- Email: [email protected]
Shrinkage in woven fabrics
5
Shrinkage in woven fabrics
Abstract: The mechanism of fabric shrinkage from hydrophilic fibers is explained using a geometrical model. The relationship between yarn and fabric shrinkage is discussed. The prediction of fabric shrinkage is made by considering changes in yarn diameter and length due to swelling, fabric geometry and crimp balance. Practical applications of modeling fabric shrinkage are given. Key words: modeling, fabric geometry, crimp balance, fabric shrinkage.
5.1
Introduction
The shrinkage of natural fiber fabrics on washing has been one of the major problems requiring attention by textile technologists. A part of fabric shrinkage is due to stretching by applied tensions during manufacturing and finishing operations [1, 2]. Fabric shrinkage is a term associated with a reduction in the dimensions of fabric. A fabric on the weaving machine is under warp and weft tensions. As soon as the fabric leaves the templates that hold it in place, its width decreases. Similarly when the fabric is taken off the loom, one can observe a reduction in length and width; which can be checked by an increase in the ends and picks per cm. This is due to the release of tensions in the warp and weft so that the yarns recover to their relaxed state. This equilibrium is achieved by balancing of internal energy with the inter-yarn frictional force. It may be termed a pseudo-equilibrium and is designated as dry relaxation. The dimensional change accompanying the release of fiber strains imparted during manufacturing which have been set by the combined effects of time, finishing treatments and physical restraints within the structure is called relaxation shrinkage [3]. Collins [4] explained that fabric shrinkage is not only due to the release of strains imposed during the manufacturing process but also caused by fiber and yarn swelling produced on wetting, which brings about an internal rearrangement of the material resulting in external shortening. Cotton fiber absorbs water and shows a contraction of 1% and an increase in diameter of about 20%. The swelling is reversible. He postulated that when the yarn diameter is increased by the swelling action of water, the fiber must move around or along the yarn to a lesser degree. In order to pass around the yarn, the swollen fiber undulates, shrinking the yarn. Yarn shrinkage on wetting rarely exceeds 2% for normal twist. Twistless yarn shows no tendency to 109
110
Woven textile structure
stretch the fibre on yarn swelling. He observed that the stretched fibers show a true contraction of about 2%, which does not account for actual fabric shrinkage of the order of 10%. Shrinkage that results from the swelling and deswelling of the fibers due to absorption and desorption of water is called swelling shrinkage. Its magnitude depends upon the way in which the fiber interacts within the complex structure of the yarn and fabric. Shrinkage is the retraction of yarn when the external forces are removed. It is a manifestation of the release of strain in material and will continue until a minimum energy level is achieved. Any material when deformed by external forces will tend to recover to a state balanced by internal frictional force. In a fabric made from hydrophilic material the release of internal residual strain can be catalyzed by either washing and drying or by setting, for example resin finishing. Fabrics made from hydrophobic yarn can be relaxed by thermal setting. In both cases, the fabrics become relaxed and are dimensionally stable at the level of zero energy.
5.2
Mechanisms of fabric shrinkage
The mechanism of shrinkage of fabrics made from hydrophilic yarn is described by Collins [4]. On wetting a fabric, water is absorbed by the fibers in the yarn and causes swelling of fiber and yarn. Typically an increase of 10% in yarn diameter can be expected. Nevertheless, transverse swelling of fibers results in longitudinal shrinkages of only 1%. Yarn shrinkage, which is related to the degrees of twist imparted on the yarn during spinning, can give rise to more shrinkage but accounts for shrinkages of only 2% in typical fabrics. The explanation of cloth shrinkage lies in the fabric structure. Figure 5.1 shows one repeat along the warp. When the cloth is wetted the yarn increases in diameter. If the crossing weft threads are to remain the same distance apart as they are in the dry state, than warp would have to extend. As the cloth is under no constraint, the weft threads move closer together in order that the warp yarn can remain the same length. Therefore the cloth shrinks in the warp direction. A similar explanation is valid for shrinkage in the weft direction. The major cause of fabric shrinkage due to the swelling of threads on wetting is that the thick warp yarn requires more space to enable fibers to pass over and under the swollen weft yarn. The warp adopts an undulating path and shrinks the cloth. Shrinkage may be regarded as a change in yarn spacing, p. From the relation p1 = l2/(1 + c2), the observed shrinkage may be considered as the result of the change in yarn length and the change in crimp. The crimp change is a combination of change in crimp distribution and in the general level of crimps and is dependent on the value of l/D. As a change in the values of l alone also involves a change in crimp, these effects are not independent, but they may be separated for the purposes of the practical analysis.
