile, shear and bending in space (2:3);

Fibres and fibre assemblies are deformed complex in space (3:3).

The numbers in the first column state the independent variables and the numbers in the

second column state the dependent variables. There are three kinds in both of them, but

their combination is named in six groups because, when worked with one independent

geometric variable, the deformations in the other directions are not also neglected. The

information about these interdependencies has to be obtained separately and worked in a

one-dimensional problem rather than in a three-dimensional problem.

Mack and Taylor [43] handle fabric deformation by the concept of ‘fit’. This concept

concerns a sphere as a prescribed surface and examines how the weft and warp yarns would

cover this area when laid over, still making intersections. They derive differential equations

for the geometry occuring. They give mathematical definitions of the different paths the yarns

would follow on the surface. In Fig. 2, woven fabric fitted to a spherical surface with different

mathematical definitions is seen. The pictures are modified to emphisize the path the yarns

are making. With those equations, the fitting of a continuum material to spheres, cones,

Fig. 1 Different kinds of deformation seen in fabrics. (a) In-plane deformation of a fabric; (b1) Uniaxialbending of a fabric in a roll; (b2) Uniaxial bending of a fabric on a surface; (c) Torque in the fabricplane; (d ) Conforming of a fabric to a spherical surface

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toroids, and spheroids is possible. In their work, Mack and Taylor assume that the woven

fabric is made up of inextensible yarns, and that the fabric is perfectly shearable and flexible.

Heisey and Haller [31] computerised Mack and Taylor’s work using numerical analysis

techniques, and were able to cover surfaces where the mathematical definition of the surface

was hard to make. The coordinates of the fabric which will fit the surface are coded like a

map and no restrictions are made about the surface. Their assumptions are the same as

Mack and Taylor’s. Their work is also based on the shear properties of the fabric. It is

concluded that the in-plane deformation occuring in the fabric is achieved by the shear and

the bending characteristics of the fabric.

Van West et al. [69] stated that a half-sphere is a good basis for both theoretical and

experimental studies and they applied differential geometry successfully. They modelled the

path of the yarns covering a half-sphere and when their drawing from the model coincided

with the real photograph, there was a good correlation between the fabric and the graphical

simulation — but the distances between the yarns are not equal to each other. The positions

of the yarns can be compared, but at particular points they cannot.

Heisey et al. [30] later used this concept in the area of garment patterning. The human

body resembles some parts of a sphere as seen in double curvature. The algorithm they used

is concerned with how a fabric regarding a plane-like shape would fully cover this area

without tension. These are all concerns of the subject of garment patterning. The only

problem they met is the physical properties of the fabric. In their work, the warp yarns are

no longer parallel with each other, but they come to the same meeting point at the top of the

curve, like the meridians on the earth.

Aono et al. [5] also did some work on the concept of garment patterning. Their

assumptions were the same as the earlier researchers. Their mathematical definitions were

more precise, their numerical analysis methods were wider, the surfaces to be fitted were

more undulating, computer simulation was easier, and no point was left uncalculated on the

surface to be fitted. The lay of the warp yarns were also like the meridians.

Terzopoulos et al. [63] worked on elastically deformable models. They wanted to simulate

the same movement on the computer screen. They applied differential equations to rigid

curves, surfaces, and solids as a function of time, so that the textile material was dynamic

around them like a flag flying in the wind on the screen of the computer. Also this concept

was used in computer technology by Ascough et al. [6], to improve the movement of a skirt

flying as one turns around, on the computer screen.

Fig. 2 Woven fabric fitted to a spherical surface with different mathematical definitions (Mack andTaylor [43], modified)

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Ramgulam [54] presented a new fitting algorithm to fit woven fabric onto a complex

surface. This algorithm could be applied to any surface which was able to be described

numerically or analytically. It was based on differential geometry, but was much stronger

and faster than the earlier developed traditional kinetic model-based algorithms. This

algorithm allowed more flexible initial conditions. The new one was compared with the

earlier ones and seen visually that the newly developed software models the actual fit of the

woven fabrics correctly. It was indicated that in-plane shear deformation occurs in woven

fabrics when they are forced to conform to a spherical surface, and that this is the most

important factor governing this behaviour. The fabric shears until its critical shearing angle,

and then wrinkling begins. The limiting shear angle is different in every fabric.

2.3 Differences Between Deformation Types

Different kinds of deformation are examined differently in fabric mechanics. As seen in

Case (i), in-plane deformations are when thematerial is in its elastic zone in a force–elongation

diagram (Fig. 3). If the force is increased, then the process can go up to tearing, but now the

small forces are taken into consideration for all the cases mentioned above. The difference in

Case (ii) is that the fabric takes a different shape all by itself when a force is exerted but there is

nomention of lateral stress. When the fabric takes a shape special to itself, it still behaves in its

elastic zone and no pressure is exerted on it. Case (iii) is a force couple partial condition but the

deformation effect occurring in the fabric is still in the elastic zone. The fabric can recover to

its initial state. The fabric is behaving freely in all these three cases but in Case (iv) it is not.

There, the fabric is under compulsion by a force transversal to its plane. This kind of a

deformation takes place in the permanent deformation zone of the material.

In Cases (i), (ii) and (iii), the fabric fully recovers after the force is lifted, but in Case (iv),

the recovery of the fabric is partial and a certain amount of permanent spatial deformation is

left on the fabric. In Case (iv), the material’s frictional and viscoelastic properties start to

show themselves. The fabric responds to these deformations by shearing.

Although in all four deformation types, the warp and weft yarn groups keep their parallel

positions within the group, in the concept of fit, these two yarn groups change their paths to

cover the double curvatured surface of a sphere and this path is mathematically defined.

Three-dimensional fabrics are produced with this concept and the mathematical definitions

are used in computer simulations.

Fig. 3 A general force-elongation diagram

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Fundamental engineering investigations are usually made for a continuum, but textile

material are not continuous. A yarn is composed of single fibres, a fabric is composed of

single yarns by their intersections, and mainly all the fibres, yarns and fabrics have very

different characteristics from one another. However, in the studies of yarn and fabric

mechanics, they are considered as a continuum and examinations are done according to

those theories. Even though this is the case, very realistic mathematical definitions are

concluded when research is done according to them [57].

There are some assumptions about the physical structure of the textile material. The

behaviour of both the natural and synthetic fibres under stress has been subject to many

researches. The fibres show fairly complex deformations in their microstructures. With

the help of twist, fibres come together and take the form of yarn; then they reach a

macrostructure [40] and the situation starts to become more complex, since the fibres, which

have finite lengths, have come together and created an endless structure. In any continuum,

there are small particules that make up the molecular structure, but in textile materials there

exist large macrostructures, up to many times greater than those of the molecular structure.

This makes the use of the continuum concept difficult. For example, if one wants to measure

the percentage of extension between two points, it can be infinitely small in a continuum,

and so that the diffusion of the extension percentage is constant along the continuum. But in

the case of textile materials, there is the macrostructure and the smallest structure that can

be taken will still possess so many macros, and this will make us think that the diffusion of

the extension percentage is not constant along the material. The important thing to be

assumed here is up to what extent the textile material can be considered as a continuum and

the known theories can be applied; and beyond which point the textile material has to be

considered as a non-continuum and different theories are needed.

The main factors giving the yarn its complexity in deformation are fibres with finite

lengths turning into an infinite structure, the internal pressures occurring with twist that

holds the fibres together, and the frictional forces occurring between the fibres.

The main factors giving the fabric its complexity in deformation are more strict. When

the yarns take the form of a fabric, the occasion becomes more complex because the yarns

have to intersect with other yarns as a requirement of the macrostructure. Intersecting is

formed by the yarns going over and under each other, both in the horizontal and the

vertical direction; so a structure as a plane is constructed. The main factors giving the

fabric its complexity in deformation are the inversion from a linear continuous structure to

a planar continuous structure, and the internal strain added by the intersections of the

yarns. In this case, factors coming from the yarns are also added to the factors belonging

to the fabric.

This phenomena becomes more complex still when the fabric takes the form of a garment,

because the planar ensemble is separated by cutting, then it is put together by sewing and it

becomes a three-dimensional non-continuous structure. The main factors giving a garment

its complexity in deformation are inversion from a planar continuous structure to a spatial

non-continuous structure, cutting and sewing again (along a stitch line with a sewing

thread), and exposure to different strains and movements persistently coming from the inside

because there is a human there. The factors existing in the fabrics add up to the factors

belonging to the garment.

When moving from fibre to yarn, from yarn to fabric, from fabric to garment, in every

step there is the continuity from finite structure to linear continuous structure, from linear

continuous structure to planar continuous structure, from planar continuous structure to

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spatial non-continuous structure. Every step shows a more complex deformation behaviour

than the former, so the investigation of deformation gets harder at every step.

Chapman and Hearle [18] defined how the textile material takes various shapes during the

production stages and how the deformation phenomena gets more complex as this proceeds.

A single fibre would have natural curves on it, but every fibre follows a migrating helical

path in the yarn along the twist. In the fabric, there is the crimp that originates from the

underlaying and overlaying movement of the yarns. In addition to all of these complexities,

in bagging, there is the force acting on the fabric in the vertical direction to the fabric plane.

3. DEFINITION OF BAGGING

As mentioned before, bagging is a three-dimentional, permanent, spatial, spherically shaped

deformation explained in Case (iv). The finished fabric is in its plane form and, when a force

perpendicular to its plane is applied, spatial deformation occurs which is called bagging.

The planar continuous structure is deformed by a spatial stress and this imposes a difference

in the material: the force is distributed planar in the fabric, but the application is spatial.

The difference in their characters is the first thing that makes this subject complex.

Deformations can recover either fully or partially. The theories are precise where the

recovery is full but they need to be developed for the conditions where it is not full. In a

condition such as bagging, recovery is not full; there is permanent deformation and this is

the second thing that makes this subject complex.

In research, a textile material which possesses a non-continuous structure is assumed to be

a continuous structure, logically this is a contradicting situation. The contrast between a

continuous and a non-continuous structure is the third thing that makes this subject complex.

3.1 Basic Theories and Methods

In this section, elasticity, elastic theory, viscoelasticity, creep-relaxation, inverse relaxation,

plasticity, membrane theory, plate and shell theories, elastica theory, finite element analysis,

energy methods, and shear property are explained briefly.

Almost every material shows some measure of elongation when a force acts upon it, but

if the same material recovers fully after the force is lifted, it is said that this material is ‘elastic’.

Elastic behaviour means that there is no permanent deformation in the material. In an elastic

material, strain is simplya functionof change in shape. If a textilematerial shows elastic behaviour,

it is also called elastic [48]. In general, there are elastic and non-elastic material kinds [53].

In engineering, there are some cases that the mechanical method of approach is not

sufficient to solve. Then, elasticity theory, which a different method of approach, is needed. In

some cases, deeper work of elasticity theory is also needed. The main application of elastic

theory is to study the deformation of bodies in which all its three dimensions possess equal

importance. For instance, the forces in cylinders or the forces acting upon rollers in bearings

can only be solved with elasticity theory. But, elasticity theory cannot explain the intimate

strength changes in shafts and bars. As Postle and Norton [50, 51] stated, mathematical

elasticity theory had undergone many changes, mainly in tensor notation, linear deviations

from geometric and material being, and numerical analysis. Lloyd [40] has stated that the

easiest way to handle mechanical properties is with the elasticity theory. Linear elasticity

makes for an easier understanding of the complex situations in real textile material behaviour.

But, the isotropic assumption in this theory is insufficient in some cases, and another

formulation which is anisotropic is required. This formulation is required to define non-linear

elasticity, viscoelastic models and elastic behaviour both related to time and to history.

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If recovery is not full in a material, then behaviour which is not elastic takes place

and strain is related both to the change in shape and to its differential equation according to

time [53]. In this case, the Young’s modulus starts to change and superposition principles are

applied to the strain properties [15]. Some material behave as elastic solids, whereas others

behave like flowing liquids; in some cases this is true for very small elongations. These kinds

of material do not deform constantly under constant force. If the material is forced to a

constant deformation, then the force needed to keep it in this shape gets less. This kind of

material is called viscoelastic [46, 48].

‘Creep’ is increases in elongation under constant force, and ‘relaxation’ is decreases in force

at constant elongation [15]. If, in successive relaxation experiments the relaxation modulus is

constant, then this is called ‘linear viscoelasticity’ [53]. If elongation and elongation rate are

very small, and the force–elongation relationships according to time can be defined with

differential equations and stable constants, then the material is called ‘linear viscoelastic’ [47].

In their work, Nachane and Sundaram [47] studied ‘inverse relaxation’ in polymeric fibres.

In this case, after some amount of elongation the material is pulled again, and if the material

feels some force, this force increases with time, first a fast increase, then some decrease, then

comes to a constant after a long time. There is a late response mechanism in this material

and inverse relaxation is taking place. In many studies, materials having an amorphous

construction (leather, textiles, etc.) show mostly viscoelastic behaviour and some evidence

which supports the theory that plastoelastic mechanism changes into viscoelastic mechanism

is gained. A membrane is a perfectly flexable plate, and it does not have bending rigidity.

In membrane theory, the membrane deformations take place in-plane of the material [10].

‘‘Plate and Shell Theories’’ are also concerned with deformations in materials, but their

difference is that in these theories, one dimension of the material under study has a different

importance than the others. The material then takes the form of a plate or a shell, in which

case the thickness is much smaller than the other dimensions. When the thickness of the so

called shell is compared with the smallest deflection radius, it is assumed to be very small [65].

According to small deformation (deflection) theory, elongations which results in membrane

elongation because of strain are regarded as normal. These may be eliminated and are very

small according to thickness [17]. In large deflections, small-strain theory, which gives

displacements as much as the thickness, is used. The displacements are small according to

plate dimensions. In real large-deformation theory, double curvatures cause extensions at the

surface and they also cause finite membrane elongations to occur. When deformation takes

place, it is considered that the elements that are in the vertical direction to the plate or the

shell are not deformed, but keep their initial forms. When the perpendicular force component

is compared with the others, it is assumed that it causes forces which can be excluded [57]. The

thin shell theory is used in the areas of aerospace, maritime (ships, submarines, etc.), pressure

pipes, water tanks, locomotives, steam pots, energy production stations, space work

(spaceshuttles), petroleum production, parachutes, construction (concrete work), etc.

because there are forces with the lateral stress and hydrostatic approach. Also, deflection

problems of conical and spherical shells are solved with this theory.

The deflection measurement generally used in thin elastic shell theory is the difference of

the bending tensors taken separately before and after the deformation of the surface [50, 51].

The theory of the thin elastic shell substances has been developed to include deflection,

plasticity, creep, breakage, sandwich construction, and fibre reinforced composites. As

Postle and Norton [50, 51] stated, since Love [17], it had been worked on this theory to be

developed how, to include the deflection and elongation effects combined; so every problem

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is searched and solved over and over again. When the mechanical model of a fabric is

constructed, the mathematics of the model and the physics of the matter should be in

coordination with each other. This point is very important for the limiting factors because,

from model to model, the limiting factor may be different. Postle and Norton [50, 51] studied

fabric deformation in the relaxed state, without any strain or stress on it, and chose their

equilibrium states freely in the Riemann space. In the model they created, it is possible to

define all the mechanical responses that could occur in any elastic fabric. If the components

of the tensor that shows the properties of the material can be contingent upon the

environmental factors, then aging, humidity, thermal effects, etc. can also be modelled there.

Both the elasticity theory and the plate and shell theories study the behaviour of the

material in the elastic zone. There seem to be some missing points for large extension and

large elongation percentages which takes place in the viscoelastic zone of the material

behaviour. Even though the theories are not perfect for textile materials, it has been possible

to calculate nearly precisely the strain and shear deformation in plain woven fabrics [42].

Postle and Postle [52] have stated that the Thin Shell Theory was able to solve most of the

complex problems in engineering applications but that this theory was not modelled enough

to be applied to textile materials under stress. In textile materials, the strain applied can be

very small but the extensions it causes can be very large, and these deformations can have

highly non-linear characteristics. In their work, they developed non-linear mathematical

methods for both elastic and non-elastic fabric behaviour, in order to solve the problems of

fabric crease, wrinkle, and fold. The non-elastic mechanisms of the fabric involve the

viscoelasticity of the fibre and the inter-fibre friction, and these properties determine the

ability of the fabric to recover after creasing, wrinkling and folding. The recovery period of a

fabric is also important from the point of view of its performance during wear.

‘Elastica’ theory studies large elongations with small extension percentages. For some

fabric deformations, small deformation theory seems to be sufficient, but for textile material

in general, the approach of large elongation and extension percentages is needed [40, 41].

The elastica theory for one dimension includes these points: (i) The differential geometry of

the curves in space and the deformation measures derived from them; (ii) The equilibrium

equations of the forces and the moments acting upon the differential element of the curve;

(iii) The equations relating the strains and the moments with the deformation measures;

(iv) Numerical analysis methods.

In the elastica theory, the fabric is treated as a surface in space that includes the same four

points in one dimension. When it has been defined in every coordinate, we get a vector zone

from the unit vectors that are tangent to the surface and to the coordinate lines, from the

unit vectors which are tangent to the surface but perpendicular to the coordinate lines, and

from the unit vectors which are perpendicular to the surface and to the coordinate lines.

From here, we get the metric tensor of the surface. There is also published work with

geodesics [52].

In fabrics that are large continuous constructions, degree of freedom can be infinite; but

to study the system and its deformations requires a limited number of degrees of freedom.

‘Finite Element Analysis’ is the formulation of the required equations in the small units that

are able to represent the whole system, and each of them possesses a limited number of

degrees of freedom; then the equations of the small units are brought together and the whole

system is defined. This has been worked with matrixes and there are also computer programs

that have been developed for this purpose [40]. Finite element analysis is a kind of numerical

analysis.

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The extension method of the Finite Element Method is appropriate for use with small

extension percentages and for linear elasticity. The fabric is regarded as a two-dimensional

continuous structure and is divided into small pieces that have tip points called ‘knots’.

Every knot has a special degree of freedom. Element e would be existing somewhere in the

x–y plane and having i–j–k knots; also u and v would be elongations in the x and y

directions. The elongations u and v are called membrane deformations.

Furthermore, when the shape function is added, the distribution of unknown

extensions from a known function can be approximately calculated. The non-linear

behaviour generally seen in fabric deformation – non-linear material properties, large

elongations and extension percentages – requires some modifications in the fundamental

theory. Time elapses are used in the ‘step-by-step increase’ method of Finite Element

Analysis for viscoelastic materials. There are different areas of application for the Finite

Element Analysis in textiles. This method can be used in yarn mechanics, and fabric

structure and mechanics, besides thermal isolation problems, chemical diffusions, dyeing,

etc.; also in finding the shape of air-filling textile materials such as sails, and in ballistic

experiments [42].

Energy methods are commonly used in deformation research in textile materials. The

deformation occurring at every point of the construction is defined by the density of the

deformation energy. In order to obtain the density of the deformation energy, special yarn

and fabric properties have to be eliminated, special deformation geometry has to be

assumed, and special energy methods have to be used. Postle and Norton [50, 51] were able

to define the recovery behaviour according to time with the formulae they developed.

In fabrics, certain extensions are not responded by yarn elongation, but responded by

relative turning at the intersection points of the yarns. This is called shear, and Chapman

and Hearle [18] state that it is strongly believed that fabrics cover double curvature surfaces

by their shear property. Hearle et al. [29] state that the definition of bending in complex

situations is much harder. Shear property plays the most important role in both plate and

shell bending. Many other researchers have done much detailed research into shear rigidity

and determined that shear behaviour plays the most important role in fabric deformation.

Fabric shear behaviour has been studied in many different cases such as constructions

working with air (parachutes, sails, etc.), conveyer belts, geotextiles, sewing of garments,

fabric handle and drape, and covering of double curvature surfaces. Kawabata et al. [32]

defined the total shear deformation as a combination of two-sided strain and shear

deformation. Shear elongation is a perpendicular shortening as a result of a regular

elongation in one dimension. So, the area and the thickness of the material stays constant.

Shear force is the perpendicular force acting along one group of yarns in the fabric; thus this

has to be equalized by an equal and opposite force, and for equilibrium a force couple has to

occur.

In practical experiments, the fabric is kept under constant force while the shear force is

increased. Compressive force occurs much more slowly, and at the end causes bending.

Kawabata et al. [32] state that, compared to strain deformation, a fabric shows very little

resistance to shear deformation. When freely put on a double curvature surface, the top part

of the fabric where the drape has not started yet, can easily cover that part. Generally,

fabrics are subject to large deformations, and under those conditions the combination of

both strain and shear deformations is seen. For example, when the knee is bent, the fabric

deformation at the knee is a result of double curvature strain and shear. Furthermore,

deformations are finite. Bassett and Postle [11] state that in shear studies, it is assumed that

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the constructive lines are straight before and after deformation and angles and strain forces

have not changed. An aluminium foil cannot cover a double curvature surface and is a good

example of not deforming in its own plane. But, woven fabrics can do this, and knitted

fabrics can cover double curvature surfaces very well because of their different elongation

characteristics.

