volume porosity and permeability in double …autexrj.com/cms/zalaczone_pliki/4-05-4.pdf · volume...

AUTEX Research Journal, Vol. 5, No 4, December 2005 © AUTEX

http://www.autexrj.org/No4-2005/0103.pdf 207

VOLUME POROSITY AND PERMEABILITY IN DOUBLE-LAYER WOVEN FABRICS E. A. Elnashar Faculty of Specific Education, Kafer ElSheikh, Tanta University, Egypt E-mail: [email protected] Abstract

Clothing for garments is designed to meet both the safety and the comfort of human beings. Porosity is considered to be one of the basic features representing a textile structure. The properties of fabrics were analyzed by determining the efficiency of fabric porosity. The woven fabric multi-layer structure, the warp and weft densities, and the type of weave are factors of a woven fabric, which as porous material enables to transmit air, heat energy, and liquid perspiration. Several methods considering thread distributions have been developed to determine the woven fabric’s porosity. A mathematical model based on an ideal geometry of the porous structure of a multi-layer woven fabric has been developed.

Key words:

multi-layer woven structure, warp-ends, warp density distribution, porosity, permeability 1. Introduction

Porosity is the ratio of the total amount of void space in a material to the bulk volume occupied by the material. Fabric porosity is an important parameter in assessment of clothing comfort and physical properties of technical textiles. This paper reports the influence of constructional parameters of a woven fabric, such as yarn linear density, type of weave, and relative fabric density on the macropore area and its distribution. Predictive models of macropore area and macropore area distribution have been developed for engineering one-layer woven fabrics. The production of modern woven fabrics demands developing strategies considering new structures. It is clear that a new fabric structure should have the desired quality at minimum production costs, and the highest possible weaving efficiency. Achieving such a demand is a complex task based on our knowledge of the connections between woven fabric structure parameters and the predetermined fabric properties that fit the desired quality. The evolution of ‘maximum construction theories’, as well as the fast development of computer science, allows us a faster and more precise planning of new products. In the field of ‘maximum construction theories’ some relationships are well known, which can, in the form of computer programs, serve as a part of an expert system for the development of new fabrics. However, in the field of connections between the woven fabric structure and the individual fabric properties, such as for example porosity, a need arise further to determine some of such relationships; firstly should be developed a ‘maximum construction theory’ about square fabrics using simple geometry. Gee introduced the well known ‘ends plus intersection theory’, which he upgraded, and named the ‘curvature theory’ [1]. Until then a ‘maximum theory’ had been the subject of several research. Some researchers, such as Peirce, Love, Kemp, Hamilton, Weiner, Peirce & Womersley [2], Love, Kemp, Hamilton, and Weiner [3, 4, 5, 6] have used a more theoretical approach, whereas some other as Armitage, Law, Brierley, Seyam & El-Shiekh (1993), Gee (1953), and Brierley [7] used more experimental means. M. Kienbaum [8] has successfully joined theoretical and experimental investigations, and presented his own theory which can be applied to all weaves and different yarn structures. Woven fabric, as a porous material, enables the transmission of energy in the form of light and heat, as well as of substances, such as liquids, gases and particles, and therefore is interesting for different



