Abbreviations
aPP
Atactic polypropylene
DMA
Dynamic mechanical analyzers
EPDM Ethylene-Propylene-Diene rubber
FS
Frequency sweep
IPPD
N-isopropyl-N
0 -phenyl-p-phenylene diamine
MWD Molecular Weight Distribution
RPA
Rubber Process Analyzer
SBR
Styrene-butadiene rubber
SS
Strain sweep
TMQ
Trimethylquinoline, polymerized
VBA
Visual basic for applications
WLF
William-Landel-Ferry
1 Introduction
As sketched out in Fig. 1, material functions are mathematical relationships
between stress, strain or rate of strain tensors that intend to describe the behavior
of a solid or a liquid when submitted to a range of strains or strain rates. With
polymer materials, temperature effects must also be taken into consideration.
Polymer systems, whose behavior is far to correspond to either the ideal elastic
solid or the ideal viscous fluid, fall in the category of so-called viscoelastic
materials whose properties, broadly speaking, are complex functions of time, strain,
strain rate, temperature (and composition if they are inhomogeneous). By definition, a modulus is the ratio of the stress tensor over the strain tensor, whatever is the
mode of deformation, for instance shear, extensional or compressive. The mode of
deformation defines the non-zero components of both the stress and strain tensors
and because, with polymers, modulus varies with time and temperature, the concept
of modulus functions was appropriately introduced. Conversely a viscosity is the
ratio of the stress tensor over the rate of strain tensor, and again non-zero components of the tensors define the type of flow, either shear or extensional. Modulus and
viscosity functions play a key role in polymer science and technology. The time,
temperature and composition dependencies of modulus and viscosity functions are
particularly important for polymer systems because, in the former case they allow
understanding how a given polymer behaves over a large time span, and in the latter
case, they position the material with respect to both its usage and processing
windows.
Within the asymptotic limit of infinitesimally small strain (and/or strain rate),
modulus and viscosity functions of polymers are nowadays understood with respect
to the theory of linear viscoelasticity [1] and, in principle, conversion between the
various functions is possible, whatever is the mode of deformation [2]. The current
practice of linear viscoelastic concepts reveals however that such conversions are
274
J.L. Leblanc
aPP
Atactic polypropylene
DMA
Dynamic mechanical analyzers
EPDM Ethylene-Propylene-Diene rubber
FS
Frequency sweep
IPPD
N-isopropyl-N
0 -phenyl-p-phenylene diamine
MWD Molecular Weight Distribution
RPA
Rubber Process Analyzer
SBR
Styrene-butadiene rubber
SS
Strain sweep
TMQ
Trimethylquinoline, polymerized
VBA
Visual basic for applications
WLF
William-Landel-Ferry
1 Introduction
As sketched out in Fig. 1, material functions are mathematical relationships
between stress, strain or rate of strain tensors that intend to describe the behavior
of a solid or a liquid when submitted to a range of strains or strain rates. With
polymer materials, temperature effects must also be taken into consideration.
Polymer systems, whose behavior is far to correspond to either the ideal elastic
solid or the ideal viscous fluid, fall in the category of so-called viscoelastic
materials whose properties, broadly speaking, are complex functions of time, strain,
strain rate, temperature (and composition if they are inhomogeneous). By definition, a modulus is the ratio of the stress tensor over the strain tensor, whatever is the
mode of deformation, for instance shear, extensional or compressive. The mode of
deformation defines the non-zero components of both the stress and strain tensors
and because, with polymers, modulus varies with time and temperature, the concept
of modulus functions was appropriately introduced. Conversely a viscosity is the
ratio of the stress tensor over the rate of strain tensor, and again non-zero components of the tensors define the type of flow, either shear or extensional. Modulus and
viscosity functions play a key role in polymer science and technology. The time,
temperature and composition dependencies of modulus and viscosity functions are
particularly important for polymer systems because, in the former case they allow
understanding how a given polymer behaves over a large time span, and in the latter
case, they position the material with respect to both its usage and processing
windows.
Within the asymptotic limit of infinitesimally small strain (and/or strain rate),
modulus and viscosity functions of polymers are nowadays understood with respect
to the theory of linear viscoelasticity [1] and, in principle, conversion between the
various functions is possible, whatever is the mode of deformation [2]. The current
practice of linear viscoelastic concepts reveals however that such conversions are
274
J.L. Leblanc