Coarse-Grained Simulations for Fracture of Polymer Networks: Stress Versus Topological Inhomogeneities

Fracture of an unfilled elastomer occurs primarily due to mechanical scission of polymer chains, which is inherently related to the topology of the underlying long-range-connected polymer network. This work presents a coarse-grained simulation framework to compute the fracture strength of elastomers by performing a tensile test at a strain rate of approximately 1/s, which is comparable to those employed in experiments and at least 10⁶ times smaller than those possible in conventional molecular dynamics simulations. The simulation framework incorporates key aspects of polymer fracture: nonlinear force-extension behavior, the mechanochemistry of polymer chains, and the stochastic nature of bond breaking. The developed framework is then used to understand the role of topological defects, such as primary, secondary, and higher-order loops, in the fracture of elastomers. It is observed that the modulus decreases while the ultimate extension increases with the increase in the concentration of primary loops in the network, in accord with the recently developed theory of network fracture and several experimental systems: bimodal elastic networks, poly­(ethylene glycol) gels, and thiol–ene elastomers. However, the increase in ultimate extension with the primary-loop fraction is not as appreciable as predicted by earlier theories and experiments. This is due to the correlation and stress redistribution among different defects; as the chains break during deformation, the stresses on defect-free linear strands are transferred to the primary-loop-containing strands, essentially creating a homogeneous stress distribution, which leads to synchronous breaking of the linear strands and the loop-containing strands. Overall, this work highlights the role of different topological defects in controlling the fracture properties of networks and thereby provides opportunities to design materials with improved mechanical performance.