Bending of Woven Fabrics - JST

Bending of Woven Fabrics

Tatsuki Matsuo, Member, TMSJ

Katata Research Institute, Toyobo Co. Ltd., Otsu, Shiga-ken

Based on Journal of the Textile Machinery Society of Japan, Transactions, Vol. 21, No. 11, T260-274 (1968)

Abstract

This article expands the theories announced by Livesey-Owen and Grosberg on the bend-ing deformation of woven fabrics. A theoretical equation (11) has been derived. Various factors which determine the bending deformation properties can be arranged as shown in Fig. 4. The bending movement vs curvature curves of various woven fabrics have been mea-sured. The effects of single filament denier, yarn density and various finishing treatments have also been examined. The bending behaviors of woven fabrics of cotton, viscose and other synthetic fibers have been compared. Data obtained from the experiments have been analyzed on the basis of the equation (1).

KEY WORDS: BENDING, WOVEN FABRICS, HYSTERESIS,

FRICTION, REGENERATED FIBERS, CELLULOSE, POLYESTER

ACRYLIC FIBERS, DESIZING, COTTON, HANDLING, FINISH

SHEARING, FRICTION, COEFFICIENT OF

FIBERS, WOOL, HEAT-SETTING, DENIER,

1. Introduction The many published works on the bending of woven fabrics mostly deal with the method of measuring bending

rigidity and treat woven fabrics as a continuous elastic body. In recent years, the bending behaviors of woven fabrics have been studied in connection with the bending

property of yarns and the construction of woven fabrics. It appears that Livesey and Owen have been instrumental

in the advancement of both experimental and thereotical

research in this field. They designed a simple apparatus to measure the bending moment-curvature curve, a funda-

mental character of bending behaviors. They measured the bending-moment curves of a few fabrics and qualita-

tively explained two terms which determine these curves. The first term, the intercept of bending moment, was

designated as one originating from inter-fiber frictions.

The second term, the slope of the curve, was explained

as the sum of the bending rigidity of yarns and an incre-mental term arising from geometrical hindrance produced by intersecting yarns. Grosberg analyzed the first in detail

and suggested a theoretical equation on it. Livesey-Owen's explanations seem basically reasonable.

Grosberg's theory on the first term also seems reasonable. Another term given by Livesey-Owen, however, seems to

be left largely unexplained. Livesey-Owen dismissed this

term as the effect of geometrical restraint generated by the intersecting of yarns and said the effect of this term

could not be changed even by set-treatment. Grosberge's data have shown, however, that this term can vary greatly,

depending on the degree of force of contact between inter-secting yarns.

Vo1.15. No. 1 (1969)

There are many other experimental data showing that

this term can vary to a large extent, depending on the

finishing treatment. Shinohara, et al, think that a yarn of

a woven fabric in the area of contact with intersecting yarns

is completely kept from bending and, in fact, makes a fixed

end. It is doubtless difficult to explain, with these two

models, the 2nd term described above.

Grosberg calculated the effect of inter-fiber friction

arising from the force of inter-yarn contact and derived a

theoretical geuation on the 1st term. The 2nd term also

needs to be explained in its relation to the force of inter-

yarn contact. It is usually not possible to determine the force of contact

acting between two intersecting yarns in a textile from their

mutual geometrical position only. The reason is that stress

relaxation makes it impossible to connect residual stress

within a yarn uniquely to apparent strain. Finishing treat-

ments relax residual strain in warp and weft and put the

yarns in a fabric in forms suited to fabric construction.

Therefore, it seems safe to think the force of inter-yarn

contact in a finished fabric is much smaller than in a grey

fabric. Accordingly, the second term, too, had better be

treated as the force of inter-yarn contact.

We have calculated this 2nd term through the force

of inter-yarn contact and derived a general theoretical

equation on bending moment vs the curvature charater-

istics of woven fabrics by connecting up Grosberg's theory

on the 1st term with our calculation of the 2nd term. We

have also measured bending moment vs the curvature

curves of various woven fabrics. The effects of single-

filament denir, yarn density, various finishing treatments

19

and the traits of fabrics made of various textile fiber ma-terials are discussed here on the basis of this general equa-

tion.

