The Mullins effect at small and moderate deformations observed on a 50phr
carbon-black filled SBR submitted to cyclic uniaxial tension are represented in
Fig. 19.
The literature reports Mullins effect for various materials (see Table 2).
The first attempt to develop a quantitative theory to account for the softening
resulting from rubber stretching was developed by [93]. They considered that value
of the shear modulus G is a measure of the total number of cross-links within rubber
and a reflection of the chemical cross-links produced within vulcanization as well as
linkages between rubber and filler. They suggested that the decrease in G was due to
Fig. 18 Pre-conditioning cycles of a particle-reinforced dumbbell specimen with 20 phr (left) and
60 phr (right) of carbon black with maximum stretch λ:¼ ‘/‘ 0 ¼ 3 [81]
1
0
F/S0 (MPa)
0.2
0.4
0.6
0.8
1
1.2
1.2
1.4
1.5
1.6
1.7
1.8
Stretch
1.3
1.1
Fig. 19 Mullins effect at small and moderate deformations observed on a 50 phr carbon-black
filled SBR submitted to cyclic uniaxial tension
Modeling of Non-Linear Viscoelastic Behavior of Filled Rubbers
215