failure. The quantity of filler present in the elastomer is measured in phr, parts per
hundred by weight of elastomer; the concentration at which maximum tensile
strength is obtained, varies with the type of carbon black. For carbon black fillers
with smaller particle size, the maximum tensile strength is attained at lower
concentrations than those for large particle sized carbon black fillers.
The resulting mechanical characteristics such as strength, tear and abrasion
resistance, along with stiffness, considerably increase with respect to the neat
elastomer. The addition of filler contributes also to alter greatly the viscous
behavior and temperature dependence. For example, unfilled elastomers exhibit a
linear viscoelastic behavior for shear strains up to 20 % or more, while a carbon
black-filled elastomer shows a pronounced nonlinear behavior at shear strains as
low as 0.5 % [43].
The standard phenomenology of carbon black-filled rubber will be presented and
the influence on the constitutive response of temperature and filler concentration
will be discussed. Although the focus is on traditional vulcanized rubber, other
thermoplastic elastomers show similar mechanical properties even if their chemical
composition is quite different. Moreover, from a macroscopic point of view, the
behavior of such materials is very close to the behavior of some biological soft
tissues, such as ligaments and tendons, for what concerns both their static and
dynamic responses.
2.1 Background
Although the reinforcement of rubber by active fillers is a well-recognized phenomenon the term ‘reinforcement’ is not well defined. Briefly it can be stated that
reinforcement means the pronounced increase in tensile strength, tear resistance,
abrasion resistance and modulus far beyond the values expected on the basis of the
Einstein-Guth and Gold theory [44], taking into account the effects caused by
colloidal spherical particles (hydrodynamic effect) and occlusion of rubber. The
reinforcement of elastomers by fillers has been studied in depth in numerous
investigations [45] and it is generally accepted that this phenomenon is dependent,
to a large extent, on polymer properties, filler properties and processing. Generally
speaking, the primary filler factors influencing elastomer reinforcement are: The
primary particle size or specific surface area, which, together with loading, determines the effective contact area between the filler and polymer matrix. The
structure or the degree of irregularity of the filler unit, which plays an essential
role in the restrictive motion of elastomer chains under strain. The surface activity,
which is the predominant factor with regard to filler–filler and filler–polymer
interaction.
Most of the elastomeric components are deformed dynamically and specified
dynamic properties are required. Therefore the effect of strain amplitude on the
dynamic modulus was observed very intensively. The modulus of filled rubbers
decreases with increasing applied dynamic strain up to intermediate amplitudes.
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
199
hundred by weight of elastomer; the concentration at which maximum tensile
strength is obtained, varies with the type of carbon black. For carbon black fillers
with smaller particle size, the maximum tensile strength is attained at lower
concentrations than those for large particle sized carbon black fillers.
The resulting mechanical characteristics such as strength, tear and abrasion
resistance, along with stiffness, considerably increase with respect to the neat
elastomer. The addition of filler contributes also to alter greatly the viscous
behavior and temperature dependence. For example, unfilled elastomers exhibit a
linear viscoelastic behavior for shear strains up to 20 % or more, while a carbon
black-filled elastomer shows a pronounced nonlinear behavior at shear strains as
low as 0.5 % [43].
The standard phenomenology of carbon black-filled rubber will be presented and
the influence on the constitutive response of temperature and filler concentration
will be discussed. Although the focus is on traditional vulcanized rubber, other
thermoplastic elastomers show similar mechanical properties even if their chemical
composition is quite different. Moreover, from a macroscopic point of view, the
behavior of such materials is very close to the behavior of some biological soft
tissues, such as ligaments and tendons, for what concerns both their static and
dynamic responses.
2.1 Background
Although the reinforcement of rubber by active fillers is a well-recognized phenomenon the term ‘reinforcement’ is not well defined. Briefly it can be stated that
reinforcement means the pronounced increase in tensile strength, tear resistance,
abrasion resistance and modulus far beyond the values expected on the basis of the
Einstein-Guth and Gold theory [44], taking into account the effects caused by
colloidal spherical particles (hydrodynamic effect) and occlusion of rubber. The
reinforcement of elastomers by fillers has been studied in depth in numerous
investigations [45] and it is generally accepted that this phenomenon is dependent,
to a large extent, on polymer properties, filler properties and processing. Generally
speaking, the primary filler factors influencing elastomer reinforcement are: The
primary particle size or specific surface area, which, together with loading, determines the effective contact area between the filler and polymer matrix. The
structure or the degree of irregularity of the filler unit, which plays an essential
role in the restrictive motion of elastomer chains under strain. The surface activity,
which is the predominant factor with regard to filler–filler and filler–polymer
interaction.
Most of the elastomeric components are deformed dynamically and specified
dynamic properties are required. Therefore the effect of strain amplitude on the
dynamic modulus was observed very intensively. The modulus of filled rubbers
decreases with increasing applied dynamic strain up to intermediate amplitudes.
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
199