Experimental validation of the tip asymptotics for a fluid-driven crack

Abstract 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.

[1]  A. Peirce,et al.  An implicit level set method for modeling hydraulically driven fractures , 2008 .

[2]  Emmanuel M Detournay,et al.  Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: Asymptotic solutions , 2002 .

[3]  Emmanuel M Detournay,et al.  Crack tip behavior in near-surface fluid-driven fracture experiments , 2005 .

[4]  I. L. Lim,et al.  Stress intensity factors for semi-circular specimens under three-point bending , 1993 .

[5]  E. Detournay,et al.  Early-Time Solution for a Radial Hydraulic Fracture , 2007 .

[6]  Emmanuel M Detournay,et al.  An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag , 2007 .

[7]  A. Peirce,et al.  An Asymptotic Framework for the Analysis of Hydraulic Fractures: The Impermeable Case , 2007 .

[8]  An Eulerian moving front algorithm with weak‐form tip asymptotics for modeling hydraulically driven fractures , 2009 .

[9]  E. Detournay,et al.  3773 - EXPERIMENTAL INVESTIGATION OF CRACK OPENING ASYMPTOTICS FOR FLUID-DRIVEN FRACTURE , 2005 .

[10]  Emmanuel M Detournay,et al.  Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution , 2005 .

[11]  R. C. Kerr,et al.  Fluid‐mechanical models of crack propagation and their application to magma transport in dykes , 1991 .

[12]  Emmanuel M Detournay,et al.  The Tip Region of a Fluid-Driven Fracture in an Elastic Medium , 2000 .

[13]  Emmanuel M Detournay,et al.  The crack tip region in hydraulic fracturing , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[14]  Emmanuel M Detournay,et al.  Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid , 2002 .

[15]  Emmanuel M Detournay,et al.  Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks , 2004 .

[16]  Andrew P. Bunger.  Near-Surface Hydraulic Fracture , 2009 .

[17]  A. Bunger.  A photometry method for measuring the opening of fluid-filled fractures , 2006 .