The Effect of Excluded Volume on Fracture Mechanisms in Coarse-Grained Simulations of Polymer Networks

Macroscopic fracture behavior of polymer networks is governed by chain scission at the molecular level, yet the mechanism of fracture remains elusive. While state-of-the-art, highly coarse-grained simulation methods have been successful at predicting macroscopic fracture properties for strain rates of approximately 1/s, they are usually limited by key assumptions of periodic boundary conditions and purely attractive interactions within network elements. Incompressibility is enforced by constraining a constant lateral contraction of periodic boundary conditions to achieve Poisson’s ratio of 0.5 throughout the linear and nonlinear tensile regimes, which restricts the network structure and dynamics, preventing accurate analysis of fracture propagation at the molecular level. Here, a new coarse-grained fracture simulation approach is presented, which models repulsive interactions within a network as a mean-field excluded volume (EV) potential and eliminates the need for imposed deformation along nontensile axes. Simulation results reveal that consideration of EV interactions in networks leads to physically consistent and more realistic fracture behavior. Networks with EV exhibit a necking regime during fracture, consistent with the behavior of real networks under pure tensile deformation. Linear elastic moduli in networks with EV show excellent quantitative agreement with previously reported experimental results. While simulations without EV can predict correct quantitative trends in toughness, which is also reproduced in the simulations with EV, the molecular-level chain scission mechanisms obtained with EV are much more physically consistent, in stark qualitative and quantitative contrast to simulations without EV. Most notably, the presence of EV interactions facilitates accurate simulation of elastic recoil of the network after fracture, whereas the lack of EV leads to network collapse post-failure. EV interactions contribute to network homogenization during stress relaxation, leading to delayed fracture under low strains, whereas stress concentration is observed without EV.