Experimental investigation of crack opening asymptotics for fluid-driven fracture

Fracture opening in the tip region of a fluid-driven fracture is governed not only by the square-root tip asymptote, well-known from linear elastic fracture mechanics (LEFM), but also by an intermediate tip asymptote that is specific to fluid-driven fracture. Additional tip asymptotes may arise when the fracture interacts with a nearby free surface. We have explored this complex tip behavior in the laboratory by growing hydraulic fractures in impermeable, transparent, brittle elastic materials, employing a method based on the Beer-Lambert law of optical absorption to measure the fracture opening. The near-tip opening matches the fluid-driven fracture tip asymptote when the effect of viscous dissipation is significant. Conversely, the LEFM tip asymptote matches the experimental behavior when the viscosity effects are negligible. Furthermore, when the fracture radius is several times its depth, a third asymptote is observed that arises from the plate-like behavior of the material between the fracture and the free-surface. The prevalence of each of the three observed asymptotes is shown to correlate with the fracture's location in a two-dimensional parametric space.