20

《 特 別 寄 稿展 望(Review)》

The Rheology of Woven and Knitted Fabrics.*

Part 1 : Fabric Geometry and Force Methods of Analysis

Applied to Fabric Mechanics.

R. Postle (Member of TMSJ) and S. de Jong,School of Textile Technology, University of New South Wales,

P. O. Box 1, Kensington, N,S.W., 2033, Australia.

SYNOPSIS

Knitted and woven fabrics are extremely complex materials that

do not conform even approximately to any of the ideal , features

normally assumed. in engineering structural analysis and

mechanics. Studies of fabric geometry have played a vital role in

the development of quality control procedures designed to improve

fabric dimensional stability and specification during manufacture

and use.

In the case of woven fabrics, force methods of analysis have

been widely used for the study and interpretation of basic fabric

mechanical properties such as fabric tension, bending and shear .

For knitted fabrics, however, the development of a physically real

istic force method of analysis is very complex because of the

three-dimensional nature of loop interlacing, within the fabric . In

both geometrical and force methods of analysis for woven and

knitted fabrics, it is necessary to include a number of initial as

sumptions relating to the nature of yarn contact and yarn cross

sectional shape within the fabric. Such assumptions usually repres

ent gross simplifications and are liable to introduce large errors in

any analysis of fabric mechanical or theological properties.

In Part 2 of this series of papers, it is shown how energy

minimization methods of analysis may be used to overcome many

of these difficulties.

1 . Fabric Geometry

There are few, if any, manufactured products whose

basic structure has changed so little over the period of

recorded history as fabrics made from natural fibres.

Despite the great machine inventions which revolu

tionised the textile manufacturing industry of late 18th

century England and despite the great proliferation of

synthetic fibre raw materials which occurred in the pre

sent century, it is indeed remarkable to contemplate that

fabrics knitted or woven from natural fibers still have

basically the same structure, properties and uses that

they have always had throughout recorded history.

Developments of great importance have most certainly

* The major part of this paper was originally presented at the Sixth International Wool Textile Research Conference,Pretoria, Sep

tember 1980 as a plenary lecture entitled "Knitted and Woven Fabrics". The work reported in this paper, together withthat to be

published in Part 2 ("Energy Minimization Techniques applied to Elastic Mechanisms of Fabric Deformation") and Part 3("Objective Specification of Fabric Mechanical Behaviour and Inelastic Mechanisms of Deformation and Recovery"), formed the basisof a

series of three lectures presented by Professor. R. Postle to the Textile Machinery Society of Japan, Osaka, 1981.

Professor Ronald Postle の 略 歴

1940年 にオー ス トラリア,シ

ドニ ー生れ,1962年 同国 ニ ュー

サ ウス ウエ ルズ大 掌 繊 維 工 学

科(繊 維 物理專 攻)を 優 等で 卒

業 し,こ の 間,ウ エ ブ ス ター賞,

ス ピー クマ ン賞 を受 賞 して いる．

引続 き,オ ース トラ リアC.S.

Ｉ.R.O.繊 維 物理 部門 に勤務 し,

直 ちに海外派遺 生 と して英国 リ

ーズ大 学 に留 学,Grosberg教

授 の下 で編布 の 力学 の研 究 によ

り,1965年 にPh.D,の 学位 を受 け る,帰 国後C.S.I.R.O.に おい

て研究に従事 し,1967年 ニュー サウス ウエルズ大学応用科掌科繊

維工学教室の繊維物理部門講師,1976年 より同準教授.最 近の研究

分野は広 く,繊 維構造から布のテーラビリティ(可 縫性)に まで及

び,特 に織,編 布の力学の研究が最近多く行われ,弟 子の一人,de

Jong博 士 とともに開発 したエネルギ最適 法によ る布力学の研究は

著名で,近 年の学会誌をにぎわせている.こ の分野の世界の第一人

者といえよ う.昨 年11月末より1981年6月 まで京都大学招へい外国

人学者として布の力学と風合いの客観評価に関す る研究のため滞在

中である.な お,同 氏は本会正会員でもある.

本稿は,1980年 南アフリカで開催 された第6回 国際羊毛研究会議

において特別講演された内容に,去 る2月,本 学会で3回 の講義を

された内容がまとめられている.(文 責;川 端季雄)

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(繊 維 工 学)Vol.34,No.5(1981) 21

occurred in the design of weaving and knitting machin

ery, e.g. the introduction of shuttleless looms and the

general development of double-knitting machines, andmany of these developments have led to a general pro

liferation of the actual variety of knitted and woven

fabrics commercially available in recent years.

