9: Internal Stress and Deformation

Transcription

1 Crepe Yarn Part 9: Internal Stress and Deformation By Ichiro Genma and Yasuji Fukushima, Members, TMSJ Industrial Research Institute of Kanagawa Prefecture, Japan Abstract The deformation of crepe yarn in water has been analyzed by examining the forces developed in wet crepe yarns and their effects on its behavior. Part 9 of this article induces theoretical expressions for untwisting moment from contraction force developed in constituent fibers and their radial distance from the yarn axis. By following these theoretical equations on untwisting moment, analyses have been made of the untwisting moment of viscose rayon, silk, acetate, nylon and terylene crepe yarns. The factors which have definite influence on untwisting moment have also been examined. In particular, the swelling property of the constituent fibers has been found to play an important part in increasing the untwisting moment of crepe yarns. Symbols used Parts 9 and 10 contain these symbols: f : Tension developed in the constituent fibers of a wet crepe yarn. fl : Tension induced in fibers by the swelling recovery of set strain. f~ : Tension appearing in a twist-set fiber when it is stretched slightly in water. fc : Tension remaining in the constituent fibers after a yarn has contracted to a certain extent. r : Radial distance of a fiber from yarn axis. R : Yarn diameter. Rn : Neutral radius of a wet yarn. Er : Strain of fibers at radial distance r from the yarn axis before swelling. Ers : Value of r- when a yarn swells laterally. Er's : Value of e. during yarn contraction. drr : Small stretch of fibers resulting from an increase in the yarn section produced by swelling. rres : Residual strain of set fibers. ER Strain of the outermost fibers. En Strain limit beyond which contraction force develops. m : Total number of fibers (if T and P on a model yarn are numerically calculated, m being the number of constituent yarns, not fibers). n : Number of twists t/cm. Vol. 10, No. 3 (1964) Ey a Q Or fir S El E2 K,k T T1 Tz P P1 P2 PC Qen Pw Pwe Pr C : Yarn shrinkage induced by twisting. : 1--E~ : 2 nn. : Twist angle of fibers at radial distance r from the yarn axis. : Twist angle of the outermost fibers. : Degree of the cross-sectional swelling of a yarn. : Young's modulus to contraction force fi. : Young's initial modulus of fibers obtained when strain-set fibers are stretched further in water. : Material constant. : Untwisting moment of a wet crepe yarn. : Untwisting moment relating to force fi. : Untwisting moment relating to force f2. : Compressional force acting on the section of a wet crepe yarn. : Compressional force relating to force f 1. : Compressional force relating to force f2. : Compressional force during yarn contraction. : Lateral compression acting on the side of the cylinder formed by fibers within neutral layer. : Contraction force developed in a wet yarn. : Contraction force Pw during yarn contraction. : Negative contraction force induced by the swelling tension of fibers within the neutral layer. : Rate of yarn contraction. 116

