Tensile Behaviour of Spun Yarns under Static State

B. R. Das
Department of Textile Technology, Indian Institute of Technology, New Delhi INDIA
Correspondence to:
Biswa Ranjan Das email: biswaiitd@gmail.com

ABSTRACT Morton, and Hearle have shown, in general that if the

The tensile properties of spun yarn are accepted as stress-strain curves are nonlinear, there will also be a
one of the most important parameters for assessment difference between the constant rate of loading
of yarn quality. The tensile properties decide the (CRL) and constant rate of extension (CRE) tests as a
performance of post spinning operations; warping, result of the different proportions of time spent on
weaving and knitting and the properties of the final different parts of the stress-strain curves. Thus, in
textile structure; hence its accurate technical studying time effects of yarn breaks, it is important to
evaluation carries much importance in industrial indicate if the tester uses the CRL or CRE method36.
applications. There is no doubt that all the studies According to Midgley & Pierce, rapid test produces a
related to tensile behaviour of spun yarns are higher breaking load than a slow test and they have
invaluable both in theory and practice. In this article, also established relationship between the strength
a critical review of the theoretical and practical aspect values obtained and the breaking time2. Meredith
of static tensile behaviour of staple yarns has been tested yarns over a million-fold range of rates of
discussed. extension and found that the relationship between
yarn tenacity and logarithm of rate of extension is
Keywords: interaction effect, spun yarn, tensile approximately linear. For breaking times ranging
properties, yarn strength. between a second and an hour, the proposed formula
is expressed in Eq. (1):
t 
INTRODUCTION F1  F2   KF1 log10  2  (1)
Standard measurement of yarn strength is executed  t1 
on a gauge length of 500 mm. A clamped yarn breaks
in its weakest place according to the so-called Where, F1 is the breaking load in time t1; F2, the
principle of the weakest link and this strength value is breaking load in time t2 and K, the strength-time
assigned to the whole length. As the test sample is coefficient3. Ghosh, Ishtiaque, and Rengasamy found
gripped at the two ends and maintains that static state that yarn tenacity increases continuously with the
during the testing process, the evaluated tensile extension rate for all spinning systems. The increase
properties are often treated as static tensile properties in the tenacity with the increase in the extension rate
and the strength measured by single thread tensile is due to the consequent increase in the proportion of
test method is referred to as static yarn strength1. fiber breakage4. Chattopadhyay showed that, with an
Among the measurable tensile properties of spun increase in the strain rate, the tenacity initially
yarn, considerable attention has been paid on the increased up to 10 mm/s for both ring and air-jet spun
evaluation of tensile strength and breaking extension, yarns and then followed by a sharp reduction5.
as these properties of the spun yarns influence the Oxenham, Zhu, and Leaf compared the effect of
efficiency of weaving and knitting machines and the gauge length on the strength of ring spun and open
quality of the fabric produced from them. However, end friction spun yarns and found that the strength of
the tensile strength and breaking extension of the ring spun yarns shows a sharp drop, as the gauge
yarns are not the unique functions, but they depend length increases from 1mm to 40 mm (which was
on the rate of extension and gauge length. From the approximately the fiber length). The strength of
practical point of view, it is desirable that the effect friction spun yarns also drops sharply as gauge length
of operating speed and gauge length on the tensile increases from 1mm to 20 mm (Which was almost
properties of yarn should be known, so that the equal to the fiber extent in the yarn). For gauge
results obtained from the instruments running at length greater than 40 mm, the strength of ring spun
different speeds and gauge lengths can be correlated yarns appear fairly constant, whereas the strength of
and compared. friction spun yarns reduced continuously with
increase in the gauge length, reflecting the
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Volume 5, Issue 1 - 2010
discontinuities in the yarn formation zone in friction According to Rengasamy, Ishtiaque, and Ghosh, the
spinning6. Hussain, Nachane, and Krishna found a tensile strength of a spun yarn depends on its
significant difference in gauge length effect on the structure, gauge length and extension rate employed
strength of ring and rotor spun yarns. The length during measurement9. Salhotra, and Balasubramanian
effect, which they expressed as a ratio between the explained that, the tensile strength of a yarn is
tenacity of a given gauge and that of a 1cm length, influenced, among other factors, by the number of
showed no difference between ring versus rotor spun fibers that break in the region of yarn rupture. This
yarns at relatively short lengths. But the difference number mainly depends on the yarn twist, length of
was statistically significant at long lengths7. Realff et the fibers and the rate of straining10. Tallant, Fiori,
al (1991) proposed that the mechanism of failure Little, and Castillan explained that, there should be
might also change due to a decrease in the test length. minimum fiber length for significantly contributing
They observed different range of failure zone size for to yarn strength. To find this minimum fiber length,
ring spun and air-jet spun yarns for different gauge he proposed a mathematical model for translation of
lengths (Table I). According to their observation, as fiber bundle strength to yarn tenacity Eq. (2):
compared to the air-jet spun yarns, ring spun yarns
yield higher strength, many broken fibers and a small Y  a  f (l , x )  S  b (2)
failure zone size at longer gauge lengths. But, at
gauge lengths well below the fiber staple length, air- Where, Y is the single-yarn tenacity; S, fiber bundle
jet spun yarn shows more strength than ring spun strength; l, length distribution of cotton; x, critical or
yarn because the difference in surface helix angle minimum length of fiber; f (l, x), effective weight
( ), since  > 0 for ring spun yarn and   0 for the and a & b , are the constants. It was found that the
core fibers of air-jet yarn. While comparing the fibers shorter than about 3/8 inch do not contribute to
influence of gauge length on yarn failure for ring yarn tenacity and a 3/8 inch portion of each longer
spun and open-end spun yarn, they found that the fiber is ineffective. It is implied that on an average,
ring spun yarns fail by fiber breakage at both long the 3/16 inch tip at each end of each fiber doesn’t
and short gauge lengths. But the open-end yarns contribute to yarn tenacity. Their investigation gave
show a change in breakage mechanism from a fiber interesting findings that the “zero” gauge fiber bundle
slippage dominant failure at long gauge length (127 test is superior to the 1/8 inch gauge length test as a
mm) to a fiber breakage dominant failure at short criterion for relating bundle to yarn tenacity, if the
gauge lengths (12.7 mm and < 2 mm)35. gauge length value is modified by the effective
weight11. Gulati, and Turner observed that the fibers
below 0.5 inch length don’t contribute to yarn
TABLE I. Range of failure zone size for different gauge lengths35
strength12.

