Tensile properties

Tensile properties
• The mechanical properties of textile fibres, the responses to applied forces
and deformations, are probably the most important property.
• The properties of a textile structure such as a yarn or a fabric depend on a
complex interrelation between fibre arrangement and fibre properties, so that,
although a knowledge of fibre properties is essential to an understanding of
the properties of yarns and fabrics.
• The mechanical properties of a fibre cover a large number of effects, all of
which combine to determine the particular character of the fibre.
• The most important mechanical properties of fibres are their tensile
properties, namely their behaviour under forces and deformations applied
along the fibre axis.

Factors determining the results of tensile
experiments
1. The material and its condition
– The nature and arrangement of the molecules
2. The dimensions and arrangement of the specimen
– The breaking load of a fibre will increase in proportion to its area of
cross-section, and its elongation will increase in proportion to its
length.
– The mean breaking load of long lengths will be less than that of short
ones.
– The properties of a composite specimen composed of many fibres are
affected by the particular arrangement of fibres in the specimen and are
not given by a simple combination of the properties of the individual
fibres.

• The nature and timing of the test
– The elongation of a textile fibre is not a single-valued function of the
applied load.
– It depends on the length of time for which the load and any previous loads
have been applied.
– If a constant load is applied to a fibre, it will, after its instantaneous
extension, continue to extend for a considerable time .
– if the load is great enough, it will eventually break.
– The load necessary to cause breakage will vary with the speed of the test.
– a rapid test requiring a greater breaking load than a slow one.
– Thus the results of experiments will be affected by the time allowed and
by the way in which the load is applied.

Load–elongation and stress–strain curves
The behaviour of an
individual fibre under a
gradually increasing
applied force is completely
expressed by the load–
elongation curve with its
end-point breakage.

Specific Stress
• In textile technology, we are more often interested in materials in terms of their
weight, rather than in terms of their bulk.
In consistent units, the following relation between stress f, specific stress σ and
density ρ
f = ρ σ
The same equation is correct with f in GPa, σ in N/tex and ρ in g/cm-3
The distinction between stress and specific stress becomes significant only when
we wish to compare materials of different density, for example silk and nylon,

• Specific stress is dimensionally equivalent to energy per unit mass. N/tex equals
kJ/g.
• Another measure of strength, the breaking length in kilometers, or more
correctly kilometer-force. 1kmf equals 1gf/tex or 9.8mN/tex.
• Load–elongation curves become stress–strain curves by a change of units,
without affecting the shape of the curve.
Strength
Strength, is a measure of the steady force necessary to break a fibre and is given
experimentally by the maximum load developed in a tensile test.
For comparing different fibres, the value of the specific stress at break is used and
is called tenacity or specific strength.
Breaking length can also be used for expressing strength.
For use in comparing strengths on the basis of area of cross-section, the stress at
break is termed the ultimate tensile stress.

Elongation at break
• The elongation necessary to break a fibre is a useful quantity, is termed the
breaking extension or break extension.
Work of rupture
For an individual fibre, the work of rupture, sometimes called the toughness, is
defined as the energy needed to break the fibre. The units for this are joules.
If we consider a fibre under a load F, increasing in length by an amount dl, we
have:
work done = force × displacement = F· dl
Total work done in breaking the fibre = work of rupture
This equals the area under the load–elongation curve.

• To compare different materials, we may use the term, specific work of
rupture.
• The specific work of rupture may be expressed in units of N/tex or kJ/ g.
• It is given by the area under the curve of specific stress against strain.
• This represents the energy in joules needed to break a 1tex filament, 1m long.
• The total work of rupture of any particular specimen is proportional to its
mass, independent of the actual values of linear density and length which
determine that mass.
Direct measurement of work of rupture
work of rupture = loss of potential energy = M g x
where M = mass of pendulum and x = difference in
height of final positions of
pendulum, with and without the specimen.

