THE CRACK-TIP REGION IN HYDRAULIC FRACTURING

We present analytical tip region solutions for fracture width and pres sure when a power law fluid drives a plane strain fracture in an imper meable linear elastic solid. Our main result is an intermediate asympt otic solution in which the tip region stress is dominated by a singula rity which is particular to the hydraulic fracturing problem. Moreover this singularity is weaker than the inverse square root singularity o f linear elastic fracture mechanics. We also show how the solution for a semi-infinite crack may be exploited to obtain a useful approximati on for the finite case.