Experimental Validation Of The Tip Asymptotics For A Fluid-driven Crack

摘要

This paper provides experimental confirmation of the opening asymptotes that have been predicted to develop at the tip of fluid-driven cracks propagating in impermeable brittle elastic media. During propagation of such cracks, energy is dissipated not only by breaking of material bonds ahead of the tip but also by flow of viscous fluid. Theoretical analysis based on linear elastic fracture mechanics and lubrication theory predicts a complex multiscale asymptotic behavior of the opening in the tip region, which simplifies either as 1/2 or as 2/3 power law of the distance from the tip depending on whether the dominant mechanism of energy dissipation is bond breaking or viscous flow. The laboratory experiments entail the propagation of penny-shaped cracks by injection of glycerin or glucose based solutions in polymethyl methacrylate (PMMA) and glass specimens subjected to confining stresses. The full-field opening is measured from analysis of the loss of intensity as light passes through the dye-laden fluid that fills the crack. The experimental near-tip opening gives excellent agreement with theory and therefore confirms the predicted multi-scale tip asymptotics.