43 research outputs found
Strain Hardening of Polymer Glasses: Entanglements, Energetics, and Plasticity
Simulations are used to examine the microscopic origins of strain hardening
in polymer glasses. While stress-strain curves for a wide range of temperature
can be fit to the functional form predicted by entropic network models, many
other results are fundamentally inconsistent with the physical picture
underlying these models. Stresses are too large to be entropic and have the
wrong trend with temperature. The most dramatic hardening at large strains
reflects increases in energy as chains are pulled taut between entanglements
rather than a change in entropy. A weak entropic stress is only observed in
shape recovery of deformed samples when heated above the glass transition.
While short chains do not form an entangled network, they exhibit partial shape
recovery, orientation, and strain hardening. Stresses for all chain lengths
collapse when plotted against a microscopic measure of chain stretching rather
than the macroscopic stretch. The thermal contribution to the stress is
directly proportional to the rate of plasticity as measured by breaking and
reforming of interchain bonds. These observations suggest that the correct
microscopic theory of strain hardening should be based on glassy state physics
rather than rubber elasticity.Comment: 15 pages, 12 figures: significant revision
The nonlinear time-dependent response of isotactic polypropylene
Tensile creep tests, tensile relaxation tests and a tensile test with a
constant rate of strain are performed on injection-molded isotactic
polypropylene at room temperature in the vicinity of the yield point. A
constitutive model is derived for the time-dependent behavior of
semi-crystalline polymers. A polymer is treated as an equivalent network of
chains bridged by permanent junctions. The network is modelled as an ensemble
of passive meso-regions (with affine nodes) and active meso-domains (where
junctions slip with respect to their positions in the bulk medium with various
rates). The distribution of activation energies for sliding in active
meso-regions is described by a random energy model. Adjustable parameters in
the stress--strain relations are found by fitting experimental data. It is
demonstrated that the concentration of active meso-domains monotonically grows
with strain, whereas the average potential energy for sliding of junctions and
the standard deviation of activation energies suffer substantial drops at the
yield point. With reference to the concept of dual population of crystalline
lamellae, these changes in material parameters are attributed to transition
from breakage of subsidiary (thin) lamellae in the sub-yield region to
fragmentation of primary (thick) lamellae in the post-yield region of
deformation.Comment: 29 pages, 12 figure