non-linear viscoelasticity
(see Non-linear viscoelasticity)
NR/BR blends, 89
NR/cis-butadiene rubber (NR/cis-BR), 89
physical properties, 89
reinforcing fillers, 99–101
silica content, 90
Rubber materials
dynamic functions, 279–280
elastic and viscous moduli, 277
extrinsic and intrinsic non-linear
viscoelasticity, 275–276
force, strain and temperature., 276
linear viscoelastic concepts, 274
mechanical and rheological properties,
274–275
polymer science and technology, 274
pseudo Newtonian viscosity, 277
shear viscosity function, 276–279
stress and strain, 274
Rubber nanocomposites
ad hoc nonlinear optimization algorithm, 7
carbon black and resin, 156–157
clay/rubber, 53–54
3D nanofillers, 79–80
FASi/PSi hybrid filler, 152–153
fiber properties, 7
graphene/rubber, 51–53
modeling
chloroprene rubber, 10
far-field matrix behavior, 8
Kraus model, 8
Mullins effect, 10
Payne effect, 7–10
plasticizing effect, 10
polymer chains and filler surfaces, 9
polymer-filler interactions, 9
polymer melts, 8
strong stress-softening effect, 10
MWCNTs, 156–157
natural rubber (NR), 155
natural/synthetic rubber materials, 68
nonlinear rate-dependent behavior, 7
Payne effect, 68
polyhedral oligomeric silsesquioxane,
68–70
properties, 67
rheology, 154
rubber compounds, 155
silicon dioxide (see Silicon dioxide)
TiO 2 , 77–79
usage, 67–68
viscoelastic properties, 152
Rubber phenomenology
carbon black-filled rubber, 196–197
carbon black loading, 208
dynamic loading, 205–206
elastic modulus curve, 199–200
elastomeric components, 199–200
elastomers behavior, 206
energy dissipation, 198
“entanglement-cohesion”, 205
fit parameters, 213–214
hydrodynamic effect, 200
langmuir isotherm formation, 213
loss modulus, 211
nonlinear behavior, 201
nonlinear constitutive models, 201
Payne effect, temperature, 212
quasi-static (see Quasi-static responses)
‘reinforcement’, 199
storage and loss moduli frequency, 206
storage modulus, 209
strain dependence, 210–211
stress softening, 200–201
temperature dependence, 207–208
tensile strength, 198–199
vulcanized and non-vulcanized rubber
specimen, 197
Rubber–rubber blend nanocomposites, 90
S
SAOS. See Small amplitude oscillatory shear
(SAOS)
SBR. See Styrene butadiene rubber (SBR)
Shear
Carreau–Yasuda model, 281
cyclic strain tests, 102
deformation, 237–239
elastic component, 30
flow curve, 167
function, 237
nonlinear behavior, 260
response function, 238
rubber specimens, 203
storage modulus, 79
strain invariants, 237
stress effects, 238–239
viscosity function, 276–278
Silicon dioxide
agglomerate size and desorption, polymer
chains, 71, 72
coupling agent, 75
elastic modulus, 73
ENR/silica and PVA/silica, 75
Index
307
(see Non-linear viscoelasticity)
NR/BR blends, 89
NR/cis-butadiene rubber (NR/cis-BR), 89
physical properties, 89
reinforcing fillers, 99–101
silica content, 90
Rubber materials
dynamic functions, 279–280
elastic and viscous moduli, 277
extrinsic and intrinsic non-linear
viscoelasticity, 275–276
force, strain and temperature., 276
linear viscoelastic concepts, 274
mechanical and rheological properties,
274–275
polymer science and technology, 274
pseudo Newtonian viscosity, 277
shear viscosity function, 276–279
stress and strain, 274
Rubber nanocomposites
ad hoc nonlinear optimization algorithm, 7
carbon black and resin, 156–157
clay/rubber, 53–54
3D nanofillers, 79–80
FASi/PSi hybrid filler, 152–153
fiber properties, 7
graphene/rubber, 51–53
modeling
chloroprene rubber, 10
far-field matrix behavior, 8
Kraus model, 8
Mullins effect, 10
Payne effect, 7–10
plasticizing effect, 10
polymer chains and filler surfaces, 9
polymer-filler interactions, 9
polymer melts, 8
strong stress-softening effect, 10
MWCNTs, 156–157
natural rubber (NR), 155
natural/synthetic rubber materials, 68
nonlinear rate-dependent behavior, 7
Payne effect, 68
polyhedral oligomeric silsesquioxane,
68–70
properties, 67
rheology, 154
rubber compounds, 155
silicon dioxide (see Silicon dioxide)
TiO 2 , 77–79
usage, 67–68
viscoelastic properties, 152
Rubber phenomenology
carbon black-filled rubber, 196–197
carbon black loading, 208
dynamic loading, 205–206
elastic modulus curve, 199–200
elastomeric components, 199–200
elastomers behavior, 206
energy dissipation, 198
“entanglement-cohesion”, 205
fit parameters, 213–214
hydrodynamic effect, 200
langmuir isotherm formation, 213
loss modulus, 211
nonlinear behavior, 201
nonlinear constitutive models, 201
Payne effect, temperature, 212
quasi-static (see Quasi-static responses)
‘reinforcement’, 199
storage and loss moduli frequency, 206
storage modulus, 209
strain dependence, 210–211
stress softening, 200–201
temperature dependence, 207–208
tensile strength, 198–199
vulcanized and non-vulcanized rubber
specimen, 197
Rubber–rubber blend nanocomposites, 90
S
SAOS. See Small amplitude oscillatory shear
(SAOS)
SBR. See Styrene butadiene rubber (SBR)
Shear
Carreau–Yasuda model, 281
cyclic strain tests, 102
deformation, 237–239
elastic component, 30
flow curve, 167
function, 237
nonlinear behavior, 260
response function, 238
rubber specimens, 203
storage modulus, 79
strain invariants, 237
stress effects, 238–239
viscosity function, 276–278
Silicon dioxide
agglomerate size and desorption, polymer
chains, 71, 72
coupling agent, 75
elastic modulus, 73
ENR/silica and PVA/silica, 75
Index
307