CHAPTER 2 LITERATURE REVIEW

Transcription

1 10 CHAPTER 2 LITERATURE REVIEW 2.1 INTRODUCTION The study of the effect of the weave structures on the properties of woven fabrics is of importance for various reasons. First, it is of interest as a property of the fabrics, it may lead to a better understanding of their nature, and, in particular, of the way in which they affect the comfort and functional properties of fabrics. Second, the weave structures can be widely used for representing the fabrics in cloth analysis division of a textile mill. Third, textile fabrics are used in technical textiles and home furnishings and for this their properties must be satisfactory. Fourth as Morino (2010) states in a recent paper in order to promote the design process for woven fabrics, new parameters are defined ; this is because the study of weave structures is an important component of designing fabrics. Seyam and El-Shiekh (1994) have presented a critical review of the fabric degree of tightness and its applications. They have suggested a new tightness factor based on a combination of Ashenhurst s end-plusintersections theory and Love s race track geometry. The advantages and limitation of the new tightness are discussed. In the past, weaving technologists preferred one or the other empirical relationships for calculating sett/count relationships in fabrics such

2 11 as Ashenhurst s ends plus intersections theory. Armitage and Brierley s maximum sett theory or mathematical theories based on Peirce s geometric model graphical solutions to optimise fabric design (Ashenhurst 1884, Armitage 1907), Brierley s and maximum sett theory, or mathematical theories. The first stage in designing of fabrics is the generalisation of the fabric structure features by one integrated factory. Peirce (1937) aptly stated It gives a very suitable basis of comparison for any experimental investigation, not only of cover but also of hardness, crimp permeability and transparency limits of picking, etc., in which fabrics of similar cover factors show similarity. The second stage is estimating the statistical dependence on the integrated fabric structure factor. The integrating fabric structure factor can be distributed into two groups; those based on Peirce s, theory and those based on Brierley s theory of maximum settling. Various factors are proposed by workers, such as Galceren (1961), Seyam and El-Shiekh (1994), Newton (1995) and Milasius (2007). 2.2 INTEGRATED STRUCTURE FACTORS It is customary to calculate a structure factor by comparing a certain mathematical expression of the parameters of the given fabric structure with the maximum value of a so called standard fabric. In Brierley s (1931) case, the fabric structure factor is the ratio of setting of the given fabric square (balanced) structure analogue with the setting of the standard wire plain weave fabric. The original Brierley factor which is called as Maximum Setting/Maximum Density, can be calculated by equation, where 1 g T 1/T Taverage 1g T 1/T2 1g T 1/T2 MS / MD.S m 2 S1 F (2.1) F m - the empirical weave factor S 1, S 2 - warp and weft setting respectively

3 12 T 1, T 2 - the warp and weft linear density, respectively g - 2/3, if F 1 F 2, and y - 3/2, if F 1 < F 2 (except weft-faced ribs, in the case g=2) - fibre density F 1, F 2 - Float lengths Brierley (1931, 1952) worked with worsted fabrics to determine the maximum threads per inch that can be woven in a square fabric for a given yarn and weave. He derived the following equation m 1/2 t f (kn) (2.2) where t = maximum ends or picks per inch, k = constant that depends on yarn type and yarn number in an indirect system, m = constant varying according to weave, and f = average float (average number of threads per float). The constant k is 134 for worsted yarn from 100% wool. The constant m was determined empirically for different weaves as shown in Table 2.1. Table 2.1 Brierley s m values for different weaves Weave m Basket weaves 0.45 Twill weaves 0.39 Satin weaves 0.42 different counts. Equation (2.2) is also valid for the case where warp and weft are of Brierley (1931) compared the earlier studies of maximum construtions to his work. He concluded that (a) his figures of twill weaves

4 13 agree with Law s results calculated upto 10 threads per floats and there is little divergence from Armitage s results which are t 1/2 S(yN) (2.3) where t = maximum ends or picks per inch, y = cloth setting constant that depends on the yarn numbering system, N = yarn count in the indirect system, and s = setting ratio varying with weave upto 4 threads per float (b) up to 4.5 threads per float the results obtained by Armitage Law and Brierley do not differ by more than a thread per inch and (c) for twill weaves of threads per float higher than 3 Ashenhurst s two theories showed lower maximum threads per inch than Brierley, Armitage and Law s experimental figures. Chamberlain and Snowden (1948), Snowden (1949, 1950) have confirmed that Brierley s and Law s rules of maximum construction of twill weaves are fairly accurate. Snowden (1967) further showed that for satin weaves, Law would have been more accurate had he added 5.5% for every end in the average float. Brierley (1952) extended his work to unbalanced fabrics, deriving three additional empirical relationships for three different unbalanced fabric categories. (a) for cloths woven from equal count in warp and weft P = CE (b) for fabrics made from thicker weft than warp P = CE -0.67A (c) for cloths woven from thicker warp than weft P = CE -2

