Large-Scale Swelling in the Plane Stress Fracture of Hydrogels

Abstract

Abstract. When a cracked hydrogel sample is stretched, a swelling zone around the crack tip occurs due to water migration. As time evolves, the swelling zone grows, from the small-scale swelling to the large-scale swelling. The growth of the swelling zone greatly affects the fracture of hydrogels, which is a fundamental problem in the fracture of hydrogels. Previous studies on this issue are limited to the plane strain analysis, while little attention has been devoted to the plane stress analysis. Here, we investigate how the swelling zone affects plane stress fracture of hydrogels, especially for the case of large-scale swelling. First, the governing equations for the plane stress analysis are presented. Different from the linear elastic analysis, the nonlinear coupling behavior of large deformation and water migration is considered. Then, a double-edge-cracked model with a permeable crack is established. The evolution of global quantities (global volumetric ratio and global stress) and local quantities (crack opening displacement and J-integral) is investigated. It is found that as time evolves, the global volumetric ratio increases, but the global stress decreases. There exists a relation between the global stress and the global volumetric ratio. Different from the monotonic behavior of global quantities, the local quantities have a nonmonotonic behavior: they increase first and then decrease, which is due to the change of deformation state of the swelling zone. Finally, it is found that the effect of the swelling zone is more significant in the plane strain analysis, compared with that in the plane stress analysis.