Shrinkage in woven fabrics
111
Peirce suggested the shrinkage may be imagined to occur in two stages; initially the change in l and D due to the wetting and drying, during which the crimp balance or ratio remain constant, followed by a crimp redistribution to the final shrunk state. In the first stage, the crimps are affected by the changes in yarn lengths but only to a small extent, any large effect being due to the swelling of yarns, resulting in a change in D. It was found that as water is absorbed into the fabric the transverse swelling of the fibers and yarns induced shrinkage in three ways: longitudinal fiber shrinkage, yarn shrinkage and crimp accentuation. The mechanism of crimp accentuation is illustrated in Fig. 5.1, which represents the position of warp and weft yarns before wetting. It also shows the swelling of both yarns when the fabric is wetted. For the fabric to maintain the same external dimensions it had before wetting, i.e. not shrink at all, the warp yarns would have to extend by a given length. An extension would be necessary for the warp yarns to travel around the swollen weft yarns. There is an energetically simpler mechanism that accommodates the increased path of the warp yarns. In this mechanism, the weft yarns move closer together and warp path length remains the same. Likewise, an increase in the diameter of the weft yarns results in the movement of warp yarns closer together. For this reason, shrinkage of the fabric in both directions is observed. From this description it is clear that the fabric structure has a significant effect on a fabric’s response to wetting. The degrees of yarn twist, yarn diameter and sizing have some influence, but the spacing of yarns (degree
Cloth length
Coarse weft
(a)
Fine warp
(b)
5.1 Shrinkage of woven fabric (a) before wetting (b) after wetting.
112
Woven textile structure
of crimp) is the most critical factor. Thus, closer yarn spacing and relatively compacted yarns give greater shrinkage effects. The mechanization of the textile industry gave rise to an abundance of tightly woven fabrics produced with power spinning and power weaving processes. This type of fabric shrinks more than a handmade fabric at high moisture levels.
5.3
The relationship between cloth and yarn shrinkage
Suppose a cloth shrinks s % and that the percentage crimps of thread before and after shrinkage are c0 % and c % respectively. Then the following relations are valid: l0 = p0 l =p
(100 + c0 %) 100
(100 + c0 %) 100
yarn shrinkage is given by: sy = 100 (l – l0 )/l0 = (100 – s%)
100 + c % – 100 100 + c0 %
Thus the physical change, the contraction of the yarn, is separated from the more purely geometrical factor in the shrinkage, the change of crimp. It has been found that the yarn shrinkage is almost entirely confined to the first of a series of washing treatments. In later shrinkages, l must therefore be assumed constant and the crimp estimated from the measurements of shrinkage by the relation: 100 + c % 100 + c0 % = 100 100 – s % In the swollen state D is increased and l decreased; both changes diminish p or the fabric dimensions. On drying, D diminishes and l increases but, in the absence of external tension, the extra length is more easily accommodated by slack inter-weaving than by an increase in external dimensions. Strictly, percentage shrinkages in successive stages are not additive, the total shrinkage s is given by (1 – s) = (1 – s1) (1 – s2) (1 – s3), where s1, s2, s3 are the successive shrinkages. In a fabric free from tension the crimps adjust so that the elastic forces are in equilibrium. The curvature of the crimped threads is not, however, all elastic; if released from all external restraint, they would retain most of the curvature as ‘set’. The setting of crimp has in general more influence on the crimp balance than the active elastic forces.