2 C1 : Limit value of yarn contraction. A,2' : Constant determined by the twist angle. The contraction force and untwisting moment of crepe yarns in water were experimentally inquired into in part 6. The inquiry showed that the internal stress of crepe yarns, which determines the pebble of crepe fabrics, can be interrelated to untwisting moment, not to contraction force.[l] Thus, the untwisting moment of a wet crepe yarn is one of the most important measures which determine the utility value of twisted yarns as a material for crepe fabrics. If untwisting moment can be improved by some means, such as chemical treatment on raw materials, then a way can be found for quality control of crepe fabrics. To use fibers well as a material for crepe fabrics, we have to know which property has definite influence on the untwisting moment of wet crepe yarns. The present article examines analytically the factors contributory to the untwisting moment of wet crepe yarns. 1. Theoretical Moment Expressions for Untwisting Untwisting moment, being similar in mechanism to twisting moment previously referred to,[21 is easily calculable from the geometry of yarn structure and forces developed in constituent fibers. The following analysis assumes yarn structure to be an ideal helical structure Force Developed in Constitueut Fibers Force induced by swelling recovery of strain As stated in a previous instalment[31, the force induced by the swelling recovery of strain previously set by twist-set conditions is expressed as f1-e1 (1) where e, is the strain of fibers at distance r from the yarn axis, E1 is Young's modulus determined by material used, and en is the strain limit beyond which fi develops. fi is the first force that appears in fibers immediately a yarn absorbs water. According to the geometry of twist structure, fiber strain e; is expressed as Force induced by slight stretch of fibers following lateral swelling of yarn section As shown before, S, the lateral swelling of the yarn section, is expressed by the relation Rw2 = R(1+S), where Rw is the diameter of a swollen crepe yarn.[41 In this case, distance r changes to r (1+S) and, consequently, strain er transforms into E,rS and is expressed as ers=nau+qrz~l+~~_1 (3) E; S being greater than e,, fibers stretch slightly, and the amount of this stretch is given as der=e,sa''+p2r (1+S) _ a'l+q2ru... (4) The force induced by this small stretch has been expressed as f2= E~ der... (5) and Young's initial modulus E2 has been given as E~=K+k8r,[3] (6) where K and k are material constants and er is the initial strain set by twist-set conditions. Therefore, f2 is expressed as f2=(k+ke ) (7) Force f developed in the fibers of the yarn in swollen state is the sum of fl and J~ Untwisting Moment To simplify calculation, untwisting moment is divided into two parts, i.e., one corresponding to f1, the other to t. They will be added up later. Assuming that fibers are distributed evenly in the section of the yarn, the number m' of fibers distributed over the distance between r and r*- dr from the yarn axis is calculable thus: m 2rcr dr 2m r dr m' _ - ~R2 - _-- -- R2-- (g) Assuming that force f1 developed in the fibers i n this layer is the same in all the fibers, and that the change of 8r due to a small displacement dr may be neglected, then untwisting moment dt, by these fibers is expressible as dt 1= 2m r dr R2 f, sin Br (9) According to the geometry sin er is given as r sin er = -- - Q + 2r of twist structure,... (l0) Journal of The Textile Machinery Society of Japan

3 + n 2 J Putting (1), (2) and (10) into (9) gives us: dt 2 rn E, 1-- R,, --f=-==_-,ja2 + p2r2 Therefore, untwisting moment Tl induced force f i is calculable thus: 2 m E, p R - T 1= R2 - R r`-1_en). J n - r3 dr... ~ a2+p2r2 When r=r, Er=~az+p2R2-1=ER, and w r=rn, Er-'&+p2R2n-1=En. Therefore, 1+ER=4Jaz+a2R~ 1+ n/2+2r2 = apn - By using the relations shown in (13), the in-... (16) tegration in eq. (12) can be solved and fin ally Putting (2), (4), (6) and (15) into eq. (16), we simplified as follows: get untwisting moment T2 as In eq. (17), 12 R~ R n - 2rn(1-+S)K R - R2 R 2ynp(1+S)k 11? JR7a ~l a2 + 9r2 (1 + S) -,/a2 +2 r2 /a2+ p2r2 (1 + S) Expanding this and neglecting the value proximate deduction: Therefore, integration (17) is mp3(1+s)sk R r6 T2= R2 - J R 7a (a+ Finally, this is solved as k E r) ( a" a~ 11) pur~( p2r~(1+s) r2s a~+p`r~) appro ximately expressible as T mf,' 1= 6p, 3RL-~ (ER-En)` {3(1+ER)2+2 + (l +En) 2-6a2}... (14) by Consider the moment induced by force fz. In this case, distance r and angle o7 change to rs and ors, and are expressed as rs= r(1+s) pr(1 +S)_2 15 p~r2 (1 + S) hen Therefore, untwisting moment induced by force f2 developed in fibers distributed between r and r + dr is expressible as follows: _mr dr f 2r(1+S)~ sin ors 13) dt2=2r r3 ~/as+q,r2(1+s) IJ n n r) n it r~;_1) r3dr...(17) / a2 + r (1 +S) _1 =1_(a~+ p2r2) 2 {a2+ p2r2(1+5)} 2 of S above second power, we arrive at this ap- m d r p3(l+s)s Rz R 2_( r6 11('1) a'+,r,) dr...(19) 18 2( m(1+s)sk 1 +ER ) `'.} {(1+ER)2+(1+E7a)2+4a~ log-_l+ + m(1+s)sk _- 6Op3Rz - 12{(1+ER )-(1- +60a2{(1+ER) (1+En) 2} }-40x2 E?z {(1--ER)3- }-15 -En) } {(1--ER)4-(1--En)4 (l+en)3} 1+E~z a~ {(1-I'ER) - (1+En)} -60a4 log X20) Vol. 10. No. 3 (1964) 118

