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A modeling study on the lateral compressive behavior of spacer fabricsM. Sheikhzadeha; M. Ghanea; Z. Eslamiana; E. Pirzadeha

a Department of Textile Engineering, Isfahan University of Technology, Isfahan, Iran

Online publication date: 17 August 2010

To cite this Article Sheikhzadeh, M. , Ghane, M. , Eslamian, Z. and Pirzadeh, E.(2010) 'A modeling study on the lateralcompressive behavior of spacer fabrics', Journal of the Textile Institute, 101: 9, 795 — 800To link to this Article: DOI: 10.1080/00405000903268796URL: http://dx.doi.org/10.1080/00405000903268796

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The Journal of The Textile Institute

Vol. 101, No. 9, September 2010, 795–800

ISSN 0040-5000 print/ISSN 1754-2340 onlineCopyright © 2010 The Textile InstituteDOI: 10.1080/00405000903268796http://www.informaworld.com

A modeling study on the lateral compressive behavior of spacer fabrics

M. Sheikhzadeh*, M. Ghane, Z. Eslamian and E. Pirzadeh

Department of Textile Engineering, Isfahan University of Technology, Isfahan, Iran

Taylor and Francis

(

Received 6 February 2008; final version received 2 July 2008

)

10.1080/00405000903268796

Van Wyk’s equation was considered to study the lateral compressive behavior of spacer fabrics. To prepare thespacer fabrics, different monofilaments were fabricated between two solid spastic sheets, one centimeter apart. Twotypes of monofilaments and three different forms of arrangement were used. Compressive tests were carried out usinga Zwick tensile tester set in compressive mode. The results show that there is a good linear correlation between thecompressive force and inverse thickness cubed of spacer fabrics as long as the fibers behave elastically. It can beconcluded that the Van Wyk’s equation can be adapted to predict the lateral compressive behavior of spacer fabricswith an acceptable accuracy. The results also revealed that the position and arrangement of the middle monofilamenthas significant effect on the lateral compressive behavior of the spacer fabrics.

Keywords:

spacer fabric; lateral compression; compressive pressure; Van Wyk’s theory

Introduction

Spacer fabrics are a combination of two separated knit-ted fabrics which are jointed together with a layer ofmonofilaments. The middle layer in these fabrics causesto establish a unique characteristic. With due attentionto the magnitude and type of pressure behavior ofdifferent fabrics in various applications, the reaction ofspacer fabrics to applied pressure forces has been inves-tigated in this research.

Spacer fabrics are much like a sandwich and featuretwo complementary slabs of fabric with a third layertucked in between. The inner layer can take a variety ofshapes, including tubes, pleats, or other engineeredforms, which gives the entire three-layer fabric a wideand ever expanding range of potential applications(Figure 1) (Bruer, Powell, & Smith, 2005; Wollina,Heide, Muller-Litz, Obenauf, & Ash, 2003). More prev-alent in the marketplace, spacer fabrics are essentiallypile fabrics that have not been cut consisting of twolayers of fabric separated by yarns at a 90 degree angle.

Figure 1. Schematic of spacer fabric [2].

There are two types of spacer fabrics; these are warpknitted spacer fabrics and weft knitted spacer fabrics.Warp knitted spacer fabric is knitted on a rip Raschelmachine with two needle bars while weft knitted spacerfabric is knitted on a double jersey circular machinewith a rotatable needle cylinder and needle dial (Brueret al., 2005).

Some applications of these fabrics are in industriessuch as automotives, medical textiles, technical textiles,

geo-textiles, sportswear, civil engineering, transporta-tion media, filtration, and other apparel products. Inmost applications, these textiles are exposed to fairlyhigh lateral compressive forces and their reaction to thecompressive forces is quite important. Bruer et al.(2005) introduced a review of literature on the history,technologies, advantages, disadvantages, and potentialend uses of knitted spacer fabrics.

Spacer fabrics have been studied globally for manyyears. However, very little attention has focused on theeffect of fabric characteristics on its physical propertiesincluding the compressive behavior of spacer fabrics.

*Corresponding author. Email: m.sh110@cc.iut.ac.ir

Figure 1. Schematic of spacer fabric.

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The purpose of this investigation is to analyze thelateral compressive behavior of these fabrics. Due to theimportance of different structural arrangements ofmonofilaments in compressive ability, the reaction ofthese monofilaments known as spacer yarns wasassessed. Subsequently, lateral deformation of monofil-aments was modeled.

