coefficients between the modeled maps and the data; correlation coefficients are
higher than 0.99 in both cases.
As shown by Figs. 15 and 16 (carbon black) filled compounds exhibit a more
complex dependency on strain and temperature essentially because strong interactions develop between the filler and a part of the rubber matrix. An approach of the
complex modulus function G * (γ, T, Φ)| ω [where Φ stands for filler volume fraction] of carbon black filled rubber compounds was recently proposed by the author
[28] but its detailed discussion is outside the scope of the present chapter. It will
only be noted here that an appropriate equation for G * (γ, T, Φ)| ω combines a
member that represents the response of the polymer matrix to increasing strain
(the so-called polymer component) and a member that describes the response of a
rubber-filler network embedded in the matrix (the so-called filler component).
Table 1 Strain sweep tests experiments on SBR based materials
SBR1500 gum
Temp.,
C
60
80
100
120
140
180
G
Ã
0 , kPa
185.0
131.6
100.4
82.2
64.0
46.4
G
Ã
f , kPa
21.6
19.3
16.8
15.2
13.5
11.6
γ md , %
199.4
208.9
201.9
193.3
180.0
163.3
B
1.692
1.644
1.585
1.587
1.597
1.732
r
2
0.9999
0.9998
0.9999
0.9998
0.9999
0.9998
SBR1500 No Black cpd
Temp.,
C :
60
80
100
120
140
180
G
Ã
0 , kPa
191.60
108.80
79.82
62.92
50.30
36.84
G
Ã
f , kPa
17.0
12.2
12.1
11.2
9.6
9.0
γ md , %
154.3
201.5
193.9
185.4
180.7
155.8
B
1.507
1.514
1.484
1.509
1.481
1.602
r
2
0.9988
0.9993
0.9993
0.9997
0.9995
0.9996
SBR1500/30phr N330 cpd
Temp.,
C :
60
80
100
120
140
180
G
Ã
0 , kPa
323.4
217.5
159.3
122.0
99.1
75.5
G
Ã
f , kPa
6.7
À1.5
1.3
3.9
5.0
6.6
γ md , %
99.9
101.1
91.3
81.7
72.9
59.5
B
1.041
0.865
0.808
0.799
0.800
0.852
r
2
0.9992
0.9973
0.9974
0.9989
0.9999
0.9981
SBR1500/50phr N330 cpd
Temp.,
C :
60
80
100
120
140
180
G
Ã
0 , kPa
608.4
408.8
331.7
258.4
232.8
186.8
G
Ã
f , kPa
À16.2
À13.3
À6.6
0.2
1.0
4.1
γ md , %
47.1
35.3
25.1
23.1
15.2
12.4
B
0.769
0.630
0.588
0.611
0.579
0.617
r
2
0.9999
0.9999
0.9998
0.9998
0.9998
0.9995
296
J.L. Leblanc
higher than 0.99 in both cases.
As shown by Figs. 15 and 16 (carbon black) filled compounds exhibit a more
complex dependency on strain and temperature essentially because strong interactions develop between the filler and a part of the rubber matrix. An approach of the
complex modulus function G * (γ, T, Φ)| ω [where Φ stands for filler volume fraction] of carbon black filled rubber compounds was recently proposed by the author
[28] but its detailed discussion is outside the scope of the present chapter. It will
only be noted here that an appropriate equation for G * (γ, T, Φ)| ω combines a
member that represents the response of the polymer matrix to increasing strain
(the so-called polymer component) and a member that describes the response of a
rubber-filler network embedded in the matrix (the so-called filler component).
Table 1 Strain sweep tests experiments on SBR based materials
SBR1500 gum
Temp.,
C
60
80
100
120
140
180
G
Ã
0 , kPa
185.0
131.6
100.4
82.2
64.0
46.4
G
Ã
f , kPa
21.6
19.3
16.8
15.2
13.5
11.6
γ md , %
199.4
208.9
201.9
193.3
180.0
163.3
B
1.692
1.644
1.585
1.587
1.597
1.732
r
2
0.9999
0.9998
0.9999
0.9998
0.9999
0.9998
SBR1500 No Black cpd
Temp.,
C :
60
80
100
120
140
180
G
Ã
0 , kPa
191.60
108.80
79.82
62.92
50.30
36.84
G
Ã
f , kPa
17.0
12.2
12.1
11.2
9.6
9.0
γ md , %
154.3
201.5
193.9
185.4
180.7
155.8
B
1.507
1.514
1.484
1.509
1.481
1.602
r
2
0.9988
0.9993
0.9993
0.9997
0.9995
0.9996
SBR1500/30phr N330 cpd
Temp.,
C :
60
80
100
120
140
180
G
Ã
0 , kPa
323.4
217.5
159.3
122.0
99.1
75.5
G
Ã
f , kPa
6.7
À1.5
1.3
3.9
5.0
6.6
γ md , %
99.9
101.1
91.3
81.7
72.9
59.5
B
1.041
0.865
0.808
0.799
0.800
0.852
r
2
0.9992
0.9973
0.9974
0.9989
0.9999
0.9981
SBR1500/50phr N330 cpd
Temp.,
C :
60
80
100
120
140
180
G
Ã
0 , kPa
608.4
408.8
331.7
258.4
232.8
186.8
G
Ã
f , kPa
À16.2
À13.3
À6.6
0.2
1.0
4.1
γ md , %
47.1
35.3
25.1
23.1
15.2
12.4
B
0.769
0.630
0.588
0.611
0.579
0.617
r
2
0.9999
0.9999
0.9998
0.9998
0.9998
0.9995
296
J.L. Leblanc