4 is: Untwisting moment T of wet crepe yarn, then, 2. Experiments T-T1+T2...(21) 2-1. Comparison of Twisting Moment with Untwisting Moment Low twisting moment is desirable for the manufacture of crepe yarns, but the use of crepe yarns as a material for crepe fabrics requires the highest possible untwisting moment. Thus, the strain energy contained in yarn during twisting, i.e., twisting moment, should not decline even after treatment, such as twist-setting and immersion in water. Therefore, we have compared twisting moment with untwisting moment in water on the same samples having the structure shown in Table 1. The samples were twisted on the apparatus for measuring twisting moment explained in part 4,[21 and twisting moment at every stage of twisting was measured. The twisted samples were then transferred to a frame under definite tension and were treated by the twist-set conditions given in Table 1. Table 1 Details Untwisting moment on these stabilized samples was measured by the apparatus explained in Part 6. Twisting moment TD, untwisting moment T and the ratio of T/TD for the various samples are given in Table 2. As shown in Table 2, the ratio T/TD is highest for nylon and terylene, medium for silk and viscose, and lowest for acetate. It does not necessarily follow from these results, however, that nylon and terylene are superior to viscose and silk as raw materials for crepe fabrics. Since twisting moment is determined by tension developed in fibers and by their radial distance from the yarn axis, the ratio T/TD can be estimated for the stress-strain diagram of each fiber in dry and wet conditions, provided the yarn radius remains constant and there is no relaxation in fiber tension throughout the experiment. Table 3 gives the ratios of tension in dry and wet conditions for each fiber at certain elongation. Comparing the results in Table 3 with T/TD in Table 2, we notice that T/TD for viscose rayon is greater than the tension ratio, but that it shows the opposite tendency for other materials. Thus, some positive factor which increases untwisting moment presumably exists in viscose rayon. As for nylon, terylene and acetate, it is clear that of Model Yarns Table 2 Comparison of Twisting and Untwisting Moment 119 Journal of The Texile Machinery Society of Japan

5 Table 3 Ratio of Fiber Tension in Wet and Dry States the strain energy contained in a yarn during twisting declines considerably through various processes after twisting. It can be said, then, that viscose rayon is far better as a material for crepe fabrics than nylon, terylene, acetate and silk Analyzing Untwisting Moment To know the factors which have definite influence on the untwisting moment of crepe yarns, the following theoretical analysis was made of each sample. Fig. 1 Untwisting moment of viscose crepe vis. 75 d. x 45 ends. -0 calculated value -x experimental value yarn Viscose rayon Material constants for viscose rayon were given as follows: E=1.04 g/d., K=0, k=40 g/d., e=0.045[3] By putting these constants into eqs. (14) and (20), untwisting moment on the samples listed in Table 4 was calculated. Untwisting moment T1 and T2 calculated and total moment T1+ T2 are shown, with experimental values, in Fig. 1. It is clear from it that the calculated values agree well with the experimental. T2 is much greater than T1. It can be said, then, that the untwisting moment of viscose rayon crepe yarn depends largely on its swelling property. It is clear from the theoretical considerations in 1-2 that T1 determined by force fl which is proportional to fiber strain, should have direct relation to twisting moment. T2, being determined only by the lateral swelling of yarn, has no direct relation to twisting moment. The great contribution of T2 to untwisting moment makes the ratio of T/TD for viscose rayon much greater than that of tension in dry and wet conditions Silk Table 4 Details of Model Yarns It is important to observe the change of the yarn diameter in silk crepe yarn through the process of twist-set treatment. The sericin surrounding the fibroin fiber softens at the time of twist-setting and fills up the space between fibers. Therefore, the yarn after twist-setting becomes noticeably thinner than before twist-setting. According to the geometrical relations for twist structure, a decrease in the yarn diameter reduces the strain of the constituent fibers. It is assumed, then, that the strain of fibroin fibers decreases somewhat at the time of twist-setting. In this Vol. 10, No. 3 (1964) 120