Gauge Failure zone TENSILE BEHAVIOUR OF PURE STAPLE

Yarn system
YARNS
length, mm size*, mm
Majumdar tested 100% cotton yarns on Uster
Ring spun 127 <3 Tensorapid-3 & Uster Tensojet for determining its
Ring spun 76.2 2-4 breaking load & extension and work of rupture.
Ring spun <2 0.5-2 Although the actual values of tenacity is not equal for
Air-jet spun 76.2 3.5-10.5 Tensorapid-3 and Tensojet, but there exists very good
Air-jet spun 12.7 3-8 correlation between the two values (r = 0.99). The
Air-jet spun <2 0.5-2 regression equation used to calculate the correlation
is as follows Eq. (3):
Hearle described that the mechanical properties of
yarn depends on the complex interrelation between T j  1.06 T R  1.80 (3)
the fiber arrangement and properties. It should
however be possible to predict the yarn stress-strain Where, TJ and TR are the corresponding tenacity
properties from knowledge of the fiber stress-strain reported by Tensojet and Tensorapid-3 respectively.
properties, if we know the arrangement of fibers in The average yarn breaking times for Tensorapid-3
the yarn. He derived a mathematical formula to and Tensojet are 0.355s and 0.004s respectively,
express its yarn structure, based on the distribution of which may have allowed more relaxation of stress in
fiber segments, diameter shrinkage function, yarn the case of Tensorapid-3, causing lower yarn
twist and number of fibers in yarn cross-section8. tenacity. He also found a very good correlation of

