103 research outputs found
Enthalpy recovery in semicrystalline polymers
Constitutive equations are derived for enthalpy recovery in polymeric glasses
after thermal jumps. The model is based on the theory of cooperative relaxation
in a version of the trapping concept. It is demonstrated that some critical
temperature and some critical degree of crystallinity exist above which the
energy landscape becomes homogeneous and structural relaxation ceases.Comment: 13 pages, 5 figures, LATE
Modelling structural relaxation in polymeric glasses using the aggregation-fragmentation concept
Governing equations are derived for the kinetics of physical aging in
polymeric glasses. An amorphous polymer is treated as an ensemble of
cooperatively rearranged regions (CRR). Any CRR is thought of as a string of
elementary clusters (EC). Fragmentation of the string may occur at random time
at any border between ECs. Two string can aggregate at random time to produce a
new string. The processes of aggregation and fragmentation are treated as
thermally activated, and the rate of fragmentation is assumed to grow with
temperature more rapidly than that for coalescence. This implies that only
elementary clusters are stable at the glass transition temperature, whereas
below this temperature, CRRs containing several ECs remain stable as well. A
nonlinear differential equation is developed for the distribution of CRRs with
various numbers of ECs. Adjustable parameters of the model are found by fitting
experimental data in calorimetric tests for polycarbonate, poly(methyl
methacrylate), polystyrene and poly(vinyl acetate). For all materials, fair
agreement is established between observations and results of numerical
simulation. For PVAc, the relaxation spectrum found by matching data in a
calorimetric test is successfully employed to predict experimental data in a
shear relaxation test.Comment: 25 pages, 15 figure
Modeling the viscoelastoplastic response of amorphous glassy polymers
Constitutive equations are derived for the viscoelastoplastic response of
amorphous glassy polymers at isothermal loading with small strains. A polymer
is treated as an ensemble of cooperatively relaxing regions (CRR) which
rearrange at random times as they are thermally agitated. Rearrangement of CRRs
reflects the viscoelastic response of the bulk medium. At low stresses, CRRs
are connected with each other, which implies that the macro-strain in a
specimen coincides with micro-strains in individual relaxing regions. When the
average stress exceeds some threshold level, links between CRRs break and
relaxing domains begin to slide one with respect to another. Sliding of
micro-domains is associated with the viscoplastic behavior of polymers. Kinetic
equations are proposed for viscoplastic strains and for the evolution of the
threshold stress. These equations are validated by comparison with experimental
data in tensile relaxation tests and in tests with constant strain rates. Fair
agreement is demonstrated between results of numerical simulation and
observations for a polyurethane resin and poly(methyl methacrylate).Comment: 19 pages, 12 figure
A tube concept in rubber viscoelasticity
A constitutive model is derived for the time-dependent response of
particle-reinforced elastomers at finite strains. An amorphous rubbery polymer
is treated as a network of long chains linked by permanent junctions (chemical
crosslinks, entanglements and filler particles). A strand between two
neighboring junctions is thought of as a sequence of mers whose motion is
restricted to some tube by surrounding macromolecules. Unlike the conventional
approach that presumes the cross-section of the tube to be constant, we
postulate that its radius strongly depends on the longitudinal coordinate. This
implies that a strand may be modeled as a sequence of segments whose thermal
motion is totally frozen by the environment (bottle-neck points of the tube)
bridged by threads of mers which go through all possible configurations during
the characteristic time of a test. Thermal fluctuations affect the tube's
radius, which results in freezing and activation of regions with high molecular
mobility (RHMs). The viscoelastic response of an elastomer is associated with
thermally activated changes in the number of RHMs in strands. Stress-strain
relations for a rubbery polymer at finite strains and kinetic equations for the
concentrations of RHMs are developed by using the laws of thermodynamics. At
small strains these relations are reduced to the conventional integral
constitutive equation in linear viscoelasticity with a novel scaling law for
relaxation times. The governing equation is determined by 5 adjustable
parameters which are found by fitting experimental data in tensile dynamic
tests on a carbon black filled natural rubber vulcanizate.Comment: 28 pages, 14 figure
Stress-softening and recovery of elastomers
A constitutive model is developed for the mechanical response of elastomers
at finite strains. A polymer is treated as a network of linear chains linked by
permanent (chemical crosslinks) and temporary (entanglements and van der Waals
forces) junctions. Temporary junctions are assumed to be in two states: loose
(passive) when they impose only topological constrains on available
configurations of chains, and tight (active) when their effect is tantamount to
that for crosslinks. Stretching of a specimen implies that some loose junctions
become active, which decreases the average length of a chain.
A long chain is treated as an ensemble of inextensible strands connected in
sequel. Two neighboring strands are bridged by a bond which may be in two
conformations: flexed (trans) and extended (cis). A bond in the flexed
conformation is modeled as a linear elastic solid, whereas the mechanical
energy of a bond in the extended conformation (two rigid rods directed along a
straight line) is disregarded. For a virgin specimen, all bonds are in the
flexed conformation. Under loading some bonds are transformed from flexed to
extended conformation.
