A network mechanics method to study the mechanism of the large-deformation fracture of elastomers

This work presents a network mechanics method to reveal the fracture mechanism of the inhomogeneous polymer network of elastomers. The polymer network in elastomers is abstracted as a network model composed of cross-linkers, polymer chains, and volume elements. The hyperelastic deformation of the network model is characterized using the total energy composed by the free energy of all polymer chains and the volumetric deformation energy of all volume elements. The fracture behavior of the network model is described by the fracture criterion of polymer chains. By comparing the large-deformation fracture simulations of homogeneous and inhomogeneous network models, we find that the network inhomogeneity is one important fundamental cause of the ductile fracture and the low notch sensitivity of elastomers. We also find that the widely used Lake-Thomas model underestimates the intrinsic fracture energy of elastomers, because the intrinsic fracture energy of an elastomer network includes the elastic energy stored not only in the broken polymer chains, but also in the newly created dangling chains on a crack surface. Our simulations show that the intrinsic fracture energy of a four-armed elastomer network is about three times of that predicted by the Lake-Thomas model. This result agrees quite well with the previous experimental results.