Interactions of a center of dilatation and an interface crack in a two-dimensional viscoelastic bimaterial

Abstract

This paper derives analytically the stress intensity factors (SIFs) of a frictional interfacial crack in a viscoleastic bimaterial subject to the action of a center of dilatation. The standard linear viscoelastic solid or “three-parameter-viscoelastic-model” is adopted. Using the correspondence principle, the problem is formulated in Laplace transform space. The problem is decomposed into two Auxiliary Problems: (I) a bimaterial containing a center of dilatation; and (II) an interfacial crack in the bimaterial subject to tractions that cancel those induced by the Auxiliary Problem I. Schapery’s direct method is used to obtain the inverse Laplace transform and, in turn, obtain the SIF as a function of time. Creeping tests for the Swiss Central Alps shales have been adopted for viscoelastic parameter calibration. When the bimaterial degenerates into a homogenous material, the SIFs are independent of time. If the medium containing the center of dilatation is stiffer, the long term SIF is larger than the instantaneous SIF; and if the medium containing the center of dilatation is softer, the long term SIF is smaller than the instantaneous SIF. Therefore, short term crack stability does not necessarily rule out long term crack propagation. If the overburden stress and the friction on crack surface are neglected, both modes I and II SIFs are induced at the crack tips. The mode II SIF is, in general, larger than that of mode I. When both friction and overburden pressure are included in the analysis, tensile cracking is unlikely whilst shear cracking remains possible. The maximum mode II SIF strongly depends on the orientation as well as the distance of the center of dilatation from the crack tip. Both overburden pressure and crack face friction decreases chance of crack propagation.