Modeling of Non-Linear Viscoelastic
Behavior of Filled Rubbers
Gordana Markovic ´, Milena Marinovic ´-Cincovic ´, Vojislav Jovanovic ´,
Suzana Samarz ˇija-Jovanovic ´, and Jaroslava Budinski-Simendic ´
In memory to my parents Gordana Markovic´
Abstract The nonlinear viscoelastic behavior of the composites of rubber filled
with carbon black, silica, carbon nanotube (CNT), clay and surface-modified
nanosilica were studied. The behavior of carbon black-filled rubber is thoroughly
analyzed with the intention of developing a constitutive model able to reproduce
both static and dynamic material responses. Several nonlinear viscoelastic models
have been examined thoroughly and for each of them advantages and disadvantages
are highlighted. A series of experiments concerning both static and dynamic tests
were performed aimed at measuring all the relevant nonlinear effects. Temperature
and strain rate dependencies were investigated and discussed. The standard methodology was applied to perform both tensile and compressive quasi-static tests.
Some shortcomings of this procedure, resulting in a unreliable stress-strain constitutive curve around the undeformed configuration, were identified. This lead to the
design a non-standard cylindrical specimen able to bear both tensile and compressive loading. Consequently, the influence of the shape factor was removed and the
same boundary conditions, in tension and compression, were applied. This allowed
the stiffness around the undeformed configuration to be evaluated in detail. The
quasi-static experimental results also allowed the influence of the Mullins effect on
the quasi-static response to be investigated: during the loading cycles, there is a
significant reduction in the stress at a given level of strain, which is a consequence
of the internal material rearrangement, i.e., the Mullins effect. This damage phenomenon is sometimes reported to induce transverse isotropy in the material, which
G. Markovic ´ (*)
Tigar, Nikole Pas ˇic ´a 213, 18300 Pirot, Serbia
e-mail: gordana1markovic@gmail.com
M. Marinovic ´-Cincovic ´
University of Belgrade, Institute of Nuclear Science Vinc ˇa, Belgrade, Serbia
V. Jovanovic ´ • S. Samarz ˇija-Jovanovic ´
Faculty of Natural Science and Mathematics, University of Pris ˇtina, Kosovska Mitrovica,
Serbia
J. Budinski-Simendic ´
Faculty of Technology, University of Novi Sad, Novi Sad, Serbia
© Springer International Publishing Switzerland 2014
D. Ponnamma, S. Thomas (eds.), Non-Linear Viscoelasticity of Rubber Composites and
Nanocomposites, Advances in Polymer Science 264, DOI 10.1007/978-3-319-08702-3_8
193
Behavior of Filled Rubbers
Gordana Markovic ´, Milena Marinovic ´-Cincovic ´, Vojislav Jovanovic ´,
Suzana Samarz ˇija-Jovanovic ´, and Jaroslava Budinski-Simendic ´
In memory to my parents Gordana Markovic´
Abstract The nonlinear viscoelastic behavior of the composites of rubber filled
with carbon black, silica, carbon nanotube (CNT), clay and surface-modified
nanosilica were studied. The behavior of carbon black-filled rubber is thoroughly
analyzed with the intention of developing a constitutive model able to reproduce
both static and dynamic material responses. Several nonlinear viscoelastic models
have been examined thoroughly and for each of them advantages and disadvantages
are highlighted. A series of experiments concerning both static and dynamic tests
were performed aimed at measuring all the relevant nonlinear effects. Temperature
and strain rate dependencies were investigated and discussed. The standard methodology was applied to perform both tensile and compressive quasi-static tests.
Some shortcomings of this procedure, resulting in a unreliable stress-strain constitutive curve around the undeformed configuration, were identified. This lead to the
design a non-standard cylindrical specimen able to bear both tensile and compressive loading. Consequently, the influence of the shape factor was removed and the
same boundary conditions, in tension and compression, were applied. This allowed
the stiffness around the undeformed configuration to be evaluated in detail. The
quasi-static experimental results also allowed the influence of the Mullins effect on
the quasi-static response to be investigated: during the loading cycles, there is a
significant reduction in the stress at a given level of strain, which is a consequence
of the internal material rearrangement, i.e., the Mullins effect. This damage phenomenon is sometimes reported to induce transverse isotropy in the material, which
G. Markovic ´ (*)
Tigar, Nikole Pas ˇic ´a 213, 18300 Pirot, Serbia
e-mail: gordana1markovic@gmail.com
M. Marinovic ´-Cincovic ´
University of Belgrade, Institute of Nuclear Science Vinc ˇa, Belgrade, Serbia
V. Jovanovic ´ • S. Samarz ˇija-Jovanovic ´
Faculty of Natural Science and Mathematics, University of Pris ˇtina, Kosovska Mitrovica,
Serbia
J. Budinski-Simendic ´
Faculty of Technology, University of Novi Sad, Novi Sad, Serbia
© Springer International Publishing Switzerland 2014
D. Ponnamma, S. Thomas (eds.), Non-Linear Viscoelasticity of Rubber Composites and
Nanocomposites, Advances in Polymer Science 264, DOI 10.1007/978-3-319-08702-3_8
193