Page 493 - Handbook of Properties of Textile and Technical Fibres

466 Handbook of Properties of Textile and Technical Fibres

The constitutive model for the viscoplastic behavior of a semicrystalline polymer
was proposed by Drozdov et al. (2004) and Drozdov and Gupta (2003). A polymer
is assumed to be a network of chains bridged by permanent joints (entanglements or
physical crosslinks on the surfaces of crystallites). The equivalent network is treated
as an ensemble of mesoregions with various activation energies for the separation of
active strands (mobile part of the amorphous phase) from their junctions. The spatial
heterogeneity of the network is attributed to interactions between amorphous regions
and crystallites. A similar model for viscoelastic behavior at finite strain is described in
the work by Drozdov (1998).
A model based on the molecular dynamics simulations of polymeric chains was
developed in Cook (1988). The model approximates the conformational motion ener-
getics by a number of chains of particles that are connected by bonds with multiwelled
potentials. Interactions between particles on adjacent chains are modeled by short-
range repulsive potentials. This model was applied for the simulation of the stresse
strain behavior of glassy polymers.

13.4.1.3 Structural models
Models in this group express macroscopic stress, deformation, time, and behavior of
the fiber by using a combination of mechanical behaviors of typical structural ele-
ments. This approach is generally referred to as micromechanical. There exist a num-
ber of models for a description of the mechanical behavior of typical structural
elements such as tie chains (McCullogh, 1977; McCullogh et al., 1977) and various
other elements (folded chains, parallel chain bundles, meanders, etc.). Many models
are based on the formal idea of a fiber as a composite structure. Arridge and Barham
(1978a) used a fiber model composed of an amorphous matrix (partially oriented), in
which needlelike fibrils oriented parallel to the axis of fiber were dispersed. Tension on
the fibrils is transmitted through shear deformation of the matrix. Fibrils the lengths of
which exceed a critical length (depending on the degree of deformation) are deformed
plastically and shorter fibrils only elastically. This model was successfully used to
describe the mechanical behavior of drawn polypropylene and polyethylene fibers
(Arridge and Barham, 1978b). The model of Gibson et al. (1978) uses as the structural
element the parts of polymer chains passing through more noncrystalline regions.
These polymeric chains consist in fact of a continuous crystalline phase.
In the series model, the polymer fiber is replaced by a parallel array of identical
fibrils that are subjected to a uniform stress along the fiber axis (Northolt et al.,
1995). Each fibril consists of a series of oblong domains arranged end to end. In a
domain the chains run parallel to the symmetry axis under an angle f with the fiber
axis. All domains in a fibril are assumed to be isotropic transverse to the symmetry
axis and to have identical mechanical properties. In the modified series model, the
mechanical properties of a domain belonging to the elastic extension of the fibril are
the chain modulus and the modulus for shear between the chains. The series model
implies that the fiber extension is governed by a sequential orientation mechanism.
The model also indicates the importance of the initial orientation distribution of the
chain axes for the deformation of the fiber (Northolt et al., 1995).