Title: 3D characterization of kinematic fields and poroelastic swelling near the tip of a propagating crack in a hydrogel

Abstract: In fracture mechanics, polyacrylamide hydrogels have been widely used as a model material for experiments, benefited from its optical transparency, fracture brittleness, and low Rayleigh wave velocity. To describe the brittle fracture in the hydrogels, linear elastic fracture mechanics comes as the first choice. However, in soft materials such as hydrogels, the crack opening can be extremely large, leading to substantial geometric nonlinearity and material nonlinearity at the crack tip. Furthermore, poroelasticity may also modify the local mechanical state within the polymer network. Direct characterization of the kinematic fields and poroelastic effect at the crack tip is lacking. Here, based on a hybrid method of digital image correlation and particle tracking technique, we retrieved high-resolution 3D particle trajectories near the tip of a slowly propagating crack and measured the near-tip 3D kinematic fields, including the displacement fields, rotation fields, stretch fields, strain fields, and swelling fields. Results confirmed the complex multi-axial stretching near the crack tip and the substantial geometric nonlinearity, particularly on the two wakes of the crack where rotation exceeds $30^{\circ}$. Comparison between the measured and predicted displacement and strain fields, derived from linear elastic fracture mechanics, highlights a disagreement in the direct vicinity of the crack tip, particularly for displacement component $u_x$ and through-thickness strain component $\varepsilon_{zz}$. Significant swelling, due to the poroelastic solvent migration, is also observed, with a strong correlation to the local stretch. Our experimental method, without any assumption of the material properties, can be readily extended to study 3D crack tips in a huge varieties of materials, and our results can shed light on the fundamental fracture mechanics.