Statistical Variation and Strain-Rate Sensitivity of the Mechanical Properties of Individual PET Fib part of Agilent Statistical Variation and Strain-Rate Sensitivity of the Mechanical Properties of Individual PET Fib Statistical Variation and Strain-Rate Sensitivity of the Mechanical Properties of Individual PET Fib, Agilent Statistical Variation and Strain-Rate Sensitivity of the Mechanical Properties of Individual PET Fib 5991-1552EN c20141030 [4].pdf text manual preview

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Statistical Variation and Strain-Rate
Sensitivity of the Mechanical Properties
of Individual PET Fibers
Application Note

Introduction crystalline phases [3]. The final part of
the curve represents slippage between
Poly(ethylene terephthalate), or microfibrils. It is important to note here
PET (also known as polyester), is a that the changes in elastic properties
thermoplastic polymer used extensively of a PET fiber during these different
as synthetic fiber. PET fibers are popular deformation regimes were significant
because of their improved wrinkle and have been measured previously
resistance, durability and high color using continuous dynamic analysis
retention [1, 2]. Most characteristic (CDA) [4].
physical properties of PET fibers are
attributed to the presence of benzene During the deformation of the
rings, which also lead to high stiffness amorphous regions, stress
of the polymer chains [1]. concentration in the surface layer of
the fiber results in surface cracks and
The polymer chains in one individual crazing in the PET fibers (horizontal
PET fiber can be distributed in arrows in Figure 1). The propagation
crystalline, oriented semi-crystalline of one or few of these cracks through
and non-crystalline (amorphous) the sample is a stochastic process
regions [3]. A PET fiber consists of depending on the distribution of
microfibrils aligned along the fiber axis. crystalline and amorphous regions in
These microfibrils, in turn, consist of the core of the fiber. Hence, it is not
crystalline and amorphous regions, only important to characterize the
and connected to other microfibrils mechanical properties of individual
by another kind of amorphous phase, PET fibers, but also to understand
known as mesamorphous phase. the statistical variability in their
The different regions observed in the response that can be extrapolated to
tensile stress-strain curve (Figure 1) the underlying molecular structure and
can be explained by the deformation of processing conditions.
Figure 1. Typical engineering stress- the different microstructural regions
strain curve of an individual PET fiber. The Failure in materials is often a stochastic
mentioned above. During the initial
schematics outline the evolution in the process because of the distributions of
molecular structure of amorphous polymer deformation, the amorphous regions
chains during different regimes of deformation. within the microfibrils align themselves defects and molecular structure, and it
in the similar orientation as the has been successfully shown to follow
mesamorphous phase. The stress-strain a Weibull statistical distribution of the
curve goes through another point of form [5]
inflexion when the applied load starts to
strain the bonds in both amorphous and (1)
where, Pf is the probability of failure of perform the Weibull analysis. The failure
a fiber at a stress less than or equal to probability, Pf, for each tensile strength
s, s0 is the characteristic strength, and was calculated as
is the Weibull modulus that describes
the variability of the failure strength. A (4)
high Weibull modulus represents a more
uniform distribution, and hence better The data were then plotted and the
reliability. Rearrangement of the Weibull Weibull modulus was determined from
distribution (Eqn. 1) provides Eqn. 2.

(2) For determination of the strain-rate
exponent, three tensile tests were
and hence the characteristic strength performed at strain-rates of 1 x 10 -1,
and Weibull modulus both can be Figure 2. Engineering stress-strain curves 1 x 10 -2 and 1 x 10 -4 per second, each.
obtained from a plot of lnln(1/1-Pf) obtained from quasi-static tensile tests on The previous set of tests used for
seven different PET fibers. Note the variation determining Weibull modulus, were also
versus lns (known as Weibull plot). The
in tensile strength values.
slope of the linear fit should produce used as the dataset for the strain-rate of
the Weibull modulus and the intercept 1 x 10 -3 per second.
should produce the characteristic
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