Page 510 - Handbook of Properties of Textile and Technical Fibres

Tensile failure of polyester fibers 483

13.4.3.4 Yield point

The yield point is determined practically by analysis of the derivatives of stress-strain
curves. It corresponds to the first minimum on the first derivative of the stress-strain
curve (see Fig. 13.28). The yield point in well-oriented fibers is in the range of
0.5%e1.0% strain, whereas isotropic samples show a yield strain at about 2.2%.
Unloading the fiber after the first extension up to a strain larger than the yield strain
results in a small but permanent extension of the fiber. There is little variation in the
yield strain, ε y , for fibers made of different kinds of polymer (Northolt et al., 1995).
The yield stress of amorphous polymers depends on time and temperature, a phe-
nomenon known as physical aging. The yield is related, above all, to the orientation
of the amorphous phase (Gupta and Kumar, 1981a). The higher the orientation factor
of the amorphous phase, the higher will be the yield stress. The yield stress s y of glassy
polymers exhibits viscous flow, which can be expressed by Eyring type model modi-
fied for normal stresses (Bauwens-Crowet et al., 1969):

s y dε Q
¼ A ln C þ (13.64)
T dt RT
where T is the absolute temperature, dε=dt is the strain rate, Q is the activation energy,
R is the universal gas constant, and A, B are parameters containing geometrical and
entropic factors. The yield stress is found to increase with decreasing temperature and
with increasing strain rate. The two-process ReeeEyring model has been used for the
description of amorphous PET yield behavior (Foot et al., 1987).
Rault (1998) applied the compensation law to the yielding of amorphous and semi-
crystalline polymers. Accordingly, the yield stress has the form

Ts 0 kT dε=dt
s y ¼ s 0 þ ln (13.65)
T g V e 0

where s 0 , e 0 , and V are parameters and T g is glass transition temperature. Parameter s 0
may be associated with the athermal stress s i (0) of the cooperative model described in
the work (Richeton, 2006). The first term of this yield stress models exhibits a linear
dependence on temperature. As mentioned by Rault (Rault, 1998), the ratio s 0 /T g is
found to be about 0.5 MPa/K for many thermoplastic polymers. The basic molecular
theories of yield are reviewed in the work Stachurski (1997).
It was found that the yield stress of amorphous polymers increases dramatically for
low temperatures as well as for high strain rates. To describe this behavior, a model
based on the cooperative model of Fotheringham and Cherry (1978) and strain rate/tem-
perature superposition principle of the yield stress was derived (Richeton et al., 2005).
This model was extended to temperatures above the glass transition temperature.
The cooperative model for the yield behavior of semicrystalline polymers is pro-
posed in the work (Gueguen et al., 2008). The semicrystalline polymer is here consid-
ered as a two-phase material, where the yield processes in the amorphous phase and in