TY - JOUR

T1 - Fluid-driven cracks in an elastic matrix in the toughness-dominated limit

AU - Lai, Ching Yao

AU - Zheng, Zhong

AU - Dressaire, Emilie

AU - Stone, Howard A.

N1 - Funding Information:
We thank the National Science Foundation for funding via grant no. CBET-1509347 and the Andlinger Center for Energy and the Environment at Princeton University for partial support of this research.
Publisher Copyright:
© 2016 The Author(s) Published by the Royal Society.

PY - 2016/10/13

Y1 - 2016/10/13

N2 - The dynamics of fluid-driven cracks in an elastic matrix is studied experimentally. We report the crack radius R(t) as a function of time, as well as the crack shapes w(r, t) as a function of space and time. A dimensionless parameter, the pressure ratio Δpf/Δpv, is identified to gauge the relative importance between the toughness (Δpf) and viscous (Δpv) effects. In our previous paper (Lai et al. 2015 Proc. R. Soc. A 471, 20150255. (doi:10.1098/rspa.2015.0255)), we investigated the viscous limit experimentally when the toughness-related stresses are negligible for the crack propagation. In this paper, the experimental parameters, i.e. Young's modulus E of the gelatin, viscosity μ of the fracturing liquid and the injection flow rate Q, were chosen so that the viscous effects in the flow are negligible compared with the toughness effects, i.e. Δpf/Δpv ≫1. In this limit, the crack dynamics can be described by the toughnessdominated scaling laws, which give the crack radius R(t) αt2/5 and the half maximum crack thickness W(t) αt1/5. The experimental results are in good agreement with the predictions of the toughness scaling laws: The experimental data for crack radius R(t) for a wide range of parameters (E,μ,Q) collapse after being rescaled by the toughness scaling laws, and the rescaled crack shapes w(r, t) also collapse to a dimensionless shape, which demonstrates the selfsimilarity of the crack shape. The appropriate choice of the viscous or toughness scaling laws is important to accurately describe the crack dynamics. This article is part of the themed issue 'Energy and the subsurface'.

AB - The dynamics of fluid-driven cracks in an elastic matrix is studied experimentally. We report the crack radius R(t) as a function of time, as well as the crack shapes w(r, t) as a function of space and time. A dimensionless parameter, the pressure ratio Δpf/Δpv, is identified to gauge the relative importance between the toughness (Δpf) and viscous (Δpv) effects. In our previous paper (Lai et al. 2015 Proc. R. Soc. A 471, 20150255. (doi:10.1098/rspa.2015.0255)), we investigated the viscous limit experimentally when the toughness-related stresses are negligible for the crack propagation. In this paper, the experimental parameters, i.e. Young's modulus E of the gelatin, viscosity μ of the fracturing liquid and the injection flow rate Q, were chosen so that the viscous effects in the flow are negligible compared with the toughness effects, i.e. Δpf/Δpv ≫1. In this limit, the crack dynamics can be described by the toughnessdominated scaling laws, which give the crack radius R(t) αt2/5 and the half maximum crack thickness W(t) αt1/5. The experimental results are in good agreement with the predictions of the toughness scaling laws: The experimental data for crack radius R(t) for a wide range of parameters (E,μ,Q) collapse after being rescaled by the toughness scaling laws, and the rescaled crack shapes w(r, t) also collapse to a dimensionless shape, which demonstrates the selfsimilarity of the crack shape. The appropriate choice of the viscous or toughness scaling laws is important to accurately describe the crack dynamics. This article is part of the themed issue 'Energy and the subsurface'.

KW - Fluid-structure interactions

KW - Geophysical and geological flows

KW - Thin films

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U2 - 10.1098/rsta.2015.0425

DO - 10.1098/rsta.2015.0425

M3 - Article

AN - SCOPUS:84988728390

SN - 1364-503X

VL - 374

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2078

M1 - 20150425

ER -