applications, e.g. for garment and technical applications. Several experimental methods including optical methods, methods on the basis of liquid penetration, absorption, filtration, and airflow have been developed to determine the woven fabric’s porosity. All these methods can be used only on real fabrics. The geometrical method developed by Jakšić.[9] differs from the above-mentioned, as it is based on an ideal geometrical model of individual textiles, which are considered as porous materials, and on input data such as fiber length, fiber diameter, yarn linear density, and thread density. Such a method obviously does not need expensive laboratory equipment or sample weaving. However, the results of the geometrical method do not compare well with the real values determined by other experimental methods [10]. A new geometrical method to predict the macroporosity of woven fabrics developed by us, which is based on the tube-like system of the porous material and on two geometrical parameters of the woven structure, namely the thread density and the yarn linear density, is more precisely described as the effect of the linear density of threads, the weave factor, and the relative fabric density on the woven fabric’s macroporosity. New experimental models are proposed to predict the porosity in terms of the pore cross-section area, and the equivalent maximum and minimum pore diameters, pore density and open porosity. The models are based on the geometrical parameters of the woven structure, the thread linear density, the weave factor, and the relative fabric density. The main difference between the theoretical model, and the experimental models proposed in this study to predict the macroporosity of woven fabrics, is that the latter models also include the weave factor and the relative fabric density, as well as the geometrical parameters, which have a direct effect on all parameters of the woven fabric’s porosity. Besides that, the proposed experimental models are not based on an ideal model of porous structure, but on experiments, which better describe the real porous structure of woven fabrics. A lot of models for description of porosity in woven fabrics can be made, among others such which describes the porosity between yarns (the inter-yarn porosity), and the porosity between fibers inside the yarn (the intra-yarn porosity). From the point of view of air permeability evaluation, this assumption is questionable for a tightly woven fabric with staple fiber yarn. Accepting the introduced assumption, a classical 2-D pore model seems to be sufficient. In a theory of a 2-D model, the porosity Ps is defined as a complement to the woven fabric cover factor CF. An area of pores is calculated as a perpendicular projection of the woven fabric. Real values can be measured as:

Ps = 1- CF = 1- (do Do +du Du - do du Do Du) (1)

where: do, du are the diameters of warp and weft yarn respectively, and Do, Du are the sets of warp and weft yarns respectively. A classical 2-D model of porosity seems as insufficient for a tightly woven fabric. Neighboring yarns are very close and the projected area of inter-yarn pores approaches to zero. As air flows through the woven fabric, it flows around the yarns and it does not flow only in the perpendicular direction [11, 12]. When a woven fabric is treated as a three dimensional formation, the void spaces (called pores) could be situated in the fibers, between fibers in the thread, and between warp and weft threads in the fabric [13]. The latter of these above-mentioned pores are also called macropores, and will be the subject of the following discussion. Woven fabrics, while compared to knitted fabrics or nonwovens, have the most exactly determined inner geometrical model of a porous structure in the form of a tube-like system, where the macropores has a cylindrical shape with a permanent cross-section over all its length [9]. To compare woven fabrics by their macroporosity, the following parameters are commonly used: the area of the pore cross-section, the pores’ area distribution, the pore density, the equivalent pore diameter, the maximum and minimum pore diameters, the pore length, and the pore volume, as well as the content of the open area and the content of the pore volume in relation to the total quantities of the fabric. Within the black frame in the weave repeat of a plain weave, the area of the thread’s intersection (TI); the area of the weave passage (WI) and the area of the macropores (MP) are designated. Because warp density is usually greater than weft density, an elliptical shape of the pore cross-section is accepted to represent the situation. Permeability is a feature, which represents the ease with which a fluid moves through a porous medium. The permeability of the textile medium is directly related to the volume of the fibre fraction of



the textile medium. The various governing relationships that are used in this study of permeability, and the relation between permeability and fiber volume fraction are described in detail in the following chapters. The most commonly used description of the flow of a Newtonian fluid through a porous medium is that proposed by Darcy [14]. Permeability of porous materials depends very strongly on their morphological structure. Due to the complexity of the fiber architecture and the lack of an adequate mathematical model, many researchers continue to determine permeability experimentally. The main aim of theoretical analysis of air permeability of textile materials is usually to find a relationship between the air permeability and the structure of textiles. A textile structure is in this case usually represented by its porosity. A number of theoretical and experimental methods exist for the determination of porosity. Every method includes some simplifying assumptions which causes inaccuracy. Generally, the porosity indicates how much air contains a textile material with a given warp-ends density distribution. Further details about the configuration of pores in textiles, such as the pore size, shape, and arrangement are very important for the description of physical properties of multi-layer woven fabrics [13], and the air flow through textile materials. The subject of this research is:

1. To study the porosity models of multi-layer woven fabrics considering the flow interaction between porosity and thread distribution; this research modifies an existing three-dimensional model to include in it the simulation capabilities, and to verify this model with the fabrication of structural composites.