The basic fabric structures which are formed when

twisted yams are interlaced by the knitting or weaving

process have become the focus of much theoretical and

experimental study. In the years prior to 1960, these

studies often were based on the assumption of arbitrary

geometrical models for either the weave crimp shape orthe knitted loop shape.

Notable examples of such geometrical models include

Peirce's model') of plain-weave fabrics and Cham

berlain's model" of plain-knitted fabrics. In both of

these models, the authors built up a two-dimensional

unit cell (or repeat) of a fabric by superimposing linear

and circular yarn segments to produce the desired

shape. As Peirce explained in his paper, his model of

plain-weave fabrics shown in Fig. 1(a) could be obtain-ed if the yarns were assumed to be circular in cross-

section and highly incompressible, but at the same time

perfectly flexible so that each set of yarns had a unif

(a)

(b)

Fig. 1

A schematic representation of: (a) Peirce's geo

metrical model of the plain-weave structure,

showing the basic geometrical parameters of the

weave crimp (note that the subscripts 1 and 2

are interchanged for the perpendicular cross

sectional view); and (b) Peirce's mechanistic

model, showing the internal lateral pressure Q

between warp and weft yarns and an externally

applied tension P

orm curvature imposed upon it by the circular cross

sectional shape of the interlacing yarns. Peirce later

attempted" to apply the same ideas to the construction

of a three-dimensional geometrical model for plain

knitted fabrics; however, the more complex twisting or

wrapping nature of the interlacing loops in knitted

fabrics (compared to the two-dimensional weave crimp

shape in woven fabrics) gave rise to difficulties in defin

ing the actual geometry of interlacing.

Many variations of these geometrical models have

been reported in the literature for both woven and knit

ted fabrics, but the principles on which they are based

remain unaltered. In particular, it is always assumed

either explicity or implicitly that the geometrical shape is

constant for each model of the unit cell (either the

weave crimp or the knitted loop); derivation of the re

lationship between the geo-metrical parameters and such

fabric parameters as thread spacing, loop spacing, fabric

thickness, weave crimp, knitted loop length, etc, usually

forms the basis of the paper in which a particular

model is first presented. It is possible to use geo

metrical models to give an estimate of the "jamming"

conditions for both woven° and knitted fabrics", i.e.

the maximum number of warp or weft threads that can

be jammed into a particular woven fabric or the

maximum number of courses or wales that can be jam

med into a knitted fabric.

2 . Fabric Quality Control and

Dimensional Stability

Fabric geometrical models and the results obtained

from them are still quite widely used for the prediction

and control of fabric weight and dimensions. In this

way, they have proved to be very useful in controllingrelaxation or "consolidation" shrinkage and thus enhanc

ing the dimensional stability of fabrics during finishing,

laundering and wear. A review of the scientific litera

ture shows that the pioneering work of Doyle') and

Munden7) for plain-knitted fabrics was based on similar

principles to those embodied in the development of geometrical models. In this work, it was shown ex

perimentally that the course and wale spacings (i.e. thelength and width dimensions) for a very wide range of

relaxed plain-knitted fabrics are directly proportional to

the knitted loop length and accordingly are independent

of the conditions imposed during the knitting operation

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22 繊 維 機 械 学 会 誌

(c)

(b)

(c)

Fig. 2

The three projections of the central yarn axes

for the plain-knitted structure drawn to scale

and showing the course and wale spacing, p

and q: (a) projection in the fabric plane; (b)

and (c) projections perpendicular to the fabric

plane.

and of the actual physical properties of the knitting

yarn. Referring to Fig. 2 showing the three principal

projections of the plain knitted loop structure, these

proportional relationships may be written as follows:

p oc L

q oc

qlp=1. 3, a constant

where p and q are the course and wale spacings of the

fabric, respectively; and L is the knitted loop length.

The constants of proportionality in these expressions

were derived by Munden for relaxed plain-knitted wool

fabrics .

The above results have been widely interpreted to

provide basic experimental evidence for the constancy ofknitted loop shape for relaxed plain-knitted wool fabrics,

thus supporting the fundamental premise used to derive

the various geometrical models of knitted fabrics.