Asvadi and Postle [8] did a numerical study, considering linear viscoelastic theory, on

viscoelastic responses and friction forces in woven wool fabrics, which show shear

deformation at large extensions. They state that the conformability of the fabric when it is

being sewn, the ability of the fabric to keep the shape given to it, and the recovery after

wrinkle, have to be estimated. These properties can be defined by the determination of the

mechanical properties at the later stages of bending and shear deformations. In such

deformations, most fabrics show some amount of behaviour that is not elastic, such as fibre

viscoelasticity and friction between fibres. The mechanics of deformation in textiles is much

affected by the shear properties.

3.1.1 Defining Bagging by Membrane Theory

According to Lloyd [40], when a flat sheet is deformed in its own plane and no transverse

displacement occurs, this means planar deformations are taking place. Strains can be

modelled and appropriate mechanical properties formulated and measured. The membrane

strains that develop in the plane of the sheet are also called in-plane strains. Even in

transverse displacements, there are in-plane strains occuring in the sheet material. In tension

membranes, there are transverse displacements of the fabric, but the bending stiffness of the

fabric is negligible [40]. Extended methods of the membrane theories are applied to the

problems in this case. Fabric is a membrane material which can bend to a cylindrical curved

surface without deformation [11]. But the fabric has to fit doubly-curved surfaces in a

garment, so it will deform in its plane or buckle and fold.

Amirbayat and Hearle [2] consider the fabric as a membrane and solve the problem with

membrane strains. They state that in the complex buckling of flexible sheet material,

membrane strains occur and they are very important. In double curvature over small

areas, membrane strains are occuring. They state that solving these kinds of problems with

membrane strains is more important than solving them with conventional shell theory.

3.1.2 Defining Bagging by Plate and Shell Theory

Womersley’s [73] work is considered to be the first step in the general evaluation of strain–

elongation relations in fabrics. In his paper, he is the first to apply differential geometry to

study fabric deformations under stress. Under ideal conditions, the warp yarns of a woven

fabric are parallel to each other, so are the weft yarns, and these two groups of yarns are

perpendicular to each other when intersected. Under any kind of a stress, they bend and

their newly deformed condition can then be defined by a curved-coordinate system.

Womersley has given the general equilibrium equations of a fabric that is stretched from the

sides and is under pressure, as in the hydrostatic approach which is perpendicular to the

fabric surface, with these assumptions: (i) The fabric is a thin lamina; (ii) The yarns are

regular, fully bendable and non-elongating, with round cross-section; (iii) The fabric

structure changes very slowly; this means that the changes in the fabric construction when

the force is applied are very small and they are the same in consecutive units; (iv) The fabric

cannot stand shear forces; in this case, only the strains occuring in the yarn will be taken into

consideration; (v) Intersections are stable, they do not slip; in this case, when the size of one

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unit and the change occurring at the surface by the changes at the axis are compared, the

quantities are very small.

The fabric construction with these assumptions and the real fabric construction are

very different because the assumptions are made in order to develop a theory for a

fundamental model and most of the fabric properties which make the fabric behaviour

complex, such as elasticity, viscoelasticity, friction, compression of yarns, are not taken

into consideration.

Womersley took Peirce’s [49] fabric geometry as the basis in his work. In Fig. 4, Peirce’s

ideal fabric geometry according to the bendable yarn model is illustrated.

When we move one intersection aside, and inspect perpendicular to the fabric axis,

we get:

h1 ¼ fl1 � ðd1 þ d2Þy1g sin y1 þ ð1� cos y1Þðd1 þ d2Þ ð1Þp2 ¼ fl1 � ðd1 þ d2Þy1g cos y1 þ sin y1ðd1 þ d2Þ ð2Þ

Similar equations apply to h2 and p1. When D¼ d1þ d2¼ 1, fabric thickness becomes a

unit measure. Then, the equations become,

h1 ¼ fl1 � y1g sin y1 þ ð1� cos y1Þ ð3Þp2 ¼ fl1 � y1g cos y1 þ sin y1 ð4Þ

Also from Fig. 4, it is deduced that h1þ h2¼D¼ d1þ d2¼ 1, which is a fundamental relation

between fabric constants. Even if the distances p1 and p2 change after deformation, l1 and l2distances do not change because it is assumed that the yarns do not elongate.

When the fabric is in the deformed state, the yarns are taken as the curves of a curved-

coordinate system. The warp yarns perform the v¼ constant curves and weft yarns perform

d1: Diameter of the warp yarnd2: Diameter of the weft yarn

Dð¼ d1 þ d2Þ: Fabric thicknessp1: Distance between the centres of two warp yarnsp2: Distance between the centres of two weft yarns

h1=2: Distance between the centre of a warp yarn and the fabric axish2=2: Distance between the centre of a weft yarn and the fabric axis

y1: The angle between the warp yarns and the fabric axisy2: The angle between the weft yarns and the fabric axisl1: Length of a warp yarn between two weft yarnsl2: Length of a weft yarn between two warp yarns

c1 ¼ l1=p2 � 1: Crimp of a warp yarnc2 ¼ l2=p1 � 1: Crimp of a weft yarn

Fig. 4 Ideal fabric geometry according to the bendable yarn model of Peirce [49]

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the u¼ constant curves; therefore u changes along the warp yarns, and v changes along the

weft yarns. A bent fabric surface is seen in Fig. 5.

AB and DC correspond to warp yarns; dv is proportional with the number of warp yarns

between AB and DC and because p1 is the distance between consecutive warp yarns along

u¼ constant curve, after deformation it becomes,

ds ¼ p1dv ð5Þand in the similar way, along the v¼ constant curve, it becomes,

ds ¼ p2du ð6ÞIn this case, one unit of fabric surface is defined as:

ds2 ¼ p22 du2 þ 2p1p2 coso du dvþ p21 dv

2 ð7ÞSince p1 and p2 are dependent variables, any fabric surface is defined as:

ABCDðareaÞ ¼ p1p2 sino du dv ð8ÞThe warp and the weft yarns intersect and cause tensions between themselves. From

Fig. 5, this relation can be written as Eq. (9) because the yarns are considered to be pure

bending;T1 sin y1 ¼ T2 sin y2 ð9Þ

T1 : Tension in warp yarns

T2 : Tension in weft yarns

Since the components of T1 and T2 in the fabric surface are F1 and F2, then;

F1 tan y1 ¼ F2 tan y2 ð10ÞF1 tan y1= tan y2 ¼ F2 ð11Þ

F2 ¼ wF1; w ¼ tan y1= tan y2 ð12Þ

If w can be written in w(p1,l1,l2) form and p1 is known in terms of u and v, this proportion can

be calculated everywhere on the fabric surface.

u ¼ constant Point A : ðu; vÞuþ du ¼ constant Point B : ðuþ du; vÞv ¼ constant Point C : ðuþ du; vþ dvÞvþ dv ¼ constant Point D : ðu; vþ dvÞ

o : Angle between the two yarn groups

Fig. 5 A bent fabric surface. Womersley [73]}

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When a force is applied in a perpendicular direction to the fabric plane and the

equilibrium equations are written for the fabric, it is seen that these do not depend upon

the assumptions of the yarn’s non-elongation and pure bending, but they depend upon the

absence of shear forces and the smallness of the construction.

The forces occuring on a piece of fabric which is bordered with

u� 1=2du; uþ 1=2du; v� 1=2dv; vþ 1=2dv

curves are seen in Fig. 6, where,

F1(u, v)¼Strain in warp yarns at Point (u, v)

F2(u, v)¼Strain in weft yarns corresponding the above strain at Point (u, v)

When the static equilibrium is considered on this piece of fabric, since the P force is

equalized with the strain in the yarns, then these equilibrium equations should be written:

F1ðuþ 1=2du; vÞdv� F1ðu� 1=2du; vÞdvþ F2ðu; vþ 1=2dvÞdu� F2ðu; v� 1=2dvÞdu ¼ PdS

ð13Þ

If n is a unit vector which is perpendicular to the surface at Point (u, v) [37], then

P!¼ P n! ð14Þ

When Equations (8) and (14) are substituted in Equation (13):

F1ðuþ 1=2du; vÞdv� F1ðu� 1=2du; vÞdvþ F2ðu; vþ 1=2dvÞdu� F2ðu; v� 1=2dvÞdu� Pn p1 p2 sino du dv ¼ 0

ð15Þ

When F1 and F2 are defined as partial differentials, then,

F1ðuþ 1=2du; vÞdv� F1ðu� 1=2du; vÞdv ¼ @F1=@u du ð16ÞF2ðu; vþ 1=2dvÞdu� F2ðu; v� 1=2dvÞdu ¼ @F2=@v dv ð17Þ

Then, we would get,

@F1=@uþ @F2=@v� P n p1 p2 sino ¼ 0 ð18ÞIf a is the unit vector in the warp direction and b is the unit vector in the weft direction, then

a, b and n make the coordinate system of the three. The vector equation of equilibrium can

be solved by multiplying a, b, and n scalars in turn.

F!

1 ¼ F1 a!; F

!2 ¼ F2 b

! ð19Þ

P : Pressure applied perpendicular to the fabricdS : Area of the piece

P dS : Force applied to the piece

Fig. 6 Forces occuring in the fabric

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can be written. Then the equations take this form:

@F1=@uþ ab @F2=@vþ F2 a @b=@v ¼ 0 ð20Þ@F2=@vþ ab @F1=@uþ F1 b @a=@u ¼ 0 ð21ÞF2n @b=@vþ F1n @a=@u ¼ P p1p2 sino ð22Þ

k1 is the curvature of the v¼ constant curve in the tangential way, and

k2 is the curvature of the u¼ constant curve in the tangential way, so

n @a=@u ¼ p2 k1; n @b=@v ¼ p1k2 ð23ÞThen the equation takes this form,

F2p1k2 þ F1p2k1 ¼ P p1 p2 sino ð24Þand this equation is similar to the equilibrium equation of a foam [73].

If the surface were flat, then the measures b @a/@u and a @b/@v would be related to the

curvature of the u and v curves with these equations:

b @a=@u ¼ p2=r1 sino ð25Þa @b=@v ¼ �p1=r2 sino ð26Þ

Here

r1¼ curvature radius of u curve

r2¼ curvature radius of v curve

When the surface is not flat, r1 and r2 become the curvature radii that are perpendicularto the tangent surface, and this means it is the radius of the geodesic arc. Geodesic

curvatures are generally shown as g and g0, so the equilibrium equations take this form:

@F1=@uþ coso @=@vðw F1Þ � wF1g0p1 sino ¼ 0 ð27Þcoso @F1=@uþ @=@vðw F1Þ þ F1gp2 sino ¼ 0 ð28Þ

F1ðk1=p1 þ wk2=p2Þ ¼ P sino ð29Þ

In these equations, w and p2 are the known functions of p1, so the three functions of

equilibrium contain three unknowns which are F1, p1 and o. In this case, k1, k2 and g, g0 aredependent upon p1, p2 and o. The forces that occur at a special deformation and the pressurein the normal direction which will keep the system in equilibrium can be calculated from

Equation (29), even it will be hard. It seems that working with coefficients will be simple [73].

Kilby [33] studied the planar stress–strain relations in a woven anisotropic fabric. He

considered the influence of the fabric anisotropy on fabric mechanical behaviour. In his

work, he considered the fabric as an anisotropic elastic lamina. He derived a coefficient that

he called the generalised modulus of the fabric, which shows the fabric’s tensile modulus in

the test direction. He worked mainly with small strains.

Kirk and Ibrahim [34] stated that if the primary requirement from a fabric is performance,

then the available stretch level of the fabric should be 20–30%; but if the primary

requirement from a fabric is comfort, then the available stretch level should be 25–40%. The

fabric tries to be in agreement with the body’s movements by sliding over the skin, leaving

some space between the body and the clothing, and by stretching. Fabric stretching causes

fabric bagging when the double curvature parts of the body are concerned.

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Postle and Norton [50, 51] later used the application of differential geometry in fabric

deformation. These researchers used tensor analysis to determine the woven fabric finite

deformation, and defined four tensor areas: (i) Tensor area for fabric extension percentage;

(ii) Tensor area for normal curvature of the fabric surface; (iii) Tensor area for yarn bending in

the fabric surface; (iv) Tensor area for yarn twist in the fabric surface. They drew curved

coordinates according to Cartesian coordinates (x1, x2, x3) of the three-dimensional Euclidian

space. They developed parameters to provide a coordinate system on the fabric surface and

these are also constant as coordinate lines. If the points of the fabric are marked to infinity,

then with a single system all the points of the fabric can be defined easily. These are called

‘convected coordinates’; and if thewarp or theweft way is taken as the axis, then they are called

‘weave coordinates’. In Postle and Norton’s work, the first and the last forms of the fabric are

simply evaluated as being positioned in two different spaces. The differences between the

tensors of these two positions are defined as the deformation occuring.

Some researchers were not concerned with the top area of the fabric where the drape did

not start yet when the fabric was bent to conform to a spherical surface, or with the very top

part of the fabric when it is thrown in an uncontrolled way to make three-fold buckling

[32, 50, 51, 57]. They developed some models and described the uniaxial and biaxial tensile

behaviour and shear behaviour of plain woven fabrics. They also calculated the lateral yarn

compression and fibre slippage during tensile deformation by using some general graphical

analysis methods and empirical calculations. If the fibre viscoelasticity is included in the

model it will then be improved. They stated that bagging deformation is composed of biaxial

tensile and shearing deformation, and that this kind of deformation is finite [32]. Some

carried out their work to model the energy of the fabric and drew force diagram of the fabric

similar to the contour lines in Moire topography [76].

Bassett and Postle [9, 11] took the concept of covering a three-dimensional surface with a

fabric in a different way and studied how the fabric would cover such a surface with warp

and weft yarns keeping their parallel positions relative to each other when force is applied on

them. They did work to combine the subjects of fabric sewability, garment appearance and

fabric drape, with fabric properties such as shear rigidity, shear hysterisis, bending rigidity

and bending hysterisis. They tried to determine the relations between fabric elongation,

shear and bending properties, and behaviour in conditions of sewing and deformation in

use. The term ‘a deformed state’ has two aspects. One is the study of the in-plane forces

reproduced by the applied external forces and how these in-plane forces are distributed in

the fabric plane; the other aspect is the study of the changes in the shape of the fabric, which

can be planar, spatial or curvature. They state that a fabric having a membrane structure can

cover only a cone without deformation (a cylinder is a cone having its top located at

infinity). The behaviour of such a fabric can be calculated from the fabric’s bending

parameters for various intersecting angles; but in different parts of a garment, a fabric has to

be able to cover the double-curvature surfaces, so it will either deform in its plane, or crease,

or buckle. In the theoretical approach of Bassett and Postle [9], there is the Elasticity Theory

on one side, where the elongations and elongation percentages are small and the material is

linear isotropic, and the Finite Element Analysis on the other side. This method showed a

parallel improvement with the developments in computers, and was adopted by Lloyd [40,

41] to succesfully solve some problems in textile technology.

Bassett and Postle [9, 11] in their work considered the fabric as a web of rod elements and

evaluated the fabric as if divided into small squares. The forces act as force couples in the

way they study the problem. The force couples equilibrate each other when they are vertical

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to each other, but when they have an angle between them they make themselves work.

Bassett and Postle [9, 11] laid a circular piece of fabric on a half-sphere to comform to a

spherical surface. Here, the friction between the fabric and the surface it covers is not taken

into consideration. The top part of the sphere covers the whole surface very well but towards

the bottom, drapes occur. Equal weights were hung at the bottom of the fabric, and as they

were hung, the part that covered the sphere surface at the top increased. In this work, it was

considered that the rod elements did not elongate but the network changed shape according

to the shear forces. The stress and strain distributions in the fabric were calculated by a

numerical method developed by the researchers. The approximation of the fabric was like a

flexible net-like grid of ‘ball-jointed’ rod elements. The forces, extensions, and shears were

calculated by an iterative method. The main focus of their work was on the mechanical

behaviour of isotropic fabrics.

The points Pu,0 and P0,v take place at the side planes of the coordinate plane when the

quarter of the sphere is studied. Point P1,1 is the intersection point of P1,0 and P0,1 which is

one intersection away. All the other Pu,v points can be found the same way. It is considered

that there is no elongation between the elements in the network when the shear angles are

calculated. The shear angle at the point Pu,v can be calculated as euv�fufv (in terms of

radians). Here, fu is the f-coordinate of Pu,0 and fv is the f-coordinate of P0,v. The shear

force couple in every element can be calculated only if it is taken as a function of the shear

angle. If it is taken as an effect of shear, tensile and bending properties, a very complex

situation comes about. Since there are weights hanging along the bottom intersections, the

force acting upon every element can be calculated. When the limiting factors are taken into

consideration, the unknown forces at the bottom edge intersections can be found by solving

the equilibrium equations. When all the calculations belonging to the bottom edge are

finished, then one can move to the next inner row, and consecutively, can come up to the

point P0,0 and exactly find the force distribution. If yarn elongation is important, then first,

the force–elongation characteristics of the fabric used are worked out. Then, starting from

the bottommost edge, the calculations are redone. If the geometry of the system comes out

differently because of the elongations, then the force distribution comes out differently also.

The relation between the weights hanging at the bottom and the curved surface covering the

the top was investigated in terms of angle f, but no sufficient relation was found. The most

important solution found was: When the fabric was first laid on top of the sphere, from the

point of preventing the bending at the edges, the effect of yarn elongation is only 1% and the

amount of weight needed to prevent bending at a specific angle of f, if elongation is

eliminated, is found to be directly proportional to the fabric’s shear resistance. This result

confirms the idea that the fabric takes three-dimensional forms according to its shear

resistance. The data found to date show that fabrics that gain double curvature, create high

pressing forces in themselves, even though the studies were done at low loadings. This may

seem contradictionary but the results obtained reflect this conclusion [9, 11].

3.2 Mechanism of Bagging

Amirbayat and Hearle [3] stated that fabric’s drape and comformability properties are those

that make it different from other layered materials. They found that the limiting

assumptions of the plate and shell theories are not sufficient for investigating the three-

fold buckling of textile materials, both for the terms used and the methods used. Calladine

[17] has made an assumption emphasizing the interaction between bending and extension,

but the application of this assumption to buckling textile material is not perfect because it

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considers elastic theory depending upon small elongation–small displacement and plastic

theory depending upon large elongation–large displacement. Calladine [17] is not concerned

with complex buckling where recovery is possible after large elongation–large displacement.

This is the difference between membrane deformation and bending deformation outside the

membrane. At a single curvature, many layers of the material behave the same; but at double

curvature, they behave very differently. The buckling shapes are various in these cases

because double curvature needs in-plane elongations. A plane-like sheet covers the double-

curvatured surface like a map of the spherical world laid flat on a sheet of paper. There is no

force applied from outside. On the contrary, textile materials and elastic materials can

behave according to membrane extensions and, if there is a force application from outside,

they can conform to them.

3.2.1 Elastic Effects

In garment production, there are areas of the body such as the shoulders where a surface

with double curvature has to be covered, and this is achieved in the fabric’s direction of

shear rigidity. Lindberg et al. [39], Hearle et al. [29], Amirbayat and Hearle [2, 3], and many

others, proved in their works that the relation between drape constant and bending rigidity

improves if shear strength is taken into consideration. Amirbayat and Hearle [2] examined

the recoverable bending of flexible fabrics under small forces, but did not examine the

unrecoverable deformation of rigid material under large forces. They state that in three-fold

buckling, two of the buckles occur in the middle layers and one buckle occurs at the side

layer. They assumed that there was a smooth passage from one to the other, but there is a

strict separation between them because the layers are sensitive to the diffusion of energy.

They state that the viscoelastic properties and creep-relaxation properties of a fabric play a

role at the conformed top part, the behaviour becomes very complex and mainly the fabric is

pushed to take the form of a different shape.

Shanahan et al. [57] in their work state that there is a considerable cooperation between

the bending, shear and tensile parameters of the fabric and if their constants were to be

calculated then the degree to which they affect each other could be worked out. But Bassett

and Postle [11] in their work considered the elongation, shear and bending features

independently of each other. Shanahan et al. studied the fabric elastic behaviour at complex

deformations. They concentrated on drape in their work and considered the fabric as a two-

dimensional continuum. They worked with this consideration and studied the behaviour of

the material in the linear elastic area. They emphasized that there are large-elongation large-

deformation conditions in textile materials, and for both isotropic and elastic material there

are non-elastic, non-linear and time-dependent relations. Even at small strains, textile

materials will show viscoelastic and frictional slides. That is why the deformation that takes

place is non-linear, cannot fully recover and is time-dependent in character. Also, they

suggest that a three-dimensional full analysis has to be done including the fabric thickness.