5 14 N 2 where A, N 1 = warp yarn count in an indirect system, N1 N 2 = filling yarn count in an indirect system, P = picks per inch, E = ends per inch, C = cloth structure constant calculated from maximum square construction. He gave several examples to illustrate the method of calculating the cloth structure constant Brierley (1952). He also explained applications of his equations to worsted and woollen fabrics of different weaves (Brierley 1952, 1953). Galuszynski (1981) has dealt with the fabric tightness, a coefficient to indicate fabric structure. He felt that Brierley s formula requires some modification of certain values of the coefficients m and g for some weft and warp faced ribs and proposed the coefficient of fabric tightness T Galuszynski. For the weft faced ribs, the value F is taken as an average for the weave with g = - 2/3 (whereas Brierley (1952) suggested that the value of F has to be taken as an average for the warp threads and g should be equal to 2). For warp-faced ribs, Galuszynski proposed the value 0.35 instead of 0.42 given by Brierley. Galuszynski (1981) asserts that the values of the coefficient of fabric tightness can be used to compare fabric structures. His results also verify the prediction that fabrics with the same value of the coefficient should have the same value of relevant mechanical properties. Also, fabric elasticity can be predicted from the coefficient of fabric tightness. One of the limitations of Galuszynski s fabric tightness is that it can only be applied only to few weave structures. Milasius et al (2000) proposed a new integrating fabric firmness factor which can be calculated by a series of equations. Newton (1995) has followed a radically different approach for comparing the woven fabrics by reference to their tightness. Newton criticises the standard fabric considered

6 15 by Seyam and El-Shiekh on the grounds that the geometry is such that it is difficult to construct the fabric. Newton s view is that the tightness of a fabric is best calculated in relation to the nearest maximum-sett fabric. This is similar to the method used by Hamilton (1964). A good review of fabric tightness has been published by Seyam and El-Shiekh (1994). In their introduction they state The ratio of a fabric structural parameters to the corresponding parameters of the standard fabric (termed, fabric degree of tightness, fabric firmness, construction factor, etc.) was thought to be useful in producing similar fabrics that might differ in one or more of the construction parameters and in predicting beat up resistance in weaving. Additionally, the fabric degree of tightness can be related to fabric properties. The recognised advantages of developing standard fabrics are to provide flexibility to the designer to construct similar cloth with the available raw materials, to allow prediction of fabric properties and performance which, in turn, help a designer construct fabrics for specific and uses, and to provide a tool to predict the weaving resistance that implies weaving efficiency and fabric quality. Seyam and El-Shiekh (1994) surveyed many methods of determining tightness that have been suggested in the past, including those based on the Peirce equations, such as the work of Love (1954) and Hamilton (1964) and those based on maximum-sett equations derived empirically, such as those proposed by Brierley (1952), Russell (1965) and Galuszynski (1981). They carried out a comparison of Galuszynski s values of tightness, based on the work of Brierley and Russell s based on that of Ashenhurst, for a variety of weaves. This led them to propose a definition of tightness based on standard fabrics. The tightness is determined by taking the ratio of the sum of the fabric warp and weft setts to the sum of the warp and weft setts calculated for the standard fabric with the same yarns.

7 16 The comparison of fabrics on the basis of their cover factor doubtless, is a good indication of the tightness of the weave; the higher the cover, the closer the threads are together, and the more tightly the fabric is woven. Since, it is possible to have fabrics with different setts, yarn counts, weaves and cover factors which are equally tightly woven, a different method of designating tightness has been developed by Newton. Hamilton (1964) used Love s suggestion that a value for tightness could be obtained by comparing the sum of the warp and weft cover factors of the maximum sett fabric. As pointed out by Seyam and El-Shiekh (1994), Love gave no indication as to which maximum sett fabric was to be used, and the method was not practicable. Hamilton (1964) gave the following equations (K1K 2)actual Tightness T = (K K )limit 1 2 (2.4) d1 where K 1 = p, K d2 2 = p and d 1, d 2, p 1 and p 2 are diameter and pick spacing in warp and weft. 1 2 Newton used tightness as a basis for comparison for designing the fabrics. He has calculated them and has compared with the values given by Peirce. He points out that Hamilton s method is incapable of determining the K1 tightness of the two poplin fabrics because of their high K 2 values. While Hamilton s values show an increase with increasing tightness his calculated values show lower values, i.e., tighter fabric shows a lower value. Newton s work stands as a milestone in this subject. 2.3 WORK OF ASHENHURST Perhaps the earliest work that highlighted the importance of the knowledge of the shape of cross sections and transverse dimensions of yarns

8 17 inside fabrics was due to Ashenhurst who, in 1884, gave the first comprehensive theory of cloth structure for estimating the maximum density of packing of threads in a cloth commonly known as the maximum sett of a woven cloth. He derived a formula for calculating the maximum square sett of a cloth in terms of the diameter of its constituent yarns, and the number of threads and intersections in its weave repeat. He assumed that the yarns were of circular cross section and that the distance between yarns at each intersection was equal to the diameter of the yarn, though this second assumption was corrected by him later. Realising that yarns compress very easily and thus offer difficulties in ascertaining their transverse dimensions, he established empirical relations between the diameter and the count of yarns for different counting systems such as woollen, worsted and cotton. The relationship first noted by Murphy (1927) in 1927 that the yarn diameter varies as the square root of the yarn count, also existed in Ashenhurst s empirical formulae. Despite being based on unrealistic assumptions, Ashenhurst s cloth setting theory provided a very useful guide to cloth construction. However, in 1922 Law (1922) criticised Ashenhurst s theory by showing that it was practically possible to weave fabrics to a greater sett than those estimated by Ashenhurst s formula. As to why Ashenhurst s formulae under-estimated the maximum square sett of a cloth, Law suggested that the estimates of yarn diameters obtained from Ashenhurst s formula were much higher than the measured values of diameter of yarns. This observation led Law to apply necessary corrections to Ashenhurst s formulae for calculating the yarn diameter, and hence the maximum square sett of a cloth. In measuring the diameter of yarns, they had recognised that different fibres and different systems of yarn manufacture were likely to affect the overall yarn density, which would itself influence the yarn diameter and hence the maximum square sett achievable in a cloth. Although Law s theory gave fairly accurate predictions of the maximum square sett of cloths, the testing of the validity of Ashenhurst s

