Experimental investigation of crack opening asymptotics for fluid-driven fracture

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 asymptotic solution which comprises a tip asymptote specific to fluid-driven fracture. These tip asymptotics were explored 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 full-field fracture opening from the intensity of light transmitted through the growing fractures. It was found that a power-law of the distance from the crack tip fit the opening data well over the outer 30 to 40 percent of the fracture. This power law was found to approximately match the fluid-driven fracture tip asymptote when the effect of fluid viscosity, quantified by a dimensionless parameter, was significant. Conversely, the LEFM tip asymptote approximated the experimental behavior when the effect of viscosity was negligible. These results give the first direct experimental evidence for the existence of the fluid-driven fracture tip solution. However, the implications will be fully understood only when solutions are developed which consider more general cases, specifically in the case with large fluid lag and the case of a fracture parallel to a nearby free surface.