6 case, since a decrease in fiber strain doubtless progresses in the form of swelling recovery, the yarn tends to increase in length, provided the amount of the decrease in fiber strain induced by a decrease in the yarn diameter greatly exceeds the amount of the swelling recovery of the strain of each fiber. We have verified these considerations by the model yarn shown in Table 5. Putting n, R and R' in Table 5 into the equation on the strain of the outermost fibers, i.e., R = /a'' + p2r2-1, we get the relation between n and ER or R. This result is shown in Table 6, where er is the value corresponding to R', and Eres is the residual strain for sr. fires for er are obtained from the experiment described in part 8 of this article. If fiber strain recovers freely during the twistsetting process, ~R will reach Leg. That is, e'r cannot become smaller than Lres. However, as shown in Table 6, calculated E'R is smaller than E,-e. This presumably suggests that, fiber strain having completely recovered to its limit at the time of twistsetting, f 1 need not be reckoned with in calculating untwisting moment. Therefore, the untwisting moment of silk crepe yarn is calculable merely by eq. (20). Material constants for silk were given as follows: K=11.9 g/d. k=190 g/d.[31 By using these constants, calculations were made on the samples listed in Table 7, where R and S are the yarn diameter and the amount of lateral swelling measured on twist-set samples. Table 7 Details of Model Yarn Curve 1 in Fig. 2 is the calculated value and curve 2 the experimental value. As shown in Fig. 2, the calculated value agrees well with the experimental, thus bearing out our assumption on the mechanism of the untwisting moment of silk crepe yarn. fi being much greater for silk than for viscose rayon, it is a big waste not to use it well in untwisting moment. To introduce fi effectively into untwisting moment, the strain recovery of each fiber has to be retarded during twist-setting. Manufacture of silk crepe yarn by the wet system seems to fill this requirement. Table 5 Change of setting Diameter of Silk Model Yarn by Twist Table 6 Strain Yarn of Fibers in Outermost Layer of Model Silk before and after Twist-setting Fig. 2 Untwisting moment of silk silk 21 d. x 90 ends. crepe yarn. 0 x - calculated value experimental value 121 Journal of The Textile Machinery Society of Japan

7 By using these constants, untwisting moment was calculated by eqs. (14) and (20) on the samples listed in Table 8. The calculated values are given, with the experimental, in Fig. 3. It is clear from the figure that the untwisting moment for acetate, like that of viscose rayon, depends largely on T2. That is to say, lateral swelling, though small in amount, has definite influence on the magnitude of untwisting moment. To see how much lateral swelling contributes to untwisting moment, the following comparisons were made on viscose and acetate model yarns of the structure shown in Table 9. Untwisting moment calculated for both model yarns is shown in Fig. 4. It shows that, at high twist, the untwisting moment of viscose rayon is about three times as large as that of acetate. Fig. 3 Untwisting moment of acetate crepe yarn. Ace. 55dx30 ends calculated value x -- experimental value Acetate Material constants for acetate were given as F_, = 0.53 g./d., K=11.25 g./d., k = 43.7 g. /d., =0.01l3] Table 8 Details of Model Yarn Fig. 4 Untwisting moment of viscose and acetate crepe yarn of the same structure. 1: T1 for viscose, 2: 7'2 for viscose, 3: T1+T2 for viscose, 4: T1 for acetate, 5 : T.2 for acetate, 6 : T1 + T.2 for acetate. Table 9 Details of Model Yarn The factors contributory to the untwisting moment of viscose rayon and acetate were compared. Details follow : (1) Forces fl and f2 for both fibers were given as: For viscose rayon, f= l 1.04 (Er-0.045) g./d.,,/240e der g./d. For acetate, f =0.53 (~;.-0.01) g./d., f 2 = ( ~r) Js g./d. Therefore, f i and f 2 at certain strain, e.g., Er=0.15 and k =0.O1, were J =1.O9 g./d., J2=0.06 g./d. for viscose rayon and f = g./d., f2 =0.178 g./d. for acetate. Vol. 10, No. 3 (1964) 122