9 18 findings remained the subject for many researchers for sometime. It was not until when Helliwell (1940), after measuring yarn diameters by various methods, showed that reasonable agreement existed between the measured values of diameters and those calculated from Ashenhurst formulae. Also, Dickson (1953) had reported that the value of yarn diameter calculated from Ashenhurst s formulae always fell between the value of diameter based on direct measurement of the free uncompressed yarn and the value of the effective diameter of compressed yarn in a fabric and was therefore a useful estimate. The findings of Helliwell and Dickson thus supported Ashenhurst s theory of cloth setting. On the otherhand, Armitage in 1907 and Brierley in 1931, in an altogether different approach to that of Ashenhurst and Law suggested that it was incorrect to regard yarns as having a definite diameter and as being circular in cross-section. With these suggestions regarding the yarns in mind, Armitage and Brierley established relationships for calculating the maximum square sett which did not carry any direct reference to the diameter of a yarn. Brierley (1931) also considered an allowance for the over-riding of threads which varied with the weave type in his relationship for the maximum square sett. From their experimental results, both Armitage and Brierley showed that setts in excess of those quoted by Ashenhurst could be obtained in all weaves. Since these theories were established independent of the diameter and the cross section of yarns, they, particularly to that due to Brierley, gave fairly accurate predictions of the maximum square sett of cloths. Yet the reasons for the ambiguity about the diameter of the yarn and the shape of its cross section were not then clearly understood and Peirce in 1937 put forward a fundamental and rather formidable mathematical treatment of the geometry of cloth structure wherein the yarns were once again assumed to be circular in cross sections, as well as being inextensible and completely flexible. As it had been in Ashenhurst s and Law s theories of

10 19 cloth setting, the diameters of the interlacing yarns figure as one of the most important yarn properties in Peirce s theory of fabric geometry. Like Ashenhurst and Law, it was realised by Peirce that the diameters of yarns could perhaps best be described from their counts. Peirce, however, also considered the effect of yarn density in deriving a relationship between the diameter and count of the yarn. From experimental work carried out mainly on thick twisted ropes of cotton yarns, Peirce concluded that a specific volume of 1.1 cm 3 /g adequately represents the overall density of yarns in cotton fabrics. Peirce, however, indicated that the apparent specific volume of a free thread would vary considerably with twist, fibre type, treatment and method of measurement. The effects of twist and fibre type on the specific volume of both staple and continuous filament yarns have been investigated later by a number of researchers and notable results of a few of these investigations are reported by Hearle (1969). Concerning the packing of fibres in yarns, Peirce introduced a term called yarn porosity. Commonly known as the yarn packing fraction which he defined as the ratio of the fibre specific volume to the yarn specific volume. He showed that a cotton yarn, with its specific volume equal to 1.1 cm 3 /g and the density of its constituting fibres equal to 1.1 cm 3 /g and the density of its constituting fibres equal to 1.52 g/cm 3 is actually composed of approximately 60% fibre the remaining 40% being air space. This porous structure of a yarn does suggest how easily the yarns might compress and their cross sectional shapes distort when acted upon by lateral comprehensive forces. By considering the yarns to be like circular cylinders and to have a specific volume of 1.1 cm 3 /g a 3 /g. Peirce derived a relationship, which like Ashenhurst s and Laws formulae expressed that the yarn diameter d, varies inversely as the square root of the yarn count (indirect) N, as is reflected in his formula: d (inch) = 1 28 N (2.5) where N is the yarn count.

11 GALCERAN (1961) Galceran s fabric structure factor is calculated as the ratio of the sum of the coefficients of the setting of the given fabric with the sum of the coefficients of the maximum warp and weft settings fabric structure factor from the following formula: S1 T1 S2 T2 O Kl 10.73Kl 1 2 (2.6) where T 1/2 are warp and weft linear densities, respectively 1/2 are warp and weft raw material densities, respectively K 1/2 are warp and weft weave factors by Galceran, respectively. In the Brierley s case, fabric structure factor is the ratio of set of the given fabric square structure analogue with the set of the standard wire plain weave fabric. The original Brierley s factor called as maximum setting/maximum density can be calculated by the following equation: 1 g T 1/T2 T average g T 1/T2 g T 1/T2 MS / MD.S m 2 S1 F (2.7) 2.5 GALUSZYNSKI Galuszynski (1981) found that Brierley s formula requires some modification of certain values of the cofficients, m and g for some weft and warp faced ribs and proposed the coefficient of fabric tightness T Galuszynski. For the weft faced ribs value F is taken as an average for the weave with g = 2/3. For warp faced ribs, Galuszynski proposed the value of 0.35 instead of 0.42 given by Brierley.

12 21 Seven parameters are considered to be important for representing fabric structure namely, warp and weft raw materials, warp and weft linear density, warp and weft settings and fabric weave. 2.6 FABRIC WEAVE FACTORS The greatest problem between all fabric structure parameters is to estimate the fabric weave which is not a digital but a graphical fabric structure picture. Fabric weave can be represented as the matrix where 1 labels the float of warp and 0 labels the float of weft. This method is the most popular due to its convenience and possibility to apply computer. Special weave matrix parameters for reflecting weave influence to fabric properties are used. The average float length F 1(2) proposed by Ashenhurst and often used for evaluation for warp and weft respectively is equal to the repeat R 1(2) divided by intersection of warp and weft in the repeat t 1(2). F 1(2) R 1(2) (2.8) t 1(2) Galceran s (1961) weave factor Kl 1(2) and Neves warp and weft interlacing coefficients CCWA and CCWE are similar to it. t (2.9) 1 Kl1 CCWA RR 1 2 and t (2.10) 2 Kl2 CCWE RR 1 2 The shortcoming of these factors is that they estimate only a single thread and do not take into account interlacing of adjacent threads.