It is stated that at large elongations, the force–elongation relations are not elastic,

non-linear, and show time-dependent differences and irregular recoveries.

3.2.2 Viscoelastic Effects

Amirbayat and Hearle [3] state that the main reason for not studying this subject earlier was

that some of the assumptions in applied mechanics are not in agreement with textile materials.

Textile constructions are not continuous; they are made up of smaller pieces. They are not

isotropic and linear, they show hysteresis and they are time-dependent in their responses.

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In general, their viscoelastic properties are not taken into consideration. In complex buckling,

very complex deformations occur as a result of large elongations and displacements. The

reason why this subject is studied now is that, in the last fifty years, there is an increase in the

use of man-made fibres and advances in the production methods of textiles. As a result of

these, the experiences and the trial–error methods that were exercised before can no longer be

used; and they were very expensive and time consuming. Also, new application areas of

textiles have been invented such as geotextiles, aerotextiles etc. A different performance from

the modern fabric is expected. As a result of developing computer technology and its

application in textile investigations, work that symbolises the behaviour of the fabric in usage,

even when the fabric is at the design stage, has improved a lot [44].

Zhang et al. [80] studied the decaying of internal energy in fabrics when they

macroscopically examined the physical mechanism of fabric bagging and the components

of stress during bagging. They also looked at the energy changes occuring when the fabric is

repeatedly bagged. They developed a test method and abstracted three mechanical criteria

for objectively evaluating fabric bagging, which are residual bagging height, bagging fatigue,

and bagging resistance. Bagging fatigue also includes the ability of elastic recovery, and

bagging resistance also includes the ability to resist deformation. If we name them in

deformation energy terms, then we can say elastic and viscoelastic energy of the fibres and

plastic deformation which results from frictional slippage between fibres and yarns. They

found from the results that fabric bagging is closely related to the viscoelasticity of fibres and

frictional restrictions in the fabric construction. They were able to predict the fabric bagging

fatigue behaviour and residual bagging height from fundamental fibre–yarn mechanical

properties and fabric sturctural parameters. They investigated the relations between the

mechanical criteria and fibre–yarn–fabric parameters, both theoretically and experimentally.

They found that the ability of the fabric to resist bagging decreased with time and that the

decrease had an exponential behaviour. They state that during the bagging process, there is

a kind of fatigue behaviour of the textile material. The work of loading in the first five cycles

of the bagging test was measured. They included the elastic energy in the fabric and the

hysteresis energy, which includes the viscoelastic energy and the plastic energy. The energies

decayed with the cycle of deformation. Then they calculated the three mechanical

parameters to describe the fatigue process. Different fibre compositions and weave

structures among the fabrics yielded to different mechanical behaviour between the fabrics.

They tried to predict the bagging performance from fibre–yarn properties and fabric

structural features and to find the relation between these two sets of parameters. They also

developed a test method for subjective evaluation, they took photographs of the bagged fabric

samples, and conducted some psychophysical perceptual tests. They found that subjective

perceptions depend mostly on fabric residual height, and the residual bagging shape is also

an important stimuli; the shape is related to fabric anisotropy. They found a high correlation

between using the photographs and the real bagged fabric samples. In their later researches,

they use image information [80].

4. TEST METHODS FOR BAGGING

4.1 Methods Related to Bagging in International Standards

It has previously been stated that the studies done of deformation in woven fabrics also

included those where the force was applied to the fabric’s plane in the vertical direction and

there was displacement where the recovery was not full. Deformation under hydrostatic

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forces and ball-penetration were used in bursting strength tests. Some researchers worked

according to these principles. Their works are summarized here.

Sommer [59] in his work used the Schopper bursting strength apparatus (DIN 53861,

Parts 1-2-3, 1970) [22]. He worked with different weaves and different compositions

(including rubber), both for woven and knitted fabrics. He evaluated the bursting strength

pressure as the main value. This researcher considered that the fabric attained a spherical

shape at bursting. According to DIN 53861, Parts 1-2-3, it also is considered that the dome

occurring in a bursting strength tester is spherical. Zurek and Bendkowska [85] proved that a

circular piece of fabric makes an elliptic dome when bursting in the apparatus.

The ball-penetration test of ASTM Standard D231-62 revised to D3887-96, D3786-01,

D3787-01 [7]; and TS 7126 [67] exerts a force on a 12.5 cm. diameter knitted fabric with a

2.54 cm. polished steel sphere at a constant speed of 305 mm/min until the ball penetrates the

fabric by tearing. The force at tearing is evaluated. In their work, Scardino and Ko [56] used

three-dimensional fabric which had yarns intersecting at 608 and measured their extension,

shear and bursting deformations in this apparatus. They also did the samemeasurements with

two-dimensional fabric and compared the two groups. They found that the force distribution

in the three-dimensional fabric when deformed was more even than that in the two-

dimensional fabric. Also they found that, at the same force measurement, the three-

dimensional fabric was deformed permanently but the two-dimensional fabric was torn.

In the literature, we meet a Chinese standard, FJ 552. 6-85 [25, 80, 82]. Even though this

standard was not seen in preparation of this text, it is understood from the literature that it

describes the bagging behaviour by means of bagging height or bagging volume, and wear

trials are also used as a subjective method in experimental investigations.

In British Standards, there is a standard regarding the woven fabric’s resistance to sagging

during wear, BS 4294 [16]. The Turkish Standard TS 6071 [66] is a translation of this

standard. Sagging is the stretch deformation occuring in the fabric in daily usage. It is

different from bagging, but is sometimes confused with bagging.

4.2 New Methods Developed

The kinds of tests we see in the standards and most of the researches which will be explained

in Section 5, work with, a sphere pressing against the fabric, either woven or knitted. This

pressing sphere method is the one which is mostly used. Another method for measuring

bagging behaviour is the wearer test. This method is subjective and is also used by some of the

researchers to confirm the test method they had developed. Another method is using the

KES-FB apparatus, used by one research worker and which will be explained in the next

sections. In that research, bagging behaviour of the fabric was determined by the variables in

the KES-FB apparatus.

This is a different point of view in bagging studies. An image processing method was also

used by one group of researchers. This method was then compared with visual tests done on

several people, and proved useful for determining the bagging of garments. It can be used

both before the fabric is sewn into a garment and after the garment has been used for a

period of time. All of these methods will be explained in detail in later sections.

4.3 Other Similar Aspects

Williams [72] in his work with parachutes found out that the inner volume of a parachute

changes very little because of the elongation of the parachute fabric. In his work, he

considered the fabric as a membrane with linear elongation. Ericksen et al. [24] applied

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longitudinal force to the parachute fabric produced from the synthetic fibre Kevlar 291

(single-ply plain woven) and measured extension and examined the changes occurring in the

fabric geometry. When the fabric reached a specific extention, they removed the force, cut

the fabric and took photographs of the cross-section. From these photographs, the changes

in the fabric geometry and yarn cross-section could be seen. They postulated that when the

fabric first starts to feel the force, yarn bending is responsible for the elastic behaviour, but

as the force gets stronger, bending turns to elongation, and when the force is extreme, yarn

elongation is mainly responsible. The effects of bending and elongation in the yarn cross-

section were very clearly detected in their work. The weft density of this parachute fabric was

much higher than the warp density.

There has also been work done with deformations under pointed forces. Shanks [58]

studied the dynamics of coarse nets by means of Finite Element Analysis. The unit area of a

net is much larger when compared with that of a fabric. These kinds of nets are used as life

protecting vests in airplanes or guards around rotating elements of machines. In these cases,

the nets serve as energy absorbers and as mechanisms that distribute the energy throughout

their own constructions. During usage, the construction of the net has to minimize the

maximum dynamic effect and should not be defective within its own body. Also, in nets that

experience strain at high levels, such as tennis rackets or squash rackets, there has to be

minimum contact time between the net and the object touching it, and the energy absorbed

by the net has to be at the lowest. Shank’s assumptions were such as these: (i) The elements

have no bending rigidity and twist, which means when under stress there is no inclination to

untwist; (ii) There is pretension given to the net before impact. This is to prevent any crimp

that could occur and to guarantee to start the experiments with the same tension every time;

(iii) The intersection points are fixed, they do not shear. This cannot be true for textile

materials; (iv) The boundary line is also fixed; no slippage occurs there; (v) The material used

is linear elastic and is uniform throughout the net; but in cases of large extentions, we can

mention geometrical irregularity.

Another approach to deformation is the deformation under pointed forces. Ballistic

studies are good examples for these. Roylance et al. [55] applied dynamic finite element

analysis, which was developed for single fibres, to model woven surfaces. Their main

purpose was to improve the performance of bullet-proof vests. In their research, they found

that the ballistic event cannot be treated separately from the construction effect, and that

there is a high correlation between the fibre’s ballistic strength and the ballistic strength of

the fabric woven from that fibre. When it was first studied in the case of a fibre, at the impact

of the bullet, the axial elongation waves, which are independent of the velocity of the impact,

get away from the impact point. Following these waves, the fibre material starts to flow

towards the impact point. Also, waves opposite to these axial waves start to propagate from

the point of impact; they propagate slowly and slow down the flow of the material. Since the

movement of the material is impeded, every time a wave comes, it vibrates. The most

important difference between the fibre and the fabric is that there is interaction between the

axial waves and the opposite waves because there are fibre intersections in the fabric. In

every intersection, an opposite wave is reflected, the magnitude of the main wave decreases,

and the elongation behind the wave increases. At this point, the geometry of the fabric is

very important.

When a signal which is perpendicular to the surface is studied, only a proportion of the

force applied to a certain intersection is passed to the next intersection. Here, the difference

between the continuous material and non-continuous material becomes obvious. The total

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energy passes through every point at the same amount in a continuum where conductance

is perfect, but in a non-continuum the signal goes back and forth between intersections so as

to decrease. At the beginning the signal is effective at one point, but as it is propagating in

wave form, it is distributed to a wide area. In a non-continuum, the density of the energy and

related extension proportions decrease if factors of the reflectance of energy and the turning

of energy into some other kind are not considered. Another difference between the

continuum and a non-continuum is this: In a non-continuum, it takes a long time for a signal

to propogate and it has a fading character; on the contrary, in a continuum, the signal keeps

all the properties it had when it left its main source, in every point [55].

There are other researchers working on ballistic impact such as Leech [38], Montgomery

et al. [45], Cunniff [19, 20] and Lloyd [40]. Lloyd [40] among these applied finite element

analysis to fabric deformation and also used this for ballistic impacts, regarding the time of

impact as a cone.

5. RESEARCHES ON BAGGING

Many experimental investigations have been done on bagging but fundamental investiga-

tion of bagging progresses slowly. One reason for this is that the deformation during bagging

is large and three-dimensional. Another reason is that there are practical difficulties in

measuring linear and nonlinear, elastic and viscoelastic, anisotropic and frictional properties

of textile materials.

5.1 Researches with Woven Fabrics

Lindberg et al. [39] made a pioneering study of how a woven fabric covers curved surfaces.

They looked at the problem from the garment-making point of view. They state that

mechanical properties such as buckling, in-plane compression and shearing are needed in a

fabric to make a garment from it, but there have to be upper and lower limits for these

requirements. Also in garment making, a flat fabric is turned into a three-dimensional shell

and this feature bears relation with mechanical properties. The ‘formability’ property of a

garment is introduced in their work. The fabric has to retain the form given to it, which

means the fabric has to be set to keep that form, and they explain that stitching with

overfeed gives the fabric what it needs to be set. Dimensional stability is discussed according

to garment production steps later in their paper.

They indicate that a garment is designed to cover the human body, so its shape resembles

a body. There are curved regions in the body; for the fabric to take that curved shape, it has to

behave like a shell rather than a membrane. In garment production, a plane-like fabric is

turned into a three-dimensional shell which has to keep its form and has complex curvatures.

When fabric is turned into a cylinder, simple bending takes place. But when it turns into a

spherical form or a saddle, distortion of the surface elements are needed. A spherical surface

can be formed by extension forces or compression forces. When a fabric is placed in a ring

and pressed by a half-sphere, extension forces take place. Biaxial stresses also will be taking

place, pressure being constant, and the height of the deformed spherical part will be deter-

mined by the biaxial extensibility of the fabric. When a fabric is woven to fit the spherical

surface, then compression forces take place. Compressibility, in such a case, is determined

by the compressibility of the fabric in various directions. They also emphasied the

importance of the bending, shear, and extensibility of a fabric by experiments and by theories.

In the photograph they present, a piece of wire gauze has been formed into a half-

spherical shape, and by using simple analysis they have calculated the average diagonal

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extension and circumferential compression of the gauze. But, they did not relate this to the

stress distribution that could occur in a similarly deformed fabric [39].

Eeg-Olofsson [23] worked on the subject of defining the shaping ability and what he called

‘comfortability’ of texile fabrics and similar materials. The necessary conditions for a fabric

to conceal cylinders, cones, and spheres were studied. The idea of comfortability, which is

the ability of a rectangular structure to conceal a spherical structure, was studied. In this

work, shaping ability is calculated from strains and compressions of the fabric. The

researcher did experiments with rubber fabric, and tried to calculate comfortability from the

force exerted and the tensile strength of the fabric obtained by tensile tests.

Fleissig [26] developed an apparatus to measure the permanent deformation in knees,

elbows, and hips. In this apparatus, a piece of round fabric is pushed with a sphere of the

same diameter. The strains in the warp and weft yarns of the fabric pushed with the spherical

surface were studied according to membrane theory. He also made some assumptions as

follows: (i) The fabric is a homogeneous isotropic membrane with a neglectable constant

thickness; (ii) The dome formed when pressed with the sphere is big enough to almost equal

the radius of the clamping circle; (iii) Bending moments and shearing forces can be neglected

at every point of the membrane; (iv) The membrane is fitted to the clamping circle as a hard

fit; (v) The external force applied by the sphere is continuous, constant and perpendicular to

the fabric at every point. In other words, the force application is assumed to be hydrostatic;

(vi) The frictional forces between the membrane and the spherical surface can be neglected.

The intention here was to deform the fabric both in the warp and the weft directions and to

study the behaviour of that part which is in the clamped area. When studying the tensile

strength of the fabric, only one, the warp or the weft, direction is taken into consideration,

but in a work such as this, both of them are taken into consideration in order to wrap up the

sphere. The researcher included the deformations which he assumed to be similar to

Hookian Laws. So it is proved by these experiments that yarn elasticity is very important at

the very top of the curvature where the strain is the maximum. The maximum dome takes

place at the maximum strain.

Yokura et al. [76] emphasized the tendency of a fabric towards bagging. As stated

before, bagging is seen after a force perpendicular to the fabric’s plane is applied to the

fabric, so the fabric loses its dimensional stability and cannot recover fully. They

developed an objective evaluation method for predicting the bagging propensity of woven

fabric. They used the increasing bagging volume to measure this bagging propensity. The

researchers named the volume of the dome occurring after the force application as the

‘bagging tendency’. They studied the volume which was formed by constant load resulting

in shear deformation. They also measured the mechanical properties of the fabrics. They

statistically examined the correlations between the bagging volume and the fabric’s

mechanical properties.

They placed the sample fabric on a half-sphere which had a 14 cm. diameter, clamped the

chucks, loadedwith a square frame, waited for five hours, and left it to recover for 19 hours. In

their experiment, load was equally distributed along the warp and the weft directions. They

name the creep occurring after repeated shear deformation under constant tension ‘dynamic

creep’; and the creep under tension ‘static creep’. Bagging shape was not taken into

consideration. They also tried to symbolize the ‘sweaty’ and the ‘normal’ stages of usage by

keeping the humidity and the temperature high at the sweaty stage. In the statistical evaluation

to predict the bagging volume, they used multiple regression analysis to the variables

they obtained from the KES-FB system. The results were in accordance with 500 hours

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of wearing tests they did before with the same fabrics and derived empirical equations for the

bagging propensity in terms of mechanical properties [76].

They worked with two groups of woven fabrics: one group of stretch fabrics with deve-

loped elastic properties, the other of classical fabrics with normal elastic properties. The stretch

fabric group consisted of fabrics made up of PE (textured) yarns and polyurethane yarns. The

classical fabric group consisted of fabrics made up of wool yarns, PE (spun) yarns and W/PE

(spun) blend yarns. For the stretch fabrics group, the bagging volume gave a high correlation

with the hysteresis behaviour in uniaxial tensile strength, bending rigidity and shear

deformation in small angles, depending much on inter-fibre and inter-yarn frictions. For the

classical fabric group, the residual bagging volume gave a high correlation with the dynamic

creep strain and rate values. They also found that in the fabrics mentioned, the residual bagging

volume is correlated more on time dependent deformation, i.e. the viscoelasticity of the

material. In different kinds of deformation, fabric mechanical behaviour is correlated with this

approach and one is able to identify possible relationships. In this approach, the roles of fibre

mechanical behaviour and yarn–fabric structural characteristics are not involved. The

correlation between bagging volume and mechanical properties of the fabric was investigated

statistically to predict the bagging propensity of woven fabrics from their mechanical properties

obtained from theKES-FB system. The three-dimensional shapes of the bagged fabrics, in other

words the bagging volume, were measured byMoire topography, which is a systemmainly used

in map drawing. The volume can be calculated from the contour waves in that method. It was

conceived that bagging in the stretch fabrics depended on the friction between fibres and yarns

when compared to the classical fabrics group, but that bagging in the classical fabrics group

depended on the deformation over time when compared to the stretch fabrics group [76].

Sengoz [62] studied this subject from the point of view that bagging is a quality factor and

determined how much bagging there would be when the fabric is in its plane form, before

being sewn into a garment. The permanent deformation behaviour of a woven fabric was

studied by model experiments analytically. The researcher used a universal tensile testing

machine, and hollow cylinder and square frames to press the woven fabric. The curved

surface of a half-sphere was pushed on a woven fabric which had a surface contact to form a

spread force in between the half-sphere and the fabric. The resistance of the fabric to the

forces that occur under this force and the permanent deformation conditions were examined.

In her study, she worked with one kind of fabric but changed the experimental parameters

many times, aiming to define the combination of parameters that would clearly determine

the permanent deformation of a fabric. One other aim was to work out a suitable test

method and to make it a standard laboratory test. It would be a great convenience to work

out the relationship between different parameters by regression equations, so as to be able to

define one parameter in terms of another and thereby interpret the force, which is very hard

to calculate, exerted by the body on the fabric. This work carries importance for examining

the effects of viscoelastic properties in different kinds of deformation on permanent

deformation, and the formation and the alteration of these effects relative to time and

pressure; also, to design a fabric which maintains suitable usage performance or to

determine the suitable usage conditions of a woven fabric by improving permanent

deformation geometry and mechanics. The experiments were done in the laboratory by

symbolizing the different forces acting upon a woven fabric during usage. For example,

experiments such as applying a pointed force to a vertical fabric, pulling the fabric between

jaws, grabbing it with jaws, or leaving a weight on it, are the commonest and such tests are

all important to survey how the force is distributed in the fabric by such applications.

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However, when the fabric is forced to take the shape of a spherical surface, it is equally

important to know the force distribution.

Sengoz [62] in this work aimed to find out the deformation occurring when a spatial force

is applied perpendicular to the fabric plane and the permanent deformation related to time.

She developed a test method to succeed in these aims. Since there are too many independent

variables acting upon deformation in experimentation, these variables were tried and the

different behaviours of the fabric studied. A combination most suitable for a standard test

method was aimed for, with the help of the graphical and statistical analysis.

The fabric used was 100% cotton, plain weave, warp and weft yarn count being the same

(Ne 30/1), the total number of yarn ends 52, being a square fabric, soft finished, sanforized,

and white. A universal tensile testing machine was used in the compression mode for the

experiments. The machine was computer-aided. The kind of experiment to be done,

the selection of the parameters suitable for the test, the limitations of the experiment, the

sensitivity of the experiment, the repeat number of the experiment, can all be programmed in

the computer, and the test can be started from the computer. A photograph of the universal

testing machine is seen in Fig. 7 and the testing principle is drawn schematically in Fig. 8 [62].

In the daily usage of the fabric, it deforms to form a dome and exhibits spatial behaviour,

and this behaviour includes a third dimension in the ‘z’ axis. Spatial pressing can only be

achieved by a hollow frame where it is possible to hold the fabric from the sides. Another

sample holder was placed at the top and held the fabric firmly with the help of the screws

placed at regular distances away from each other. Also, the friction between the sample

holder surface and the fabric was increased by sticking extra fabric over the holder surfaces.