Shrinkage in woven fabrics
113
Almost any balance of crimps geometrically possible may be imposed on any cloth. That balance of crimps which corresponds to the equilibrium of elastic thread should, however, be favored by cloth subjected to changes of swelling while free from restraint, so that shrunk fabrics should show a tendency to approximate to this balance. According to this analysis, the balance should be given by a crimp balance equation, which may be expressed in the form: log
5.4
c1 t m = 4 logg 1 + 2 log 2 c2 t2 m1
Predicting fabric shrinkage
Peirce [1] separated fabric shrinkage due to yarn shrinkage and yarn swelling from the fabric on the loom and the fabric after a standard washing treatment. He analyzed the contribution of causes of shrinkage in terms of yarn shrinkage, swelling and crimp redistribution from the total fabric shrinkage. The shrinkage was imagined to occur in two stages: first the change in l and D due to wetting and drying, during which crimp balance (ratio) remains constant, followed by crimp redistribution to the final shrunk state. The crimps are affected by the changes in yarn length to a small extent, the significant effect being due to swelling of yarns causing a change in D. The fabric shrinkage was predicted [5] considering the mechanism of fabric shrinkage as explained above and using the changed parameters l¢ and D¢ along with crimp balance using the following four equations and the eligible domain for q1¢ and q2¢ considering the constraints to the value of q1¢ and q2¢. This process is explained in the algorithm as shown in Fig. 5.2. Ê p2 ˆ ¢ Ê p1 ¢ ˆ Ê p ˆ¢ – q1 ¢˜ cos q1 ¢ + sin q1 ¢ + K , Á 2 ˜ = f (q1 ¢ ) ÁË ˜¯ = ÁË ¯ Ë D¯ D D¢
5.1
Ê p1ˆ ¢ Ê p2 ¢ ˆ Ê p ˆ¢ – q2 ¢˜ cos q2 ¢ + sin q2 ¢ + K , Á 1˜ = f (q2 ¢ ) ÁË ˜¯ = ÁË ¯ Ë D¯ D D¢
5.2
1 = h1/D + h2/D ˆ ˆ Êl ¢ Êl ¢ 1 = Á 1 – q1 ¢˜ sin sin q1 ¢ + (1 – cos q1 ¢ ) + Á 2 – q2 ¢˜ ¯ ¯ Ë D¢ Ë D¢ sinn q2 ¢ + (1 (1 – cos q2 ¢ )), q1 ¢ = f (q2 ¢ ) sin q1 ¢ q1 ¢ Ê p2 ¢ˆ Ê b2 ˆ ¢ ª = sin q2 ¢ q2 ¢ ÁË p1 ¢˜¯ ÁË b1 ˜¯
5.3
2
5.4
114
Woven textile structure Start
Read l1/D, l2/D, q1¢, q2¢, b1 and b2 No
Is q1 ≥ 1.57?
q1 = q1 + 0.1 Yes
Is q2 ≥ 1.57?
No
Yes
a = (l1/D – q1) sin q1 + 1 – cos q1 b = (l2/D – q2) sin q2 + 1 – cos q2
Is | a + b – 1 | £ 0.001?
q2 = q2 + 0.1
No
Yes Is | R1 – R2 | £ 0.001?
No
End
5.2 Flowchart for prediction of fabric shrinkage.
Constraints:
q 1¢ > q 1
q2¢ > q2, provided q1¢ and q2¢ > p/2
For any q1¢, q2¢ < p/2, the shrinkage will be restricted to this limiting value Logic for shrinkage prediction: for given values of (l1/D) and (l2/D) p2 Ê l1 p ˆ = Á – q1 ¢˜ cos q1 ¢ + sin q1 ¢ fi 2 = f (q1 ¢ ) ¯ Ë D D D
5.5
Shrinkage in woven fabrics
p1 Ê l2 p ˆ = Á – q2 ¢˜ cos q2 ¢ + sin q2 ¢ fi 1 = f (q2 ¢ ) ¯ Ë D D D
115
5.6
ˆ Êl ˆ Êl (1– cos q2 ¢¢) 1 = Á 1 – q1 ¢˜ sin sin q1 ¢ + (1– coss q1 ¢ ) + Á 2 – q2 ¢˜ sinn q2 ¢ + (1– ¯ ËD ¯ ËD Therefore q2 ¢ = f (q1 ¢ )
5.7 2
q1 ¢ Ê P2 /dˆ Ê b2 ˆ = q2 ¢ ÁË P1 /d ˜¯ ÁË b1 ˜¯
5.8
Constraints:
q 1¢ > q 1
q2¢ > q2 , provided (l1/D) and (l2/D) > p/2 A Æ if
p l l1 p l £ then q1 ¢ = 1 and 2 = sin q1 ¢ = sin 1 D D D 2 D
5.9
B Æ if
p l l2 p l £ then q2 ¢ = 2 and 1 = sin q2 ¢ = sin 2 D D D 2 D
5.10
(p1/D) and (p2/D) will be obtained from equations 5.5 and 5.6. Initial start checks (l1/D) and (l2/D) for A and B follow equations 5.5 and 5.6 or else equations 5.1 and 5.2. Initially take q1¢ = q1 + Dq1 (assume small increment) and find q2¢, from equation 5.3. Then find (p1/D) and (p2/D) for corresponding value of q1¢ and q2¢. Finally check if equation 5.4 is satisfied for the calculated values of q1¢, q2¢, (p1/D) and (p2/D). If not give increment to q1¢, get the corresponding q2¢, then again (p1/D) and (p2/D) and recheck validity of equation 5.4. Iterate until equation 5.4 is satisfied for the small value.
