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Irwin׳s conjecture: Crack shape adaptability in transversely isotropic solids

TitleIrwin׳s conjecture: Crack shape adaptability in transversely isotropic solids
Publication TypeJournal Article
Year of Publication2014
AuthorsLaubie H, Ulm F-J
JournalJournal of the Mechanics and Physics of Solids
Volume68
Pagination1 - 13
Date PublishedAug-2014
ISSN00225096
Abstract

The planar crack propagation problem of a flat elliptical crack embedded in a brittle elastic anisotropic solid is investigated. We introduce the concept of crack shape adaptability: the ability of three-dimensional planar cracks to shape with the mechanical properties of a cracked body. A criterion based on the principle of maximum dissipation is suggested in order to determine the most stable elliptical shape. This criterion is applied to the specific case of vertical cracks in transversely isotropic solids. It is shown that contrary to the isotropic case, the circular shape (i.e. penny-shaped cracks) is not the most stable one. Upon propagation, the crack first grows non-self-similarly before it reaches a stable shape. This stable shape can be approximated by an ellipse of an aspect ratio that varies with the degree of elastic anisotropy. By way of example, we apply the so-derived crack shape adaptability criterion to shale materials. For this class of materials it is shown that once the stable shape is reached, the crack propagates at a higher rate in the horizontal direction than in the vertical direction. We also comment on the possible implications of these findings for hydraulic fracturing operations.

Fig.1. Top view of an elliptical crack (en, et and eb are the unit vectors normal to…

Fig.2. Definition of the θ angle for a penny-shaped crack

Fig.3. Definition of the α-angle for an elliptical vertical crack (θ=π/2)

Fig.4. Zoom at the crack tip (vertical crack)

Fig.5. Comparison of the H(ϕ)/H2 obtained numerically – solid line – and its…

Fig.6. Comparison of the H(ϕ)/H2 obtained numerically – solid line – and its…

DOI10.1016/j.jmps.2014.03.004
Short TitleJournal of the Mechanics and Physics of Solids
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