2. Theory Let us try to deIuce the relation between the bending

moment and curvature of a woven fabric from given bend-

ing characteristics of a yarn and given force of inter-yarn contact which has a uniform distribution as shown in Fig. 1

(a). Where yarns have a linear relation between bending

moment and curvature, their local bending rigidity kY is

definable by the equation duds where i is the bent angle of yarns, M is the total bending

moment needed to bend yarns, s is the tangential

cordinate of the yarn axis. From the above equation we obtain :

.4-=iAB=- J Mds ........................ (1) Pe k Y AR The suffix AB means the total region of area A; O~x<2b

and area B; -2b<x<0, i AB is the bent angle of a yarn in region AB, pe is the radius of the curvature in a bent fabric, as shown in Fig. 1(a). Assuming MY to be the bend-ing moment needed to bend yarns to radius pe of curvature, then their bending rigidity is

:.kY=MY Pe SAB ................................. (2 46

where SAB is the tangential length of the yarn axis in region AB. Total bending moment M acting to bend yarns is

believed, in the light of the following equation, to consist of three components:

M=Me+Mc+Mfi .............................. (3)

First component M e is the external bending moment acting on a fabric. Second component Me is the bending moment arising directly from the force of inter-yarn con-tact and its distribution. Third component M fI is the in-cremental bending moment arising from the inter-fiber friction within yarn.

Before a fabric is bent, contact forces f A and f B are equal in distribution density and the bending moment diagram makes the dotted line in Fig. 1(c). Therefore, f Mcds=O

When fabric is bent, the radius of the curvature of the axial curve in area A decreases and then the distribution of the force of contact in this area broadens. The radius in area B increases and the force of contact concentrates on point x=-b. In other words, CA becomes larger than CB, as shown in Fig. 3(a). Therefore, Me makes the solid line in Fig. 1(c) and fMds<O. AB

Eqs. (1), (2) and (3) lead to this further equation:

Me=MY- 1 J Mfz dS- 1 J Me ds ...... (4) SAB AR SAB AR

(a) Axial curve of yarn and distribution of force of contact

(b) Shearing force diagram generated by force of contact

(c) Bending moment Mc generated by force of contact

(d) Relation between bent angle and radius of curvature of bent yarn

Fig. 1 Axial curves of yarn and the effects of force of

inter-yarn contact

20 Journal of The Textile Machinery Society of Japan

Eq. (4) can be expanded to apply to a case where the relation between MY and 1 /pe is non-linear. MY is approxi-mately equal to the bending moment of the residual yarns remaining in a fabric after all the interesing yarns are removed. Generally, there is a non-linear relation between bending moment MY of yarns and curvature 1/9e, as sche-matically shown in Fig.2. This relation is measurable by the experimental method described in chapter 3-2(i). Assume that this relation is given in advance. MY can then be approximated by the following equation, as shown in Fig. 2 .

MY=-pY-±Mfy ................................. (5) e Intercept oa in Fig. 2 corresponding to M fV. M ft was

given by Grosberg as shown in the following equation :

-1- Mfg=-1-,i Ve1 ......................... (6) nY 8

where V is the total force contact between warp and weft;

e~ is the thickness of yarn; µ is inter-fiber frictional co-

efficienct; and nY is yarn density. Assuming that w is the ratio of the area where inter-

fiber slippage within a yarn is resisted by the force of inter-

yarn, we get :

1 JMfids= 1 ~Ve1 m nY .............(7) SAB AB 8

Now to calculate moment Me originating directly from

the force of inter-yarn contact. To avoid complications

in calculation, we assume that the uniform pressure f A of inter-yarn contact per unit length acts in area

b-cA<x<b+cA

and uniform pressure fB per unit length acts in area b-cB<x<-b+cB, as shown in Fig. 1(a). In this case, the following relaction is obtained:

V=- 2fBCB= 2fACA

The shearing force diagram and the bending moment diagram for this case are given in Figs. 1(b) and 1 (c). Mc is obtained from the equations:

nY Me 2 Vx (-b+cBZ x/b-cA)

= 1 C-x2+ 2bx--(b-cA)2) 4 CA

(b-CA/x/ b)

, C-x2 + 2bx- (b-CB) 2) =-! 4 CB

(-b+CB>x>-b)

1 f Me d s=2f b`Cn _ V x+- V (_x2 nY AB b-CA 2 4 CA

+ 2 b x-(b-CA)2) (ds )dx dx

b _CA(_x2 2 CA CB Jb-CB ,

+ 2bx- (b-CB) 2)+CB(-x2

+ 2 bx - (b-CA)2) d s d x d

fb-_--- V -J ,B (x+6+cA)2(-~ d x 2 CA b-rA dx

- V (CA-CB) jh CCA CB 2 CA CB n -CB

_(x_b)2J(d s d x d x

Therefore, Approximating ds by approximate value (sAB/4b)dx,

we get : fly -L J Me ds= - V (CA+CB) (CA-CB) 4

b

SAB J AB 6 .................. (8)

