The role of chain stretch heterogeneity on the uniaxial failure response of rubbery networks

The macroscopic failure response of rubbery networks such as elastomers and hydrogels involves the scission of individual polymer chains, mediated by the network topology. However, the precise mechanisms by which individual chain scission events result in macroscopic failure remain poorly understood. In this work, we use Discrete Network (DN) simulations to investigate failure mechanisms in model random networks in uniaxial tension. Our DN simulation results suggest that macroscopic failure, characterised by a sharp drop in the macroscopic stress-stretch response, only requires the scission of a small fraction of chains in a localised region of the network, even in perfect monodisperse networks. Localised failure is triggered by pre-existing heterogeneities in the chain stretch and is further modulated by network parameters such as the chain length or chain strength. Simple micromechanical models of rubber elasticity, such as the three-chain and eight-chain models, fail to capture the onset of damage because they do not capture the chain stretch heterogeneity. More sophisticated microsphere theories in their affine and non-affine versions only partially address this shortcoming. Overall, our results provide new insights into failure mechanisms of rubbery networks, while providing reference results useful for the validation of improved constitutive theories.