There has been a plethora of papers in the literature

throughout the past two decades dealing with the practi

cal ramifications of the proportionality between relaxed

plain-knitted fabric dimensions and loop length. Threeimportant lines of development can be discerned

throughout this period . Firstly, great strides forward

were made in the control of fabric quality (i.e. unif

ormity, dimensional stability and control of fabric weight

and width) by the introduction of positive feed units

and positive tension control devices on knitting machin

ery and by a general upsurge in the awareness of the

vital importance of loop length control during the knit

ting operation itself8)

The second line of development is focussed on the

meaning of fabric "relaxation" and the investigation Of

methods by which a fully relaxed fabric could be

obtained in practice9) is) " ) . It has been generally con

cluded that, despite the great ease with which knitted

fabrics can be extended, these fabrics should be allowed

to relax as freely as possible during finishing in order

that they approach as closely as possible their stable

shape and dimensions which are governed by the normal

physical principles of minimum energy stored within the

fabric structure .

The work on knitted fabrics was further developed

along a third path in order to investigate the control of

fabric quality and dimensional stability for other weft

knitted wool fabrics") i3) " ), such as rib constructions,

cardigan fabrics, interlock, Punto-di -Roma , double pique

and other double-knitted constructions . In these inst

ances, the unit cell of the fabric structure contains more

than one knitted loop and geometrical models have been

proposed for relaxed rib and interlock fabrics. For ex

ample, Fig. 3 shows the three principal projections of

loop interlacing for a geometrical model of interlock

fabrics proposed by the Postle"' . These models together

with associated experimental results for the dimensions

of relaxed rib, cardigan and interlock knitted fabrics,

may be regarded as a direct extension of results obtain

ed for relaxed wool plain-knitted fabrics where the unit

cell or repeat may be considered constant (or at least

(a) ( (c)

Fig. 3

The three projections of the central yarn axis for

the basic interlock knitted structure: (a) pro

jection in the fabric plane; (b) and (c) pro

jections perpendicular to the fabric plane. Thethree projections are drawn to scale.

P266

(繊 維工 学)Vol.34,No.5(1981) 23

reasonably similar) for all relaxed wool fabrics of that

particular construction.The situation, however, changes radically for double

knitted constructions, such as Punto-di-Roma or double

pique, having alternate plain and interlock (in the caseof Punto-di-Roma ) or rib ( in the case of double-pique)

courses; in these instances, it is possible to vary the

run-in ratio" by redistributing the length of yarn

between adjacent courses whilst keeping the total length

of the yarn in the unit cell constant. Thus, very large

variations in the shape of the structural unit cell occur

for relaxed fabrics of this type, but nevertheless, it is

still possible to express the fabric shape, weight and

dimensions in terms of, not a single loop length but, the

two lengths of yarn knitted into adjacent courses ( or

alternatively, the "tightness factor" and "run-in ratio"

parameters often derived from these two lengths). Fig.

4 shows the relationships") for finished Punto-di-Roma

double-knitted wool fabrics between the run-in ratio R

and the numbers of courses and wales per cm of fabric,

air flow permeability, fabric tensile and bending rigidities

for three levels of fabric tightness ( or "cover") factor

(14.0, 14.8 and 16.0 (tex )1/2cm-1). Although thesituation is clearly more complex for such double-knitted

fabric construction, it is still possible by understanding

the basic fabric geometry to predict and control the

(a) (b)

(c) (d)

Fig. 4

Relationships for finished Punto-di-Roma fabrics between run-in ratio R and:

(a) number of courses per cm. c and wales per cm. w (measured on the face of the fabric);

(b) air flow (litres air/m2/sec) measured by German standard method");(c load (gf.) required to extend fabric 25% in length L and width W directions; and

(d) fabric bending rigidities 13, and Bw for bending about an axis parallel to the courses andwales, respectively.

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24 繊 維 機 械 学 会 誌

fabric quality during the actual knitting operation and

further to ensure that a finished fabric of the required

weight is produced having good dimensional stability and

shape retention properties during laundering and wear.

The practical application of these relatively simple

principles of fabric geometry has thus greatly enhanced

our understanding and appreciation of the important

factors which determine the control and stability of

fabric weight, shape and dimensions. Because fabric di

mensional stability has been a traditional problem area

with respect to wool knitted fabrics and garments, it is

hardly surprising that the geometrical approach described

above has been largely concentrated in this area. Taken

into conjunction with the great progress made in the ap

plication of resin-based shrinkproofing treatments to wool

knitwear, it is now evident that technological solutions

are available to overcome most problem areas directly

related to dimensional stability of wool knitted fabrics.

In these areas, the work on fabric geometry has played,

and will continue to play, a vital part in the improve

ment and development of wool fabrics.

