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TECHNICAL PAPERS

The Tip Region of a Fluid-Driven Fracture in an Elastic Medium

[+] Author and Article Information
D. Garagash, E. Detournay

Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive SE, Minneapolis, MN 55455

J. Appl. Mech 67(1), 183-192 (Jun 22, 1999) (10 pages) doi:10.1115/1.321162 History: Received August 14, 1998; Revised June 22, 1999
Copyright © 2000 by ASME
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References

Figures

Grahic Jump Location
Semi-infinite fluid driven crack with the lag zone adjacent to the tip
Grahic Jump Location
Bounds ξo and ξ of the regions where solution is dominated by corresponding asymptotes, and lag Λ versus dimensionless toughness κ in log-log scale. (Dashed lines show the large κ asymptotes of ξo(κ),ξ(κ).)
Grahic Jump Location
Dimensionless lag length Λ versus dimensionless toughness κ (solid line), together with the large κ asymptote (dashed line)
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Dimensionless net-loading Π along the crack for κ=0, 2.08, 3.33, 4.11. The dashed line corresponds to Π(ξ).
Grahic Jump Location
Dimensionless fluid pressure Π along the crack for κ=0, 2.08, 3.33, 4.11 in semi-log scale. Corresponding values of fluid lag Λ are given by the intersection of a curve with the ξ-axis. The dashed line corresponds to Π(ξ).
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The dimensionless crack opening Ω along the crack in log-log scale for dimensionless toughness varying from κ=0 (Λ≃0.3574) to κ=4.1 (Λ=10−6), (see Table 1). The dashed line corresponds to the asymptotic solution at infinity, Ω(ξ).
Grahic Jump Location
The opening Ω along the crack in near tip region for κ varying from κ=0 (Λ≃0.3574) to κ=4.1 (Λ=10−6), (see Table 1). The dashed line corresponds to Ω(ξ).
Grahic Jump Location
Scaled opening Ω̃ along the crack in log-log scales. Dashed lines correspond to the solution asymptotes and black dots to ξ̃o and ξ̃.
Grahic Jump Location
Scaled pressure Π̃ along the crack in semi-logarithmic scales. Dashed lines correspond to the solution asymptotes and black dots to ξ̃o and ξ̃.

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