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Research Papers

Quasi-Static Crack Growth Under Symmetrical Loads in Hydraulic Fracturing

[+] 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.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 12, 2017; final manuscript received June 4, 2017; published online June 20, 2017. Assoc. Editor: Thomas Siegmund.

J. Appl. Mech 84(8), 081009 (Jun 20, 2017) (10 pages) Paper No: JAM-17-1143; doi: 10.1115/1.4036988 History: Received March 12, 2017; Revised June 04, 2017

Symmetrical load on the crack surfaces is found in many fluid–solid problems. The combined effect of symmetrical normal and shear stresses is investigated, which impacts on the displacement and stress fields and the predictions of crack initiation and deflection. The boundary integral equations of displacement and stress fields are formulated using the integral-transform method. The equations of the displacement and stress are reduced using the Abel integral equations. The analytical solution of the full space for uniform normal and shear stresses is obtained. The asymptotic solution of the displacement of the crack surface is obtained near the crack tip under specific normal and shear stresses. Results show that shear stress tends to inhibit the crack, and the predictions of crack initiation and deflection could be inappropriate for a slit crack under a singular shear stress. This study may be useful for future investigations of the fluid–solid problems and help to understand the hydraulic fracturing.

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Figures

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Fig. 1

Schematic diagram of symmetrical normal and shear stresses on a slit crack. The stresses are symmetrical about both the coordinate axes.

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Fig. 2

Normalized displacement of the solid in the first quadrant. A uniform and negative shear stress acts on the crack surface. Arrows represent displacement vectors. Solid lines are tangent to the displacement.

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Fig. 3

Dimensionless stress component, σ̃11, in front of the crack tip under different normal stresses (x̃2=0+)

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Fig. 4

Negative dimensionless stress component, −σ̃11, in front of the crack tip under different shear stresses (x̃2=0+)

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Fig. 5

Angular distributions of normalized strain energy density, fS, and stress components, frr, frθ and fθθ, near the crack tip (r̃=10–4)

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Fig. 6

Angular distributions of normalized maximum principal stress near the crack tip (r̃=10–4)

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