2. To characterise the eight-harness fabric (for use in processing) by the porosity, the thread distribution in the multi-layer woven fabric, the thickness, and the permeability.

3. To use the model for analysis of the manufacturing process, where this model should enable the user to design the best process for manufacturing composites of high quality.

2. Experimental study 2.1. Materials Experiments were carried out on woven fabrics, which were constructed according to the setting theory. The following yarns were used: combed warp yarns of 20.4 tex for the upper fabric, 39.4 tex for the lower fabric, and weft yarns of 39.4 tex for the upper & lower fabrics, spun from 100% cotton staple fiber (Giza 70), on a ring spinning machine. The packing factor and the factor of thread flexibility were determined according to literature. The parameters of the woven fabric structure accepted by us are the weave factor and the fabric density. All variables used for determining the weave factor were collected (maximum densities, setting thread densities, actual thread densities and relative densities). All fabric samples were woven on a Stuble weaving machine under equal technological conditions. 2.2. Multi-Layer Two-layer woven fabrics (100% cotton) were designed and manufactured with variations in distribution of warp types as given in Table 1. Table 1. Description of the experimental weaves

Woven fabric Upper weave Lower

weave

Linear density of upper warp,

tex

Linear density of upper & lower

weft, tex

Linear density of lower warp,

tex

Fabric density - warp×weft,

per/cm I Plain1/1 Plain1/1 20.4 39.4 39.4 48X18 II twill 3/3 Plain1/1 20.4 39.4 39.4 48X18 II Satin 6 weft Plain1/1 20.4 39.4 39.4 48X18

The fabrics were designed in the Faculty of Applied Arts, Textile Department, Helwan University. 3. Experimental methods The experimental study was carried out as a new approach to predict the parameters of the woven fabric’s macroporosity by using a factor analysis based on the mathematical model developed by us.



3.1. Macroporosity measurements We used an optical method with the use of SMZ-2T Nikon computer-aided stereomicroscope with special software to measure the area of the macropores' cross-sections for each fabric specimen,. 3.2. Permeability testing The air permeability of fabrics was tested by an air flow tester, according to D1175-80 A.S.T.M Standard A.S.T.M in the Consolidation Fund of Alexandria [14]. 4. Results and discussion The Modified 2-dimensional model of porosity, includes partly a 3-D structure of pores in the multi-layers. Various types of pores do not show the same relationship between the designed and the real effective area opened for the flow. The influence of the pores was described by a basic denting system of unit cells. According to [11], each type of woven fabric can be described by the following pore types. We created the pores into the double-layer of a woven fabric by the denting systems as are shown in Figures 1, 5 and 6 and Tables 2÷5 Correlation between porosity and air permeability of a fabric is very complicated because changes of the textile structure (by influence of the denting system), can be possible classified as a horizontal increase in porosity, by removing the free yarn section. Yarn are interlaced very closely in a plain weave; in twill or satin weaves a relative removing of yarns causes an increase in its porosity, predominantly in vertical direction. Air-flow through the fabric causes a move of not interlaced parts of yarn-floats which in textiles depends on the length of these floats. So the horizontal increase in porosity can result in a considerable increase in air-, moisture, and vapour permeability.

Figure 1. Denting regular system as 2/gate in reed for upper layer fabric (plain weave for lower layers)

Table 2. Woven fabric construction Parameter Upper fabric Lower fabric

Linear density of warp, tex 20.4 39.4 Linear density of weft, tex 39.4 39.4 Warp density, threads/cm 32 16 Weft density, threads/cm 18 16 Reed dents, threads per dents 2 2 Open Porosity, % 24.2 45.3 Weave structure plain1/1 plain1/1



Figure 2. Cross-section (plain weave 1/1 for tow layers)