8 Thus, f 1 is greater for viscose rayon than for acetate, although the difference is slight. 12 for acetate is three times as large as for viscose rayon. (2) The two yarns differ considerably in lateral swelling : S for viscose rayon, at high twist, is about four times as large as for acetate. Fig. 5 Change in fiber tension during twist set A re-examination of the results given in Fig. 4 with due consideration of the above comparisons showed that the influence of lateral swelling on the magnitude of untwisting moment was greater than the influence of f~ and f2. To enlarge untwisting moment, then, something must be done to increase lateral swelling even at the sacrifice of f 1 and f According to our experiments so far, it is difficult to develop crepe pebble from crepe yarn of regular acetate, but it is possible to develop crepe pebble from crepe yarn of partially saponif ied acetate, presumably because partial saponification increases the lateral swelling of acetate. Fig. 6 Contraction force developed mersed in hot water (Nylon in set 70d) fiber when im Nylon and Terylene The lateral swelling of nylon or terylene yarn need not be considered, and untwisting moment is decided only by force fi. As shown in Table 2, ratio of T/TD is 0.4 for nylon and 0.5 for terylene Since yarn structure and diameter did not vary during our experiment, this ratio should agree with the ratios of fiber tensions in dry and wet conditions. As we have said, twist-setting for nylon and terylene differs widely in mechanism from twist- Fig. 7 Contraction force developed in mersed in hot water (Terylene set fiber 40 d) when im- 123 Journal of The Textile Machinery Society of Japan

9 untwisting moment of nylon and terylene crepe yarn have thus been ascertained. Summing up In nylon and terylene, however, both the residual shrinkage and the residual stress remaining after twist-setting are too large to be capable of release within the yarn structure by the same mechanism as that for viscose, acetate and silk, consequently residual shrinkage e1 shown in Fig. 5 remains after twist-seting. The force f mentioned so far is a force obtained when a fiber from which residual shrinkage fit has been removed is immersed in water again. fl of this kind is, therefore, not usable for nylon or terylene. For nylon and terylene we must use f i that can be obtained when the fiber is immersed in hot water immediately after setting, without removing residual shrinkage e1. fi thus obtained is shown, against initial strain e;, in Figs. 6 and 7, where curve 1 is an original stress-strain diagram measured under the standard condition, 20 C and 65% R.H. In this experiment, both fibers were set in water at 95 C for 3 minutes and dried in stretched state for 3 hours under the standard condition. f1 also was measured in water at 85 C. The ratios of fiber tensions in wet and dry states have been obtained from the stress-strain diagrams shown in Figs. 6 and 7, and are given in Table 10. The mean value of these ratios is about 0.4 for nylon and 0.5 for terylene. It is clear that these values agree with the mean values of the moment ratios given in Table 2. The forces which determine the Part 9 has induced theoretical expressions fo the untwisting moment of wet crepe yarns anc analytically examined the factors contributory tc untwisting moment on model yarns of viscose rayon silk, acetate, nylon and terylene. The results art summed up as follows: 1. The untwisting moment of wet crepe yarns i~ determined by the force developed in the constituent fibers and their radial distance from the yarn axis The force considered here is composed of two elements, i.e., force f1 induced by the swelling recovery of set strain, and force f2 produced by a small stretch resulting from the swelling of the yarn section. Therefore, untwisting moment T can be divided into T1, which relates to force f, and T., which relates to force f2. 2. T for viscose rayon is composed of T, and T.. "F 2 contributes inure to untwisting moment than T1 does. 3. T for silk is determined only by force f. The reason is that the set strain of the constituent fibers recovers almost completely to its limit during twistsetting, thus keeping fl from showing up when the fibers are immersed in water again. 4. T for acetate, like that for viscose rayon, is composed of T1 and T,, but it cannot grow because acetate fibers are lacking in swelling property. 4. T for nylon and terylene is determined only by force f i. f need not be considered here. f i for nylon and terylene, however, is not the same as for viscose and acetate. Force f1 for nylon and terylene is a force obtainable when fibers set by hot wet treatment after stretching are immersed again in hot water without removing the residual shrinkage after setting. Vol. 10, No. 3 (1964) 124