Stress-strain relations for a rubbery polymer and kinetic equations for the
trans-cis transition are derived using the laws of thermodynamics. Governing
equations are determined by 5 adjustable parameters which are found by fitting
experimental data in uniaxial tensile tests on natural rubber vulcanizates with
various amounts of crosslinks. Fair agreement is demonstrated between results
of numerical simulation and observations with the elongation ratio up to .
We analyze the effects of cyclic loading, thermal annealing and recovery by
swelling on the material constants.Comment: 42 pages, 18 figure
Buckling of rods with spontaneous twist and curvature
We analyze stability of a thin inextensible elastic rod which has
non-vanishing spontaneous generalized torsions in its stress-free state. Two
classical problems are studied, both involving spontaneously twisted rods: a
rectilinear beam compressed by axial forces, and a circular ring subjected to
uniform radial pressure on its outer perimeter. It is demonstrated that while
spontaneous twist stabilizes a rectilinear rod against buckling, its presence
has an opposite effect on a closed ring.Comment: 8 pages, 1 figur
The viscoelastic and anelastic responses of amorphous polymers in the vicinity of the glass transition temperature
The time-dependent response of polystyrene and poly(methyl methacrylate) is
studied in isothermal long-term shear creep tests at small strains and various
temperatures in the vicinity of the glass transition point. A micromechanical
model is derived to describe the experimental results. Constitutive equations
are developed under the assumption that the behavior of amorphous polymers is
governed by two micro-mechanisms: rearrangement of cooperatively relaxing
regions (CRR) reflects the viscoelastic response, whereas displacement of CRRs
with respect to each other is responsible for the anelastic response. It is
demonstrated that some critical temperature exists slightly above the glass
transition temperature, where the dependences of adjustable parameters on
temperature are dramatically changed. The critical temperature is associated
with transition from dynamic heterogeneity in amorphous polymers to static
inhomogeneity.Comment: 27 pages, 14 figure
The effect of temperature on the viscoelastic response of rubbery polymers at finite strains
Constitutive equations are derived for the viscoelastic response of rubbery
polymers at finite strains. A polymer is thought of as a network of long chains
connected to temporary junctions. At a random time, a chain detaches from a
junction, which is treated at transition from its active state to the dangling
state. A dangling chain randomly captures a new junction in the vicinity of its
free end and returns to its active state. Breakage and reformation of long
chains are modeled as thermo-mechanically activated processes. Stress-strain
relations for a rubbery polymer are developed using the laws of thermodynamics.
Adjustable parameters in the model are found by fitting observations in
uniaxial tensile tests for a carbon black filled rubber at various
temperatures. Fair agreement is demonstrated between experimental data and
results of numerical simulation.Comment: 33 pages, 5 figure
Finite viscoelasticity of filled rubbers: experiments and numerical simulation
Constitutive equations are derived for the viscoelastic behavior of
particle-reinforced rubbers at isothermal loading with finite strains. A filled
rubber is thought of as a composite medium where inclusions with high and low
concentrations of junctions between chains are randomly distributed in a host
matrix. The inclusions with high concentration of junctions are associated with
regions of suppressed mobility of chains that surround isolated clusters of
filler and its secondary network. The regions with low concentration of
junctions arise during the mixing process due to the inhomogeneity in spatial
distribution of a cross-linker. The viscoelastic response of elastomers is
ascribed to the thermally activated processes of breakage and reformation of
strands in the domains with low concentration of junctions. Stress-strain
relations for particle-reinforced rubbers are developed by using the laws of
thermodynamics. Adjustable parameters in the constitutive equations are found
by fitting experimental data in tensile relaxation tests for several grades of
unfilled and carbon black (CB) filled rubber. It is demonstrated that the
relaxation rate is noticeably affected by strains. Unlike glassy polymers,
where the growth of longitudinal strain results in an increase in the rate of
relaxation, the growth of the elongation ratio for natural rubber (unfilled or
CB reinforced) implies a decrease in the relaxation rate, which may be
explained by partial crystallization of chains in the regions with low
concentration of junctions.Comment: 33 pages, 10 figure
Elasticity of thin rods with spontaneous curvature and torsion - beyond geometrical lines
We study three-dimensional deformations of thin inextensible elastic rods
with non-vanishing spontaneous curvature and torsion. In addition to the usual
description in terms of curvature and torsion which considers only the
configuration of the centerline of the rod, we allow deformations that involve
the rotation of the rod's cross-section around its centerline. We derive new
expressions for the mechanical energy and for the force and moment balance
conditions for the equilibrium of a rod under the action of arbitrary external
loads. Several illustrative examples are studied and the connection between our
results and recent experiments on stretching of supercoiled DNA molecules is
discussed.Comment: 28 pages, 2 figure
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