Table 3. Woven fabric structure

Parameter Upper fabric Lower fabric Linear density of warp, tex 20.4 39.4 Linear density of weft, tex 39.4 39.4 Warp density, threads/cm 32 16 Weft density, threads/cm 18 18 Reed dents, threads per dents 3 2 Open Porosity, % 15.9 45.3 Weave structure basket 3/3 plain1/1

Table 4. Woven fabric structure

Parameter Upper fabric Lower fabric Linear density of warp, tex 20.4 39.4 Linear density of weft, tex 39.4 39.4 Warp density, threads/cm 32 threads/cm 16 Weft density, threads/cm 18 threads/cm 18 Reed dents, threads per dents 3 2 Open Porosity, % 15.9 45.3 Weave structure Twill 3/3 plain1/1

Figure 3. Cross-section (Twill weave 3/3 for upper and plain weave 1/1 for lower fabric)



Table 5. Woven fabric construction

Parameter Upper fabric Lower fabric Linear density of warp, tex 20.4 39.4 Linear density of weft, tex 39.4 39.4 Warp density, threads/cm 32 threads/cm 16 Weft density, threads/cm 18 threads/cm 18 Reed dents, threads per dents 3 2 Open Porosity, % 18.6 45.3 Weave structure Satin 6 weft plain1/1

Figure 4. Fabric cross-section (Satin weave 6 weft for upper fabric and plain weave1/1 for lower fabric)

Figure 5. Reed dents system as 3:1 /2gate in reed for upper babric

Figure 6. Reed denting system as 3:3:0 /3gate in reed for upper fabric



Table 6. Air permeability of fabrics with various densities

Type of Weave warp Crimp C,% Weft Crimp C,%

Fabr

ic

Fabric code

upper lower

Weight per square

meter, g

Cloth thickness,

mm Upper lower Upper Lower

Air permea-

bility, Ft3/ cm2

s tandard Plain1/1 Plain1/1 276.6 0.82804 23.4 13.6 5.2 4.8 38 B 1 268.8 0.82042 18.6 12 5.8 8.2 B 2 288.7 0.82804 19.8 12.8 4.7 6.0 B 3

Plain1/1 Plain1/1

297.6 0.82804 27 15.4 4.6 5.2

42 40 50

C 1 292.05 0.87122 29.8 22.81 4.2 2.8 C 2 292.6 0.8636 21.2 13.4 6.0 7.0 C 3

Plain1/1 Plain1/1 299.4 0.82042 20.0 13.6 4.6 4.4

43 43.5 45

D 1 317 0.90424 15.4 17 5.2 5.4 D 2 321 0.8636 21.8 20.6 7.4 8.4

I

D 3 Plain1/1 Plain1/1

316 0.889 26.6 20.6 10.4 8.6

69 63 75

standard twill 3/3 Plain1/1 252.4 0.92202 10.4 11.8 5.2 6.2 35 B 1 275 0.87884 8.4 13.6 4.8 4.3 B 2 281.6 0.904 9.2 13 3.4 3.7 B 3

twill 3/3 Plain1/1 292 0.92202 11.8 15.6 4.4 4.0

39 40 49

C 1 294.65 0.889 13.6 15.2 7.2 5.8 C 2 289.89 0.9144 14.4 16 11.8 7.2 C 3

twill 3/3 Plain1/1 305 0.9398 23.8 18 5.8 5.4

47 54 54

D 1 305 0.9271 23 16 6.8 8.4 D 2 297 0.94488 25 16 6.5 5.6

II

D 3 twill 3/3 Plain1/1

294 1.00 19 12.5 8.9 8.8

46 58 55

standard Satin 6 weft Plain1/1 289 0.980 11.6 12.8 3 3.2 35

B 1 281.3 0.8788 8.4 13.6 4.8 4.3 B 2 280.78 0.955 9.2 13 3.4 3.7 B 3

Satin 6 weft Plain1/1

293.5 0.9728 11.8 15.6 4.4 4.0

49 57 58

C 1 295.66 0.9271 12.6 18.2 3.4 4.2 C 2 300.75 0.9398 10.2 13 4.2 2.4 C 3

Satin 6 weft Plain1/1

306.5 0.9398 7.6 8 6.2 3.8

51 72 76

D 1 327 0.998 13 22 4.2 5.8 D 2 324 1.02362 12 19.8 5.4 4.8

III

D 3

Satin 6weft Plain1/1

317 1.1684 11 22 5 5.6

49 76 99

The fabrics were made from cotton yarns produced at twist factor 4 with (S) direction for warp and with twist factor 4.4 with (Z) direction for weft. 4.1. Factors influencing porosity in multi-layer woven fabrics