Before a fabric is bent, cA=cB=c. When a fabric is bent in curvature 1 / pe, CA increases and CB decreases by reason of the geometrical relation illustrated in Fig. 3(b). In this case, the following relations are obtainable:

cA-c c Cos j c-CB = c Cos j e2 Pe e2 Pe

where e2 in the radius of curvature of the surface of con-tact, as shown in Fig. 3(b). From these relations, we may reasonably assume the following equations:

CA+CB= 2 C

CA-CB ' e2 Cos j 2c PP . (9)

Fig. 2 Bending hysteresis of yarns and fabrics

Vol. 15, No. 1 (1969) 21

From eq. (9), eq.(8) reduces to

.. l j~Mc dsL: V (C )2b e2 nY cos j .•. (10) sAB R 6 b Pe

Introducing eqs. (5), (7) and (10) into eq. (4) gives u~ the theoretical equation on the bending behaviors of wover fabrics :

Me=±MfF+KFP 1 (11)

e where

Mfl~MfY+ 8 t1 Vel w nY ............... (11 a)

KF=KY+V-)Zbe2 • cos j • nY (lib) 6(b

The term of M fF and KF in eq. (11) correspond to the

intercept (the line ob in Fig.2) and the slope in the bending moment vs curvature curve of a woven fabric. Both the terms are experimentally obtainable. Non-linear component M fY in the bending hysteresis of yarns can be expressed by

ns nY RMfY= -- 4 _f' ei U+Nlfs .................. (12)

where U is the internal mean pressure present within an isolated yarns; M f8 is the intercepts in the bending hys-teresis loop of single filaments within a yarn.

It is believed that KY can be determined from yarn den-sity fly, the number ns of single filaments within a yarn, their bending rigidity, the corss-sectional shape of a yarn, twist factors, etc. and can be approximately expressed by the equation

KY = 4-6- nx ns k, X the correction term SAB arising from twist, etc

..................(13)

The theory advanced above can be summed up as in Fig. 4. The following equation on force V of inter-yarn contact in unrelaxed grey fabrics was presented by Peirce and Grosberg :

Bending hysteresis of woven fabrics

Me- ~e

intercept M fF

slope KF

intercept M fY (l2) of yarns

(11-a)

the frictional term originating from force of inter-yarn contact

1uVeiw 8

slope KY (13) of yarns

(11-b)

slope originating from force of inter-yarn contact

6(6 )2b ez cosj

a. b.

c. d. e.

a.

b.

c. d. e.

a. b.

C.

d.

e.

a. b.

c.

C.

intra-yarn pressure U frictional coefficient between fibers thickness of a yarn ei yarn density fly intra-fiber frictional

term M fs

the proportion of restraint area frictional coefficient between fibers s contact force v thickness of a yarn el yarn density nr

yarn density fly the number of single fiber within a yarn ns bending rigidity of single fiber ks the crimp ratio of yarn axis 4 b/s.(„ correction term

contact force v the ratio of length of contact c/b yarn density nY thickness of a yarn e2 cosine of contact angle cos j

Fig. 4 Factors Contributing

of Woven Fabrics.

to Bending Hysteresis

V==(4 sin8/b2) x kY

Generally, finishing treatments relax yarns in fabrics

greatly and reduce stress arising from weaving within a yarn. The swelling and shrinking of the cross-sectional

Fig. 3 The model of variations in length of contact

between warp and weft


area in single filaments by various finishing treatments, the stretching of fabrics by tentering etc. also influence force of inter-yarn contact and length c of contact. Force of inter-yarn contact and length c of contact make major factors in the bending behaviors of woven fabrics, but they cannot be easily determined from external con-ditions. Grosberg measured the shape of the axial yarn crimp and obtained the value of V by the equation V=(4sin 8/b2) x k y. To the best of our knowledge, however, this method of measuring V is highly inaccurate. It is necessary to develop a more accurate method to evaluate the values of V and c.

