Stress distribution in a two-dimensional infinite anisotropic medium with collinear cracks

Abstract

The plane problem of an anisotropic material with cracks, whose surfaces are subject to surface tractions of a general kind, is studied. The medium considered if of infinite extent and the cracks are located on a single line. The Fourier transform method is employed to derive the stress and displacement components at an arbitrary point of the medium in terms of the dislocation densities and the stress discontinuities on the crack line.

These formulae for stress and displacement components involve the roots of a quartic equation whose coefficients are the material constants. The cases of different roots and pairwise coincident roots are examined separately. An orthotropic medium is an important example for the case of different roots while an isotropic medium is that for the case of pairwise coincident roots. These examples are discussed in detail.

As an illustration of the use of these formulae the problem of a single crack in an infinite anisotropic medium is examined in detail.