value of two billion euro. The term rubber is actually misleading: it is used both to
indicate the material, technically referred to as natural rubber, and the broad class of
synthetic elastomers which share with natural rubber some fundamental chemical
properties. Indeed, the majority of rubber used for industrial applications are
synthetically produced and derived from petroleum 1. Rubber, or elastomer, has
an internal structure which consists of flexible, long chain molecules that intertwine
with each other and continually change contour due to thermal agitation. Elastomers are polymers with long chains [40]. The morphology of an elastomer can be
described in terms of convolution, curls and kinks. Convolutions represent the longrange contour of an entire molecular chain, which forms entanglements (knots).
Curls are shorter range molecular contours that develop between entanglements and
crosslinks, and kinks are molecular bonds within a curl. Each molecular bond has
rotational freedom that allows the direction of the chain molecule to change at
every bond. Thus the entire molecular chain can twist, spiral and tangle itself or
with adjacent chains. This basic morphology is shared among all the fifty thousand
compounds used in the market today and generically referred to by the term rubber.
Despite this intricate internal structure, the random orientation of the molecular
chains results in a material which is externally isotropic and homogeneous.
Prior of using, the neat elastomer is subjected to physical/chemical treatments to
enhance its mechanical properties. One of these treatments consists of the addition,
through heating, of sulfur-based curatives which create crosslinks among the
macromolecules chains; this process is commonly called vulcanization [41].
Figure 2 highlights the different behavior of a vulcanized and a non-vulcanized
rubber specimen subjected to a tensile loading. Initially, both of the elastomers have
a similar intertwined internal structure. When stretched, the macromolecules of the
non-vulcanized compound disentangle themselves according to the direction of the
applied force. This microstructural change results in a more ordered internal state
with a subsequent reduction in entropy. Thereafter, the macro-brownian motions of
the macromolecules cause the chains to slide back, one onto each other, to the
disordered state. Finally, once the external load is removed (step d in the figure),
each macromolecule maintains its state of maximum entropy. Therefore, the initial
overall shape is not recovered: all the energy externally supplied to stretch the
specimen is dissipated by the viscous friction among the macromolecules.
A different microstructural response occurs during the deformation of the vulcanized specimen.
Indeed, when subjected to an external traction, the molecular chains dispose
parallel to the macro-displacement and because of the crosslinks introduced by the
vulcanisation, they cannot slide back to the initial disordered state. By removing the
external loading, the system tends towards the initial state of maximum entropy and
the specimen recovers the initial length. In this case, the external supplied energy is
totally recovered. The behavior of a real elastomer slightly differs from this
simplified description. Indeed, even if the elastomer is vulcanized, the macromolecules can partially slide one onto each other with a dissipation of the mechanical
energy.
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
197
indicate the material, technically referred to as natural rubber, and the broad class of
synthetic elastomers which share with natural rubber some fundamental chemical
properties. Indeed, the majority of rubber used for industrial applications are
synthetically produced and derived from petroleum 1. Rubber, or elastomer, has
an internal structure which consists of flexible, long chain molecules that intertwine
with each other and continually change contour due to thermal agitation. Elastomers are polymers with long chains [40]. The morphology of an elastomer can be
described in terms of convolution, curls and kinks. Convolutions represent the longrange contour of an entire molecular chain, which forms entanglements (knots).
Curls are shorter range molecular contours that develop between entanglements and
crosslinks, and kinks are molecular bonds within a curl. Each molecular bond has
rotational freedom that allows the direction of the chain molecule to change at
every bond. Thus the entire molecular chain can twist, spiral and tangle itself or
with adjacent chains. This basic morphology is shared among all the fifty thousand
compounds used in the market today and generically referred to by the term rubber.
Despite this intricate internal structure, the random orientation of the molecular
chains results in a material which is externally isotropic and homogeneous.
Prior of using, the neat elastomer is subjected to physical/chemical treatments to
enhance its mechanical properties. One of these treatments consists of the addition,
through heating, of sulfur-based curatives which create crosslinks among the
macromolecules chains; this process is commonly called vulcanization [41].
Figure 2 highlights the different behavior of a vulcanized and a non-vulcanized
rubber specimen subjected to a tensile loading. Initially, both of the elastomers have
a similar intertwined internal structure. When stretched, the macromolecules of the
non-vulcanized compound disentangle themselves according to the direction of the
applied force. This microstructural change results in a more ordered internal state
with a subsequent reduction in entropy. Thereafter, the macro-brownian motions of
the macromolecules cause the chains to slide back, one onto each other, to the
disordered state. Finally, once the external load is removed (step d in the figure),
each macromolecule maintains its state of maximum entropy. Therefore, the initial
overall shape is not recovered: all the energy externally supplied to stretch the
specimen is dissipated by the viscous friction among the macromolecules.
A different microstructural response occurs during the deformation of the vulcanized specimen.
Indeed, when subjected to an external traction, the molecular chains dispose
parallel to the macro-displacement and because of the crosslinks introduced by the
vulcanisation, they cannot slide back to the initial disordered state. By removing the
external loading, the system tends towards the initial state of maximum entropy and
the specimen recovers the initial length. In this case, the external supplied energy is
totally recovered. The behavior of a real elastomer slightly differs from this
simplified description. Indeed, even if the elastomer is vulcanized, the macromolecules can partially slide one onto each other with a dissipation of the mechanical
energy.
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
197