Page 438 - Handbook of Properties of Textile and Technical Fibres

The chemistry, manufacture, and tensile behavior of polyamide fibers 411

There are two regions of mechanical response of a microfibril: the small-strain
region with ε a < 0:08 and the large-strain region with ε a 0:15.
For the first load cycle in Fig. 12.37, initial modulus E l is 4.6 GPa. Taking into
account the intermicrofibrillar amorphous fraction of 0.4, a modulus of the amorphous
regions was deduced to be E la ¼ 2.88 GPa for the microfibrils. In the second load
cycle it is E 2 ¼ 1.80 GPa and E 2a ¼ 1.13 GPa. The decrease of the initial modulus
after a first load cycle is well known and can be explained by the “destruction of
some structure.”
In the small-strain region the initial modulus decreases with strain due to the
gradual destruction of hydrogen bonds by segment deformation and orientation.
Above the small-strain region the amorphous initial modulus increases by combined
entropy and energy elastic loading of extended tie chains (Frank and Wendorff, 1981).
Peterlin (Khan and Huang, 1995) assumed that the ends of microfibrils, preferen-
tially situated on the outer surface of the fibrils, retract under stress. In low-strength
3
PA 6 they thus open up about 10 16 oblate spheroids per cm having 6 nm diameter
in fiber axis direction and 10 nm in the perpendicular direction. The number and
size of cracks in high-strength polyamide is considerably smaller and is in agreement
with the much higher draw ratio employed for these fibers. The submicrocrack forma-
tion is a process inherently independent of chain scission or end-group formation.
Their direct influence as individual stress concentrator is weak and ineffective with
regard to accelerating chain scission (Kausch, 1985).
Moseley (1963) concluded that at relatively high temperatures the strength of a
polyamide monofilament depends on the whole internal fiber structure and local

defects were of negligible importance. Whereas, below 100 C, local defects were
the dominant factor. This conclusion was supported by the different effects of test
length on the break statistics at low and higher temperatures.
Understanding yield and plasticity effects in polymers can also help to illuminate
the fracture process in polyamides, since these phenomena precede fracture and are
responsible for much of the damage accumulation that is experienced by the material.
Timoshenko and Goodier (1970) have developed a rigorous elasticity framework that
is applicable to most engineering materials. Specifically, the classical theory of
plasticity was developed to study the stress-strain relationship of plastically deformed
metals. However, these laws are applicable to a wide range of materials and can be
utilized to quantify plasticity effects in polyamide fibers. Generally, plastic deforma-
tion involves dissipation effects in materials, which affirms that it is an irreversible pro-
cess (Khan and Huang, 1995). Because of the nature of irreversibility, plastic
deformation is a path-dependent process. Krempl and Bordonaro (1998) have vali-
dated path dependence for biaxial-torsional loading of 50% crystalline tubular speci-
mens of nylon 66, in which they performed displacement-controlled experiments. For
the classical theory of plasticity, plastic deformation is considered to be rate insensi-
tive. However, the viscous component in the constitutive model for nylon fibers pre-
cludes this assumption, and rate sensitivity should be considered. The constitutive laws
for polyamides in general will include time-dependent parameters, which serve as an
auxiliary factor in quantifying the effects of creep, strain rate, and viscosity (Khan and
Huang, 1995).