Rate dependent fracture of hydrogels: from small to large-scale swelling

Abstract

When a cracked hydrogel sample immersed in water is stretched, a swelling zone near the crack tip emerges. Within the swelling zone, water diffusion occurs and swells the hydrogel. Outside the swelling zone, water diffusion is negligible, and the material behaves like an incompressible elastomer. Since water diffusion is a time-dependent process, the size of the swelling zone changes with time. As time evolves, the size of the swelling zone grows until to the size of the hydrogel sample. There exists a competition between the size of the swelling zone and the size of the hydrogel sample, which results in complex rate-dependent fracture behavior of hydrogel. In this article, the competition effect is studied theoretically and numerically. We find that the hydrogel undergoes three stages gradually: small-scale swelling, large-scale swelling, and equilibrium as the size of the swelling zone approaches the size of the hydrogel sample. In the stage of small-scale swelling, the first invariant of stretch at the notch tip I_1notch increases with the decrease of the stretch rate. In the stage of large-scale swelling, I_1notch increases first and then decreases with the decrease of stretch rate. In the stage of equilibrium, the effect of water diffusion is negligible, and I_1notch is independent of stretch rate. This work reveals the connection between the stretch rate, the size of the swelling zone, and the crack tip quantity I_1notch, which is used to establish the fracture criterion and predict rate-dependent fracture of hydrogel. Particularly, the previous works on different trends of rate-dependent behavior of hydrogel can be unified in this work, when both small-scale swelling and large-scale swelling are considered.