Comparison of methods of specifying breakage
• There are three ways of specifying breakage or resistance to breakage:
by the force, elongation or energy necessary.
• Whenever breakage occurs, the values of each of these appropriate to the
conditions of test must be reached.
• But, usually the limiting value of only one of the three will be inherent in
the conditions causing breakage, while the other two follow automatically.
• Strength, or tenacity, gives a measure of the resistance to steady forces. It
will thus be the correct quantity to consider when a specimen is subject to
a steady pull, as, for example, in a rope used for slow hoisting of heavy
weights.
• The breaking elongation gives a measure of the resistance of the material
to elongation. It is thus important when a specimen is subject to stretching,
for example the neck of a garment being pulled over the head, or the warp
extension in weaving.

• The work of rupture, which is the energy needed to break a fibre, gives a
measure of the ability of the material to withstand sudden shocks of given
energy. eg. opening of a parachute, a falling climber being stopped by a rope
etc.
• In comparing materials to see which is least likely to break, it is important to
consider the conditions under which breakage would occur and then to decide
which quantity is the appropriate one to use.
work of rupture = 1/2 (breaking
load × breaking elongation)
work factor =work of
rupture/(breaking load 
breaking elongation)
Work factor

• The tangent modulus is the slope of the stress– strain curve at any given position.
It is relevant when materials are subject to cyclic loading. Plots of tangent modulus
against strain are another useful way of showing the changes in extensibility as
fibres are increasingly strained.
• The secant modulus is stress/strain at any position on the stress– strain curve.
• Dynamic modulus.
• The reciprocal of modulus is called the compliance.
Initial modulus and other moduli
The initial modulus is equal to the slope of
the stress–strain curve at the origin (after
the removal of any crimp).

Yield point
• After an initial period with a steep slope, extension suddenly becomes much
easier. It is in this region that the yield point occurs.
• yield point as the point at which the tangent to the curve is parallel to the line
joining the origin to the breaking point.
• This point is then characterised by its stress and strain as the yield stress and yield
strain.
• the yield point as occurring at
the stress given by the
intersection of the tangent at
the origin with the tangent
having the least slope.

• the yield point as occurring at the stress given by the intersection of the tangent at
the origin with the tangent having the least slope.
• Alternatively, particularly when there are considerable linear regions both above
and below the yield region, the point of intersection of the tangents may be taken as
the yield point
• yield point is important
because for most
materials, elastic
recovery, which is good
up to the yield point.

Crimp
• The crimp is given by AO and may be expressed as a percentage of the initial
length.

Stress–strain curves of various fibres tested at 65% r.h., 20 °C, 0.15mN
tex–1 s–1.

Variability, specimen length and strength:
The weak-link effect
• Textile fibres are not uniform: their composition and fineness vary both from one
fibre to another in a sample and along the length of each fibre.
• Consequently, their tensile properties are also variable.
• Suppose that we could determine the strength at every point along the length of a fibre.
• It varied from point to point
• If a gradually increasing
load is applied to this
whole specimen, it will
break at its weakest
point, giving a strength
S1.
• if the specimen is
tested in two half-
lengths, each will break
at its own weakest
place, one giving the
value S1, and the other
a value S , which is necessarily greater than S1

• The mean strength S1/2, measured on half-lengths, is the mean of S1 and S2, and
must therefore be greater than the strength measured on the whole length.
• Similarly, going to quarter-lengths, we get the four values, S1, S2, S3, S4, and the mean
strength S1/4 is greater still.
• This increase will continue until at very short lengths the mean strength tends to the
value S0, which gives equal areas of the curve above and below the line S = S0,
The weak-link effect described above has the following results:
1. The mean measured strength of a specimen decreases as the test-length is
increased.
2. The decrease in mean measured strength will be more rapid the more irregular
the fibre is.
3. The order of ranking of specimens may alter if the test-length is altered.
Change in order of ranking of
materials. S0 is greater for (a) than for
(b), but S1 is greater for (b).