5.5
Application of fabric shrinkage model
Q1. A poplin fabric has p1 = 0.023 cm, p2 = 0.042 697 cm, D = 0.020 07 cm and q1 = 21.8525, q2 = 26.6058. After washing, shrinkage percentages of 2.98 in warp and 1.61 in the weft direction of fabric are observed. The percentage crimps are 4.25 in the warp and 6.3 in the weft before shrinkage and 7.03/7.6 in the warp/weft after the shrinkage. The percentage shrinkage in the warp/weft yarn is 0.399/0.415 respectively and the change in D is 17.5%. Predict the thread spacing in the fabric using the above logic given in the algorithm and calculate the percentage
116
Woven textile structure
error in the prediction. Solution: l1 = p2 (1 + c1) = 0.042 697 ¥ 1.0425 = 0.044 526 cm l2 = p1 (1 + c2) = 0.023 × 1.063 = 0.024 485 6 cm D = h1 + h2 = 0.020 066 cm D¢ = D ¥ 1.175 = 0.020 066 ¥ 1.175 = 0.023 571 2 cm l1¢ = l1 ¥ 0.9702 = 0.044 526 ¥ 0.9702 = 0.044 348 4 cm l2¢ = l2 ¥ 0.9839 = 0.024 486 ¥ 0.9839 = 0.024 384 cm l1 0.044 526 = = 2.218 98 > p D 0.020 066 2 l2 0.024 485 6 = = 1.220 25 < p D 0.020 066 2 l1 ¢ 0.044 348 4 = = 1.88147 > p D 0.0235712 2 l2 ¢ 0.024 384 = = 1.0345 < p D 0.0235712 2 q1 = 106 0.0425 = 21.8525° q2 = 106 0.063 = 26.6058° Since (l2/D) ≤ p/2, the fabric before washing has tendency for jamming in the weft if deformed, but the warp direction has no constraints. One can infer that the warp direction can shrink more than the weft direction; the weft direction can shrink only until the weft is jammed. This inference is supported by the actual shrinkage percentage in warp being 2.98 and 1.61 in the weft direction. Again since (l1¢/D’) and (l2¢/D¢) are less than their counterparts in the fabric; therefore crimps in both warp and weft will be greater after washing. In this case the solution is obtained by taking q1¢ > 21.8525°, that is equal to 21.8525 + Dq1 and corresponding q2¢ is calculated from equation 5.3. Then (p1¢/D¢) and (p2¢/D¢) are calculated from equations 5.1 and 5.2 respectively for these values of q1¢ and q2¢. Finally the authenticity of the value is checked using equation 5.4. In this example the ratio of bending rigidity was taken as unity. The iteration for q1¢ and corresponding q2¢ was repeated until equation 5.4 was satisfied.
Shrinkage in woven fabrics
117
In this case the solutions are obtained for q1¢ = 30.21° and q2¢ = 11.68°. Calculated p1¢ and p2¢ are:
p1¢ = 0.023 98 cm
p2¢ = 0.039 44 cm
The actual values are:
p1¢ = 0.022 657 cm
p2¢ = 0.041 427 cm
The percentage error for p1¢ is 5.84 and for p2¢ is 4.8. This is reasonable as the bending rigidity is ignored.