3. Simple Modes of Fabric Deformation

Woven fabrics have a relatively simple interlacing

geometry and much smaller extensibility when compared

to knitted structures. Accordingly, research workers

have put much greater emphasis on the study of woven

fabric mechanical properties than on studies of fabric re

laxation and dimensional stability during finishing and

laundering. Typical tensile stress-strain curves are shown

in Fig. 5 for a single uncrimped wool fibre, a crimped

fibre, a wool woven fabric and a typical wool weft

knitted fabric (in this last case showing the approximate

STRAIN (%)

Fig. 5

Typical stress-strain curves (plotted in terms of"relative stress" q

uoted as the percentage ofbreaking stress) for a single uncrimped wool

fibre, a crimped fibre, a woven fabric, and a

weft-knitted fabric showing the difference in wale

and course wise extension.

twofold increase in extensibility that occurs when the

fabric is extended parallel to the courses or width-wise

compared to the situation where the fabric is extended

paralled to the wales or length-wise).

The initial region of very low slope for the fabric

stress-strain curves shown in Fig. 5 represents the re

gion of decrimping and crimp interchange in wovenfabrics or of loop shape changes in knitted fabrics, for

which only very small fibre stresses are developed with

in the fabric. Because of the inherently high levels of"crim

p" in knitted fabrics (of magnitude between 100%and 600%) compared to woven fabrics (usually less

than about 25%), the initial. low-stress region is generally much longer in the case of knitted fabrics. In allfabrics, the initial low-stress region of a tensile stress

strain curve is followed by a very rapid increase in the

fabric stress developed when the weave crimp or knitted

loop has been fully extended so that further extension of

the fabric is possible only by extension of fibres within

the interlaced yarns; this region of rapidly increasing

stress is, of course, limited by the actual breaking stress

of the fibres themselves which governs the specific

breaking stress (or tenacity) of the fabric as a whole.

It is noteworthy that the yield region which is so

characteristic of the fibre stress-strain curve is almost

hidden in the knitted fabric curves and is only partially

evident for the woven fabric curve because of the av

eraging effect caused by the wide spread of fibre ori

entation within a fabric.

In practical terms, the extension or loads applied to

both woven and knitted fabrics during manufacture, fin

ishing, garment construction and during wear are gen

erally well within the initial low-stress region of their

characteristic stress-strain behaviour. Textile materials

are therefore very easily distorted during use to give

their familiar properties of drape, handle, comfort in the

sense of ease of body movement, and so on; at the

same time, the textile material is extremely resistant to

the application of high loads which generate very large

internal pressures acting between fibres in the fabric so

preventing any further fibre redistribution during fabricextension (leading to a kind of self-locking mechanism

of the fibres within the fabric). This mechanical com

bination of extreme ease of fabric deformation at very

low stress levels coupled with the self-locking nature of

the structure at higher stress levels is a unique and

vitally important characteristic of knitted and woven

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(繊 維 工 学)Vol.34,No.5(1981) 25

materials which explains their universal acceptance and

use throughout recorded history. A single wool fibre, or

indeed any other natural or man-made fibre, will only

exhibit a similar combination of mechanical properties if

the fibre contains a high degree of crimp and if the in

itial fibre decrimping region is included in the fibre

stress-strain behaviour (as shown in Fig. 5). Indeed,

fibre physicists could usefully pay more attention to the

detailed analysis of fibre decrimping curves, as these,

together with the decrimping curves of yarns unravelled

from knitted or woven fabrics, are of direct relevance

to our understanding of fabric mechanics.

In the case of woven fabrics, the low-stress mechani

cal properties of fabric bendine15) 16) 17) and shear18) 19)

have been extensively studied and attempts have been

made to relate these properties to complex perfor-mance

characteristics such as fabric drape, buckling behaviour,

handle, wrinkling behaviour, shape retention properties,

resistance to creasing and bagging, etc. Also, the un

iaxial and biaxial tensile properties20), 21), 22) of woven

fabrics have been studied both theoretically and experi

mentally, particularly for the relatively low fabric stress

levels likely to be met in practice. Because of the

trellis-like nature of a woven fabric, the fabric behaviour

in shear can be related to its extensibility in the bias

direction (i.e. at an angle of 45° to the principal warp

and weft directions of the fabric)23),24).