This sample of fabric, which was held freely and firmly in space, could be pressed easily with a

half-sphere. When the half-sphere acted upon the fabric, the fabric moved downwards and

elongated the rest of the fabric in its direction. This design is both similar and not similar to

the daily usage of a fabric because, although at the elbows and at the knees the fabric would

seem to be acting freely, the continuity of the fabric is interrupted with the seams, because it

was cut before with the curvatures of the arm, the leg, etc. So in reality the fabric exhibits a

limited behaviour. To resemble the most realistic form in the experiments and to achieve the

highest permanent deformation possible, it was decided to work with a limited fabric area

held in the sample. The deformation depending on the different independent variables is

Fig. 7 Photograph of the universal testing machine

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performed in this limited area. Another reason why such a construction was chosen is that the

fabric has to be laid on the same frame for a second time to measure the permanent

deformation. At this time, the measurement has to be done exactly at the same point where

the deformation was done at the first time. The screw points helped to find the same

deformation point easily. The possibility of deforming from one point and measuring the

permanent deformation from a different point was eliminated. The fabric distance from the

cut point to fit the screw until the fabric sample body was sufficient to hold the fabric firmly

in place and eliminate any slippage [62].

The dimension of the frame is an independent variable in this experiment. The dimensions

of the circular frames used are given in Table 1. It was desired to make the area increases to

be about double from one frame to the next and to study the deformations accurately, so it

was decided to work with five frames.

It was thought that square frames with a side length the same as the diameter of the

circular, would also be worth to try, so that a more realistic daily usage of the fabric could be

symbolized and also a basis for comparison could be created. A photograph of all the frames

is given in Fig. 9. Since we do not know where the force distribution ends in-plane of a fabric

in its daily usage, this kind of an approach will be symbolizing both the limited and the

Table 1

Frame Diameter and Sample Fabric Area

Diameter (cm) Area (cm2)

4 12.5666 28.2748 50.26612 133.09816 201.062

Fig. 8 Schematic drawing of the testing principle of Sengoz [62]

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unlimited behaviour of it, so the effect of the frame shape was thought to be helpful at this

stage. The dimensions of the square frames used in these experiments are given in Table 2.

The idea of keeping the area increase nearly double is still maintained in the square frames.

The difference here is that, while the force distribution is constant at the edges of a circular

frame, it is different in a square frame because when we go to the corners we move a longer

distance and this obviously affects the force distribution at the edges. Its importance was

found very clearly after statistical analysis.

A half-sphere pressing from above was thought to be suitable since just this part will be in

contact with the sample fabric, and it was designed with a suitable attachment to be easily

connected to the machine. The dimensions of the spheres used in these experiment is an

independent variable.The diameters of the half-spheres were 2, 4, and 8 cm. The surface

characteristic of the sphere is also important, and, in order to resemble the small amount of

friction between the skin and the fabric and to allow the yarns to elongate, brass material

with an even surface was chosen. The weight of the half spheres is not important since they

are held by the machine and are only used to press the fabric.

Another centralizing frame was constructed to ensure that the pressing comes from

exactly the centre and to measure the permanent deformation repeatedly from the centre

after some relaxation time of the fabric. A photograph of the spheres and the attachment

used are shown in Fig. 10.

It was questionable whether the fabric should be pressed until a specific load or until a

specific displacement, and so pre-experiments were carried out with constant loads and

constant displacements. It was finally decided to take the displacement as an independent

variable and to keep the load as a dependent variable because it would then be possible to

calculate the force exerted by the body on the fabric with the help of regression equations

derived from later statistical analysis. The specific load and the specific displacement where the

Fig. 9 Photograph of all the frames

Table 2

Square Frame Side Length and Sample Fabric Area

Side Length (cm) Area (cm2)

4 166 368 6412 14416 256

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fabric starts to tear were calculated and it was decided to work with 2.3, 3.6, 4.9, 6.2, and

7.5 mmdisplacements confidently, without tearing the fabric. Also, the amount of pre-tension

to be applied to the fabric before the experiment starts was decided to be 0.1 N [62].

The rate of pressure exertion is also important. A sudden impact is more effective than

a gradual one. The rate is also an independent variable, but in the pre-experiments five

different rates were tried and 60 mm/min was decided on because this rate gives enough time

for the yarns in the fabric and for the fibres in the yarns to change their places and take a

new deformed shape. In the rest of the experiments, this rate was used all the time.

The tests were done in two separate groups, one being the half-sphere pressing the fabric

up to the specific displacement and immediately going back, and the other being holding the

sphere pressed into the fabric at the specific displacement for three minutes, which is long

enough for a spatial deformation to occur. Immediate release or waiting came out as an

independent variable also.

Repeated force exertion at the same point is important and is also an independent

variable. It is started by being pressed from the smallest displacement measurement and is

pressed to one longer in every cycle. In the other group, it is started from the second smallest

displacement measurement and is pressed in cyles until the longest. At the last step, it is

directly pressed until the longest displacement measurement.

Relaxation time is an important independent variable also. One group was relaxed for one

hour and the other group was relaxed for forty-eight hours.

The number of repeats for one group of testing conditions was tried with five, ten and

fifteen repeats and the results were compared with t-tests. Sufficient results were achieved

with ten repeats, so from then on ten repeats were used for each group of testing

conditions.

Sengoz [62] tried many different combinations of many different parameters affecting

fabric bagging testing. Hydrostatic pressures and spread loads were both considered in the

experiments done. The results were evaluated with both statistical and graphical methods,

regression equations were derived, and the relations between parameters were stated, so that

it became possible to reach an unknown value with values in hand.

The notations in the regression equations are as follows:

Fa ¼Load needed to deform up to a specific displacement

a ¼Displacement

Fig. 10 The spheres and the attachment used in the experiments

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h1 ¼Residual bagging height after one hour relaxation time

h48¼Residual bagging height after forty-eight hours relaxation time

The regression equation derived for the load dependent variable according to the

displacement independent variable is:

Fa ¼ �0:455þ 5:247 a� 4:304 a2 þ 1:515 a3 � 0:206 a4 þ 0:012 a5 ð30ÞAs seen from Fig. 11, the polinomial equation was derived for this relation. The polinomial

equation had a correlation coefficient of r2¼ 0.9957, which explains the relationship well.

The regression equations derived for the residual bagging height of the deformed dome

dependent variable according to the displacement independent variable are given for one-

hour relaxation time and 48-hours relaxation time, separately:

h1 ¼ �0:222þ 0:362 a� 0:120 a2 þ 0:014 a3 ð31ÞAs seen from Fig. 12, the polinomial equation was derived for this relation. The polinomial

equation had a correlation coefficient of r2¼ 0.8099, which also explains the relationship well.

Fig. 11 Load vs displacement curve

Fig. 12 Residual bagging height (after one-hour of relaxation time) vs displacement curve

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8 h48 ¼ �0:810þ 0:771 a� 0:215 a2 þ 0:019 a3 ð32Þ

As seen from Fig. 13, the polinomial equation was derived for this relation. The

polinomial equation had a correlation coefficient of r2¼ 0.8044, which also explains the

relationship well.

The one-hour relaxation time values were compared with 48-hour relaxation time values.

It was seen that at one hour relaxation, the fabric had not yet completed its recovery

hysteresis curve, but at 48-hours relaxation time, the fabric had completed its recovery

hysteresis curve. The two sets of values had a high correlation coefficient of r2¼ 0.8086 so it

was decided to work with one-hour relaxation time values because they were higher, and this

can also be seen from Fig. 17. When we relate the load and the residual bagging height at

one-hour relaxation time and derive the regression equation between them:

F ¼ 4:518þ 21:690 h1 þ 40:999 h21 ð33ÞAs seen from Fig. 14, the polinomial equation was derived for this relation. The polinomial

equation had a correlation coefficient of r2¼ 0.7892, which also explains the relationship

well.

Experiments were also done to continue pressing the fabric up to tearing as in the ball

penetration tests and they were statistically studied, but they are not included here.

The load and residual bagging height parameters are dependent variables in this

experiment. The combination of alternatives which would give the best explanation of

residual bagging for the independent variables in this experiment was also searched for;

statistical and graphical analysis was done for every kind of combination. Graphical

presentations were used especially where no regression equations were derived and how the

phenomenon behaves was studied from these.

As previously stated, there were two kinds of frames, the circle and the square and five

different frame dimensions, 4, 6, 8, 12, and 16 cm. In Fig. 15, these two parameters are

examined together for residual bagging height. As seen from this figure, the square frame

with 6 cm dimension gave the highest residual bagging height value.

Fig. 13 Residual bagging height after 48-hours of relaxation time vs displacement curve

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There were three different sphere dimensions and there were five different displacement

measurements, 2.3; 3.6; 4.9; 6.2; and 7.5 mm. The results of 2.3 mm displacement were

eliminated because they were too small to be interpreted and the recovery behaviour of the

fabric was unsatisfactory. So we see the rest, four displacement measures, in Fig. 16. In this

figure, these two parameters are examined together for residual bagging height. As seen from

this figure, the sphere with 2 cm dimension at 7.5 mm displacement gave the highest residual

bagging height value.

There were five different pressing speeds, 20, 30, 60, 120, and 180 mm/min and there were

two different relaxation times, 1 and 48 hours. In Fig. 17, these two parameters are examined

together for residual bagging height. As seen from this figure, the 60 mm/min rate at one

hour relaxation time gave the highest residual bagging height value.

There were two different pressing types, immediate release and waiting for three minutes,

and there were five different pressing cyles, starting from 1 up to 5. In Fig. 18, these two

parameters are examined together for residual bagging height. As seen from this figure,

Fig. 14 Load vs the residual bagging height (after one-hour of relaxation time) curve

Fig. 15 Residual bagging height vs frame shape and dimension

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Fig. 16 Residual bagging height vs sphere dimension and displacement

Fig. 17 Residual bagging height vs pressing rate and relaxation hours

Fig. 18 Residual bagging height vs pressing type and pressing cycle

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waiting for three minutes at the fifth cycle gave the highest residual bagging height value.

The immediate release values were compared with waiting for three minutes values. The two

sets of values had a high correlation coefficient of r2¼ 0.8090 and, since the difference

between immediate release and waiting for three minutes was small, it was decided to work

with immediate release.

The best combination which gave the highest residual bagging height in a sample fabric

was concluded as [62]:

Independent Variable Alternative

Shape Square

Frame Dimension 6 cm

Half-sphere Dimension 2 cm

Displacement Measure 7.5 cm

Pressing Rate 60 mm/min

Time Immediate

Cycle 5

Relaxation Time 1 hour

Repetition 10 times

In this work, permanent deformation is regarded as a quality factor and a standard test

method that can be worked in a laboratory regularly to figure out the permanent

deformation beforehand in a fabric which is to become a garment has now been developed.

The interesting point here is that square frames gave more definitive general results than the

circle frames which were used by all the other researchers. Also, as the load applied to the

fabric to be deformed is chosen as a dependent variable, when the other factors are known it

will be easy to reach this unknown value. This kind of approach is easy to relate to daily life

because, in any one of the used garments, when the permanent deformation is measured, the

force applied from the human body to the fabric to cause it to deform when using that

garment can easily be calculated with the help of the regression equations given previously.

Zhang et al. [77, 78] also examined thebaggingbehaviour ofwoven fabrics. Theydeveloped a

test method using an Instron tensile machine. They clamped the fabric sample in a circular

holder and deformed it repeatedly by loading it from the centre, using a steel ball. The relative

residual bagging height was measured after five load cycles. They obtained a loading curve for

the first cycle and the residual bagging height over five cycles. But during these tests they

emphasized some other ideas. One was bagging resistance, which is the load work in the first

cycle, and the other is bagging fatigue which is the difference of the load work between the first

and the last cycles. They predicted the woven fabric bagging height to be a function of bagging

resistance and bagging fatigue by usingmultiple regression analysis. In their work they also did

some subjective assessments. They developed a model for predicting the rating values. They

used only the residual bagging height as the independent variable in predicting the rating

values. They found that during the deformation process, fabric strain behaved as a nonlinear

function of bagging height.

They clamped the specimen in a circular ring and had a pre-tension load to keep the fabric

flat. The fabric was bagged to a pre-determined height, then returned to its original position

on the Instron. This pushing was repeated five times in succession. They measured the non-

recovered bagging height of each of the cycles under the same pre-tension load. They did

fifteen cycles of repeated bagging deformation to find out the fabric energy changes. At the

end of the fifteenth cycle, the elastic energy still in the fabric was approximately 35–50% of

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the initial internal energy of the fabric [77, 78]. When a single fibre’s relaxation time was

measured, it was found to be longer than a single fibre’s relaxation time in a fabric that had

bagged. This means that the relaxation of fibre stress during the bagging process is faster

than that of the single fibre when averaged. They state that if the strain in the fibres is larger,

the stress relaxation is faster.

Kisilak [35] studied spherical fabric elongation under cyclic stresses where, in a garment,

they are mostly seen, at the knees and the elbows. He developed a new modified apparatus

and a new method to test the spherical deformation of woven fabric. With the algorithm

developed, he was able to calculate the elongation of the warp and the weft yarns. So the limit

stress a yarn can take could also be calculated. When a garment is worn, the shape of it keeps

changing; these changes are due to the elasticity and the viscoelasticity of the fibres. These

changes are temporary, but if the stress is too large or if it lasts too long then they are not.

Permanent or irreversible deformations occur. It was aimed to develop an algorithm to

calculate the deformation of flat textiles under dynamic loads. The procedure developed

seems suitable for predicting the quality of fabric from the properties of the constituent fibres.

The steps followed by this researcher were: (i) Testing the tendency of textiles to spherical

deformation with an artificial joint, similar to DIN 53860 [21]; (ii) Testing the tendency

of textiles to spherical deformation on the modified apparatus with an artificial joint;

(iii) Developing a new modified apparatus and a new method for testing spherical

deformation of textiles. Different methods were used to fix the samples, trying to provide

better imitations of wear. Also, exceptional wearing conditions of a garment, such as humid

and warm, were also tried [35].

In this experiment, a sphere was fixed to a computer-controlled dynamometer (Instron

6022), trying to create laboratory conditions which were similar to that of wearing the

garment in daily life. The size of the sphere was close to the size of the elbow, and the size of

the circularly fixed fabric sample was close to the size of the model of the sleeve. The base of

the fabric holder was fixed in the lower jaw. The sample stayed between two rings which

were fixed with a threaded clamp. The sphere was made of polished metal, and was fixed to

the upper jaw from where it pressed fabric. In this way, the simulation of the fabric strain at

the knee and the elbow was achieved. The diameter of the fabric sample used was 78 mm;

the inner diameter at the clamp was 61 mm. The diameter of the sphere was 48 mm. The test

procedure went as follows: Cyclic loading was carried out. The sphere pressed the fabric with

100 N for 15 minutes then was lifted and touched the surface of the fabric with 0.6 N for

again 15 minutes. This was repeated five times, then was relaxed for 3 hours. Then the cycle

was repeated two more times. The final relaxation was for 15 min. The test takes 13 hours.

The computer records the forces and the sphere shifts every time deformation occurs. The

fabric is spherically broken at the end. The load is also increased gradually at the end until

fibre breakage occurs, the force values and the sphere movements being recorded every 20

seconds [35].

In the graphical picture given inKisilak’s experiments, thedeformed fabricwasdrawn.There

seems to be sharp changes between the conical part and the straight part. There is the truncated

cone and a spherical cap at the edge. The surface area of the truncated cone and the surface area

of the spherical cap are calculated and added together. The surface area of the fabric sample

before deformation is subtracted from this sum. This difference is divided by the surface area

before deformation and the result is expressed as a percentage. In every cycle, this area

elongation is recalculated and the evaluation is carried out according to these values. In the

experiments, 100% wool and 45/55 wool/polyester fabrics were used because these are worn

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as daily standard suits in business life. There were two different weaves; they were woven and

finished under controlled conditions, and they all had equal weights per unit area [35].

It was found that the twill wool fabric had the greatest spherical elongation and the plain

blend fabric had the smallest spherical elongation; the differences in elongations were the

same, regardless of the duration of testing; the first loading cycle was the one that affected

the length of elongation. Elongation decreased during the three hours of relaxation, but it

never recovered fully. In analysing the spherical loading until breakage, theoretical

calculations referring to a thread going through the sphere centre were made. It was found

that the plain blend fabrics were the firmest and the wool twill fabrics were elongating the

most. It was concluded that the deformation in the 100% wool fabric was greater than the

wool/polyester blend. The explanation of this point was because of the structural changes in

individual fibres. The deformations in the twill fabrics were more than the deformations of

the plain fabrics; this shows the effect of the weave. Twill weave has less yarn interlacings per

unit area than plain weave which means there is less reactive force to the deformation

process. As the researcher states, 100% wool fabrics have more relaxation than blends and

this is because of their structure [35].

Abghari et al. [1] developed a new test method to investigate woven fabric bagging

deformation and they used a real time data acquisition and strain gauge technique. While

the fabric was deformed by bagging, they also measured the tensile deformations in the warp

and weft directions.

They used bagging resistance, bagging fatigue, residual bagging height and residual

bagging hysteresis to characterize the fabric bagging behaviour and also simulated it with

Finite Element Analysis.

As a result of their experiments, they found that the bagging load, work, hysteresis,

residual hysteresis and fatigue are highly linearly correlated with corresponding parameters

in the warp and the weft directions. They obtained an empirical relationship between

residual bagging height and bagging fatigue and resistance, which proved that the new test

method was able to evaluate the bagging behaviour of woven fabrics. By using Finite

Element Analysis, they were able to show that the theoretical model predicts and simulates

the bagging behaviour of woven fabrics. In the theoretical analysis, the residual bagging

height, bagging load and tensile forces in the warp and the weft directions are linearly

correlated with the corresponding parameters in this new test method. They state that all the

methods in the literature measure the fabric bagging load while a constant tension is applied

to the fabric sample. It was stated that biaxial tension and shearing played an important role

in fabric bagging, and the stress distribution in isotropic and anisotropic fabrics is related to

the bagging force’s internal stresses in the fabric section. This was theoretically investigated

and it was found that the internal stresses distributed non-uniformly between the warp and

the weft yarns for an anisotropic fabric. In their work, they were measuring the bagging

force distribution between the warp and the weft yarns experimentally [1].

In the apparatus developed in the above research, a fabric sample is placed in a

rectangular clamp with inner dimensions of 24 and 17 cm. There are four jaws that precisely

pretension the clamped fabric sample. The exact magnitude of the fabric pretension is

controlled and determined with two load cells which are connected to the two horizontal

jaws. There are two other jaws which can be moved in the plane of the fabric, under a screw

control system. There is a third load cell attached to the upper jaw of the bagging tester and

the speed and the direction of this jaw can be controlled for cyclic loading. A steel sphere

with various diameters is fixed to this load cell. When the sphere contacts the fabric sample

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and exerts a pressure on the clamped fabric, the vertical load cell measures the compression

force, i.e. the bagging force, and the other two load cells measure the tensile forces along the

warp and the weft directions. In the experiment, 5 cyclic loadings were done and diagrams

and hysteresis curves drawn for the warp and weft tensile forces and the bagging force. They

used woven twill worsted and plain cotton/polyester shirt fabrics in their research. The

sphere pressing rate was 4 mm/min, bagging height was set to 30 mm, the sphere contacted

the fabric at the maximum pressure at each cycle for 5 min, then recovered for 2 min.

The cyclic loading was done 5 times and the whole cycle was repeated 5 times, resulting in

25 bagging deformations. Ten fabric samples of each kind were used.

They measured the maximum load and corresponding work of loads and percentage

hysteresis at the first and the last cycles for weft, warp and bagging directions, and then

bagging resistance, bagging fatigue and residual bagging height were calculated according to

Zhang’s test method. They introduced a new parameter named the ‘residual hysteresis’ for

warp, weft and bagging directions. They calculated this parameter by finding the difference

between the % hysteresis in the first cycle and the % hysteresis in the last cycle, dividing it

by the% hysteresis in the first cycle, and multiplying by 100. They suggest that this parameter

indicates the percentage of residual internal energy of the fabric during bagging deformation.

