A fully equilibrated microsphere model with damage for rubberlike materials

Abstract

A non-affine microsphere model for rubberlike materials is proposed, based on a local minimization of the network free energy under a maximal advance path constraint. It accounts for any chain weight distribution and for damage such as Mullins softening observed in filled rubber materials. The non-affine equal-force model is compared to the common affine model and a hybrid equal-force model from the literature, when considering the isotropic hyperelastic behavior without damage of rubber materials presenting chains of various lengths. The non-affine model shows an improved deformability compared to the affine model limited by the maximal extension of the shorter chains and a significantly softer behavior. Possible damage is introduced by increasing the chain lengths according to the submitted maximal chain traction force. Each chain are impacted independently resulting in a directional softening that introduces the evolution of the stress-free configuration that needs to be assessed over the loadings. The model was successfully tested on the cyclic uniaxial tension stretch-stress responses of carbon-black filled styrene butadiene rubbers that were well fitted with three parameters only.

Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds

“…Relaxing some of these assumptions is expected to yield better fittings for the experimental comparisons presented in this work. In particular, the Mullins-like effect observed in Figure b that was not captured by this model has been explained by other researchers by network alteration (reflecting the changes of non-affine deformation) as well as nonlinear viscoelasticity …”

“…We emphasize the intention of this work to provide a qualitative understanding of the governing physics outlined in Section and note that a more sophisticated numerical strategy could mitigate this. For instance, reducing the model to the domain of a microsphere ,, could significantly reduce computational cost and open the possibility for implementation in finite element method models. We finally note that our usage of a first-order kinetic law, with constant rates of k a and k d , does not account for the force sensitivity of bond lifetime in many physical systems .…”

The Influence of Filler Size and Crosslinking Degree of Polymers on Mullins Effect in Filled NR/BR Composites

“…It was also found that higher ν would lead to smaller Δ r , which could be ascribed to increased chemically crosslinked network; higher molecular weight polymer network provided more extra reversible deformation, thus there would be less energy dissipation. Zhong et al [ 49 , 50 ] proposed that increasing the elastomer crosslinking degree would result in chain entanglement, slippage, and twisting more likely to occur, therefore leading to the magnitude of strain energy change. However, this strain energy change would also be averaged over the different strains.…”

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

“…To develop a model that accounts for the collective impact delocalized chain rupture events play on the bulk material response, and more specifically on the fracture energy, several key building blocks are needed. Incorporating a chain length distribution to reflect the structural heterogeneity of non-uniform chain length in an elastomer network is a vital starting point that has already been proven to impact elastomer mechanics and fracture (Dargazany and Itskov, 2009;Diani and Le Tallec, 2019;Falender et al, 1979;Guo and Zaïri, 2021;Itskov and Knyazeva, 2016;Lavoie et al, 2019;Li and Bouklas, 2020;Lu et al, 2020;Mark, 2003;Wang et al, 2015;Xiao et al, 2021). Incorporation of chain length polydispersity into the network requires defining the chain-level load sharing behavior.…”

“…Incorporation of chain length polydispersity into the network requires defining the chain-level load sharing behavior. The equal strain assumption is commonly employed, where all chains, independent of initial length, are assumed to be deformed to the same stretch (Diani and Le Tallec, 2019;Itskov and Knyazeva, 2016;Tehrani and Sarvestani, 2017). The equal force assumption may also be implemented, where all chains are assumed to bear the same force (via a virtual series arrangement of chains with respect to the loading mechanism) (Li and Bouklas, 2020;Verron and Gros, 2017).…”