Moving Griffith crack in an orthotropic material

In this paper, an integral transform technique is employed to solve the plane elastodynamic problem of a crack of fixed length propagating at a constant speed in a uniformly stressed medium. It is assumed that the crack is located in a plane of elastic symmetry of the material. The stresses and strains ahead of the crack tip are determined explicitly and the conditions governing the initial growth of the crack are investigated using two current theories of fracture (Maximum normal stress and Minimum strain-energy density). Based on these theories, it appears that, depending upon the particular orthotropy of the material, the crack may extend in a straight line for all velocities or may immediately branch out at low velocities (compared to the shear wave velocity of the material) or may start propagating along its initial position for small velocities and then, as the velocity increases, may curve and branch out.