Elliptical cracks arbitrarily oriented in 3D-anisotropic elastic media

Abstract

An elliptical crack in an infinite anisotropic elastic medium is considered. For a polynomial external stress field, an efficient numerical algorithm of the solution of the problem is developed. The discontinuity of the displacement field on the crack surface (the crack opening vector) is presented in the form of 2D-regular integrals that can be evaluated numerically for any crack orientation with respect to the principal axes of the anisotropy of the medium. The integrand functions in these integrals are expressed via the Fourier transform of the Green function of the medium. The cases of constant and linear external stress fields are considered in detail. Simplifications for particular crack orientations in the cases of orthotropic and transversely isotropic media are indicated. The stress intensity factors are obtained in the form of regular integrals that depend only on the Fourier transform of the Green function of the medium. An equation for the tensor of effective elastic constants of an anisotropic media containing a random set of elliptical cracks is presented.