Vol. 10, No. 3, 2015

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ISSN: 1559-3959
Fracture development on a weak interface near a wedge

Alexander N. Galybin, Robert V. Goldstein and Konstantin B. Ustinov

Vol. 10 (2015), No. 3, 265–282
DOI: 10.2140/jomms.2015.10.265
Abstract

Formation of a fracture consisting in shear-opening delamination and Coulomb’s frictional sliding zones along a weak interface in an elastic isotropic homogeneous plane subjected to wedging and external compression is studied. The shear-opening delamination is modelled by a mixed-mode crack; the frictional sliding zones are modelled by pure shear cracks. The interface is assumed to be much weaker than the material of the plane, so that only interface cracks are considered. The wedge is modelled by a pair of edge dislocations. Two particular cases have been considered: far-field and near-field asymptotics, corresponding to the cases of large and small ratios of the distance between the wedge and the interface and the distance between two dislocations modelling the wedge, respectively.

The possibility of formation of finite sliding zones ahead of the delamination on the weak interface is demonstrated. It is shown that, depending on the combination of external parameters (ratio of the dislocation burgers vector and elastic modulus, distance from the dislocation to the interface, magnitude of applied compression, cohesion and friction angle of the interface), two configurations of cracks may be observed: one mixed-mode crack, and three cracks—one central mixed mode crack and two external symmetrical shear cracks. The central part of the sliding zone is also open.

Keywords
mixed-mode interface crack, edge dislocation, delamination, sliding, singular integral equations
Milestones
Received: 1 December 2014
Revised: 19 January 2015
Accepted: 23 February 2015
Published: 26 August 2015
Authors
Alexander N. Galybin
The Schmidt Institute of Physics of the Earth
Russian Academy of Sciences
Gruzinskaya str. 10-1
Moscow
123995
Russia
Robert V. Goldstein
A. Yu. Ishlinsky Institute for Problems in Mechanics
Russian Academy of Sciences
prosp. Vernadskogo 101-1
Moscow
119526
Russia
Konstantin B. Ustinov
A. Yu. Ishlinsky Institute for Problems in Mechanics
Russian Academy of Sciences
prosp. Vernadskogo 101-1
Moscow
119526
Russia