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yarn breaking extension and work of rupture results obtained by Salhotra and Balasubramanian on
measured by Tensorapid-3 and Tensojet. The ring and rotor spun cotton yarns. According to
coefficient of correlation for yarn breaking extension Salhotra, and Balasubramanian, the increase in
and work of rupture were (r = 0.95) and (r = 0.99) tenacity with an increase in extension rates can be
respectively. The regression equations explaining accounted for two factors, the percentage of ruptured
their relationship are as follows Eq. (4) & Eq. (5): fibers and the realignment of fibers during tensile
loading. When a yarn specimen is strained during
E J  0.86 E R  0.99 (4) tensile loading, the interfiber pressure tends to
increase, which leads to build up of frictional
W J  1.04W R  2.25 (5) resistance owing to an increase in transverse forces.
As the rate of extension increases, the percentage of
ruptured fibers increases, resulting in a higher
Where, EJ & ER are the breaking extensions and WJ & breaking strength (i.e. greater numbers of fibers are
WR are the work of rupture measured by Tensojet and contributing to the breaking load). At slow rate of
Tensorapid-3 respectively. The values of work of extension, these authors attributed the lower tenacity
rupture measured by Tensorapid-3 and Tensojet are to the non-catastrophic nature of the yarn break (i.e.
closer to each other, because the lower yarn breaking dominance of fiber slippage). On the other hand, yarn
force obtained from Tensorapid-3 is compensated by strength appears to decrease slightly, when tested it at
the corresponding higher values of breaking very high rates of extension. This trend was due to
extension. His experiment also concluded that the the low contribution of individual fibers, owing to an
effect of rate of extension on breaking extension is insufficient time for realignment of fibers. This loss
smaller than its effect on strength. The average values in yarn strength may more than offset any increase
of strength- time coefficients of cotton yarns lies caused by a higher percentage of ruptured fibers. The
between -0.069 to -0.076 and extension-time time dependence of this mechanism is further
coefficient lies between -0.07 to -0.063. His results strengthened, when one observes that the maximum
are supported by Meredith’s similar experiments on tenacity for the 500 mm test length was measured at
viscose rayon yarns13, 3. the 1000 mm/min extension rate. This value was
either equal to or slightly higher than the tenacity
Luca, and Thibodeuax were the pioneers to show value observed at 500 mm/min. The breaking
analytically how low or high speed testing affects extension is low in yarns tested at the longer lengths,
yarn tenacity. They used USDA Acala cotton as a test which was attributed to the increased probability of
sample and the tested speeds were ranging from 100 weak spots in a longer specimen, as indicated by the
mm/min to 5000 mm/min. They found that, as the weak link theory. Breaking extension increases with
rate of extension increased, yarn tenacity increased increasing rate of extension and tends to reach the
linearly with the logarithm of the rate of extension elongation of the fiber bundle. Increased breaking
from 0.1 m/min to 1m/min. At 2 m/min, yarn tenacity extension at a higher rate of extension can be
increased slightly, reached a maximum and then at 5 ascribed to an increase in the proportion of ruptured
m/min, it decreased or remained constant. However, fibers16.
there are several limitations in their research. They
only tested speeds ranging from 0.1 m/min to 5 Oxeham, Kurz, and Lee, investigated how the yarns
m/min, which are relatively low speeds compared to react differently according to the different testing
the testing speeds employed for USTER Tensojet and machines; the preliminary trials are done by testing
used 100% cotton yarn, which has larger deviation cotton, acrylic, and polyester/cotton spun yarns.
than the blended yarns or man-made yarns14. The USTER Tensojet showed consistently higher value of
similar results were claimed by Kaushik et al. (1989) yarn tenacity for 100% cotton yarn than USTER
and Salhotra et al. (1985). Kaushik, Salhotra, and Tensorapid, however, in the case of 50/50
Tyagi studied the influence of extension rate and test polyester/cotton yarn, the tenacity value did not show
length on the tenacity and breaking extension of the same trend as that of 100% cotton yarn. The
acrylic and viscose rotor spun yarns and their blends. tenacity value from USTER Tensojet and USTER
They used extension range of 50 mm/min to 1000 Tensorapid has revealed no significant difference in
mm/min and test length of 100 mm and 500 mm. The case of 50/50 polyester/cotton spun yarns. It was
open end yarns showed maximum yarn strength at an found that the elongation values from the USTER
extension rate of 200 mm/min (100 mm test length). Tensorapid are 1% to 1.5 % higher than those from
The strength remained the same or drops slightly, the USTER Tensojet and that trend was consistent
when the extension rate is increased to 1000 across all the samples tested in their research. It was
mm/min15. This finding is in agreement with the possible to obtain a stronger correlation of the
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elongation value than that of the tenacity between the rigidity21. Chasmawala, Hansen, and Jayaraman
two testing machines. Their research clearly divided the wrapping fibers in to five classes- core,
demonstrated that the force depends on the testing wrapper, wild, core-wild and wrapper wild. They
speed and that the amount of force is proportion to showed that, yarn strength depends on the proportion
the logarithm of the speed17. These findings are of each class of fibers in the yarn structure and that
contradictory to the observations of Luca and yarn strength decreases with an increasing number of
Thibodeaux, Kaushik et al. and Salhotra et al. 14-16. wild and wrapper wild fibers and increases with an
The formers found that, yarn tenacity increases up to increasing number of core, wrapper & core-wild
a certain testing speed. However, in this research, the wrapper fibers22. Chasmawala claimed that the air-jet
yarn tenacity shows a continuous increase with the spun yarn displays two distinct failure modes –
logarithm of the testing speed. Aggarwal developed a catastrophic and non catastrophic23. Lawrence, and
mathematical model to estimate the breaking Baqui divided the structure of air-jet spun yarn into
extension of ring spun yarns from the fiber three classes, according to the properties of wrapper
characteristics. The model was of the form Eq. (6): fibers. Class-I, characterized by uniform wrapping
angle; class-II, with wrapper fibers at different
E y  E f (1  BTM 2 ) (6) wrapping angles and class-III, with no wrapper
fibers24. Rajamanickam, Hansen, and Jayaraman
analyzed three kinds of tensile fracture behavior in
Where, E y is the yarn extension at break (%); E f , air-jet spun yarns. Catastrophic, when all fibers in the
fiber bundle elongation at 1/8 inch gauge length (%); failure region slip and break at the same load, Non
B, fiber obliquity parameter and TM, twist multiplier. catastrophic, if fibers do not break or slip completely
The accuracy of estimation of the model was very at the same load and failure by total fiber slippage.
high and the model was applicable to both carded and They showed that yarn strength increases with high
combed cotton of particular type18. Bogdan suggested frequency of class I structure and decreases with a
that for cotton yarns, the value of B is 0.01419. high frequency of the class III structure, especially if
Aggarwal modified his previous model to apply his these sections are agglomerated in some particular
model for mixtures of cottons Eq. (7). regions of the yarn length25. Lawrence et al. and
Rajamanickam explained air-jet spun yarns produced
 0.023W  using different fiber, yarn, and process parameters
E y  0.90 E f (1  0.014TM 2 )  1   (7) exhibit different tensile properties and yarn tensile

