thermoplastics, rubber materials can in principle be tested with both types of
instruments, but experience reveals that closed-cavity torsional rheometers are
easier to handle and provide more accurate and reproducible results with rubber
systems, even simple gum rubbers [14], as will be shown in Sect. 2.2 below.
Whatever are the test techniques, cyclic strains applied to materials correspond
to easy and simple mathematical definition, e.g. γ(t) ¼ γ 0 sin(ωt) where γ 0 is the
maximum strain amplitude, ω the frequency (rad/s) and t the time (s). In all
generality, one expects the stress response to be described through a summation
of terms, i.e. σ t
ð Þ ¼
X
i
σ i sin ωt À δ i
ð
Þwhere the δ i terms allow accounting for an
out-of-phase retard of the stress with respect to the applied strain. In the limit of
very small strains, such a series is expected to reduce to only the first term when the
material is exhibiting a so-called linear viscoelastic response [15]. When higher
terms are necessary to (mathematically) describe the actual stress response of the
material, the latter is said to be in its nonlinear viscoelastic domain. It has been
established either through numerical simulation [16] or through experiments [17],
that only odd terms of the summation do contain material’s information. Even terms
are due either to imperfect boundary conditions or secondary flows in the testing
gap, or more simply imperfections in the (mechanically) applied strain.
There are essentially two types of test protocols with dynamic rheometers,
depending one want to probe the material in the linear viscoelastic or in the
nonlinear viscoelastic domain. Providing the strain amplitude is small enough for
no strain-dependency of the (complex) modulus to be observed, then frequency
sweep (FS) tests document the linear viscoelastic character of the material (at the
test temperature). When performing FS tests at several temperatures, results can be
treated to build a mastercurve at a reference temperature by making use of the timetemperature superposition principle. Strain sweep (SS) tests allow investigating
material responses in the whole viscoelastic domain, from the linear to the
nonlinear range, depending on the capabilities of the instrument. For instance,
with commercially available closed-cavity rheometers operated at frequencies
below 0.5 Hz, one can routinely probe materials in the 0.1–1,000 % strain range.
Modern rheometers are computer controlled so that, with most commercial instruments, quite complex test protocols can be designed by the user, by combining test
sequences in many ways to investigate frequency, strain and temperature ranges.
Correctly treating experimental data is consequently the key aspect in obtaining
meaningful results, as will be shown below.
280
J.L. Leblanc
instruments, but experience reveals that closed-cavity torsional rheometers are
easier to handle and provide more accurate and reproducible results with rubber
systems, even simple gum rubbers [14], as will be shown in Sect. 2.2 below.
Whatever are the test techniques, cyclic strains applied to materials correspond
to easy and simple mathematical definition, e.g. γ(t) ¼ γ 0 sin(ωt) where γ 0 is the
maximum strain amplitude, ω the frequency (rad/s) and t the time (s). In all
generality, one expects the stress response to be described through a summation
of terms, i.e. σ t
ð Þ ¼
X
i
σ i sin ωt À δ i
ð
Þwhere the δ i terms allow accounting for an
out-of-phase retard of the stress with respect to the applied strain. In the limit of
very small strains, such a series is expected to reduce to only the first term when the
material is exhibiting a so-called linear viscoelastic response [15]. When higher
terms are necessary to (mathematically) describe the actual stress response of the
material, the latter is said to be in its nonlinear viscoelastic domain. It has been
established either through numerical simulation [16] or through experiments [17],
that only odd terms of the summation do contain material’s information. Even terms
are due either to imperfect boundary conditions or secondary flows in the testing
gap, or more simply imperfections in the (mechanically) applied strain.
There are essentially two types of test protocols with dynamic rheometers,
depending one want to probe the material in the linear viscoelastic or in the
nonlinear viscoelastic domain. Providing the strain amplitude is small enough for
no strain-dependency of the (complex) modulus to be observed, then frequency
sweep (FS) tests document the linear viscoelastic character of the material (at the
test temperature). When performing FS tests at several temperatures, results can be
treated to build a mastercurve at a reference temperature by making use of the timetemperature superposition principle. Strain sweep (SS) tests allow investigating
material responses in the whole viscoelastic domain, from the linear to the
nonlinear range, depending on the capabilities of the instrument. For instance,
with commercially available closed-cavity rheometers operated at frequencies
below 0.5 Hz, one can routinely probe materials in the 0.1–1,000 % strain range.
Modern rheometers are computer controlled so that, with most commercial instruments, quite complex test protocols can be designed by the user, by combining test
sequences in many ways to investigate frequency, strain and temperature ranges.
Correctly treating experimental data is consequently the key aspect in obtaining
meaningful results, as will be shown below.
280
J.L. Leblanc