For theoretical simulation, they used non-linear visco-elastic and numerical calculation in

finite element analysis. They calculated the compressional bagging force, tensile forces along

the warp and the weft directions for different bagging cycles, and residual bagging height,

and then compared them with the experimental results. The maximum bagging force in

the first and the last cycle correlated linearly with the maximum force in the warp and the

weft directions for all fabrics, and these had correlation coefficients of r2¼ 0.97 and 0.83,

respectively. This shows that the maximum bagging force distributes between the warp and

the weft yarns, but is non-uniformly distributed, and anisotropic fabric properties are

involved during bagging deformation. The work of the bagging load in the first and the last

cycle correlates linearly with the work of loads in the warp and the weft directions for all

fabrics and these have correlation coefficients of r2¼ 0.9 and 0.83, respectively. This shows

that fabric deformation is different in bagging, warp and weft directions, non-linearly. The

bagging hysteresis in the first and the last cycles correlates linearly with corresponding

parameters in the warp and the weft directions for all fabrics, and the correlation coefficients

are r2¼ 0.78 and 0.93, respectively. This shows that all the fabrics are well deformed and

the residual energy of bagging deformation is well distributed along the warp and weft

directions. It also shows that shear deformation has occurred, particularly in the last cycle,

and stress relaxation was created in the warp and weft yarns. The residual bagging hysteresis

is linearly correlated with corresponding parameters in the warp and the weft directions

and the correlation coefficient is r2¼ 0.9. This shows that this new parameter of bagging

deformation, which demonstrates the non-recovered stored fabric energy, is highly

correlated with corresponding parameters along the warp and the weft yarn directions.

It can be noted that the non-recovered work of loads or the frictional and viscoelastic

components of the fabric during bagging deformation had decayed in the last cycle. The

relationships between fabric bagging fatigue and tensile fatigue in the warp and the weft

directions are linearly correlated with each other (r2¼ 0.83) and it can be concluded that the

residual elastic stored energy in the fabric due to the fatigue process of fabric bagging is

distributed in two principal warp and weft directions. The residual bagging height correlates

linearly with bagging fatigue for all the fabrics with correlation coefficient of r2¼ 0.98, 0.99

and 0.99 respectively. This shows that the residual bagging deformation in the twill structure

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is more sensitive to fatigue performance than the plain structure. The viscoelastic behaviour

and the frictional effect of worsted fabrics may have influence on fatigue performance of

those fabrics. The relationships between the residual bagging height and bagging resistance

are non-linearly correlated with each other for all the fabrics, and the correlation coefficients

are r2¼ 0.99, 0.99 and 0.97, respectively. It can be explained as the bagging resistance is

mainly related to work of load at the first cycle and it represents the ability of fabric to resist

bagging deformation at the initial stage, so the residual bagging height and bagging

resistance are non-linearly correlated with each other. The bagging fatigue and bagging

resistance are non-linearly positively correlated with each other for all the fabrics, with

correlation coefficients of r2¼ 0.99, 0.98 and 0.99, respectively. This shows that as the initial

energy of the fabric, which reflects both elastic and the initial viscoelastic, frictional energy

increases, the fabric bagging fatigue increases. It may be said that correlation coefficient of

bagging fatigue and resistance for shirt fabrics are much higher than those for worsted

fabrics. This shows that the viscoelastic–frictional component of the wool component and

twill structure of worsted fabrics may have influence on the experimental results [1].

Multiple regression analysis for residual bagging height was done with bagging fatigue

and bagging resistance. An equation was obtained and the correlation is seen to be highly

significant, with r2¼ 0.83 (p< 0.001). It can be concluded that the residual bagging height is

affected by the combined influence of bagging fatigue and resistance. The residual bagging

height obtained by the new fabric bagging tester is linearly correlated with simulation results

(r2¼ 0.8) and also with the finite element analysis results of tensile forces in the warp and

the weft directions. The bagging forces during fabric bagging simulation are linearly

correlated with experimental values (r2¼ 0.68, 0.76 and 0.74, respectively). These results

also indicate that the FEM simulation of woven fabric as a non-distructive method is

reliable and permissible. From the experimental results, different parameters including,

load, work, hysteresis at the first and the last cycles for three different bagging, warp and

weft directions were calculated and also the bagging behaviour of the woven fabrics’ four

physical criteria (bagging fatigue, bagging resistance, residual bagging height and residual

bagging hysteresis) were characterized and measured. The experimental results show that

the bagging load values are in the range of 50–100 N. It was also found that the bagging

load, work, hysteresis, residual hysteresis and fatigue are highly linearly correlated with

corresponding parameters in the warp and the weft directions. The experimental and FEM

simulation results of their research show that the bagging behaviour of woven fabrics can

be predicted in terms of bi-axial tensile properties under low-stress fabric mechanical

conditions [1].

5.2 Researches with Knitted Fabrics

Thomas [64] developed an apparatus to perform the so called Celanese bagging test for

knitted fabrics. He used an Instron tensile tester, and tensile stretch and recovery principles

are the fundamentals used in this test. A circular fabric sample of 10 inch diameter was

clamped between the two plates of an extensometer, and an 8 inch diameter testing area was

left. Repeated loads were then applied to the circular fabric sample, loads changing from

0.5 to 15 lb for two minutes, but keeping a 15 lb force for one minute. At the end of this

time, the load was reduced to 0.5 lb and the ‘growth’ occuring immediately in the sample

fabric was recorded. The load was lifted for one minute. After this time, again 0.5 lb force

was applied to the circular fabric sample between the clamps. The ‘distortion’ occurring

immediately in the fabric was recorded. The ‘recovery’ occurring immediately was obtained

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from the immediate growth and the immediate distortion values. Knitted fabrics were used

in the tests. Thomas had the fabrics made into garments. Two or three garments made from

different fabrics were worn at least once a week. After wearing for 28 and 32 hours, the

garments were given back and they were subjectively evaluated according to the standard

AATCC ranking board. Ranking (1) was severe which was considered to be failing; Ranking

(2) was moderate; and Ranking (3) was slight. He correlated the results from the wear trials

and the results he obtained from the Instron loading tests, which were immediate recovery

data. If the immediate recovery values were greater than 59%, this was regarded as

satisfactory; if they were between 53–59%, this was regarded as borderline, which means the

fabrics may or may not bag during wear, depending on the wearer and the nature of the

construction of the fabric; if they were less than 53%, this was regarded as unsatisfactory.

Fabric construction and the wearer’s fit and size also affected the bagging severity, but their

effect on garment performance was not so clear.

Yaida [74] has worked with immediate recovery values in percent to evaluate the bagging

in knitted fabrics. He made a similar apparatus to the Celanese bagging tester and worked

with four sample of each knitted fabric. They were of 8 inch diameter. First, 0.5 lb force was

applied on the fabric as a pretension. The Instron then cycled between 0.5 lb and 15 lb for

two minutes at 200 mm/min. Then the half-sphere was held on the fabric at 15 lb for one

minute, then went back to the 0.5 lb gauge length. Then it was totally lifted and held for one

minute; afterwards the half-sphere came back to the 0.5 lb gauge length. It was attempted to

find the relation between the immediate recovery value in percent and the density,

compressive modulus and thickness of the fabrics. There was no relation between the

immediate recovery value in percent, and the density and compressive modulus. But there

was correlation between the immediate recovery value in percent and thickness.

Ucar et al. [68] studied the bagging of a set of knitted fabrics in their work. The fabrics

they used varied in design, tightness factor, and blend ratio. They determined the residual

bagging height from the tests they did, and they mechanically characterized the fabrics using

the KES-FB system. They worked out the relations in between and concluded that, by using

the standard KES-FB test, the bagging height could be predicted for knitted fabrics without

doing any additional bagging tests for them. They also did some subjective analysis. They

explained that bagging occurs in apparel fabrics during sitting or squatting for a long time,

or from repeated movement. Bagging is the result of dimensional stability missing or lack of

recovery when repeated and long lasting force is applied on the fabric. Fabric mechanical

properties, such as ease of recovery and loss of energy with use, are very important in fabric

bagging. These mechanical properties also reflect the resistance to deformation. Mechanical

properties of fabrics depend on their fabric parameters, yarn parameters, and relaxation

state.

During bagging, the sample fabric was subjected to a complex pattern of loading. They

measured the tensile, shear, and bending properties of their sample fabrics. The fabrics’

diameter was 135 mm, the inner diameter of the clamp being 56 mm. The pressing sphere was

steel and had a diameter of 48 mm. The displacement measurement was 21 mm, the rate of

pressing was 20 mm/min and then the pressing sphere returned to its original position. The

sample fabric waited for two minutes under zero load to recover, then the non-recovered

bagging height was measured. They chose most of their testing parameters similar to Zhang’s

[77, 80]. Their bagging heights were different because they worked with knitted fabric and

Zhang worked with woven fabric. They expressed the residual bagging height as a percentage

by dividing the non-recovered bagging height by the predetermined bagging height.

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The researchers used a bivariate correlation analysis to find the relation between the

residual bagging height they obtained from their experiments and the fabric mechanical

properties they obtained from the KES-FB tests. For plain knitted fabrics, they found a

negative correlation, which means that as the elastic restraint and frictional resistance (fabric

rigidity) against deformation increases, the residual bagging height decreases. When the

tightness factor of a plain knit increases, fabric rigidity also increases because of increased

inner pressure, resulting in an increase in the loop curvature, causing the fabric to behave

more like a spring. This kind of a fabric finds it easier to recover than a slack one. For

double knitted fabrics, they found a positive correlation, which means that as the elastic

restraint and frictional resistance (fabric rigidity) against deformation increases, the residual

bagging height increases. The double fabrics have more crosslinkages and this structure

makes them rigid to deformation. Also, more intricate and longer linkages makes the knitted

fabrics less recoverable because there is more inner friction in the fabric, so the residual

bagging height increases [68].

A regression equation was obtained where residual bagging height is determined in terms

of shear rigidity, hysteresis of shear force at 5 degrees, bending rigidity and hysteresis of

bending moment. For the subjective assessments, it was stated that it is important to know

where the fabric will be used so that the tests will be done according to those conditions. For

example, compression wear in medical textiles was evaulated with the residual bagging

height. The researchers took photographs of the fabric they were testing when the fabric was

still on the bagging apparatus, after two minutes of recovery time. Afterwards, people were

asked to rank and rate these photgraphs. The researchers included bending and shear

parameters in the model they developed to predict the rating values. One reason for doing

that was to take in the influence of gravity upon the knitted fabric. Another reason was the

different relation between the fabric tightness and the residual bagging height seen in the

plain knitted and the double knitted fabrics. Bending and shear properties are very

important factors to the drape of weft knitted fabrics. It is well known that when the rigidity

decreases, the drape of the fabric increases. It was concluded that the KES-FB system gives

data that can be used to predict the bagging behaviour measures needed for fabrics that are

different in fibre type, fabric structure, and yarn size. Fabric properties such as handle and

sewability can be derived from the KES-FB system. The work shows that by measuring

shear and bending properties of a fabric, bagging properties can be evaluated and a formula,

explained above, can be derived. Using the KES-FB system needs less effort in determining

the bagging behaviour because no apparatus need be set up for the experiment. Subjective

analysis showed that when fabric rigidity increases, the impact of bagging on appearance is

more severe [68].

5.3 Researches with both Woven and Knitted Fabrics

Wegener and Scoulidis [71] symbolized some conditions met in daily life in an apparatus

they developed to determine the curvature elasticity. They measured the force to make

curvature in a deformed fabric and the distance withdrawn vertically from the plane of the

fabric. They did not use these values for evaluation; instead they calculated relative values of

the shape the fabric formed in the jaw (as did Sommer [59] in some bursting strength tests).

Linear curvature strength and curvature elongation were the relative values used. Woven

and knitted and rubber construction fabrics were utilised in their work. They named their

apparatus ‘curvature tester’. They derived some regression equations and discussed the

effects of testing parameters on curvature magnitudes.

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Grunewald and Zoll [27] developed an apparatus similar to the moving human arm. It was

an artificial arm with an elbow joint. They sewed a fabric in a tubular form, drew the tube-like

fabric onto this arm, where the tubular fabric represented the sleeve or the trouser leg, bent

the arm in a suitable way, keeping the fabric in this bent form for five hours, which means

static strain on the fabric, then the arm was straightened and the fabric recovered for

10 minutes this way. The fabric was taken out and the bagging height at the elbow region

measured on a different, straight horizontal tube. Garments sewn from the same fabric were

given to people to be worn for fifty days, but every five wear days the garments were assessed.

The degree of bagging was measured in the laboratory and, if it was below 5 mm, the

garments were worn more by the people after being cleaned and pressed. At the assessment,

three independent persons examined the garments and said if they could still be worn and

were acceptable (not bagged at all or just a little which means the fabric remained

dimensionally stable) or unacceptable. The results achieved by the tests in the laboratory and

the results achieved by the wear trials correlated highly, even though the test method did not

include any cycles and the wearer trials included repeated motion. Also, the limits of the

wearable and unwearable regions could be derived. They worked on both woven and knitted

fabrics. The Zweigle type bagging tester is designed on the Grunewald and Zoll principle.

Strazdiene and Gutauskas [60] studied biaxial punch deformation in anisotropic textile

materials. To evaluate the textile punch deformation, the authors tried to find a new

criterion. Their other aim was to find the effects of the anisotropy of the material on the

forming shell, and they also attempted to find the strain distribution in the forming shell.

They used X-ray diffraction analysis, and were able to study the friction at the sample and

punch contact. They state that this friction has much effect on the punching process

parameters. They found out that the anisotropic shell forming in the punching process had a

complicated geometry. They suggest that this does not confirm the earlier presumption

about rotating surfaces. The friction in the contact zone is what makes the geometry

complicated. They applied the punch both dry and lubricated. After the X-ray diffraction

analysis, they found that with the dry punch, which has a high friction coefficient, the

structural changes at the top of the shell can be neglected. When this is compared with the

lubricated punch, which has a low friction factor, this one has much more structural change.

They relate this behaviour to the crystallinity at the top of the shell [60].

Strazdiene and Gutauskas’s later work [61] is involved with spatial loading of highly

stretchable textiles and the textile materials are orthotropic. Biaxial deformation can either

be membrane or punch. The researchers state that textiles can be affected by forces

perpendicular to their planes during production or usage, and shells occur on their surfaces.

There are three reasons why biaxial deformation is gaining importance recently: (i) The

behaviour of the textile material under usage circumstances is reliably simulated (ii) Test

methods are realized with very simple experiments and the results are reliable when the

tearing location and character in the sample is studied; (iii) The testing methods are

universal: that is, by doing a single test many properties of the textile material are obtained

such as strength, properties creep or relaxation parameters, etc.

The researchers state that in most of the earlier investigations concerning biaxial

deformation, the test material was assumed to be isotropic and the surface of the shell which

was formed in the deformation was axisymmetric. When it is a membrane deformation, the

shell forming has a kind of a segment of a sphere; but when it is a punch deformation, the

shell forming has a kind of a segment of a sphere and a cut of a cone added together. In their

research, they studied shell formation phenomena in textiles when there is very high

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orthotropy in them. In their work, they compared the punch and the membrane biaxial

deformation types of textile materials, which are both spatial. Punch tests were done with

disc-shaped samples having a radius of 28.2 mm, cut from knitted and woven fabrics, with

different orthtropy levels. For the punch size, a radius of 9.5 mm was used. They did the

membrane tests with an HDR-type hydrorelaxometer which they designed and manufac-

tured themselves [61].

In membrane deformation, load is transmitted to the textile material by compressed air or

liquid through a rubber membrane so possesses a hydrolic character. In punch deformation,

the textile sample is loaded with a rigid sphere. The shape of the shell-forming will be related

to the size of the punch (radius of the punching sphere divided by the radius of the textile

material) and to the textile material’s orthotropy level. Since most textile materials behave

more or less orthotropically, the uniformly distributed pressure in the membrane

deformation will not form a kind of a segment of a sphere, it will form a non-axisymmetric

surface. It will look like an ellipse because the stresses in the meridian direction and in the

circumferential direction will be different and will depend on the geometry of the shell

formed and on the the internal pressures in the textile material. When two perpendicular

lines are taken in the directions of the main axes, they will be different by the radii of their

curvatures, the maximum difference being at the top of the shell. Zurek and Bendkowska

[85] had done a similar study and confirmed that the distorted sample was not like a part of a

sphere. In the case of a punch deformation, the part of the sample fabric covering the

punching sphere will be taking its shape, but starting where the sample fabric is not touching

the sphere any more, the shape will be like a concave curve until the clamps. The effect of

friction can be seen when the contact region of the punching sphere and the sample fabric is

analyzed from the point of view of local displacements in the fabric. There are small

deformations at the contacting region but the sample fabric is deformed in two directions

because it is under biaxial tension. Starting from the line where the fabric leaves the

punching sphere, the sample fabric is under uniaxial tension and that depends on the

orthotropy level of the fabric. In order to describe the shape of the shell formed there, if two

lines are generated, they will be concave at different levels. They conclude that besides the

information of the affecting force and the deformed height, additional information about the

parameters of thin-shell geometry are also needed, which are mainly anisotropy details,

stress distributions, and time dependent changes. They also conclude that the warp direction

in woven fabrics and the wale direction in the knitted fabrics are deformed less [61].

5.4 Researches with Nonwovens and Technical Textiles

Villard and Giraud [70] studied the behaviour of reinforcements made from geotextile sheets

under pressure. They state that there is an increase in geotextiles used under roads and rails

that are built on weak or collapse-risking ground. Since the possibility of damage or break-

down increases at those places, geotextiles serve to decrease this possibility, but the three-

dimensional behaviour of such membrane geotextiles under pressure needs to be examined.

They model this behaviour with anisotropic and non-elastic behaviour and this does not

depend on the kind of loading. They introduce an original finite element calculation and

compare it with analytical solutions of some other cases. For more complex cases of

reinforcement, they suggest a horizontal sizing nomograph and some practical solutions.

They conclude that promoting the sheet reinforcement along a single direction such as the

production direction is to be preferred. It is emphasized that behaviour under pressure is

very important for the end-use mechanical performance of the industial fabrics.

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Anand et al. [4] have studied needlepunched geotextiles. Performance characteristics such

as puncture resistance and tensile properties are important in these. Since they are used

as separators, filters, reinforcements and drainage materials, they have to have a

required strength, dimensional stability, and abrasion and puncture resistance to be able

to withstand the forces acting upon them in the long term. They tried to develop

mathematical models to predict the dimensional and functional properties of the

needlepunched geotextiles from the known set of machine parameters. They were able to

predict the puncture resistance from fabric area density and fabric thickness with a

correlation coefficient ofR¼ 0.99 (r2¼ 0.98). And also, they were able to predict the puncture

resistance from web area density, needle penetration and punch density with a correlation

coefficient of R¼ 0.984 (r2¼ 0.9683).

Bilisik [14] has investigated the structural properties of textile preforms and composites. He

found that the matrix contribution to tensile strength of composites was reduced before

plastic deformation. He also found that tensile behaviour in the structure completely

depended on individual fibre strength and fibre architecture. Tensile failure causes fibre

breakage. In-plane shear strength was effected adversely by the Z-fibre fraction, but

this supports the interlaminar shear strength of the woven structure. The type of fibre

architecture affected entirely the fracture toughness and crack initiation with crack

propagation in the woven composite. The woven composite shears when the matrix reaches

the ultimate strength limits, then plastic deformation is seen in the structure. Z-fibre fraction

carries the impact energy and distributes in neighbouring regions to prevent the damage

threshold being reached and reduce the damaged area.

Hearle [28] worked on industrial yarns. Nylon is the premium fibre in production of

strong industrial yarns for ropes. It has a low modulus which means it has less resistance

to extension but it has a good recovery from high stresses. Polyester fibres are also used in

high-performance ropes. Linear-polymer fibres can bend without breaking to a great extent.

Deformation analysis was done on ropes with differential geometry. It was assumed that the

planes perpendicular to the axis of the helical structure within each component yarn

remained planar and perpendicular to that axis. Viscoelastic fibre properties were also

important in these analyses.

6. FACTORS EFFECTING FABRIC BAGGING

Zhang et al. [79] studied the influence of fibre–yarn–fabric properties on wool fabric

bagging. Fibres are linked to each other at different compactness, different degrees and kinds

of order, and different degrees of extension, curl and twist in a finished fabric. Bagging is a

large, three-dimension deformation, and the viscoelastic properties of the fibres and the

friction in the textile structure are very important. So, during bagging, the mechanical

behaviour of the fabric is a complex function of fabric parameters. By applying regression

analysis, the relation between the fatigue behaviour of the fabric and the fibre–yarn–fabric

properties can be examined.

In contact between the body and the fabric, bending and compression arises. In this

deformation, some structural changes occur in the fabric which can be listed as: (i) During

shearing, yarn rotation and slippage occur at the interlacings; (ii) During tensile deformation

and shearing, yarn bending and compression occur at the interlacings; (iii) Yarn extension

occurs between the interlacings; (iv) Fibre slippage and extension occur at the yarns in the

interlacing points and between the interlacings.

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As the bagging deformation develops in a fabric, the above processes interact with each

other and meet the requirements of the different stages of bagging deformation. There are

many sophisticated structural changes in fabric bagging, but there are three main cate-

gories: elastic, viscoelastic, and plastic. The fibre’s viscoelastic deformation plays the

largest part in the total deformation. Frictional deformation is the slippage between the

fibres and between the yarns, and the rotation of the yarns at the interlacings. Olofsson [48]

says that at large deformations, fibres themselves can be deformed in the plastoviscous range.

