The Rules of Roughness: Understanding the Dynamic Generation of 3D Complexity in Fractures

There is a disconnect between our theoretical understanding of brittle fracture, where 2D (effectively 1D) mathematical descriptions generate idealized fractures that are flat, smooth, and stable, and most brittle fractures we encounter in natural or manmade materials (rocks, bones, ceramics), which have significant 3D complexity. However, much of the basic physics that governs this complexity is not well understood. We have developed an experimental system to study 3D fracture mechanics by observing hydraulic fractures in brittle hydrogels. Heavily cross-linked hydrogels have been shown to be a good model system for brittle materials, with the benefits of highly tunable rheology, transparency, and low breakdown pressures. Studying hydraulic fractures allows us to match the refractive index of the interior of the fracture to the bulk, which combined with high speed photography and scanning laser sheet illumination, enables us to resolve the fracture dynamics in three dimensions at up to 1000 volumes per second. We observe that macro-scale roughness comes in the form of step-like perturbations of the fracture front, resulting from material heterogeneity, which leave in their wake a curved linear scar known as a step line. Our dynamic three-dimensional observations of these steps and their interactions allow us to understand the surprisingly elegant topological rules that govern their growth and interaction.