The Rules of Roughness: An Experimental Investigation Into the Origins of Brittle Fracture Complexity

Abstract

Brittle fractures are a universal phenomenon that play a critical role in many aspects of human life. The roughness, or complexity, of a fracture is an important parameter to consider for many applications but is difficult to study because the roughness is three-dimensional and forms dynamically. In this thesis, I have developed a new experimental modality for studying the dynamics of fracture roughness formation by using hydraulic fractures to break brittle hydrogels. Hydrogels are used to allow for experimental flexibility and active control over rheological properties. Hydraulic fractures can be produced such that they are governed by linear elastic fracture mechanics and can be studied using a new imaging system that combines methods of laser sheet microscopy and high-speed imaging. This system allows for unprecedented three-dimensional dynamic measurements of brittle fractures at 5 x 5 x 10 $\mu$m voxel resolution at 1000 volumes/second. Using my experimental system, I show that the formation of step lines, one of the largest and most fundamental brittle fracture surface features, arises from interactions between the fracture front and material heterogeneity, and that the density of step lines present depends on both the number and size of the heterogeneities. Higher densities of steps lines lead to increasingly rough surfaces because they can interact. The rules and dynamics that govern these interactions are described for all possible classes to provide a clear picture of how roughness forms dynamically in brittle fractures.