The viscoelastic and the plastic energies cannot be distinguished in practice, so in their

studies, they included the recoverable elastic energy and the decaying viscoelastic-plastic

energy as two essential components of the energy involved during bagging. In the

experiments, they took the yarn out of the fabric and measured its tensile property in the

same way as in fabric bagging. The mechanical property of yarns was called the specific

work of deformation, Ywork. The anisotropic feature of the fabric was called the unbalanced

specific work of the yarn (also unbalanced work of the yarn). The ability of the fabric to

resist bagging deformation was called the criterion of bagging resistance W0, the initial

energy of the fabric, W0 is a function of interlacings per unit area of the fabric, fabric

thickness, yarn work, and fabric cover factor. W0 is also a function of the fibre’s initial

modulus, which means that when the fabric’s structural properties are the same, the fibre’s

mechanical properties are the determiners. The decay rate of loss energy is a function of yarn

unbalanced work, and shows the effect of the anisotropy of the fabric. The initial

viscoelastic-plastic energy, Q, is a function of yarn and fabric cover factor, and shows that

the loss energy is determined by the mechanical properties of the yarns and fabric tightness.

Q is also a function of fibre modulus and fabric thickness, which means that these two

factors determine the fabric viscoelastic–plastic energy. The elastic energy, U, is a function of

fabric interlacing, fabric cover factor and yarn work, and shows that the fabric’s elastic

behaviour is determined by the yarn’s mechanical properties and the fabric’s structural

features. U is also a function of fibre initial modulus [79].

They found that the twill wool fabrics have lower specific loading work than the plain

wool fabrics because the twill weave has less interlacings per unit area of the fabric. Among

the twill wool fabrics, there was the gabardine with more than 608 twill angle and the serge

with 458 twill angle. The gabardine had more loading work than the serge. This showed the

effect of the unbalanced weave structure on loading work. In plain wool fabrics, the fabric

with less interlacings had lower specific loading work. The initial energy W0 of the fabric

increases with the blend ratio of polyester, but the decay rate of the specific loading work

with the bagging cycles is not influenced by the blend ratio. The decay rate of the

viscoelastic-plastic energy, d, is constant as the blend ratio changes. This can be explained bythe close recovery properties of wool and polyester. All the values of W0, Q, and U increase

with the increasing blend ratio of polyester. This may be because polyester has higher initial

modulus and higher constant of friction coefficient than wool fibres [79].

When they compared the results, they concluded that when the fibre’s mechanical properties

are fixed, fabric structural properties are the key factors; when the fabric structural properties

are fixed, the fibre mechanical properties are the key factors in determining the fabric bagging

behaviour. The two main cause of fabric bagging behaviour are the stress relaxation of the

fibres, owing to the fibre’s viscoelastic behaviour, and the friction between fibres and yarns,

owing to the frictional restraints in the fabric structure. Fibre–yarnmechanical properties and

fabric structural properties, such as fabric thickness, weight, cover factor and interlacing

points, are the important factors influencing the bagging behaviour of a fabric [79].

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6.1 Fibre and Yarn Properties and Parameters

Zhang et al. [82] aimed to study the viscoelastic behaviour of fibres during the bagging of

woven fabrics and to create a mathematical model to simulate bagging while it is tested.

With computational experiments, they determined the elastic modulus E1, viscoelastic

modulus E2, fibre relaxation time t, three weighing coefficients (k3, k4, k5) for different

fabrics with K3, the elastic weighting coefficient; K4, the viscoelastic coefficient; K5, the

frictional coefficient of different fibres. They compared the experimental measurements with

the predicted bagging behaviour of the fabrics and found that the mathematical model

they developed predicted the bagging behaviour with reasonable accuracy. Their results

show that the viscoelastic behaviour of the fibre is very different during bagging in the

different types of fabrics they used. They state that elasticity ratio (E1) is high, viscoelasticity

ratio is low (E2) and relaxation time t is large in nylon and polyester fibres. Also, they state

that elasticity ratio (E1) is low, viscoelasticity ratio is high (E2) and relaxation time t is smallin silk, viscose and cotton fibres. When cotton and wool have the same viscoelasticity level

(E2), then relaxation time t is the determiner in the stress relaxation process. They point outthat fibre viscoelastic behaviour is playing a key role in determining fabric rheological

behaviour in bagging.

Multidimensional deformations occur in a bagging process, and it involves complex

mechanisms of fibre mechanical behaviour and yarn–fabric structural changes. Tradition-

ally, fabric bagging is defined by residual bagging height or bagging volume. In various

kinds of deformation, fabric mechanical behaviour is correlated with some previous

approaches and one is able to identify possible relationships. In these approaches, the role of

fibre mechanical behaviour and yarn–fabric structural characteristics is not involved. From

their earlier work, they found that fabric bagging is the result of two basic causes: one is

stress relaxation due to fibre viscoelastic behaviour, and the other is interfibre and interyarn

frictions. Fibre mechanical behaviour gains importance in determining fabric bagging

behaviour when fabrics have the same construction [82].

In their work which will be explained later [81], they developed a mathematical model on

the basis of rheological mechanisms and intended to simulate fabric bagging from

fundamental fibre mechanical properties and yarn–fabric structural features. Their model

successfully simulated the woven wool fabric’s bagging behaviour and could reflect the

relative contributions of the fibre’s elastic and viscoelastic behaviour and interfibre frictions

which are affected by yarn–fabric structural properties. They did not involve different

fibres in that work [81], but in this work [82], they introduced different fibres in the form

of different fabrics. Relative residual bagging height was obtained. Bagging fatigue, which is

the percentage of loss of energy after repeated bagging deformation in a fabric, is obtained.

Bagging resistance which is the ability of the fabric to resist bagging deformation is in this

order, from the highest: silk fabric, cotton, viscose, polyester, wool, nylon. Residual bagging

height is in this order, from the highest: viscose fabric, silk, polyester, cotton, wool, nylon.

Viscose fabric has the highest residual bagging height and nylon the lowest. Cotton goes up

to 7.5 mm and this result is similar to that of Sengoz [62].

The loading curve in the first cycle was predicted and it showed good agreement with the

experimental results with the wool, silk, and nylon fabrics. For polyester, viscose, and cotton

fabrics, the predicted and the experimental curves showed some deviations. Residual

bagging height over five cycles was also predicted and the predicted and the experimental

curves fitted reasonably well, besides showed the trends in the alterations of residual height

with increasing cycles. So, the model can successfully be used to determine the viscoelastic

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behaviour of fibres in fabric bagging. Viscoelastic modulus came out in this order, from the

highest: silk, viscose, wool, cotton, polyester, nylon. Elastic modulus came out in this order,

from the highest: polyester, cotton, viscose, nylon, silk, wool. These results show that in

fabric bagging, the contributions of elasticity and viscoelasticity are different from fibre to

fibre. In synthetic fibres such as polyester and nylon, their elastic modulus is much higher

than their viscoelastic modulus. In natural fibres such as wool, silk, and viscose (man-made),

their elastic modulus is lower than their viscoelastic modulus [82]. The relaxation time t isthe highest in nylon fibre (990 seconds), then comes wool (100 seconds) and polyester (90

seconds), the rest having the lowest time (�30 seconds). The relaxation time t found in the

experiments is in agreement with the corresponding fabric bagging fatigue. It can be stated

that when the value of the relaxation time t is small, which means the stress relaxation of thefibre is fast, then the bagging fatigue and the residual bagging height is larger.

The relative contributions of elasticity, viscoelasticity and interfibre friction are different

from fabric to fabric. In the wool and nylon fabrics, elastic components contribute more to

the fabric’s bagging behaviour than the viscoelastic and the frictional components. In the

polyester, silk, viscose, and cotton fabrics, the elastic components contribute less than the

viscoelastic components. Since the relaxation time t is the highest in nylon fibre

(990 seconds), this means that its stress relaxation is very slow and viscoelastic stress

decays very slowly when compared with the other fibres. On the other hand, it means

excellent elastic recovery for that fibre. For the wool and the polyester fabrics, the bagging

behaviour depends on the viscoelastic modulus and the relaxation time of the fibre, and also

on the time of fabric deformation. Cotton, viscose, and silk fabrics have the lowest

relaxation time; this means they have fast stress relaxation. Cotton and wool fabrics have the

same viscoelastic modulus but their relaxation times are different, wool being 100 seconds

and cotton being 30 seconds. This means their stress relaxation rates are different, wool

being slow and cotton being fast. Nylon and polyester fibres have high elasticity ratios and

low viscoelasticity ratios and long relaxation times. Silk, viscose, and cotton fibres have low

elasticity ratios, high viscoelasticity ratios and short relaxation times. Cotton and wool have

the same viscoelasticity, but their relaxation times are different. These results show that fibre

viscoelastic behaviour is very important in defining the fabric rheological behaviour during

bagging [82].

Fibre viscoelasticity, and inter-fibre and inter-yarn frictional forces determine the fabric

bagging deformation. If the fibres were perfectly elastic, residual extension of the yarn would

be caused only by the frictional forces between the fibres and the yarns. But, fibres are

viscoelastic in general, which means that their deformation and recovery behaviour is time

dependent. When a force is applied, extension occurs; this is dependent on the period of

application and on the earlier mechanical history of the fibre. There is not a uniform stress

distribution among the fibres in a yarn. Some may be stretched up to their yield region,

others may not be stretched at all. The viscoelastic behaviour observed can be described

by some other rheological models. Permanent fabric deformation is affected mostly by

inter-fibre friction and creep. Also, a fibre’s viscoelastic property is affected by ageing.

A fibre’s geometrical parameters such as diameter, shape of its cross-section, and crimp are

affected much less [78]. The frictional energy is the result of the relative movement of the

yarns or the fibres, the frictional force between them, and the coefficient of friction at these

points. The force at those points comes from either the forces that occurred in the yarn or

fabric production stages or internal forces arising from fabric deformation itself. During

cyclic deformation of a fabric, hysteresis occurs. The plasticity and the creep effects in the

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fibre play an important role as well as the frictional forces arising between fibres and yarns

during deformation. In fabric mechanics, woven fabric bagging has to be studied in terms of

its mechanical properties [78].

6.2 Fabric Properties and Parameters

Zhang et al. [84] did some experiments to investigate the relationship of elasticity and

viscoelasticity of fibres and inter-fibre friction to bagging behaviour. They used wool fabrics

in their tests. They also applied mathematical models to simulate the behaviour of the fabric

under bagging test conditions. With computation experiments, they found the relaxation

time of the fibres t and three weighting coefficients (k3, k4, k5). They worked these in

different wool fabrics woven with different wool fibres and found that the frictional weighting

coefficient k5¼ 0.1 and the relaxation time t¼ 100 seconds were constant for all the wool

fabrics tested. The relative contribution of elasticity, k3¼ 0.6 on average, and the relative

contribution of viscoelasticity, k4¼ 0.3 on average, have narrow distributions. They state

that the results show the stability of the three weighting coefficients and the fibre relaxation

time, and also that they are not sensitive to structural changes in the fabric. They maintain

the idea that they have achieved a consistent agreement between the experimental results and

the mathematical simulation, and that their model is quite successful in simulating fabric

bagging behaviour with reasonable accuracy. Wool fabrics have many variations in their

structural parameters affected by fabric weave, yarn count, thickness, weight, and cover

factor. Their model gave some deviations in the residual bagging height between the

simulation and the experiment in the first cycle. This may be due to an assumption they

made in determining the fitness of the simulation. The method gives good overall fitness,

when some specific points are not taken into consideration.

Bagging is a result of complex deformations such as tension, shearing, bending, and

compression occuring in different directions. Fabric deformation is not elastic in general;

it is mostly viscoelastic and includes hysteresis. These complexities were determined recently

and as a consequence a mathematical model using the fabric’s mechanical properties to

predict fabric bagging was developed. A textile fabric is generally considered as a continuum

sheet when observed macroscopically, but at the microscopic scale, it is not homogeneous.

The hysteresis behaviour of the fabric is dealt with in their work. The hysteresis behaviour is

not included in any of the elastic mechanic models. So, the mechanics of garment bagging

are studied from both the micro-mechanical and the macro-mechanical point of views.

Micro-mechanics studies how the textile material behaves when it interacts with the material

making it up at the microscopic level. Macro-mechanics studies how the fabric reveals the

effects of the material making it up as its average apparent properties where it is considered

homogeneous [78].

The macro-mechanical problems of apparel fabrics are also divided into two classes:

(i) Free form problems; in this case, fabric stresses are supported by fabric curvature, as in

fabric drape, buckling, and wrinkling: (ii) Form fitting problems; in this case, larger stresses

and prescribed curvatures are involved as in garment bagging.

Multi-directional tensile deformation and shearing deformation are the main causes of

fabric bagging. The effects of fabric bending are insignificant because the thickness of the

fabric is much less than the radius of the knee curvature and the fabric’s other dimensions.

This leads us to the assumption that the fabric is a membrane and a perfectly flexible sheet

and supports only planar stresses. So, in a bagging test, the tensile and shear characteristics

of the textile material have to be evaluated. In laboratory tests for bagging, either the

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extension limits are constant or the loading limits are constant. The researchers found that

the biaxial and uniaxial tensile testing load–extension curves were not linear. This was due to

the weave structure and the non-linear tensile behaviour of the textile material itself. In this

curve, the regions where there was resistance to bagging and the ability to recover from

bagging had to be defined. The resistance to bagging is the deformation when a force is

applied to the fabric. The ability to recover from bagging is the elastic recovery when the

force is lifted. So, both the initial tensile modulus of the fabric and the deformation

behaviour near the yield point of the load–extension curve are important. The shear

behaviour of the fabric is related to its extensibility in the bias direction because of its

interlaced construction. When a woven fabric is confronted by a spherical surface, the warp

and the weft yarns shear to take the shape of that surface. So, the tensile deformation of

woven fabrics is a complex situation since the fabric is anisotropic and its modulus changes

with strain. When stress is applied to anisotropic textile materials, both the Poisson effects

and shear deformation occur. The opposite is also true, that shearing stresses causes both

Poisson effects and relative rotation between the warp and the weft yarns. When the

mechanism of garment bagging is studied, the factors that affect elastic recovery from stretch

are very important. In the simulation of bagging, stretch and recovery procedures were

developed. But in this case, there was just the uniaxial stretch [78].

Zhang et al. [83] studied the internal stress distribution of bagged fabrics. They did

theoretical and experimental studies to find the influence of the stress distribution on the

residual bagging deformation of the fabric. They developed a model using the membrane

theory and analysed the stress distributions at different boundary conditions for isotropic

fabrics. They considered different bagging heights and the friction between the fabric sample

and the pressing steel ball. They concluded that there was a non-uniform stress distribution

along the meridian direction, and a non-continuous stress distribution along the hoop

direction. These stresses and the bagging height are important factors affecting the residual

bagging deformation of fabric and cause localised damage. They aimed to study how the

bagging behaviour of the fabric is affected by fabric anisotropy. In their study, they chose

seven directions by using fabric strips and measured the tensile moduli in each of them; from

the relation between the geometrical deformation and the bagging height, they calculated the

strain of the fabric. With the tensile moduli and the fabric strain, they investigated the stress

distribution of an anisotropic fabric. They detected different yarn stresses between the warp

and the weft directions that resulted in different bagging shapes. The reason for this is the

non-uniform stress distribution along the meridian direction and the variations in the tensile

angle y. They also predicted the bagging forces and compared them with the measured

forces; and concluded that the method approximately predicts the trend of the bagging

force.

They found that the fabric’s mechanical behaviour essentially influenced the fabric’s

residual bagging deformation. A fabric can be stretched in several directions at the same

time. If one direction has more extensibility than the others, that direction will feel less load.

The direction which has low extensibility will suffer more load. In order to reach the same

stretch ratio at the bias direction and the warp direction, approximately one tenth or one

hundredth of the force required for the warp is required for the bias. This means that

some of the threads are stretching in the yield region, but others have rigid movements

such as decrimping or shearing rotation. This will result in an unbalanced stress or strain

distribution in the fabric, and the recovery will also be non-uniform, so the bagging shapes

will be different. The mechanisms involved in forming non-uniform shapes is not known.

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They investigated the stress distributions of woven fabric during bagging by considering

different boundary conditions, different bagging heights, the friction between the fabric and

the pressing ball, variations in the tensile modulus of the fabric with strain, and fabric

isotropy and anisotropy. With this investigation, the influence of the internal stresses of the

fabric on its residual bagging deformation were also able to be analysed. They worked only

with a fabric radius of 76 mm and a sphere radius of 48 mm. They subjected the fabric

sample to an axial-symmetric deformation by a steel ball. The part of the fabric which is in

touch with the pressing ball forms a spherical corona, and the rest of the pressed fabric

forms a conical section. While the fabric is deformed, it receives the bagging force and

transmits it to the ring clamps. The bagging force induces many internal forces, such as

tension, shearing, and bending, to the fabric in many directions. The bending force is

ignored because the thickness of the fabric is much less that the radius of the pressing ball.

There is a localised bending moment region in the ring clamps [83].

Since the fabric is anisotropic, the internal stresses that occur in the fabric are not axially

symmetric even if the fabric is subjected to axial-symmetrical deformation. The tensile and

the shear internal stresses are balanced by the boundary forces at the ring clamps. No

buckling or torsion behaviour was seen in the bagging tests. The orthotropic plain fabric

used in the tests had symmetrical mechanical properties in the warp and the weft directions.

So it can be concluded that the internal shear stresses should be balanced in the symmetrical

range. So it is just the pressing force that bags the fabric. The assumptions they made are:

(i) They considered the fabric to be an elastic membrane which had no bending rigidity, and

the unit thickness of the fabric was uniform; (ii) The region between the spherical corona

and the conical section was a continuous and smooth surface, so the bagging angle was just a

function of the bagging height; (iii) In the small strain region of the fabric, Hooke’s law

could be applied for the stress–strain relations; (iv) Along the bagging height at any

circumference, the stress distribution in the warp and the weft directions was symmetrical;

(v) The pressing force was p, the pressure at the corona was q, the pressure had an axial-

symmetrical distribution, and it was in the vertical direction. With these assumptions, the

problem becomes similar to the mechanical behaviour of a two-dimensional elastic

membrane in three-dimensional deformation, and this can be analysed by the membrane-

shell theory. The advantage here is the elimination of the bending moment. They describe

fabric bagging as a shell of an elastic membrane. They derived equations to calculate the

stress distribution in the spherical corona and in the conical section with the membrane

theory and the assumptions they had made. Then they applied these equations to calculate

the stress distribution in a wool plain-weave fabric. They applied different boundary

conditions for different applications [83].

In the spherical-corona section, the meridian and the hoop stresses were seen in the

fabric. In the conical section, only the meridian stresses were seen. They say that at the

change of the section, the meridian stress was at a maximum and it decreased at the ring

clamp. At the top of the fabric, the hoop stress was at the maximum and it decreased at

the intersection region. In the meridian direction, both the meridian and the hoop stresses

distributed non-uniformly, but the hoop stress was non-continuous in the meridian

direction. At the intersection region where it was the turning point of the fabric, stress

concentration was seen at the maximum. In an isotropic fabric at equilibrium, bagging

force, the most important component of the internal stresses, is the meridian stress. In all

the areas of the deformed fabric, the meridian stress was always larger than the hoop

stress [83].

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In an anisotropic fabric, they assumed that the tensile strength of the fabric in the

meridian direction was balanced with the external bagging force. With the fabric strain eand fabric tensile modulus in different directions, they could calculate the distribution of

the meridian stress and the bagging force. Also, in the hoop direction, a non-uniform

distribution of the stress concentration was seen. So, when the bagging force was lifted,

this non-uniform distribution caused a non-uniform recovery. If the bagging force was to

be increased, there would be localised structural damage in the fabric at the bursting stage,

and that localisation would be near to the intersection region. If the tensile stresses are in

an off-axial direction, then the stresses in the warp and the weft directions would be

different and would cause shear stress. Non-uniform stress causes different yarn stresses in

different directions, so the yarn elastic recovery was influenced, and it resulted in different

bagging shapes. Effective tensile modulus means the combined effects of the tensile and

shearing deformations in different directions. They also derived equations to calculate the

stress distribution at the spherical corona, at the conical section, and at different

conditions. Their experimental results were higher than the predicted results. If they

calculated the bagging force for the constant tensile modulus under maximum strain, it

came out closer to to the experimental results. At the initial stage, the experimental and the

predicted results were away from each other; they explain this as caused by the change in

the fabric tensile modulus with the fabric strain during the loading process. They also got

high experimental results for polyester-fibre fabric. They explain this as due to the

polyester having less crimps and less friction between the yarns. Another explanation they

made was that, in the bagging test, the fabric was subject to biaxial extension at the

spherical corona region. No Poisson effect occurs there but there are the two tensile

stresses. Another explanation is that the length of the fabric strip in the tensile test is

longer than the effective radius of the fabric clamped at the ring for the bagging test, and

this increases the weak-link effect. Another explanation is that they assumed there was no

slippage at the spherical corona region between the fabric and the pressing ball, but there

may be. They suggest that because the higher stress causes poorer recovery of the fabric, in

high-quality outerwear a smoother lining should be used at the knees or elbows of the

garment. This will reduce the friction between the garment and the skin, and will result in

less bagging deformation [83].