5.6
References
1. Peirce F T (1937), J. Text. Inst., 28, T80 2. Marsh J T (1953), An Introduction to Textile Finishing, Chapman and Hall, London, p 241 3. Abbott N J, Khoury F and Barish L (1964), J. Text. Inst., 55, p T111-T127 4. Collins G E (1939), J. Text. Inst., 30, p 46 5. Hari P K (1970), M. Tech Thesis, IIT Delhi
Shrinkage in woven fabrics
Abstract: The mechanism of fabric shrinkage from hydrophilic fibers is explained using a geometrical model. The relationship between yarn and fabric shrinkage is discussed. The prediction of fabric shrinkage is made by considering changes in yarn diameter and length due to swelling, fabric geometry and crimp balance. Practical applications of modeling fabric shrinkage are given. Key words: modeling, fabric geometry, crimp balance, fabric shrinkage.
5.1
Introduction
The shrinkage of natural fiber fabrics on washing has been one of the major problems requiring attention by textile technologists. A part of fabric shrinkage is due to stretching by applied tensions during manufacturing and finishing operations [1, 2]. Fabric shrinkage is a term associated with a reduction in the dimensions of fabric. A fabric on the weaving machine is under warp and weft tensions. As soon as the fabric leaves the templates that hold it in place, its width decreases. Similarly when the fabric is taken off the loom, one can observe a reduction in length and width; which can be checked by an increase in the ends and picks per cm. This is due to the release of tensions in the warp and weft so that the yarns recover to their relaxed state. This equilibrium is achieved by balancing of internal energy with the inter-yarn frictional force. It may be termed a pseudo-equilibrium and is designated as dry relaxation. The dimensional change accompanying the release of fiber strains imparted during manufacturing which have been set by the combined effects of time, finishing treatments and physical restraints within the structure is called relaxation shrinkage [3]. Collins [4] explained that fabric shrinkage is not only due to the release of strains imposed during the manufacturing process but also caused by fiber and yarn swelling produced on wetting, which brings about an internal rearrangement of the material resulting in external shortening. Cotton fiber absorbs water and shows a contraction of 1% and an increase in diameter of about 20%. The swelling is reversible. He postulated that when the yarn diameter is increased by the swelling action of water, the fiber must move around or along the yarn to a lesser degree. In order to pass around the yarn, the swollen fiber undulates, shrinking the yarn. Yarn shrinkage on wetting rarely exceeds 2% for normal twist. Twistless yarn shows no tendency to 109
110
Woven textile structure
stretch the fibre on yarn swelling. He observed that the stretched fibers show a true contraction of about 2%, which does not account for actual fabric shrinkage of the order of 10%. Shrinkage that results from the swelling and deswelling of the fibers due to absorption and desorption of water is called swelling shrinkage. Its magnitude depends upon the way in which the fiber interacts within the complex structure of the yarn and fabric. Shrinkage is the retraction of yarn when the external forces are removed. It is a manifestation of the release of strain in material and will continue until a minimum energy level is achieved. Any material when deformed by external forces will tend to recover to a state balanced by internal frictional force. In a fabric made from hydrophilic material the release of internal residual strain can be catalyzed by either washing and drying or by setting, for example resin finishing. Fabrics made from hydrophobic yarn can be relaxed by thermal setting. In both cases, the fabrics become relaxed and are dimensionally stable at the level of zero energy.
5.2
Mechanisms of fabric shrinkage
The mechanism of shrinkage of fabrics made from hydrophilic yarn is described by Collins [4]. On wetting a fabric, water is absorbed by the fibers in the yarn and causes swelling of fiber and yarn. Typically an increase of 10% in yarn diameter can be expected. Nevertheless, transverse swelling of fibers results in longitudinal shrinkages of only 1%. Yarn shrinkage, which is related to the degrees of twist imparted on the yarn during spinning, can give rise to more shrinkage but accounts for shrinkages of only 2% in typical fabrics. The explanation of cloth shrinkage lies in the fabric structure. Figure 5.1 shows one repeat along the warp. When the cloth is wetted the yarn increases in diameter. If the crossing weft threads are to remain the same distance apart as they are in the dry state, than warp would have to extend. As the cloth is under no constraint, the weft threads move closer together in order that the warp yarn can remain the same length. Therefore the cloth shrinks in the warp direction. A similar explanation is valid for shrinkage in the weft direction. The major cause of fabric shrinkage due to the swelling of threads on wetting is that the thick warp yarn requires more space to enable fibers to pass over and under the swollen weft yarn. The warp adopts an undulating path and shrinks the cloth. Shrinkage may be regarded as a change in yarn spacing, p. From the relation p1 = l2/(1 + c2), the observed shrinkage may be considered as the result of the change in yarn length and the change in crimp. The crimp change is a combination of change in crimp distribution and in the general level of crimps and is dependent on the value of l/D. As a change in the values of l alone also involves a change in crimp, these effects are not independent, but they may be separated for the purposes of the practical analysis.
