At the breaking point: Three-dimensional fracture in soft brittle solids

Fracture is a leading cause of failure in both natural and engineered systems, across vastly different length and time scales. Despite the diversity of materials and systems, the underlying phenomenon of fracture tells a common story: a localized defect concentrates stress and energy, and evolves into a propagating crack. Fracture mechanics is traditionally formulated under planar assumptions, yet real cracks are intrinsically three-dimensional and often develop complex front geometries that cannot be fully described within a two-dimensional framework. This thesis investigates the three-dimensional mechanics of crack propagation in soft brittle solids through direct experimental measurements of crack geometry and near-tip mechanical fields, focusing primarily on brittle polyacrylamide hydrogels under nominally mode~I, quasi-static loading.

First, the small-scale yielding region near the crack tip is characterized using crack tip opening displacement and $J$-integral measurements. These experiments identify the scale and structure of the process zone and show that fracture energy is partitioned between a localized crack tip contribution and a distributed process zone dissipation. Building on this foundation, the thesis then examines the in-situ non-planar crack morphology and demonstrates that crack front geometry itself can enhance the effective fracture toughness: the critical strain energy release rate increases proportionally to the crack front complexity, which is validated across several brittle materials. The thesis then addresses the energy storage along segmented crack fronts, with material ligaments bridging adjacent crack segments. Using volumetric imaging and particle tracking, the ligament is shown to localize both stretch and strain energy density. A ligament equivalent energy is introduced and found to scale directly with the excess fracture energy, while an effective traction-separation law reveals that the ligament behaves as a localized cohesive zone. Finally, a high-speed volumetric imaging platform is developed for quantitative measurement of the evolving crack surface, deformation fields, as well as the far-field mechanics, providing a versatile tool for a wide range of future studies on fracture over spatial and time scales.

Through these investigations, this thesis characterizes the near-tip energy dissipation, demonstrates the energetic role of localized non-planar crack front features, and highlights the importance of a spatially resolved three-dimensional description of fracture. The outcomes of this thesis opens the door for future investigations not only on physical interpretation of failure mechanisms, but also on engineering applications of material and structural design in systems with complex three-dimensional fracture behaviors.