Rate-Dependent Damage and Fracture of Dynamic Networks*

Dynamic networks made of polymer chains connected by weak and transient bonds are found in a majority of biological and synthetic polymers but also in active matter. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, transient fracture, self-healing and growth. This presentation will discuss a theoretical framework, a.k.a., the transient network theory (TNT) that provides a useful tool to track the chain conformation space of a dynamic polymer network. Extending the theory to account for chain rupture at a critical stretch, we scrutinize how damage initiates, grows, and competes with stress-relaxation in these networks. We find that permanent damage is largely rate-dependent and governed by two timescales that respectively describe stress relaxation and self-healing time. Based on this framework, we then explore the fracture of vitrimers that exhibit non-steady crack propagation patterns despite a constant loading rate. This motivates us to extend the TNT and present a time-dependent fracture criterion for crack initiation in dynamic networks. We show that in these networks, fracture is mainly governed by two parameters: the Weissenberg number, that defines the history path of crack-driving force, and an extension parameter that tells how far a crack can grow. These predictions are compared with experimental observation to verify the adequacy of the model.