Shrinkage in woven fabrics
111
Peirce suggested the shrinkage may be imagined to occur in two stages; initially the change in l and D due to the wetting and drying, during which the crimp balance or ratio remain constant, followed by a crimp redistribution to the final shrunk state. In the first stage, the crimps are affected by the changes in yarn lengths but only to a small extent, any large effect being due to the swelling of yarns, resulting in a change in D. It was found that as water is absorbed into the fabric the transverse swelling of the fibers and yarns induced shrinkage in three ways: longitudinal fiber shrinkage, yarn shrinkage and crimp accentuation. The mechanism of crimp accentuation is illustrated in Fig. 5.1, which represents the position of warp and weft yarns before wetting. It also shows the swelling of both yarns when the fabric is wetted. For the fabric to maintain the same external dimensions it had before wetting, i.e. not shrink at all, the warp yarns would have to extend by a given length. An extension would be necessary for the warp yarns to travel around the swollen weft yarns. There is an energetically simpler mechanism that accommodates the increased path of the warp yarns. In this mechanism, the weft yarns move closer together and warp path length remains the same. Likewise, an increase in the diameter of the weft yarns results in the movement of warp yarns closer together. For this reason, shrinkage of the fabric in both directions is observed. From this description it is clear that the fabric structure has a significant effect on a fabric’s response to wetting. The degrees of yarn twist, yarn diameter and sizing have some influence, but the spacing of yarns (degree
Cloth length
Coarse weft
(a)
Fine warp
(b)
5.1 Shrinkage of woven fabric (a) before wetting (b) after wetting.
112
Woven textile structure
of crimp) is the most critical factor. Thus, closer yarn spacing and relatively compacted yarns give greater shrinkage effects. The mechanization of the textile industry gave rise to an abundance of tightly woven fabrics produced with power spinning and power weaving processes. This type of fabric shrinks more than a handmade fabric at high moisture levels.
5.3
The relationship between cloth and yarn shrinkage
Suppose a cloth shrinks s % and that the percentage crimps of thread before and after shrinkage are c0 % and c % respectively. Then the following relations are valid: l0 = p0 l =p
(100 + c0 %) 100
(100 + c0 %) 100
yarn shrinkage is given by: sy = 100 (l – l0 )/l0 = (100 – s%)
100 + c % – 100 100 + c0 %
Thus the physical change, the contraction of the yarn, is separated from the more purely geometrical factor in the shrinkage, the change of crimp. It has been found that the yarn shrinkage is almost entirely confined to the first of a series of washing treatments. In later shrinkages, l must therefore be assumed constant and the crimp estimated from the measurements of shrinkage by the relation: 100 + c % 100 + c0 % = 100 100 – s % In the swollen state D is increased and l decreased; both changes diminish p or the fabric dimensions. On drying, D diminishes and l increases but, in the absence of external tension, the extra length is more easily accommodated by slack inter-weaving than by an increase in external dimensions. Strictly, percentage shrinkages in successive stages are not additive, the total shrinkage s is given by (1 – s) = (1 – s1) (1 – s2) (1 – s3), where s1, s2, s3 are the successive shrinkages. In a fabric free from tension the crimps adjust so that the elastic forces are in equilibrium. The curvature of the crimped threads is not, however, all elastic; if released from all external restraint, they would retain most of the curvature as ‘set’. The setting of crimp has in general more influence on the crimp balance than the active elastic forces.