Elastic recovery
• Elastic recovery, that is, the behaviour on removal of stress, is only a special case
of the general phenomenon of hysteresis.
• In a cyclic change of stress or strain, the results will not fall on a single line.
• After a few initial cycles, the fibre will become conditioned and the results will
tend to fall on a loop, as in Fig.
• This means that energy is used up by internal friction, and consequently the
material will heat up and may tend to dry out.
• This is important where fibres are subject to repeated loading, as in tyres, and
the heating will affect their properties.
• In these uses, fibres showing little hysteresis are desirable.
• As with other tensile properties, recovery is time
dependent. This leads to hysteresis, even if,
after time, the recovery is complete.

Elastic and Plastic Deformation
• On a molecular scale, recoverable or elastic deformation is due to a stretching
of inter-atomic and intermolecular bonds, while non-recoverable or plastic
deformations result from a breaking of bonds and their re-forming in new
positions, or to the stabilisation of new chain conformations.
Schematic illustration of elastic and plastic deformations: (a) initial
configuration; (b) elastic deformation with straining of links; (c) plastic
deformation with re-forming of links in new positions.

Elastic Recovery
• Elasticity: that property of a body by virtue of which it tends to recover its
original size and shape after deformation.
• A deformation may be divided up, as shown in Fig, into an elastic part, which is
recovered when the stress is removed, and a plastic or permanent part.
• Quantitatively, it is convenient to use the following definition:
• Complete recovery will then have the value 1 (or 100%), incomplete recovery
will have a proportionately lower fraction, and no recovery at all will have the
value zero.
• It should be noted that (1– work recovery) gives the proportion of the total work
that is dissipated as heat.

Experimental methods
• Meredith used the Cliff constant-rate-of-loading tester and applied the load at a
rate of 10 gf/(den min) (0.15 mN/(tex s). When the required load had been
reached, it was left on the specimen for 2 min. The load was taken off at the same
rate and left off until 1 min after the start of unloading. The procedure was then
repeated for higher loads.

• In an Instron test at constant rate of extension, there would be a decrease of
stress at constant extension due to stress relaxation

Effect of stress and Strain on Elastic
Recovery
• Cotton shows no yield point (or it may be more correct to say that the yield point
is at zero stress and zero strain). The elastic recovery falls steadily to about 0.3.
• The bast fibres show poor recovery from strain but can withstand large stress
without great permanent damage.

• Viscose rayon and acetate show a marked yield point. Below this point, the
recovery is good, but above it the curve drops rapidly, and the recovery is poor.
• Wool and hair also show a yield point, but the drop in the curve is less rapid,
and even near break there is still considerable recovery. These fibres are not
good under high stresses but can recover from large strains. Thus they show
60% recovery from an extension of 35%.
• Wet wool fibres show complete recovery up to the end of the yield region
(30% extension) and very good recovery from higher strains.

• Silk shows fairly good elastic recovery from both stress and strain.
• Nylon shows the best elastic recovery of any of the fibres tested by Meredith,
Even near break, its recovery falls only to 0.7.
• Although, in strength and extension at break, nylon is
• surpassed by some other fibres, these curves show its superiority in resisting
permanent damage as a result of undue stress or strain.
• After some time on a package, spandex
fibres such as Lycra acquire a temporary
set, and the first elongation shows a high
stiffness. a small amount of the initial
extension is not recovered; in
subsequent elongations, a steady
hysteresis cycle with good reversible
behaviour is established.
Cycling response of spandex fibre: 1, first
elongation; 2, 6th cycle loading
and unloading

It is interesting to compare values of the yield point obtained from stress–strain
curves with those from recovery curves (arbitrarily defined as the point of 95%
recovery).
It will be seen that there is qualitative agreement, though the values from the
stress–strain curves are generally higher than those from the recovery curves.

Work recovery
Work recovery of fibres After Beste and
Hoffman [4]:
A, wool;
B, Dacron polyester fibre;
C, acetate;
D, casein;
E, nylon;
F, Orlon acrylic fibre;
G, silk;
H,cotton;
I viscose rayon.