- Type of material - Linear density of yarns "warp-weft" - Warp and weft density per cm - Twist factors - Type of spinning - Difference of denting system - Type of stitches - Form and relative porosity - Type of woven construction - Thickness & weight

4.2. Types of woven fabrics While the effects of weave ability are effectively limited by the distribution of floated in the woven fabric and considering the steadiness of woven repeat the weave factor can be expressed as following: M = nr / ni where: M – weave factor, nr – number of yarns in the repetition of the woven structure, ni - number of sett interlacing through the woven structure.



)2( where: Rv - total porosity, TTK - thickness of double cloth . UP - upper cloth, LW - lower cloth.

Table 7. Description of symbols for equation (2)

Warp Weft Description UP doB UP dyB Vertical Cross section for yarn "warp-weft" UP dor UP dyr Horizontal Cross section for yarn "warp-weft"

UP LoR UP LyR Length of yarn "warp-weft" extended between tow intersection in perfect repeat of woven construction

UP LRo UP LRy Width of repeat of "warp-weft" UP Ro UP Ry Number of yarn repeats for "warp-weft" UP ao UP ay Crimp for "warp-weft" LW doB LW dyB Vertical Cross-section for yarn "warp-weft" LW dor LW dyr Horizontal Cross-section for yarn "warp-weft"

LW LoR LW LyR Length of yarn "warp-weft" extended between two intersection in perfect repeat of woven construction

LW LRo LW LRy Width of repeat of "warp-weft" LW Ro LW Ry Number of yarn repeat for "warp-weft" LW ao LW ay Crimp for "warp-weft" IFC Integration factor construction

IFC = Σ (α X W ) / n [13] (3)

Where: α - balance factor of the woven structure. W - width of stripe (density). n - number of stripes (density).

K = C n √ N For the direct system: C - is the constant for material, (0.04126 for tex). n - number of threads per inch. N - yarn count. By appropriate conversion of the quantities used in equation (1) and use of the calculated cross-section areas we can obtain the following equation for the porosity volume, which can be practically applied:

)4( Where the description of symbols is given in Table 8.



Table 8. Description of the symbols for equation (12)

warp Weft Description UP ηor UP ηyr Considerable (grate) of yarn Cross-section LW ηor LW ηyr Considerable (grate) of yarn Cross-section UP ηoB UP ηyB Smallness of yarn cross-section LW ηoB LW ηyB Smallness of yarn cross-section UP ao UP ay Crimp of yarn LW ao LW ay Crimp of yarn UP Po UP Py Number of yarn in inch for "warp-weft" LW Po LW Py Number of yarn in inch for "warp-weft" UP Co UP Cy Yarn twist factor LW Co LW Cy Yarn twist factor UP To UP Ty Linear density in tex LW To LW Ty Linear density in tex

The internal porosity of cloth can give a view about the porosity considering the the air vacancy between yarns; between the inner of the yarn, and between the interiors of fibers as the following:

Ri = RM - Rv, (5)

where: Ri - the air vacancy between the inner of yarn. RM - general porosity, Rv - volume porosity, Maybe calculate the general porosity of multi-layer woven fabric, it describe all the air between distances, between yarn, so, inner of textile fibers as the following:

))66(( where: γ = theoretical density for spun fibers which form the warp and weft yarns. By compensation of the volume porosity "Rv", and the general porosity "RM" from the previous equation, we can obtain a new equation to calculate the inner porosity of a woven double cloth, which takes into consideration the significant principal factors of the woven structure:

))77(( This equation gives us more fitting results, in attention to calculate the volume porosity and the inner porosity, especially if the woven cloth is used in garments. This model was constructed to have a geometry, on one hand complicated enough to see the effect of changing the location of the medium, but on the other hand simple enough to save computational time.



