Indian Journal of Textile Research

Vol. 8, December 1983, pp.IIl-1l4

Tearing Strength: An Evaluation of Taylor's Equation

I C SHARMA, D ADHIKARY & 0 P JAISWANI

The Technological Institute of Textiles, Bhiwani 125022

Received 24 March 1983; accepted II August 1983

An effort has been made to assess the merit of Taylor's equations for single rip and double rip tear tests in respect of itsapplication to blended fabrics. The equation does not appear to be very exact, especially for double rip test. The results ofsingle

rip test, howevc;r, show better agreement with this equation.

The equation for double rip strength was:

R - 2 = s ( W log f/( + n )t log {3

Very few attempts have been made so far to analyze thetearing mechanism of single rip and double rip tests.The most notable among these is that of Taylor 1 . Hiswork related to empirical estimation of the single anddouble rip tearing strengths of cotton fabrics fromtheir yarn and cloth constructional parameters. Hegave the following equation for single rip tearingstrength:

where [R = T/j]; T, the tearing strength;!, the singleyarn breaking strength; t, the number of transversethreads; s, the average distance by which the spacebetween the threads is reduced-(measured along theslipping threads); W, the weave factor which is theratio of the number of crossing threads in the weaverepeat and the number of interlacements per repeatby the longitudinal threads; fs' the experimentally

R - 1

t = !.. ( W log f/f, + n )2 log {3

measured force to cause slippage of transverse threadsover n number of longitudinal threads; and {3, aconstant factor by which tension of the crossingthreads at each crossing point is multiplied.

The aim of the present study was to assess theapplicability of Taylor's equation to blends.

Materials and MethodsNine fabric samples were prepared from yarns of

three different polyester/viscose blends, viz. 48/52,60/40 and 80/20, using them in both warp and weftways. This was done to observe the effect of blendcomposition on the tear strength of the fabric. Thewarp and weft counts were 2/36's; ends/in, 64;picks/in,56;and the weave used was plain. In the nomenclatureused for the samples (Table I), the first digit denotesthe warp blend composition (polyester: viscose), i.e. A­60/40, B-80/20 and C-48/52, the second digit thepicks/in, i.e. R-56, and the third digit, the weft blendcomposition, i.e. X-60/40, Y-80/20 and Z-48/52. Allthe samples were tested only in the filling direction.'

Prior to testing, all the samples were conditioned in astandard atmosphere (RH, 65% and temperature, 27±2°C) for 48 hr. The tests were carried out on an

Table I-Single Yarn Strength, Single Yarn Withdrawal Force and Single and Double Rip Tear Strengths

Sample Single yarnSingle yarn withdrawal force. gTear strength, kg

strength, g I in3/4 in1/2 in1/4 inSingle ripDouble rip

ARZ

482.490.231102.056118.366131.3204.8517.976

ARX

547.194.562105.123121.256134.626.0679.640

ARY

653.198.723109.236126.123137.7608.15811.559

CRZ

482.486.540100.123115.236121.2504.7657.901

CRX

547.190.320101.254118.125124.3505.9829.500

CRY

653.195.100105.372122.472127.3107.92611.396

BRZ

482.495.866106.066122.466134.2004.9488.446

BRX

547.198.800109.200123.332137.8005.8349.884

BRY

653.1103.266113.066128.466140.9327.25411376

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INDIAN J TEXT. RES., VOL. 8, DECEMBER 1983

Fig. I-Dimensions of specimen [(A) Central thread across the cut,(B) central cut, and (C) crossing thread unravelled]

·Il

WEFT BLENO(P:V) (1)48/52 SAMPLE BRZ

(2 ) flO/4 0 SAMPLE BR X

(3)80/20 SAMPLE BRY

CIIIJIIII11-1·5 in

-llIj-1. t

21n A lin.1 I SinB 0.5 in-1I

2in

1

1~ lP 3~CUT LENGTH, in

95

110

100

105

145

140

150

135'"UJUg; 130......J<I

~ 125<Ia:or':: 120~z~ 115>

Fig. 2-Dependence of yarn withdrawal force on cut length [Count,2/36' x 2/36'; reed x pick, 64 x 56; warp blend (P/V), 80:20; stripwidth through which yarn is withdrawn, I in; and yarn withdrawn,

filling]

results noted. The effect was obvious, the withdrawalforce showing a sharp decrease with increase in the cutlength (Fig. 2 and Table 1). A close inspection of thespecimen revealed that the geometry of the withdrawalzone changed considerably during yarn translation.Each time the withdrawing yarn carried with it the setof threads in the vicinity of the cut and created a gapsimilar in shape to an isosceles triangle whose sideswere not exactly straight lines. The thread adjacent tothe cut and being carried away by the withdrawing one