Influence of test conditions on
recovery
• influence of the time:
the influence of the
time te for which
viscose rayon fibres
were held at constant
strain and the time tr of
recovery at zero stress.
• Temperature
S, as received tested at 65% r.h., 20 C; ST, 65% r.h., 20 C after water at 95 C;
W20, in water at 20 C; W95, in water at 95 C:

Creep
• On the application of a load to a fibre, it will, after an instantaneous extension,
continue to extend as time goes on. On removal of the load, the recovery will
not be limited to the instantaneous recovery but will continue to take place.
• This behavior is illustrated in Fig. is known as creep and creep recovery.
• Creep is extension with time under an applied load: the complementary effect
is stress relaxation, the reduction of tension with time under a given extension.
• when the fibre is stretched, an instantaneous stress is set up, but this gradually
decreases as time passes.
1. creep: long times, from 1 minute to 1 month
2. stress relaxation: medium to long times, from 1 second to 1 hour
3. stress–strain curves, including impact methods: short to medium times, from
1/100 second to 10 minutes
4. dynamic testing: short times, from 0.1 millisecond to 1 second.
stress–strain curve obtained, will depend on the timing.

Creep under constant load and recovery under zero load, showing
instantaneous extension, A–B and D–E;
total creep, B–C;
primary creep, E–F;
and secondary creep, G–H.
(b) Relaxation of stress under constant extension.

• The total extension may therefore be divided into three parts: the immediate
elastic deformation, which is instantaneous and recoverable; the primary creep,
which is recoverable in time; and the secondary creep, which is non-recoverable.
• At low stress, creep is due to localised molecular rearrangement, which may or
may not be recoverable. At high stress, molecules slide past one another in non-
recoverable deformation.
• O’Shaughnessy made division of the
total extension of viscose rayon yarn
into its three parts. He measured the
creep under a constant load and the
recovery after various times of loading.
• Results are shown in Figure in log
scale.
• If, after recovery, the same load is
applied again, the rate of creep is less
than that in the first test on the
specimen. The primary creep takes
place at its initial rate, as before, but
the secondary resumes at the rate at
which it left off.

Generalised creep curves
• The creep of viscose rayon at various loads showed a certain regularity when the
elongation divided by the stress was plotted against the time,

Influence of various factors on creep
• Steinberger [6] found that the
creep of acetate increased with
the humidity,
• the creep of acetate fibre
increased as the temperature
increased.

Stress relaxation
• When a fibre is held stretched, its stress gradually decays. It may drop to a
limiting value or may disappear completely. This phenomenon is known as
relaxation.
• after a rapid initial decay of stress, the rate of decay drops to zero.
• In fact, on plotting on a logarithmic scale, it becomes clear that the stress is
still decreasing after 24 hours.
Stress relaxation in viscose rayon
In log scale

Effect of temperature on stress
relaxation
Relaxation of wool fibres in
water with 15% extension at
various
Temperatures.
(f/f1 is the ratio of the stress
after the given time to the
stress after 1 h).

Time and tensile testing
• At low speeds, that is, for tests lasting more than a few seconds, the
conventional methods can be used.
• At higher speeds, other methods must be adopted.
• One way is to use an impact test. In this method, a moving large mass is
engaged with one end of the specimen, while the other end is held fixed and
connected to a load-measuring device. There must be appropriate mechanical
arrangements to ensure that the free jaw is engaged only after the mass has
attained its required speed.
• The moving mass may be a rotating flywheel, the bob of a pendulum, a falling
weightor a rifle bullet.
• In the past, the load measurement could be by means of a cantilever arm and
mirror, recording on photographic paper, or by a resistance strain-gauge, a
capacitive or inductive pick-up, or a piezo-electric crystal, connected through an
appropriate circuit to an oscilloscope.
• Nowadays, digital recording would be used.
• If the weight is massive, its speed will not change on breaking the specimen,
and thus there will be a constant rate of extension.