Lateral compressive behavior of the fabric was firstinvestigated by Van Wyk (1946). Various modificationswere made to Van Wyk’s model by different researchers(Beil & Roberts, 2002b; De Jong, Snaith, & Michie,1986; Duckett & Cheng, 1978; Hu & Newton, 1997). Inorder to derive an equation that was based on the phys-ics of the fibers, he made some assumptions to simplifythe model. The first assumption was that the bending ofthe fiber was the only important process in fiber motion,and twisting, slippage, and extension were neglected.The crimp of the fiber was also neglected as they weretreated as initially straight rods. A further assumptionwas that the fiber elements are randomly orienteduniformly packed and there was no frictional forcebetween them (Van Wyk, 1946). Considering the struc-tural form of the spacer fabrics, with rod like middlemonofilaments bent spartanly, it seems that they cansignificantly satisfy the Van Wyk’s assumptions. Thus,it can be concluded that Van Wyk’s equation can beapplied to the compression of the spacer fabrics.

Theory of the lateral compressive behavior of simulated samples

We considered Van Wyk’s law for compressed fibers toinvestigate the lateral compressive behavior of the spacerfabrics. In this model a mass of fibers with two fixed endsand bending ability is known as compressed fibers.

In order to adapt Van Wyk’s model for spacerfabrics, certain assumptions have been made:

(1) The monofilaments used in spacer fabrics areconsidered the same as fibers in mass fibers inVan Wyk’s model.

(2) Each monofilament can be bent easily like acircular rod.

(3)

V

0

value in Van Wyk’s model is the initialvolume of the samples.

(4) The mass of fibers bent by compressive forceare known as monofilaments.

(5) The external pressure is related to fiber bendingby the average distance between fiber contactpoints.

(6) The distance between fiber contact points isrelated to the sample volume.

The following equation was considered to investigatethe relation between the pressure

P

(N/mm

2

) and thevolume of the sample,

V

(mm

3

) (Van Wyk, 1946):

where

E

is the elastic modulus of monofilament,

m

isthe mass of monofilament,

ρ

is the fiber density,

V

isthe volume of sample under the pressure.

K

is an empir-ical constant which accounts for varying distancebetween fiber contacts as well as variations in elementlength, diameter, contour, elasticity, and other fibercharacteristics (Van Wyk, 1946). For the constant areaof samples, Equation (1) can be re-written in thefollowing form:

number of monofilaments

×

length of monofilament,

where

m

a

is the surface mass of the samples,

t

is thethickness of sample under pressure,

t

0

is the initialthickness of sample, and

A

is the area of sample.Equation (2) shows that the variation of

P

againstinverse thickness cubed (1/

t

3

), is a straight line with aslope equal to .

Experimental

Materials

For this study, we used different samples which arecharacterized in Table 1. For preparation of thesamples, five holes per cm are punched in a high-packplate 60

×

60 mm

2

wide; each hole has a diameter of 1mm. Then monofilaments are passed through the twopunched plates fixed at 1 cm distance from each other.The different designs used can be seen in Table 1. Forstrengthening the linkage of monofilaments to theplates, two similar plates are adhered on the punchedplates. The area of all samples (

A

) was 3600 mm

2

. Thevalues of surface mass (

m

a

) of the samples are shown inTable 2.

Two real spacer samples produced in a Raschelmachine (Table 3) are used to compare the behavior ofthe simulated samples with the actual spacer fabrics.

Lateral compressive test

A strength tester (Zwick 124174, Germany) was used.The speed of the test was set at 5 mm/min. The samplewas placed between two clamps. The test was thencarried out in compressive mode. The crush of the

P KEm

V V= −( ) ( ) ( )

ρ3

303

1 11

P KEm

t ta= −( ) ( ) ( )

ρ3

303

1 12

mmA

mTex

a = = ×, ( )1000

KEma( )ρ

3

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sample against the inserted compressive force wasassessed.

Results and discussion

For each sample, the test of crush against lateralcompressive force was implemented. Force–crushcurves are shown in Figures 2–7. The curves increaseswiftly, and incline to the linear relation between crushand force of the samples.

Figure 2. Force–crush curve for Sample 1Figure 3. Force–crush curve for Sample 2.Figure 4. Force–crush curve for Sample 3.Figure 5. Force–crush curve for Sample 4.Figure 6. Force–crush curve for Sample 5.Figure 7. Force–crush curve for Sample 6.

Force–crush curves for the real spacer samples areshown in Figures 8 and 9. Excluding the tiny initial part,the curves are similar to simulated sample curves.

Figure 8. Force–crush curve for first real spacer fabric.Figure 9. Force–crush curve for second real spacer fabric.