Permeability is an important material property which knowledge is required in various flow simulations while processing composites. This quantity is defined as the property of a porous material, which characterizes the ease with which a fluid is forced to flow through the material under an applied pressure gradient. Both, the steady state and the impact permeability measurement techniques were used in this work. The model elaborated was used as a process analysis tool. This enabled the user to determine such important process parameters as the location and type of injection ports, as well as the permeability and location of the high-permeable textile products. A process for a three-stiffener composite panel was proposed by using a denting system as shown in Table 9 (B, C, D). This configuration evolved from the variation of the process parameters while modelling several different composite panels.

Table 9. Specification of the denting system

Distributing yarn system Repeat Wide /M.M

Denting system Area

code including 2 layers

2 A A 1 4:5 2 B 1 6: 3: 6 B 2 6: 6: 6: 3: 3: 3:

12

B 1 2 3 B 3 6: 6: 6: 6: 6: 6: 3: 3: 3: 3: 3: 3:

10 C 1 7: 6: 5: 4: 3: 2: 3: 4: 5: 6: 12 C 2 7: 7: 6: 6: 5: 5: 4: 4: 3: 3: 2: 2: and mirror copy 38

C 1 2 3 C 3 7: 7: 7: 6: 6: 6: 5: 5: 5: 4: 4: 4: 3: 3: 3: 2: 2:2: and mirror copy

24 D 1 7: 7: 0: 7: 6: 0: 7: 7: 7: 0: 0: 0: and mirror copy 31 D 2 7: 7: 7: 7: 7: 7: 0: 0: 7: 7: 7:7:0:6:6:6:6:0:6:6:6:6:6 26

D 1 2 3 D 3 7: 7: 7: 7: 7: 7: 7: 7: 6: 6: 0: 0: and mirror copy

From the above demonstrated can be stated that the results for single layer fabrics do not represent the actual behavior of the fabric. They overestimate the permeability, as the layers in the experimental rig are shifted and compressed to fit the cavity. We do not know the exact placement of the layers. In our calculations it was assumed that the thickness of 2 layers of the fabric is equal to the cavity depth; the dimensions of the (compressed) yarns were chosen in such a way that they would secure the given thickness for the cases of minimum and maximum nesting. The actual placement of the layers is somewhere between these two extremes: it was stated that this is indeed the case. 5. Conclusions The modelling strategy, which was presented, provides a unified approach towards a mechanical and flow analysis of the textile reinforcement on a macro-scale. This approach allows a straightforward analysis of the reinforcement properties considering the variations in reinforcement structure, the tow properties, as well as also the material nonuniformity, as for example unbalanced crimp, deviations in the yarn cross section,s area, and in spacing. An emphasis was made on the problem of resin flow through the reinforcement. A correlation relationship has been elaborated between the percentage of open porosity for double-layer fabrics and air permeability, considering the use of the difference system of reed denting. We differenciated the system of reed denting by the ‘integration factor construction’ (IFC); the decrease in the (IFC) means that the open porosity for double-layer fabrics increases and at the same time the air permeability also increases. If IFC = 2.488 for a regular reed dents system with plain weave 1/1 in a double-layer fabric then open porosity for the double-layer fabric is 21.025 %, and the air permeability is 38 Ft3/ cm2.



