2.2 Non-linear Viscoelasticity in Rubber Nanocomposites
The non linear viscoelasticity of various particles filled rubber is addressed in range
of studies. It is found that the carbon black filled-elastomer exhibit quasi-static and
dynamic response of nonlinearity. Hartmann reported a state of stress which is the
superposition of a time independent, long-term, response (hyperelastic) and a time
dependent, short-term, response in carbon black filled-rubber when loaded with
time-dependent external forces. The short term stresses were larger than the long
term hyperelastic ones. The authors had done a comparative study for the non linear
viscoelastic models undergoing relaxation, creep and hysteresis tests [20–22]. For
reproducible and accurate viscoelastic parameters an experimental procedure is
developed using an ad hoc nonlinear optimization algorithm.
The time dependence of the matrix properties greatly enhances when the material undergoes adverse environmental conditions. The stresses cause matrix cracking, softening and fiber-matrix debonding leading to premature structural failure of
the fibers, and thus shortening the life of the structure. A theoretical study of these
effects was done in the work of Schapery [23, 24], and good experimental techniques and testing methodologies are later developed by some other groups. The
initial constant stress and constant stress-rate tensile response of the rubber-glass
composite are derived at various temperatures to see the temperature dependence of
the damage growth rate. A nonlinear rate-dependent behavior is observed during
the first loading of the material due to damage and thus the intrinsic viscoelasticity
of the polymer matrix is obtained [25, 26]. The authors found that the study of stress
and time dependence depend on the fiber angles and layups and also proposed a
quasi-elastic constitutive equation for constant stress and strain rate conditions.
Different fiber properties are taken into account using the semi-empirical HalpinTsai equations and the importance of this study lies in the tremendous applications
of a glass reinforced rubber composite.
2.3 Modeling
The dynamic properties of filled rubbers are widely studied by many researchers in
this field of which the contribution made by Payne is the most significant. The
dependence of strain amplitude on the storage modulus in filled rubbers is known as
the “Payne effect” [27]. At a strain more than 0.1 %, the storage modulus of filled
rubber collapses from a plateau value of G
0 0 to a minimum value G1
0 and this
decrease is accompanied by a maximum of the loss modulus, G
00 . The variation in
this storage modulus value with respect to the minimum value is called amplitude of
the Payne effect, and this increases with the filler content, specific surface and
properties of the filler and its dispersion within the matrix. The amplitude inversely
changes with temperature. A lot of investigations were performed in order to
explain the Payne effect and reasons behind it. Payne neglected the contribution
Origin of Nonlinear Viscoelasticity in Filled Rubbers: Theory and Practice
7
The non linear viscoelasticity of various particles filled rubber is addressed in range
of studies. It is found that the carbon black filled-elastomer exhibit quasi-static and
dynamic response of nonlinearity. Hartmann reported a state of stress which is the
superposition of a time independent, long-term, response (hyperelastic) and a time
dependent, short-term, response in carbon black filled-rubber when loaded with
time-dependent external forces. The short term stresses were larger than the long
term hyperelastic ones. The authors had done a comparative study for the non linear
viscoelastic models undergoing relaxation, creep and hysteresis tests [20–22]. For
reproducible and accurate viscoelastic parameters an experimental procedure is
developed using an ad hoc nonlinear optimization algorithm.
The time dependence of the matrix properties greatly enhances when the material undergoes adverse environmental conditions. The stresses cause matrix cracking, softening and fiber-matrix debonding leading to premature structural failure of
the fibers, and thus shortening the life of the structure. A theoretical study of these
effects was done in the work of Schapery [23, 24], and good experimental techniques and testing methodologies are later developed by some other groups. The
initial constant stress and constant stress-rate tensile response of the rubber-glass
composite are derived at various temperatures to see the temperature dependence of
the damage growth rate. A nonlinear rate-dependent behavior is observed during
the first loading of the material due to damage and thus the intrinsic viscoelasticity
of the polymer matrix is obtained [25, 26]. The authors found that the study of stress
and time dependence depend on the fiber angles and layups and also proposed a
quasi-elastic constitutive equation for constant stress and strain rate conditions.
Different fiber properties are taken into account using the semi-empirical HalpinTsai equations and the importance of this study lies in the tremendous applications
of a glass reinforced rubber composite.
2.3 Modeling
The dynamic properties of filled rubbers are widely studied by many researchers in
this field of which the contribution made by Payne is the most significant. The
dependence of strain amplitude on the storage modulus in filled rubbers is known as
the “Payne effect” [27]. At a strain more than 0.1 %, the storage modulus of filled
rubber collapses from a plateau value of G
0 0 to a minimum value G1
0 and this
decrease is accompanied by a maximum of the loss modulus, G
00 . The variation in
this storage modulus value with respect to the minimum value is called amplitude of
the Payne effect, and this increases with the filler content, specific surface and
properties of the filler and its dispersion within the matrix. The amplitude inversely
changes with temperature. A lot of investigations were performed in order to
explain the Payne effect and reasons behind it. Payne neglected the contribution
Origin of Nonlinear Viscoelasticity in Filled Rubbers: Theory and Practice
7