Van Wyk’s modeling

According to the theory mentioned above, the behaviorof the monofilaments is assessed as a homogeneousmass with bending ability. According to Van Wyk’s

equations for a mass of wool fiber, the inserted pres-sure on the mass has a reverse relation with thicknesscubed.

For all samples the curve of the pressure against theinverse thickness cubed is drawn. A typical graph isshown in Figure 10. As can be seen from Figure 10, thevariation of pressure against the inverse thicknesscubed is linear. The data points at high pressure deviatefrom the straight line. To explain this, it should beconsidered that the basic assumption of Van Wyk’smodel is the elastic behavior of the fibers. The devia-tion of the data points from the straight line is a clearindication of non-elastic behavior of the fibers under

Table 1. The characteristics of simulated samples.

SamplesType and linear density (den) of monofilaments Placement of monofilaments

Schematic of monofilament placement

1 Nylon (180) Direct with angle of 90 degree relating to the substrate

2 Nylon (180) Intersecting with angle of 168.5 degree relating to each other

3 Nylon (180) Combination of direct and intersecting forms

4 Nylon (174) Direct with angle of 90 degree relating to the substrate

5 Nylon (174) Intersecting with angle of 168.5 degree relating to each other

6 Nylon (174) Combination of direct and intersecting forms

Table 2. Numerical values obtained from Van Wyk’sequation.

Samples

R

2

Slope of curves (N.mm)

K

m

a

(g)

1 0.94 101.02 0.77 1.2602 0.93 101.1 0.75 1.2663 0.98 75.26 0.56 1.2634 0.97 62.56 0.73 1.2185 0.97 50.81 0.58 1.2236 0.97 22.73 0.20 1.220Real spacer 1 0.98 5.2Real spacer 2 0.98 4.9

Figure 2. Force–crush curve for Sample 1.

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Figure 3. Force–crush curve for Sample 2.

Figure 4. Force–crush curve for Sample 3.

Figure 5. Force–crush curve for Sample 4.

Figure 6. Force–crush curve for Sample 5.

Figure 7. Force–crush curve for Sample 6.

Figure 8. Force–crush curve for first real spacer fabric.

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high compression force. It can be concluded that VanWyk’s equation (Equation (2)) holds as long as thefibers deform in elastic mode.

Figure 10. The pressure against inverse altered thickness cubed for Sample 1.

The linear regression coefficient (

R

2

) and theslope of the curve for all samples are shown in Table 2.The results obtained from the experiment are in goodagreement with Van Wyk’s equation. In the model for

wool mass of fibers, implemented by Van Wyk (1946)(Beil & Roberts, 2002a; Komori & Itoh, 1991),

K

intro-duces an empirical constant. From the slope of thecurves, the values of

K

, for all samples, were also calcu-lated and are shown in Table 2. In the case of verticaland regular arrangement of monofilaments, the

K

factorhas maximum value. To explain the differencesbetween the

K

values, it should be considered that the

K

value is an empirical constant affected by fiber arrange-ment, diameter, elasticity, etc.; the yarns used in modelSamples 4–6 have less linear density, thus less diame-ter, in comparison to the model Samples 1–3, respec-tively. The type and elasticity of the yarns are alsodifferent. These can significantly affect the

K

valuesand lead to difference between them.

In real spacer fabrics, because of the irregular place-ment of the monofilaments, the slope of the curves willbear significant reduction.

Conclusion

The lateral compressive behavior of simulated spacersamples were compared with the real spacer fabric. Theresults revealed similar trend in both cases. The resultsfrom modeling show high compatibility of experimentalcurves with curves obtained from Van Wyk’s theory.The results also revealed that the position and arrange-ment of the middle monofilaments have significanteffect on the lateral compressive behavior of the spacerfabrics.

Acknowledgement

The authors would like to express their sincere thanks andgratitude to the deputy of research of Isfahan University ofTechnology for financial support.

References

Beil, N.B., & Roberts, W.W. (2002a). Modeling andcomputer simulation of the compressional behavior offiber assemblies: Part I.

Textile Research Journal,

72,

341–351.Beil, N.B., & Roberts, W.W. (2002b). Modeling and

computer simulation of the compressional behavior of

Figure 9. Force–crush curve for second real spacer fabric.

Figure 10. The pressure against inverse altered thicknesscubed for Sample 1.

Table 3. The physical properties of real spacer samples.

Samples Weight (g/m

2

)Type of

monofilamentLinear density of

monofilaments (dtex) Arrangement of monofilament

1 736 Polyester 954

2 630 Polyester 820

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