6.3 Production Parameters

By production parameters, we mean the general factors we deal with in production. One

production parameter would be machine adjustments, such as the machine production rate

(which is the speed of the machine), the pressures between adjacent parts of the machine

(which directly affect the produced textile material) and so on. Another production

parameter would be the environmental factors (such as the climatic conditions). Others

would be the technology of the machine in which the studied textile material is produced, the

production direction of the textile material, the finishing parameters, etc. But, in literature,

no research regarding these factors has been found. It is believed by the author that these

points are of equal value to be looked for.

7. MATHEMATICAL MODELS OF BAGGING

Zhang et al. [81] studied physical mechanisms during woven fabric bagging by developing a

test method, and also developed some theoretical models in order to analyze the stress–strain

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relations in fabrics at different deformation stages. They assumed that the stress–strain

relationships in fabrics comprised three components, and put them in their model. The first

two were elastic and viscoelastic deformation of fibres, and the third was the friction

between fibres and yarns in the fabric. The loading and unloading process in each cycle,

change of bagging force with cycles, relative contributions of the three components in each

cycle, and residual bagging height in each cycle were all predicted by the model when the

fundamental parameters of fibre mechanical properties and yarn–fabric structural features

are specified to the model. They compared the theoretical predictions and the experimental

results and obtained good agreement between them. The fabrics they used were wool with

various structures. The model could sufficiently simulate fabric bagging rheological

behaviour and predict fabric bagging performance. Fibre mechanical behaviour increases

in importance in determining fabric bagging behaviour when fabrics have the same

construction. They developed a mathematical model on the basis of rheological mechanisms

and intended to simulate fabric bagging from fundamental fibre mechanical properties and

yarn–fabric structural features. Their model successfully simulated the woven wool fabric’s

bagging behaviour and could reflect the relative contributions of the fibre’s elastic and

viscoelastic behaviour and interfibre friction, which are affected by yarn–fabric structural

properties [81].

In their rheological model, they described the physical mechanisms of fabric bagging.

The model had three components parallel to each other. There, fibre elasticity is represented

by a spring, fibre viscoelasticity is represented by Maxwell’s unit of a spring and Newton’s

viscous dashpot put in series, and interfibre friction is represented by a frictional element.

These three components have relative contributions which are represented by three

different weighting coefficients. They assumed a linear relationship between stress and strain

during small deformation intervals. Fibre stress was represented by applying Boltzmann’s

superposition principle and there the representation is as a function of the strain history of

the fibres. They specify the fundamental fibre properties, the measured yarn and fabric

parameters and the three weighting coefficients for the model, then the model is able to

simulate fabric bagging behaviour. The model describes fabric bagging behaviour by the

residual bagging height and the peak load in each cycle, the loading process in the first cycle

and the alterations in the three components during repeated bagging [81].

The relaxation time t of the fibre indicates the rate of fibre stress relaxation. The

relaxation time, the elastic modulus and the viscoelastic modulus should be determined

from experimentally measured values of the related fibre, because, in the literature there

is little information about most textile fibres’ viscoelastic behaviour. Also, there may be a lot

of difference in the viscoelastic behaviour of the same kind of fibre, where dyeing

and finishing has affected the viscoelastic behaviour; also there can be differences

from fibre to fibre in different areas of the same fabric. They state that the researches

found in literature deal mainly with simple fabric deformation such as tension, bending, and

shearing. There is very little work done on bagging. Bagging involves three-dimensions,

fibre viscoelasticity, interfibre friction, is subject to repeats, is a rheological process

with nonlinear strain, and is a complex deformation. They indicate that when repeated

deformation occurs in a fabric, the recovery ability of the fabric decreases because the stress

relaxation of the fibre and the frictional restrictions in the fabric construction cause residual

bagging deformation [81].

They point out that many of the fibres have natural crimp before they are spun when

looked at from the microscopic point of view. In the yarn, every fibre follows a migrating

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helix. When the yarns are woven into a fabric, they are crimped into a complicated

configuration. So, when the fabrics bag, fibres may be behaving differently, some stretching

to their yielding points, some decrimping during yarn extension between interlacing

points, and some shearing and bending at the interlacing points. At that time, fibres are

experiencing a combination of tension, shearing, bending, and compression forces. So, there

are very complex interactions between elastic and viscoelastic behaviour of fibres and yarn–

fabric constructions. In a spun yarn, the friction between fibres is very important for holding

the fibres together in the yarn. In the woven fabric, the friction between the interlacing yarns

is very important. They assume a linear relation between stress and strain and a following of

Hooke’s law in the small strain region. The average elastic modulus of fibres is related to the

amorphous morphological components of the fibres. Bagging height is a nonlinear function.

The more the cycles, the less the bagging load; the more the cycles, the higher the residual

bagging height. Less bagging load shows the loss of internal energy in the fabric. The

mathematical model is based on fibre elastic and viscoelastic behaviour and interfibre

friction which is time dependent, and is able to simulate fabric bagging fatigue behaviour.

These items are given to the model: (i) The fundamental properties of the fibres; (ii) The

measurable parameters of yarn and fabric structural features; (iii) The geometric relation

between fabric deformation and bagging height. The model predicts fabric bagging

performance during the bagging test and this consists of: (i) Bagging force changes during

the loading and unloading process in each cycle; (ii) Changes in bagging force with cycles;

(iii) Relative contributions of the elastic, viscoelastic and frictional force components in each

cycle; (iv) Residual bagging height in each cycle [81].

They developed a mathematical model from their rheological model to obtain a

quantitative description of the physical mechanism. There are five aspects of the bagging

force being a non-linear function of the parameters: (i) Fibre parameters are the

fibre’s average elastic modulus E1, average viscoelastic modulus E2, relaxation time t, andinter-fibre frictional coefficient m; (ii) Yarn and fabric structural parameters are the ratio of

yarn curvilinear length to its projected length C1, yarn count C2, fabric density C3, and the

fabric’s interlacing density per unit area Z; (iii) Fabric strain efab geometric parameters of thetest which are the radius of the pressing steel ball r0, the radius of the fabric sample R0, and

the bagging angle a0; (iv) Empirical coefficients Y1 and Y2, where Y1 is the fibre-strain

coefficient which estimates the influence of the yarn structure on the fibre strain, and Y2 is

the fabric tensile force coefficient which estimates the effect of fabric anisotropy on the

bagging force. These coefficients represent the factors that influence the bagging force and

can be analysed quantitatively; (v) Weighting coefficients (k3, k4, k5) which are the relative

contributions of elasticity and viscoelasticity of the fibres, and inter-fibre friction to the

bagging force, consecutively [81].

8. COMPUTER SIMULATION MODELS OF BAGGING

Baser [13] developed approximate solution computer programs with several mathematical

models to predict the spatial deformation occurring in fabrics, which are mainly perpen-

dicular to the fabric plane. In one of these models, it was assumed that the deformation

occurs because of the elongation of the yarns, and in another an approximate solution was

obtained on a model depending on the fabric geometry assuming large deformations [12].

These mathematical models were worked into different computer programs with different

assumptions [13]. In these programs, the kind of deformation occuring with the effect of a

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spatial force acting upon a fabric placed on a square frame was studied. The main

assumptions here were the yarn elongation, the intersection angles between the yarns staying

at 908, and during the deformation period, as a consequence of yarn elongation, a shape like

a pyramid having occurred. So the force needed for deformation was calculated with the

computer program named ‘gnyn01.bas’ and presented in Appendix 1.

The conditions that these computer programs symbolize in general are represented in

Fig. 19.

L0 : The side length of the square frame in which the fabric is placed

N : The number of the warp yarns in the frame

M : The number of the weft yarns in the frame

N/2 : The number of the warp yarns to the middle point of the the frame

j : The warp indices

i : The weft indices

The fundamentals of the geometric assumptions of the computer program are shown in

Fig. 20(a), (b) and (c).

As will be seen in Fig. 20(b), Ln=2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðL0=2Þ2 þD2

qand sina¼ D

Ln=2

can be determined. So,

j

N=2¼ l0j

L0=2ð34Þ

l0j ¼ j

N L0 ð35Þ

lj ¼ 2j

N Ln=2 ð36Þ

j : The sequence of any warp yarn

l0j : The initial length of any one of the warp yarns

lj : The length of any one of the warp yarns after deformation

Fig. 19 Top view of the fabric laid on the frame to be deformed. Baser [13]

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So, Equations (34)–(36) can be written, and all the warp yarns starting from the edge of the

frame until the middle point can be determined.

For the weft yarns, with the help of the i indices, similar formulas can be obtained. If,

P : Total pressing force

Pj : The force occuring in the warp yarns

Pi : The force occuring in the weft yarns

Tj : The strain occuring in the warp yarns

Ti: The strain occuring in the weft yarns

then from Fig. 20(a), Equations (37)–(40) can be written:

Tj ¼ lðlj � l0jÞ=l0j ¼ lðlj=l0j � 1Þ ð37Þ

Pj ¼XN=2

j¼1Tj sin a ¼

XN=2

j¼1ljðlj=l0j � 1Þ

!sin a ð38Þ

Fig. 20 Geometric assumptions forming the fundamentals of the computer programs(a) Distribution of the pressing force(b) Position at the perpendicular cross-section after deformation

L0=2: The length until the middle point of the frame sideLn=2: The length of the yarn until the middle point of the frame side after deformation

(c) Comparison between before and after deformation (Top view)

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Pi ¼XM=2

i¼1Ti sin a ¼

XM=2

i¼1liðli=l0i � 1Þ

!sin a ð39Þ

P ¼ 4ðPj þ PiÞ ð40ÞThe application of this yarn elongation assumption was done in the computer program

‘gnyn01.bas’ in Appendix 1 and the calculated P force was written by the program. Then,

Coulomb friction was applied as the friction coefficient m¼ 0.3, and the force was

recalculated and rewritten with the friction force included [13].

In the computer program ‘gnyn10.bas’, given in Appendix 2, the crimp in the yarns is

taken into consideration and the fabric geometry of Peirce [49] is applied with a bending

assumption. This assumption is explained in Fig. 21.

Here, since,

l0j : Warp length

lj : Deformed warp length

then

l0j/(M/2): Unit warp length (as seen in Peirce geometry)

lj/(M/2): Unit of the deformed warp length

In Fig. 22, the geometric assumption made is drawn out.

Fig. 21 Fabric geometry of Peirce [49]c : Elongation proportion of the fabricl : Final lengthl0 : Initial lengthc ¼ ðl� l0Þ=l0 ¼ ðl=l0Þ � 1

Fig. 22 The geometric assumption

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Here, we can write,

s0j ¼ l0j= cos yj ð41Þ

h0j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis0j

2 � l0j2

qð42Þ

According to Peirce’s theory, yj ¼ffiffiffiffiffiffi2cj

pis approximately true in the case of deformation, so

we can obtain the situation in Fig. 23. In this way, such a phenomenon is turned into a bending

problem with the application of Baser’s [12] approximate theory, and assuming that no yarn

elongation takes place, on this basis the computer program was worked out.

Here, since there is no yarn elongation, s0j¼ constant, and Equations (43) and (44) can be

written:

hj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis0j

2 � lj2

qð43Þ

h0j � hj ¼ The amount of bending ð44ÞThe force at bending, the pressure at the unit yarn length, is obtained from the differences in

the heights can be written as follows:

P0 ¼ P01 � P02 ¼ 12ðEIÞjðh0j � hjÞ=l0j3 ð45Þ

The strain force occurring in the deformed fabric plane with the application of this force will

be as:

Tj ¼ Poj=2 sin yj cos yj ð46ÞAlong both of the warp and the weft yarn groups, the same process is carried out and the

total force is calculated; then the effect of friction is included and the total force is again

calculated.

The pressing force formed by the unit yarn lengths, as described above, are added with the

method of numeric integration,

Fj ¼XN=2

j¼1Tj ð47Þ

Fi ¼XM=2

i¼1Ti ð48Þ

From here, the total pressure is calculated:

P ¼ 4 sin aðFj þ FiÞ ð49Þ

Fig. 23 The geometric assumption according to Baser’s [12] approximate theory

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In the computer program ‘gnyn20.bas’ given in Appendix 3, the phenomenon is

considered as a problem of elongationþ bending. The maximum yarn shape retention is

assumed to be 50%, and from that point on, it is assumed that elongation will take place,

and when hj < 0.5 h0j, then hj¼ 0.5 h0j was used. The indices are not shown separately for

the warp and the weft every time, but in each case, both are applied [13].

These computer programs were applied to the experimental results of Sengoz’s work and

the calculations obtained are given in Table 3. The program ‘gnyn01.bas’ was done with the

assumption of elongation; the program ‘gnyn10.bas’ was done with the assumption of

bending; and the program ‘gnyn20.bas’ was done with the assumption of elongationþbending, the limit being 50% yarn shape retention. In Table 3, the load results for different

sphere diameters, different displacement values and different frame dimensions are given,

and they are all in Newtons. Both the experimental results and the computer calculations are

in this table.

It is seen in the table that as the displacement value increases with every frame dimension

increase, the load value also increases. The same trend is also seen in the computer

calculations. The program ‘gnyn01.bas’, which assumes elongation, gives very high results.

The program ‘gnyn10.bas’ gives lower results because the phenomenon is described by

bending. The program ‘gnyn20.bas’ gave similar results with the experimental results for

middle-dimension frames. In the column for ‘gnyn10.bas’, the amount of force performed by

bending can be seen. It can be concluded from these results that the programs are logically

correct but require more work to be done upon them.

Table 3

Comparison of the Computer Results with the Work of Sengoz

Frame Experimental Results (N) Computational Results (N)

mm Sphere2 Sphere4 Sphere8 gnyn01.bas gnyn10.bas gnyn20.bas

Lo¼ 4 2.3 – – – 23.64 0.93 3.903.6 24.8 38.42 – 89.39 2.04 21.124.9 63.44 93.27 – 220.97 5.22 69.836.2 63.36 98.24 – 436.47 8.72 152.627.5 61.36 98.62 – 749.67 12.88 275.34

Lo¼ 6 2.3 – – – 10.64 0.64 2.483.6 11.83 15.83 – 40.52 2.27 10.024.9 36.71 48.46 – 101.26 4.73 28.936.2 61.00 83.27 – 202.75 7.82 68.427.5 67.09 91.44 – 353.84 11.85 128.67

Lo¼ 8 2.3 – – – 6.07 0.49 1.873.6 6.60 7.28 9.84 23.20 1.80 7.364.9 22.71 25.82 30.38 58.20 4.27 19.386.2 37.91 42.71 52.13 117.11 7.64 42.957.5 58.87 68.66 85.26 205.62 11.30 80.10

Lo¼ 12 2.3 – – – 2.70 0.32 1.233.6 3.32 3.54 5.00 10.34 1.21 4.764.9 10.67 12.11 16.38 26.02 2.99 12.176.2 16.97 19.88 27.55 52.56 5.86 25.217.5 26.15 30.70 43.05 92.70 9.89 46.17

Lo¼ 16 2.3 – – – 1.53 0.24 0.923.6 – – 2.59 5.85 0.92 3.564.9 – – 9.83 14.74 2.28 9.056.2 – – 14.98 29.81 4.55 18.537.5 – – 22.68 52.66 7.88 33.29

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Yeung et al. [75] aimed to develop a new method to evaluate garment bagging and they

used image processing with different modeling techniques. Garment bagging can be

characterized by bagging height, volume, and anisotropy parameters. It is stated that in the

traditional methods, bagging is evaluated by the height and that this parameter cannot

represent the information given by appearance. In the new method they developed, they

capture images from bagged fabrics by image processing and they abstract criteria to

recognize the bagging height. According to the intensity of the images, they work with eight

criteria and characterize the image features of bagging such as the height, volume, shape,

and fabric surface pattern. Fabric surface pattern is an important parameter because the

human eye can detect whether a garment is more or less severely bagged according to

the pattern on it, so the method they developed also includes this feature. They indicate that

the earlier work done on fabric bagging was on measuring residual bagging height, and

relate this to fabric mechanical properties. They proved that using the photograph is highly

correlated with the real bagged fabric samples in their earlier researches, so they used the

image information in their later research.

Image analysis is applied in many areas in textile engineering – in fibre analysis (crimp,

neps, trash), in wrinkling analysis, in weave pattern identification and fault detection in

woven fabrics. In their work, the reseachers captured digitized images of bagged fabric

samples, the captured images were image processed, the criteria to describe the bagging

appearance was selected, and finally the bagging magnitude from the selected criteria was

recognized [75]. In the photographs, deformation is in two-dimensions, but the uneven

illuminations on the shadings in the photographs makes it perceived in three-dimensions by

the human eye. Also, fabric surface pattern has a reflectance influence in the sample and

causes local variations in intensity images. These intensity variations in the images are

different from fabric to fabric and from warp to weft because of anisotropy. So, when the

intensity changes are measured, then it is possible to evaluate fabric bagging according to

bagging height, bagging shape, bagging volume, bagging anisotropy, and fabric surface

patterns. They used three approaches to model fabric bagging when evaluating the

subjective perception data of the bagging appearance. These were multiple regression, linear

modelling, and neural networks. The regression model achieves a good fit with a correlation

coefficient of r2¼ 0.92, the linear model achieves a good fit with a correlation coefficient of

r2¼ 0.93, and the neural network achieves a good fit with a correlation coefficient of

r2¼ 0.94. So it is concluded that bagging appearance can be predicted from the criteria they

abstracted from the images of the bagged fabrics [75].

9. CONCLUSION

The bagging behaviour in all kinds of fabrics has gained importance throughout recent years

both because it is regarded as a quality factor and because of improving computer technology.

Being a quality factor, fabric bagging is an unwanted fault in the appearance of the garment in

daily use, and still does not have numerical standards to be evaluated. As the computer

technology improves continuously, fabric bagging has been mathematically modelled and

simulated on the computer screen, this will be very helpful in the developments in standards.

In this issue of Textile Progress, a review of fabric bagging has been given by elucidating

the importance, the definition, the test methods, the research work done, the factors affecting,

the mathematical models, and the computer simulations of fabric bagging. It is hoped by the

author that the information gathered here will lead to new developments in the future.

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10. FUTURE PROSPECTS

In the research work explained here, it will be noticed that the measurement, characterization,

affecting factors, modelling and simulating work on bagging has been given importance, but

work to prevent bagging in fabrics is missing. How to prevent bagging in fabrics, so to reach

higher quality in the garments has to be searched for. By taking all the fibre, yarn, fabric, and

production parameters, and the usage of the fabric into consideration, the preventing factors

of bagging have to be elucidated. When it becomes evident what kind of factor affects bagging

and how, then computer simulations will also develop, and moving screen images will also be

obtained. Then it will be easier to see on the screen what we have in hand as our starting fibre,

and how we will finish up at the end fabric, by feeding the throughout information for the

yarn, fabric, production, and usage. Also, moving backwards should also be possible; the

required fabric would be designed in the computer and all the factors to achieve that fabric

could be chosen by going back to the yarn parameters, then the fibre parameters, and then the

production parameters, and deciding them one by one. Afterwards, the creation of the ideal

fabric for that usage without bagging would be realized.

With all the information in the research work explained here, it is believed that a full

understanding of fabric bagging has been accomplished and that this will lead to much

newer methods being developed with novel techniques.

REFERENCES

[1] R. Abghari, S.S. Najar, M. Haghpanahi and M. Latifi, An Investigation on Woven Fabric BaggingDeformations Using New Developed Test Method, In II. International _IIstanbul Textile CongressIITC2004, _IIstanbul, Turkey, 2004.

[2] J. Amirbayat and J.W.S. Hearle, The Complex Buckling of Flexible Sheet Materials Part I: TheoreticalApproach, International Journal of Mechanics and Science, 1986, 28(6), 339–358; Part II: ExperimentalStudy of Three-fold Buckling, International Journal of Mechanics and Science, 1986, 28(6), 359–370.

[3] J. Amirbayat and J.W.S. Hearle, The Anatomy of Buckling of Textile Fabrics: Drape andConformability, Journal of the Textile Institute, 1989, 80(1), 51–70.