13 22 tenseness factor Skliannikov (1974) proposed the following equation of weave 6 6R R 2n K n C 6RR 1 2 f 1 fi i1 1 2 (2.11) where R 1 and R 2 are the warp and weft repeat of the weave respectively, n f is the number of free fields, n fi the number of free fields belong to group i (all free fields are distributed into six groups k i elimination factor of group i. Milasius (2000) has found that there exists a relationship between F m of Brierley and C of Skliannikov (1974), which is given below: F (2.12) c m 1 Based on this equation, Milasius has suggested a new weave factor: P 1 3RR 1 2 1(2) 6 C n 1(2) 3RR 1 2 2nf1(2) K1(2) f l /2i i1 (2.13) These factors evaluate not only a single thread float but an interlacing of adjacent threads too and can be calculated for all types of the weaves while the Brierley s factor F m can be calculated only for those types of weaves Brierley investigated. structure of fabrics. All the seven parameters are encompassed in integrated fabric

14 INTEGRATED FABRIC STRUCTURE FACTORS The integrated fabric structure factors are used for estimation of fabric structure tightness. Newton (1995) distributed integrated fabric structure factors into groups: some of them refer to the Peirce s theory, others to the theory of Brierley. In the first case, it is a ratio of a surface covered by one or two threads systems with the whole fabric area. In the second case it is a ratio of the setting of the square analogue of the given fabric with the setting if the standard wire plain weave fabric. Peirce (1937) introduced the concept of cover factor, which is equal to the ratio of thread s diameter d 1(2) with a distance between threads p 1(2) : K 1(2) d 1(2) (2.14) p 1(2) Seyam and El-Shiekh (1994) suggested the estimation of fabric structure by using determination of fabric tightness concept. Their fabric geometry is composed from threads racetrack shape geometry and Ashenhurst s end-plus-intersection geometry. This structure factor is calculated by the following equation: S 1(2) (F2(1) 1) TS1(2) d1(2) 2 F2(1) 4 (2.15) where d 1(2) are warp and weft diameters, respectively, F 1(2) are warp and weft average float lengths respectively, S 1(2) warp and weft settings respectively.

15 24 Newton (1995) suggested calculating fabric tightness as a distance between point corresponding to the fabric and the nearest point on the Peirce maximal density curve ( ). This factor, can be calculated by an equation L (K K ) (K K ) (2.16) where K 1(2) d F d S 4 1(2) 2(1) 1(2) (2) 2(1) F 1 (2.17) K 1(2) can be calculated from the curve which was plotted by Peirce according to his formula of maximal setting. Galceran s (1961) structure factor is calculated as follows: S T1 S2 T2 OG Kl 10.73Kl 1 2 (2.18) where T 1(2) are warp and weft linear densities, respectively, weft weave factors by Galceran, respectively. k (1/2) are warp and The main shortcoming of Peirce s group factor is their establishing on the average float length F or Kl, which do not estimate exactly the weave. For this reason Brierley s and Galuszynaski s fabric structure factors can be calculated not for all types of the weave. Skliannikov (1974) proposed Weave Tenseness factor (c) based on the fabric fields (Figure) to relate woven structure to fabric properties.

16 25 Fabric fields are division of weave area in three types of fields, namely contact (c), interlacing (i) and float fields (contact field is defined as the porjected region occupied by both three systems (warp and weft). Interlacement is the region of cross-over the warp yarn from one plane to another between two contact fields, then it can be termed as float (f) (Fig 2.1). Figure 2.1 Fabric fields 6 6RT Zn Kn C 6RR 1 2 f i fi i1 1 2 (2.19) where R 1 and R 2 are the warp and weft repeat of the weave, respectively, n f is the number of free fields defined in the woven structure between the yarns, n fi the number of free field s belonging to group i (all free fields are distributed into six groups), K i is the elimination factor of group, and subscripts 1 and 2 denote warp and weft, respectively. Further, using similar methodology Milasius (2000) suggested a new factor called as weave firmness factor (P) derived from the weave tenseness factor and Brierley s fabric tightness factor P 3RR 3R1R 2 2nfi92) Kin fi (2) i (2) 6 (2.20)

17 26 These factors evaluate not only a single thread float but an interlacing of adjacent threads as well and can be calculated for all the types of the weaves. Further, a most convenient form of structural factor called firmness factor () has been proposed by Milasius, which has been demonstrated to be applicable universally. This firmness factor can be used in the design of new fabrics, to evaluate their properties, estimate fabric weavability, and consider the weaving process parameters. 121 P 1 Tav SS a b 1 2 (2.21) where T is yarn linear density; S setting of yarns; is fibre density given by the following Equation; a, b are given by Equation; subscripts 1 and 2 denote warp and weft respectively. S S S S (2.22) T av ST S ST S (2.23) a 1 2 T 1 3 T 1, b 2 T1 3 T 2 2 T1 1 3 T (2.24) 2 2 Milasius s index is very useful for characterising fabrics on the basis of their structure. His contribution to fabric structure area is quite significant and monumental. Morino et al (2005) have proposed a crossing-over firmness factor (CFF) and floating yarn factor (FYF) parameters of weave structure based on