The tensile properties of knitted fabrics have been

studied at much larger strain levels25), 27) than for woven

fabrics but relatively little work has been reported for

shear properties26) 27) of knitted materials; this is not

surprising as knitted fabrics are generally less extensible

in the bias direction than in either of their principal

directions and consequently fabric shear represents a less

important mode of deformation in practice than in the

case of woven fabrics. These differences in fabric

mechanical behaviour between woven and knitted mat

erials are related directly to their different end-uses re

quiring characteristically different qualities of tailorability, extensibility and drape. It is possible to con

struct a fabric chart from measurements of fabric bend

ing and shear stiffness29). In Fig. 6, the shear stiffness

is plotted against bending stiffness for a very wide

range of commercially produced woven, double-knitted

and warp-knitted men's suiting materials. It is evident

from Fig. 6 that, although all fabrics were produced for

essentially the same garment application, they fall into

BENDING MOMENT, M0 . weft or M0. courses ( mg•Ef-cm)cm-1,

Fig. 6

A fabric chart showing the separation of fabrics

into distinct structural groupings. In this chart,

the shear stress •• is plotted against the bending

moment Mo (for the case where the bending

moment is applied parallel to the warp or

wales).

clearly defined areas of the fabric chart according to

their basic construction. Warp-knitted fabrics have the

highest resistance to shear because of the resistance of

the underlap in this construction to fabric extension in

the bias (or 45°) direction. Woven fabrics, because of

their essentially trellis-like construction, exhibit the lowest

resistance to shear. Double-knitted fabrics exhibit values

of shear stiffness intermediate between woven and warp

knitted fabrics; wool double-knitted fabrics exhibit gen

erally larger bending stiffness than textured polyester

double-knits because of the greater thickness and weight

of the wool fabrics. In each group of outerwear fabrics

shown in Fig. 6, there is a good correlation between

bending stiffness and fabric thickness or weight per unit

area such as that shown in Fig. 7 for finished woven

outerwear suiting materials29). Factors other than fabric

thickness or weight per unit area play a relatively minor

role in determining fabric bending rigidity for com

Thickness t(mm)

Fig. 7

Graph showing the relationship between thickness

t and the elastic bending rigidity B for finished

woven outerwear fabrics.

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26 繊 維 機 械 学 会 誌

mercially finished outerwear suiting materials. The flexi

bility of wool knitted fabrics of different construct

ions27),28) has been related to the details of loop inter

lacing geometry as well as to the fabric thickness.

4. Fabric Mechanics Using Force

Methods of Analysis

The fabric geometrical models described earlier in this

paper, although relatively successful when applied to thestudy of fabric shape and dimensional properties for

both woven and knitted structures, have been singularly

unsuccessful when applied to the analysis of fabric

mechanical properties. The basic reason for this lack of

success is that the assumption of an essentially arbitrary

geometry for the unit cell of a knitted or woven fabric

(inherent in a fabric geometrical model) does not allowreliable evaluation or prediction of the internal forces or

pressures acting between fibres and yarns as they interlace to form the fabric structure. Indeed, if in deriv

ing a geometrical fabric model, we assume that a yarn

is perfectly flexible, then no forces or internal stresses

are developed within the fabric when the yarn is bent

or twisted around the interlacing yarns to form the

shape of the weave crimp or the knitted loop. Further

more, there would be no strain energy stored within

such a structure meaning that the model could not be

reliably applied to predict or analyse fabric mechanical

properties.The realization of these difficulties in the 1960s led to

the rediscovery of a mechanical analysis of the plain

weave structure reported by Peirce in an appendix to

his 1937 paper1). In this analysis, Peirce considered the

shape of the weave crimp as governed by the condition

for which the internal forces, exerted by the warp

threads on the weft threads are exactly balanced by

forces exerted by the weft threads on the warp threads

as shown in Fig. 1(b). These internal forces, acting

within the plain-weave structure can be evaluated by

assuming that the yarn has linear elasticity in bending.

It is important to note that Peirce did not have to

make any assumption about the shape of the yarncross-section in this mechanical force analysis.

Grosberg and his co-workers and Olofsson have appli

ed this basic mechanical model of woven fabric derived

by Peirce as shown in Fig. 1(b) to the prediction and

analysis of woven fabric mechanical properties in ten

sion,20),21) bending,16),17) buckling30) and shear18). In this

way, it is possible to derive a stress-strain curve for the

fabric in any of these modes of deformation and to

evaluate the build-up in the level of internal forces or

lateral pressures acting within the fabric as it is deform

ed. A detailed study of the mechanisms of fabric de

formation is the refore possible thereby yielding relation

ships between the structural parameters of a woven

fabric and its important mechanical propertles. Such

work provides the basis for an understanding and ana

1ysis of the complex performance characteristics of

woven materials, such as handle, drape, wrinkhng

behaviour, dimensional stability, tailorability, shape re

tentlon, etc.