Here the author presents briefly a theory on the shearing of woven fabrics which may be useful in estimating the value of the product V~. When a woven fabrics is subjected to shearing of a type which deforms the fabric under a slight, constant normal load, the shearing force vs the shearing angle curve is usually as shown in Fig. 5 (a). It is believed that F f in Fig. 5(a)

reflects the frictional motion by which the angle between warp and weft changes. Assuming that a fabrics is de-

formed to shearing angle 1s by shearing force F f, volume

W of work done by the frictional motion per crossing area,

can be approximated, as shown in Fig. 5 (b), by the follow-ing equation:

W-:2 xO,dx=..~--VI Bs 02

The work done per unit area of the fabric is

Ff d 4 s b b~_ Therefore,

1 cVt FJ 8 b b ................................. (14)

With the aid of eq. (14), the value V can be estimated from the experimental value of F f in shearing.

3. Experiments 3-1. Samples

Table 1 gives data on the samples used in our experi-ments. The twist factors of samples C-1, 2, 3, 7 and 9 are 3.5; those of samples C-4, 5, 6 and 8 are 4.5. The samples of the series B were resin-finished by urea-formalin. The amount of resin in those fabrics was 4 % after resin-finish-ing and about 2 % after washing. The samples of the series C were finished by urea-formalin resin. The amount of resin was about 7 % after resin-finishing and about 2 after washing. Desizing was done in water at 80 °C. 3-2. Experimental Methods

(i) Bending moment vs curvature curves of fabrics and yarns. :

The apparatus described by Livesey-Owen was used. The bendings of yarns were measured with the specimens of fabrics of which crossing yarn was removed. KF and KY are the averages of the slopes in curvature 0 in forward and backward directions.

(ii) Flexural rigidity measured by Clark's method. (iii) Shearing force vs shearing angle curves measured by Morner and Eeg-Oloffson's method. The normal load was 2.7 g/cm2.

(iv) Young's modulus of fibers : The initial slopes of stress vs strain curves were measured with an Instron tensile tester at an elongation rate of 100%! min.

(v) Inter-fiber frictional coefficient measured by Roder's method.

4. Experimental Results Some examples of the bending moment vs curvature

curves, obtained experimentally in the samples of the series A to G, are given in Figs. 6 to 11. The characteris-tic values of these curves are summarized in Table 2,

(a) Typical shearing hysteresis of woven fabrics

(b) Model of shearing deformation of woven fabrics Fig. 5

Vol. 15, No. 1 (1969) 23

Table 1 Data on Samples

Table 2 (a) Bending Characteristics of Cellulose Fabrics

I .. I


Table 2 (b) Bending Characteristics of Cellulose Fabrics at Dry and Wet State

(c) Bending Characteristics of Polynosic Poplins

(d) Changes in Bending Hysteresis by Heat-Set

Vol. 15, No. 1 (1969) 25

The variations in the characteristic values of bending hysteresis by desizing and heat set are summerized in Figs. 12(a) and (b). Some experimental results of shearing force vs the shearing angle are given in Figs. 13 and 14 and Table 3. The various data on the properties of fabrics, yarns and single filaments are summarized in Table 4. 5. Discussion

It would be very helpful if it were possible to calculate the bending moment vs the curvature curve for a given fabric on a purely theoretical basis. As it is, theoretical equation (11) includes terms V, and w, to which it is very difficult to give reasonable values, because they depended delicately on how a fabric is constructed, on the methods finishing, the properties of fiber, etc. and are not easy to evaluate. We will proceed to investigate whether theoretical results on bending and shearing hysteresis consist with experimental results, and then analyze the bending cha-

racteristics of various fabrics by deviling them into the four terms included in eq. (11).

Eq. (14) shows intercept F f of shearing hysteresis to be

proportial to c V. Both KF-KY and M JF-M fY are assumed to be incremental functions of the values of cV Therefore, these values ought to increase with an increase in F f. The experimental results shown in Figs. 13 and 14 and Table 3 bear out this assumption. Now about the difference in deformation characteristics between woven fabrics of cotton and regenerated (viscose and polynosic) fibers. Fig. 7 and Tables 2(a) and (e) show that cotton fabrics (and fabrics blended with cotton) far exceed regenerated fabrics in the value of M fF. This comes mainly from the difference between them in the values of M fF-M fY. Cotton fabrics (and fabrics blended with cotton) exceed regenerated fabrics in the values of KF-KY also. This explains the very large values of KF in sample D shown in Table 2(e).