 N  failure modes. This difference may be attributed to
variations in yarn structure, yarn count, and fiber
Where, W= toughness index, N = number of fibers in properties.
yarn cross section.
TENSILE BEHAVIOUR OF BLENDED
Krause, and Soliman analysed the tensile behaviour STAPLE YARNS
of air-jet spun yarns. He tried a mathematical The first theoretical work published concerning the
approach to calculate and predict the strength of false mechanics of blended yarn was by Hamburger. He was
twist yarn, spun by means of a single air- jet, based concerned with the fact that the blended yarns have
on an idealized yarn structure model. The strength of breaking strengths lower than those expected from the
wrapping fibers, the core fibers and the frictional summation of the proportioned constituent fiber
resistance of the slipping fibers in the core is the load component strengths. Considering the two components
bearing components of the yarn. Their equation A and B (with A representing viscose and B
indicated to what extent yarn strength depends on the representing polyester), to have independent load
following major parameters: position of the wrapping elongation curves and to be under tension in parallel,
fibers, average wrapping length, the angle, fiber he predicted the behaviour of the blended yarn from the
strain, fiber-to-fiber friction and fiber slenderness20. tensile behaviour of its components. The tensile
Tyagi, Goyal, and Salhotra studied the effect of behaviour of the viscose and polyester fiber used in his
various process parameters on the sheath slippage research is shown in Figure 1. For a blended yarn, the
resistance of air-jet spun yarns. They claimed that the tensile resistance will correspond to the blend-
higher first nozzle pressure is advantageous for proportion weighed average of the tensile resistance of
improving sheath-slippage resistance. Higher the two components up to the limit of strain, at which
spinning speed and wider condenser significantly the less extensible component A failed. At strains
improves the tenacity, breaking extension, initial beyond this point, yarn resistance is fully corresponds
modulus and sheath slippage resistance, but adversely to the resistance of the unbroken component. Thus a
affect yarn hairiness, mass irregularity and flexural blended yarn was expected to have two breaking
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points- one for its less extensible component and the Kemp and Owen investigated the stress-strain
other for its more extensible one. The breaking strength characteristics and cotton fiber breakage during
of the blend was reported as the higher of these two tensile failure of a series of nylon/cotton blended
values. The first rupture level would be maximum for a yarns. At strains above the breaking strain of all
yarn made of 100 % of fiber A, and its minimum would cotton, the stress–strain curve of the 60/40 and 80/20
occur in a yarn containing no portion of fiber A. The nylon/cotton blended yarns did not follow the
first rupture point would never fall to zero in the predictions of Hamburger, nor did the plot of yarn
absence of component A. Similarly, the second rupture tenacity versus blend ratio produce a linear
level will be maximum for a yarn containing 100% of relationship as predicted by hamburger. They
fiber B and would be minimum for yarns containing developed a similar equation in the form Eq. (10):
less or no portion of fiber B. The solid lines of Figure 2
reflect the generally reported variations of breaking  y   y 
strength with blend levels. In general the first and y    n  1   c (10)
second ruptures are as given below Eq. (8) and Eq. (9):  100   100 

