Combined Effect of Pressure and Shear Stress on Penny-Shaped Fluid-Driven Cracks

Abstract

Penny-shaped fluid-driven cracks are often detected in many fluid–solid interaction problems. We study the combined effect of pressure and shear stress on the crack propagation in an impermeable elastic full space. Boundary integral equations are presented, by using the integral transform method, for a penny-shaped crack under normal and shear stresses. The crack propagation criterion of stress intensity factor is examined with the strain energy release rate. Dominant regimes are obtained by using a scaling analysis. Asymptotic solution of the toughness-dominant regime is derived to show the effect of shear stress on the crack opening, crack length, and pressure distribution. The results indicate that a singular shear stress can dominate the asymptotic property of the stress field near the crack tip, and the stress intensity factor cannot be calculated even though the energy release rate is finite. Shear stress leads to a smaller crack opening, a longer crack, and a slightly larger wellbore pressure. A novel dominant-regime transition between shear stress and pressure is found. Unstable crack propagation occurs in the shear stress-dominant regime. This study may help in understanding crack problems under symmetrical loads and modeling fluid–solid interactions at the crack surfaces.