Tadle 2 (e) Bending Hysteresis of Fabrics Made of Various Fibers

(f) Bending Hysteresis of Serge [5]

Table 3 Relations between Bending and Shearing Hysteresis


The analytical diagram in Fig. 4 suggests that the value of M fF-M fY depends on the inter-fiber frictional coefficient on the force of inter-yarn contact and on the length of inter-yarn contact in fabrics of uniform construction. Generally, the inter-fiber frictional coefficient is larger in cotton fibers than in regenerated fibers, as shown in Table 4. Yet there are notable differences in the value of M fF-M fY between samples A-1 and A-2 and between samples D and C-9. It seems difficult to explain these differences only on the basis of inter-fiber frictional coefficients. There are also differences in the values of KF-KY between

cotton fabrics (and fabrics blended with cotton) and re-

generated fabrics. This facts can be theoretically explained as being traceable to the effect of the difference in the force of inter-yarn contact and in the length of inter-yarn contact between warp and weft shown in Fig. 4.

After all, it seems quite all right to attribute the differ-ences in bending hysteresis between cotton fabrics (and fabrics blended with cotton) and regenerated fabrics to two factors. The first factors is that cotton fiber exceeds regenerated fibers in the value of inter-fiber frictional coefficient. The second factor is that warp and weft in cotton fabrics intersect each other more closely than in regenerated fabrics. The bending hysteresis of cellulose fabrics in dry and

wet states are summarized in Table 2(b). Fig. 9 and Table 2

(b) show that a heavy increase in M fF and a heavy decresae in KF occur in wet state. This is presumably because the intersection between warp and weft gets tightened by swelling in cellulose fibers and by a drop in the value of Young's modulus of single fibers in wet state.

Table 4 Properties of Fabrics, Yarns and Fibers

Vol. 15, No. 1 (1969) 27

However, the data on samples C-9 and D in Table 2(b)

show that the differences between bending hysteresis in dry and wet states are much smaller in the cotton fabric

than in the polynosic fabric. This presumably comes from a difference in the degree of wet swelling between the two

fibers. The large difference between the dry and wet values

of M1 F in samples G and C-9 seems to suggest that regene-

rated fibers in wet state swell more than do cotton fibers;

that while they remain swollen, warp and weft are in tight

contact; but that when the fibers return from wet to dry

state, the cross-sectional area of the fibers shrinks, thus

loosening the warp-weft contact.

This suggestion is borne out by the shearing hysteresis

curves shown Figs. 13 and 14. Polynosic fabric B-1 in wet

state is similar in bending hysteresis to cotton in dry state.

Fig. 6 Heavy cotton fabric (bent in warp directio n)

Fig. 7 (a) B-4 viscose singham (washing)

(bent in warp direction)

Fig. 7(b) B-6 Cotton-polynosic gingham

(washing) (bent in warp direction)

Fig. 8 (a) C-1 polynosic poplin (scouring)



This fact suggests that the inter-yarn contacts in Poly-

nosic fabrics in wet state are close in tightness to those in

cotton. The bending characteristics of polynosic poplins (the

samples of the series C) are shown in Fig. 8 and summa-rized in Table 2(c). Resin-finished fabrics have much larger

values of KF than scoured fabrics do, but after washing,

they come close to scoured fabrics in these values. The

very large values of KF in resin-finished fabrics come from

the large values of KF. The latter apparently arises from

the higher values of Young's modulus in single fibers,

as shown in Table 4. It is common knowledge based on

Fig. 8(b) C-2 Polynosic poplin (resin finishing)


Fig. 9 G Polynosic twill (bent in warp direction)

F g. 10 (a) E-1 Polyester poplin (gray fabric)


Fig. 10 (b) E-2 polyester poplin (desizing)

Vol. 15, No. 1 (1969) 29

experience that a fabric stiffens with an increase in the denier of single fibers even if yarn denier remains station-ary. Consider the value of KF. nsds=dY where ds is single fiber denier; and dY is yarn denier. Beacuse ks = C SEd s2 (C3 being constant), the following equation is obtainable from eq. (3) :

KY =.4 b_ nY C~ E d Y d s X (the correction term arising SAR

from twist etc).................................(13') This theoretical equation also shows that KY is the incre-mental function of single-filament denier d8. Experimental results shown in Table 2(e) agree exactly with this theory. The difference between single-fiber deniers 1.2 and 1.5 reflects the difference in the values of KF between samples C-1 and C-9, and between samples C-4 and C-8. The ratio of KF between samples made of 1.2d and 1.Sd fibers is about 1.3, which is nearly equal to the ratio 1.5/1.2=1.25 This corresponds to eq.(13) showing that KY is propor-tional to d8. The values of KF vary as much with single-fiber denier as the values of KY do. Variations in weft yarn density result in differences in

the values of KF and 2M fF between samples C-1 and C-7 and between samples C-9 and C-4. At a glance, both KF and 2M fF seem to vary in proportion to yarn density nY, but the experimental data in Table 2(C) show that KF increases by about 1.4 times and 2MJF by about 1.5 times if yarn density increases by about 1.1 times from 28.8 to 32.0. This is presumably because an increase in

yarn density increases the force of inter-yarn contact force in addition to the simple effect associated with an increase in fly.