18 27 the interlacements and floats in the structure for predicting the mechanical parameters and fabric hand values. The CFF is given by equation where crossing-over line is defined as the place at which interlacing point changes, for example, the warp yarn changes from over to under the weft yarn, or vice versa for weft in the warp direction (Figure 2.3). Similarly, FYF is calculated from the type of floats, number of floats of each type and overall interlacing points in the repeat as given by the following expression (Figure 2.2). Figure 2.2 Details of FYF Figure 2.3 Details of CFF Number of cross over lines in the complete repeat CFF = (2.25) Number of interlacing points in the complete repeat

19 28 FYF = (Type 1-1X -1) x (Existing number of type 1-1X -1 in the complete repeat Number of interlacing points in the complete repeat (2.26) Padaki et al (2010) have suggested two indices, namely, interlacement index (1) and float index (F) to represent CFF and FYF. Interlacement index is defined as the ratio of number of interlacements in the given weave repeat to that of maximum possible contact field in the design as given by the following equation, where i wp and i wf are interlacements in warp and weft, respectively. Product of warp repeat (R 1 ) and weft repeat (R 2 ) of a woven design gives the maximum possible contact fields in the woven design repeat. Highest interlacement is in plain woven structure (T=2) and noninterlaced structure would have 1 value of 0. iwp i 1 R.R wf 1 2 (2.27) Float index (F) is defined as ratio of number of floats in the weave structure to the maximum possible floats in the weave repeat as given by equation where f wp and f wf are floats in warp and weft, respectively. For a plain woven structure, float index will be 0 as the floats are absent in it and it increases with number of floats in the structure with a maximum value of 2 for all unidirectional structure without interlacement. Both interlacement and float indices complement each other and the sum of interlacement index (I) and float index (F) is always 2 as expressed in the following equation. fwp f F R.R 1 2 wf (2.28) IF 2 (2.29)

20 29 Padaki et al (2010) assert that, in view of the tedious methods of calculating CFF and FYF suggested by Morino et al (2005) their method is quite simple and easy to understand. Hewitt et al (1996) have analysed the preform structural variations such as weave, fabric and yarn parameters for plain, twill and satin structures using a fortran program. 2.8 CRITIQUE OF THE PARAMETERS WHICH REPRESENT WEAVE STRUCTURES Matsudaira s parameters, namely, CFF and FYF are easy to calculate and, do not take into account fabric sett and count. The parameter FFF takes into account fabric sett and the concepts put forward by Brierley. Also, these parameters are affected by warp and weft tensions in the loom and finishing treatments. 2.9 DESIGN PARAMETERS AND SAMPLE DESIGNS There are certain relevant parameters for evaluating weaving tightness in earlier models (Newton 1995, Seyam and El-Shiekh 1994). For instance, Brierley s experimental parameters, F m for weaves F m and Peirce s average float length F or K for weaves are located at the maximum weaving setting and anchored in textiles with limited primary structures and the fixed common materials as well (Seyam and El-Shiekh 1994). Morino s crossingover firmness factor (CFF) and floating yarn factor (FYF) (Morino, Matsudaira and Furutani 2005) and Milasius s weave factors C and P (2000) are demonstrated to be directly extractable from any weave pattern. However, Milasius argued that the parameters FYF and CFF neglected considerations of resistances between yarns (Milasius, Katunskis and Milasius 2007). By contrast, C and P proposed by Milasius (2000) are sophisticated and reasonable, whereas their calculations particularly involve K i defined by Skliannikov and become rather complex. These parameters provide primary definitions or references for the tightness of textiles.

21 30 Weave patterns can be used for distinguishing different weaves. The size of the weave pattern is coded as R W and R F to denote the numbers of warps and fillings within a complete repeat. Weave patterns also show all the information about intersections on each yarn. Ashenhurst (1884) defined the average float length of yarns for weaves, and the distance of intersections (D1) on a yarn within a repeat was given to show the frequency of yarn intersections and to represent the weaving level of each single yarn within a repeat. When D1 increases, the weave structure of fabrics loosens. Formulas for D1 are as follows: D1 W R F Number of int er sec tions in warp (2.30) D1 F R W Number of int er sec tions on filling (2.31) D1 on warps (D1 W ) may be different from D1 on fillings (D1 F ) such as R6*12 (D1 W = 6, D1 F = 4). When the D1 of each yarn is variable such as R16*16, its average value is more effective and should be considered as the accurate D1. Reversed intersections on two neighbouring warp and wefts cause Repulsion (RP)1 between yarns. Repulsion between adjacent yarns is obviously affected by a distance between reverse intersections on two of the nearest parallel yarns. For instance, a twill with 5-end behaves more firmly and tightly than a 5-end satin, because there is a 1-step between inersections on the twill, but there is a 2-step between intersections on the satin. RP can particularly differentiate weaves with the same repeat and D1. Generally weaves with a large D1 cannot attain a large RP. However, there is almost no regular connection identified between them so far.