• If the recorder or oscilloscope has a linear time-base, it will record the load–
elongation curve directly.
• In this way, rates of extension of from 10 to 3000% per second can be
obtained.
• At still higher rates of straining, the velocity of transmission of the strain along
the specimen becomes important, and more complicated experimental
arrangements are necessary.
• It was possible to work out stress–strain curves at rates of straining of 1000–
15000% per second.
Temperature and time: isothermal and adiabatic changes
• In an imperfectly elastic material, energy will be dissipated in internal friction
when the material is extended.
• This energy is represented by the area inside a hysteresis loop and is turned
into heat.
• In a slow test, this heat will be given off to the surroundings and there will be
no appreciable change of temperature of the specimen, but in a rapid test
there will be less opportunity for loss of heat and the specimen will rise in
temperature.

• Experiments thus range between two limiting cases: the isothermal, with no
change of temperature, and the adiabatic, with no loss of heat.
• Since the properties of a fibre vary with temperature, the results obtained in the
two types of test will be different, and this must be remembered in interpreting
the effect of time.
• An interesting example of adiabatic (or nearly adiabatic) conditions occurs in the
drawing of fibres. It offers an explanation of the occurrence of characteristic
draw-ratios.
• Any attempt to alter the draw-ratio by changing the relative speeds of the
• rollers merely results in the neck’s moving backwards or forwards, the actual
draw ratio remaining constant.
• If the neck reaches the back roller, the filament breaks, and, if it reaches the front
roller, intermittent portions of undrawn material pass through. In either case, the
technical consequences are serious.

• Figure shows the isothermal stress–strain curves for (undrawn) polyester fibre.
• If extension takes place adiabatically, however, the temperature rises and the
path OABC should be followed. But, under actual drawing conditions, a
decreasing load is an unstable condition, so that the line AC is followed.
• It is this sudden increase in length past the unstable region ABC that results in
the formation of a neck and determines the characteristic draw-ratio.
• If the whole process is slowed down, there will be some loss of heat, the
temperature rise will be smaller, and thus the draw-ratio will be reduced.

Influence of rate of loading on breakage
• The breaking load of a fibre depends on the rate at which the load is applied.
• If we apply a constant load to a fibre, then instantaneous extension followed by
creep and then, when the critical extension is reached, breakage.
• Thus the time to break decreases with increasing load.
• If the rate of increase of
load is slow, there is more
time for creep to occur,
and consequently the
breaking extension is
reached at a lower load.
where F1 is breaking load in a
time t1, F2 is breaking load in a
time t2, and k is the
strength–time coefficient (0.06-
0.088)

• The strength of these textile fibres increases by 6–9% for each tenfold increase
of rate of extension.
Stress–strain curves
• Stress–strain tests take some time, and consequently there is an opportunity for
creep to occur.
• Because of creep, the slower curves are nearer to the strain axis than the faster
curves.
• The stress–strain curves
obtained for a fibre thus
depend on the time taken in
the test and on the way in
which the time is distributed.

• If the stress–strain curves are non-
linear, there will also be a difference
between constant rate of loading
and constant rate of extension
tests, owing to the different
proportions of time spent on
different parts of the curves.
• There will be consequent effects on
the quantities, such as modulus and
yield point
wool

Dynamic tests
• The tests may be described as static (or quasi-static) tests if the stress–strain
relation is obtained without considering the equation of motion of the system.
• if there is a monotonic increase of stress, they are considered with the static
tests.
• The high-speed impact tests described earlier are examples of this situation.
• It is necessary to take account of the dynamic effects when the inertia, either of
part of the apparatus or of the specimen, cannot be neglected.
• Thus the inertia effects involved in old-fashioned pendulum testers or in
inclined-plane testers are examples of the occurrence of dynamic effects as
sources of error in what are intended to be static tests.
The dynamic tests dealt with in this section are of two types:
(1) cyclic loading and
(2) tests in such a short time that the propagation of the stress wave means that
the stress cannot be regarded as constant along the specimen.

