Research Papers

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

[+] Author and Article Information
Wenhao Shen

State Key Laboratory of
Nonlinear Mechanics (LNM),
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China;
School of Engineering Science,
University of Chinese
Academy of Sciences,
Beijing 100049, China

Ya-Pu Zhao

State Key Laboratory of
Nonlinear Mechanics (LNM),
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China;
School of Engineering Science,
University of Chinese
Academy of Sciences,
Beijing 100049, China
e-mail: yzhao@imech.ac.cn

1Corresponding author.

Manuscript received October 12, 2017; final manuscript received December 7, 2017; published online January 4, 2018. Assoc. Editor: N. R. Aluru.

J. Appl. Mech 85(3), 031003 (Jan 04, 2018) (10 pages) Paper No: JAM-17-1569; doi: 10.1115/1.4038719 History: Received October 12, 2017; Revised December 07, 2017

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.

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Grahic Jump Location
Fig. 1

A penny-shaped crack driven by a viscous fluid flow and a uniform normal stress at infinity

Grahic Jump Location
Fig. 4

Time evolution of the first-order asymptotic expansion of crack opening

Grahic Jump Location
Fig. 5

Transition of the dominant regimes with respect to the flow behavior index

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Fig. 2

Displacement field under uniform shear stress on the crack surfaces: (a) contour lines of total displacement and (b) streamlines of the displacement vector. The dot (1,0) represents the crack tip

Grahic Jump Location
Fig. 3

First-order asymptotic expansion of crack opening, crack length, and pressure in the toughness-dominant regime

Grahic Jump Location
Fig. 6

Angular distribution of normalized stress components around the crack tip. The normalized distance from the crack tip is ρ̃=10−4.



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