Unique Nonlinear Behavior of Nano-Filled Elastomers: From the Onset of Strain Softening to Large Amplitude Shear Deformations

Abstract

Adding fillers in elastomers is known to increase the elastic modulus and the wear resistance of elastomers, but also to increase nonlinear dissipation, a phenomenon known as the Payne effect. Indeed, when submitted to deformations of the order of a few per cents or more, the elastic modulus can decrease down to values much smaller than the initial one. On the other hand, when submitted to large amplitude oscillatory shear at a frequency ω, frequency analysis shows that the contribution of higher harmonics 3ω, 5ω, ..., to the response is quite small. This might appear somehow as a paradox since the nonlinear behavior of filled elastomers can be strongly marked. We discuss here in detail a possible physical origin of these various features. We do it by comparing experimental results performed on model elastomers to the prediction of a model proposed recently, based on the presence of glassy bridges linking neighboring particles. We show that the kinetics of rupture and rebirth of these glassy bridges can explain these effects.

Micromechanical model for isolated polymer-colloid clusters under tension

“…There are different theories on contribution of clusters to the deformation-induced damage of the matrix, and rubber in particular. Some associate damage to the yielding and reformation of the clusters [26][27][28][29], some to gradual softening of the particle-particle bonds [30][31][32], and some to the changes in cluster sizes and structural rearrangement [33][34][35]. So far, no consensus on the micromechanics of PC clusters has emerged and, despite its ubiquity and significance, it remains far from understood; even the classification of interparticle forces is not agreed on.…”

Concurrent two-scale model for the viscoelastic behavior of elastomers filled with hard nanoparticles

“…In [16], the properties of a polystyrene matrix filled with nanoparticles were investigated by coarse-grained MC sampling, and a substantial segmental ordering close to the particle surface was found. On coarser scales, the very broad study of filled (either carbon black or silica particles) elastomers from the microscopic perspective was made in [17][18][19][20], where the authors developed a numerical scheme akin to dissipative particle dynamics (DPD) technique. The dynamics of the filler particles has been studied, taking into account soft spring forces, representative of the rubbery matrix, and temporary hard spring forces, representative of the transient network of glassy bridges.…”

“…The essential idea in their approach is that each glassy bridge has got a finite lifetime that depends on the local glass transition temperature, which in turn is affected by the particle distance and the local load (i.e., the lifetime is changing in the course of time). This concept proved to be key for appropriately simulating [18][19][20] various nonlinear effects of filled elastomers, e.g., the Payne effect [11] and the Mullins effect [12,13]. On the other hand, fully macroscopic numerical approaches, based on providing a multi-level finite element method (MLFEM) simulation for heterogeneous polymeric systems, have been employed to study specifically polymeric matrices with either voids or filled with rubber inclusions [21][22][23][24].…”

“…This last criterion in combination with the requirement for dynamics asks for alternatives to the approaches mentioned in the previous paragraphs. The work of Long et al [18][19][20] discussed above shows the significance of the local glass transition temperature and dynamics that depend on the local structure and load, and this complexity helps to understand why until recently no mechanical (viscoplastic) model was able to satisfactorily explain and reproduce mechanical properties of these systems, and in particular their dissipative properties. However, since their model considers a many-particle system to obtain the effective constitutive behavior (at each macroscopic material point), it is computationally rather demanding.…”

“…However, since their model considers a many-particle system to obtain the effective constitutive behavior (at each macroscopic material point), it is computationally rather demanding. Therefore, the aim of this paper is to propose a drastically simplified description of the model developed in [18][19][20] and to combine that with macroscopic elastoviscoplasticity (e.g., see [4,28]) in a thermodynamically consistent manner.…”