22 31 Proper design of fabrics and efficient use of weave structures require a serious study of textile materials. This thesis on the prediction of mechanical properties from weave structures was undertaken to develop means of achieving this understanding. During usage, textile fabrics having different weave structures are considered. For example, bed linen is made of 5-end satin weave and towels are made of honey comb weave. Plain and twill weaves are used for producing shirts, pants and dress materials. The concept of fabric properties weave structures interaction which is developed represents a departure from the traditional study of the effect of weave structures. Previously, the studies of weave structures were concerned strictly with the weaves. Plain, twill, satin and mock leno weave have been studied and analysed by textile technologists for several years. These studies usually neglect and rightfully so, the number or designation of the weave which is being used. The fabrics which are used are of huge quantities and are currently used in technical textiles in addition to apparels. For this reason, this study deals exclusively with what happens to the properties of fabrics as a result of the interaction. It is anticipated that in future each fabric will be designated by the parameters which represent the weave structure and then marketed. Since seven parameters, namely raw materials in warp and weft, warp and weft counts, number of end, and picks per cm and fabric weave, the subject assumes considerable importance. Thus Galuszynski (1981) has carried out studies relating weave resistance and weave structures. A number of studies have been made in correlating weave structures to beat up and other fabric structures such as air permeability and mechanical properties. Thus combination of all factors must be considered in the material and property interaction. In order to define quantitatively and analyse the effects of weave structures, it is important to delineate both the fibre, yarn sett and weave.

23 32 Most of the important recent contributions on the prediction of mechanical properties have come out of the Kanazawa University, Japan. This work has been led by Matsudaira (2011). The research work carried out by him stands out as a milestone in this subject. In his papers, the relationship between weave structure and fabric properties is discussed in depth. Structure property relations of fibres and yarns have been studied by many in the past, and in respect of fabrics, it is found to be sparse. A systematic work in this area is warranted and this thesis delineates this aspect. The relationship between the parameters is not known and it is imperative to investigate this aspect in depth. It is important to relate the weave parameters to the low stress mechanical properties and comfort characteristics so as to have a better understanding of weave structures. It is interesting to note that since weave structures affect the low stress mechanical properties as evidenced by the work of Morino et al (2005), considerable changes are to be made in the models which have been developed for predicting them. Still the development of weave parameters is in its infancy as only a few weaves have been considered. Also, designating the fabrics using Matsudaira s and Milasius s parameters will help in identifying fabrics in the cloth Analysis Division of a Textile Mill. For denims which are fashion garments, these parameters will be very helpful FUNDAMENTALS OF FABRIC STRUCTURE Fabrics, which are produced from a variety of yarns, differ in counts, threads per inch and weave. What is required is the adjustment of warp and weft setts (threads per inch) to suit the yarn counts in production of fabrics for specific end uses. The product development is focused on the

24 33 development of the novelty products at economic prices. Stoll (1949) demonstrated that fabric breaking strength and elongation at break of resistance to surface abrasion are unreliable parameters in predicting wear resistance of fabrics. He showed that count balance, warp to weft weight ratio, fabric tightness expressed as cover factor, staple length of constituent fibers, yarn twist and crimp balance between the warp and weft have important bearing on wear resistance of woven fabrics. The only way of improving the wear performance of Civilian, Industrial and Defence fabrics is by applying the principles of fabric engineering. These are the points to bear in mind to design maximum weavability of fabrics which comprise duck, canvas, tarpaulin, parachute and wind resistance fabrics. It was Peirce who did pioneering research in fabric engineering in 1937 which laid the scientific foundation of fabric geometry. The equations provided by him were meant for plain weave. He referred to the effect of weave on maximum warp and weft setts, but it was left to Louis Love (1954) in mid fifties to extend Peirce's equations to weaves other than plain, namely, l/2, 2/2 and l/3 twills, satin and oxford. Dickson developed a system of numbers called 'compact cover factors' based on the cotton system of yarn counts, for maximum weavability constructions using synthetic filament yarns- nylon, polyester, Kevlar, aramid and glass having densities different from those of cotton TERMS USED IN FABRIC STRUCTURE (Peirce 1937) Fabric Cover It is the amount of space occupied by yarn and is expressed by the term 'cover factor' which is given by Thread per inch K (2.32) yarn count

25 34 Warp cover factor (K 1 ) and weft cover factor (K 2 ) serve as a measure of the relative tightness of fabric Yarn Balance This is expressed by the term 'Beta factor' by Warp yarn count (2.33) Weft yarn count This is an essential part of the maximum weavability equations mentioned later. Cover factor was defined as Fabric cover factor= K f = C warp + C weft - C warp C weft (2.34) Where C warp and C wcft = 4.44 x 10-3 x Tex f x Yarn count / cm (2.35) Weave Factor It is defined by Number of threads per repeat M (2.36) Number of int erlacing per repeat Fabric Tightness This is given by Sum of actual Warp and Weft coverfactors Tightness (2.37) Sum of theoretical maximumwarp and Weft cover factors This tightness affects the mechanical properties of fabrics.

26 Maximum Weavability Given the warp cover factor (Ki) and.yarn balance (Beta factor) Peirce (1937) developed the following equation for arriving at the maximum weft cover factor (l< 2 ) in plain cotton woven fabrics having a weave factor (M) of (1 )K (1 )K 1 1 (2.38) Fabrics other than Plain Weave It is a well known fact that when cotton yarns of normal twist or softness are woven in fabrics in weaves other than plain, say, twill, satin or oxford the maximum weavable cover factors exceed 28 which is meant for plain weave. This is due to the lateral compression in yarns beneath the 'weave floats'. The yarn compression in a fabric woven to maximum tightness would produce a change in the shape of the cross section, but does not alter the fibre packing density within the yarn. Complete flattening of yarn, which is the contact with the neighbouring yarn under a single float i.e., the original, semi-circle of the yarn half-section becomes a rectangle under compression The weave factor is 1.5 for 2/1 twill, 2.0 for 1/3 twill and 2.5 for 1/4 satin. Louis Love developed four equations for arriving at the maximum weft cover factor (K 2 ) given the warp cover factor (KJ and yarn balance (beta cover factor) for 1 / 2 twill (M=1.5), 1/3 and 2/2 twill (M=2.0) 1/4 and 2/3 twill or 5 end satin (M=2.5) and oxford weave (M 1 =2.0, M 2 =1.0). U.S. Army Natick laboratories have published (1972) a series of reports which contain tables that came as ready reckoners for cover factor, beta factor and maximum weavability for cotton fabrics, covering a wide range of yarn counts (Ne 1 to Ne 84) ends and picks per inch (11 to 200) and