Progress in developing a successful mechanical model

for the plain-knitted structure was much slower than for

the plain-weave structure, because of the inherently com

plex three-dimensional nature of loop interlocking in a

knitted fabric as shown in Fig. 2. It could also be

argued that, because knitted structures are so very easi

1y deformed to very large fabric strain levels, the inher

ent limitations of the geometrical models are less evident

than for woven materials. Recent years have seen two

essentially parallel attempts31) 32) to develop a consistent

mechanical model of the plain-knitted structure based on

similar assumptions to those used originally by Peirce

for woven materials, i.e. linear yarn elasticity in bend

ing and balance of the internal forces of interlocking

within the fabric. However, in these instances, it was

not possible to completely avoid all assumptions about

the yarn cross-sectional shape or the nature of the loop

lnterlocking geometry. For example, Hepworth andLeaf31) and later Hepworth33) have developed a mechani

cal model assuming an incompressible yarn of circular

cross-sectional shape which bends according to linear

elasticity to form interlacing knitted loops with two

point-contact forces acting at each interlacing as shown

schematically in Fig. 8. However, a completely in

compressible yarn would also be inflexible, or al

ternatively, a flexible yarn would not retain a perfectly

circular cross-section when bent and twisted in three-di

mensional space. In other work, Postle and Munden5),

followed later by Shanahan and Postle32), assumed that

the three-dimensional continuous force distribution result

ing from two interlacing yarns twisted together to form

interlocking knitted loops, could be replaced in order to

simplify the analysis by a single force and couple

P270

(‘@ˆÛ•HŠw) Vol. 34, No. 5 (1981)27

(which are statically equivalent to the original force dis

tribution): in making this assumption, however, it is

again necessary to make some further assumptions about

the cross-sectional shape of the interlacing yarns in

fabrics. Clearly, such assumptions are liable to introduce

very large errors as the yarn is so easily distorted, com

pressed or flattened when interlaced to form a fabric.

The difficulties associated with assumptions related to

the nature and geometry of interlacing yarn contact in

knitted fabrics are demonstrated in Fig. 9 and 10. In

Fig. 9, two fabrics knitted from the same wool yarn, a

tight and a relatively loose construction, are shown

photographed under identical conditions (including

magnification). The differing degree of yarn compres

sion in the two fabrics is obvious. Fig. 10 shows the

two principal cross-sectional views of a wool plain

knitted fabric from which it is clear that any assump

tion about the cross-sectional shape of the interlacing

yarns must necessarily represent a gross simplification.

Fig. 8

Schematic representation of die two-point contact

system of forces for a plain-knitted structure

produced from perfectly elastic flexible but in

compressible long thin rods.

Fig. 9

Two plain-knitted wool fabrics produced from

identical yarn, photographed and reproduced

under the same conditions of magnification,

clearly showing the much greater degree of yarn

compression for the tightly constructed fabric

(top) compared to the relatively loose fabric

(bottom).

Fig. 10

Cross-sectional views across the two principal

directions for a typical wool worsted plain

knitted fabric: the top photograph shows a sec

tion cut parallel to a course (width wise): and

the bottom photograph shows a section cut

parallel to a wale (length wise).

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28 繊 維 機 械 学 会 誌

11. Conclusion

Knitted and woven fabrics are extremely complex

materials that do not conform even approximately to

any of the ideal features listed in Table 1 that are

normally assumed in engineering structural analysis and

mechanics, viz. low-strain deformation, structural

homogeneity and incompressibility, linear elasticity and

mechanical isotropy. The problems inherent in analysing

such complex structures as knitted and woven fabrics

may first seem to be intractable. Nevertheless, success

in this field leads directly to progress in the very practi

cal areas of objective specification and quality

standardisation of fabrics, development of new textile

materials with improved processing and performance

characteristics, optimisation of the use of different fibre

types (including blends), selection of yarn and fabric

constructions for particular uses, and development of

reproducible objective methods of testing and controlling

fabric mechanical behaviour during processing and use.

Very real progress has been made along the lines outlin

ed in the present paper.

Fabric geometrical models have played a vital role in

the improvement of procedures designed to control fabric

weight and dimensional stability during manufacture and

use. Structural analysis of knitted and woven fabrics as

essentially elastic structures of complex geometry has en

abled their deformation properties to be investigated in

tension, bending and shear.