Results and Discussion

Realizing the limitations of the method and alsokeeping in view the fact that the yarn withdrawal forcemight vary with change in the cut length, four differentcut lengths, viz. 1/4, 1/2,3/4and I in, werechosen and the

Instron tester. For the single rip test, the specificationas given in ASTM 2 was used. The determination of thestrength of single yarn (taken out from the fabric) anddouble rip tear tests were carried out as per theprocedures laid down in B.s. Handbook 3. The cross­head speed ofInstron was maintained at I IOmm/min.Taylor has, however, suggested the use of fabric tensilestrength per single yarn in place of single yarn strengthto include the assistance rendered by the other set ofthreads in the fabric. But his suggestion does notappear[ to be very correct, because the del structure inthe tearing zone consists only of a single set of threadsand these threads have no interlacement with the otherset within the del region.

Because of the non-availability of suitableequipment and lack of details in literature about themethod of determining the yarn withdrawal force froma strip of fabric, a procedure specially worked out by usfor this study was used. Taylor! , in his experiment, diddetermine the yarn withdrawal force from a strip offabric, but details of the experiment have not beengiven, except that the strip width through which theyarn had been withdrawn was I in and/or 1/4in. Keepingparity, with his experiment, a strip of fabric (5 in longand 3 in wide) was taken. Leaving 2 in from one end ofthe longer sides to allow the specimen to be gripped bythe fabric jaws, and another 1/2 in for a clearance fromthe jaw line, a transverse cut was made across the widthof the specimen. The specimen was then marked acrossits width at a distance of I in from the transverse cutand all the crossing threads in the remaining portion ofthe specimen were unravelled, so that the length, ofeach of the freed longitudinal yarns from the markedline was I! in. The main purpose of making atransverse cut and then freeing the. longitudinal yarnsby unravelling the crossing threads from the rest of thefabric strip was to allow a longitudinal thread to beplaced centrally across the cut, to be withdrawnthrough a strip of fabric of I in width. So, the job thatremains now is to locate the central thread across thecut and to clamp it in the yarn clamps, the rear end ofthe specimen in the fabric form being already grippedby a pair offabricjaws. The yarn clamp, initially beingseparated from the fabric jaws by a distance of2 in, wasthen moved apart until the said yarn was completelywithdrawn from the strip, the force required to removeit being recorded in the autographic device. Thespecimen dimensions are given in Fig. I. In the presentstudy, only the filling yarns were withdrawn.

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SHARMA el at.: TEARING STRENGTH: AN EVALUATION OF TAYLOR'S ,EQUATION

was extended forming the two equal sides of thetriangle; the fabric area around the triangle wasconsiderably distorted, the effect diminishingprogressively from near to the far region of thetriangle. When the cut length was increased, the twoequal sides increased in length and formed a moreacute angle at their apex. This happened with yarnspositioned next to these two equal sides. Thus, theangle of contact between the two sets was reduced andhence the resistance offered by the crossing threads tothe withdrawing thread was reduced, ultimatelylowering the withdrawal force.

Increase in polyester content results in a higher valueof yarn coefficient of friction and a lower yarn crimplevel. The former may be attributed to the higher staticcoefficient of friction of polyester fibre and the latter toits higher bending rigidity compared to that of viscosefibre. The increased static coefficient of friction tendsto offer more resistance to yarn withdrawal from afabric and conversely lower crimp tends to minimize it,but the effect of the former has a greater impact on theyarn withdrawal force and causes a rise in its value(Fig. 2 and Table I).

The coefficient of correlation between the yarnwithdrawal force and the yarn blend composition wascomputed individually for all the cut lengths. Thevalue was found to be maximum ( + 0.6676) for 1in cutlength and had thus been applied to Taylor's equation.The results of single yarn strength and tearing strengthtests are given in Table I. The values of W, nand tare

1, 64 and 56 respectively for all the samples.Taylor gave the values of the two unknown factors,

viz. {3and s, for his fabric samples as follows:

Ends/in {3sWarpcount

158

1.0121.2530'

xlO-3 in1001.0100.61530'

x 10-3 in

Putting these values in Taylor's equation, the doublerip tearing strengths of the fabrics were calculated. Thecalculated values showed a variation of7-12% from theexperimental values.

In the present case, for 1 in cut length, data from thetwo fabric samples, BRZ and BRX, were used in thesaid equation to determine the values of sand {3.Thesevalues were then put in the equation for sample BRY(both for single rip and double rip) and its tearingstrength was calculated.