27 36 beta factors (0.109 to 10). These Tables are very useful to fabric engineer in arriving at the practical design parameters related to the textile structures. Although these tables are very useful in predicting the theoretical maximum level of picks in a given fabric, the actual number of picks depends upon the loom mechanism, its condition and some other factors Synthetic Yarn Fabrics Dickson (1954) developed a system of calculating fabric cover based on cotton system of yarn counts to arrive at ' compact cover factor' which varies according to fibre density and bulk density of filament yarns. This is defined as the maximum number of cotton yarns of Ne 1 count that can lay side -by-side in one inch without any interlacing. It is given by : Maximum threads per inch Compact cover factor x Cotton count (2.39) Compact cover factors for some of the synthetic filaments are as follows: Nylon : 24.4 Polyester : 26.8 Kevlar aramid : 27.4 Glass : 36.5 Thus the maximum number of filament yarns in the one inch of the four synthetic fibers can be arrived at by first converting the filament denier into cotton count by dividing 5315 by denier and multiplying the same by respective compact cover factors. Sulzer (1982) have published charts for the range of weft density feasible for specific fabrics woven on their shuttleless projectile weaving

28 37 machines based on their practical experience, assuming that the warp and weft yarns are of medium quality Fabric Tightness Factor (K) This was calculated by using the equation (Dhingra et al 1981) Fabric tightness factor, K T w w T f f (2.40) Where, T = yarn count in tex. w = Modular length or average curvilinear length of yarn per W = warp interlacing (in cm) F = filling Fabric Tightness Coefficient (t) Some New Concepts Galuszynski (1981) defines fabric tightness as the ratio of actual square fabric sett over the theoretical maximum square fabric sett for a defined weave and yarn. The coefficient of fabric tightness, as explained, by him depends on raw material, yarn linear density (count) weave and fabric sett. Galuszynski incorporated Brierley's setting formula into his own equations whereby coefficient of fabric tightness N a t (2.41) N

29 38 Where N a = N 1 -g/g-1, N 2 1/1-g and N KF m 4 (2.42) Tex In Equations (2.41) and (2.42) N 1,2 = the unknown values of warp and weft setts, respectively g = a first coefficient dependent on the weave K 4 = a coefficient dependent upon the raw material and count system F = the average warp or weft float of the weave m = a second coefficient dependent on the weave Tex = the average yarn count. Thus Tex was calculated Tex ntex 1.Tex 2 n Tex n Tex (2.43) where, n = The total number of threads in the weave repeat Tex 1,2 = The defined counts of threads within the weave repeat and n 1,2 = The numbers of threads of a defined count within the weave repeat Fabric Tightness Cloth cover factors for different weaves assuming balanced tight ; (maximum) construction are arrived at on the basis of weave texture which is given by: Weave Texture Ends per weave repeat Ends per repeat Interlacings in the repeat (2.44)

30 39 Thus, for plain weave, the texture is 0.5(2 divided by 2+2); for 1/3 twill, the texture is 0.667(4 divided by 4+2); and for 8 end satin, the texture is 0.8 (8 divided by 8+2) the maximum cloth cover factor for plain weave would be given by W c = 0.5, Fc = 0.5, C c = ( )-(0.5 x 0.5) = 0.75; for 1/3 twill, ( ) - (0.667 X 0.667) = 0.889; and for 8 end satin, ( ) - (0.8 x 0.8) = 0.96 The 'tightness' or 'openness' of a synthetic yarn fabric can be assessed by comparing the actual fabric cover factor with maximum cover factor for a given weave; for example (a) Kevlar style -713 has 31 ends and 31 picks per inch of 1000 denier yarn in plain weave. Maximum threads per inch = compact cover factor of Kevlar (27.4) x cotton count (2.305) = 63; Warp cover factor (W c ) = 31 divided by 63 = Weft cover factor (F c ) = 31 divided by 63 = Cloth cover factor (CC) = ( ) - (0.492 x 0.492) = As the maximum possible texture for plain weave is 0.75, Kevlar style-713 can be considered as nearly 'tight' with 98.93% tightness (ratio of actual texture to maximum one, expressed as percent) (b) Kevlar style -328 having 17 ends and 17 picks per inch of 1420 denier Kevlar in plain weave and having cloth cover factor (C c ) of is by comparison with style-713 relatively loose construction with 71.87% 'tightness' (0.539 divided by 0.75 x 100)