The effects of desizing on polyester poplins are summa-rized in Fig. 10 and Table 2(d). Desizing greatly reduces

the values of both KF and 2MJF and KF-KY and 2(M fF-

M 1Y). The declines in 2M fY and KY are understood to mean a decrease in the internal pressure of yarns and the

consequent loosening of a cluster of fibers in the yarn by desizing. There is a great difference between undesized and de-

sized fabrics in the effect on them of heat-setting at about 160°C as shown in Fig. 12 (a). Therefore, the declines in the values of KF-KY and 2(M fF-M fY) are attributable

mainly to a decrease in the cross-sectional area of a

yarn and other various effects produced by the removal of the sizing agent, rather than to the effect of

heat setting in desizing. The effect of heat-treatments on the bending character-

istics of synthetic fabrccs are summarized in Fig. 12 and

Fig. 11 Prue-wool serge (bent in warp direction)

Fig. 12 (a) Changes in bending characteristics of a polyester poplin by heat-treatments in fixed length

Fig, 12 (b) Changes in bending characteristics of acrylic plain-weave worsted fabric heat- treated in hot water and in fixed length


Table 2(d). Heat-treatments are not as conspicuous in their effects as desizing, but they do produce effects which are not to be ignored. Fig. 12(a) shows that a fabric becomes more pliable with an increase in heat-treatment tempera-ture but stiffens if the temperature rises above a certain critical degree. These phenomena in bending character-istics correspond exactly to variations in the crease angle vs heat-treatment temperature curves~4~. The values of the characteristics of sample H are notably affected by heat-treatments. The values of KF and 2M1F drop by heat-treatments, but the drops are attributable chiefly to the decrease in the values of KF-KY and 2(M JF-M fy). These phenomena can be explained by the fact that, although weaving produces strain, which, in turn,

generates large force of inter-yarn contact in a grey

fabric, heat treatment produces thermal stress relaxations, which reduce the force of inter-yarn contact greatly. The bending characteristics of poplins made of different fibers are summarized in Table 2(e). It reveals interesting features of fiber types. A distinctive feature of polyester is that it equals cotton in the value of 2M fF.

This presumably explains why polyester fabrics have cotton-like traits of handling. Polynosic ranks lowest in the value of 2M fF and cotton and polyester highest, with acrylic fibers coming in between. Note that these facts about 2M fF are determined not from the value of 2M fY but mainly from the value of 2(M fF-M fy).

As we have said, the inter-yarn intersections in Poly-nosic fabrics are loosened by the change of the cross-sectional area from swelling to shrinking: This presumma-bly accounts for the small values of 2(M fF/M fy) in poly-nosic fabrics. The reason for the very large values of M fF and KF in sample D can almost be explained by the ch trac-ter of cotton fibers, although the effect of mercerization has to be borne in mind.

The swelling and shrinking of the cross-sectional area in synthetic fabrics do not come from ordinary finishing treatments. Therefore, they should have large values of 2(M fF-M fY) than regenerated fabrics. Why, then, do acrylic fabrics have rather smaller values of 2(M fF-M fy)? Presumably because the force of inter-yarn contact in them is brought down to a very low level by the nearly complete stress relaxation generated in hot water above 60°C.

Fig. 11 and Table 2 show the bending characteristics of serge. It is worth noting that they take relatively small values of 2M fF in relation to those of KF. The values of 2(M fF-M fY) and KF-KY, especially, are very small. Sample H-5, an acrylic plain-weave fabric made of worsted yarns, also has smaller values of (KF-KY)/KY and 2(M fF-M fy/KY than do plain-weave fabrics made of

yarns spun by the cotton system. Samples I-1 and I-2 have still smaller values. Fabrics blended with polyester have larger values of both 2M fy and 2(M fF-M fy than do

pure-wool fabrics. This difference is not limited to samples I-1 and I-2 but seems general in comparisons between pure wool fabrics and blended fabrics. It seems that worsted fabrics, unlike cellulose fabrics, are

required to have very small values of M fF, i.e., pliability and resilience. It is interesting that polyester fibers have an action to increase the value of M fF. This is true of the

poplins mentioned in Fig. 2(e) and also of worsted fabrics. The ratio of warp yarn density to weft yarn density in

polpins is about 2:1. The measured values of KF given in Tables 2(c) and 2(d) reflect this ratio fairly accurately. However, experimental data on 2Mf F show that weft and warp are nearly equal in values. Therefore, the values of 2M fF per thread for weft are about twice those for warp. There can be no difference in the value of M fF

