Page 511 - Handbook of Properties of Textile and Technical Fibres

484 Handbook of Properties of Textile and Technical Fibres

the crystalline phase are taken into account separately. The Takaynagi type model is
used to predict an effective activation volume and effective activation energy, which
are then implemented in the cooperative model. This model has been used for descrip-
tion of the yield behavior of polyethylene and PET.

13.4.4 Tensile strength of polyester fibers
Generally, fiber strength is a rather sophisticated parameter. It will decrease as the
degree of arrangement of the chain folds in crystallites rises (Prevorsek and Sibilia,
1971). The strength of drawn PET at a given draw ratio increases with increasing
molecular mass (Huang et al., 1994; Ziabicki, 1996). For PET, such molecular weight
dependences are explained by the suppressions of disentanglement and relaxation of
oriented molecular chains during deformation (Huang et al., 1994). For many pro-
cesses dealing with ultimate strength, like crazing or fracture, the molecular mass
between entanglements, Me, is probably a more important molecular characteristic
(Monnerie et al., 2005). As the orientation factor of the amorphous phase in PET fibers
grows, the strength also grows (Gupta and Kumar, 1981a).
In addition to the molecular mass, chemical composition of chains, and the inter-
chain cohesion forces, the strength is also influenced by the presence of different types
of defects and heterogeneities. The strength has therefore a statistical nature and its dis-
tribution (the probability model) is related to the rupture mechanism.
The strength variability of fibers is usually described in the framework of a weak-
est link model. This model assumes that the fiber can be replaced by a series of
randomly assembled uniform strength links, the strengths of which are independent,
identically distributed, random variables with a common cumulative distribution
function. Break occurs in the link with the smallest strength. Another model is simply
described as a random defect model. This model considers the fiber to have some
constant strength, upon which dimensionless noninteracting strength reducing
defects randomly occur. Choice of the model primarily depends on the proposed
hypothesis regarding the nature of the strength variability of the particular fibers.
Suitability of the proposed model to represent the fiber variability can be then eval-
uated by comparing predictions of the model with actual data. The probabilistic
approach to the fracture of fibers is based on the following assumptions (Kittl and
Diaz, 1988):
1. fiber breaks at a specific place with a critical defect (catastrophic flaw) and fracture behavior
is time-independent,
2. defects are distributed randomly along the length of fiber (model of Poisson’s marked
process),
3 fracture probabilities at individual places are mutually independent.
The cumulative probability of fracture FðV; s f Þ depends on the tensile stress level
and fiber volume V. The simple derivation of the stress at break distribution described
for example by Kittl and Diaz (1988) leads to the general form

FðV; s f Þ¼ 1 expð Rðs f ÞÞ (13.66)