The crack tip region in hydraulic fracturing. (English) Zbl 0813.73051

Summary: We present analytical tip region solutions for fracture width and pressure when a power law fluid drives a plane strain fracture in an impermeable linear elastic solid. Our main result is an intermediate asymptotic solution in which the tip region stress is dominated by a singularity which is particular to the hydraulic fracturing problem. Moreover, this singularity is weaker than the inverse square root singularity of linear elastic fracture mechanics. We also show how the solution for a semi-infinite crack may be exploited to obtain a useful approximation for the finite case.


74R99 Fracture and damage
76A05 Non-Newtonian fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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