Both geometrical and force methods of analysing

woven and knitted fabrics have been used extensively by

several authors in the past. However, the limitations of

these methods of analysis have become clearly evident

in recent years, particularly in relation to the prediction

of basic fabric mechanical properties and their detailed

interpretation. For example in the case of knitted

fabrics, the three-dimensional nature of loop interlocking

makes the development of a physically realistic geo

metrical or force analysis very difficult.

Many of these problems can be overcome by the

application of energy minimisation techniques to pro

blems in fabric mechanics. These energy methods and

their application to the study of elastic mechanisms of

fabric deformation are discussed in Part 2 of this series

of papers. In Part 3, the inelastic mechanisms of de

formation and recovery are analysed by both theoretical

and experimental methods.

References

(The following is a consolidated reference list for Parts 1 and2 of this series of papers.)

1) F.T. Peirce; J. Text. Inst ., 28, T45, (1937).2) J. Chamberlain; "Hosiery Yarns and Fabrics", Vol. II, Leic

ester College of Technology and Commerce, Leicester,

p.107, (1926).3) F.T. Peirce; Text. Res. J., 17, 123, (1947 ).4) J.W.S. Hearle, P. Grosberg and S. Backer; "Structural

Mechanics of Fibres, Yarns and Fabrics", Vol. I , Interscience, New York, 40, 330, (1969).

5) R. Postle, and D.L. Munden; J. Text. Inst., 58, T329,352, (1967).

6) P.J. Doyle; J. Text. Inst., 44, P561, (1953).7) D. L . Munden; J. Text. Inst . , 50, T448, (1959 ).8) D. L. Munden; J. Text. Inst . , 53, P628, (1962).9) K . Baird; Proc . Third Int . Wool Text . Res . Conf . , Paris,IV

, 295, (1965).10) R. Postle; J. Text. Inst . , 59, 65, (1968 ).11) J.J.F. Knapton, F.J. Ahrens, W.W. Ingenthron and W.

Fong; Text. Res. J., 38, 999, (1968).12) J.J.F. Knapton; Text. Res. J., 39, 889, (1969).13) R. Postle; Appl. Pol. Symposium No.18, Part II, J. Appl.

Pol. Sci., 1419, (1971).14) R. Postle and H. J. Suurmeyer; Anna les, Sci. Textiles

Beiges, No.1, 7, (1974).15) N. J. Abbot, M.J. Coplan and M.M. Platt; J. Text.

Inst ., 51, T1384, (1960).16) P. Grosberg; Text. Res. J., 36, 205, (1966).17) G.M. Abbott, P. Grosberg and G.A. V. Leaf; Text. Res.

J., 51, 345, (1971).18) P. Grosberg and B.J. Park; Text. Res. J., 36, 420,

(1966).19) L. R.G. Treloar; J. Text. Inst., 56, T533, (1965).20) B. Olofsson; J. Text. Inst., 55, T541, (1964).21) P. Grosberg and S. Kedia; Text. Res. J., 36, 71,

(1966).22) S. Kawabata, M. Niwa and H. Kawai; J. Text. Inst.,

64, 21, 47, 62, (1973).23) W.F. Kilby; J. Text. Inst., 54, T9, (1963).24) B. Olofsson; "Rheology of Textile Fabrics" in `Rheology',

Vol. V., ed. F.R. Eirich, Acadamic Press, (1969).25) W.J. Shanahan and R. Postle; J. Text. Inst., 65, 200,

Table

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(繊 維 工 学)Vol.34,No.5(1981) 29

254, (1974).26) G.A. Carnaby and R. Postle; J. Text. Inst., 65, 87,

(1974).27) R.J. Hamilton and R. Postle; Proc. Fifth Int. Wool Textile

Res. Conf., IV, Aachen, 434, (1975).28) R.J. Hamilton and R. Postle; Text. Res. J., 44, 336,

(1974).29) V.L. Gibson and R. Postle; Text. Res. J., 48, 19,

(1978).30) P. Grosberg and N.M. Swani; Text. Res. J., 36, 338,

(1966).31) B. Hepworth and G.A.V. Leaf; "Studies in Modern

Fabrics", ed. P.W. Harrison, The Textile Institute, Manchester, p.181, (1970).

32) W.J. Shanahan and R. Postle; Text. Res. J., 40, 656,

(1970).33) B. Hepworth; J. Text. Inst., 69, 101, (1978).34) S. De Jong and R. Postle; Text. Inst. and Ind., 15, 376,

(1977).35) S. De Jong and R. Postle; "Energy Optimisation Methods in

Fabric Mechanics". Paper presented at NATO AdvancedStudy Institute on "Mechanics of Flexible Fibre Assembles",Greece, (1979).