The values of {3and s for fabric samples BRZ andBRX, having 64 ends/in and 2/36's yarn count, werefound to be 1.008 and 1.33 x 10-3 in respectively for

the single rip test. The single rip strength of sampleBRY was calculated to be 7.286 kg, which differedfrom the experimental value (7.254) by +0.3%.

For the double rip test, the values of {3and s werefound to be 1.0165 and 1.71 x 10-3 in respectivelyfrom the equations for samples BRZ and BRX. Thecomputed double rip strength of sample BRY wasfound to be 12.299 kg. This varied from theexperimental value by + 8.1%. Similar calculations fortearing strength were also made for the cut lengths of3/4, 1/2 and 1/4 in. The results are given in Table I.Calculations for sand {3were also made for the othertwo pairs of samples, viz. ARZ and ARX, and CRZand CRX. These values were then put in the equationsfor samples ARY and CRY respectively to calculatethe single and double rip tear strengths for all the fourcut lengths, i.e. 1, 3/4, 1/2 and 1/4 in. The results aregiven in Table 2.

It is evident from the above that Taylor's equationdoes not satisfactorily compute the tearing strength ofa fabric, especially for the double rip test, and gives acalculated value which differs from the experimentalvalue by 2-8% for double rip and 0.13-3.38% for singlerip at all the cut lengths.

Further, Taylor used 1/2 in cut length, but theresultsin the present study show best correlation with I in cutlength. However, it might be noted that theex~rimental values for the single rip tear testapproach qnite near Taylor's theoretical value, thedifference being within 3%. For the double rip, thedifference is about 10%. This is certainly not ignorableand proves that the equation suffers from seriousdrawbacks. Taylor himself has admitted that hisexpression isjust an approximation to the tear strengthand is not compatible in yielding an accurate result.This is because his analysis is based on simplifiedassumptions and ignores some essential aspects offabric tear behaviour. The most important omission isthe role of yarn extensibility. Taylor assumed that theemergence of del is due entirely to the incidence ofthread slippage and yarn extensibility plays no role init. But Backer and Hamkin4 showed that both yarnslippage and yarn elongation occur during tear and areequally important in determining del geometry.

Taylor also ignored the incidence of jamming andtrellis type distortion in the fabric ahead of del. Thesetwo factors, in fact, make a fair contribution inassisting the del structure to share the load. Taylor'scloth was, however, prepared in an already jammedstate and hence did not permit any further jamming ordist6rtion; this might be the reason for these factorsescaping his attention. Taylor's commitment is furtherintensified in assuming that the thread spacings in del

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INDIAN J TEXT. RES., VOL. 8, DECEMBER 1983

Table 2-Calculated Single and Double Rip Tear Strength with Their Percentage Variation

Actual tear

strength, kg

Cut length, in

3/4

1/21/4

Single

DoubleSingleDoubleSingleDoubleSingleDouble

rip tearrip tearrip tearrip tearrip tearrip tearrip tearrip tear

strengthstrengthstrengthstrengthstrengthstrengthstrengthstrength

kg

kgkgkgkgkgkgkg

8.390

12.7078.21712.5318.16012.4678.27512.593

(2.841)*

(9.931)(0.72)(8.4)(0.1)(7.855)( 1.438)(8.944)7.586

12.2997.35512.3387.43512.2167.37212.369

(0.13)(8.1)(1.3)(8.4)(2.5)(7.3)(1.4)(8.7)

8.187

11.5787.97112.1148.10012.2408.19412.328

(3.27)

(1.16)(0.57)(4.78)(2.15)(5.88)(3.38)(6.59)

11.396

11.559

11.3767.254

7.926

8.158

Single Double

rip rip

Sample

ARY

CRY

BRY

*The values within parentheses show percentage variation.

are equal and hence the load on the del yarns increasesproportionately. But the del area is defined by astraighti base line provided by the outermost crossingyarn and two hyperbolic curves provided by the twolongitudinal threads, which are in the vicinity of thetear. Thus, the thread spacing in del reducesprogressively from the apex to the base of del andhence the load increases progressively from theinnermost to the outermost del yarn.

AcknowledgementThe authors are thankful to Prof. R.C.D. Kaushik,

Director, T.I.T., Bhiwani, for invaluable guidance andhelp during this study.

References

I Taylor H M. J Text 1nsl, 50 (1959) T-i61.

2 ASTM siandards 0/1 texlile materials, 1958.

3 B S handbook No II, (1974).

4 Hamkin C P & Backer S, Text Res J. 50 (1980) 323.

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