Delayed fracture in gels

Abstract

Subject to a subcritical load, a swollen polymeric gel may hesitate for a prolonged period of time without showing any macroscopic symptom, and then break suddenly. Such a phenomenon is usually referred to as the delayed fracture in gels. In this paper, we present a possible mechanism for the delayed fracture in gels from the continuum and fracture mechanics point of view. Using a continuum visco-poroelastic model for polymeric gels, we calculate the evolution of the inhomogeneous stress field around a pre-existing crack, in consequence of the coupled viscoelastic creep and solvent migration. We invoke the instantaneous energy release rate as the local driving force for a crack, and find it to be an increasing function of time. With the dissipation from viscoelastic creep and solvent migration excluded, the criterion for crack advancing is that the instantaneous energy release rate equals the intrinsic fracture energy of the polymer. The fracture delay could thus be attributed to the time needed for viscoelastic creep and solvent migration to bring the instantaneous energy release rate to the level of the intrinsic fracture energy. For most swollen gels, solvent migration is the limiting process, and therefore the delay time depends on the size of a pre-existing crack in a similar way as common diffusion-limited processes. Finally, by assuming a specific size distribution of microcracks, we provide a simple statistical analysis towards the lifetime prediction of a swollen gel.