bD Where,  n ,  c and y are the stresses in the nylon,

P1  (aS A  bS B ) (8) cotton, and nylon/cotton blended yarns containing y
100
percent of nylon. The predicted values fit the
experimental values up to 7.5% strain level. The
bD
P2  SB (9) cotton fibers contribute to an amount of cf to the
100 blended yarn stress over the rupture strain of the all
cotton yarn, so the cotton contribution cf estimated
Where, P1 = first rupture, P2 = second rupture, D = by modifying the above equation to the form Eq.
total yarn denier, SA= breaking tenacity of fiber A, SB = (11):
breaking tenacity of fiber B, and a & b are weighted
ratios of fiber A and B in the yarn26.
  y   y 
 cf   y    n 1   (11)
  100   100 

The cotton fibers in the blended yarns sustain a high

stress at strains above which all cotton yarns break.
This stress, in fact rises considerably above the
breaking stress of all cotton yarns. They have found
that at high strains, the cotton fibers often broke more
than once27. Owen presented a scheme for predicting
the tensile properties of blends. The scheme requires;
the single-fiber stress-strain curves for each
component & the stress-strain curves for yarns spun
from 100% of each component of lower breaking
FIGURE 1. Stress-strain curves of viscose and polyester fibers26
strain. The methodology used was primarily graphic,
but it produced predictions that agreed reasonably
well with the experimental results28.

Machida carried out the most extensive experimental

investigation on the mechanics of rupture of blended
yarns. His investigation was concerned with the
transfer of stresses from low elongation fiber
components to the high elongation fiber component.
He produced gross-model yarns consisting of ninety-
one component yarns twisted, without migration, in
five helical layers about a central core yarn. In many
models the occurrence of a break in one cotton
element was accompanied by breaks in adjacent
FIGURE 2. Theoretical effect of blend proportion on yarn strength26 cotton element across a narrow zone of rupture. This

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Volume 5, Issue 1 - 2010
occurrence was dependent on the direct contact increase of modulus at 10% polyester probably could
between elements and sufficient lateral pressure to be due to fiber clustering in the yarn cross-section30.
transmit the forces on the first element to the other
elements. If the cotton elements were sufficiently
congregated, propagation of element rupture across a
narrow zone caused failure of the entire model at
strains lower than those sustained by uniformly
blended models. His observation also claims that at
low twist level, the low elongation components
“dropped out” (slipped) after they started to rupture.
As a result, at strains above the breaking strain of the
low elongation component, the yarn properties
became highly dependent on the properties of the
high elongation component29.