Fig, 13 Shearing hysteresis of cotton-polynosic

gingam H: shearing angle

and Polynosic

Fig. 14 Shearing hysteresis of polynosic twill (sample in dry and wet states

G)

Vol. 15, No. 1 (1969) 31

between warp and weft, yet it turns out that weft far ex-

ceeds warp in the values of MJF-M JY. This is presumably

because weft has much larger values of restrained area w

than does warp, as shown by the schematic sectional shapes

of warp and weft in Fig. 15.

We notice in Table 2(a) large differences in the value of KF-KY between samples B-1 and 2, on the one hand, and B-5 and 6, on the other; in Table 2(d) between samples E-1 and E-2, on the one hand, and samples H-6 and H-5, on the other; between the various samples tabulated in Table 2(e). Shinohara, et al. and Livesey, et al. dismiss the differ-ence between KF and KY as the effect of the geometrical restraint arising from the intersecting of yarns. It seems difficult throughly to explain this difference from such a standpoint. Note that both KF-KY and 2(M fF-M fY) are reduced measurably by the heat-treatments described in Fig. 12 (b). This being the case, it seems reasonable to discuss the KF-KY difference as we discussed the 2(M JF-M fY) difference i.e., on the theory proposed in chapter 2 and which is based on the force of inter-yarn contact and its distribution. It is a fact of major importance that the bending beha-

viors of woven fabrics can be approximated by Fig. 11, which means that they can be approximately expressed by the two terms, intercept M fF and slope KF. Many methods of measuring the bending rigidity of woven fabrics have been suggested by Peirce and others. They are mostly based on the assumption that the bending of woven fabrics can be sufficiently expressed by only one parameter, i.e., bending rigidity. However, from the wealth of experi-mental data on bending obtained since Livesey-Owen's work was published, we can easily see that it is highly inadequate to express bending behavior by only one para-meter.

It has been found that several deformation character-istics of fiber assemblies can be sufficiently expressed by the two terms, the intercept and the slope -linear and non linear components. Kitazawa suggested that the ratio of these two terms was the key parameter expressing

the general pattern of various deformation characteris-

tics in heavy worsted fabrics. Many research works, in-

cluding Howorth's and Kobayashi's, have been made on the

relation between the mechanical properties and the handle

of woven fabrics. However, they treat the deformations

of woven fabrics one-dimensionally and, therefore, are

open to the charge of inadequancy.

Bending is perhaps the most important factor influencing

the handle of woven fabrics. If we extract these two terms;

the intercept and the slope or a certain suitable parameter

combined by these two terms from the bending behavior

and connect these parameter to the handling, the closer

ralations must be found between the handling and bending

property.

Fig. 16 shows the realtions between the scale of handle,

or the degree of "Yawarakasa" (pliability), and bending

moment M fF in curvature 1 cm-1 in cellulose ginghams

(series B) and polinosic poplins (series C). Good corre-lations are found between them. A sensory test of these

Fig. 15 Sectional shapes of warps and wefts in poplin

Fig. 16 Relations between pliability (determined by sensory test) and bending moment in curvature 1 cm-1


samples reveals good correlations between the scales of "Yawarakasa" (pliability) and "Darakan" (limpness) . It seems all right to conclude from these test results that the higher degree of "Darakan" (limpness) in regenerated fabrics than in cotton fabrics, can be explained mainly by the difference in the value of 1V1 fF-M fY between regenerated and cotton fabrics. Fig. 16 (b) suggests that "Darakan"