31 40 Various integrated structure factors are used for a full fabric evaluation. Newton classified integrated fabric structure factors into groups; some of them refer to Peirce theory, others to the theory of Brierley. In the first case, it is a ratio of a surface covered by one or two systems of threads with the whole fabric area. In the second case, it is a ratio of the setting of the square analog of the given fabric with the setting of the standard wire plain weave fabric. The evaluation of some fabrics parameters is rather simple as they are expressed by specific numbers, the only exception of these parameters being fabric weave. It is a picture of fabric structure and can be represented only graphically or as the two -dimensional matrix of number 1 and 0. It greatly complicates its estimation and generalization of the results of experiments. The main problem of all integrated factors is the kind of weave factor they use. Average float length F or Kl is used in Peirce group factors; they evaluate only a single thread whereas it is well known that maximum setting (as well as fabric properties) of such weaves as twill 2/2, hopsack 2/2 differs widely. Brierley suggested evaluation of fabric weave by the function F m. The power 'm', was determined experimentally,it depends on the weave type, for example, for twill weaves it is 0.39, for satin weaves 0.42, for hopsack weave 0.45 etc. Consequently weave factor F m takes into account the interlacing of adjacent threads, Despite this, its shortcoming is experimental determination of power 'm' and the values of 'm' for other weaves. Milasius has proposed both weave factor P 1; which belongs to Brierley group and which can be calculated directly from weave matrix and based on it the integrated fabric structure. The weave factors floating yarn factor (FYF) and crossing over firmness factor (CFF) proposed by Morino et al (2005) belong to Peirce group and like all the factors of this group, they do not take into account an interlacing of adjacent threads.

32 41 mentioned below: Morino et al (2005) have suggested a new measure FYF which is FYF Type 1 x existing number of type -1 in the complete repeat 11x 11x Number of interlacingpoints in the complete repeat (2.45) Where Type 1-1x is the length of the float. Ashenhurst has dealt with the sett of fabrics in his book. Seyam has critically reviewed the concept of fabric tightness in his work. A series of papers published by Seyam has dealt with the fabric structure and its effect on fabric properties GOSWAMI S WORK Goswami (1978) did a pioneering study on the effect of weave structures on fabric properties but he confined to the shear properties only. He made plain, basket and satin weaves from polyester cotton blended yarn having two twist levels, 14 and 18 tpi. The fabrics had 60 x 60 fabric count and the plain woven fabric was heat set. Shear parameters were studied by attaching a device to Instron Tensile Tester, as suggested by Spivak (1966). The shapes of the shear stress strain curves were found to be different (Figure 2.4). The shear stress and hysteresis were found to be less for 2 x 2 basket and satin in comparison with plain weave. The CFF values for the three weave structures and their shear parameters are given in Table 2.2.

33 Figure 2.4 Shear stress strain curves of different weaves 42

34 43 Table 2.2 Relationship between CFF and shear properties CFF Shear hysteresis (G/cm) Shear stress (G/cm) Shear strain Tan Plain Basket Satin It is apparent that the relationship between CFF and shear parameters is excellent. As CFF increases, shear stress, shear hysteresis and shear hysteresis show an increase. Shear strain, on the other hand, shows a decrease with an increase in CFF. Although this paper was published in 1978, it was found to be very useful for this research FATAHI AND ALAMDAR YAZDI S WORK In a recent series of papers by Fatahi and Alamdar Yazdi (2010, 2012) the air permeability of the fabrics has been measured exprimentally and modelled theoretically. With weave structures such as CFF and FYF, the air permeability of eight fabrics has been related (Figure 2.5). The model they have obtained is Air permeability = (CFF) + () FYF + () (,, - constants) (2.46) The result of the multiple regression equation is Air permeability = (CFF) (FYF) (2.47) They state that it is possible to predict the value of air permeability by the multiple regression equation.

35 44 The FFF (Fabric Firmness Factor) values for all the eight fabrics have been calculated and they are given in Table 2.3 along with CFF and FYF. Table 2.3 Calculated results of CFF and FYF and FFF for 8 fabrics of Fatahi and Alamdar Yazdi (2012) (Figure 2.5) # Weave CFF FYF FFF a Plain b 2/2 Twill c 2/6 Twill d Warp rib e Basket Weave f Dice Weave g Rib h Crepe (a) Plain (b) 2/2 Twill (c) 2/6 Twill (d) Warp Rib (e) Basket weave (f) Dice weave (g) Rib (h) Crape weave Figure 2.5 Weave structures used by Fatahi and Alamdar Yazdi (2012)

36 INITIAL MODULUS OF FABRICS The subject of initial modulus of woven fabrics has attracted the attention of many research workers, namely, Grosberg and Kedia (1966) Leaf and Kandil (1980), Hearle and Shanahan (1978) and De Jong and Postle (1977) using many techniques such as Castigliano s theorem for small deformations. It is a pity that there is a perpetual error in the units of initial moduli provided by Leaf and Kandil in that mn/cm is given which in reality is N/cm. Hadizadeh, Jeddi and Tehran have correctly given the unit in N/cm. These authors predicted the initial load-extension behaviour of woven fabrics using artificial neural network. Behera and Muttagi (2004) considered the yarn flexural rigidity, yarn modular length, and yarn spacing as inputs and initial modulus of fabric as output in their Artificial Neural Network (ANN) modeling of fabrics load extension behaviour. They indicated that their radial basis function network model could predict the tensile moduli of fabric to provide a very good and reliable reference compared to the other modeling methodologies. Hearle and Shanahan (1978) have pointed out that the inclusion of a bending energy term allows the Peirce geometry to be used for calculations involving extension. They have provided the predicted load extension curves of a plain weave fabric. Clulow and Taylor (1963) have looked at the relationship between the theoretically predicted and experimental values of fabric and have pointed out the need to include flexural rigidity for accurately predicting the load extension curves. Leaf and Kandil (1980) have proposed the following mathematical model for predicting initial Young s modulus of fabrics. E 12B P 1 B cos P11sin 1 B1 2cos 2 (2.48)