A mesoscopic computer model for reinforcement in filled and strain-crystallizing elastomers / Lena Tarrach

Tarrach, Lena

In this thesis, a mesoscopic model for reinforcement in filled and strain-crystallizing elastomers is developed and applied to study their mechanical behavior from small deformations to failure. For this purpose, the model for strain-induced crystallization (SIC) proposed by Plagge & Hentschke [1] is combined with the model for filler in rubber designed by Viktorova et al. [2]. The utilization of the so-called morphology generator (MG) produces model elastomer networks containing finely or coarsely dispersed filler. The unfilled non-crystallizing model networks obey Neo-Hookean behavior according to the theory of rubber elasticity and the modeling of the polymer chains as freely-jointed.For unfilled crystallizing model networks, the stress-stretch and crystallinity-stretch curves align with experimental observations. In particular, the typical plateau of the stress and the characteristic hystereses of both of the curves attributed to SIC can beobserved. Snapshots of the model network show that layers of crystalline model polymer chains aligned with the stretching direction evolve perpendicularly to the direction of the deformation until crystalline strands traverse the polymer network. In filled model networks, the Payne effect can be observed at small deformations and it is attributed to breaking of filler-filler bonds in this model. At larger deformations, the stress is amplified which is advanced if the filler is finely dispersed compared to coarsely dispersed filler and if the filler content is increased. The filler particles are tightly bound in aggregates, while mainly the model polymer chains bear the load. Thus, these polymer chains predominantly strain-crystallize. The onset of SIC also shifts to smaller stretches when the filler content is increased as it is observed in experiments. Simultaneously, the plateau of the stress and the hysteresis vanish. Furthermore, the model is extended by a rupture criterion for the model polymer chains to investigate their rupture behavior. The threshold value for rupture, whichis the so-called critical free energy density, is defined based on the analysis of free energy density histograms and by the comparison of the relation of the tensile strength and the elongation at break of crystallizing and non-crystallizing model networks with experimental observations.For a suitable choice of the critical free energy density, both the tensile strength and the elongation at break of crystallizing model networks are enhanced compared to non-crystallizing model networks. These quantities are also raised when the filleris finely dispersed. With increasing filler content, the elongation at break decreases as expected. In contrast to experimental observations, the tensile strength of poorly filled networks is reduced compared to the unfilled networks and it only increases beyond a minimum. If the filler content reaches the percolation threshold, the model networks do not fail because a percolating structure is formed. Although large fractions of filler-filler bonds break and polymer-filler bonds weaken, the formation of holes is initiated by rupture of model polymer chains which is promoted in filled networks by stress amplification. Failure of the model networks originates from the growth of these holes due to the same effect. As expected, SIC particularly evolves at the boundaries of the holes. Under cyclic deformation, the fatigue in terms of stress softening can be observed. Wöhler curves indicate that the fatigue life is enhanced by SIC. As the filler content increases, the fatigue life is reduced first and, then, increases for small filler contents. For larger filler contents, failure of the model networks is not detected.

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