So if we use the difference system of reed denting at fabric code B1, with plain weave 1/1 for double-layer fabrics then we have: (A) 4 upper +2 lower: (B) 2 upper+1 lower with IFC = 2.0, and the open porosity for this double-layer fabric will raise up to 26.15 % with (42) air permeability Ft3/ cm2. The presented approach allows us taking into account the stacking and forming of the layers, both in the flow and structural analyses. In the case of flow analysis, this allows us accurately study the effect of a multi-layer reinforcement structure (nesting deformation etc.) on air permeability. The lattice method should be chosen for a numerical analysis of flow through the reinforcement. In our case a specially designed interface, serving as a geometrical pre-processor, allows us reading the geometrical data The calculations were tested against problems of flow in open and filled channels, and flow through a parallel array of tows. The results have shown a very good agreement with theoretical and existing numerical data. This provides a basis for numerical analysis of permeability of more complex structures such as woven fabrics. The tests announced in this paper of the calculations for two types of double-layer fabrics reveal the following:

- The calculation can be carried out with a modest spatial resolution per layer (of the laminate in its thickness direction) if we use a Nikon SMZ-2T computer-aided stereomicroscope with special software.

- The calculation is extremely time-consuming. - The difference between the computed permeability for the cases of permeable and not

permeable systems is within the range of 20…30%. The calculation enables achieving realistic quantitative results with a wide interval of uncertainty caused by variations of nesting of the layers (uncontrolled in the experimental procedure). References

1. Gee N.C.; “Cloth Setting and Setting Theories”, Text. Manufacturer. , Vol. 80, 381 (1953). 2. Peirce F.T., and Womersley F.T., “Cloth Geometry” ;Text. Institute, Manchester, England.

(1937) and (1978). 3. Love L.; “Graphical Relationships in Cloth Geometry for Plain, Twill and Sateen Weaves”; Text.

R. J. vol.24, (1954) ,pp.1073-1083. 4. Kemp A.; “An Extension of Pierce's Cloth Geometry to the Treatment of Non-circular Threads”. J

Text. Inst., vol.( 49),(1958) ,pp.44-49. 5. Hamilton J.B.; “A General System of Woven-Fabric Geometry”. J Text. Inst., Vol. 55, (1964). ,pp.

66-82. 6. Weiner L.I.; ”Textile Fabric Design Tables” . Technomatic Publishing Co., Inc.,Stamford, CN.

(1971). 7. Seyam A.,and El-Shiekh.A.;“Mechanics of Woven Fabrics” . Part III: Critical Review of Weability

Limit Studies. Text. R. J., Vol. 63, (1993). ,pp. 371-378. 8. M. Kienbaum; “Gewebegeometrie und Produktentwicklung”. Melliand Textilberichte., Vol. 71,

737. (1990). 9. Jakšić.D.; “The Development of the new Method to determine the Pore Size and Pore Size

Distribution in Textile Products”. Part I., Faculty of Natural Sciences and Technology, Department of Textile Technology, Ljubljana, Slovenia. (1975).

10. Dimitrovski K.; “New Method for determination of Porosity in Textiles”. Faculty of Natural Sciences and Technology, Department of Textile Technology, Ljubljana, Slovenia, (1996).

11. Gooijer.H,; “Flow resistance of textile materials”, 1998. 12. Szosland J., ‘Air Permeabilityof Woven Multilayer Composite Textiles’, Fibres & Textiles in

Eastern Europe, vol.7, No,1 (24), 1999, pp.34-37. 13. Szosland J., ‘Identification of Structure of Inter-thread Channels in Models of Eoven Fabrics’,

Fibres & Textiles in Eastern Europe, vol.7, No,2 (25), 1999, pp.41-45 14. Szosland J., “Modelling the Structural Barrier Ability of Woven Fabrics”, AUTEX Research

Journal, Vol. 3, No3, September 2003, pp.102-110. 15. Darcy H. L.; “Fontaines Publiques de la Villa de Dijon. Dalmount”. (1956).



16. Elnashar E.A.;“Effect of Warp-ends Densities Distribution on Some A esthetical and Physical Properties of Multi-layer Woven Fabrics”, Msc Thesis, Faculty of Applied arts. Helwan university Egypt. (1995).

17. A.S.T.M. Annual Book;“Standards, Textiles-Yarn-Fabric General Test Methods”-part, 22. (1981).

∇∆

volume porosity and permeability in double …autexrj.com/cms/zalaczone_pliki/4-05-4.pdf · volume...

Documents