46
Dynamic Mechanical Analysis (DMA)
• Dynamic Mechanical Analysis (DMA) is a technique in which the elastic
and viscous response of a sample under oscillating load, are
monitored against temperature, time or frequency.
• The modern DMA systems are nearly always fixed frequency systems
operating at frequencies between about 0.01 and 100 Hz.
• Temperature region is ranging from about – 150ºC to 300ºC.
• In DMA, instead of keeping the strain constant, as in a stress relaxation
test, the strain is oscillated at constant amplitude, ε0, and a constant
frequency, ω.
• the strain input is
ε(t) = ε0sin ωt.
• Stress will respond at the same frequency but may have a phase difference
and different amplitude.
• The stress will be given by
σ(t) = σ0 sin(ωt + δ) = G(ω) ε0 sin(ωt + δ)
where, G(ω) is the dynamic modulus, and δ is the phase angle.

47
• The dynamic modulus G(ω) is the ratio of stress to strain; in this case we take the ratio
of the amplitudes of the stress and the strain:
• G(ω) or the dynamic modulus defines the modulus of a viscoelastic material.
• The phase angle (δ), describes the viscous character of the material.
• If δ = 0, the stress is in phase with the strain and the material is totally elastic.
• If δ = π/2, the stress is completely out of phase and is completely viscous.
• In general, δ will be between 0 and π/2 and the material will be viscoelastic.
• In alternative representations, we can expand the stress function:
σ(t) = G(ω)ε0cos δ sin ωt + G(ω)ε0sin δ cos ωt
= G’(ω)ε0sin ωt + G”(ω)ε0cos ωt
Where, G’(ω) = G(ω) cos δ and G”(ω) = G(ω) sin δ
• G’(ω) is known as the storage modulus.
• G”(ω) is known as the loss modulus

48
• The storage modulus G’(ω) is proportional to that part of the strain energy
that is stored and then recovered during one cycle. It also describes the
elastic part of the stress response, or the part of the stress in phase with the
strain.
• The loss modulus G”(ω) is proportional to that part of the strain energy that
is lost during a cycle due to viscoelastic dampening. It also describes the
viscoelastic part of the stress response, or that part of the stress that is out of
phase with the strain.
Complex modulus is defined as

49
• Sample is fixed between 2 parallel
arms that are set into oscillation by
an electromagnetic driver at an
amplitude selected by operator.
• DMA module measure changes in
viscoelastic properties of materials
resulting from changes in
Temperature, amplitude and time.
• It then detects changes in the
system’s resonant frequency and
supplies the electrical energy
needed to maintain the preset
amplitude.
Principle
• Samples – fibers, films, molded sheets, powder.
• Frequency of oscillation is a measure of modulus of the material. The amount of
electrical energy needed to maintain constant amplitude  damping properties.

• DMA – sample subjected to
sinusoidally varying strain of
angular frequency.
• For viscoelastic material, resulting
stress will also be sinusoidal, but
will be out of phase with the
applied stress owing to energy
dissipation as heat, or damping.
• Damping can be calculated by
h = (v2 – v1)/vr, or measure
driving force to maintain constant
amplitude.
50

51
• Below Tg, G’(ω) is fairly constant.
• At Tg, G’(ω) drops dramatically,
while, tan δ goes through a peak.
• Peaks in tan δ can also be observed
below Tg : sub-glass relaxations.
• Typical DMA characteristic of a semi-crystalline polymer as a function of
temperature is plotted

Transitions in dynamic moduli
• There are many mechanisms by which a fibre can deform.
• Some of these, such as the stretching of atomic bonds, are characterised by large
stresses and small strains but occur at very high speed;
• others, such as the uncoiling of chains, lead to large strains under low stresses
but take a long time owing to viscous drag.
• At high frequencies, only the stiff mechanism operates and the modulus is high,
• but at low frequencies the soft mechanism can operate and the modulus is low.
• At the extremes, there is little energy loss: at high frequencies, there is little
viscous displacement; at low frequencies, there is little viscous resistance.
• But near the transition, when the structure is just becoming mobile, the viscous
resistance is very important in causing a large energy loss, or, what comes to the
same, in causing a large phase lag. The ‘loss’ quantities (E″, ηpω, tan δ) will
therefore go through a maximum,
Simple model of viscoelastic behaviour.

Simple model of viscoelastic behaviour. (b) Real and imaginary moduli of model.

Real and imaginary dynamic moduli of
nylon 6.6 fibres.

Tensile properties

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