[4] S.C. Anand, T.H.Shah, and A.Rawal, Developments in Design and Performance of NeedlepunchedGeotextiles, In Proc.I. International Technical Textiles Congress, (edited by S. Yesilp�nar, M. Sar��s�k, andG. Karbay), _IIzmir, Turkey, 2002, 97–109, p.268.

[5] M. Aono, D.E. Breen, and M.J. Wozny, Fitting a Woven Cloth Model to a Curved Surface: MappingAlgorithms, Computer-aided Design, 1994, 26(4), 278–292.

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[7] ASTM Standard D231-62 revised to D3887-96 Standard Specification for Tolerances for Knitted Fabricsand D3786-01 Standard Test Method for Hydraulic Bursting Strength of Textile Fabrics-DiaphragmBursting Strength Tester Method and D3787-01 Test Method for Bursting Strength of Textiles-Constant-Rate-of-Traverse (CRT) Ball Burst Test, ASTM International, USA.

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[9] R.J. Bassett and R. Postle, The Fitting of Woven Fabrics to Three-dimensional Surfaces Using a Rod-element Model, In Objective Evaluation of Apparel Fabrics, (edited by R. Postle, S. Kawabata, andM. Niwa), Textile Machinery Society of Japan, Osaka, Japan, 1983, 379–386, p.550.

[10] R.J. Bassett, The Measurement of Biaxial and Shear Properties of Apparel Fabrics, In The Application ofMathematics and Physics in the Wool Industry, (edited by G.A. Carnaby, E.J. Woo, and L.F. Story),WRONZ Special Publications, New Zealand, 1988, 417–428, p.625.

[11] R.J. Bassett and R. Postle, Fabric Mechanical and Physical Properties Part IV: The Fitting of WovenFabrics to a Three-dimensional Surface, International Journal of Clothing Science and Technology, 1990,2(1), 26–31.

[12] G.Baser, A Mechanical Approach to the Determination of the Geometry of a Woven Fabric and to theAnalysis of Subsequent Changes in Its Geometry Part I: A Theory for the Crimping of the Weft YarnDuring Weaving, Journal of the Textile Institute, 1989, 80(4), 507–520; Part II: The Development of aGeometry of Plain-woven Fabric in the Loomstate and a Theory of Weaving Contractions, Journal ofThe Textile Institute, 1989, 80(4), 521–536.

[13] G. Baser, Unpublished work, 1996.

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[14] K. Bilisik, Multiaxis Three Dimensional Woven Fabrics for Composites, In Proc.I. InternationalTechnical Textiles Congress, (edited by S. Yesilp�nar, M. Sar��s�k, and G. Karbay), _IIzmir, Turkey, 2002,129–141, p.268.

[15] I. Birkan, Problems Related to Elastic Hysteresis in Textile Fibres and Filaments: Creep and Relaxation(Tekstil Elyaf ve Flamanlar�nda Elastik Histerezis ile Alakal� Problemler: Krip ve Relaksasyon), Ph.D.Thesis, _IIstanbul Technical University, _IIstanbul, Turkey, 1958, p.82.

[16] BS 4294, TEXTILES – Test Method to Determine Woven Fabric Resistance to Sagging or Stretch inWear, 1967, British Standards, UK.

[17] C.R. Calladine, (Anniversary for LOVE), The Theory of Thin Shell Structures 1888-1988, Proc. Instn.Mech. Engrs., 1988, 22(A3), 41–49.

[18] B.M. Chapman and J.W.S. Hearle, The Bending and Creasing of Multicomponent Viscoelastic FibreAssemblies Part I: General Consideration of The Problem, Journal of the Textile Institute, 1972, 63,385–403; Part II: The Mechanics of a Two-dimensional Assembly of Long Straight Fibres of DifferentTypes, Journal of theTextile Institute, 1972, 63, 404–412.

[19] P.M. Cunniff, An Analysis of the System Effects in Woven Fabrics Under Ballistic Impact, TextileResearch Journal, 1992, 62 (9), 495–509.

[20] P.M. Cunniff, A Semi-empirical Model for the Ballistic Impact Performance of Textile-based PersonnelArmor, Textile Research Journal, 1996, 66 (1), 45–60.

[21] DIN 53860, Prufung der Ausbeulneigung von textilen Flachengebilden, 1981, Teil 1(2), 277–281.[22] DIN 53861, Prufung von Textilien Wolb-und Berstversuch Blatt 1,2,3, Beuth-Vertrieb GmbH, Berlin,

1970, 199–232.[23] T. Eeg-Olofsson, On the Shaping of Textile Fabrics and Similar Materials and a Definition of

The Shaping Ability (Uber die Formbarkeit von textilen Stoffen und ahnlichen Materialien sowie eineDefiintion der Formbarkeit), Faserforshung und Textiltechnik, 1966, 17(9), 418–422.

[24] R.H. Ericksen, A.C. Davis and W.E. Warren, Deflection-force Measurements and Observations onKevlar 291 Parachute Fabrics, Textile Research Journal, 1992, 62(11), 628–637.

[25] FJ 552. 6-85, Testing Methods for Bagging of Woven and Knitted Fabrics, A Standard of The Ministryof Textiles of the People’s Republic of China.

[26] J. Fleissig, The Elasticity of a Fabric Stretched Over a Spherical Surface in Radial and TangantialDirections (]�ACTIIYHOCTb TKAHEII B PA�IIA�bHOM II TAH�EHIIIIA�bHOMHAIIPAB�EHIIII IIPII HATR�EHIIII HA IIIAPOBYIO IIOBEPXHOCTb), Veda A Vyzkum VText. Prum., 1968, 9(5), 5–29.

[27] K.H. Grunewald and W. Zoll, Practical Methods for Determining the ‘Bagging’ Tendency in Textiles,ITS Weaving, 1973, 3, 273–275.

[28] J.W.S. Hearle, Advances in Rope Technology, In Proc.I. International Technical Textiles Congress,(edited by S. Yesilp�nar, M. Sar��s�k, and G. Karbay), _IIzmir, Turkey, 2002, 32–43, p. 268.

[29] J.W.S. Hearle, P. Grosberg and S. Backer, Structural Mechanics of Fibres, Yarns, and Fabrics, Vol:1,John Wiley & Sons, New York, U.S.A., 1969, p. 469.

[30] F. Heisey, P.Brown, and R.F.Johnson, Three-dimensional Pattern Drafting, Part I: Projection, TextileResearch Journal, 1990, 60(11), 690–696.

[31] F.L. Heisey and K.D.Haller, Fitting Woven Fabrics to Surfaces in Three Dimensions, Journal of theTextile Institute, 1988, 79(2), 250–263.

[32] S. Kawabata, M. Niwa, and H. Kawai, The Finite-deformation Theory of Plain-weave Fabrics, Part I:The Biaxial-deformation Theory, Journal of The Textile Institute, 1973, 64(1), 21–46; Part II: TheUniaxial-deformation Theory, Journal of The Textile Institute, 1973, 64(2), 47–61; Part III: The Shear-deformation Theory, Journal of The Textile Institute, 1973, 64(2), 62–85.

[33] W.F. Kilby, Planar Stress–Strain Relationships in Woven Fabrics, Journal of The Textile Institute, 1963,54, T9–27.

[34] J.W. Kirk and S.M. Ibrahim, Fundamental Relationship of Fabric Extensibility to AnthropometricRequirements and Garment Performance, Textile Research Journal, 1966, 36, 37–47.

[35] D. Kisilak, A New Method of Evaluating Spherical Fabric Deformation, Textile Research Journal, 1999,69 (12), 908–913.

[36] M. Konopasek, Classical Elastica Theory and its Generalizations. In Mechanics of Flexible FibreAssemblies, (edited by J.W.S. Hearle, J.J. Thwaites, and J. Amirbayat), Sijthoff& & Noordhoff, Holland,1980, 255–276, p.653.

[37] H. Lass, Vector And Tensor Analysis, McGraw-Hill Book Company Inc., New York, U.S.A., 1950,p.347.

[38] C.M. Leech, The Dynamics of Flexible Filament Assemblies, In Mechanics of Flexible Fibre Assemblies,(edited by J.W.S. Hearle, J.J. Thwaites, and J. Amirbayat), Sijthoff& & Noordhoff, Holland, 1980,343–390, p.653.

[39] J. Lindberg, L. Waesterberg, and R. Svenson, Wool Fabrics as Garment Construction Materials, Journalof The Textile Instiitute, 1960, 51, T1475–T1493.

[40] D.W. Lloyd, The Analysis of Complex Fabric Deformations. In Mechanics of Flexible Fibre Assemblies,Hearle, (edited by J.W.S. Hearle, J.J. Thwaites, and J. Amirbayat), Sijthoff& & Noordhoff, Holland,1980, 311–342, p.653.

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[41] D.W. Lloyd, The Mechanics of Drape, In Flexible Shells Theory and Applications, (edited by E.L.Axelrad and F.A. Emmerling), Euromech-Colloquium 165, Springer-Verlag, 1984, 271–282, p.552.

[42] D.W. Lloyd, An Integrated Approach to the Mechanical Modelling of One, Two and Three-dimensionalTextile Structures, In The Application of Mathematics and Physics in the Wool Industry, (edited byG.A. Carnaby, E.J. Woo and L.F. Story), WRONZ Special Publications, 1988, 21–42, p.625.

[43] C. Mack and H.M. Taylor, The Fitting of Woven Cloth to Surfaces, Journal of the Textile Institute, 1956,47, T477–488.

[44] H. Matsuoka, S. Nagae, and M. Niwa, Evaluation Methods for Bagging of Garments, Journal of JapanResearch Association Textile End-Uses, 1984, 25, 502–509.

[45] T.G. Montgomery, P.L. Grady and C. Tomasino, The Effects of Projectile Geometry on the Performanceof Ballistic Fabrics, Textile Research Journal, 1982, 52(7), 442–450.

[46] W.E. Morton and J. W. S. Hearle, Physical Properties of Textile Fibres, The Textile Institute, London.1975, p.660.

[47] R.P. Nachane and V. Sundaram, Analysis of Relaxation Phenomena in Textile Fibres, Part I: StressRelaxation, Journal of the Textile Institute, 1995, 86(1), 10–19; Part II: Inverse Relaxation, Journal of theTextile Institute, 1995, 86(1), 20–32.

[48] B. Olofsson, A Study of Inelastic Deformations of Textile Fabrics, Journal of the Textile Institute, 1967,58(6), 221–241.

[49] F.T. Peirce, The Geometry of Cloth Structure, Journal of The Textile Institute, 1937, 28(3), T45–96.[50] R. Postle and A.H. Norton, Physical and Mathematical Considerations for the Modelling of Fabric

Deformation. In The Application of Mathematics and Physics in the Wool Industry, (edited by G.A.Carnaby, E.J. Woo and L.F. Story), WRONZ Special Publications, 1988, 63–73, p.624.

[51] R. Postle and A.H. Norton, Mechanics of Complex Fabric Deformation and Drape, Journal of AppliedPolymer Science: Applied Polymer Symposium, 1991, 47, 323–340.

[52] J.R. Postle and R. Postle, Nonlinear Mechanics and Dynamics of Fabric Manipulation. In Proceedings ofthe 3rd Asian Textile Conference, The Textile Institute, 1995, 1, 569–573.

[53] E.P. Popov, Strength: Introduction to Solid Material Mechanics (Mukavemet Kat� CisimlerinMekani�ggine Giris), (Trans. H. Demiray), Ca�gglayan Kitabevi, _IIstanbul, Turkey, 1976, p.662.

[54] R.B. Ramgulam, A Novel Algorithm for Fitting a Woven Cloth to Complex Surfaces, InternationalJournal of Clothing Science and Technology, 2001, 13(3/4), 198–207.

[55] D. Roylance, A. Wilde and G. Tocci, Ballistic Impact of Textile Structures, Textile Research Journal,1973, 43(1), 34–41.

[56] F.L. Scardino and F.K. Ko, Triaxial Woven Fabrics Part I: Behaviour Under Tensile Shear, and BurstDeformation, Textile Research Journal, 1981, 51(2), 80–89.

[57] W.J. Shanahan, D.W. Lloyd, and J.W.S. Hearle, Characterizing the Elastic Behaviour of Textile Fabricsin Complex Deformations, Textile Research Journal, 1978, 48(9), 495–505.

[58] J.M. Shanks, The Dynamics of Reinforced Coarse Nets Using a Finite Element Analysis, InternationalJournal of Mechanics and Science, 1979, 21, 131–138.

[59] H. Sommer, Grundlagen der Berstfestigkeitsprufung von geweben. 1, Melliand Textilber., 1941, 22,414–462; II: 22, 462–468; III: 22, 516–564; IV: 22, 564–570.

[60] E. Strazdiene and M. Gutauskas, The Peculiarities of Textile Behaviour in Biaxial Punch Deformation,International Journal of Clothing Science and Technology, 2001, 13(3/4), 176–185.

[61] E. Strazdiene and M. Gutauskas, Behaviour of Stretchable Textiles with Spatial Loading, TextileResearch Journal, 2003, 73(6), 530–534.

[62] N. G. Sengoz, Permanent Deformation of Woven Fabrics Under Stress (Dokuma Kumaslar�n GerilmeAlt�nda Kal�c� Deformasyonu), Ph.D.Thesis, Aegean University, _IIzmir, Turkey, 1997, p.274.

[63] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, Elastically Deformable Models, Computer Graphics,1987, 21(4), 205–214.

[64] W. Thomas, Celanese Bagging Test for Knit Fabrics, J. Am. Assoc. Textile Chem. Colour. 1971, 3,213–233.

[65] S. Timoshenko, Plate and Shell Theory (Plak ve Kabuklar Teorisi) (Tran. M. _IInan, F. Sonmez), UclerBas�mevi, _IIstanbul, Turkey, 1950, p.468.

[66] TS 6071 Dokunmus Kumaslar�n Giyim Sebebiyle Torbalanma ve Uzamaya Kars� MukavemetlerininTayini Metodu, 1988, Turkish Standards Institute, Ankara, Turkey.

[67] TS 7126 Orulmus Tekstil Mamullerinin Patlama Mukavemetinin Tayini – Sabit Traves H�zl� (CRT) Bilyaile Patlatma Metodu, 1989, Turkish Standards Institute, Ankara, Turkey.

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[69] B.P. Van West, R.B. Pipes and M. Keefe, A Simulation of the Draping of Bidirectional Fabrics OverArbitrary Surfaces, Journal of the Textile Institute, 1990, 81(4), 448–460.

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APPENDIX 1

Baser’s Computer Program According to the Assumption of Elongation

10 REM ad:gonul00.bas gnyn01.bas guzama2.bas

20 REM bu program kare cerceveye gerilmis kumasta belirli bir cokmeye

30 REM yol acan kuvveti uzama+surtunme varsaym yaparak hesaplar

40 PRINT

50 LO¼ 4:D¼ .1:M¼ 105:N¼ 105:LAMJ¼ 6038:LAMI¼ 6038:SURT¼ .3

60 D¼D+.13

70 LII¼ 0:LJJ¼ 0

80 LN2¼ SQR((LO/2)^2+D^2)

90 SINA¼D/LN2

100 FOR J¼ 1 TO N/2-1

110 LJO¼ 2*J/N*LO/2

120 LJ¼ 2*J*LN2/N

130 LJJ¼LJJ+(LJ/LJO-1)

140 NEXT J

150 FJ¼ 2*LAMJ*LJJ*(1+SURT)

160 FOR I¼ 1 TO M/2-1

170 LIO¼ 2*I/M*LO/2

180 LI¼ 2*I/M*LN2

190 LII¼LII+(LI/LIO-1)

200 NEXT I

210 FI¼ 2*LAMI*LII*(1+SURT)

220 P¼ 2*SINA*(FJ+FI)

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230 PRINT P/102

240 PRINT

250 IF D<.74 GOTO 60

260 END

APPENDIX 2

Baser’s Computer Program According to the Assumption of Bending

10 REM ad:gnyn10.bas gonul666.bas gegilme.bas

20 REM bu program kare cerceveye gerilmis kumasta belirli bir cokmeye

30 REM yol acan kuvveti eggilme+surtunme varsaym yaparak hesaplar

40 PRINT

50 LO¼ 4:D¼ .1:M¼ 105:N¼ 105:CJ¼ .016:CI¼ .15

60 D¼D+.13

70 TETC¼SQR(2*CJ):TETA¼ SQR(2*CI)

80 SURT¼ .3:EIJ¼ 5.02/1000:EII¼ 5.02/1000

90 TOJ¼ 0:TOI¼ 0

100 LN2¼SQR((LO/2)^2+D^2)

110 SINA¼D/LN2

120 LJO¼LO/M

130 FOR J¼ 1 TO N/2-1

140 LJ¼ 2*LN2/M

150 HOJ¼LJO*SIN(TETC)/COS(TETC)

160 SOJ¼ SQR(LJO^2+HOJ^2)

170 IF LJ<SOJ THEN HJ¼ SQR(SOJ^2-LJ^2):GOTO 190

180 IF LJ>SOJ THEN HJ¼HOJ/2

190 S1J¼ SQR(HJ^2+LJ^2)

200 TJ2¼ 12*EIJ*(HOJ-HJ)/LJ^3*HJ/S1J

210 TOJ¼TOJ+TJ2/(LJ/S1J)+J*SURT*TJ2

220 NEXT J

230 LIO¼LO/N

240 FOR I¼ 1 TO M/2-1

250 LI¼ 2*LN2/N

260 HOI¼LIO*SIN(TETA)/COS(TETA)

270 SOI¼SQR(LIO^2+HOI^2)

280 IF LI<SOI THEN HI¼ SQR(SOI^2-LI^2):GOTO 300

290 IF LI>SOI THEN HI¼HOI/2

300 S1I¼SQR(HI^2+LI^2)

310 TI2¼ 12*EII*(HOI-HI)/LI^3*HI/S1I

320 TOI¼TOI+TI2/(LI/S1I)+I*SURT*TI2

330 NEXT I

340 P¼ 4*SINA*(TOJ+TOI)

350 PRINT P/102

360 PRINT

370 IF D<.74 GOTO 60

380 END

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APPENDIX 3

Baser’s Computer Program According to the Assumption of Elongation+Bending

(Limit: 50% Yarn Compression)

10 REM ad1:gnyn20.bas gonul666.bas gegsuuz2.bas

20 REM bu program kare cerceveye gerilmis kumasta belirli bir cokmeye

30 REM yol acan kuvveti uzama+egilme+surtunme varsaymna gore hesaplar

50 PRINT

60 LO¼ 4:D¼ .1:M¼ 105:N¼ 105:LAMJ¼ 6038:LAMI¼ 6038

70 D¼D+.13

80 CJ¼ .016:CI¼ .15

90 TETC¼SQR(2*CJ):TETA¼SQR(2*CI)

100 SURT¼ .3:EIJ¼ 5.02/1000:EII¼ 5.02/1000

120 TOJ¼ 0:TOI¼ 0

130 LN2¼SQR((LO/2)^2+D^2)

140 SINA¼D/LN2

150 LJO¼LO/M

160 FOR J¼ 1 TO N/2-1

170 LJ¼ 2*LN2/M

180 HOJ¼LJO*SIN(TETC)/COS(TETC)

190 SOJ¼ SQR(LJO^2+HOJ^2)

200 IF LJ<SOJ THEN HJ¼ SQR(SOJ^2-LJ^2):GOTO 220

210 IF LJ>SOJ THEN HJ¼HOJ/2

220 S1J¼ SQR(HJ^2+LJ^2)

230 TJ¼LAMJ*(S1J/SOJ-1)

240 TJ2¼ 12*EIJ*(HOJ-HJ)/LJ^3*HJ/S1J

250 TOJ¼TOJ+(TJ2+TJ)/(LJ/S1J)+J*SURT*12*EIJ*(HOJ-HJ)/LJ^3

260 NEXT J

270 LIO¼LO/N

280 FOR I¼ 1 TO M/2-1

290 LI¼ 2*LN2/N

300 HOI¼LIO*SIN(TETA)/COS(TETA)

310 SOI¼SQR(LIO^2+HOI^2)

320 IF LI<SOI THEN HI¼SQR(SOI^2-LI^2):GOTO 340

330 IF LI>SOI THEN HI¼HOI/2

340 S1I¼SQR(HI^2+LI^2)

350 TI¼LAMI*(S1I/SOI-1)

360 TI2¼ 12*EII*(HOI-HI)/LI^3*HI/S1I

370 TOI¼TOI+(TI2+TI)/(LI/S1I)+I*SURT*12*EII*(HOI-HI)/LI^3

380 NEXT I

390 P¼ 4*SINA*(TOJ+TOI)

400 PRINT P/102

410 PRINT

420 IF D<.74 GOTO 70

430 END

64 Textile Progress