(limpness) can be reduced by increasing the value of KF by resin-finishing, etc. The elongational of woven fabrics includes a mechanism in which the force of inter-yarn contact arises anew mainly from elongational force, and this newly arising force of contact influences the elongational characteristics. In bending deformation, however, the force of inter-yarn contact and its distribution originate directly from resi-dual stress within a yarn and the intersecting of warp and weft. This fact, it is believed, makes a minute analysis of the bending characteristics difficult. However, if we keep analyzing them, we shall make an advance in the effort to find out how they bear on the handle of various woven fabrics. 6. Conclusion 1. We have expanded the theories announced by Livesey-Owen and Grosberg on the bending deformation of woven fabrics and derived theoretical equations (11)-(13). Various factors which determine bending properties can be summed up as in Fig. 4. The bending characteristics of various woven fabrics have been discussed on the basis of the theory which this figure expresses. 2. The difference in bending hysteresis between regenerated fabrics and cotton fabrics (and fabrics blended with cotton) arises mainly from the difference between these two fabrics in intercept M fF of the hysteresis curve. This difference

presumably explains why regenerated fabrics have de-fective handle, or "Darakan" (limpness). These pheno-mena, in turn, presumably come from differences between the frictional coefficient of fibers and the force of inter-yarn intersecting. 3. In Polynosic fabrics in wet state, inter-yarn contact between warp and weft is tighter than in cotton fabrics. The change from wet to dry state generates larger cross-sectional shrinkage in polynosic fibers. Therefore, poly-nosic fabrics have loosely intersecting yarns and, in dry state, are low in the value of M fF. 4. An analysis has been made of an example of the fact that resin-finishing stiffens cellulose fabrics. This analysis has shown that the stiffening comes from an increase in the value of KF which, in turn, comes from an increase in Young's modulus of fibers. 5. The values of, successively, KY and KF increase in pro-

portion to an increase in single-fiber denier. 6. With an increase in weft yarn density, the values of KF

Vol. 15, No. 1 (1969)

and 2Mf F in the direction of weft (the direction of bending) increase at a higher rate than the increase in weft yarn den-sity. At the same time, the values of KF and 2M fF in the

perpendicular direction slightly increse. 7. Desizing lowers the values of KF, 2M fF, KY, 2M fY, KF-KY and 2(M fF-M fy) considerably.

8.. Heat-treatment lowers the values of KF and 2(M fF-M fy) in fabrics made of synthetic fibers. This is pre-sumably because heat-treatment relaxes the force of inter-

yarn contact. 9. A comparison of various poplins made of different fibers in their bending characteristics shows that cotton

(mercerized) and polyester come highest in the values of intercept Mf F and polynosic the lowest, with acrylic com-ing in between. These differences in the value of MfF can be attributed mainly to the difference in the value of 2(M fF-M fy).

10. Worsted fabrics represented by the samples of the series I have a very small value of 2M fF in relation to the values of KF. Fabrics blended with polyester have larger values of 2Mf F than do pure-wool fabrics. 11. Fabrics, such as poplin, consisted of warps denser than wefts, have a larger value of 2(M fF-M fY) per thread in the direction of weft than in the direction of warp. 12. The value of KF-KY can vary with the kinds of fiber and the method of finishing-treatment. These variations bear out the theory that the value of KF-KY depends on the force of inter-yarn contact and its distribution. It is believed unreasonable to explain away the difference between KF and KY merely by simple geometrical inter-

yarn restraint, as Livesey, et al, and Shinohara et al, do.

Reference

[1] R.G. Livesey, J.D. Owen; J. Text. Inst„55, T516 (1964)

[2] P. Grosberg ; Text. Res. J.,36, 205 (1966) [3] B.Morner, T. Eeg-Oloffson; Text. Res. L, 27, 611 (1957) [4] T. Matsuo; J. Text. Mac. Soc. Japan. (English ed)

10, 44 (1964)

[5] Y. Sawaguchi; private communication (1967) [6] S. Kitazawa, K. Susami; J. Text. Mac. Soc. Japan

(Japanese ed) 21, T21 (1968) [7] A. Shinohara, Y.Go, F.Matsuhashi; J. Soc. Text. Cell.

Ind. Japan. (Sen-i-Gakkaishi), 1', 78 (1958)

[8] F.T. Peirce; J. Text. Ins., 221, T377, (1930) [9] W.S. Howorth; J. Text. Inst., 55, T251, (1964) [10] S. Kobayashi; Bulletin of Text. Res. Inst. (The Text. Inst. Japan Government)

[11] T. Matsuo ; J. Text. Mac. Soc. Japan (Japanese ed) 16, 513 (1963)

[12] M. Niwa, S. Kawabata, H. Kawai: J. Text. Mac. Soc. Japan (Japanese ed) 20, T12, 258 279, (1967)

33

Bending of Woven Fabrics - JST

Documents

Transcript of Bending of Woven Fabrics - JST