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.

References

References
1.
Spence
,
D. A.
, and
Sharp
,
P.
,
1985
, “
Self-Similar Solutions for Elastohydrodynamic Cavity Flow
,”
Proc. R. Soc. London, Ser. A
,
400
(
1819
), pp.
289
313
.
2.
Tsai
,
V. C.
, and
Rice
,
J. R.
,
2010
, “
A Model for Turbulent Hydraulic Fracture and Application to Crack Propagation at Glacier Beds
,”
J. Geophys. Res. Earth Surf.
,
115
(
F3
), p.
F03007
.
3.
Lister
,
J. R.
, and
Ross
,
C. K.
,
1991
, “
Fluid-Mechanical Models of Crack Propagation and Their Application to Magma Transport in Dykes
,”
J. Geophys. Res. Solid Earth
,
96
(
6
), pp.
10049
10077
.
4.
Yang
,
F. Q.
, and
Zhao
,
Y. P.
,
2016
, “
The Effect of a Capillary Bridge on the Crack Opening of a Penny Crack
,”
Soft Matter
,
12
(
5
), pp.
1586
1592
.
5.
Verdon
,
J. P.
,
Kendall
,
J. M.
,
Stork
,
A. L.
,
Chadwick
,
R. A.
,
White
,
D. J.
, and
Bissell
,
R. C.
,
2013
, “
Comparison of Geomechanical Deformation Induced by Megatonne-Scale CO2 Storage at Sleipner, Weyburn, and in Salah
,”
Proc. Natl. Acad. Sci. U. S. A.
,
110
(
30
), pp.
2762
2771
.
6.
Vasco
,
D.
,
Rucci
,
A.
,
Ferretti
,
A.
,
Novali
,
F.
,
Bissell
,
R.
,
Ringrose
,
P.
,
Mathieson
,
A.
, and
Wright
,
I.
,
2010
, “
Satellite-Based Measurements of Surface Deformation Reveal Fluid Flow Associated With the Geological Storage of Carbon Dioxide
,”
Geophys. Res. Lett.
,
37
(
3
), p.
L03303
.
7.
Abe
,
H.
,
Mura
,
T.
, and
Keer
,
L. M.
,
1976
, “
Growth-Rate of a Penny-Shaped Crack in Hydraulic Fracturing of Rocks
,”
J. Geophys. Res.
,
81
(
29
), pp.
5335
5340
.
8.
Dong
,
X.
,
Zhang
,
G.
,
Gao
,
D.
, and
Duan
,
Z.
,
2017
, “
Toughness-Dominated Hydraulic Fracture in Permeable Rocks
,”
ASME J. Appl. Mech.
,
84
(
7
), p.
071001
.
9.
Mishuris
,
G.
,
Wrobel
,
M.
, and
Linkov
,
A.
,
2012
, “
On Modeling Hydraulic Fracture in Proper Variables: Stiffness, Accuracy, Sensitivity
,”
Int. J. Eng. Sci.
,
61
, pp.
10
23
.
10.
Shen
,
W. H.
, and
Zhao
,
Y. P.
,
2017
, “
Quasi-Static Crack Growth Under Symmetrical Loads in Hydraulic Fracturing
,”
ASME J. Appl. Mech.
,
84
(
8
), p.
081009
.
11.
Geertsma
,
J.
, and
de Klerk
,
F.
,
1969
, “
A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures
,”
J. Pet. Technol.
,
21
(
12
), pp.
1571
1581
.
12.
Savitski
,
A. A.
, and
Detournay
,
E.
,
2002
, “
Propagation of a Penny-Shaped Fluid-Driven Fracture in an Impermeable Rock: Asymptotic Solutions
,”
Int. J. Solids Struct.
,
39
(
26
), pp.
6311
6337
.
13.
Bunger
,
A. P.
, and
Detournay
,
E.
,
2007
, “
Early-Time Solution for a Radial Hydraulic Fracture
,”
J. Eng. Mech.
,
133
(
5
), pp.
534
540
.
14.
Garagash
,
D. I.
, and
Detournay
,
E.
,
2000
, “
The Tip Region of a Fluid-Driven Fracture in an Elastic Medium
,”
ASME J. Appl. Mech.
,
67
(
1
), pp.
183
192
.
15.
Garagash
,
D. I.
,
Detournay
,
E.
, and
Adachi
,
J. I.
,
2011
, “
Multiscale Tip Asymptotics in Hydraulic Fracture With Leak-Off
,”
J. Fluid Mech.
,
669
, pp.
260
297
.
16.
Lawn
,
B.
,
1993
,
Fracture of Brittle Solids
,
Cambridge University Press
,
Cambridge, UK
.
17.
Zhao
,
Y. P.
,
2016
,
Modern Continuum Mechanics
,
Science Press
,
Beijing, China
(in Chinese).
18.
Detournay
,
E.
,
2004
, “
Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks
,”
Int. J. Geomech.
,
4
(
1
), pp.
35
45
.
19.
Detournay
,
E.
,
2016
, “
Mechanics of Hydraulic Fractures
,”
Annu. Rev. Fluid Mech.
,
48
, pp.
311
339
.
20.
Sneddon
,
I. N.
, and
Lowengrub
,
M.
,
1969
,
Crack Problems in the Classical Theory of Elasticity
,
Wiley
,
New York
.
21.
Yang
,
F.
,
1998
, “
Indentation of an Incompressible Elastic Film
,”
Mech. Mater.
,
30
(
4
), pp.
275
286
.
22.
Bunger
,
A. P.
, and
Detournay
,
E.
,
2008
, “
Experimental Validation of the Tip Asymptotics for a Fluid-Driven Crack
,”
J. Mech. Phys. Solids
,
56
(
11
), pp.
3101
3115
.
23.
Lai
,
C. Y.
,
Zheng
,
Z.
,
Dressaire
,
E.
,
Ramon
,
G. Z.
,
Huppert
,
H. E.
, and
Stone
,
H. A.
,
2016
, “
Elastic Relaxation of Fluid-Driven Cracks and the Resulting Backflow
,”
Phys. Rev. Lett.
,
117
(
26
), p.
268001
.
24.
Lai
,
C. Y.
,
Zheng
,
Z.
,
Dressaire
,
E.
,
Wexler
,
J. S.
, and
Stone
,
H. A.
,
2015
, “
Experimental Study on Penny-Shaped Fluid-Driven Cracks in an Elastic Matrix
,”
Proc. R. Soc. A.
,
471
(
2182
), p.
20150255
.
25.
Lecampion
,
B.
,
Desroches
,
J.
,
Jeffrey
,
R. G.
, and
Bunger
,
A. P.
,
2017
, “
Experiments Versus Theory for the Initiation and Propagation of Radial Hydraulic Fractures in Low-Permeability Materials
,”
J. Geophys. Res: Solid Earth
,
122
(
2
), pp.
1239
1263
.
26.
Zhao
,
Y. P.
,
2014
,
Nano and Mesoscopic Mechanics
,
Science Press
,
Beijing, China
(in Chinese).
27.
Bui
,
H. D.
,
1977
, “
An Integral Equations Method for Solving the Problem of a Plane Crack of Arbitrary Shape
,”
J. Mech. Phys. Solids
,
25
(
1
), pp.
29
39
.
You do not currently have access to this content.