Shrinkage in woven fabrics
113
Almost any balance of crimps geometrically possible may be imposed on any cloth. That balance of crimps which corresponds to the equilibrium of elastic thread should, however, be favored by cloth subjected to changes of swelling while free from restraint, so that shrunk fabrics should show a tendency to approximate to this balance. According to this analysis, the balance should be given by a crimp balance equation, which may be expressed in the form: log
5.4
c1 t m = 4 logg 1 + 2 log 2 c2 t2 m1
Predicting fabric shrinkage
Peirce [1] separated fabric shrinkage due to yarn shrinkage and yarn swelling from the fabric on the loom and the fabric after a standard washing treatment. He analyzed the contribution of causes of shrinkage in terms of yarn shrinkage, swelling and crimp redistribution from the total fabric shrinkage. The shrinkage was imagined to occur in two stages: first the change in l and D due to wetting and drying, during which crimp balance (ratio) remains constant, followed by crimp redistribution to the final shrunk state. The crimps are affected by the changes in yarn length to a small extent, the significant effect being due to swelling of yarns causing a change in D. The fabric shrinkage was predicted [5] considering the mechanism of fabric shrinkage as explained above and using the changed parameters l¢ and D¢ along with crimp balance using the following four equations and the eligible domain for q1¢ and q2¢ considering the constraints to the value of q1¢ and q2¢. This process is explained in the algorithm as shown in Fig. 5.2. Ê p2 ˆ ¢ Ê p1 ¢ ˆ Ê p ˆ¢ – q1 ¢˜ cos q1 ¢ + sin q1 ¢ + K , Á 2 ˜ = f (q1 ¢ ) ÁË ˜¯ = ÁË ¯ Ë D¯ D D¢
5.1
Ê p1ˆ ¢ Ê p2 ¢ ˆ Ê p ˆ¢ – q2 ¢˜ cos q2 ¢ + sin q2 ¢ + K , Á 1˜ = f (q2 ¢ ) ÁË ˜¯ = ÁË ¯ Ë D¯ D D¢
5.2
1 = h1/D + h2/D ˆ ˆ Êl ¢ Êl ¢ 1 = Á 1 – q1 ¢˜ sin sin q1 ¢ + (1 – cos q1 ¢ ) + Á 2 – q2 ¢˜ ¯ ¯ Ë D¢ Ë D¢ sinn q2 ¢ + (1 (1 – cos q2 ¢ )), q1 ¢ = f (q2 ¢ ) sin q1 ¢ q1 ¢ Ê p2 ¢ˆ Ê b2 ˆ ¢ ª = sin q2 ¢ q2 ¢ ÁË p1 ¢˜¯ ÁË b1 ˜¯
5.3
2
5.4
114
Woven textile structure Start
Read l1/D, l2/D, q1¢, q2¢, b1 and b2 No
Is q1 ≥ 1.57?
q1 = q1 + 0.1 Yes
Is q2 ≥ 1.57?
No
Yes
a = (l1/D – q1) sin q1 + 1 – cos q1 b = (l2/D – q2) sin q2 + 1 – cos q2
Is | a + b – 1 | £ 0.001?
q2 = q2 + 0.1
No
Yes Is | R1 – R2 | £ 0.001?
No
End
5.2 Flowchart for prediction of fabric shrinkage.
Constraints:
q 1¢ > q 1
q2¢ > q2, provided q1¢ and q2¢ > p/2
For any q1¢, q2¢ < p/2, the shrinkage will be restricted to this limiting value Logic for shrinkage prediction: for given values of (l1/D) and (l2/D) p2 Ê l1 p ˆ = Á – q1 ¢˜ cos q1 ¢ + sin q1 ¢ fi 2 = f (q1 ¢ ) ¯ Ë D D D
5.5
Shrinkage in woven fabrics
p1 Ê l2 p ˆ = Á – q2 ¢˜ cos q2 ¢ + sin q2 ¢ fi 1 = f (q2 ¢ ) ¯ Ë D D D
115
5.6
ˆ Êl ˆ Êl (1– cos q2 ¢¢) 1 = Á 1 – q1 ¢˜ sin sin q1 ¢ + (1– coss q1 ¢ ) + Á 2 – q2 ¢˜ sinn q2 ¢ + (1– ¯ ËD ¯ ËD Therefore q2 ¢ = f (q1 ¢ )
5.7 2
q1 ¢ Ê P2 /dˆ Ê b2 ˆ = q2 ¢ ÁË P1 /d ˜¯ ÁË b1 ˜¯
5.8
Constraints:
q 1¢ > q 1
q2¢ > q2 , provided (l1/D) and (l2/D) > p/2 A Æ if
p l l1 p l £ then q1 ¢ = 1 and 2 = sin q1 ¢ = sin 1 D D D 2 D
5.9
B Æ if
p l l2 p l £ then q2 ¢ = 2 and 1 = sin q2 ¢ = sin 2 D D D 2 D
5.10
(p1/D) and (p2/D) will be obtained from equations 5.5 and 5.6. Initial start checks (l1/D) and (l2/D) for A and B follow equations 5.5 and 5.6 or else equations 5.1 and 5.2. Initially take q1¢ = q1 + Dq1 (assume small increment) and find q2¢, from equation 5.3. Then find (p1/D) and (p2/D) for corresponding value of q1¢ and q2¢. Finally check if equation 5.4 is satisfied for the calculated values of q1¢, q2¢, (p1/D) and (p2/D). If not give increment to q1¢, get the corresponding q2¢, then again (p1/D) and (p2/D) and recheck validity of equation 5.4. Iterate until equation 5.4 is satisfied for the small value.