Shiekh studied the various properties like tenacity,

elongation, initial modulus, dynamic modulus of
polyester/viscose blended yarns by using different
blend proportions. He compared the experimentally FIGURE 3. Effect of blend level on yarn tenacity; comparison of
theoretical and experimental results30
observed tenacity values with the values predicted
from the mixture theory proposed by Hamburger.
Pan, and Chen explained that, in a blended system or
Here the agreement appears to be fairly good at the
mixture, the overall properties of the system are related
extreme points, but appreciable differences are
to the proportion and corresponding properties of each
present at the transition regions, as shown in Figure
component. If the mixture is not uniform, the
3. The reason for this discrepancy was explained by
distribution or local concentration of each constituent
Kemp and Owen and later by Machida, to be due to
plays an important role in determining some aspects of
the multi-breakage of the low elongation
the system’s behaviour. The remaining factor has to
components27,29. The effect of twist is to lower the
with the interactions of the components themselves,
percentage of high tenacity fiber (polyester) in the
which complicate an otherwise much simpler
yarn, at which the blended yarn strength starts to
relationship between the blend system and its
increase. At this critical percentage the yarn has its
component properties31. Many properties of a material
lowest tenacity. The effect of blend levels on
mixed or blended from two or more different
elongation follows the prediction of Hamburger at
components can be calculated using the simple rule of
high twist levels. At low twist level, however, the
mixture (ROM); such properties include the elastic
elongation at break is independent of the blend level,
moduli, electrical and thermal conductivities,
where the yarn elongation is mainly due to the fiber
dialectical constant and thermal expansion coefficients.
slippage rather than fiber extension. The modulus of
However, there are other properties of a material, like
blended yarn has been thought to follow the mixture
its overall strength or elastic lifetime, which are
theory as given below Eq. (12):
influenced by the interaction of the different
components in the system and therefore, cannot be
aE A  bE B
Eb  (12) accurately predicted by the simple ROM. According to
ab Nielsen, if we have a mixture of two different
constituents, type 1 and 2 in general, the system
Where, Eb is the modulus of the blended yarn; EA, property Xs can be calculated by a general ROM:
modulus of yarn made of 100% fiber A; EB, modulus of
yarn made of 100% fiber B; a, fraction of fiber A in the X S  X 1W1  X 2W 2  IW1W 2
blend; b fraction of fiber B in the blend. The
 X 1W1  X 2 (1  W1 )  IW1 (1  W1 ) (13)
experimental result showed an abnormal trend, where
the modulus has a consistent maximum value at the
10% level of polyester (low modulus fiber). This could Where, Xi and Wi are the corresponding property and
be due to a sudden increase in the drafting forces at this the volume fraction of the constituents i =1 & 2, and I
level, but the relative measurements of the drafting is a coefficient representing the intensity of interactions
forces of the ten blends were made on a cohesion tester of the two constituents32. There are three cases based
proved that the drafting forces increased with on the value of I: for I >0, the interactions of the
increasing the percentage of polyester component. The constituents 1 and 2 will enhance the overall system
property and lead to a synergetic effect, I<0 represents
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Volume 5, Issue 1 - 2010
a case where the interactions actually reduce system properties, such as the tensile modulus. The increase in
property and I=0 means that the interaction does not modulus ratio leads to increase in interaction effect33.
exist, so that the Eq. (13) degenerates in to the simple
ROM. The expression for I can be expressed as Eq. Pan, and Postle derived a statistical model for
(14): prediction of blended yarn strength. He explained that
the blended yarn strength  y is a statistical variable
I  4 X 50%  2( X 1  X 2 )  4[ X 50%  0.5( X 1  X 2 )] with a normal distribution function H ( y ) , which can be
 4[ X 50%  x ]  4X (14) expressed as Eq. (18):

1 ( y   y )
Where, X50% is the actual system property Xs, when the H ( y )  exp[ (18)
W1 = W2 = 0.5 and x = 0.5 X1 + 0.5 X2 are the 2 y 2 y 2
arithmetic mean of the property for homogeneous
constituents composed of X1 and X2 alone. If there are
Where,  y is the average strength of blended yarn and
no interactions of the two constituents, there will be
X50% = x, so that X = 0 and I = 0.  y 2 is the variance of yarn strength. The distribution
parameters can be calculated, according to the statistical
Marom, Fischer, Tuler, and Wagner explained that the
theory as follows Eq. (19) and Eq. (20).
alteration of the system’s overall properties caused by
the interaction of the different constituents can be
1
 