36) J.W.S. Hearle and A. Newton; Text. Res. J., 37, 778,

(1967).37) J.W.S. Hearle and W.J. Shanahan; J. Text. Inst., 69,

81, (1978).38) H. Goldstein; "Classical Mechanics", Addison Wesley,

(1968).39) S. De Jong and R. Postle; J. Text. Inst., 68, 350, 362,

(1977).40) S. De Jong and R. Postle; J. Text. Inst., 68, 307, 316,

324, (1977).41) S. De Jong and R. Postle; Text. Res. J., 48, 127,

(1978).42) A.L. Knoll; J. Text. Inst., 70, 355, (1979).43) R. Postle and S. De Jong; "Development of Woven Fabric

Mechanics by means of Optimal-Control Theory". Proc.Text. Inst. Conf:, New Delhi, p.234, (1979).

44) S. De Jong, R.C. Dhingra and R. Postle; "An Analysis ofWoven Fabric Shear using Energy Optimisation Techniques".Paper presented at Int. Wool Textile Res. Conference, Pretoria, (1980).

45) B. Olofsson; J. Text. Inst., 58, 224, (1967).46) S. De Jong and R. Postle; "Mechanisms of Set and Recov

ery in Wool Yarns and Fabrics". Paper presented at Int.Wool Textile Res. Conference, Pretoria, Vol.IV,(1980).

新 刊 紹介

繊 維 の 仕 上 加 工

〈原 題〉Textile Finishing(Papers of the 62

nd Annual Conference of the Tex

tile Institute)

〈編 集 ・発 行 〉The Textile Institute.

〈発 行 年 〉1978年9月

〈体 裁 〉A4判,320ペ ー ジ,図89,表44,写 真12,

ソフ トヵバ ー

〈価 格 〉Stg.£11.00

本書は,英 国繊 維学会(The Textile Institute)第62

回年次大会 における研究発表講演集 で,17件 の論文が収

録 されて いる.い ず れも,去 る1978年9月19～21日 に,

英国エ ジンバ ラで発表 された論文 であ る.

染色仕上の分野は,近 年 ますますその重要性 を増 しつ

つ ある.新 しい素材の 出現,特 に合繊 加工糸織編物 の普

及 によ り,新 しい染色仕上方 法の開発が急がれてい る.

さらに,廃 水 によう環境汚染 の問題,オ イル ショックに

伴 う省エネルギ ・省資源 と,い ずれ も困難 な問題が山積

してい る.し か し,染 色仕 上の工程は,従 来 からやや も

すれば勘 や経験 に頼 るところが大 きく,科 学的 な研究対

象にな りに くい分野であった.そ ういった意味 からも,

この種 の まとまった論文集は,我 国の関係者 にとって,

絶 好の刺 激 になるで あろう.ま た,前 刷 とは違 い.紙 数

を制限せず に,具 体的 なデー タが豊富 にのせ てあるのも

ありがた い.

参考までに,次 に収録論文の標題 を紹介 する.く わ し

い内容は,海 外繊維 技術文献集,1981年5月 号,p.37～41,

45,46及 び50の 文献抄録 を参照 されたい.

(1)繊 維 の仕 上加工(基 調報告)

(2)綿 布の液体 アンモ ニア処理― 特にイージ ケア仕

上に対す る前処理 と して

(3)漂 白 とバ ッ ト染色 のモニ タリングと制御

(4)66ナ イロン織物 のカ レンダ仕 上

(5)合 成繊維 で作 った産業資材用織 物の特殊仕上加工

(6)高 周波加熱 によ る天 然繊維 の転 写捺染

(7)樹 脂加工 をしたセルローズ製品の転写捺染

(8)布 の風合 いの改良

(9)紡 毛及 びそ毛 用連 続仕上機「EKOFAST」 の開発

(10)防 縮羊毛 に防縮 ポ リマ を塗布す るための大浴比

吸尽法

(11)ポ リエステ ル品 ならびにポ リエ ステル/セ ルロー

ス混紡 品の染色 におけるプロセ ス コ ントロール

(12)イ ージ ケアー加工における仕上液 の低 ア ドオ ン管理

(13)カ ーペット バッキ ングの新 しい仕上 法

(14)羊 毛混紡布の吸 引脱水

(15)合 成繊 維及 び天然繊維 のあ らゆ る混紡布の乾燥方

法

(16)繊 維の仕上加工 におけ る乾燥機管理の諸問題

(17)全 幅織物の予備処理 のための種々のスチーマの設計

P273