5.5
Application of fabric shrinkage model
Q1. A poplin fabric has p1 = 0.023 cm, p2 = 0.042 697 cm, D = 0.020 07 cm and q1 = 21.8525, q2 = 26.6058. After washing, shrinkage percentages of 2.98 in warp and 1.61 in the weft direction of fabric are observed. The percentage crimps are 4.25 in the warp and 6.3 in the weft before shrinkage and 7.03/7.6 in the warp/weft after the shrinkage. The percentage shrinkage in the warp/weft yarn is 0.399/0.415 respectively and the change in D is 17.5%. Predict the thread spacing in the fabric using the above logic given in the algorithm and calculate the percentage
116
Woven textile structure
error in the prediction. Solution: l1 = p2 (1 + c1) = 0.042 697 ¥ 1.0425 = 0.044 526 cm l2 = p1 (1 + c2) = 0.023 × 1.063 = 0.024 485 6 cm D = h1 + h2 = 0.020 066 cm D¢ = D ¥ 1.175 = 0.020 066 ¥ 1.175 = 0.023 571 2 cm l1¢ = l1 ¥ 0.9702 = 0.044 526 ¥ 0.9702 = 0.044 348 4 cm l2¢ = l2 ¥ 0.9839 = 0.024 486 ¥ 0.9839 = 0.024 384 cm l1 0.044 526 = = 2.218 98 > p D 0.020 066 2 l2 0.024 485 6 = = 1.220 25 < p D 0.020 066 2 l1 ¢ 0.044 348 4 = = 1.88147 > p D 0.0235712 2 l2 ¢ 0.024 384 = = 1.0345 < p D 0.0235712 2 q1 = 106 0.0425 = 21.8525° q2 = 106 0.063 = 26.6058° Since (l2/D) ≤ p/2, the fabric before washing has tendency for jamming in the weft if deformed, but the warp direction has no constraints. One can infer that the warp direction can shrink more than the weft direction; the weft direction can shrink only until the weft is jammed. This inference is supported by the actual shrinkage percentage in warp being 2.98 and 1.61 in the weft direction. Again since (l1¢/D’) and (l2¢/D¢) are less than their counterparts in the fabric; therefore crimps in both warp and weft will be greater after washing. In this case the solution is obtained by taking q1¢ > 21.8525°, that is equal to 21.8525 + Dq1 and corresponding q2¢ is calculated from equation 5.3. Then (p1¢/D¢) and (p2¢/D¢) are calculated from equations 5.1 and 5.2 respectively for these values of q1¢ and q2¢. Finally the authenticity of the value is checked using equation 5.4. In this example the ratio of bending rigidity was taken as unity. The iteration for q1¢ and corresponding q2¢ was repeated until equation 5.4 was satisfied.
Shrinkage in woven fabrics
117
In this case the solutions are obtained for q1¢ = 30.21° and q2¢ = 11.68°. Calculated p1¢ and p2¢ are:
p1¢ = 0.023 98 cm
p2¢ = 0.039 44 cm
The actual values are:
p1¢ = 0.022 657 cm
p2¢ = 0.041 427 cm
The percentage error for p1¢ is 5.84 and for p2¢ is 4.8. This is reasonable as the bending rigidity is ignored.
5.6
References
1. Peirce F T (1937), J. Text. Inst., 28, T80 2. Marsh J T (1953), An Introduction to Textile Finishing, Chapman and Hall, London, p 241 3. Abbott N J, Khoury F and Barish L (1964), J. Text. Inst., 55, p T111-T127 4. Collins G E (1939), J. Text. Inst., 30, p 46 5. Hari P K (1970), M. Tech Thesis, IIT Delhi