(l c1 1  1 ) 1 exp  1  (19)
specified by using the concept of hybrid effect. One Ef2
 y   q V1  V 2   
definition of the hybrid effect is given as the deviation  E f1   1 
of behavior of hybrid structure from the ROM. A  
positive hybrid effect means the synergetic case, and
the actual property is above the ROM prediction, where 2
 Ef2     1 
as a negative hybrid effect means the property is below  y 2   q 2 V1  V 2  (l c1 1  1 ) 1 exp  
the prediction. Therefore, numerically the value of X  E f 1     1 
can used to indicate the hybrid effect and can be   1 
written from Eq. (14) as:  1  exp  .(a1 N ) 1 (20)
   1 
X  X 50%  x  X 50%  (0.5 X 1  0.5 X 2 ) (15)
Where,  q is called the orientation efficiency factor; V1
The Eq. (13) can be normalized to eliminate the effect & V2, fiber volume fractions of type 1 & 2; Ef1 and Ef2
of twist as follows Eq. (16):
are the tensile modulus of type 1 & 2 fibers; l c1 is the
Xs X I fiber length;  1 &  1 are the scale & shape parameter of
X sn   1 W1  (1  W1 )  W1 (1  W1 ) (16)
X2 X2 X2 fibers respectively; a1 , N are the number proportion of
fiber 1 and total number of fibers respectively.
The more efficient way of normalizing the Eq. (13) to According to the hypothesis on estimating the
eliminate the effect of twist to develop the relationship maximum range of statistical distribution, based on this
between relative tenacity and blend ratio is as follows normality of the strength distribution, there is a 99%
Eq. (17): chance that the actual blended yarn strength will fall in
to the range of  y  3  y . He also quantified the
Xs X1 I
X sn %   W1  (1  W1 ) strength hybrid effect by a new parameter  y , which
X 50% X 50% X 50%
predicts the deviation of the actual yarn strength from
I
 (1  W1 ) (17) the strength predicted by the Rule of Mixture. This can
X 50% be expressed as Eq. (21):

[X50% include the effect of both twist and interactions], 1


the model indicated good correlation with the practical l  1
 y   c1  (21)
observations. The nature and results of the interactions lf 
 
of different fiber types are determined by their

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Journal of Engineered Fibers and Fabrics http://www.jeffjornal.org
Volume 5, Issue 1 - 2010
Where, l c1 is the critical fiber length and l f is Different Gauge Lengths using Weibull
34 Distribution; Indian Journal of Fiber
original fiber length . &Textile Research 2005, 30, 283-289.
[10] Salhotra, K.R.; Balasubramanian, P.;
CONCLUSION Estimation of Minimum Fiber Length
The foregoing discussion gives an overview of the Contributing to Tenacity of Rotor Spun
theoretical and experimental aspects of the static Yarns; Indian Journal of Fiber & Textile
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reported so far in the literature, since the interest of [11] Tallant, J.D.; Fiori, L.A.; Little, H.W.;
this topic made a beginning. The yarns representing Castillan, A.V.; Investigation of the
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that the discussions made in this article is useful for IV: The Influence of Yarn- twist on the
textile researchers as a tool for further research in the Diameters of Cotton Yarns and on the
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Journal of Engineered Fibers and Fabrics http://www.jeffjornal.org
Volume 5, Issue 1 - 2010
 [21] Tyagi, G.K.; Goyal, A.; Salhotra, K.R.; [33] Marom, G.; Fischer, S.; Tuler, F.R.;
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AUTHORS’ ADDRESS
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Biswa Ranjan Ranjan Das, Research Scholar
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Department of Textile Technology
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New Delhi, Delhi 110 016
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[32] Nielsen, L.E.; Predicting the Properties of
Mixtures; Marcel Dekker, New York, 1978.

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Journal of Engineered Fibers and Fabrics http://www.jeffjornal.org
Volume 5, Issue 1 - 2010