Center of Dilatation and Penny-Shaped Crack in Viscoelastic Bimaterial

Abstract

This paper derives analytically the stress intensity factors (SIFs) of a frictional interfacial pennyshaped crack in a viscoleastic bimaterial subject to the action of a center of dilatation (see Fig. 1). This work is an extension of the 2-D problem considered by Chau and Wong [1].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. The elastic solution of Auxiliary Problem I has been given by Yu and Sanday through the use of Galerkin vector in 3-D space, which can easily be extended to that of a viscoelastic bimaterial subject to a sudden applied center of dilatation. Auxiliary Problem II can be solved by a Fourier transform technique proposed by Shifrin et al. [2] through the solution of a pseudodifferential equation subject to an arbitrary boundary traction condition. The applied traction from Auxiliary Problem I is first approximated by polynomials, and balancing coefficients yield a system simultaneous equations. The stress intensity factors can then be obtained. The approximate inverse of Laplace transform of Schapery is used to obtain the solutions in time. Creeping tests for the Swiss Central Alps shales have been adopted for viscoelastic parameter calibration. Frictional and overburden effects are also incorporated. For the limiting case of homogenous material, our solution agrees with the isotropic case [3]. When the number of terms needed for polynomials interpolation equal 15, the solutions converge to steady solution. In contrast to the 2-D cases, all mode I, II and III may appear.